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FAMIAS User Manual

1. S N level Multiplicity factor of the signal to noise level The displayed noise level will be multiplied by this factor Box size Box size b for the computation of the noise level in units of the frequency The significance level is computed from the running mean of the pre whitened Fourier spectrum For each frequency value F the noise level is calculated from the mean of the range F b 2 F b 2 e Calculate Fourier Computes the discrete Fourier transform DFT according the user s set tings and displays it in the plot window as a blue line The mean intensity value of the time series is automatically shifted to zero before the Fourier analysis is computed The peak having highest amplitude in the given range is marked in the plot window A dialogue window reports the fre quency having the highest amplitude in the selected frequency range and asks if it should be added to the frequency list of the Least Squares Fitting Tab 5 2 2 List of Calculations Previous Fourier calculations can be selected from the list and viewed Each computed Fourier spectrum is saved and listed here If a project is saved the list of computed Fourier spectra is also saved but compressed to decrease the project file size only extrema are saved The following operations are possible via the Data Menu e Remove Data Set Removes the currently selected data set from the list e Rename Data Set Renames the currently selected data set
2. oN X CuS G 21 Xv j l C lt yl gt O lt u gt where N is the number of measurements of the time series and the indices o and t denote observed and theoretical values respectively To speed up the computations of the theoretical moments a grid of integrals is precomputed for all possible and m combinations for 0 lt lt 4 and all inclinations between 0 and 90 This computation is performed once the mode identification has been started and may take a few minutes The precomputed integrals depend on the limb darkening coefficients and the number of segments on the stellar surface They are thus only recomputed in a subsequent mode identification if the latter parameter or the parameters Teff log g Metallicity or Central wavelength have been modified 4 5 5 Practical information for applying the moment method e The dispersion range that is imported to the Mode Identification Tab should cover the complete range of the line profile from continuum to continuum The best approach would be to extract the line profile see p 36 and select the complete dispersion range when computing the least squares fit The least squares fit should include all significant frequencies as well as combination and harmonic frequencies During the mode iden tification the latter should not be set as free parameters unless one has a reason to assume that they are pulsation modes intrinsic to the star e The stellar parameters radius ma
3. Here v is the velocity across the line profile F F takes the surface flux of the emitting segment into account Wint Ter is the equivalent width as a function of the effective temperature see Eq 14 and is the width of the intrinsic profile The distorted line profile is calculated by summation over all visible segments on the surface grid of 0 weighted over the projected surface The response of a line s equivalent width to local temperature changes is dependent on the involved element its excitation and the temperature in the zone where the line originates In order to take this effect into account a variable equivalent width of the intrinsic line profiles must be considered for calculating the distorted profile Since there is no phase shift between dWint T and T we can write following Schrijvers amp Telting 1999 Wint Terr Wo 1 awodTerr 14 The Spectroscopy Modules 53 where aw is a parameter denoting the equivalent width s linear dependence on OTe which can be approximated for Te lt 1 In FAMIAS this parameter is denotes as d EW d Teff For calculating the local temperature surface gravity and flux variations we closely followed Balona 2000 and Daszynska Daszkiewicz et al 2002 Since the flux variation 6F F is mainly a function of Ter and log g we can write in the limit of linear pulsation theory OF H OT ete ba g Fo Te o OR 1 3w 15 S Ze Vj Je Ro artie a
4. The Spectroscopy Modules SP RMS version 094 O balas 7 one Rama emda sapere FAMIS Ca Aalis Cohel Spee lalla Packs tiers ec smamariali ip Fie Edit Tools Hele Ma of pama 400 Seale Angstom Tra aijaa Specrum mia Dain Cakuime Data Ss a 538730409 1 00060 ree DOSTO F1 ae ode 0 F260 Z040 oA E381 AT GGT 1 a0 zm 02237 91 E 5381 51758 10000 I ZEH mirog Fi FIRI Sate OTD Izaia i 5351 6005 0ra 24 ens G DART Ge 1 OHMED lzm 05671 9i i SUB 1 G10 099959 jaa Dose 91 EBIT Oro Z 0THA 91 5381 75554109147 za pees 1 5381 80697 1 Googe TS MES ant Ari ie l h 5351 66355000757 zma 10728 G1 ade pagea d Sagi jm 11636 Fi 5381 072i OSS zaa 91 1 gagi 01347 0 8002 Z ie Fj EIRT OT 1 OAITH 24 14148 51 Ssh e600 05315 e 15055 i SGA 1720 Obs 734 15663 94 O38 I7ESE 1 00120 zza 16758 21 H San zaia OST HST jeu Poet pi I SURE 26117 0 RSee Zaga gi 6383 30248 OST 22100 84 TIRA TS OST isa zoea 91 S33 3R505 0Ha iiaii 61 ASA Adc Os ims 07I 91 E387 46783 0 SEDO lzm SF 91 Sate B08S9 0 Sarre ZOAB Gl TIR Saipe ags zinn 4 eA E F ppa 42077 i SIH A281 091515 z a35 a g S3627 000I rrr rrr rrr rrr rrr rrr errr rrr 5 4 2 AE SH T STOT ENS 67 Gea Re DOAI OS S Select Al Figure 12 Data Manager after importing the tutorial time series of spectra 4 8 2 Select dispersion range The synthetic data consist of one absorption line In general one has to select a suited spectral line for an
5. Data Manager Fourier LeastSquares Fang Mode Mersicaion Results Logbook 245055006 2450550 2a5055e0 2450560 Teme Figure 20 Screenshot of the Data Manager Tab e Combine Data Sets Combines the selected data sets to a new single time series The data sets to be combined must have the same units of the dispersion Moreover all times of measurement have to differ e Change Assigned Filter Change the filter that is assigned to the current time string The correct filter has to be assigned to assure correct working of the mode identifi cation 5 1 2 Time Series Box This list shows the measurements of the currently selected light curve It con sists of three columns times of measurement magnitude and weight Multiple measurements can be selected by clicking with the left mouse button on several items in the list while pressing the Ctrl key or the Shift key All items can be selected by pressing Select All Only items that have been selected in this list The Photometry Modules 95 with blue background are taken into account for the data analysis e g Fourier analysis or least squares fitting Selected items are marked with a red cross in the Plot Window The following commands are available in the Data Menu e Edit Data Opens a table of times and weights in a new window with the possibility to edit these values Modifications can be written to the current data set e Copy Selection t
6. Box The Plot Window shows the currently selected spectrum statistics of a spectrum mean or standard deviation or a time series of moments if selected in the Data Sets Box A screenshot of the Data Manager Tab is shown in Figure 1 Once you have successfully imported a set of spectra its name will be added to the list of data sets Data Sets Box The times of measurements number of wavelength bins and the weight of each spectrum will be listed in the Time Series Box The Plot Window will remain empty until you click on one of the spectra in the Time Series Box In this case the dispersion in Angstrom or km s dependent on your selection and intensity of the selected spectrum will be listed in the Spectrum Box and the spectrum will be plotted as a blue line in the Plot Window You can select multiple wavelength bins in the Spectrum Box They will be displayed as red crosses in the Plot Window 30 Data Manager 4 1 1 Data Sets Box This box shows a list of the different data sets that have been imported or created The data can consist of a time series of spectra green background or of line moments yellow background To select a data set click on it or select it in the combo box at the top right of the information bar The selected data set is used for all operations of FAMIAS The following commands can be selected in the Data Menu e Remove Data Set Removes the currently selected data set from the list e Rename Data Set
7. frequency and t the time The spherical harmonic can be written as Y 6 0 N PI cos 0 ee 7 Here pi denotes the associated Legendre function of degree l and az imuthal order m given by _ Pn L m Pre a 0 a 174 8 and N 1 2L 1 m 9 Ar ml is a normalisation constant The definition of N changes from author to author which must be taken into account when comparing derived amplitudes In our formalism a positive value of m denotes a pro grade mode i e a wave propagating in the direction of the stellar rotation around the star We model uniform stellar rotation including first order corrections due to the Coriolis force which gives rise to toroidal motion The resulting displace ment field in the case of a slowly rotating non radially pulsating star cannot be described by a single spherical harmonic anymore It consists of one spheroidal and two toroidal terms which only have a horizontal component and is given for an angular frequency w in the stellar frame of reference and a time t by Vin ass 1 e k L Yo 80 sind Od 1 oO o fe eS m Wwt s I g o Potz 7 pe ym i wt F F At g 1 o sin 8 Od z 01 9 p Martens amp Smeyers 1982 Aerts amp Waelkens 1993 Schrijvers et al 1997 Note that the term proportional to Y is not defined for radial and sectoral modes Here as denotes the amplitude of the spheroidal componen
8. frequency the integral of the amplitude across the dispersion range and its uncertainty are shown If Compute signal to noise ratio has been se lected the amplitude SNR of each frequency is shown in the column SNR This value refers to the SNR of the dispersion bin where the particular frequency has its highest amplitude e Least squares fit with the option Moments Equivalent width and 1st through 6th moment The zero point its formal uncertainty and the standard deviation of the residuals are shown at the top The improved values of frequency am plitude and phase and their formal statistical uncertainties are shown in the list The phase and its uncertainty is in units of 27 The last column lists the SNR for each frequency only shown when the box Calculate signal to noise ratio has been checked The SNR is computed from the Fourier spectrum after pre whitening with all selected frequencies For each frequency the assumed noise level is computed from the mean am plitude around the frequency value with the box size indicated in the field Calculate signal to noise ratio e Export frequencies Exports all frequency amplitude and phase values of the List of frequen cies to an ASCII file The file format is compatible with the program Period04 Lenz amp Breger 2005 e Import frequencies Imports an ASCII list of frequencies having the following four column format separated by tabulators frequency counter frequency value am plitud
9. kms PoP Daia Manager Founer LewsSquares Fang Une Protle Syrihews Mode Kenticason Resuta Lagtock j 7 Stelle Parameters Line Prods Parameters Radus acter units garat Cerial wavelanghh A Eei aa haas eolar urita 185000 Equivalent with k55 en Tal RK F516 GOH SEOWiaT emi Bo bgg PORT ea niiae wach kms EE 20000 birahi 0100 Z ra pori ahi kms 0 0100 incision degrees 18 0 vain fiona ell 0000 Pulmion Mode Parameters General Senny use Fregi m Velamp pone PIP A OP eh frac ag ars ace rt iz7ieoo fo e o2000 i22000 22100 Dispersion range fens 50 00 60 000 1 ood re em 2 foeooo p0 aoo00 t750 aN Time range fi 000d fy 000d o o0sd ra mar o o fosooo p500 tao00 21000 Fa imperi Bman inom bie F5 Ji ber Fa i FY FE Fo T Fi0 FH Fiz Fila Fia mim Figure 9 Screenshot of the Line Profile Synthesis Tab In FAMIAS the following non linear limb darkening law described by Claret et al 2000 is used to determine the brightness of the surface elements as a function of the line of sight angle a I p k O a 17 Here I u is the specific intensity on the stellar disk at a certain line of sight angle 0 with u cos and a is the k th limb darkening coefficient The limb darkening coefficients are determined through the values of Teg log g and metallicity by bi linear interpolation in a precomputed grid Clare
10. the observed values are displayed as black crosses with error bars The theoretical values are displayed as lines Each colour represents another value of the degree and coincides with the colour scheme in the field Settings Generally more than one theoretical pulsation model is found that matches the input criteria e g Ter and logg All these models are displayed as apart lines in the plots as well as listed in the field Mode Identification e Amplitude ratio This plot displays the amplitude ratio oe relative to the reference filter r see Settings as a function of the central wavelength of the corresponding filter x The values of each fitting theoretical model are drawn as apart lines Plots of this kind are suited to identify modes in SPB or 8 Cep stars i e stars where the amplitude ratio depends strongly on the degree of the mode The Photometry Modules 111 e Phase difference This plot displays the phase difference P x r relative to the reference filter r see Settings as a function of the central wavelength of the corresponding filter x Values of different fitting theoretical models are plotted as apart lines e Phase diff Ampl ratio These plots display the amplitude ratio a as a function of the phase difference P r x for each filter x of the selected filter system relative to the reference filter r Each plot displays the results for another com bination of r and x In these plots the lines of a certain
11. with the program gnuplot with the commands set pm3d map and splot Pixel with highest amplitude at f Computes a Fourier spectrum at the pixel where the given frequency has the highest amplitude The purpose of this task is to determine the significance of a frequency peak in a line profile You must indicate a frequency value to carry out this operation This task computes for each pixel across the selected dispersion range a Fourier spectrum and determines at which position in the profile the given frequency has the highest amplitude Equivalent width Computes the equivalent width of the line profile inside the indi cated dispersion range and calculates its Fourier spectrum 1st moment radial velocity Computes the first moment lt v gt of the line profile inside the indicated dispersion range and calculates its Fourier spectrum 2nd moment variance Computes the second moment lt v gt of the line profile inside the indicated dispersion range and calculates its Fourier spectrum 3rd moment skewness Computes the third moment lt v gt of the line profile inside the indicated dispersion range and calculates its Fourier spectrum Ath moment Computes the fourth moment lt v gt of the line profile inside the indicated dispersion range and calculates its Fourier spectrum 5th moment Computes the fifth moment lt v gt of the line profile inside the indicated dispersion range and calculates its Fourier spectru
12. The Fourier spectrum will be computed from the minimum to the maximum value Nyquist frequency Estimate of the Nyquist frequency mean sampling frequency For non equidistant time series a Nyquist frequency is not uniquely defined In this case the Nyquist frequency is approximated by the inverse mean of the time difference of consecutive measurements by neglecting large gaps Frequency step Step size resolution of the Fourier spectrum Three presets are available Fine 20AT Medium 10AT and Coarse 5AT The corresponding step size depends on the temporal distribution of the measurements i e the time difference AT of the last and first measure ment It is recommended to select the fine step size to ensure that no frequency is missed The step value can be edited if desired Use weights If the box is checked the weight indicated for each spectrum is taken into account in the Fourier computations Otherwise all weights are assumed to have equal values Compute spectral window If the box is checked a spectral window of the current data set is com puted A spectral window shows the effects of the sampling of the data on the Fourier analysis and thus permits to estimate aliasing effects The spectral window is computed from a Fourier analysis of the data taking the times of measurements and setting all measurement intensities to the value 1 The shape of the spectral window does not depend on the se lecte
13. The Main Window After the start up of FAMIAS the Data Manager Tab of the Spectroscopy Module is shown If you wish to work with photometric data you have to switch to the Photometry Module In this chapter the main menu entries of FAMIAS are described 2 1 The File Menu This menu contains entries for opening and saving project files and importing time series of spectra or photometric measurements A session with FAMIAS can be saved as a project file Such a project file contains all the data included in the current session of FAMIAS The following entries are available in this menu e New Project Creates a new empty project All entries of the current FAMIAS session will be cleared e Open Project Opens an existing project All current entries in FAMIAS will be cleared and replaced by the opened project e Recent Projects Shows a list of previously opened project files e Save Project Saves the current session of FAMIAS as a project file with the current file name if existent In a project the complete content of all modules of FAMIAS is saved This includes time series data diagrams results from the analyses and the logbook e Save Project as Saves the current session of FAMIAS as a project file with a new file name e Import Set of Spectra Opens a dialogue to import a time series of spectra The selected file must be in ASCII format and list the filenames of the spectra the observation 24 The File Menu time
14. The other possibility is to choose a time series of spectra and then to select the option Settings Calculations based on n th moment in the Fourier Tab and the Least Squares Fitting Tab In this case the corresponding time series of moments is computed automatically for the selected dispersion range If you then pre whiten your data the residuals are written as time series of moments to the Data Manager Tab yellow background in the list of Data sets You can calculate a Fourier transform of these residuals to search for further peaks If you want to compute another least squares fit with an additional frequency you have to select the original time series of spectra green background in the list of Data sets Compute Fourier spectrum of residuals Compute a Fourier spectrum of the residuals A frequency at F3 17 5 d is significant and should also be included in the least squares fit Also select this frequency in the Least Squares Fitting Tab List of frequencies and compute a least squares fit for both frequencies si multaneously You have to select the original data set that was prepared for computing the moments Pre whiten the data and compute a Fourier spectrum of the residuals No significant peaks are left Analyse the first three moments Analyse also the second and third moments since modes of higher degree The Spectroscopy Modules 83 D FAMAS version St Ole 720m home ried apareis FAMIAS Coast G5 Conk gt Seecial c
15. computing the mean spectrum with Time series Calculate Mean Spectrum and noting the Doppler velocity of the left and right borders of the line transition to the contin uum Select the original data set non interpolated and extract the line with Time series Data Extract dispersion range The extracted spectra are written into a new data set Select this data set and press Select All The Spectroscopy Modules 19 2 Call the dialogue for computing the moments by pressing Time series Calculate Compute Moments Select Individual signal to noise ratio and the moment that you want to compute in the combo box below Press OK and leave the centroid velocity at the proposed value mean barycentre of the line 3 The time series of moments is written as a new data set It is advisable to check for systematic trends especially in the equivalent width and the first moment 4 8 6 Interpolate on common dispersion scale The tutorial spectra have different dispersion scales Therefore they have to be interpolated onto a common dispersion scale to carry out several tasks such as to compute a two dimensional Fourier transform or a least squares fit across the line profile pixel by pixel and to apply the FPF method This is not mandatory when only line moments are used To carry out a linear interpolation on a common dispersion scale select all spectra and click on Time series Modify Interpolate Dispersion It is advi
16. data set In the Data Manager or the use combo box top right select the data set you want to analyse Calculate Fourier spectrum Switch to the Fourier Tab Select a reasonable frequency range and click on Settings Calculate Fourier to compute a Fourier spectrum A dialogue box will pop up and ask you if you would like to include the highest frequency peak in the Least Squares Fitting Tab Before doing so it is a good idea to check for the statistical significance of this peak 114 ea Tutorial Photometric mode identification Compute significance level Mark the check box Settings Compute significance level The fre quency value of the highest peak is automatically written to the corre sponding text field Modify this value if you are interested in the signifi cance of another frequency peak Click on Calculate Fourier to compute another Fourier spectrum The significance level will be shown in the plot as a red line If the examined frequency peak is significant include it in the List of Frequencies of the Least Squares Fitting Tab EI FAMIAS version 0 41 6 tela 72000 homelimadaia papers FAMIAS CoAgi CoAntSpectalisnue Pakage tuioiialcosstutorialpholtp IBak Fis Eda Took Halp KP Spectroscopy Froiemaiy ieee Gera U Dati Manager Fourier LiakerSquanda Filing Made identhcaion Aguile Leghsca Seings Last of Comic haber Frequency hange Eom a 3 Data Nyquialtequency 1 871 Frecunency
17. does not have a physical meaning In this case it is best to enter the mean value of the cross correlated range into this field The other parameters in this field can be determined during the mode identification In the case of the moment method also the centroid velocity and the signal to noise ratio have to be set See Section 4 5 9 for details about these parameters Pulsation Mode Parameters This field controls the settings for the parameters of each imported pulsa tion frequency A frequency will be taken into account for the optimisation if the check box next to the field Frequency c d is checked Optimisation Settings This field controls how the mode identification is applied as well as the settings for the genetic optimisation For a detailed explanation of the settings we refer to Section 4 5 10 General Settings For the tutorial spectra you can leave the number of segments that are taken into account for the computation of the line profile at the value of 1000 For rapidly rotating stars and high degree pulsation modes a higher value is required For details we refer to Section 4 5 11 FAMIAS The Spectroscopy Modules 87 proposes default parameter settings for the optimisation if you press Set fields to default ELS EEA A ea AA home AMAA Arpa FEARS COANA Dok el ope alee Poche EN EnaA Ip File Edt Tools Hop O l i Gp dpsogy Photometry Cate set eed mengrien linaria PIFF pei Ne of epeta 450 Scale imis tar AES
18. field Frequency Select the filter system of your observations and input the observed amplitude and phase in the corresponding fields To add values for an additional frequency use the function Action Add frequency e Automatic input To use this function you need to import light curves from different filters and assign to each light curve the correct filter name during import or in the Data Manager Mark the frequencies in the Least Squares Fitting Tab List of Frequencies that have significant 116 Tutorial Photometric mode identification amplitude in all filters that you want to use for the mode identifica tion Press Copy values to MI to compute a least squares fit and copy the frequency amplitude and phase to the Mode Identifica tion Tab In this least squares fit the frequency is kept constant whereas amplitude and phase are improved Repeat this procedure for the light curves taken in other filters with out modifying the frequency values or the number of marked fre quencies TE PRMIAS yarelen Gol Blase fae MEM AMEA PE TAMAS Connlise Conarapiel Mino UEP ib age util EE AAPS Fila Edit Tools Halp K Spectroscopy Photomatry uia Geneva Vi Dala Manager Fourear Leasl Gouares Fitting R suis Logbook Observed Values Talar Model Parameters Fi 4gcoe0s Tat 20000 s 1000 bggi48 09 Frequency od 4 BSShoe 00000000 A Mass T2 Mo Geneva aytkim Aimoaphore gid Kunz Fi
19. free parameters for the optimisation In this case vsin t the equivalent width the intrinsic width and the zero point shift are set as free 90 Tutorial Spectroscopic mode identification Press General Settings Start mode identification to start the optimi sation The results are written to the Results Tab Figure 17 shows the results of the fit to the zero point profile The field Best Models shows the 20 best solutions You can click into the table to display the fit in the plotting window Comparison between Fit and Observation Here the observational zero point profile is displayed as blue line its statisti cal uncertainty as green lines and the modeled profile as red line The chi square plots can be used to estimate the uncertainty of the fit It is evident in Figure 17 that the best solution can still be improved It is a good idea to note the parameter values for the best solutions and refine the search range of these parameters in the Mode Identification Tab to the following values min max step v sin i 30 50 1 equivalent width 7 9 0 01 intrinsic width 7 15 1 and zero point shift 13 11 0 01 Reset the optimisation procedure by pressing General Settings Reset and start another optimisation This optimisation should result in a much lower chi square value and thus a better constraint on the free parameters We will take the obtained solution as a starting point for the mode identific
20. gre search indmdual ugnal D notse rato Number of CPUs b use 1 Figure 19 Settings of the Mode Identification Tab for the moment method Moment method 1 Determine pulsation frequencies Determine all frequencies that have significant amplitude in the first mo ment including harmonics and combination frequencies see previous section Compute a multi periodic least squares fit using the option Least Squares Fitting Tab Settings Calculations based on gt 1st moment radial velocity MI moment 2 Import frequencies to Mode Identification Tab Switch to the Mode Identification Tab and click on Pulsation Mode Parameters Import data for moment method from current LSF 92 Tutorial Spectroscopic mode identification After the import you can switch between the two pulsation frequencies in the field Pulsation Mode Parameters with the top left combo box Mark the check box next to the frequency value for both imported frequencies Identify pulsation modes The starting parameters and settings should be adopted as displayed in Figure 19 Start the mode identification by clicking on General Settings Start mode identification The results are written to the Results Tab 5 The Photometry Modules The Photometry Module contains tools that are required to search for frequen cies in photometric time series and to perform a photometric mode identifica tion The tools are located in tabs that have the followi
21. if the check box has been checked In this case two additional input 66 Mode Identification boxes appear and values for the search range Min Max Step have to be en tered Some parameters such as Teg or log g cannot be set as free parameters since they determine the limb darkening coefficient The more parameters are set as variable simultaneously and the finer the step the larger the parameter space becomes This must be taken into account when setting the optimisation parameters to avoid ending up in a local minimum see Section 4 5 10 for more details 4 5 7 Stellar Parameters This box defines the global stellar parameters that should be used for the opti misation e Radius Stellar radius in solar units In combination with the stellar mass this parameter determines the k value of the pulsation mode i e the ratio of the horizontal to vertical displacement amplitude e Mass Stellar mass in solar units In combination with the stellar radius this parameter determines the k value of the pulsation mode i e the ratio of the horizontal to vertical displacement amplitude o Teff Effective temperature of the star in Kelvin Together with the param eters log g and Metallicity this parameter defines the limb darkening coefficients by linear interpolation in a precomputed grid Claret et al 2000 e log g Value of logarithm of the gravity at the stellar surface Together with the parameters Teff and Metallicity this
22. line profile computation Data set name Name of the data set of synthetic line profiles that is written to the Data Manager Tab Save parameters Saves the parameters you entered in this tab to a file Load parameters Loads the parameters for computing synthetic line profiles from a file Compute line profiles Computes the synthetic line profiles and writes them into a new data set to the Data Manager Tab 58 Mode Identification 4 5 Mode Identification This module is dedicated to the spectroscopic mode identification with the Fourier parameter fit FPF method and the moment method Its main func tions are importing the observational data for the mode identification least squares fit across the line profile or line moments setting stellar and pulsational parameters defining the free parameters for the optimisation mode identifi cation and setting the parameters of the optimisation procedure The results of the mode identification are written to the Results Tab and to log files on the disk A screenshot of the Mode Identification Tab is displayed in Figure 10 Observational data can be imported and the parameters to be optimised can be chosen Two different approaches for the identification of pulsation modes are available the FPF method Zima 2006 and the moment method Balona 1986a b 1987 Briquet amp Aerts 2003 Both methods assume the fol lowing oscillations in the limit of linearity sinusoidal variations slow
23. must be interpolated on each other to use this function The new spectra will be written into a new data set e Add Noise Add white Gaussian noise to the selected spectra The continuum SNR must be indicated in the dialogue window The new spectra will be written into a new data set 4 1 3 Spectrum Box This box shows a list of the currently selected spectrum in the Time Series Box It consists of two columns dispersion and intensity The dispersion can be in 38 Data Manager units of Angstrom or km s dependent on the selected data set Multiple bins can be selected by clicking with the left mouse button on several items in the list while pressing the Ctrl key or the Shift key All items can be selected by pressing Select All Selected items are displayed in the plot window as red crosses The following commands are available in the menu Data e Edit Data Opens a table of dispersion values and intensity in a new window with the possibility to edit these values Modifications can be written to the current spectrum e Remove Selection Remove the selected bins from the spectrum data set Use this function to remove bad pixels with deviating intensities from the spectra After removal of a pixel interpolation of the spectra onto a common velocity grid might be necessary 4 1 4 Plot Window The plot window shows the currently selected spectrum with selected wave length bins a time series of moments or the statistics of a time se
24. parameter defines the limb darken ing coefficients by linear interpolation in a precomputed grid Claret et al 2000 e Metallicity Stellar metallicity m H relative to the Sun in logarithmic units To gether with the parameters log g and Teff this parameter defines the limb darkening coefficients by linear interpolation in a precomputed grid Claret et al 2000 e Inclination Angle between the line of sight and the stellar rotation axis in degrees The Spectroscopy Modules 6 7 The models assume that the axis of rotation is aligned with the symmetry axis of the pulsational displacement field v sin i Projected equatorial rotational velocity v sin in km s t 4 5 8 Pulsation Mode Parameters This box defines the parameters of the pulsation modes that should be identified The observed data can be imported by clicking on the button The imported frequencies can be selected with the combo box Each frequency that should be taken into account for the mode identification must be selected by clicking on the check box next to the frequency value e Button Import Data Import the observational data for the mode identification You must first compute a least squares fit across the line profile for FPF method or the first moment for moment method in the Least Squares Fitting Tab For the moment method Select in the combo box Calculations based on of the Least Squares Fitting Tab the option 1st moment and compute the least s
25. rotation neglecting second order rotational effects a limb darkening law according to Claret 2000 a symmetric intrinsic line profile which is a Gaussian for the FPF method and a displacement field that can be described by a sum of spherical harmonics The FPF method furthermore permits to model a variable equiv alent line width caused by local temperature variations on the stellar surface Both methods rely on the fact that the bin intensities across an absorption line profile vary with the period of the associated non radial pulsation mode Whereas the FPF method makes use of the intensity information of each dis persion bin across the line profile the moment method uses integrated values across the profile This is the main difference between the two methods and leads to a difference in the capability of identifying pulsation modes For the FPF method there is in principle no upper limit for the identification of 2 m but a very small value of vsinz as well as a large pulsation velocity relative to the projected rotational velocity can make mode identification impossible In the latter two cases the moment method is better suited but this method is only sensitive for low degree pulsation modes with lt 4 In the way as they are implemented in FAMIAS both methods take into account the uncertainties of the observations and the goodness of the fit mode identification is expressed as a chi square value The optimisation is carried o
26. shep 0000121 Fra Geneva U Freg tom Gio 20 Mar ied E595 Garava U Freq tam Oio 20 Mar lad 4500 E Use weghis i j Compute spada window E Compis signdicance loyal mMbequency 4255607 SH irral 4000 Smoching iador 50ER Catat Foun E ije Founar Spectrum HaT ee a Highest peak is al 4 85950 cid win an amoltude of 0 03241 is TT rd aa The mignal io noiss rato ig according io your sangs SN 26 1500 e E Should d be inserted inio the frequency kst i ams EEE a HS y O01 E ii 0005 J FAI a rat IF i 1 i 64 i T T T a L 0 5 10 15 at Frequency Figure 26 Fourier spectrum of the Geneva U band 4 Compute least squares fit Switch to the Least Squares Fitting Tab and mark the check boxes of all frequencies in the List of Frequencies that you want to include in the fit Also mark the check box Settings Compute signal to noise ratio to determine the statistical significance of the selected frequency peaks Click on Calculate Amplitude Phase to compute a least squares fit to the data by improving amplitude and phase values Click on Calculate All to compute a fit by improving frequency amplitude and phase The List of Frequencies box shows the results of the fit The frequency is The Photometry Modules 115 displayed in inverse units of the input time and the phase is indicated in units of the period 5 Pre whiten light curve To pre whiten the light curve with the obtained fit mark the check box Pre
27. you import an import dialogue will open Select the columns that you want to import and specify the photometric passband of The Photometry Modules 113 the observations For a more detailed description of the import dialogue see Section 2 1 The successfully imported data sets will be listed in the Data Manager You can use the tools in the Data Manager to edit your data delete data points change weights etc See Section 5 1 2 for further details 5 7 2 Searching for periodicities The search for periodicities should be carried out in the following iterative schematic way 1 Compute a Fourier spectrum in a frequency range where you expect pul sation Compute the significance level at the frequency having the highest am plitude and include this frequency in the least squares fitting if it is sig nificant Compute a multi periodic least squares fit of the original data with all detected frequencies In case that no unique frequency solution exists due to aliasing compute least squares fits for different possible frequencies The solution resulting in the lowest residuals should be regarded as best solution Exclude frequencies from the fit that do not have a SNR above 4 3 5 for harmonics and combination terms Pre whiten the data with all significant frequencies Continue with the first point using the pre whitened data until no signif icant frequency can be found FAMIAS follow the following procedure Select
28. 05 T Fi AP mong gi Wod Jul 73 2008 ie 1102 Fat AP mons of Thu dul 24 20008 1 Fa AP morgi od Th Ju 24 FOC 1 16 agre Fa AP morna od Thu a 2d 2 T 1059r is LAP a mong gi i Thu Jul 24 aoa eH IS ERS le tarse s0 esc 7 T4785 au aSr P6509 ig tem 50 196505 27 PB or Lbs eg gn Lii rii a a i a fs t a211 50 Karer 27 4 igri Os Fi AP mono of Thu Jui 24 2008 7 a 4 4 4 ia Ree Chivaquane plots Cocpansen between Fa ard Observation SBOE TREES he een Core LRGs hago Lip aie hagas 2 Fe 7 B50 160000 Pie Figure 11 Screenshot of the Results Tab Press the button Update to update the list of best models and the plots with the current status of the mode identification 74 Results 4 6 1 Best models This table lists the parameters of the 20 best fitting models The first column always shows the y2 value The other columns contain the parameters that have been set as free for the mode identification Two display options are possible and can be selected in the combo box above e Best models List the free parameters of the models having the lowest 7 values e Best 1 m combinations List the free parameters of the models having the lowest 2 values and different m combinations For each possible combination of and m the best model is shown 4 6 2 Chi square plots This plot window displays the x values log scale of all models that have been computed in the current opti
29. 82 a ignore 2450090 885 amp S587 2450090 845 5 2450096849 6557 2450006 843 6557 is 2450097 849 6585 450097 84 2450400 832 6560 2450400 2450400853 6574 46040 2450401 835 6541 245040 5 2650401 863 6552 24650601 B43 2450407 B13 6548 2450407 813 2450407845 6574 x 2450454 712 6577 4 gt aaa ae aa aS E Se e a E a E ef amp Figure 3 Screenshot of the dialogue for importing light curves Figure 3 shows a screenshot of the dialogue for importing light curves The left column shows the raw data file You can indicate the number of header lines to be skipped Skip first X lines At the top of the right part of the window you can select the column number which contains the data type selected in the box below The time must be in units of days You must select a passband for the magnitude and the weights are point weights per data point Click Ignore if no column with weights is available All weights are then automatically set to a value of 1 If your selections are valid and the file structure is acceptable for import ing the text box on the lower right will display File OK Otherwise you will have to check the structure of your data file If the import was successful you will see the imported data in the Data Manager of the photometry module e Quit Exit FAMIAS 26 The Help Menu 2 2 The Edit Menu The items in this menu provide the possibility to clear the input fields plots and stored data of selected tabs of
30. 98 Fourier Analysis ELD FAMAS version 091 9 beta 2 73008 home simada papers FAMIAS CoA aNSN CoA skipari alieu ya Parkaga tuted al co ma Meera tp iter File Eda Tools Help i pedomp Photomety ube Geneva U gt i Data Manager Founer Loasi Squares Faing Mode derticaion Aesufts Logbook Sain List ofl Cakcuaions Frequaincy nange from 0 fo 10 Daw Ayu frequency 12877 Frequency aap 000071 Fir s Geneva U Frog kom dio 19 Mar ted RESIDUALS of Ganava UFI Frog Foi H Use wengnis Geneva U Freq fom 0 w 10 Mar fed 5 i Geneve Ui Freq tam Oto 10 Mar fed states zao Genava U Frag ksm Oia 10 Mar be x Compute signdcance level abequency 4850602 SN level 4 0000 Smoothing laciot ED ps fd frequen rot haka pn ms F Ta ti ggunr F frequency Wat 4 Hihona poak is al 485580 off wth an amplitude ol 0 09241 The signais ncise rato is according b your seings SN a 25 150 Should i be maenad inio the inequency fet Calculate Fawet st a Yes io Fount Spactrum a Pot aa 0 095 om firs 02 E ogs 001 ao Frequency Figure 21 Screenshot of the Fourier Tab e Export Data Set Exports the currently selected data set to an ASCII file having the follow ing three column format frequency amplitude power 5 2 3 Fourier Spectrum Plot Shows the most recently computed Fourier analysis or the selection from the list of calculations The Fourier spectrum is shown as a blue line the signi
31. C01 HEE AeA 20006401120 OO008TzEre0 OO0GE1I0gC0 O0007TE4160 ON0DSE26610 prani tenggo OBES 7085 hesee erase ere TAIHA ME DEHAT OO0sEsTEsoO O008467800 oooes7ressoo poner Papin CETE la pos465100 0007357800 Cvarnhootng Matalicty 0 0 2 es Weraaw New Jerse p Dioemioask Grid entis Figure 23 Screenshot of the Mode Identification Tab 5 4 3 Observed values This box contains the frequencies amplitudes and phases of the observed pul sation frequencies in different photometric filters These values can be imported from the Least Squares Fitting Tab or entered manually e Frequency selection Different frequencies can be selected with this combo box Each item in the combo box is related to a frequency value and its amplitudes and phases in different filters Frequencies can be added by importing from 5 4 4 The Photometry Modules 107 the Least Squares Fitting Tab or by selecting in the Action menu the option Add frequency Action menu This menu allows to add or remove frequency sets Frequency value Frequency value in d Filter system Select the filter system for which the mode identification should be carried out Three different systems are available Johnson Cousins UBV RI Str mgren wuby and Geneva Table of amplitudes and phases This table contains for each filter the observed values of Ay and o4 in mmag and of and ag In units of 27 You do not have to fill out all f
32. FAMIAS e Clear Spectroscopy Tabs Clear all data in the selected tabs of the spectroscopy module e Clear Photometry Tabs Clear all data in the selected tabs of the photometry module 2 3 The Tools Menu This menu provides some useful tools that are related to asteroseismology and mode identification e Stellar Rotation Compute the equatorial rotational velocity rotation period or rotation fre quency theoretical critical Keplerian break up velocity or critical v sin t and the critical minimum inclination for a given stellar mass radius vsint and inclination angle e Pulsation Parameters Compute the horizontal to vertical amplitude ratio the frequency in the stellar frame of reference and the rotation frequency and the ratio of the rotation to the pulsation frequency for a given pulsation mode stellar mass radius vsinz and inclination angle 2 4 The Help Menu The Help Menu provides access to the FAMIAS manual enables to submit bug reports and provides general information about the software e FAMIAS Help This opens the built in user manual of FAMIAS The manual is regularly updated with new versions of FAMIAS e Update Information This shows a list containing update information about the current and previous versions of FAMIAS e Report a Bug Provides a link to the webpage of FAMIAS where bug reports can be submitted on line The Main Window 27 e Copyright and User Agreement View general copyright informat
33. FAMIAS User Manual Wolfgang Zima Instituut voor Sterrenkunde K U Leuven B 3001 Leuven Belgium e mail zimaQster kuleuven be http www ster kuleuven be zima famias 1 Introduction FAMIAS Frequency Analysis and Mode Identification for AsteroSeismology is a collection of state of the art software tools for the analysis of photometric and spectroscopic time series data It is one of the deliverables of the Work Package NAb Asteroseismology of the European Coordination Action in Helio and Asteroseismology HELAS Two main sets of tools are incorporated in FAMIAS The first set allows to search for periodicities in the data using Fourier and non linear least squares fitting algorithms The other set allows to carry out a mode identification for the detected pulsation frequencies to determine their pulsational quantum numbers the harmonic degree 2 and the azimuthal order m The types of stars to which FAMIAS is applicable are main sequence pulsators hotter than the Sun This includes the Gamma Dor stars Delta Sct stars the slowly pulsating B stars and the Beta Cep stars basically all pulsating main sequence stars for which empirical mode identification is required to successfully carry out asteroseismology This user manual describes how to use the different features of FAMIAS and provides two tutorials that demonstrate the usage of FAMIAS for spectroscopic and photometric mode identification 1 1 Overview The following key fe
34. If the frequency is not detected in the first moment the phase value has to be set as free in the range between 0 and 1 with a step size of lt 0 01 After a first run of the mode identification with and m as free parameters see field Optimisation Settings one normally has a constraint on the phase value and it should be set to 0 5 with a step of 0 5 different pulsation modes have their best fit at phase values that differ by half a period this is due to the fact that we limit the inclination angle to a range between 0 and 90 degrees and not between 0 and 180 degrees The further mode identification should be carried out by setting the search method to and m grid search e Equivalent width variations of the line profile due to local temperature variations at the stellar surface can be taken into account by considering the parameters f and Phase see Eq 15 in combination with the parameter d EW d Tef f which can be positive or negative see Eq 14 The parameter space is significantly enlarged by setting these parameters as variable so it is important to already have some constraints on and m before attempting to fit the equivalent width variations e Multi mode identification gives only good results if already some con straint about and m of the pulsation modes has been obtained Other wise the genetic optimisation algorithm may end up in a local minimum due to the large parameter space e The nu
35. Model Huna hou awersie Maia 0 Wacriurbulence veno 2 imiu Mee peat Aira Ney bein ep reer ke EE Nae aba os le atta Figure 28 Results of the tutorial data The best identification is achieved for 0 red lines 2 Set stellar model parameters In the Mode Identification Tab the parameters of the stellar models and the source of the non adiabatic observables that should be used for the mode identification have to be set See Section 5 4 4 for detailed information about these parameters 3 Start mode identification Start the mode identification by pressing the button Identify mode The results will be written to the Results Tab 4 Interpretation of results The Results Tab displays the results of the mode identification in text form and in several plots The text field Mode Identification lists the input parameters and the observed and theoretical amplitude ratios and phase differences Its contents are described in detail in Section 5 5 As can be seen in Figure 28 the observed amplitude ratios are most consistent with theoretical models that have a degree 0
36. Renames the currently selected data set e Export Data Set The currently selected data set will be exported as ASCIl file s to the disk The suffix of the files has to be entered by the user For a time series of spectra the exported files will have the following structure One file called times suffix consisting of a list of three columns namely spectra filenames times and weights Each spectrum of the time series will be written into a separate ASCII file and called number suffix where number is a running counter If a data set of line moments is exported a single ASCII file having the following four columns is created time moment value uncertainty and weight e Combine Data Sets Combines the selected data sets to a new single time series The data sets to be combined must have the same units of dispersion Moreover all times of measurement have to differ e Change Dispersion Scale Select wavelength in Angstrom or Doppler velocity in km s as dispersion scale of the current data set of spectra A conversion between the two scales can be carried out in the Modify Menu of the Time Series Box 4 1 2 Time Series Box The content of this list depends on the selected data set If a time series of spectra is selected in the Data Sets Box the list will consist of three or four columns times of measurement number of wavelength bins and weight and optionally signal to noise ratio If a moment time series is selected in the Data Se
37. SOWALS of oasiagrjal joonverted io ins 2Pe5389 57 Data Manager Founes Laast Sguargs Piang Line Probie Synhigsis Moxie derticeton Aasutu Logpock Stellar Parameters Pubnaiicn Mode Panamera Mater Step Pinase tretoompute a lash spas as bt Fi 11530055200 Aadass sotar uris 3373000 Mass Solar mii 1850000 Eee siars eee 7E16 000000 MiniGonal Ba00000 H Degna Order m I incknatan jsepreas H Vel amp Ams 00 E Phase pry 000 A a0 Presa M reat d E v en i ena Lina Prolia Parameters pimza on Setings Gonera Serge My ort mh ia Compute waini EGW amp rimai wath it 2 No cl segments 1000 Dannie opimirmor Enenion vain E Equivaieni wth ove 1 AJECWYA Ta Da eee ee Mar number of terahons 155 Sanna amea E minae wm am ie Max Danaina wo imoran 10 Coregance speed o o00000 Na ol olu modek 1 R feo pod eh ims 20 A mi fee parameters umber of CP Lis to une i Figure 16 Settings of the Mode Identification Tab Fourier parameter fit method 1 Determine pulsation frequencies Determine all pulsation frequencies including harmonics and combina tions that have significant amplitude across the line profile pixel by pixel as described in the previous section Select all frequencies in the List of frequencies and compute a least squares fit across the line profile with the option Settings Calculations based on Pixel by pixel MI FPF 2 Selection of dispe
38. Version O St Olea 7200 hone ried sa pares FAMIAS CG SA oy COORG Soecl ai seule Park ape Worl a coss tubra fp File Edt Tools Help Li Specroscopy Photometry Data sat namesstutcriat converted to ims ZP 538937 wegnied No ct spacia 490 Scale urs usa coastuteial converted o kts ZP Data Manager Fourier Least Squares Fang Line Profle Synthesia Mode Kenticaton Resuts Logbook Senge Leas squares 4 Diapersion range for F7 11 5308000000 z Use wegtts Prewhmen Gata Pael by pxel Mi FPF a Compie signal to noise rate Cakulate Anglaise Phase Lst of requerces Zerogoet Resduels 00044804417 use Frequercy Ca Ampito dA Prase dP SNAmo 3 148514106 0 0027283297 0 00SSS4 0334022206 0032341 3961 11 59047632 0 1 4877247 12 0062624 39716 17499955710 046667487 0 056615 16497 3499911574 0001979 787496613 1 235 0829073559 464616 6552 23 05805262 00028048 285759107 1 41551 067740202 65004 5992 7399870606 000129 5683734577 144469 0536795713 781849 5109 2005 na lo 1457702061 0 056535 47300 E a a 44 E24 so 4A oe oe ho ee CO ee ec 180 100 100 Figure 15 Results of the least squares fit across the line profile 10 The period analysis of the tutorial data set reveals three frequencies Fy 11 53 d t F 17 50 d t and F3 2F 23 06 d The frequency F3 is a harmonic of F 4 8 9 Mode identification FAMIAS provides two different approaches for the spectroscopic mode identi ficat
39. a across the line profile To determine the significance of a frequency peak across the line profile one should use the function Pixel with highest amplitude at f in combina tion with Compute significance level By doing so only the dispersion bin having the largest amplitude of the indicated frequency is taken into account for the computation of its SNR e Calculations based on Defines what the calculation of the Fourier analysis is based on The following settings are possible Pixel by pixel 1D mean Fourier spectrum Computes a Fourier spectrum which is the mean of all Fourier spec tra across the selected dispersion range The resulting Fourier spec trum is therefore one dimensional with frequency on the x axis and mean amplitude on the y axis The signal to noise ratio of a peak 42 Fourier Analysis cannot be determined since a frequency can have different ampli tudes across the line profile For this use the option Pixel with highest amplitude at f in combination with Compute significance level Pixel by pixel 2D only export Computes a Fourier spectrum for each pixel bin across the se lected dispersion range The output is a two dimensional Fourier spectrum where the amplitude is a function of frequency and dis persion Due to the generally large data size of such a Fourier spectrum some megabytes it can only be exported to an ASCII file A contour plot of these data can easily be created by the user e g
40. a dialogue for computing line moments of the selected spectra The dispersion scale of the spectra must be in Doppler velocity expressed in km st The moments time series can either be written into a new data set to the Data Sets Box or directly to the disk as ASCII files if the option Write Moments 0 to 6 in a file has been checked The nt normalised moment lt v gt of a line profile I v t corrected for the velocity of the star with respect to the sun at the time t is defined by fou I v t dv FOO gr A a f I v t dv OO lt u gt l 1 where v denotes the line of sight Doppler velocity of a point on the stellar surface and the denominator of this expression is equal to the equivalent width of the line The 1st moment is the radial velocity placed at average zero the 2nd moment describes the line variance and the 3rd moment describes the skewness of the profile If the shape of the line profile changes periodically due to stellar pulsations the line moments also vary with the period of pulsation or a sub multiple thereof For more details we refer to Aerts et al 1992 34 Data Manager FAMIAS can compute the uncertainties of the different line moments if the SNR of the spectra is known The uncertainty is used to derive the value of the theoretical moments when applying the moment method and consequently to determine the statistical significance of obtained solutions of the mode identification W
41. a mode identification has stopped the results are written to the file bestFitsLog extension The best 20 fits ASCII files and plots containing theoretical and observed zero point amplitude and phase or moments are written to files in the directory defined in Settings see below e Set fields to default Set the optimisation line and stellar parameters to default values depen dent on the selected mode identification method The proposed values are just a guidance and have to be adapted for many optimisation problems e Settings Opens a menu that provides the following functions silent mode save load parameters set output path for the logfiles and clear all fields of the Mode Identification Tab The silent mode toggles the updating of the progress bars For some optimisations the computational performace decreases significantly if the progress bars are updated e Reset Resets the previous optimisation Must be pressed if a new optimisation procedure should be started e Start mode identification Starts the mode identification The optimisation process can be stopped at any time by clicking again on this button The results of the mode identification will be written into the Results Tab After an optimisation process has stopped again clicking this button will continue the optimi sation at the stage where it stopped To begin a new process click the button Reset 42 Mode Identification e Progress bars and counter The progr
42. ables independent of the inclination angle 2 and the az imuthal order m in the case of zero rotation approximation 5 4 2 Approach for mode identification in FAMIAS FAMIAS computes the theoretical amplitude ratios and phase difference accord ing to the above described scheme in different photometric passbands To identify the spherical harmonic degree the user must provide its frequency amplitude and phase in different filters ranges for Teg and logg a number of stellar model parameters such as mass and metallicity and the source of the stellar models FAMIAS then derives the theoretical values from pre computed model grids and displays the results of the mode identification on the Results Tab At the time this manual was written we had pre computed grids of the parameters QT Qy Bry Bg b at our disposal These atmospheric parameters have been computed by Leszek Kowalczuk and Jadwiga Daszynska Daszkiewicz using Kurucz and NEMO atmospheres The grids are available for the following photometric systems Johnson Cousins UBV RI Stromgren uvby and Geneva and for different values of metallicity parameter m H and microturbulence velocity All these results can be found on the Wroctaw HELAS Webpage These model grids contain stellar evolution tracks for different masses com puted by the Warsaw New Jersey code Paczy ski 1969 1970 and pulsational http helas astro uni wroc pl deliverables php The Photometr
43. al mean for each pixel of the selected spectra is computed and displayed in the Plot Window Important All spectra must have the same dispersion scale i e they must be interpolated on a common scale use the tool Interpolate Dispersion in the Modify Menu e Median Spectrum The weighted temporal median for each pixel of the selected spectra is computed and displayed in the Plot Window Important All spectra must have the same dispersion scale i e must be interpolated on a common scale use the tool Interpolate Dispersion in the Modify Menu e Std Deviation Spectrum The weighted temporal standard deviation a for each pixel of the se lected spectra is computed and displayed in the Plot Window Important 32 Times of observa on and S N rato Settings Data Manager all spectra must have the same dispersion scale i e must be interpolated on a common scale use the tool Interpolate Dispersion in the Modify Menu Compute Signal to Noise Ratio Opens a dialogue for computing the signal to noise ratio SNR of the selected spectra by making use of sigma clipping to determine the contin uum range The calculated SNR of each spectrum can be used to set the weights of the data In order to compute the SNR of the spectra a suffi ciently large range of continuum must be present in the selected spectra Description of the SNR dialogue see Figure 4 Initially the Time and SNR Box displays only the list of times of the selected spec
44. also be estimated within FAMIAS see p 32 If your selections are valid and the file structure is acceptable for import ing the text on the lower right will read File OK Otherwise you have to check the structure of your data file Still if there is a problem with the structure of the spectrum files FAMIAS might give an error message during importing indicating in which file the read in error occurred After you click on OK you must select the dispersion scale of your spectra units of Angstrom or Doppler velocity km s If the import was successful you will see the imported data in the Data Manager Tab of the spectroscopy module The Main Window 25 e Import Light Curve s Opens a dialogue to import a time series of photometric data You can import several files simultaneously by making a multi selection in the file import window by pressing the Shift or Ctrl key when selecting files Imported files are required to be in ASCII format and must consist of two or three columns separated by spaces or tabulators The following two columns are mandatory time in days Heliocentric Julian Date and differential magnitude A third column can consist of weights for the single measurements A file header can be skipped during import Raw tie A al a 7 otumn ve n eT mJ home pmadata PROGRAMME FAMAS jes erateie phommetythd7 1917 b z z z Skip iest 0 lines Tene id Sromgren u Wagh 2450391 659 6582 2450391 659 a 65
45. alysis Such a line should be an unblended metallic line Balmer and He lines are not well suited for the mode identification since they cannot be well approximated with an intrinsic Gaussian line profile To study a specific line with FAMIAS follow the following procedure Click on one spectrum of the time series Zoom in on the line in the plot window Click on Time Series Select All and then select Time series Data Extract Dispersion Range You can modify the dispersion range in the dialogue window that opens After you clicked OK a new data set has been written that only contains the selected dispersion range 4 8 3 Convert from wavelength to Doppler velocity To compute moments and to carry out a mode identification the dispersion scale of the spectra has to be converted from Angstrom to km s To do so select all spectra click on Time series Modify Convert Dispersion 18 Tutorial Spectroscopic mode identification and enter the value of the central wavelength in the dialogue window which is 5383 369 Angstrom in this case The converted spectra are written as a new data set 4 8 4 Compute signal to noise ratio and weights Computing the SNR of the spectra is important for weighting the spectra for calculating the statistical uncertainty of the moments and for enabling the calculation of chi square with the moment method There are two ways to estimate the SNR of your spectra The simple way is to compute the
46. amaw range 4547 5 i 4559 7 Data Manager Founer Least Squares Fang Line Protie Syrihess Mode kensicaton Resuta Logbook Data Sets Tie Series Daia Dat amie bodi 551317 489 EE eas 35551747 485 ia 270A 38552121 469 138 m5 jassa 4B 1 07 atas jJasSmo0 eg 135 24145 33554510 469 oot 187 43 ane708 4B 1 00 2073 3563640 489 O98 205 14 33634790 469 116 2254 15035445 no itt 218 81 JAEI71BE 489 120 nea 557 12500 100274 76 35085 469 114 22137 14557 15000 100910 386 8008 460 109 2078 4557 17500 1 00289 G 7E7 Agi agg 204 0 38641265 469 114 2713 386 42100 460 1 25 2225 8642024 489 1 29 Pas 67n a8 115 22258 4557 30000 1 00175 ljaddigi7 agi 105 21084 455732500 1 00280 3e845085 dep 105 Bane 4557 35000 0 00771 JAG sbean 465 117 ga 455737500 0 99481 35647511 485 1 08 2848 4557 40000 1 00028 557 42500 1 MTS FAb4g7Ss 465 1 16 73 60 a557 42000 1 007E 35651208 460 146 eho Sa 2557 47500 1O0TES 38852075 4a0 iz 2a 17 a557 50000 100206 SS6S2887 469 ne 206 89 33654243 48 116 2275 38654050 480 EEN 183 85 39655700 469 oF 188 Be SAG S6499 4B oat 14801 38650001 ano 11 22073 j s3650015 468 114 23117 zeco 460 125 216s 455770000100128 lagita 46g 106 els 4557 72500 1 ENH FSbS2904 489 One 190 32 Figure 1 Screenshot of FAMIAS 22 Requirements 1 2 What Data C
47. an Be Used The spectroscopic as well as the photometric data that can be analysed with FAMIAS must fulfill specific quality criteria and must have been fully reduced More specifically this implies the following requirements e Requirements for spectroscopic data Time series of fully reduced and normalised spectra including barycen tric time and velocity correction Dispersion better than 40000 Signal to noise ratio higher than 200 Unblended absorption line e Requirements for photometric data Time series of fully reduced differential photometric data including barycentric time correction Multi colour data in Stromgren Johnson Cousins or Geneva filters for mode identification Milli mag precision 1 3 Requirements FAMIAS has been written in the programming language C For the graphical user interface the open source version of the Qt 4 library from Trolltech has been adopted This combination enabled the development of a software tool that requires high computational speed in combination with the ability to create cross platform versions for Linux and Mac OS X FAMIAS also features a built in help system with an extended manual describing the tools and providing introductory tutorials The homepage of FAMIAS provides the possibility to download the software read the on line documentation and to submit bug reports http www trolltech com http www ster kuleuven be zima famias 2
48. apted for different data sets Sigma clipping iteratively removes outliers of a Gaussian distribution In this case the sigma clipping algorithm tries to find the continuum and to exclude the spectral lines The Spectroscopy Modules 33 After clicking on Calculate the position of the pixels detected as contin uum is marked as red crosses in the Current Spectrum Box The three plots at the right side show information about all spectra of the time se ries in order to check the overall results The top plot shows the number of bins detected as continuum of each spectrum The middle plot shows the SNR of all spectra and the overall mean SNR The bottom plot shows the mean intensity value of the pixels detected as continuum The latter values should be around 1 Outliers in this plot can indicate that the continuum has not been detected properly in some spectra In this case the settings for the sigma clipping must be adapted If Write SNR as normalised weights is clicked the time series is written into a new data set having normalised weights W SNR Also each spectrum of the time series is assigned its SNR value fourth column in the Time Series Box Compute Weights from SNR This function computes the weights of each spectrum according to its SNR The values of the SNR must already have been imported together with the spectra The weights are calculated from SNR and normalised such that the mean value is 1 Compute Moments Opens
49. ast Squares Fitting Compute a non linear multi periodic least squares fit across a line profile pixel by pixel or for the different line moments and pre whiten the data Line Profile Synthesis Compute a time series of theoretical line profiles of a radially or non radially pulsating star Mode Identification Identify pulsation modes by means of the Fourier parameter fit method or the moment method Results The results of the mode identifications are displayed and logged in this tab Logbook Log of all actions that were carried out in the spectroscopy module Photometry Tabs Data Manager Edit and modify the photometric time series Fourier Analysis Compute a Fourier analysis DFT and determine the statistical signifi cance of detected frequency peaks Introduction 21 e Least Squares Fitting Compute a non linear multi periodic least squares fit and pre whiten the data e Mode Identification Carry out a photometric mode identification with the method of amplitude ratios and phase differences in different photometric passbands e Results The results of the mode identification are displayed and logged in this tab e Logbook Log of all actions of the photometry module FAES version 091 0 beteroy S008 home cima de peers FAUTES Co RS i Gok Spec la sede Package epeperd tp Fle Edt Toots Help Kr Geecroncopy Phoomany Daia sof name epspertaw range 4547 5 io 4683 7 onrada No of spodna 445 Scale Angazom Lo opip
50. ation Generally the equivalent width and the zero point shift are quite well constrained and can be set as constant during the optimisation Figure 18 shows the parameter range we selected for the mode identification Identify pulsation modes Select the Fourier parameter fit method with the option to fit zero point amplitude and phase across the line profile through the combo box Op timisation Settings Select MI method FPF Method fit ZAP Select the option Optimisation Settings amp m grid search to obtain more reliable results of the optimisation procedure Click on General Settings Set fields to default The inclination 2 is now also set as free parameter Enter the following values as range i 5 90 10 Select the frequency 11 53 d in the field Pulsation Mode Parameters and mark the check box next to the frequency value The parameter ranges should be as follows degree 0 3 1 order m 3 3 1 vel amp v 0 30 1 and phase w 0 4715 0 9715 0 5 The value of the phase is taken from the least squares solution of the first moment of this fre quency see Section 4 5 4 for details The maximum value of the velocity amplitude should be set at least an order of magnitude higher than the amplitude of the first moment In general you should extend the range of a parameter if the lowest chi square value was found at one of the search border minimum or maximum of the range Start the optimi
51. atures are provided by FAMIAS e Search for periodicities in photometric spectroscopic time series using Fourier analysis and multi periodic least squares fitting techniques e Spectroscopic mode identification using the moment method Briquet amp Aerts 2003 and Fourier parameter fit method Zima 2006 e Photometric mode identification using the method of amplitude ratios and phase differences based on pre computed model grids Balona amp Stobie 1979 Watson 1988 Cugier et al 1994 Daszynska Daszkiewicz et al 2002 e Efficient usage of multi core processors with parallel computing 20 Overview The user interface of FAMIAS is structured into different tabs that contain the modules dedicated to the different tools The tabs can be selected by click ing on their descriptive name The two main modules are for the spectroscopic and photometric analysis Each of these modules is subdivided into tools for data management frequency searching and mode identification In the following the different available tabs are briefly described Spectroscopy Tabs Data Manager Edit the time series of spectra or moments perform statistics compute line moments examine the spectra extract spectral lines etc Fourier Analysis Compute a Fourier analysis Discrete Fourier Transformation for each pixel of a spectrum pixel by pixel or for the different line moments in order to detect periodicities and their statistical significance Le
52. be included the line has to be extracted This tool determines the position of the left and right line limits through a sigma clipping algorithm which detects the continuum Description of the extract line dialogue see Figure 6 The Times of Observations Box shows the list of times of the selected spectra Clicking on a time will show the according spectrum in the Current Spectrum Box limes of obs ervabon 331 2408 a 231251699 3331 259336 pool ea ac 391282450 3331 290147 a 29784 Taa 13055410 T J206 didida ridt 3331 331374 So 3969 Jid 28 10E 3333 299363 0 E ag 904757 333 3 12465 aa S201 be 3 328047 3333 333799 AE 341161 3339 346563 JaV Ke ERTAN pa selngs Fadar for sigma clipping 2 0000 Expand limita WT i Number ol iteralions 10 Calculate Let limit at 533500 Aight limit at 55 1359 Set current limits for all spectra Gurren sp cirurm 105 1 ae 0 95 Haien sity r g o Number of bins a2 z serre s M ESE SAE r LL JHU AS A40 JJ45 JI HIS W F3 im Dispersion limits a o 45 0 JF 30 Lef birit Ok Cancel Figure 6 Screenshot of the dialogue for extracting a spectral line The Spectroscopy Modules of In the Settings Box the sigma clipping factor and the number of it erations can be indicated and must be adapted for different data sets Sigma clipping iteratively removes outliers of a Gaussian distribution In thi
53. cal values of the amplitude ratio and phase difference in different filters in a text window as well as in diagrams 5 5 1 List of Calculations Each time a mode identification is carried out its results are saved as a new data set in this list Click on an item to display the results in the field Mode identification and the corresponding diagrams in the field Mode identification plots ee kM i hig home rimad nepara FAMINAS CIAMIS COLP Spec issie Pac kap anton al op eter ee ip File Edt Tools Hop MP lt a E Speckoscopy Protomoty a use RESIDUALS ol Geneva U F 1 Data Manager Founer Least Squares Fang Mode Wenticaton Resuts Logtcok is of Calsuatons Data s ees Mode kderticaton Fri dul 18 2008 17 07 lt 5 a On ease ee Mode iderticaon Fridul 18 2008 17 0821 Found 4 Gierent modak in he gwan ranpa of Taf logo and mass Mode identification Fri Jul 18 2008 17 08 59 a hinia erbiicadon iEn Jul 16 2008 17100 Fire hora Funai PA OGRA AME FAAS grde apani pulsator GHSO 2020 iis ena 06 el Mose Wenticaton Fri jul 18 2008 17 104 Tef ZSIR Miche ideaticamon Fri Jul 15 2008 17 200 r denticason Fr Jui 16 2008 17 290 Moga Harbication Fridu 16 2008 17 30 15 T Mote ijaniicasyn Fridu 18 2008 1731 21 i J PG a 22i LOPS areca UE UTET rr RRITAN s Agog Mode Genticabon Picts Figure 24 Screenshot of the Results Tab 5 5 2 Settings This b
54. check the box next to the detected frequency and press Calculate Amplitude Phase to compute the least squares fit Zero point amplitude and phase will be displayed in the plot panel at the right hand side The blue lines denote the derived fit whereas the green lines indicate the statistical uncertainty range of the fit The List of frequencies shows the results of the computed fit The field Results shows the mean standard deviation of the residual spectra The frequency is indicated in inverse units of the input time string The IAD is the integrated amplitude distribution and is calculated from the integral of the amplitude across the line profile inside the selected dispersion range Pre whiten spectra Pre whiten the data with the determined least squares fit by checking the box Settings Pre whiten data and clicking Calculate Amplitude Phase The pre whitened spectra are written as a new data set to the Data Manager Tab Select the time series of residual spectra in the Data Manager Tab and click on several spectra to check the quality of the fit red line Compute Fourier spectrum of residuals Compute a Fourier spectrum of the residuals by selecting the time series The Spectroscopy Modules 85 of residual spectra in the Data Manager Tab and proceeding as described In point 2 9 When computing further multi periodic least squares fits the original time series of spectra has to be selected gt FAMAS
55. colour represent the range of all found models that fulfil the search criteria 5 6 Logbook The logbook shows the list of actions that have been performed with the pho tometric set of tools of FAMIAS and corresponding information Each time an operation is carried out in FAMIAS a new log entry is written to the List of actions Clicking on an entry of this list shows the corresponding information in the text box Entries of the List of actions can be renamed or deleted by using the menu Data The text box can be modified and saved in FAMIAS by clicking on the button Save 112 Tutorial Photometric mode identification 5 7 Tutorial Photometric mode identification This tutorial demonstrates the use of FAMIAS for the photometric mode iden tification based on multi colour light curves 5 7 1 Importing and preparing data 1 Select the Photometry page and click on File Import Light curve 2 Select one or several files that contain the photometric data A data file must be in ASCII format and consist of at least two columns sepa rated by a space or tabulator Columns of observation time in d and magnitude are required An additional column listing the weights of the measurements is optional Once you have selected your files click on Open Data Seta Daia EBE 245ies0h 2a 2450500 24h 24507e 05 24S0ke05 24504505 Time Figure 25 Data manager after importing Geneva light curves of an SPB star 3 For each file that
56. cond moment respectively 4 6 4 List of calculations This box lists all previously performed optimisations By clicking on an item in the list the corresponding parameters are shown in the other windows of this tab 4 7 Logbook The logbook provides the list of actions that have been performed with FAMIAS and corresponding information Each time an operation is carried out in FAMIAS a new log entry is written to the List of actions Clicking on an entry of this list shows the corresponding information in the text box Entries of the List of actions can be renamed or deleted by using the menu Data The text box can be modified and saved in FAMIAS by clicking on the button Save 16 Tutorial Spectroscopic mode identification 4 8 Tutorial Spectroscopic mode identification This tutorial demonstrates how to perform a mode identification of a time series of synthetic spectra with FAMIAS The synthetic spectra can be found in the installation directory of FAMIAS in the directory tutorial coasttutorial The synthetic data simulate spectroscopic observations of a multi periodic Scuti star which consist of one absorption line having realistic observation times and signal to noise ratio The time series contains 490 spectra that con sist of 91 and 77 pixels respectively and cover a wavelength range between 5381 and 5385 Angstrom These spectra have been computed using the tool Line Profile Synthesis of FAMIAS The input parameters of the
57. converted o kavs ZP asaid converted to kms ZP 538197 wagt coastutorial converted to km s ZP 5385 57 weg RESIDUALS of coastal converted io keys P comstuiorial converted tb ims ZP 538337 wegt pmasiar Ometo o is 2P S36037 weothal tat momert radal yebaty Calculate Fourier isi sje Fourer spacium Piot Data Selected tequercy 11 50058 od wih an amplitude of 278799 The signal to noise rato is according your sefings SN 75 697 Should be inserted mio the bequercy is Figure 13 Fourier spectrum of the first moment after pre whitening with i ad 4 Compute least squares fit Go to the Least Squares Fitting Tab and select the field Settings Compute signal to noise ratio and the frequency Fl Compute a least squares fit by pressing Settings Calculate Amplitude Phase Im prove the frequency solution by clicking Settings Calculate All Ac cording to the List of frequencies this frequency has a SNR of 3 96 which is just below the significance limit The difference with the SNR determined in the Fourier transform is due to the fact that in this case the amplitude determined from the least squares fit is taken as signal We can conclude now that there are no significant periodic equivalent width variations in the line profile 5 Calculate Fourier spectrum of first moment Select the option Fourier Tab Settings Calculations based on lst moment and click on Calculate Fourier The
58. d dispersion range and should be plotted for a frequency range that is symmetric around O for visual inspection The Spectroscopy Modules 41 e Compute significance level If the box is checked the significance level at a certain frequency value is Computed and shown in the plot window as a red line The following parameters can be set Frequency Frequency value of the peak of interest The data will be pre whitened with this frequency and the significance level will be com puted from the pre whitened Fourier spectrum S N level Multiplicity factor of the signal to noise level The displayed signif icance level will be multiplied by this factor Box size Box size b for the computation of the noise level in units of the frequency The displayed significance level is computed from the running mean of the pre whitened Fourier spectrum For each fre quency value F the noise level is calculated from the mean of the range F b 2 F b 2 You must choose what data the calculations are based on and then press Calculate Fourier The significance level will be shown as a red line in the plot window together with the Fourier spectrum of the data blue line This option cannot be selected when computing a Fourier spectrum across the line profile In this case no signal to noise criterion e g significance of a peak when SNR gt 4 can be applied because the computed Fourier spectrum is an average of all Fourier spectr
59. ds for geometrical effects For computing b we use a non linear limb darkening law defined by Claret et al 2000 as i Yoautt 3 27 where u is the specific intensity on the stellar disk at a certain line of sight angle 0 with u cos and ay is the k th limb darkening coefficient The parameters ay and a are the partial flux derivatives over effective temperature and gravity respectively that are calculated from static model atmospheres for different passbands O log Fy o log Fy O log Test 2 logg 28 QT and Ugi whereas the parameters Gr and g are partial derivatives of the b7 factor log by m log b O log Tere logg The f parameter is a complex value which results from linear non adiabatic computations of stellar pulsation and describes the relative flux perturbation at the level of the photosphere OT og Tii Pr d 65 29 Rel ive 30 104 Mode Identification According to Eq 23 the complex amplitude of the light variations is expressed as Daszynska Daszkiewicz et al 2002 A i 1 086eY i 0 b Dh pf Do e D3 31 and the amplitudes and phases of the light variation are given by Ay A VAR r Ais yy arg A arctan A Ap and where A r 1 086eY i 0 b D efr D2 D3 2 A r 1 086eY i 0 b D fr Calculating amplitude ratio and phase differences the Y i 0 term goes away making these observ
60. e phase see example below Bracketed values are unchecked frequencies This format is compatible with the program Period04 Lenz amp Breger 2005 F1 5 2861 0 029179815 0 534 F2 6 2566 0 017759398 0 7461502 F3 5 885284 0 029203887 0 47617591 F4 10 583572 0 022958049 0 55097456 http www univie ac at tops The Spectroscopy Modules 49 4 3 3 Least Squares Fit plot The plot window displays zero point amplitude and phase and their uncertain ties of the current least squares fit across the line profile only active when pixel by pixel was selected for the calculations The frequency can be selected in the combo box at the top e Export current LSF Export the current least squares fit across the line profile to ASCIl files You must indicate a file name with an extension like name ext For each frequency x a separate output file called name_Fx zap is created The files consist of the following columns dispersion value zero point standard deviation of the zero point amplitude standard deviation of the amplitude phase in units of 277 standard deviation of the phase For more information about the plot window we refer to p 28 50 Line Profile Synthesis 4 4 Line Profile Synthesis This module can be used to compute a time series of synthetic line profiles of a multi periodically radially or non radially pulsating star The synthetic line profiles are written as a new data set to the Data Manager Tab The F
61. e provide here the formalism to calculate the uncertainties of the moments The formal uncertainty of each wavelength bin of a line profile o7 4 can be derived from the signal to noise ratio SNR of the spectrum by SNR OT v t JI v t 2 If sc A lt v gt t J loron dol 3 and sc A lt v gt t J V ort dv 4 then the variance o2 of the moment lt v gt is gt _ Ax lt u gt t V A lt v gt Joo Iwt dv Tau Poo aay a T Faaa Ja Iv t dv f7 uv t do 5 Description of the line moments dialogue see Figure 5 Select the dispersion range for the computation of the line moments The range must be large enough to include the complete line profile i e from continuum to continuum Optionally the complete dispersion range can be selected for the computations by checking Complete range The mean SNR of all spectra or the individual SNR of each spectrum is required to compute the statistical uncertainties of the moments The mean SNR of all selected spectra at the continuum can be estimated by computing the standard deviation spectrum and taking the inverse of the standard deviation at the position of the continuum When selecting Individual SNR each spectrum must be assigned a specific SNR column 4 in the Time Series Box The following procedure is strongly recommended for the calculation of line moments compute the SNR of each spectrum with the function Compute signal to
62. ed mass is searched for models that lie in the given range of Tig and logg e For each found model the atmospheric parameters Q amp T Qg BT A Bg r and by are determined by bi linear interpolation in the grid of the indicated filter set metallicity and micro turbulence e The program searches in the lists of the found non adiabatic pulsation models for different values For each the frequency that is closest to the observed value is searched for The values of the real and complex non adiabatic parameters fr and fr respectively are taken from this frequency value 106 Mode Identification e The theoretical amplitudes and phases are computed from Eq 31 for each selected filter e The amplitude ratios and phase differences are computed with respect to a selected filter ideally the one with the largest observed amplitude FAMIAS creates an error message if no atmospheric or evolutionary models have been found in the grids for the indicated parameters DC FEMES pe eee r home rial He poeee FAME S Co kel Se Godel a Seal coos eoiree ape Fila Edt Tools Holp Ke Speckoscopy Promomeby usa RESIDUALS of Geneve UF 1 Daa Manager Foune Least Squares Feng Disawed Values Stelat Model Parametens Tet 22700 ogg 35 Mass Fi 4BSsea 7082 Frequency od 18596700 Garava syaiem Amosphere od Fa er Ampitude mag dal Prase pencd gP u acastazabse Erara a raei EEE DO1a1BIS5a4 Dosa 1h MEAN
63. eld and the corresponding line profiles are computed for 10 phase bins evenly distributed over one pulsation cycle The theoretical values for AP are computed from a mono periodic least squares fit to these synthetic line profiles A chi square value is computed by taking into account the ob served and theoretical Fourier parameters and their observational uncer tainties for details see Zima 2006 The zero point across the line profile The Spectroscopy Modules 61 which gives a strong constraint on vsin2 the intrinsic line width and the equivalent width is ignored in this case Therefore this option should only be chosen if already good constraints on these global parameters are known This method assumes that the different pulsation modes do not have a significant influence on each other s ZAP values Such an assumption is valid if the ratio of the radial velocity amplitude to the projected rotational velocity for all frequencies is lt 0 2 For higher values the ZAP values across the line profile might be distorted and impossible to model with a single mode displacement field In this case the approach FPF Method complete time series fit AP see below or the moment method are better suited FPF Method fit ZAP This option is identical to FPF Method fit AP with the exception that also the observed and theoretical zero points are taken into account for computing the fits FPF Method complete time series fit AP With this
64. ele Package Winns Coss Ora fp File Edt Tools Help W Spectroscopy Photometry Data set namesstutrial converted o em 6 2 5383 37 wegnied No of spactra 499 Scale ons usa coastuteiai converted io km s ZPa Data Manager i Fourier Least Squares Fang Line Protie Synthesis l Mode denticston Resuts Logbook Settings Leas squares Dispersanrange for x Use weights Prewhten data Ist momert radial velooty MI moment at Compie signal to noise rato Sox sze 3 Cakulate Anpiide Phase Candme Al Usi of requenrges Zeropoet 1200197122 i 00187622 Resduals 04950905 use Frequency E Anpiade aA Phase dP SNRato FI 11 53009652 0000106 3 801570233 0 026518 04728568680 0 28495 90 291 x F2 174990557 0000840482852315 002665E 0 6008I9054 199476 16105 Phase P O E N 2 MAE ee ee ee ne ee ee 180 100 sO 0 a t00 kas Figure 14 Results of the least squares fit to the first moment might only have significant amplitudes for these diagnostics The analysis of the second moment should reveal F 2F5 2F3 and an additional fre quency at Fy 23 998 d7 The third moment only has F gt as significant peak 11 We can conclude that three significant independent frequencies are present in the first three moments of the tutorial data Only two of them are vis ible in the first moment and thus analysable with the moment method Figure 14 displays a screenshot of FAMIAS showing the results of the least squares fit t
65. er frequency value amplitude phase see example on p 48 102 Mode Identification 5 4 Mode Identification This module can be used to perform a photometric mode identification based on the method of amplitude ratios and phase differences of pulsation modes in different photometric passbands Balona amp Stobie 1979 Watson 1988 Cugier et al 1994 This method permits to determine the harmonic degree of pulsation modes in general up to 6 This upper limit is due to partial geometric cancelation of the observable pulsation amplitude over the stellar disc The determination of the degrees is based on static plane parallel mod els of stellar atmospheres and on linear non adiabatic computations of stellar pulsation In the present version of FAMIAS these are provided in the form of pre computed grids and interpolated linearly to obtain values appropriate for the observed parameters The theoretical values of the amplitude ratio and phase difference in a certain filter depend strongly on pulsational input This points out a very important difference between spectroscopic and photometric mode identification the former is model independent the latter is not To be able to compare the results FAMIAS incorporates grids computed from different pulsational codes and from different atmosphere models The present version of FAMIAS includes grids from two different scientific institutions see details below It is planned to include model
66. ere you expect pul sation Compute the significance level at the frequency having the highest am plitude and include this frequency in the least squares fitting if it is sig nificant Compute a multi periodic least squares fit of the original data with all detected frequencies In case that no unique frequency solution exists due to aliasing compute least squares fits for different possible frequency sets The solution resulting in the smallest residuals should be regarded as best solution Exclude frequencies from the fit that do not have a SNR above 4 3 5 for harmonics combination terms Pre whiten the data with all significant frequencies Continue with the first point using the pre whitened data until no signif icant frequency can be found Line moments 1 Select data set Select the spectra that were prepared for the analysis of the line moments and go to the Fourier Tab Calculate Fourier spectrum of equivalent width Select the option Fourier Tab Settings Calculations based on Equivalent width and click on Calculate Fourier The plot window now displays the Fourier spectrum of the equivalent line width A dialogue opens indicating the highest frequency peak at F 3 148 d and asking if this frequency should be added to the frequency list of the Least Squares Fitting Tab Since we first want to check the significance of this frequency click on No Compute significance level Select the option Setti
67. ess bars show the total progress and the progress in the current iteration Below the bars a counter gives the total number of computed models The Spectroscopy Modules 13 4 6 Results This window shows the results of the current and previously derived spectro scopic mode identifications A list of the parameters of the best fitting models the fits of the theoretical models to the observations and diagrams where the free parameters are plotted against the corresponding y2 values are displayed The results of previously performed mode identification process are logged Once a mode identification has been started this window is updated regularly with the actual status of the optimisation A screenshot of the Results Tab is displayed in Figure 11 RAS rarelon da mised Sie home cmd pies PAU Go Ratios Gon ST Opec Manele Packinjge paperd fp File Edi Took Help k Speco py Phaomaty Daia sol nameacted jagad range 25409 io 45555 priae Noal apacia 445 cas hms Geg opspamaw L1 bms PoP Daa Managar Founet Least Squires Fang Line Probie Smiheia Mode danticatan Resubs Logaaok z3 aes Beat Models Beni models m orm wes einaton yahni ni sigma 18 Fe Vet Arp Fe Phase Fal l H Dia fi taa 50 a eaa 18110 s a 117 50 nam 27 ja 141706 50 138 27 in 50 Gas 26300 i FAP more of Wed Jul 27 ace 1a a97 FIAP mane of Wed Jul 20 2008 ie B976 i Fa AP moro gi Wad Ju 23 70
68. ficance level is shown as a red line The frequency and amplitude of the peak having the highest frequency are indicated For more information about the plot window we refer to p 28 The Photometry Modules 99 5 3 Least Squares Fitting This modules provides tools for the computation of a non linear multi periodic least squares fit of a sum of sinusoidals to your data The fitting formula is Z D A sin an Ft b 22 a Here Z is the zero point and A F and are amplitude frequency and phase in units of 27 of the i th frequency respectively The least squares fit is carried out with the Levenberg Marquardt algorithm For a given set of frequencies either their zero point amplitude and phase can be optimized Calculate Amplitude amp Phase or additionally also the frequency value itself Calculate All The data can be pre whitened with the computed fit and written to the Data Sets Box of the Data Manager Tab Before a mode identification can be carried out a least squares fit to the data must be calculated To carry out a photometric mode identification light curves from different filters must be imported to FAMIAS and amplitudes and phases of the pulsation frequencies must be determined by least squares fitting These values can then be copied to the Mode Identification Tab to carry out the mode identification method using amplitude ratios and phase differences 5 3 1 Settings Defines the settings for the calculat
69. grids from more groups in the future whenever they are provided 5 4 1 Theoretical background In FAMIAS we apply the approach proposed by Daszynska Daszkiewicz et al 2002 to compute the theoretical photometric amplitudes and phases due to pulsation For more details see instruction on the Wroctaw HELAS Webpage In the limit of linear pulsation zero rotation approximation and assuming static plane parallel atmospheres we can write the flux variations in the passband A caused by a oscillation mode having a frequency w and a degree as AF F eY i O bXRe D ef Doe DajJe 23 where A _ 1 log F b 1 4 Alog Tor Doe 2 H 1 9 24 N a h O log Fy b D3 P a E i GM O log gg http helas astro uni wroc pl deliverables php The Photometry Modules 103 or equivalently Doe 2 H 1 9 25 2 p3 D34 Sa 2 asat ag 10 b gt Here is the pulsation mode amplitude expressed as a fraction of the equilib rium radius of the star Y i 0 describes the mode visibility with the inclina tion angle 2 and m being the spherical harmonic degree and the azimuthal order respectively G is the gravitational constant M is the stellar mass and b is the disc averaging factor defined as b J hS u uPi u dp 26 The D and D2 3 terms describe temperature and gravity effects respectively and both meud the perturbation of the limb darkening The D2 term stan
70. he values of the SNR can be imported with the spectra additional column in the list of times or computed in FAMIAS in the Data Manager Calculate Compute Signal To Noise Ratio see p 32 4 5 10 Optimisation Settings In this box the settings for the optimisation procedure are defined The op timisation is carried out with a genetic algorithm Michalewicz 1996 These 10 Mode Identification settings are crucial for the mode identification and must be chosen very carefully The most important aspect is to avoid ending up in a local minimum Since the computations of theoretical line profiles and moments is generally very time consuming one must find a compromise between the coverage of the parameter space and CPU time efficiency Although FAMIAS provides default values for different optimisation problems the best way to proceed is trial and error i e to test different optimisation settings and to proceed iteratively e Select MI method Selection of the mode identification method See above for a description of the different possibilities In the case of the moment method only the option Moment method is available e No of starting models Generation size during the genetic optimisation Larger values for a larger parameter space e Max number of iterations Stop criterion for the genetic optimisation This number defines after how many iterations generations the optimisation will stop e Max iterations w o improveme
71. highest peak is at the frequency Fy 11 53 d Check for significance as described in the previous point Since this peak is highly significant it should be included 82 10 Tutorial Spectroscopic mode identification in the List of frequencies A screenshot of FAMIAS showing the Fourier spectrum of the first moment is displayed in Figure 13 Compute least squares fit and pre whiten data Select the detected frequency F in the Least Squares Fitting Tab com pute a least squares fit and pre whiten the data Settings Pre whiten data The residuals are written as a new data set in the Data Man ager Tab The List of frequencies shows the results of the computed fit and the derived uncertainties of the parameters The value of the field Residuals is computed from the standard deviation of the residuals The frequency is always indicated in units of the inverse of the input time string The units of the amplitude depend on the selected calculation basis The equivalent width is in units of km s The n th moments is in units of km s The phase is in units of 27 In the Data Manager Tab select the time series of residuals and check the computed fit red line If you want to compute a Fourier spectrum or a least squares fit of line moments you have two possibilities The first option is to compute the moments of the line profile in the Data Manager Tab see Section 4 8 5 and then analyse this one dimensional time series
72. ields Empty fields or 0 are not used for the computation of the amplitude ratios and phase differences Theoretical values are anyway computed for all filters Stellar model parameters Teff Observational value of the effective temperature in Kelvin and its uncer tainty log g Observational value of the logarithm of the gravity in c g s and its uncer tainty Mass Stellar mass in solar units The available values depend on the selected non adiabatic model source You can only obtain a mode identification for one selected mass value at a time Atmosphere grid Model source of the grid of the atmospheric parameters a7 y Qg y Orr Bg r and b Overshooting This box indicates if models with core overshooting should be taken into account 108 Mode Identification Metallicity Stellar metallicity value m H The available range depends on the selected non adiabatic model source Micro turbulence Micro turbulence value of the stellar atmosphere models Non adiabatic obs source Select here the source for the grid of non adiabatic observables Identify mode Start the mode identification FAMIAS computes the observed amplitude ratios and phase differences as well as the corresponding values for all found pulsation models The results are written to the Results Tab The Photometry Modules 109 5 5 Results This module contains the results of the photometric mode identifications It gives the observed and theoreti
73. ing Tab The original data minus the least squares fit are shown Show Phase Plot Plot the data phased with the indicated frequency 4 The Spectroscopy Modules After the start up of FAMIAS the Data Manager Tab of the Spectroscopy Module is shown The Spectroscopy Module contains the tools that are re quired to search for frequencies in time series of spectra and to carry out a spectroscopic mode identification Additionally synthetic line profile variations of a multi periodic pulsating star can be computed The tools are located in tabs that have the following denominations Data Manager Fourier Least Squares Fitting Line Profile Synthesis Mode Identification Results and Logbook These tools are described in the following sections 4 1 Data Manager The Data Manager Tab provides information about the data that have been imported and permits to edit the data calculate statistics compute moments of a spectral line set the weights of individual spectra or extract a line using sigma clipping The window is structured into three data boxes and one plot window A menu is located above each box In the Data Sets Box you can select the time series of spectra you want to work with The Time Series Box shows the time number of dispersion bins weight and optionally the signal to noise ratio of all spectra of the selected data set The Spectrum Box shows the dispersion and intensity of the spectrum currently selected in the Time Series
74. ion the moment method and the Fourier parameter fit method In the following we will describe in detail the approach for each method separately e Setting the parameters Parameters on the Mode Identification Tab that have a check box next to the parameter name can be set as variable during the optimisation In 86 Tutorial Spectroscopic mode identification this case a minimum maximum and step value have to be indicated If the box is unchecked the parameter is set as constant during the optimisation with the value indicated Stellar parameters You need to provide estimates for the stellar radius mass Tog log g and metallicity in the field Stellar Parameters The indicated radius and mass mainly affect the numerical calculation of the horizontal to vertical pul sation amplitude and can be set as variable during the optimisation The three other parameters determine the limb darkening coefficient which is interpolated linearly in a pre computed grid Claret et al 2000 The inclination and vsinz can be fixed when they are known Otherwise they can be estimated during the mode identification and should be set as variable in a reasonably large range see Figure 16 Line Profile Parameters The only parameter which has to be known a priori is the Central wave length of the considered line profile This parameter determines the adopted limb darkening coefficient If one deals with a cross correlated profile this value of course
75. ion for FAMIAS and the user agreement e About FAMIAS Provides some general information about FAMIAS e About Qt Provides an information box about the version of Qt that was used for the current version of FAMIAS The graphical user interface of FAMIAS has been programmed with the Trolltech Qt library 3 The Plot Window A plot can be zoomed in by pressing the left mouse button while moving the mouse to draw a zoom box Pressing the right mouse button zooms out Keep the middle mouse button pressed to pan the plot The following commands are available in the menu Plot Refresh Plot Show All Refresh the contents of the current plot Set Viewport Set the viewport of the current plot Detach Plot Open current plot in a new window Print Plot Print the current plot Export Plot To PDF Write the current plot into a PDF file If this is a multi plot e g zero point amplitude and phase from least squares fitting the sub plots will be written into separate files The following commands are available in the menu Data Overplot If this option is checked the plot window is not cleared when a new plot is drawn Show Original and Fit If a least squares fit has been computed for these data this option shows the original data spectrum line moments or light curve and the multi periodic least squares fit Show Residuals Only available if the current data set consists of residuals pre whitened in the Least Squares Fitt
76. ion of the least squares fit e Use weights If this box is checked the weight indicated for each data point is taken into account in the least squares fit Otherwise all weights are assumed to have equal values e Pre whiten data If this box is checked the data will be pre whitened with the computed least squares fit and written as a new data set to the Data Manager Tab e Compute signal to noise ratio Computes the amplitude signal to noise ratio SNR of each selected fre quency and displays it in the List of Frequencies The noise is computed from the Fourier spectrum of the pre whitened data The Boz size is the width of the frequency range which is taken into account for the cal culation of the noise For a box width of b the noise of frequency F is the mean value of the Fourier spectrum of the residuals in the range F 6 2 F b 2 The SNR is the ratio of Ap and the noise level of the pre whitened Fourier spectrum at the position of f 100 Least Squares Fitting L TAMILS vets En ret fiala 7 Tiin pry r sana pope j 1 mE ESK Ena TSR Tasei iri Par hagqe eT E Bi r Fie E i Took Help KF Spades Prolomety Data Manager Fourier Laan Squares Filing Mode Gerticaion Alesufs Logbook Saree E Use weaghis Prowheten dati K Compus signato noisa raio Bor sza 3000000 Caico Ampiiuja Phasa Li gl Frequencses feropomd A PISIBTES h CESS Rescues 000 28RRT use Frequency a Amplitude dA Phase do EN Rats EFi 4h5osa r
77. ions The Fourier spectrum is shown as a blue line the significance level if included is shown as a red line The frequency and amplitude of the peak having the highest frequency are indicated For more information about the plot window we refer to p 28 44 Least Squares Fitting 4 3 Least Squares Fitting This module provides tools to compute a non linear multi periodic least squares fit of a sum of sinusoidals to your data The fitting can be applied for every bin of the spectrum separately pixel by pixel or for the different line moments The fitting formula is Z 2 A sin a R 63 6 a Here Z is the zero point and A Fi and are respectively amplitude fre quency and phase in units of 277 of the i th frequency The least squares fit is carried out with the Levenberg Marquardt algorithm For a given set of frequencies either their zero point amplitude and phase can be optimised Calculate Amplitude amp Phase or additionally also the frequency value itself Calculate All The latter is only available for one dimensional time series i e the line moments The data can be pre whitened with the computed fit and written to the Data Sets Box of the Data Manager Tab A screenshot of the Least Square Fitting Tab is displayed in Figure 8 Before a mode identification can be carried out a least squares fit to the data must be calculated In order to apply the Fourier parameter fit method the fit must be based on
78. ith identical frequency values must be computed to ensure that the phases in the different filters can be compared 5 3 2 List of Frequencies The List of Frequencies Box shows the results of the least squares fit Fre quencies that should be included in a least squares fit can be entered in the column Frequency and selected by clicking on the check box in column Use The following values are shown in this box after a least squares fit has been calculated The zero point its formal uncertainty and the standard deviation of the residuals are shown at the top The improved values of frequency amplitude and phase and their formal statistical uncertainties are shown in the list The phase and its uncertainty in units of 27 The last column lists the SNR of each frequency only shown when option Calculate signal to noise ratio has been checked The SNR is computed from the Fourier spectrum pre whitened with all selected frequencies For each frequency the assumed noise level is computed from the mean amplitude around the frequency value with the box size indicated at the option Calculate signal to noise ratio e Export frequencies Exports all frequency amplitude and phase values of the List of frequen cies to an ASCII file The file format is compatible with the program Period04 see example on p 48 e Import frequencies Imports an ASCII list of frequencies having the following four column format separated with tabulators frequency count
79. ler Ampiiud mag GA Phase penod Overshookng without U OOHH B1 ae Wi Y G E 020240566 00166 72081 00161657725 PO1BSBS9668 007043 EAE 000a Soera Doone 1261 10 00008131110 OOO0RSa2110 irala IETA OIF75RIATE 01807065845 0176430757 M1855300 AEE 01841604606 fiajeses reo EE 0 0063405600 nigas 74za00 ee Para aa 0007 m2400 00054783200 Do0Tse72600 Metalet Maco umianmce Ne adiabahe cbs sutt a kma War aaw hiiw Jersey Oziombowek Grid exists Figure 27 Mode Identification Tab of FAMIAS The observed amplitude and phase are listed in the left field whereas the options for the stellar models can be set in the right field For each imported frequency a new item is added in the top combo box of the field Mode Identification Tab Observed Values To carry out a mode identification it is only obligatory to provide the observed frequency value It is not necessary to input observed amplitude and phase values The theoretical amplitude ratios and phase differences are in any case always computed for all filters of the selected filter system The Photometry Modules 117 ITEMA anani A ma oe ma oe ne a para ANAA EA A CAN e l a la enla renha pal Ep Fie Edt Tools Heip K Specroscopy Phokemetry Data Mauger Founer Leasl Squares Fang Mode kertficaton Aes Lostock Lai of Caos Dra Moia Kentiicaton Wed Aa 2 2008 17 a4 7 oa a3 sadias Aimane g
80. m The Spectroscopy Modules 43 6th moment Computes the sixth moment lt v gt of the line profile inside the indicated dispersion range and calculates its Fourier spectrum e Calculate Fourier Computes the discrete Fourier transform DFT according to your settings and displays it in the plot window as a blue line The mean of the time series is automatically shifted to zero before the Fourier transform is computed The peak having highest amplitude in the given range is marked in the plot window A dialogue window reports the frequency having the highest amplitude in the selected frequency range and asks if it should be added to the frequency list of the Least Squares Fitting Tab 4 2 2 List of Calculations Previous Fourier calculations can be selected from the list Each computed Fourier spectrum is saved and listed here If a project is saved the list of computed Fourier spectra is also saved but compressed to decrease the project file size only extrema are saved The following operations are possible via the Data Menu e Remove Data Set Removes the currently selected data set from the list e Rename Data Set Renames the currently selected data set e Export Data Set Exports the currently selected data set to an ASCII file having the follow ing three column format frequency amplitude power 4 2 3 Fourier Spectrum Plot Shows the most recently computed Fourier analysis or the selection from the list of calculat
81. mber of segments on the stellar surface see field General Set tings should have a value of at least 1000 The lower this number the lower the precision of the computations For slowly rotating stars having low degree modes lt 4 a value between 1000 and 3000 in general is sufficient For more rapidly rotating stars vsinz gt 50 km s and high degree modes this value should be between 3000 and 10000 4 5 4 The moment method This method uses the first radial velocity and second line width moments of a line profile as a discriminator for mode identification The version of the moment method we adopted has been described in detail by Briquet amp Aerts 2003 and has been slightly modified in FAMIAS The complete time series of 64 Mode Identification observed moments is fitted with theoretical moments to determine and m The main assumptions for the computation of the theoretical moments have been described above We take into account the uncertainties of the observed moments that can be computed numerically if the signal to noise ratio of the spectra is known The observational uncertainties are used to compute a chi square value which provides a statistical criterion for the significance of the mode identification The formalism for the calculation of the statistical uncertainty of the mo ments has been described on p 34 The reduced x2 goodness of fit value is computed from N 1 1 5 2 2 a 1 lt 0 oo SF LU gt lt Sy
82. mean SNR of all spectra To do so compute the standard deviation of your spectra see Section 4 8 7 The mean SNR is the inverse value of the standard deviation at a dispersion position of the continuum A more sophisticated and better approach is of course to calculate the SNR of each spectrum separately If these values have been determined with an external program they can be imported with the list of times and file names The weight of each spectrum can then be computed with the function Time series Calculate Compute weights from SNR To compute the SNR with FAMIAS select the function Time series Calculate Compute Signal to Noise Ratio Adapt the parameters Factor for sigma clipping and Number of iterations in such a way that only continuum is selected in all spectra Click on Write signal to noise ratio as normalised weights to write a new weighted data set 4 8 5 Compute moments 1 Compute the SNR and weights as described in Section 4 8 4 Before com puting the moments the spectral line should be extracted by excluding the continuum We refer to Section 4 1 2 for a detailed description how to extract a spectral line with FAMIAS If the line borders do not move sig nificantly due to the pulsation low radial velocity one can cut out the line assuming fixed left and right limits The position of these limits can be determined by interpolating the dispersion scale of the spectra onto a common scale see Section 4 8 6
83. misation as a function of the free parameters The uncertainty of the fit for the different parameters can thus be estimated The free parameter can be selected in the combo box above By selecting Model in the combo box the temporal evolution of the y2 values during the optimisation is plotted 4 6 3 Comparison between fit and observation This box shows the fit of the theoretical values to the observations The content depends on the selected mode identification method and is described below The model can be selected by clicking on the corresponding row in the table of best models The observed values are shown as blue line or symbols the statistical uncertainty as a green line and the modelled values as a red line e Compute vsini EW intrinsic width and velocity offset fit Z The observed blue line with uncertainty range as green line and synthetic red line zero point profile are displayed e FPF methods Three panels are displayed zero point top panel amplitude middle panel and phase bottom panel in units of 27 are shown as a function of Doppler velocity km s The fit is shown as a red line whereas the observed values are shown as a blue line with the uncertainty range indicated by green lines The fit for a certain frequency can be selected in the combo box above The Spectroscopy Modules 15 e Moment method The complete time series of observed and modeled moments is shown The two panels show the first and se
84. model can be found in the file tutorial coasttutorial star References to functions of FAMIAS are written in the following manner Main Window File Import Set of Spectra which could be translated as Select in the Main Window the function Import Set of Spectra in the menu File In each tab there are named boxes which can also be referred to For instance Fourier Tab Settings Calculations based on Ist moment implies that you have to select the Fourier Tab and choose the option lst moment in the combo box denominated Calculations based on in the box called Settings 4 8 1 Import spectra Follow the following procedure to import the spectra to FAMIAS 1 Import the spectra by selecting Main Window File Import Set of Spectra In the file manager that opens select the directory tutorial located in the installation directory of FAMIAS and double click on the file times coasttutorial This file contains the observation times and file names of all spectra of this time series Figure 12 shows a screenshot of FAMIAS after importing the tutorial time series of spectra 2 The Import file dialogue that opens shows the contents of this file Click OK to import this file In the following dialogue that opens select Angstrom as dispersion scale and click OK 3 After successful import the spectra are displayed as data set in the Data Manager Tab Click into the Time series list to display specific spectra in the plot window
85. mperature variations This parameter can have positive as well as negative values in the latter case the equiva lent width decreases with increasing temperature For a definition see Eq 14 e Intrinsic width Width of the intrinsic Gaussian line profile in km s e Velocity offset Offset of the line profile with respect to zero Doppler velocity in km s The synthetic line profiles are computed for the assumption that the barycentre of the line profile is at zero Doppler velocity In general this is not the case for the observed line profiles The following parameters are only available for the moment method e Centroid velocity Centroid velocity of the line profile In ideal cases this is the mean radial velocity lt vt gt of the star It is in any case best to use the zero point of the least squares fit to the first moment which is automatically done in FAMIAS especially if the time series consists only of few measurements or the radial velocity amplitude is large e Mean signal to noise ratio This value is used for the computation of the statistical uncertainties of the line moments if the SNR of the individual spectra is not known In this case the determined 2 values might not be reliable if some individual spectra deviate strongly from this value e Individual signal to noise ratio If the SNR is known for each spectrum this option should be chosen to determine the statistical uncertainties of the line moments T
86. n range in the field Set tings or zoom into the selected region in the plot window In the latter case the left and right dispersion values of the zoomed range are au tomatically written to the Settings field Uncheck the box Settings Complete range and compute a least squares fit In the tutorial example a range between 70 and 45 km s would be optimal Import frequencies to Mode Identification Tab Switch to the Mode Identification Tab and import the current multi periodic least squares fit by clicking on Pulsation Mode Parameters Import data for FPF method from current LSF In the field Pulsation Mode Parameters you can now switch between the different imported pulsation frequencies Determine pulsationally independent parameters For the tutorial spectra the stellar parameters have been saved in a file called coasttutorial star You can import this file by selecting Gen eral Settings Settings Import stellar parameters We will first de The Spectroscopy Modules 89 FAM See TEE h maa Toad Nome AMAA Ma pieets TERIA Gy Leifer tod el apeclallasie Package Won EA AANS ip Fle Edt Tools Hop O Spectoscopy Photometry Cun get pamorverted kev Pese waghiad Mie of epea 450 Scale imis Ut oeio joonveried to kev gPeS38 37 ered int Data Manager Founer Leasi Squares Fiing Live Peotle Syrtwesis Mode kientication Resuts Logtock Ban Moses List of Gaians Dan Met Amp Ft Phase FI Zereport W
87. ng denominations Data Manager Fourier Least Squares Fitting Mode Identification Results and Logbook These tools are described in the following sections 5 1 Data Manager The Data Manager Tab gives information about light curves that have been imported allows to edit them and select the data sets for analysis The window is divided into two data boxes and one plot window A menu is located above each box In the Data Sets Box you can select the light curve you want to analyse The Time Series Box displays the time of measurement magnitude and weight of the selected data set The Plot Window displays the currently selected light curve and data points that have been selected in the Time Series Box A screenshot of the Data Manager is displayed in Figure 20 5 1 1 Data Sets Box This box contains a list of the different data sets that have been imported or created To select a data set click on it or select it in the combo box at the top right of the information bar The following commands can be selected in the Data Menu e Remove Data Set Removes the currently selected data set from the list e Rename Data Set Renames the currently selected data set e Export Data Set Exports the currently selected light curve as an ASCIl file to the disk The suffix of the files has to be entered by the user The exported files have the following three columns time magnitude and weights 94 Data Manager AS LOR en Sa on T E a PE Sia ee
88. nge where the amplitude reaches significant values In general the continuum should therefore be excluded and the line wings can in many cases be ex cluded The least squares fit should include all significant frequencies also combination and harmonic frequencies since they can have a signifi cant effect on the Fourier parameters of the other pulsation frequencies During the mode identification combination and harmonic frequencies should not be set as free parameters unless one has a reason to assume that they are pulsation modes intrinsic to the star e The stellar parameters radius mass Jeg logg and metallicity should be quite well known Radius and mass can be set as variable during the fit and have an influence on the k value ratio of horizontal to vertical displacement amplitude of the pulsation modes The three other pa rameters determine the limb darkening coefficients and slightly affect the fitted vsinz and intrinsic line width e Before starting the mode identification one should determine starting values for v sini the intrinsic width the equivalent width and the velocity zero point offset This can be done by selecting Compute vsini EW intrinsic width and velocity offset fit Z in the field Optimisation Settings For this optimisation no pulsation mode should be selected and vsinz the equivalent width the intrinsic width and the zero point shift should be set as a variable in a reasonable range This mode of optimi
89. ngs Compute significance level The field at frequency should now contain the value 3 148038 Compute the Fourier spectrum once more by clicking on Calculate Fourier The plot window now also displays the significance level as a red curve and the dialogue window indicates the SNR of the highest peak Since it has a SNR of 4 1 click on Yes to include it in the frequency list The Spectroscopy Modules 81 DI FAMIAS version 0 91 0 beta 272000 homeximaddata papers FAMIASCOAStI SCOAS Specialis sue Package tutorial coastutorialt fp l l IDRA Fie Edt Tool Help La Spectoscogy Phobmery Oma sat namesstuteial converted io ims ZP 538937 waghad No of spactra 499 Seale ams usa coastuteiai converted io m s ZPa Data Manager Fourier Least Squares Fang Line Profle Synthesia Mode Wenticaton Resuts Logbook Senget List of calculatons Draperson range t 3 Complete range sta Ft neyt from 0 vl op of wasara converted o kas Pas SIDUALS of coasfutorial converted fb keys ZP RESIDUALS of coastutorial converted kavs ZP Soqueney 708 Frequency slap 0 001746 Fre z coastutcrial converted to ims ZP 38337 weg it Use wegnts RESIDUALS of coastutyial converted keys 7P coastutcrial converted io wns 2 383 37 weg Comp te spect al wendow RESIDUALS of coasiiaorial Converted o kais ZP Compute significance levei at tequency 11500584 S N level 4 0000 Smoothing tector 5 RESIDUALS of coastutrial
90. noise ratio in the Calculate Menu Then extract the line profile with the function Extract line in the Modify Menu Use the resulting spectra for computing the moments by selecting the complete The Spectroscopy Modules 35 Dispersion range Complete range Mean signal to noise rabo 200 000000 individual Signal 0 Nose rao Oh moment equivalent with Write moments 0 t 6 in fil File extension vr Figure 5 Screenshot of the dialogue for computing the line moments dispersion range and the option Individual signal to noise ratio Note that the function Extract line determines integration boundaries for the moments that are different from one spectral line to another in order to avoid the noisy continuum in the moment computations The use of this function is thus indispensable when the line profile is moving a lot in time If the user wants the n moment to be written to the Data Sets Box the moment index n must be indicated in the combo box below The moments 0 to 6 can be exported as ASCII files by selecting the check box Write Moments 0 to 6 in a file and indicating a file suffix The output files will be written into the directory selected in the following dialogue and called Moment suffix The following commands are available in the Modify menu e Interpolate Dispersion Linear interpolation of all selected spectra onto a common grid of disper sion values This is necessary for most data operations such as comp
91. nt Stop criterion for genetic optimisation The optimisation stops if no improvement of the best found model has been achieved after n iterations e Convergence speed Defines how quickly the algorithm is forced to converge Value must be between 0 and 1 Higher values cause quicker convergence at the cost of parameter space exploration and thus precision e No of elite models This number defines how many of the best models will be copied unaltered to the following generation This parameter ensures quicker convergence o l amp m free parameters grid search Defines if the and m values are free parameters in the given range or if they are subsequently fixed grid search while the other parameters are being optimised e Number of CPUs to use Number of processors that are used in parallel during the optimisation The Spectroscopy Modules 71 4 5 11 General Settings e No of segments Total number visible invisible of segments on the stellar surface to compute the line profiles Higher numbers provide higher accuracy but slower computational speed linear dependence e Extension Extension of output and log files The output directory can be cho sen in the Settings menu see below The default output directory is the directory of the project file During the mode identification a log file called logMI extension is written to the disk It contains a list of all computed models their x values and parameter values After
92. o New Set A new data set with currently selected measurements is created and writ ten to the Data Sets Box Use this option to create subsets of your data e Remove Selection The currently selected measurements are removed from the time se ries data set 5 1 3 Plot window The plot window shows the currently selected light curve as blue symbols Selected measurements are marked with a red cross For more information about the plot window we refer to p 28 96 92 Fourier Analysis Fourier Analysis With this module a discrete Fourier transform DFT can be computed to search for periodicities in the data set selected in the Data Sets Box of the Data Manager Tab The Fourier spectrum is displayed in the plot window and saved as data set in the List of calculations A screenshot of the Fourier Tab is displayed in Figure 21 5 2 1 Settings Box In this box the settings for the Fourier analysis are defined Frequency range Minimum Maximum values of the frequency range The Fourier spectrum will be computed from the minimum to the maximum value Nyquist frequency Estimation of the Nyquist frequency mean sampling frequency For non equidistant time series a Nyquist frequency is not uniquely defined In this case the Nyquist frequency is approximated by the inverse mean of the time difference of consecutive measurements by neglecting large gaps Frequency step Step size resolution of the Fourier spectrum Three pre
93. o the first moment Pixel by pixel across the line profile 1 Select data set Select the data set that was prepared for the frequency analysis across the line profile pixel by pixel and go to the Fourier Tab 2 Calculate Fourier spectrum Select the option Fourier Tab Settings Calculations based on 84 Tutorial Spectroscopic mode identification Pixel by pixel 1D mean Fourier spectrum and click on Calculate Fourier Compute significance level The plot window now shows the mean of all Fourier spectra across the line profile A dialogue opens indicating the highest frequency peak at F 11 53 dt Since we first want to check the significance of this frequency click on No To determine the significance of Fi check the field Settings Compute significance level and select the option Settings Calculations based on Pixel with highest amplitude at f The latter option is necessary since the significance level cannot be determined from the mean Fourier spectrum across the line profile Click Calculate Fourier to compute the Fourier spectrum and its significance level at the dispersion position where the given frequency has its highest amplitude Since this frequency is highly significant add it to the List of frequencies in the Least Squares Fitting Tab Compute least squares fit In the Least Squares Fitting Tab select the option Settings Calcu lations based on gt Pixel by pixel MI FPF
94. ode A O06 t42955 GOODE CaonedS CORRE 27 561 Fz Fa Figure 22 Screenshot of the Least Squares Fitting Tab e Calculate Amplitude Phase Computes a least squares fit with the Levenberg Marquardt algorithm using the above mentioned fitting formula The zero point amplitude and phase are calculated whereas the frequency is kept fixed The following optimized values are written to the frequency list zero point and its uncertainty the standard deviation of the residuals for each selected frequency its amplitude and phase and their formal uncertainties derived from the error matrix of the least squares fitting algorithm e Calculate All Computes a least squares fit with the Levenberg Marquardt algorithm using the above mentioned fitting formula The zero point amplitude phase and frequency are improved The following optimized values are written to the frequency list zero point and its uncertainty the standard deviation of the residuals for each selected frequency its frequency value amplitude and phase and their formal uncertainties derived from the error matrix of the least squares fitting algorithm The Photometry Modules 101 e Copy values to MI Computes a least squares fit by improving amplitude and phase equiv alent to Calculate Amplitude Phase and copies the derived values frequencies amplitudes and phases and their uncertainties to the Mode Idenitification Tab For different filters a least squares solution w
95. ollowing optimised values are written into the frequency list the zero point and its uncertainty the standard deviation of the residuals for each selected frequency its amplitude and phase and their formal uncertainties derived from the error matrix of the least squares fitting algorithm e Calculate All Computes a least squares fit with the Levenberg Marquardt algorithm using the above mentioned fitting formula The zero point amplitude phase and frequency are improved This option cannot be selected for computing a least squares fit across the profile pixel by pixel For the moments the following optimised values are written to the frequency list the zero point and its uncertainty the standard deviation of the residuals the frequency amplitude and phase and their formal uncertainties derived from the error matrix of the least squares fitting algorithm 4 3 2 List of Frequencies The List of Frequencies Box displays the results of the least squares fit Fre quencies that should be included in a least squares fit can be entered in the column Frequency and selected by clicking on the check box in the column Use The following values are shown in this box after a least squares fit has been calculated Least Squares Fitting e Least squares fit across the profile with the option Pixel by pixel The mean standard deviation of the residuals pre whitened spectra across the selected dispersion range Residuals and for each selected
96. om complex amplitudes in order to combine amplitude and phase information as follows 2 1 5 A o AR i wa AS E At 4 18 wo nx N on o7 i 1 yt yt Here n is the number of pixels across the profile N is the number of free parameters A and A t denote observationally and theoretically determined values respectively Ar Aycos and A Aysin y are the real and imaginary part of the complex amplitude and is the observational error Since the amplitude and phase of a given wavelength bin are treated as independent variables the variances are calculated from oR 0 Ay cos b oy Aj sin oy 19 Of 0 A sin a o dy A3 cos dy 20 4 5 2 Optimisation settings for the FPF method In the drop down menu Select MI method the following selections are possible as optimisation settings e Compute vsini EW intrinsic width and velocity offset fit Z With this setting the pulsationally independent parameters vsin the equivalent line width the intrinsic width o and the Doppler velocity offset are determined from a fit of a rotationally broadened synthetic line profile to the observational zero point profile This method only provides reliable results if the line profile is not significantly broadened by pulsation The determined values can be used as starting values for the mode identification e FPF Method fit AP For each selected pulsation frequency a single mode displacement fi
97. option multi periodicity and the complete series of observa tional times are considered for applying the FPF method Synthetic line profiles are computed from a multi mode displacement field taking all se lected pulsation modes into account For each time step of the observed time series one profile is computed The theoretical AP across the profile are derived from a multi periodic least squares fit Since multi periodicity is considered for this method it can in principle be applied to stars for which the radial velocity amplitude to the projected rotational velocity is of the order of 1 This method is computationally much slower since not only 10 synthetic profiles but the complete time series have to be modelled The zero point across the line profile which gives a strong constraint on vsinz on the intrinsic line width and on the equivalent width is ignored in this case Therefore this option should only be chosen if already good constraints on these global parameters are available FPF Method complete time series fit ZAP This option is identical to FPF Method complete time series fit AP with the exception that also the observed and theoretical zero points are taken into account for computing the fits 62 Mode Identification 4 5 3 Practical information for applying the FPF method e The dispersion range of the least squares fit ZAP across the line profile that is imported to the Mode Identification Tab should cover the ra
98. ot Thu Ad 17 2008 12 12 a0 FTAA Ihr 1 I 19 3548 O9F 1505 ara 107m 2 20 0971505 ao7ieajit2ee7 2 2 temor pa71505 SO71439 tibet 3 2 193548 METALE aie la fi Jan O97 1505 0 4 1A TLE 1 11 612 Dar 1505 Caguana pots organsan btwn Fit and Sine qman Modal Si Fl 1 SAS Pol CH faire SSS pe pgs Boo TOG bi Modis Figure 18 Results of the mode identification for Fy 11 53 d termine starting values for the pulsationally independent parameters i e vsint the equivalent width the intrinsic width and the velocity zero point shift of the profile The search range of these parameters should be sufficiently large with a reasonable step size For the tutorial exam ple good starting values would be min max step vsini 1 100 1 equivalent width 1 20 0 1 intrinsic width 1 20 1 and zero point shift 20 20 0 1 The step width should generally not be smaller than the precision to which a parameter can be determined The best approach is to begin with a relatively large search range and step size and to iteratively narrow the range See Figure 16 for a screenshot of the Mode Identification Tab with the settings before the first optimisation Select the option Select MI method Compute vsini EW intrinsic width and velocity offset fit Z and press on General Settings Set fields to default to set default parameters for the genetic optimisation and to let FAMIAS propose
99. ourier parameter fit method in FAMIAS uses the same implementation for the computation of the synthetic line profiles A screenshot of the Line Profile Synthesis Tab is displayed in Figure 9 4 4 1 Theoretical background We now briefly describe the approach for computing the line profiles For a more detailed description we refer to Zima 2006 The following is slightly modified from this publication We assume that the displacement field of a pulsating star can be described by a superposition of spherical harmonics Our description of the Lagrangian displacement field is valid in the limit of slow rotation taking the effects of the Coriolis force to the first order into account Schrijvers et al 1997 Since deviations from spherical symmetry due to centrifugal forces are ignored our formalism is reliable only for pulsation modes whose ratio of the rotation to the angular oscillation frequencies Q w lt 0 5 Aerts amp Waelkens 1993 This limitation excludes realistic modeling of rapidly rotating stars and low frequency g modes For higher frequency p modes such as observed in many Scuti and B Cephei stars the given criterion is fulfilled and a correct treatment is provided The intrinsic line profile is assumed to be a Gaussian This is a good approximation for strong spectral lines of metals where the rotational broad ening dominates over other line broadening mechanisms A distorted profile is computed from a weighted summation of Do
100. ox can be used to set the reference filter and to set which values should be displayed in the plot window 110 Results e Reference filter This is the reference filter r for the amplitude ratio and phase difference with respect to filter x The amplitude ratios are computed as A A The phase difference is calculated as y Exceptions are the mode identification plots where the phase difference is plotted against the am plitude ratio There the indices r and x are exchanged e Box of values You can select here which values should be displayed in the plot window e Update This updates the Mode identification box and plot window with the current settings 5 5 3 Mode Identification Report This field displays the main information about the observed and theoretical parameters for the obtained mode identification It lists the input values and settings for the models the observed amplitude ratios and phase differences and for each pulsation model that matches the search criteria its degree and corresponding amplitude ratio and phase differences Amplitude ratios in the filters z and y are denoted as A x A y Phase differences are indicated as P x y and in units of degrees For the observed values the lo standard deviation is indicated 5 5 4 Mode Identification Plots Three kinds of plots that can be selected via the combo box above are available in this field They are described in detail below In each plot
101. ppler shifted profiles over the vis ible stellar surface Additionally we take into account a parametrised variable equivalent width due to temperature and brightness variations across the stellar surface We assume an unperturbed stellar model to be spherically symmetric in hydrostatic equilibrium and unaffected by a magnetic field or rotation The position of a mass element of such a star can be written in spherical coordinates r 0 defined by the radial distance to the stellar centre r the co latitude 0 0 7 i e the angular distance from the pole and the azimuth angle o 0 27 Any shift of a mass element from its equilibrium position is given by the Lagrangian displacement vector amp amp 4 This displacement modifies the initial pressure po the density and the gravitational potential o as a function of r 0 and the time t The linear adiabatic perturbations of these parameters are governed by the four equations of hydrodynamics i e Poisson s equation the equation of motion the equation of continuity and The Spectroscopy Modules 51 the energy equation which translates into the condition for adiabacity in the absence of non adiabatic effects in the stellar envelope This set of differential equations is solved by assuming that all perturbed quantities depend on Y 6 e where Y 0 denotes the spherical harmonic of degree and of azimuthal order m w is the angular pulsation
102. quares fit by clicking on Calculate Amplitude Phase or Calculate All The import button in the Pulsation Mode Parameters Box of the Mode Identification Tab will now display Import data for moment method After clicking the spectra on which the least squares fit was based and the selected frequencies and their phases are im ported and displayed in the Pulsation Mode Parameters Box The frequencies can be selected from the combo box next to the import button For the FPF method Select in the combo box Calculations based on of the Least Squares Fitting Tab the option Pixel by pixel and compute the least squares fit by clicking on Calculate Amplitude Phase The import button in the Pulsation Mode Parameters box of the Mode Identification Tab will now display Import data for FPF method After clicking the parameters zero point amplitude and phase across the line pro file and the selected frequencies are imported and displayed in the Pulsation Mode Parameters Box The frequencies can be selected from the combo box next to the import button 68 Mode Identification Frequency Value of the pulsation frequency as it was imported from the Least Squares Fitting Tab This value cannot be modified only by importing a new least squares fit Degree Spherical degree of the pulsation mode gt 0 Defines the search parameter space for the associated pulsation mode The step size must have a value of gt 1 Order m Azimu
103. ries of spectra mean standard deviation For more information about the plot window we refer to p 28 The Spectroscopy Modules 39 4 2 Fourier Analysis With this module a discrete Fourier transform DFT can be computed to search for periodicities in the data set selected in the Data Sets Box of the Data Manager Tab The data can consist of a time series of spectra two dimensional or of a time series of moments one dimensional For the latter we refer to the photometry manual see p 96 To compute a Fourier analysis for a time series of spectra you must indicate the dispersion range in Angstrom or km s that should be taken into account the frequency range and what the calculations are based on pixel by pixel line profile or moments The Fourier spectrum is displayed in the plot window and saved as data set in the List of calculations A screenshot of the Fourier Tab is displayed in Figure 7 RAS tartini ai mines Sel home cima dm pieeis FAUT LAAN Cons Opec Me nel Packinje paperd fp Fie Edi Took Help i Speco py Photomatry Data sof name escted set range 2645 i 25555 erected hic of spect 445 kes ieee opspamaw L1 kms PoP Daia Manager Founer Leas Squares Fang Line Protle Syrthena Mode Wanslicaton Henua Logtock Sena List of Calculasons Di peraion range ber in 20 Te hives san TR RESIDUALS cf expecetraw L1 iTS Momerssi RESIDUALS of epuceerm iLi kma Mome
104. roadened by stellar rotation and pulsation e Zero point shift Shift of the line profile with respect to zero Doppler velocity in km s The synthetic line profiles are computed for the assumption that the barycentre of the line profile is at zero Doppler velocity 56 Line Profile Synthesis 4 4 4 Pulsation Mode Parameters In this list the parameters of the pulsation modes are defined Use If a box is checked the corresponding pulsation mode is taken into ac count for the computation of the synthetic line profiles Frequency Value of the pulsation frequency in d in the observer s frame of refer ence Degree Spherical degree of the pulsation mode gt 0 Order m Azimuthal order m of the pulsation mode m lt A positive value of m denotes a pro grade pulsation mode Vel Amp Velocity amplitude of the pulsation mode in km s t The amplitude is normalised in such a way that it represents the intrinsic velocity for a radial pulsation mode P Phase of the pulsation mode in units of 27 Fal Absolute value of the complex non adiabatic parameter f For a defini tion we refer to Eq 30 on p 103 In combination with the parameter d EW d Teff this parameter controls the equivalent width variations of the line profile P f Phase lag wr between the radius and temperature eigenfunctions in units of radians 4 4 5 General Settings In this box some general parameters for the computa
105. rs Humosa of CPL o usa T Figure 10 Screenshot of the Mode Identification Tab 4 5 1 The FPF method This method relies on the rotational broadening of a line profile and thus delivers good and reliable results for vsini gt 20 km s The main assumptions of the models have been described above For a more detailed description of this method we refer to Zima 2006 For each detected pulsation frequency and each dispersion bin across the line profile a multi periodic non linear least squares fit of sinusoids is computed use the Least Squares Fitting Tab of FAMIAS This delivers the observational values of zero point Z amplitude Ao and phase P as a function of the position in the line profile These observational values are fitted with theoretical values derived from synthetic line profiles The FPF method comes in different flavours in FAMIAS the main differences concerning the temporal distribution of the synthetic line profiles and the num ber of pulsation modes taken into account simultaneously The FPF method makes use of the fact that the zero point amplitude and phase ZAP across 60 Mode Identification the line profile depend on the m values of the associated pulsation modes By comparing the theoretical values of ZAP with the observed ZAP values one can in principle determine the degree and azimuthal order of a pulsation mode The reduced y2 which is regarded as goodness of the fit is calculated fr
106. rsion range After you have imported the current least squares fit to the mode identi fication tab the dispersion range that is taken into account for the mode identification can no longer be modified Therefore you have to define the dispersion range already when you compute the least squares fit An optimal range excludes the continuum and the line wings Only the range 88 Chat aad Ramey meghat inharpolated F IF EFI pred Ne of epeta 451 Scale imis Tutorial Spectroscopic mode identification ni FEMA S onl phen aT Tele Soe MOME AMAA Mapieets TERIA Coke fet od el Speci allesue Package Sen EAn ANNS Ip File Edt Tools Help Ki Spectoscopy Photometry usa AE SDUALS of coasiuional joonvaried io kms ZP a538337 Dai Manager Pouner Leasi Sguaras Fang Line Peoble Syren Mode identicston Fesuta Logteck Chi nquars veni ECW sigma d 407553 BOTAS 11 aige 120S 407559 MOTHS 114188 11 074 40 7559 BOR 114194 12 0008 407559 ADTA 120079 120187 415054 BOTAD 11 4194 120157 SR S764 BOG 120029 11 sare Ghe squane pols Compaen bataien Fit and G n enman w Gri CR tqiaire Pel nana mie raat Se a ee ors Sg Sg pp Spe pt ee pe pe Bo B too al G r 20 20 ao 6a 20 i V in Dopelar waidai fins Figure 17 Results of the fit to the zero point profile where the amplitude across the profile reaches significant values should be selected You can either modify the dispersio
107. rted from the Mode Identification Tab Equivalent width Computes the equivalent width of the line profile inside the in dicated dispersion range and calculates a least squares fit The results are written to the frequency list 1st moment radial velocity MI moment Computes the first moment lt v gt of the line profile inside the indicated dispersion range and calculates a least squares fit This option has to be chosen if the moment method should be applied for the mode identification The computed least squares fit and time series of moments can be imported from the Mode Identification Tab 2nd moment variance Computes the second moment lt v gt of the line profile inside the indicated dispersion range and calculates a least squares fit 3rd moment skewness Computes the third moment lt v gt of the line profile inside the indicated dispersion range and calculates a least squares fit 4th moment Computes the fourth moment lt v gt of the line profile inside the indicated dispersion range and calculates a least squares fit 5th moment Computes the fifth moment lt v gt of the line profile inside the indicated dispersion range and calculates a least squares fit 6th moment Computes the sixth moment lt v gt of the line profile inside the indicated dispersion range and calculates a least squares fit e Compute signal to noise ratio Computes the amplitude SNR of each selec
108. rts RESDUALS cf epapetraw L1 ima Por F ara Frequency nanpa bom a ie i ee Pracpianey Map 0002782 RESIDUALS of epspatraw L1 kms PhP j F2FJ BE Uia weigh FIESICIUALS of apige aw L1 kma PRE FOPSL RESOUALS of epaceermw L1 kima Poe Farah Compule spectral window RESIDUALS of epapertaw L1 ima PbP FFII z PEEP 3 rer aooi RESIDUALS of epee aw L1 bma PoP F iFH H Compus pgnicanpy kinal ai frequency S769940 N bevel biai Smoothing factor 00m pete isese Li lien POPE RESIDUALS cf epacetraw L1 kma PLE P TFS RESDUALS cf apecetirawy L1 kma PhP F OFS speperaw 1 ams PoP Arps fine Diag ig apipi LI as PHP 1 Momen Disp fat Spacer aw L1 kma PoP cra bna Disp ie Powel wt higheri aapkiua al i 5355540 8 Fourier Species f FaG 2644 ch Ae 012A li bad Aine M WA hy W ME Iai i Naat W i w oa wena vi Mh i lan i im WINE Figure 7 Screenshot of the Fourier Tab 40 Fourier Analysis 4 2 1 Settings Box In this box the settings for the Fourier analysis are defined Dispersion range Minimum Maximum values of the dispersion range in Angstrom or km s7 dependent on the input data The range specifies which wavelength bins of the spectrum will be taken into account for the computation of the Fourier spectrum The Complete range is selected if the corresponding box is checked 1 Frequency range Minimum maximum values of the frequency range
109. s ass where ar and a given by o log F o log F s a da 16 ae a ana Ag OR 16 are partial derivatives of the flux which can be calculated from static model atmospheres for different passbands Here Ro is the unperturbed radius G denotes the gravitational constant lt p gt is the mean density of the star f the absolute value of the complex fr ifr and Yp the phase lag of the displacement between the radius and temperature eigenfunctions Then f describes the ratio of flux to radius variations which can be transformed into the ratio of temperature to radius variations due to the fact that the flux is proportional to T 4 4 2 Stellar Parameters In this box the global stellar parameters that should be used for the computation of the synthetic line profiles are defined e Radius Stellar radius in solar units In combination with the stellar mass this parameter determines the k value of the pulsation mode i e the ratio of the horizontal to vertical displacement amplitude e Mass Stellar mass in solar units In combination with the stellar radius this parameter determines the k value of the pulsation mode i e the ratio of the horizontal to vertical displacement amplitude 54 Line Profile Synthesis PFAWAS vertiond a Visine sie ome cman papers FAUT ES Go Matin Cons AAN AREE Packinje paper tp Fie Edi Took Help tl Daia sol nameacted weegiied range 2540 io 2555 5 priae No of spect 245 Soaks kma Gra opsponay iL1
110. s Heliocentric Julian Date and optionally the weights of the spectra and their signal to noise ratio The separate spectrum files must also have ASCII format and require the following two column structure wavelength or Doppler velocity in km s and normalised intensity File headers can be skipped during the import of the files Raw te Eban lt 2 2 Aare 1 Cot g Column 3 r homenmadata PROGRAMME F AMAS Ileserangienmes les z z z z Sko teat 0 ines Filenames of specta EIET Al Skip fre 0 lines n spatz S91 263808 t TESE ee ae 7 o O o O O FF amp Figure 2 Screenshot of the dialogue for importing a time series of spectra Figure 2 shows a screenshot of the dialogue for importing spectra The left column shows the raw data file You can indicate the number of header lines to be skipped Skip first X lines At the top of the right part of the window you can select the column number which contains the data type selected in the box below If your spectrum files have headers you can skip them by choosing the number of lines to skip The time must be in units of days Heliocentric Julian Date and the weights are point weights per spectrum Click on Ignore if no column with weights is available All weights are then automatically set to 1 Optionally a column with the signal to noise ratio per spectrum can be imported These values are used to estimate the uncertainties of the line moments in FAMIAS The SNR can
111. s case the sigma clipping algorithm tries to find the pixels belonging to the continuum and thus to determine the limits of the line These limits can be expanded with a number of pixels indicated with Expand limits Alternatively the limits can be set at certain dispersion values indicated in the spin boxes The limits can be changed for each spectrum individ ually or applied to all spectra when clicking on Set current limits for all spectra After clicking on Calculate the position of the pixels detected as con tinuum are marked as red crosses in the Current Spectrum Box The two plots on the right hand side show information about all spectra of the time series in order to check the overall results The top plot shows the number of bins detected as line of each spectrum The bottom plot shows the left and right dispersion limits of each spectrum Outliers in this plot marked red in the plots and in the Times of Observation Box can indicate that the line position has not been detected properly in some spectra When clicking on OK the extracted line will be written into a new data set e Shift Dispersion Shift the zero point of the dispersion of the selected spectra with a fixed value positive or negative The shifted spectra will be written into a new data set e Subtract Mean Subtract the temporal mean from all selected spectra i e compute the difference of each spectrum from the mean spectrum The dispersion scale of all spectra
112. s number the lower the precision of the computations becomes For slowly rotating stars having low degree modes lt 4 a value between 1000 and 3000 is in general sufficient For more rapidly rotating stars v sini gt 50 km s this value should be between 3000 and 5000 e The chi square values of the fits are derived numerically from the compu tation of the line moments taking into account the SNR of the spectra If the SNR is not known for the single spectra one can provide a mean SNR in the box Line Profile Parameters This mean value can be obtained by computing the inverse of the standard deviation at the con tinuum close to the line profile In this case the chi square value is based on the assumption that all spectra have the same SNR and may thus not be reliable If the SNR of each spectrum is known and listed in the Data Manager one should select the option Individual signal to noise ratio in the box Line Profile Parameters 4 5 6 Setting of parameters During the mode identification several values can be set as fixed or free parame ters These values are listed in the boxes Stellar Parameters Pulsation Mode Parameters and Line Profile Parameters If the check box associated with the parameter is unchecked the parameter is fixed at a constant value during the optimisation In this case a value must be entered in the input box of the column Min Const A parameter can be set to be variable free during the op timisation
113. sa tion by pressing Start mode identification The other pulsation mode at The Spectroscopy Modules 91 17 5 d can be analysed in the same manner You can compare your results with the input values by loading the file coasttutorial star into the Line Profile Synthesis Tab All computed mode identifications are saved in the Results Tab List of Calculations and are logged in the Logbook of FAMIAS CVS Wee a heme Head a papers TAMATEA SS CoA ct Speci all see fae hace tutorial Co ae riat fp Fie Edt Tools Help K Spectoscopy Photometry Data sot namerted d ims ZP 5383 37 weghted No of spectra 490 Scale uns Use Castuorial converted b km s 772538337 weghted ra Data Manager Fouriet Least Squares Fang Une Profle Synthess Mode Wenticaton Resuts Logbook Siela Par aneters Pulsaton Mode Parameters MavConet Siep import data for moment method tom current LSF Ft 115300965200 Radius solar unts 2272000 Mass solar unas 1 850000 W Frequency cd 11 530037 7516000000 MryConst 3900000 Degree 9 100000 st Order m 3 3 it Wcineton egress 5 Vel amp Pms 00 30 10 Vv sin i ps 1 100 x Phase 2P 0472857 0972857 0 500000 Une Protio Parameters Momert Method Genetic optimization No of startng models 30 r 100 X ranse with fm s Max number of teratons or Max tetatons wo engrovemert g z Corwergorce spood 1 000000 No of ete models 2 Certo veincty 12001971 Mean sgnal o moise ra o 200 000000 18 m
114. sable to interpolate onto the spectrum having the highest resolution in order not to lose information In our case the first spectrum of the time series has the highest resolution Therefore select the function Interpolate onto scale of first spectrum and click OK The following dialogue window shows the dispersion values of the mask To start the interpolation click on OK 4 8 7 Compute line statistics The temporal weighted mean of the spectra can be computed with the func tion Time series Calculate Mean Spectrum To check for line profile variability and estimate the SNR the standard deviation at each pixel of the spectrum can be computed with the function Time series Calculate Std Deviation Spectrum 4 8 8 Searching for periodicities It is advisable to search for periodicities in the data in the pixels across the line profile as well as in the line moments For the first approach a data set should have the following properties interpolated on a common dispersion scale converted to kms and weighted For the analysis of the line moments the data should be converted to km s weighted and the SNR should be computed for each spectrum The two approaches can reveal pulsation modes having different characteristics 80 Tutorial Spectroscopic mode identification The search for periodicities should be carried out in the following iterative schematic way 1 Compute a Fourier spectrum in a frequency range wh
115. sation fits a theoretical rotationally broadened line profile to the observational zero point profile Any pulsational broadening of the latter is neglected during the fit and can lead to an overestimation of v sini or the intrinsic width e The most reliable results for the mode identification will be obtained when following an iterative scheme In general one can fix the equivalent width and the zero point shift once they have been determined with sufficient precision in the previous step The values of wsinz and the intrinsic width should be set as variable in a range that is determined by the fit in the previous step taking the chi square values into account The inclination should be set as variable in the complete possible realistic range between about 5 and 90 degrees taking a step of about 10 degrees It does in general not make sense to set the lower range to 0 since this would imply infinitive equatorial velocity if vsini gt 0 km s7 For each pulsation mode a separate mode identification should be acquired first The Spectroscopy Modules 63 using FPF Method fit AP or FPF Method fit ZAP The degree the azimuthal order and amplitude should be set to reasonable ranges e If the pulsation frequency has a significant amplitude in the least squares fit of the first moment its phase value can be used for the mode identifi cation In this case the phase can be set as variable in the range e 1s eyis 0 5 with a step of 0 5
116. sets are available Fine 20AT Medium 10AT and Coarse 5AT The corresponding step size depends on the temporal distribution of the measurements i e the time difference AT of the last and first measure ment It is recommended to select the fine step size to ensure that no frequency is missed The step value can be edited if desired Use weights If the box is checked the weight indicated for each data point is taken into account in the Fourier computations Otherwise all weights are assumed to have equal values Compute spectral window If the box is checked a spectral window of the current data set is com puted A spectral window shows the effects of the sampling of the data on the Fourier analysis and thus permits to estimate aliasing effects The spectral window is computed from a Fourier spectrum of the data taking the times of measurements and setting all intensities to the value 1 The shape of the spectral window should be plotted for a frequency range that is symmetric around O for visual inspection The Photometry Modules 97 e Compute significance level If the box is checked the significance level at a certain frequency value is computed and displayed in the plot window as a red line The following parameters can be set Frequency Frequency value of the peak of interest The data will be pre whitened with this frequency and the noise level will be computed from the pre whitened Fourier spectrum
117. sgduais 0 0060746953 vis oA Pha Fi i ismen isa Fe PR l i ragragiog aere sr E Teresa Tas 0 149735 wre i Marroia 0121 HFS 4517818 0161987 HPE 7E EEE EE Fr miaren 0155801 Fe Ogelsoocay 0 165284 Fa F10 7 PT ee pe pe ep pe ep ee pe ey OO 150 10 5 g 50 150 6 6150 kmr Expon curren LSF Figure 8 Screenshot of the Least Squares Fitting Tab this case the zero point profile will not be taken into account for the pre whitening to preserve the mean shape of the line profile When a least squares fit of a line moment is computed the pre whitened time series of moments is written into a new data set one dimensional time series e Calculations based on This drop down box defines what the computation of the least squares fit is based on The following settings are possible Pixel by pixel MI FPF For each pixel dispersion bin across the selected dispersion range a separate least squares fit is computed by improving zero point amplitude and phase For this option the frequency value cannot be improved The results of the fit for each frequency are dis played in the plot window The integral of the amplitude across the line in the indicated dispersion range is written to the frequency list 46 Least Squares Fitting This option has to be chosen if the Fourier parameter fit mode iden tification method should be applied The computed least squares fits can be impo
118. ss Tag logg and metallicity should be quite well known Radius and mass can be set as variable during the fit and have an influence on the k value ratio of horizontal to vertical displacement amplitude of the pulsation modes The three other param eters determine the limb darkening coefficients and thus mainly affect the fitted vsinz and intrinsic line width The Spectroscopy Modules 65 e The inclination should be set as variable in the complete possible real istic range between about 5 and 90 degrees taking a step of about 5 degrees It does in general not make sense to set the lower range to 0 since this would imply infinite equatorial velocity if vsini gt 0 km s t e After importing the line moments the phase of each pulsation mode is set as free parameter between e 15 and 2 1 0 5 with a step of 0 5 different pulsation modes have their best fit at phase values that differ by half a period This is due to the fact that we limit the inclination angle to a range between 0 and 90 degrees and not between 0 and 180 degrees e To obtain the most reliable results with the moment method one should set all detected pulsation frequencies except combinations harmonics as free parameters during the fit This is due to the fact that the complete time series of observed moments is fitted with theoretical moments The number of segments on the stellar surface see General Settings Box should have a value of at least 1000 The lower thi
119. t et al 2000 o Teff Effective temperature of the stellar surface in Kelvin The Spectroscopy Modules 55 e log g Value of the logarithm of the gravity at the stellar surface in c g s units e Metallicity Stellar metallicity m H relative to the sun e Inclination Angle between the line of sight and the stellar rotation axis which is assumed to be the symmetry axis for pulsation in degrees e v sin i Projected equatorial rotational velocity in km s t rigid rotation The model assumes 4 4 3 Line Profile Parameters In this box parameters of the synthetic line profile are defined e Central wavelength Central wavelength of the line profile in units of Angstrom This pa rameter determines the limb darkening coefficients which are linearly interpolated in precomputed grids using the formalism by Claret 2000 e Equivalent width Equivalent width of the line profile in km s e d EW d Teff Ratio between the equivalent width variations of the local intrinsic Gaus sian line profile and the local temperature variations This parameter can have positive as well as negative values in the latter case the equivalent width decreases with increasing temperature In combination with the non adiabatic parameter f this parameter controls the temporal equiva lent width variations of the line profile e Intrinsic width Width of the intrinsic Gaussian line profile in km s7 This is the width of the line profile unb
120. t of the displacement field whereas at 1 and a _1 are the corresponding amplitudes 52 Line Profile Synthesis of the toroidal components We neglect the first order correction of the ampli tude a due to rotation whereby the amplitudes of the toroidal terms can be approximated by the following relations L mF1 2 a ae T EF ores 1 1 C Dk 1 _ tk 11 Qte 1 as 7 0 1 The factor v4r in Eq 10 is introduced in order to scale the normalisation VATNE 1 such that a represents the fractional radius variation for radial pulsation The ratio of the horizontal to vertical amplitude which attains quite differ ent values for p and g modes can be approximated by the following relation in the limit of no rotation kaha 12 a wR where ap and a are the horizontal and vertical amplitude G is the gravitational constant M is the stellar mass and R is the stellar radius We assume that the intrinsic line profile is a Gaussian which may undergo equivalent width changes due to temperature variations The distorted line profile is calculated from an integration of an intrinsic profile over the whole visible stellar surface which for computational purposes numerically results in a weighted summation over the surface grid We define the intrinsic Gaussian profile in a surface point having the line of sight velocity V as OF Wint Ter _ v vy2 I vu Tafel to e ee 1 v ff og g F on 3
121. ted frequency and displays it in the list of frequencies The noise is computed from the Fourier spectrum of the pre whitened data The Box size is the width of the frequency range which is taken into account for the calculation of the noise For a box width of b the noise of a given frequency F is the mean value of the Fourier spectrum of the residuals in the range F b 2 F b 2 How the SNR is computed depends on the selected calculation basis In the case of pixel by pixel for each frequency the dispersion bin where this The Spectroscopy Modules 41 frequency has the highest amplitude is determined The SNR is derived from this bin alone For the moments the SNR is computed from the ratio of Ar and the noise of pre whitened Fourier spectrum at the position of F e Calculate Amplitude Phase Computes a least squares fit with the Levenberg Marquardt algorithm using the above mentioned fitting formula The zero point amplitude and phase are calculated whereas the frequency is kept fixed If the computations are based on pixel by pixel the determined im proved values of zero point amplitude and phase are plotted for each frequency in the plot window The uncertainties are derived from the error matrix of the least squares fitting algorithm The residuals mean standard deviation of the residuals and the integral of the amplitude across the selected dispersion range are written to the frequency list For the moments the f
122. thal order m of the pulsation mode m lt Defines the search parameter space for the associated pulsation mode The step size must have a value of gt 1 Vel Amp Velocity amplitude of the pulsation mode in km s The amplitude is normalised in such a way that it represents the intrinsic velocity for a radial pulsation mode Phase Phase of the pulsation mode in units of 27 Fal Absolute value of the complex non adiabatic parameter f For a defini tion we refer to Eq 30 on p 103 In combination with the parameter d EW d Teff this parameter controls the equivalent width variations of the line profile P f Phase lag s between the radius and temperature eigenfunctions in units of radians 4 5 9 Line Profile Parameters In this box the parameters of the line profile are defined e Central wavelength Central wavelength of the line profile in units of Angstrom This parame ter determines the limb darkening coefficients which are linearly interpo lated in precomputed grids using the formalism by Claret et al 2000 The limb darkening coefficients slightly influence the derived values of v sini and the intrinsic width but generally have negligible effect on the mode identification The Spectroscopy Modules 69 e Equivalent width Equivalent width of the line profile in km s e d EW d Teff Ratio between the equivalent width variations of the local intrinsic Gaus sian line profile and the local te
123. the pixel by pixel values To apply the moment method the fit must be based on the first moment 4 3 1 Settings Defines the settings for the calculation of the least squares fit e Dispersion range Minimum Maximum values of the dispersion range in Angstrom or km s7 dependent on the input data The range specifies which wavelength bins of the spectrum will be taken into account for the computation of the least squares fit 1 e Use weights If this box is checked the weight indicated for each spectrum is taken into account in the least squares fit Otherwise all weights are assumed to have equal values e Pre whiten data If this box is checked the data will be pre whitened with the computed least squares fit and written into a new data set If the calculations are based on pixel by pixel a new time series of spectra will be created In The Spectroscopy Modules 45 CFR AS mreiond a Vieigsa S Hone Ama dna paea FAUT ES Go Balint COAST Opec Aike Package Epa pert hp Fie Edt Toole Help W Gata set name sied weeghted range 25465 io 4555 5 puiain No of epoca 245 cas kmt iso opsponay iL kms PoP Data Manager Foume Lewst Squares F ng Lina Probie Synihee Mode denticaton Resuba Logbook Janya Least squares Fil Diipa range ton 3 of Fa 05805 720000 sa weagits Prewh an da Pical by poet hE FPF H Compute gagril io nore rabo Boz site 7 OOD000 Cabulate Ampitiude Phase Lat ol Frequencies 2erapond Ro
124. tion of the synthetic line profiles can be defined e No of segments Total number of segments visible and invisible on the stellar surface The Spectroscopy Modules 57 The segments are uniformly distributed across the surface i e each seg ment covers approximately the same surface area The segments lie on a spiral that has its endpoints at the poles of the sphere At each segment a local intrinsic Gaussian profile is defined and shifted by the local Doppler velocity The overall synthetic line profile is computed by summing up over all visible local profiles The higher the number of segments is the better the precision of the computation gets at the cost of computational speed linear increase Dispersion range These values define the dispersion grid in Doppler velocity km s7 for the computation of the synthetic line profiles A minimum maxi mum and a step value must be indicated Internally a fixed step size of 1 km s t is taken and the minimum and maximum limits expanded by 20 km s t to ensure that the profile is computed correctly at the lim its These synthetic profiles are then linearly interpolated onto the grid defined by the dispersion range Time range Defines the minimum maximum and step values of the grid of times that should be used for the computation of the line profiles Import times from file This allows the user to import a file that contains a list of time values that should be used for the
125. tra Once a SNR computation has been performed it also displays the SNR of each spectrum Clicking on a time will show the according spectrum in the Current Spectrum Boz Number of bins 3331 2463908 195 50 _ 3331 251639 206 41 Soe a g i Hi i 9001 259036 158 23 Number of flevafone 10 shy ains t 3331 267033 21071 BARAA RAADS 02225 62205 02555 BAAGA LARAS 3331 282450 235 40 Peire mo ms NO 95 BE 95 90 m 3331200147 22427 ba me 9031297849 205 92 3331305540 195 95 Current spectrum Signal to noise rato Overall mean 215 077 3391313249 17168 3331320946 265 89 3331327149 27250 3331331374 248 29 3533 273968 207 45 3333 281685 179 94 3393 289363 218 26 3333 297060 156 60 3553304757 234 41 3333312465 20391 3333320162 22585 3533 328947 19830 3333 335799 198 65 3333341181 20264 3333 346563 156 99 3333351944 206 65 3333357107 16605 3393 361331 216 50 3333365556 196 74 S339 368760 168 46 3333 374005 246 61 3771378241 7080A Figure 4 4l 400 39 wet g 20 i Tak ae i i 6 20 g i gt j ih teet ae 3y SS 3340 Ja NS SS SH mma Time Mean of comtewum Overall maan 0 899751 tonal p nee ii bree ES S a SS 35 NO VJ HD NSD HO w5 Time Write S N ratio as normalized weights Return Screenshot of the dialogue for computing the SNR of the spectra In the Settings Box the sigma clipping factor and the number of it erations can be indicated and must be ad
126. ts Box the list will consist of times of measurement moment value and weight The Spectroscopy Modules 31 Click on an item of the list to display dispersion and intensity of the selected spectrum in the Spectrum Box The selected spectrum will also be displayed in the Plot Window Multiple spectra can be selected by clicking with the left mouse button on several items in the list while pressing the Ctrl key or the Shift key All items can be selected by pressing Select All Only items that have been selected in this list with blue background are taken into account for the data analysis e g Fourier analysis or least squares fitting The following commands are available in the Data Menu e Edit Data Opens a table of times and weights in a new window with the possibility to edit these values Modifications can be written to the current data set e Copy Selection to New Set A new data set with currently selected spectra is created and written to the Data Sets Box Use this option to create subsets of your data e Remove Selection The currently selected spectra are removed from the time series data set e Extract Dispersion Range A new data set with the currently selected spectra and the indicated dispersion range is created and written to the Data Sets Box Use this option e g to cut out certain spectral lines from your data set The following commands are available in the Calculate Menu e Mean Spectrum The weighted tempor
127. ut using genetic optimisa tion Such an approach permits to search for local minima and consequently the global minimum in a complex large multi parameter space For excellent reviews of spectroscopic mode identification techniques we refer to Aerts amp Eyer 2000 Balona 2000 and Mantegazza 2000 The Spectroscopy Modules 59 DFARS persion 31 i era home made neea PAU ES Co hall Cons oye niiku Packmjeapapert ipo Ale Et Took Hel il Specroscpy Photomotry Data sot namei weegiied range 5499 io 45555 porrada fic of spacing 65 Soap ken ite ops ponay iL1 kee PoP Data Manager Fouret Leest Squares Fang Line Probie Syntheen Mode idendicasan Resubs Logtook Stelle Parameters Pulao Mode Patamesens Sep impon dma br FPE maiad bom current LSF EREE aE tarl Fada fooler urets Meve footer une 115 fa Frequency fou 5 886551 Fost a Minors jas ie E Degree H Onder m i Val amp km s t w Phase eri 0 te A aE Phase ijira 00 retinaton egress 20 v ani e s iJa Line Ficia P arameteta Ophrataton Feary General Setings hin Gonal PPE Meee E JAP ha oi sagmanis 4000 A e552 z Genete opbmza on Enorma umama Equvalent wath kma 206 SEQW ia Te a No of itaring models 30 Sal bedi to dalal i Tre renee with km jt f Miao numer gi derasons i Senra m Mee derahoos wis eptovement B Zero poe shih emia 676 Convergence speed Phir No Of elle models 2 am hes paramete
128. uting line statistics Fourier analysis least squares fitting and mode identifica tion with the FPF method In the dialogue window three different options for the interpolation can be selected In all three cases the interpolated spectra will be written to a new data set Interpolate onto scale of first spectrum all spectra will be interpo lated onto the dispersion scale of the first spectrum of the currently selected spectra Choose a file to interpolate interpolate onto the scale read from an ASCII file In the dialogue window you can select in which column the dispersion values are listed Compute grid for interpolation interpolate on a grid of equidistant dispersion values The minimum maximum and step values must be indicated by the user 36 Data Manager e Convert Dispersion Convert the dispersion scale of the selected spectra from Angstrom to km s_ or vice versa dependent on the dispersion scale of the current spectra The value of the zero point for the conversion must be indicated in the dialogue window The converted spectra will be written into a new data set Extract Line Opens a dialogue for determining the position of a line profile using sigma clipping This tool is especially useful when line moments have to be calculated for a time series where the wavelength position line profile shifts significantly due to pulsation Since ideally for the computation of the moments the continuum should not
129. whiten data and compute another fit The pre whitened light curve is written to the Data Manager Tab as a new data set 6 Compute Fourier spectrum of residuals Select the pre whitened light curve and compute a Fourier spectrum thereof to search for further frequencies If you want to compute another least squares fit with additionally found frequencies you must select the original light curve 5 7 3 Mode identification The photometric mode identification as it is implemented in FAMIAS uses the method of amplitude ratios and phase differences in different photometric pass bands You therefore have to provide for each pulsation frequency that should be identified its amplitude and phase for different filters These values can be determined with a multi periodic least squares fit of sinusoids to the data under the assumption that the variations are sinusoidal To be able to compare the phase values determined for the different filters the same frequency values have to be taken into account in the least squares fits for all filters Important note the frequency has to be in units of d 1 Insert frequencies You can either enter input the observed values of frequency amplitude and phase manually or copy directly the results from the least squares fit e Manual input Switch to the Mode Identification Tab see Figure 27 In the field Observed Values select the option User input in the top combo box You can input the frequency value in the
130. y Modules 105 models from ZAMS to TAMS with some step in time or effective tempera ture computed for mode degree from 0 to 6 The full description of the evolutionary and pulsational models is given at the Wroctaw HELAS Webpage Furthermore we used pulsational models from two different sources avail able First a grid for main sequence stars with masses from 1 8 to 12 Mo com puted by Jadwiga Daszynska Daszkiewicz Alosha Pamyatnykh and Tomasz Zdravkov using the non adiabatic Dziembowski code Dziembowski 1971 1977 which can be downloaded also from the above mentioned web site Second a grid for 6 Sct stars computed with ATON Ventura et al 2007 and MAD by Montalban amp Dupret 2007 The grids included in the present version of FAMIAS cover the following range e 1 6 lt Mo lt 12 e 3500 lt Teg lt 47500 K 1 lt logg lt 5 e 5 lt m H lt 1 e 0 lt Vmicro lt 8 km s7 for some metallicities In more detail the mode identification is carried out in the following way e The user must provide the pulsation frequency F its amplitude Ay the uncertainty of the amplitude o4 the phase and the uncertainty of the phase og e The following values and options for the stellar models must be indicated ranges for T and log g stellar mass metallicity micro turbulence source of the atmosphere grid and the source of the non adiabatic observables e The evolutionary stellar model grid for the indicat

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