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Nightfall User Manual

1. EM CEET TOA OQ tp t fuz 1 tt A A oe eS Gare 10 5 Eclipse testing ece Net a A a a A ce de a E AE 10 6 Fractional visibility s 239 8 a AR AA 8 10 7 Eccentric orbits e TE TE A ee ee 10 3 Optimization ee Zen A ow A AS BE aS oa References A Command line Options 1 Introduction NIGHTFALL is an interactive application that introduces into the fascinating realm of eclipsing binary stars Apart from their light variations that make them interesting objects for observations eclipsing binaries are of fundamental importance for astrophysics e g for measuring the mass of stars NIGHTFALL is capable of producing e animated views of eclipsing binary stars e lightcurves and radial velocity curves e best fit binary star parameters for a given set of observational data It is however not able to fry your breakfast egg on your harddisk Eclipsing binary stars are most often very close systems In such systems owing to tidal forces the shapes of both stars can be highly nonspherical up to the possible formation of an overcontact system where both stars form a single dumbbell shaped object NIGHTFALL is a mildly ultramundane program of baroque complexity I like Verdi and Handel on lazy sunday mornings friday evenings are better with Iron Maiden and a good whisky NIGHT FALL is based on a physical model that takes into account the nonspherical shape of stars in close binary systems as well as mutual i
2. Kepler equation to determine the distance of the stars and their position in the orbit 2 Re scale the distance to unity 3 Scale the stellar volume by the the cube of the distance scale factor 4 Find the mean radius as the root of an analytical expression for the stellar volume of 11th order in this mean radius 5 Compute the new surface potential as a function of the mean radius Numerical details including the definition of the mean radius can be found in 18 10 8 Optimization For local optimization the Simplex algorithm is used This is a direct search algorithm that does not require derivatives For N free parameters the simplex is a polyhedron with N 1 vertices or points in the N dimensional parameter space At each step the simplex moves through this parameter space according to some rules basically moving away from its worst point Details of the algorithm can be found in 17 22 For global optimization an implementation of the simulated annealing method is provided Basi cally simulated annealing does a stochastic search of the parameter space Replacing the current best point with a better point i e a downhill step is always allowed replacing it with a worse point an uphill step is allowed with some probability depending on the steadily decreasing temperature of the system The implementation is based on the Very Fast Simulated Re Annealing algorith
3. While in a circular orbit the stellar surface is calculated only once and then just rotated in space in an eccentric or bit the stellar surface must be re calculated at each step in orbital phase thus causing substantial computational overhead To switch on this option use e eccentricity periastron_length where eccentricity range 0 1 0 is circular orbit is defined as Ta T1 H Tot with r2 is the largest and r the smallest distance Clearly e 0 0 if ra r which is the case for a circular orbit e 1 0 is a degenerate case a parabola which cannot be handled by the program periastron_length is the length in degree of the periastron i e the point of closest approach in the orbit To find out how it is counted you may set the Roche lobe filling factor to 1 0 and e to a high value like 0 5 Then using the animation option A you can identify the periastron easily as the star will fill the Roche lobe at closest approach The input Roche lobe filling factor is assumed at Periastron Due to the variable orbital velocity synchroneous rotation is not really synchroneous rotation will lag behind the orbital motion for part of the orbit and advance for the other part of the orbit Surface spots if there are any will move accordingly 7 6 Limb Darkening The depth to which you can see into a star s atmosphere where the visible light comes from varies with the viewing angle As the temperat
4. as a technical reference for experts who want to familiarize themself with the nasty details and the algorithms used 10 1 Geometry The geometric setup is based on a paper 11 by Djurasevi 1992a In a cartesian coordinate system x y 2 the stars are located at 0 0 0 and 1 0 0 and the z axis is perpendicular to the orbital plane A normalized dimensionless Roche potential is used which at a point P zx y z is given by the value C as 1 1 q 1 C q 2 4 rar r ra 2 with ry y 27 rg 2 1 y 2 mass ratio q m2 m and nonsynchronism parameter f w w i e the ratio of the angular velocity to the Keplarian angular velocity For practical purposes a spherical coordinate system r 17 d is used which is defined by x fT COSn r sinn coso z r sinn sing The surface of the star is then divided into elementary areas by a grid in 7 ol and for each surface element the gravity acceleration g r 17 the area dS r 1 and the normal vector 1 m n is computed as outlined in 11 Notes i Equation 1 16 in 11 has a minor typo wrong sign for ii Djurasevi 11 apparently uses equidistant steps in thus leading to very unhomogeneous elementary areas NIGHTFALL avoids this by adjusting the number of steps Ng as Ng 10 N sinn with N a compile time constant 10 1 1 Accretion disk Eclipse testing for the accretion disk is based on the method described i
5. texture on off S toggle secondary texture on off toggle axes on off m toggle movie mode on off With textures enabled the default is to use a pixmap as texture All other textures display the variation of physical quantities caused by the non spherical shape and or limb darkening across the stellar surface Available choices are surface temperature surface gravity flux towards the observer and the velocity of surface elements towards the observer relative to the star s centre of mass 3 6 MPI Please read the documentation of your MPI library for details about how to start a parallel appli cation The MPICH library and some other MPI implementations provides a command mpirun that handles everything mpirun np number_of processes nightfall nightfall options Note that for MPICH you need to enter the machines where the different processes should run into a machines file See the MPICH documentation 3 7 Problems e OpenGL can lead to program crashes with some graphic cards e Overcontact systems are not displayed correctly with OpenGL e The GNUPLOT PS driver apparently does not support the multiplot option e For eccentric non circular orbits very small fill factors produce strong numerical artifacts in the light curve e There seem to be some numerical artifacts also in the line profiles sometimes preferentially at quadrature 3 8 Configuration File NIGHTFALL comes with a set of configuration files each
6. the bandpass and the current phase will be appended No surface map will be output if this environment variable is not set NIGHTFALL SMAP BAND bandpass 0 11 for UBVRIJHKuvby for which surface map is output NIGHTFALL MONO_WAVE a comma delimited list of up to twelve monochromatic wavelengths unit micrometer to replace the effective wavelengths for the blackbody ap proximation 4 Introduction to Binary Stars This section and the next provide s an introduction to the problem at a popular science level hopefully the options and the algorithm s used More technical aspects are in italics If you find the less technical part too arcane feel free to supply constructive suggestions 4 1 The Roche Geometry Imagine two lakes seperated by a ridge There are about three possible configurations e In both lakes the water level is well below the level of the ridge This is a detached system e One of the lakes reaches up to the lowest point of the ridge and water may spill over to the other lake This is a semi detached system e Both lakes overflow the ridge and form one single lake This is a contact overcontact system Replace water by gas lake by star and you have the possible configurations of a close binary star system The stellar shapes in such a system are given by the sum of the gravitational forces and the centrifugal force due to the orbital motion Instead of using the forces it is ea
7. 11 section 1 3 In the detailed reflection treatment reflection is calculated with spots Le the spots are applied first then the reflection is calculated For overlapping spots in the overlap area the mean value of their A is used 10 4 Output flux In the blackbody approximation for each stellar component and each filter a temperature dependent effective wavelength is computed following Equation 3 30 in 4 5u2 Ap Ao V o where Ay is the filter wavelength and Ap the wavelength of the blackbody peak for the effective temperature of the respective component The required second moments ua of the filter passbands are computed following the prescription by 25 Equation 12 Aeff An _ FW 0 05 pa 44 D where FW 0 05 is the full width at the 0 05 level For the model atmosphere option fluxes for temperatures below 9800 K are from Hauschildt et al private comm 2006 PHOENIX models otherwise flux tables from Kuruzc models 19 are used All models are for solar abundances PHOENIX models below 2000 K incorporate dust formation with dust remaining in situ no settling The originally monochromatic fluxes have been integrated over the filter passbands as given in 20 Surface gravities log g 3 5 5 0 in steps of 0 5 are available Three different limb darkening approximations are available a linear a quadratic and a square root one which are given by the following expressions respe
8. 89 J Math Comput Modelling 12 967 Kallrath J Linnel A P 1987 ApJ 313 346 Kopal Z 1989 The Roche Problem Kluwer Academic Publishers Kurucz R L 1998 http kurucz harvard edu grids gridp00 ip00k2 pck19 accessed 2006 04 12 Landolt Boernstein 1982 Numerical Data and functional Relationships in Science and Tech nology New Series Berlin Springer Matsumoto M amp Nishimura T ACM Transactions on Modeling and Computer Simulation Vol 8 No 1 p 3 Nelder J A Mead R 1965 Comput J 7 308 Van Hamme W 1993 AJ 106 2096 Wilson R E 1990 ApJ 356 613 Young A T 1992 A amp A 257 366 A Command line Options Educational edu Mandatory q i rf f rfl rf2 N tl t2 SAS switch on highly simplified educational mode mass Secondary mass Primary inclination angle degree Primary Roche fill factor Secondary Roche fill factor Primary temperature Secondary temperature Interactive U Interactive mode Graphic Output A Animated view Vlv i c a Visualize geometry default v v view of stars i image of potential c contourmap of potential a all of the above G P S 1 2 Graph of lightcurve default 1 P S close up of Primary Secondary eclipse 1 2 display 1 2 orbital cycles B U B V Bandpass to display in graph default V H Hardcopy postscript plot Files I datafile Read in a data file containing observed data
9. C cfgfile Read in a configuration file Advanced System Parameters f P S F s P S longitude latitude radius dimfactor e W t P M D value asynchroneous rotation ratio Period Period_Orbit Spot on Primary Secondary eccentric orbit e eccentricity w periastron length period total mass separation in days solar masses solar radii Debugging Options D vwb Debug verbose warn busy Computation Options Plamda_zero Nnn M O P S value F L 0 2 R 1 9 a P S value 3CM Profile of absorption line at rest wavelength lamda_zero nm nn steps for lightcurve default 80 use Model atmosphere log g surface gravity Primary Secondary compute Fractional visibility Limb darkening method default linear 0 0 linear 1 quadratic 2 square root Reflection treatment 0 Point source 1 9 iterations for mutual reflection Albedo of Primary Secondary default 0 5 for T lt 7700 1 0 otherwise Third light C colour code M magnitude Data Fitting X Tolerance Fit the parameters coded in string 012345 q i rfl rf2 t1 t2 67 e w eccentric orbit 89 F Primary F Secondary asynchroneous rotation A H 2 Spots Primary I P 2 Spots Secondary QR Mass Separation a l Third Light UBVRIJHKuvby Tolerance 0 001 to use Simulated Annealing Y as above Step1 Step2 Chi Square Map 2 Parameters
10. ICH library has been compiled using the flags configure with device ch_p4 rsh ssh e If you have installed the Gnome Desktop on your system NIGHTFALL will build with support for it However Gnome is not required for NIGHTFALL it compiles just as well without Gnome Note With GNUPLOT plots are not that nice sometimes but animated mode runs much smoother with GNUPLOT than with PGPLOT GNUPLOT does not support incremental plotting and display of images thus a few options are only available with PGPLOT 2 2 Installation After downloading the source code do gunzip c nightfall version number tar gz tar xvf cd nightfall version number Dolnstall sh The Dolnstall sh script will query you for some information e g where to install the program and then optionally build test and install the application H you want to do it by hand instead of DoInstall sh run the following sequence of commands configure make make install If you want to use PGPLOT configure might find it by itself otherwise you might need the configure option with peplot include PFX where PFX should be the directory where the PGPLOT header file cpgplot h is installed and with pgplot lib PFX where PFX should be the directory where the PGPLOT library files libpgplot a libcpgplot a are installed If you want to build a parallelized version you need the configure option enable mpi and you nee
11. Nightfall User Manual by R Wichmann rwichmanQlsw uni heidelberg de Contents 1 Introduction ETRE A A A ii E T27 A EE e e EE A as A e ete Get 2 Requirements and Installation SL RequirementS A 203 E A e a AI EE eo 22 nstallati ue eer ok A a e hk dh A E Te 2 2 1 Installlocations 000400400 RE E E A EE A 2 3 Compile configure problems o 2 4 Compile time configuration 3 Usage 3 1 Simplified educational mode 3 2 General oil a a a ees E aE eae A 3 35 Plotting Graphics uno eae A A AE AS aT 3 4 Interactive usage the graphical user interface OUT 30 OpenGL u ad a ia bt fle 2 pih FOAMEI A dh Atak es lee ch ho fo te i ts Gee os a Ge ea Ge ee ae 326 Problems A Ae eet ee ha See DO A E te ole ph 8 3 8 Configuration File oir rca eee Ee ee A ae eo ee es 3 9 Data files 2 a sek ast ge Pe ean ee eS aS alee ee Ge Ras 3 10 Environment variables 4 Introduction to Binary Stars 4 1 The Roche Geometrie aa ca EEN ERE he aw 4 2 Shape of the light curves EEN oe ee ER A Oe Ee KA 4 3 Suggested experiments e 5 More details DL Which star ds whieh Z e ds a la E ee EELER e E 5 2 How is eclipse testing done o e e e 5 3 Temperature and Brightness e 000000000000 54 Output Lighteurves EN eee a AER A Ee i Se AC Y Ach Gravity Brightening 2 Geer sa ele oe E A a alas aed 6 Disk Dk Disk model a A dt e i e OR dd Poe ea E DT Simple disko pur eek ee A A E e BL I
12. _MESSAGES or LANG in this order of priority will be used to determine your language The default is English At the time of this writing the only other supported language is German LANG de NIGHTFALL_DATAROOT the root directory to search for the data cfg and doc subdirectories containing data config and help files respectively Only needed if this directory has been moved after installation NIGHTFALL_ DATA DIR the directory where data are located Only needed if these have been moved after installation and NIGHTFALL_DATAROOT is not set or data are not in NIGHTFALL_DATAROOT data NIGHTFALL_CFG_DIR for location of config files See NIGHTFALL_DATA_DIR NIGHTFALL_DOC_DIR for location of help files See NIGHTFALL_DATA_DIR NIGHTFALL LOCALE_DIR for location of data for localization Only important if you use internationalization to support your language See NIGHTFALL_DATA_DIR NIGHTFALL_PLOTFILE the name of the output file for plots Default is nightfall ps GNUPLOT_GEOMETRY the window size for gnuplot Default is 550x424 300 20 PGPLOT_XW_WIDTH fractional display width for PGPLOT X window NIGHTFALL_RADIATIVE limiting upper temperature for stars with convective enve lope default is 7700 unit is Kelvin Above that temperature the envelope will be considered radiative The only effect this has to to switch the albedo from 0 5 below to 1 0 above NIGHTFALL_SMAP_PATH base path to the surface map To this the index for
13. anymore Otherwise your results may be completely meaningless swich on the Db option to see SDV Chi square for each iteration see Section 9 1 Output is always written to a file NightfallFitted dat 8 4 Goodness of fit To evaluate how good a fit is NIGHTFALL offers the following options 1 if you plot the lightcurve residuals will be plotted as well Look at them to check whether there are systematic trends bad fit 2 for a good fit the residuals should scatter randomly around the model with no systematic trends This can be quantified by computing the runs statistic the number of runs occurences of two or more consecutive residuals above or below the model curve Obviously a large number of runs would occur for a strictly alternating sequence which is very unlikely for a random se quence Likewise only two runs would occur for the first half of the data below the second above the model curve also suspiciously non random The expected number of runs can be calculated analytically NIGHTFALL will print out the actual number of runs and the lower and upper limits for a 90 percent confidence interval 3 in theory the goodness of fit can be evaluated from the x Chi Square value of the fit the function actually minimized in parameter fitting which should be close to unity for a good fit However this only works if the error estimates for the measurements are realistic neither to high nor to
14. ctively Jul IDU ul a I u Ia JO II E where y is the cosine of the angle subtended by the emergent radiation and the direction perpen dicular to the stellar surface Limb darkening coefficients are from 7 A discussion of the relative merits of these three approximations can be found in 10 Notes i When tabulated values are used for temperatures out of range below 2000 K and above 31000K for log g 3 5 39000 K for log g 4 0 49000 K for log g 4 5 50000 K for logg 5 0 the lowest highest value is used i e no extrapolation is attempted 10 5 Eclipse testing Eclipse testing follows the method proposed in 11 First the contact angle of the Roche lobes is used to exclude eclipses if possible If an eclipse is possible for each surface element dS the line of sight LOS towards dS is tested for intersection with the smallest sphere enclosing the eclipsing star no intersection not eclipsed Then the LOS is tested for intersection with the largest sphere within the eclipsing star intersec tion eclipsed This procedure takes advantage of the simplicity of testing the intersection of a line with a sphere Tf the LOS intersects the outer but not the inner sphere as a last and computationally expensive resort the minimum of the Roche potential along the LOS is searched and compared against the surface potential of the eclipsing star Notes i In 11 the osculating cone i e the tangent co
15. d By default the map will be output for the V band you can change that with the environment variable NIGHTFALL_SMAP_BAND 0 11 for UBVRIJHKuvby The map includes for each visible surface element 1 the index of the star 2 the index of the surface element 3 4 x y coordinates in the viewing plane of the observer with the star at 0 0 5 6 x y coordinates as above but with the centre of mass at 0 0 7 cosy the line of sight angle 8 temperature 9 dimensionless gravity 10 area 11 flux The flux is not normalized to the area it is the flux that this surface element contributes to the total flux 9 3 User defined wavelenghts It is possible to compute monocromatic fluxes at up to twelve different user defined wavelengths These wavelengths unit micrometer must be provided as a comma seperated list in the en vironment variable NIGHTFALL_MONO_WAVE They will replace the wavelenghts used in the blackbody approximation e If less than twelve wavelengths are given the remaining ones will be filled in with the wave lengths of the corresponding passbands e For each wavelength NIGHTFALL will use the limb darkening coefficients of the passband whose wavelength matches best the monochromatic one e Blackbody approximation must be selected i e the model atmosphere option must be switched off otherwise these user defined wavelengths do not take effect 10 Technical details This section is intended
16. d to set the compiler flags to indicate the location of include and library files if these are not in the default search path There are two ways to do this a The MPICH library provides a C compiler wrapper mpicc that will automatically set the correct flags so if mpicc is in your PATH you may just say for compiling with PGPLOT you need also the Fortran77 compiler wrapper mpif77 configure enable mpi CC mpicc F77 mpif77 or configure with gnuplot enable mpi CC mpicc b If this fails e g because configure may not find the correct preprocessor you have to specify the correct flags mpicc show cc DUSE_STDARG L usr local lib Impich configure enable mpi CC cc CFLAGS DUSE_STDARG LIBS L usr local lib Impich 2 2 1 Install locations By default the binary is installed to usr local bin the data help configuration files to usr local share nightfall If you don t like this use the configure option prefix where to install where where to install will replace usr local 2 3 Compile configure problems If you want to use a different compiler you can supply the option CC myCCompiler to configure and also F77 myFortranCompiler if you compile with PGPLOT e Have gnuplot but configure does not find it is gnuplot in your path if no update your PATH environment variable does it support set multiplot start interactively by typing gn
17. de radius dimfactor or sS longitude latitude radius dimfactor sP for a spot on the Primary sS for a spot on the secondary Spots are circular The arguments are longitude and latitude of the spot s centre the radius all in degree and the factor by which the surface temperature is changed in the spot area You can have multiple spots on each star For overlapping spot areas dimfactor is averaged It is possible but physically very unrealistic to set dimfactor to rather low or high values 0 5 2 0 Temperature deviations of more than about 1000 K may be not realistic Hot spots are seen only in exceptional cases 7 8 Radial Velocities Unlike lightcurves which can be expressed in a relative unit radial velocity curves only make sense in absolute units km s in NIGHTFALL Thus they require absolute dimensions as input for the system NIGHTFALL supplies default values however if you don t want to bother about this Use tP period or tM mass or tD distance period in days mass total mass of both stars in solar masses distance in solar radii You need to give two of these the third can and will be calculated from Kepler s third law Radial velocities are computed as the sum of the orbital velocity of a point mass plus corrctions flux weighted contributions from each surface element In animated view you can see the result ing sum as well as the correction term the latter mult
18. depends on the mass ratio see Section 4 1 for an explanation The Roche lobe fill factor is in units of the polar radius of the Roche lobe The allowed range is 0 001 1 3 For values above 1 0 both stars merge into a common envelope overcontact system e 5 6 surface temperatures of both stars in Kelvin range 350 350000 Kelvin degree Celsius 273 15 Just for comparison the surface temperature of the sun is 5780 K If you use the model atmosphere option the minimum temperature is 2000 K the maximum temperature is 31000 K for surface gravity log g 3 5 39000K log g 4 0 and 49000 K log g 4 5 5 0 These six numerical arguments are always required if NIGHTFALL is used in command line i e non interactive mode without reading in a configuration file see below nightfall U C ty_boo cfg will read parameters from a configuration file and start NIGHTFALL in interactive mode The con figuration file is a simple text file that can be edited by hand In interactive mode you can also write out the current parameters to a configuration file nightfall without arguments will produce a full list of options many By default NIGHTFALL will do nothing more than run in non interactive mode compute the lightcurve write it to an output file NightfallCurve dat and exit silently If you want more nifty plots etc read on 3 3 Plotting Graphics requires that NIGHTFALL has been compiled with suppor
19. e for each pair the distances d to the shadow limb are taken as proportional to the differences between the minimum Roche potential p 99 along the LOS and the surface potential px Of the eclipsing star d _ p px Ge Px da p The surface element with the larger distance is assumed to be completely eclipsed or visible and the other one of the pair is assigned a fractional visibility 1 2 f based on the above approximation This is not exact for individual surface elements as the dividing line between them may not be parallel to the shadow limb However averaged over all surface elements on the limb the error should be negligeable 10 7 Eccentric orbits In an eccentric orbit the complete geometry and temperature distribution is re calculated at each step step in mean anomaly As the Roche potential is used in a dimensionless form the change in distance is equivalent to a change in the Roche volume filling factor surface potential with an unchanged unit distance This implies that the correct new surface potential must be found as a function of the stellar volume which is scaled up down with the distance To avoid an iterative numerical integration of the stellar volume i e varying the surface potential until the correct volume is found which would be prohibitively expensive the algorithm uses analytical approximations from 18 to derive the new surface potential The following procedure is used 1 Solve the
20. e and brightness relative sizes and shapes of the stars which are determined by the mass ratio that determines the relative sizes of both Roche lobes and the Roche lobe filling factors see Section 4 1 temperature distribution on the stellar surface If the Roche lobe filling factor is large the star is very nonspherical and its temperature can vary significantly over its surface This effect is known as gravity brightening see Section 5 5 The result is that the lightcurve varies strongly even if there is no eclipse mutual irradiation of both stars see Section 7 2 cool hot surface spots like sunspots but can be much larger in some stars see Section 7 7 Suggested experiments to begin set the mass ratio to 1 0 both stars to equal fill factor and both temperatures to equal values You will find that both eclipses have the same depth as the eclipsed areas are equal and have the same limb darkening as soon as one star is hotter than the other the depth of the eclipses will become different the width of the eclipses depends on the sizes of the stars the textbook case of a flat lightcurve between eclipses is very rare The reason is that due to the aspherical shape of stars in close binary systems the visible surface area of the star varies during the orbit Also this aspherical shape causes strong temperature brightness variations over the surface of the star an effect called gravity brightening or
21. e lab settings In this mode NIGHTFALL always starts in interactive mode with a much simpler GUI stripped of almost all more or less advanced options In additions the sizes of the stars have to be specified in units of solar radii instead of fractions of the critical Roche volume which allows to use NIGHTFALL without having to explain the concept of the Roche volume To start NIGHTFALL in this mode use the command line parameter edu like nightfall edu 3 2 General If used in interactive mode only the command line parameter U is required nightfall U If used in non interactive mode unless a configuration file is read in at startup see Section 3 8 NIGHTFALL requires at least the following six numerical arguments on the command line in that order e 1 the mass ratio of both stars mass Secondary mass Primary allowed range 0 0001 10000 0 For Roche lobe fill factors see below above one the mass ratio is restricted to 0 003 50 e 2 orbital inclination viewing angle of orbital plane range 0 90 degree where 0 deg corresponds to face on view no eclipse possible and 90 deg to edge on view eclipse guaranteed For angles in between the occurence of an eclipse depends on the mass ratio and the Roche fill factors see below e 3 4 Roche lobe fill factors The Roche lobe is the maximum volume a star can fill in a binary system Its size is in general different for the two stars and
22. ead the online help for more details In the toolbar below there are buttons for computing a lightcurve Compute toggling animated view of the binary Animate while computing writing out the current binary configuration Write and getting help on the currently active notebook page Context The rest of the GUI is layed out as a notebook with several different pages for setting options e Basic Here you can define the basic configuration of the binary mass ratio inclination fill out ratios and temperatures I know reading manuals is not much fun but you should read at least Section 4 to know what s going on Use animated mode for learning by doing Disk For defining the parameters of an optional accretion disk See See Section 6 Advanced For advanced options like asyncroneous rotation non circular orbit etc See Section 7 Plot Options for the selection of output filter see Section 5 4 and plot window for lightcurve as well as options for geometry visualization If compiled with OpenGL support you can also switch on off OpenGL viewing mode here Data Fiting Computation of best fit parameters Also definition of absolute system pa rameters for radial velocity See Section 8 Spots Here you can interactively define up to two spots per star additional spots can be defined on the command line or in a configuration file Both spots can be switched on off independently See Section 7 7 Third Light For de
23. ect use of this parameter may make a fit look better but the fitted parameters might be meaningless Do not shift to anywhere else than the starting point of the lightcurve The source code distribution includes example files for the binaries TY Boo an overcontact system and some more If in doubt look into them 8 3 Finding a local optimum Determining a best fit model means to optimize the parameters like inclination temperature mass ratio etc in such a way that the mismatch between model and observation is minimized This mismatch is measured by a suitable merit function sometimes also called cost function NIGHTFALL uses the chi square function as merit function General problems of determining best fit parameters are 1 uniqueness there may be several many nearly equally good solutions Do a few trials Restart fitting with last best fit as starting point 2 overfitting the information content of a lightcurve is limited Fitting too many parameters might produce good looking but meaningless results Use as few free parameters as are sufficient for a good fit 3 local vs global optimum just that you find a valley doesn t mean this is the deepest valley on Earth The same applies to optimization problems Any local optimization algorithm will only find a local optimum If the problem is well behaved this will be the one and only global opti mum If the problem is badly behaved you might need a few trials with d
24. finition of the brightness of an eventual third star in the system Third Light is just added to the total brightness never eclipsed i e it only has an effect on the relative depth of the eclipses See Section 7 10 On the bottom of the GUI there is a status progress bar 3 5 OpenGL Note that OpenGL can lead to program crashes with some graphic cards If compiled with OpenGL support the animated display will by default run in OpenGL mode You can switch to GNUPLOT PGPLOT mode in the PlotOptions page in the GUI In OpenGL mode you have the following options Zoom by clicking into the display area and drag with the middle mouse button Change viewpoint by clicking into the display area and drag with the left mouse button Reset with the space bar Save animation as JPEG images with File Save animation Edit preferences with Edit j Preferences You can switch between wireframe solid and points display For solid mode you can switch on textures and choose different texture types You can switch on off the display of labels and axes The following keybindings are available in the OpenGL window right arrow zoom out left arrow zoom in space reset to real observer viewpoint f switch to points display mode l switch to wireframe display mode o switch to opaque display mode t toggle textures on off Ww cycle through texture type image temperature gravity flux velocity p toggle primary
25. gain assuming that your data are already folded in phase B filter gives the filter UBVRIubvyJHK in which your data have been observed Default is V For radial velocities use 1 for Primary 2 for Secondary FW error gives the average estimated error of measurements if you do not have individual ones Default is 0 01 brightness or 1 0 radial velocities You can mix individual and average error estimates e g if you have individual error estimates only for some of your data V system_velocity For radial velocity curves use this parameter to set the system velocity Radial velocities will be set to data system_velocity N normalisation_phase Use this parameter to set the phase at which to normalize the light curve The default is the starting point of the lightcurve S shift This is a particular important parameter that requires some care As noted in in Section 5 3 NIGHTFALL will normalize its lightcurves to light at the normalisation_phase see above which by default is the starting point of the lightcurve the leftmost in the plotted lightcurve Thus at this point the brightness is zero magnitudes For a meaningful fit your observed lightcurve must be shifted up down to have the value zero at this point as well within the measurement errors NIGHTFALL will try to do it automatically but some correction may be required Plot the lightcurve data will be overplotted if there are any and check Note incorr
26. gravity darkening For more details see Section 5 5 You will see that the lightcurve only becomes flat between eclipses if the Roche lobe fill factors and thus the aspherical distortions of the stars are very small Which means that the distance of the two stars is large compared to their sizes and an eclipse con only be observed if the orbital inclination is very close to 90 degrees a rather rare case on the other hand the aspherical shape of the stars can cause deep throughs in the lightcurve even if there is no eclipse at all To see this set the mass ratio to 0 9 the Primary fill factor to 1 0 the Secondary fill factor to 0 1 and the inclination to 40 degree just as an example In animated mode you can verify that there is no eclipse at all but still you see deep throughs in the light curve the bottom of an eclipse only becomes more or less flat if the star is eclipsed for a prolonged time i e if it is significantly smaller than the other eclipsing star in an eccentric non circular orbit the velocity of the stars is not constant Thus also the width of both eclipses may be different and the times between them as well see Section 7 5 There is a config file v541_cyg cfg for the binary system V541 Cygni which shows both effects e the shape of the stars can vary a lot in an eccentric orbit because the varying distance is equivalent to a varying Roche lobe filling factor To demonstrate this set the mass
27. her surface gravity having higher brightness This effect is called gravity brightening or gravity darkening depending on which article you read Gravity brightening can produce deep minima in the lightcurve even if there is no eclipse at all NIGHT FALL always takes care of this effect there is no option to switch it off 6 Disk In a binary system where one star fills its Roche lobe there may be mass transfer via Roche lobe overflow l e at the L1 point between the two stars matter from the Roche lobe filling star can flow into the Roche lobe of the other star For physical reasons conservation of angular momen tum this matter will not just fall onto the other star but rather form a so called accretion disk Within this disk the gas orbits the star and loses angular momentum by friction thus slowly moving towards the stellar surface If the star has a strong magnetic field this field may disrupt the disk close to the star Le the disk will not reach all the way to the stellar surface but rather there will be a gap between the inner edge and the star and the gas will take the last part of its journey along the magnetic field lines The disk is characterized by inner and outer radius temperature height and the disk model Furthermore optionally a hot spot may be included in the model The outer and inner edge of the disk are modelled as vertical walls 6 1 Disk model For all models the height of the disk at radiu
28. ht curve programs used in the literature I hope that I have found most flaws in the logic of the code at least in the scientific part If you want to use NIGHTFALL for a publication you may want to evaluate its performance by yourself NIGHTFALL comes WITHOUT ANY WARRANTY see also Section 1 3 for more information 1 2 Bugs Several probably If you find a bug and can eliminate it send me a diff If you find a bug and can t cope with it send me a report and wait for the next version If you would like a feature tell me 1 3 Copyright NIGHTFALL is copyright c 1998 2008 Rainer Wichmann c 2001 2002 Markus Kuster c 2001 2002 Patrick Risse NIGHTFALL is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the Li cense or at your option any later version NIGHTFALL is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details You should have received a copy of the GNU General Public License along with this program if not write to the Free Software Foundation Inc 675 Mass Ave Cambridge MA 02139 USA This document is considered part of the NIGHTFALL program 2 Requirements and Installation 2 1 Requirements NIGHTFALL has been developed wi
29. ifferent starting points to find hopefully the global optimum If the problem is even worse you might need an awful lot of computing time to find the global optimum Most examples in textbooks are nice Most real world optimization problems turn out to be bad or even ugly NIGHTFALL uses the so called Simplex algorithm for local optimization This is a direct search algorithm that is not terribly fast and not terribly slow either but very robust To switch on optimization use Xparameters tolerance where parameters is a string of characters indicating the parameters you want to fit all others kept fixed and tolerance is the stopping criterion something like 0 1 or less would be appropriate 0 001 has a special meaning see Section 8 5 Use nightfall without options to get the character codes for fit parameters If more than one data file is input e g lightcurves in different filters NIGHTFALL will fit all data simultaneously This will probably work well only if different datasets are properly weighted i e if the error estimates or at least their ratios are ok Have a cup of coffee ready Use the Db option switch on Busy in interactive mode to see what is going on meanwhile IMPORTANT Restart fit with last best fit as starting point Continue this until you are sure that the solution has converged and does not improve anymore i e the value of SDV Chi square does not significantly change
30. iplied by 2 7 9 Line profiles NIGHTFALL can calculate spectral line profiles at each phase step which are output to files one for each phase step You can specify the rest wavelength lambda_zero for the line The luminosities of individual surface elements used to compute the profile are those for the passband with the closest effective wavelength To switch on use Plamda_zero In interactive mode you have the option to view the line profiles and change the phase interactively Some numerical artifacts present probably due to finite surface grid 7 10 Third Light The presence of an additional light source in the system e g a third star will decrease the con trast between eclipsed and non eclipsed parts of the lightcurve To include this effect use 3filter fraction where filter is one of the supported filters UBVRIJHKuvby and fraction is the relative contri bution of third light to the total system luminosity Le L14 12 13 1 0 where L1 L2 is the combined light flux from Primary and Secondary and L3 is third light This option is not tested yet 8 Fitting observed data NIGHTFALL offers the possibility of determining a best fit model for observed data Several datasets can be fit simultaneously Both a local and a global optimization algorithm are available Fit results are written to a file NightfallFitted dat 8 1 Important note If you require sub millimagnitude accuracy s
31. istic Surface spots if there are any will move with the stellar rotation rate just as they should 7 5 Eccentric Orbit According to Keplers laws the shape of the orbit is an ellipse Often it is close to a special case of an ellipse a circle However sometimes binary orbits are markedly eccentric i e non circular In an eccentric orbit the distance and the orbital velocity is not constant The stars will gain velocity as they fall toward each other and move fastest at Periastron closest approach They will lose velocity again as they move away from each other and move slowest at Apastron largest distance Thus the time between first and second eclipse in general is different from the time between second and first Also the width of the eclipses may be different as in general the stars will move with different velocities during the two eclipses NIGHTFALL comes with sample data for the star VI Cygni an eccentric binary system where you can observe both effects Similar to asynchroneous rotation the comment applies that tidal forces will act towards circular ization of the orbit Eccentric orbits are more likely in wide binaries than in close ones The problem is that in an eccentric orbit the changing distance is equivalent to a changing Roche lobe filling factor and thus a changing shape of the star remember the larger the Roche lobe filling factor the larger also is the nonspherical distortion of a star s shape
32. ity of the human eye For broadband filters the V filter gives the best match to the human eye In the Stroemgren filter system you might want to choose Stroemgren v Lightcurves are output in magnitudes This is a relative unit commonly used in astronomy and defined as flux flux f For magnitude differences smaller than about 0 4 the difference in magnitude times 100 is nearly equal to the percentage difference in flux i e 0 1 mag is about 10 per cent difference The brighter an object the smaller its magnitude Sun is 26 7 in the V filter while the faintest stars visible by naked eye are about 6 NIGHTFALL uses the brightness at quadrature phase 0 25 in a circular orbit both stars fully visible as normalization i e as fluxz in the equation above M ma 2 5 x log Output goes to a file NightfallCurve dat To select plotting of output light curve use G To select the filter for the plotted lightcurve use Bfilter where filter should be one of UBVRIJHKuvby The default for plotting is the V filter which is the best match to the human eye If you read in data files with observed lightcurves see Section 8 2 for more info the default will be the filter of the first lightcurve read in To obtain a hardcopy i e PS file use H 5 5 Gravity Brightening The nonspherical shape of both stars causes a non constant surface gravity This in term causes brightness variations with regions of hig
33. l assume its teardrop like shape A star filling only a small fraction of its Roche lobe will be more spherical distortion increases with the Roche lobe filling factor Note that the relative size of the Roche lobe of the two stars in the system depends on their mass ratio The absolute size of the Roche lobe also scales with the separation of the two stars Thus with a fixed mass ratio and fixed absolute sizes of the stars e g in kilometers a star may fill its Roche lobe and have a highly distorted figure if the stars are rather close but the same star might fill just a tiny fraction of its Roche lobe and thus would be nearly spherical if the binary separation would be rather large To define the sizes of stars in NIGHTFALL you have to give the Roche lobe filling factor which is defined in units of the Roche lobe actually its polar radius NIGHTFALL uses a dimensionless potential i e the distance between both stars is arbitrarily set to unity Thus for a fixed absolute size of the stars decreasing the Roche lobe filling factor would be equivalent to increasing the distance 4 2 Shape of the lightcurve The shape of the lightcurve depends mainly on three factors e temperatures as the eclipsed areas are equal for the eclipse of the Primary and the eclipse 4 3 of the Secondary the depths of the eclipses are only different if the temperatures of both stars differ See Section 5 3 for details on temperatur
34. layed Of course you can also experiment by yourself and try to fit the lightcurve by varying the system parameters or use the automatic fitting option To read in a single data file use I path to data file If you don t give the full path NIGHTFALL will search in this order the present working directory an eventual subdirectory data and the default data directory set at compile time If the data file is in one of these only the name not the full path is required For details on the format of the files see Section 8 2 Data are available for the following systems e TY Boo a common envelope overcontact system with two cool stars This is a so called shallow overcontact system as the stars are only slightly overfilling their Roche lobes for the explanation of the term Roche lobe see Section 4 1 The two stars have slightly different temperatures e MR Cyg a semi detached system the cooler fills its Roche lobe with two stars of very different temperature but both much hotter than the Sun Lightcurve should be computed with some advanved options model atmosphere fluxes detailed reflection 2 3 iterations quadratic limb darkening e DD Mon another semi detached system the cooler star fills its Roche lobe The cooler star is slightly cooler than the Sun the other one slightly hotter than the Sun The total mass is very low both stars together have only about 0 6 solar masses I
35. low This is very rarely the case in astronomy 8 5 Finding a global optimum To find a global optimum basically a stochastic search strategy is required or an exhaustive seach of the complete parameter space There are different possibilities ranging from com plete random search to some intelligent variation of random search NIGHTFALL offers Simulated Annealing which is a kind of mathematical implementation of the cooling of matter leading to crystallization i e an energy optimum if cooling is slow enough Switch on by setting the fit tolerance to 0 001 in command line mode Be prepared for a computing time on the order of a day or more if you have no other CPU expensive job running I am not sure whether the algorithm is correctly implemented In the present implementation cooling might be too fast or might stop at a too high temperature However my own experi ments were rather satisfactory most of the time Apparently Simulated Annealing does not mathematically guarantee that the global optimum is indeed found unless cooling proceeds infinetely slow 8 6 Mapping the Chi Square function This option will create a two dimensional map of the merit function i e in the case of NIGHTFALL the Chi Square function that measures the goodness of a fit with respect to two parameters Start values are the current values step values can be entered The gridsize is fixed at compile time defaul
36. m 16 however the re annealing part is not included For random number generation the Mersenne Twister random number generator period length 21999 1 by Makoto Matsumoto and Takuji Nishimura 21 is used It has a Mersenne prime period of 219937 1 about 106000 and is equi distributed in 623 dimensions Mainly for debugging purposes the seed is fixed thus the generated sequence is always the same and the results are reproducible References a A WwW O oO N O 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Alencar S H P Vaz L P R 1997 A amp A 326 257 Antokhina E A 1996 ARep 40 483 Brent R 1973 Algorithms for minimization without derivatives Prentice Hall Budding E 1993 An Introduction to Astronomic Photometry Cambridge University Press Chanan G A Middleditch J Nelson J E 1972 ApJ 208 512 Claret A 2000 A amp A 359 289 Claret A 2000 A amp A 363 1081 Diaz Cordov s J Claret A Gim nez A 1995 A amp ASS 110 329 Claret A Diaz Cordov s J Gim nez A 1995 A amp ASS 114 247 Diaz Cordov s J Gim nez A 1992 A amp A 259 227 Djura evi G 1992a Ap amp SS 196 241 Djura evi G 1992b Ap amp SS 196 267 Hendry P D Mochnacki S W 1992 ApJ 388 603 Hauschildt P H Allard F Baron E 1999 ApJ 512 377 Hauschildt P H Allard F Ferguson J Baron E Alexander D R 1999 ApJ 525 871 Ingber L 19
37. n 11 by Djurasevi 1992b 10 2 Reflection and gravity darkening brightening There are two options available for the treatment of reflection Both are bolometric corrections in the sense that the bolometric flux of the irradiating component is used to modify the temperature distribution on the irradiated component See 24 for a discussion of this issue The simple option for the treatment of reflection is described in 11 The correction should be exact for spherical stars The detailed reflection treatment loops over all pairs of surface elements dS1 dS2 and sums up for each surface element dS the irradiation by all visible surface elements dS2 of the other star Again bolometric irradiation is computed Of course the true temperature of the irradiating surface elements including reflection is not known thus it is necessary to iterate the algorithm Convergence is typically reached after 2 3 iterations The algorithm is described in 13 For both treatments by default for convective stars below 7700 K an albedo of 0 5 and for radiative stars an albedo of 1 0 is used It is possible to choose different albedo values at program start using the command line option s aP value for the primary and aS value for the secondary Gravity darkening is computed by em al ye T r 1 ol Teff Jeff For the gravity brightening exponent the results from 6 Fig 1 in the paper are used which provide a smooth tra
38. n of a respective utility on your system For solving this you should choose one of the following switches for the configure script disable nls with included gettext like e g configure with included gettext The first switch will completely disable internationalization i e only the english version will be available The second switch will use the internationalization program that is included in this source code distribution thus bypassing any preinstalled maybe broken utility on your system 2 4 Compile time configuration This section is targeted at researchers wanting to adjust NIGHTFALL to their needs Several aspects limits of NIGHTFALL can be configured at compile time Mostly these are related to fixed array sizes For most users the defaults should be sufficient To configure edit the file Light h and change the default value s of the define ITEM state ment s in the first section of this file where ITEM stands for any of the bold words on the list below Configuration options include but are not limited to e NIGHTFALL_PLOTFILE the name of the output plot file default is Nightfall ps STEPS_PER_PI MAXELEMENTS the number of surface elements for stars This number cannot be set exactly as the algorithm determines it at run time trying to achieve a more or less constant area per surface element for the lightcurve computation of course the exact surface area is taken into accou
39. nchronization is the Earth Moon system where Moon s rotation has been synchronized already while Earth s rotation is known to slow down gradually This would eventually lead to Earth s synchronization as well but I suspect it might take longer than the lifetime of our solar system To switch on asynchroneous rotation use fP fratio or fS fratio fP for Primary fS for Secondary fratio is the ratio between stellar rotation period and orbital period Asynchroneous rotation modifies the Roche potential see Section 4 1 and hence the equipotential surface which defines the stellar shape One effect is a flattening of the star for faster rotation Another effect is that the critical lobe i e the largest possible surface is modified For faster rotation it becomes smaller than the Roche lobe which is the critical lobe for a synchroneously rotating star as discussed in Section 4 1 In this situation you might have two binary component both filling their critical lobes but well separated from each other For slower rotation the critical lobe can become larger than the Roche lobe NIGHTFALL will check and complain if both stars intersect While an overcontact system with synchroneous rotation is no problem asynchroneous rotation with contact will cause heavy friction I would think presumably leading to rapid synchronization Thus a contact system with asynchroneous rotation probably is unreal
40. ne to the Roche surface at the inner Lagrangian point L is used as the first eclipse criterion According to 5 this can lead to serious errors for mass ratios very different from unity as the larger Roche lobe is concave at the L NIGHTFALL uses tabulated values from 5 the cone angle max as given in their Table 2 ii In 11 the coordinate frame of the eclipsed star is used for eclipse testing which seems not to work for asynchroneous rotation NIGHTFALL therefore uses the coordinate frame of the eclipsing star following 2 iii In 11 it is proposed to evaluate the potential along the LOS at six steps only NIGHTFALL uses a more rigorous approach with a minimum finding routine Brent s algorithm 3 10 6 Fractional visibility The eclipse testing routine assigns to each surface element a visibility of 0 eclipsed or 1 visible However the visibility is only evaluated for the centre of the element This can lead to spikes in the light curve if large numbers of surface element centres become visible at once Therefore an option is provided to compute a fractional visibility for surface elements on the shadow limb The algorithm first searches all pairs of elements on the shadow limb i e pairs with one element eclipsed the adjacent element uneclipsed and determines the potential minimum along the LOS towards them which is typically already available from the eclipse test Then a linear approxi mation is mad
41. nsition to the Von Zeipel 1924 exponent of 0 25 for radiative stars Notes i The simple reflection treatment in 11 has been supplemented by a penumbral cor rection for the partial visibily of the other star if it is at the horizon This penumbral correction assumes that the horizon is flat and that the other star is spherical i e that the visible part is a segment of a circle ii For the detailed reflection treatment instead of the quadratic limb darkening law used by 13 a square root law 10 I u DD e 1 ni dl YA is used where p is the cosine of the angle subtended by the emergent radiation and the direction perpendicular to the stellar surface and bolometric limb darkening coefficients are taken from 7 The normalization factor for the square root law was calculated as 1 n 1 c 3 d 5 iii The temperature limit of 7700K dividing stars with convective radiative envelopes can be changed by the environment variable NIGHTFALL RADIATIVE within the range 4000 12000 K This changes the albedo only 0 5 below 1 0 above 10 3 Spots Spots are always circular and characterized by four parameters longitude A latitude 8 radius r and a dimming factor A T T i e the ratio of the local temperature T with spot to the temperature T without spot A detailed discussion of the trigonometric expressions used to identify surface elements within the spot area can be found in
42. nt You can however set the number of steps per one Pi 180 degree on the equator which is STEPS_PER_PI You also have to adjust the size of the array holding the surface which is MAXELEMENTS MAXOBS the maximum number of observational data per filter PHASESTEPS the maximum number of steps for a full orbit N_SPOT the maximum number of spots per star GNU_GEOMETRY the plot window geometry if you use GNUPLOT as plotting program Please note it is not possible to fully specify the PGPLOT plot window geometry from within the program It can be defined in pixels by X resource pgxwin Win geometry WIDTHxHEIGHT X Y or environment variable PGPLOT_XW_WIDTH fractional display width PGPLOTS s default is width 867 height 669 and aspect 8 5 11 If P PLOT_XW_WIDTH is undefined NIGHTFALL will set it to scale down the window width to the GNU_GEOMETRY width Set PGPLOT_XW_WIDTH to 1 0 if you don t like this bash ksh PGPLOT_XW_WIDTH 1 0 export PGPLOT_XW_WIDTH csh tesh setenv PGPLOT_XW_WIDTH 1 0 OUT_FILE OUT_SIMPLEX the names of output files for the lightcurve OUT_FILE and eventual fit results OUT_SIMPLEX PROFILE_ARRAY PROFILE_RES the size of the array for line profile computation PRO FILE_ARRAY and the default resolution PROFILE_RES 3 Usage 3 1 Simplified educational mode As of version 1 64 NIGHTFALL supports a simplified educational mode that is targeted at under graduat
43. oche fill factor or the temperature difference is large NIGHTFALL offers two options 1 by default the irradiating star is treated as a point source This is ok for low Roche lobe filling factors but not very accurate for stars filling a large fraction of the Roche lobe It is rather fast however 2 it is possible to compute the mutual irradiance of all pairs of surface elements with up to nine iterations usually two to three are sufficient This is an N algorithm N the number of surface elements and thus computationally very expensive To switch on use Rn where n is the number of iterations 7 3 Overcontact systems For overcontact systems the second Lagrange point L2 comes into play It is located behind the less massive star as seen from the more massive and has the same property as Ll i e the force vanishes there and matter might flow out of the common envelope of an overcontact system I suppose by now you know where L3 is L4 and L5 are in the orbital plane left and right of the line connecting the centres of both stars L3 5 are not terribly important for binary stars Thus the surface of the common envelope of an overcontact system has to be between the two equipotential surfaces given by the potentials of L1 and L2 remember the force is the derivative of the potential thus if the net force is zero the potential can still have a non zero value it just has to be Hat locally To have an ove
44. odel and isothermal disk model 6 3 Hot spot parameters The disk may have a hot spot where the accretion stream from the donor star hits the outer edge of the disk The hot spot is assumed to have constant temperature and constant depth as measured from the outer edge of the disk To switch off the hot spot set the extent in longitude to zero e 1 T hot spot the temperature of the hot spot assumed constant e 2 Longitude hot spot the longitude where the hot spot centre is located on the disk rim e 3 Extent hot spot the extent in longitude and e 4 Depth hot spot the depth as measured from the outer disk edge to which the hot spot extends into the disk 7 Advanced Options 7 1 Fractional Visibility As eclipse testing is only done for the centres of surface elements the coarse surface grid introduces numerical artifacts that are readily visible sometimes To fix this problem it is possible to compute fractional visibilities for the surface elements i e compute what fraction of a surface element is eclipsed To switch on use F Note this option is not available if NIGHTFALL is compiled in high precision mode enable high precision since flux is not sufficiently accurate conserved 7 2 Reflection Due to the mutual irradiance of both stars in addition to its own light each star will also reflect light of its companion This can be a very important effect especially if the two stars are close large R
45. of which will set the system parameters for a particular real binary system and automatically load some data files with observed data for this particular binary star see next section For the file format see the commented example file ty_boo cfg in the source code distribution To read in such a file on the command line use C path to config file If you don t give the full path NIGHTFALL will search in this order of priority the present working directory an eventual subdirectory cfg and the default data directory set at compile time If the configuration file is in one of these only the name not the full path is required 3 9 Data files NIGHTFALL comes with a set of sample observational data for several different eclipsing binaries For each included binary system the data comprise lightcurves in several filters as well as radial velocity curves Also for each of these systems there is a configuration file see Section 3 8 Load ing this configuration file will set the appropriate parameters for that particular system and also read in the data You can then compute the lightcurve and visualize the binary with the observed data overlayed on the lightcurve E g you might call NIGHTFALL as nightfall U C data ty_boo cfg then press ANIMATE to switch on the real time animation and press COMPUTE to compute the lightcurve With PlotCurve you can then get a plot of the final lightcurve with the data over
46. ratio to 1 0 and both Roche lobe filling factors to 1 0 Set the eccentricity to a large value say 0 6 and the orbital inclination to 0 0 to see what s going on don t forget to switch on eccentric orbit if you are in interactive mode Use animated mode and enjoy 5 More details 5 1 Which star is which Stars in binary systems are labelled Primary and Secondary In NIGHTFALL the star called Primary is the star which is eclipsing first i e the star that passes in front of the other one at orbital phase zero orbital phase indicates the position of the stars in the orbit on a scale from zero to one The secondary is the star that is eclipsed first In animated view at start the Primary is left the Secondary right Note that this labelling of Primary and Secondary is inverse to the usual convention mea culpa Maybe I fix it sometime To exchange the stars if needed you can either i swap the eclipses in your data or ii swap the stars themselves For i add half an orbital period to the phase zeropoint in your datafile for a circular orbit or the time lag of the second eclipse for an eccentric orbit For ii swap temperatures and Roche lobe fill factors and replace the mass ratio q by 1 q Don t forget to swap spots if you have For an eccentric orbit add or subtract 180 deg to from the Periastron length For a circular orbit NIGHTFALL starts at orbital phase 0 25 which is iden
47. rcontact system set the Roche lobe filling factor of one star larger than 1 0 as there is only one surface now the smaller Roche lobe filling factor will be ignored If you choose a too large value NIGHTFALL will adjust it The largest possible value depends on the mass ratio Anything larger than about 1 3 is rather unreasonable for any mass ratio The combination of overcontact and non circular orbit or asynchroneous rotation see below is not supported It would be rather unphysical anyway as the strong interaction tidal forces and friction would circularize and synchronize the system extremely rapidly 7 4 Asynchroneous Rotation Tidal forces in close binaries will tend to enforce synchroneous rotation both stars rotating with the orbital period thus showing each other always the same side on a timescale usually shorter than stellar lifetimes There are however occasions when stars might rotate asynchroneously e g young stars that are not yet rotating synchroneously or massive stars that have short livetimes anyway too short for synchronization to occur during their lifetime Also tidal forces fall off very rapidly with increas ing distance thus wide binaries are likely candidates for asynchroneous rotation the tidal force is inverse proportional to the cube of the distance unlike e g gravity which is inverse proportional to the square of the distance and thus falls off much less rapidly A nonstellar example for sy
48. rmal radiation such as infrared radiation of your own body or radiation by stars it is not applicable to non thermal radiation sources like lasers By default NIGHTFALL uses the blackbody law which is neither terribly good nor terribly bad It is possible to use instead light fluxes from detailed numerical computations of stellar atmospheres Contrary to blackbody fluxes these model atmosphere fluxes like real stellar fluxes depend not only on temperature but also mildly on surface gravity and on the chemical composition of the stellar atmosphere As actual atmosphere calculations would be prohibitively expensive model atmosphere fluxes are taken from tables that cover only a limited range in temperature 3000 K to 35000 K Tables are hardcoded and only available for one surface gravity value a compromise value that should be ok for most cases and solar chemical composition To switch on model atmosphere fluxes use M 5 4 Output Lightcurves Lightcurves are output in eight commonly used broad band filters UBVRIJHK from near UV to near infrared and four narrow band filters Stroemgren uvby The shape of the lightcurve de pends on the filter passband The human eye itself also is not equally sensitive to all wavelengths of light it also is a kind of filter for light To create a lightcurve that looks like the human eye would see it you have to choose an output filter that matches as close as possible the sensitiv
49. rradiance of both stars and a number of additional physical effects NIGHTFALL can handle a large range of configurations including overcontact systems eccentric non circular orbits surface spots and asynchroneous rotations stars rotating slower or faster than the orbital period and the possible presence of a third star in the system NIGHTFALL supports OpenGL or MesaGL for an animated display of binary systems Individual frames of the animation can be saved as JPEGs to create am MPEG movie NIGHTFALL can be build in a parallelized version if you have an implementation of MPI De an MPI library installed NIGHTFALL supports the GNOME desktop if installed but does not require it Also NIGHTFALL supports internationalization Currently besides the default language english only german is supported The language is selected by the environment variable LANG must be set before starting the program in sh bash LANG de export LANG in csh tesh setenv LANG de 1 1 Remarks NIGHTFALL is not part of my research work rather it is the result of a recreational activity aimed at distracting myself from daily research work I have tested NIGHTFALL with published data on several binary stars Data for these systems are included in the source code distribution As no two light curve programs use exactly the same algorithms results are never identical however results from NIGHTFALL appear to be within the range of similar lig
50. s r is computed as a bxr 6 1 1 Simple disk For a simple disk c 1 a is set equal to half of the thickness parameter and b is set equal to the H R parameter Setting H R to zero results in a flat disk The temperature is constant and equal to the respective input parameter 6 1 2 Isothermal disk While the simple disk model is isothermal it s run of the height with radius is not physically correct for an isothermal disk In the isothermal disk the exponent c is set to c 1 5 which is the correct value for an isothermal disk Furthermore the H R parameter is ignored the constant a is set to a 0 0 and the factor b is chosen such that at the inner disk radius the disk thickness equals the thickness input parameter 6 1 3 Reprocessing disk The reprocessing disk is the model for a disk that is reprocessing absobing re radiating the radiation from the central star The exponent c is set to c 9 8 which is the correct value for a reprocessing disk Furthermore the H R parameter is ignored the constant a is set to a 0 0 and the factor b is chosen such that at the inner disk radius the disk thickness equals the thickness input parameter Lastly the temperature falls off with radius as 7 700 6 2 Disk parameters e 1 2 inner and outer radius e 3 thickness at inner edge 4 H R height radius only used in simple disk model 5 temperature at inner edge constant throughout the disk for simple disk m
51. sier to use a po tential forces can then be expressed as the derivative of the potential if needed In the case of binary stars this potential is called the Roche potential named after the French mathematician Edouard Albert Roche 1820 1883 The stellar surface is then given by an equipotential surface a surface on which the potential is constant Thus the introduction of the potential makes the computation of any forces superfluous in this particular application The largest size a single star can have in a binary system is given by the Roche lobe a teardrop shaped equipotential surface whose cusp touches the cusp of the Roche lobe of the other star at a point called Lagrange 1 L1 there are four more Lagrange points which are of less interest here L1 is located between both stars on the line connecting their centres At L1 the sum the forces is zero thus if a star fills its Roche lobe at L1 matter can flow into the Roche lobe of the other star provided it is not filled as well Thus L1 would correspond to lowest point of the ridge in the two lake example above and the Roche lobes would correspond to the two valleys below that point that potentially can be filled by the two lakes But just as the two lakes in the example above may be smaller than their maximum size before flowing together also the stars in a binary system may be smaller than their respective Roche lobes A star that completely fills its Roche lobe wil
52. sothermalidisk ecc a arte o tee aoa ela bh a er GS 6 1 3 Reprocessing disk o o 6 27 Disk parameters vu sols io e ol A Gee ERE Wek da da bo 6 3 Hot spot parameters ci a re m ana aa de E e a e A E E E A 7 Advanced Options T L Fractional Visibility 3 dba e wap eee eS a ee Tod leet dest ded hee A AE Ae be a e e e AE wh ds 7 3 Overcontact systems 7A Asynchroneous Rotation EELER ee a EE A To Eecentie Orbit 6 eck oe a a en hs OS ee ee aS oe a eS 4 0 Taimb Datkening da Bete AA at A td ook A OO 000000 18 18 19 19 21 21 21 22 22 24 24 24 24 24 24 25 E HEED a E ee ako ae E e e En dee aes 1 8 Radial Velocibi s gt sa e bi ee oe i A e e a eee gab bee ee E CH Lime profiles hea as a oe A ee ee ood A A ALO Third ight a a a AS al AAA Fitting observed data Sl Important note asor ang a a Dee Pe da A a as 8 2 Reading 10 the data bd o o A A E aes 8 3 Finding a local Optimum SL GOOANESSs OE A E hee A ee ee E A OES el es a 8 5 Finding a global optimum 0 00 00 0 000000000 8 6 Mapping the Chi Square function 020002 ee ee ee Miscellaneous d SDEbUs options void dre e a AE ss a tl air a 9 2 Output of the surface Map 9 3 User defined Wavelenghts e 10 Technical details TOT Geometry atras e oa e sae alt a e a 10 0 Accretion disk isis a ke Res Roe aa AS 10 2 Reflection and gravity darkening brightening
53. t 16 x 16 i e 256 lightcurves will be evaluated To switch on this option use Xparameters stepl step2 Parameters are coded like in the fitting option see above but only two parameters should be chosen 9 Miscellaneous 9 1 Debug options Dcharacterstring Most debug options selected by characterstring are of little use unless you know the code rather well Some will produce excessive and excessively messy output Exceptions are e b busy which keeps your screen somewhat busy in case you do something computationally expensive data fitting elliptical orbit e w warning which will print out warnings Usually these refer to problems that the program can deal with and thus you can ignore them If you do not get the output you expect you might want to turn them on to see what the program complains about e v verbose which will print out a moderate amount of information will grow excessive during data fitting use b instead if you just want to see what s going on 9 2 Output of the surface map It is possible to obtain the 2D surface map of the stars as seen by an observer i e the map displayed in animated mode You have to set the environment variable NIGHTFALL_SMAP_PATH to the path of the map file the program will append the index of the phase to this i e you will get a seperate file for each step in orbital phase If NIGHTFALL_SMAP_PATH is undefined no map will be printe
54. t for PGPLOT or Gnuplot In interactive mode there are several menu options available to produce plots In non interactive command line mode you can choose from the following e For a real time animation of the two stars orbiting each other use A e To select plotting of the output light curve use G e To select the filter for the plottted lightcurve use Bfilter where filter is one of UBVRI JHKuvby see Section 5 4 e To visualize the geometry use V There are four sub options Va Vi Vc Vv Vc for a contour plot of the potential Vi for an image of the potential Vv for viewing the stars Va for all in one plot The default is c Only c and vi are supported by GNUPLOT GNUPLOT cannot display images e To obtain a hardcopy use H Detailed output is always written to a file NightfallCurve dat 3 4 Interactive usage the graphical user interface GUI Use command line option U to choose this option A GUI will hopefully come up In the menu bar there is a File menu for reading data configuration files Please note that you need to reset the data memory Reset Memory before reading in data for another binary oth erwise you will end up in a mess The Output menu allows to choose between several facilities for viewing the output of a computa tion and visualizing the binary system Some of them allow interactive change of parameters like viewing angle etc Please r
55. t seems difficult to fit the lightcurve without spots did not try as yet e BH Vir a detached system with two stars one slightly hotter the other slightly cooler than the Sun At least one of the stars has surface spots which cause a slight but noticeable distotion of the lightcurve The config file includes two spots on the cooler star The BV lightcurves and the uvby lightcurves are from different years As the stars exhibit some variability you might want to use either the BV or the uvby lightcurves but not all six simultaneously e LZ Cen a detached but near contact system with two rather similar stars both very hot The stars are rotating very slightly faster than synchroneously Lightcurve should be computed with some advanved options model atmosphere fluxes detailed reflection 2 3 iterations quadratic limb darkening e ER Vul a detached system of two stars that are both slightly hotter than the sun and also have masses only slightly higher than the sun The stars show strong and variable activity i e large starspots that are varying with time Thus the derived parameters of the spots can vary a lot from one observation to the next e V541 Cyg a well detached i e wide binary system with an eccentric i e non circular orbit As the binary is very wide the eclipses are narrow and it is important to set the number of steps for the lightcurve to a high value say 600 instead of the default of 80 in order to resolve
56. th the aim of being able to compile and run the program on a typical Linux system without any need of downloading installing additional libraries or programs Although I have not tested this NIGHTFALL should compile on other Unix systems as well For command line use file output all you need is a C compiler e g gcc For interactive use and plotting NIGHTFALL requires additional libraries programs Note for compiling a program e g for compiling NIGHTFALL you need so called development packages of the required libraries These development packages are usually not installed by default e For interactive use of NIGHTFALL a GUI is provided which is based on the GTK library available at http www gtk org GNU Library General Public License GTK should com pile on most Unix systems If you have a recent Linux distribution GTK should already be included Ubuntu libgtk2 0 0 libgtk2 0 dev To see whether GTK is installed try to run gtk config libs which should yield something like L usr lib L usr X11R6 lib lgtk lgdk lglib 1Xext 1X11 lm might be different for your system If you get a message like sh gtk config not found you might need to install GTK On most Linux distributions GTK is split in two packages For running GTK applications you need only the gtk package For compiling applications like NIGHTFALL you also need the gtk dev package Ubuntu package name libgtk2 0 dev e For plo
57. the eclipses e 51 Peg an extrasolar planetary system Only the radial velocity curve of the primary is known thus for the planet only the product m x sin z is known 0 45 Jupiter masses Depending on the unknown inclination angle the mass may be as high as 15 Jupiter masses while higher masses are probably ruled out because a higher mass companion would have synchronized the primary which is not the case the rotation period of 51 Peg is 29 37 days while the orbital period of the planet is 4 23 days The model assumes an inclination angle of 25 deg and a density similar to Jupiter s for the planet The parameters of the star mass radius temperature are well known the temperature of the planet can be calculated from its distance to the star No eclipses by the planet have been observed but the amplitude would be at the limit of even the most sensitive measurements 3 10 Environment variables The run time behaviour of the program can be modified by the value of some environment variables To set an environment variable to some value depending on your shell the following command is required in csh tesh setenv VARIABLE value in sh bash VARIABLE value export VARIABLE e HOME your home directory usually automatically set by your shell e TEMPDIR or TMPDIR location for temporary files should not be on NFS mounted filesystem If these variables are not set NIGHTFALL will use tmp as default e LANGUAGE or LC_ALL or LC
58. tical to 0 75 and calculates up to 0 75 In a circular orbit eclipses are at orbital phase 0 0 and 0 5 NIGHTFALL uses a dimensionless potential i e the distance between both stars is arbitrarily set to unity The relative size of both Roche lobes then depends only on the mass ratio of both stars The size of both stars has to be given as a fraction of the Roche lobe actually its polar radius This fraction might be larger than one if you want to specify an overcontact system To specify a semi detached system set the Roche lobe filling fraction to 1 0 for one star less for the other 5 2 How is eclipse testing done NIGHTFALL divides each stellar surface into a grid of a few thousand elements Eclipse testing is done by checking for each surface element individually whether the line of sight towards that surface element intersects the other star For overcontact systems a star might eclipse its own throat region the region connecting both stars This condition is tested as well Although simple tests based on orbital phase or intersection of sperical regions suffice in most cases still sometimes a rigorous and expensive test is needed 5 3 Temperature and Brightness Stellar surface temperatures can range from a few 1000 Kelvin to several 10000 Kelvin The re spective brightness can be calculated from the so called blackbody law a blackbody is an idealized thermal radiation source The blackbody law is applicable to the
59. ts and graphs NIGHTFALL requires either e For GNUPLOT version 3 5 pre 3 6 patchlevel beta 347 or higher Debian gnuplot Earlier versions may or may not work You need a version with multiplot support To verify this try gnuplot gnuplot set multiplot If you get an error message you have to update your GNUPLOT You also need write permission to the directory tmp on your system To test this try touch tmp foo or the PGPLOT Fortran graphics subroutine library Debian pgplot5 also available at http astro caltech edu tjp pgplot free for non commercial use You need a Fortran compiler g77 is fine to compile it You have to compile it with the Xserver and postscript drivers and also have to compile the C wrapper library that comes with PGPLOT OpenGL support NIGHTFALL requires OPENGL or MESAGL Ubuntu libgll mesa dev GLUT the OpenGL Utility Toolkit Ubuntu freeglut dev GTKGLAREA Ubuntu libgtkgl2 0 dev and LIBJPEG Ubuntu libjpeg62 dev e For building a parallelized version NIGHTFALL requires a MPI Message Passing Interface library If your vendor does not supply one you may consider the MPICH library which is freely available from http www unix mcs anl gov mpi mpich With MPICH you can easily run a parallelized version of NIGHTFALL e g on a cluster of networked PCs Debian mpich MPI parallelization has been tested with the MPICH library on a Linux PC cluster The MP
60. uch as e g for modelling exoplanet transits you must compile NIGHTFALL in high precision mode enable high precision NIGHTFALL has been tested with data for the exoplanet TrES 2 and is able to fit the transit and recover the parameters cited by Holman et al 2007 ApJ 664 1185 Note however that planetary transits can be computed analytically which is faster than a full fledged binary star model as done by NIGHTFALL 8 2 Reading in the data In order to determine a best fit model to observed data you first have to read them into memory Use I path to data file Only one file is read To read more files prepend each of them with a I You can read in only one datafile for each filter Each row in the file should consist of two or three numbers The first is the date of the observation as decimal number in any unit you like the second the measurement value in magnitudes for brightness in km s for radial velocity and the third optional the estimated error of the mea surement Lines starting with a are ignored with the following exceptions no blank after FP period gives the orbital period of the system same unit as dates The program will use this value to fold the data into orbital phase The default is 1 0 thus assuming that your data are already folded in phase HZ zeropoint gives the zeropoint for orbital phase i e the time of Primary eclipse same unit as dates The default is 0 0 a
61. uplot then type set multiplot to test if no update your gnuplot does gnuplot_x11 persist work or does it give an error message like gnuplot bad option persist if error update your gnuplot There was at least one gnuplot version that supports the required multiplot option but does not list it as supported In this case enforce gnuplot support with configure with gnuplot Have gnuplot and pgplot want gnuplot support use configure with gnuplot Have pgplot but configure does not find it do you have a fortran compiler required the following files are required cpgplot h libcpgplot a libpgplot a Use configure with pgplot include my pgplot include dir with pgplot lib my pgplot where my pgplot include dir is the directory where cpgplot h is located and my pgplot lib dir is the directory where libcpgplot a libpgplot a are located Have pgplot get compile error maybe your fortran compiler does not understand the link options required by Gtk upgrade to a recent version of g77 maybe pgplot was compiled with a different fortran compiler Recompile it with the fortran compiler found by configure or convince configure to use a different compiler use the configure option F77 myFortranCompiler and or CC myCCompiler e Other compile errors There might be problems related to internationalization that may be caused by a broken installatio
62. ure which determines the light flux increases with depth you can see hotter brighter layers of the atmosphere towards the centre of the star s disk where you can look deeper Towards the limb you see shallower cooler and thus less bright layers of the atmosphere This results in the limb of a star being darker than the centre of its visible disk an effect that can be seen readily on good photographies of the Sun Limb darkening as a function of the cosine of the viewing angle towards the stellar surface is well aproximated by simple expressions NIGHTFALL offers three different options with expressions that are linear or include additional square or square root terms The square root law is probably most accurate but you will find that there is not much difference The default is the linear law To change this use Ln with n a number in the range 0 2 0 default 7 7 Surface Spots Cool stars like the sun i e stars with surface temperatures of a few thousand Kelvin only often have surface spots which are regions of somewhat lower temperature on the surface Among such stars some are known to have surface spots starspots much larger than those shown by the Sun In extreme cases spots may cover a few tenths of the stellar surface Usually these are cool spots i e a few 100 K cooler than the surrounding area caused by magnetic activity like on the Sun To include spots use sP longitude latitu

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