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GALFIT USER`S MANUAL ABSTRACT Galfit is a tool for extracting

1. 6 2 Different Variations of the Truncation Function Truncation models appear in many physical contexts e g dustlane rings spirals that do not reach the center joining a spiral with a bar cut off of the outer disk etc To allow the truncation function to be intuitively to use as the situations require GALFIT allows for several vari ations In addition to inner and outer truncations trun cation functions can share in the same parameters as the parent light profile There are radial and length height truncations softening radius vs softening length de fault vs Type 2 inclined vs non inclined default vs Type b truncations and lastly 4 different ways to nor malize the flux the most intuitive choice depends on how a profile is truncated We now discuss each of these 16 1000 gt 7m 100 f o S 10 1 0 1 0 10 20 30 40 50 Radius 104 1000 gt m 100 c o p 10 1 0 1 0 10 20 30 40 50 Radius Fic 14 Examples of hyperbolic truncation function on n 4 and n 1 S rsic profiles a a continuous n 4 model represented as two truncated models of otherwise identical re n and central surface brightness with truncation radii at r 15 and r 20 as marked by the vertical dashed lines The black curve is the sum of the inner and outer functions This shows that outside the truncation region there is very little crosstalk between the inner and outer comp
2. 90 deg is perfectly edge on As shown in Figure 10 a face on model does not necessarily mean that the outer most isophotes are round Rather the ellipticity of the outer most isophotes is related to the asymptotic behavior of the rotation function which asymptotes to a constant PA beyond a radius of roy for a pure hyperbolic tan gent a 0 Figure 9a The isophotes only appear circular in the main body of the spiral structure when it has a large number of windings Figure 11 shows several examples of bar and non barred galaxies with different a values sky inclination angle and rotated to different sky position angles O64 When the powerlaw index a is negative the spiral pattern can reverse course after reaching a maximum value see Figure 11 In summary the hyperbolic tangent powerlaw function has 6 free pa rameters Out Tins Touts Finel ony The thickness of the spiral structure is controlled by the axis ratio q of the el lipsoid being modified by the hyperbolic tangent or by 11 Bending Modes Fic 8 Examples of bending modes modifying a circular profile q 1 0 and Co 0 unless indicated otherwise Top row Low m bending modes Bending modes can be combined amplitude am 0 05r2 bending modes Bottom High amplitude am 0 2r le with Fourier modes to change the higher order shape Power Law Tanh Spiral Pure Tanh Spiral a 0 100 100 oo oo o S 50 S 0 50 100 150
3. total electrons detected so that Eq 83 applies When in doubt first let GALFIT generate a a image internally even if the ADU normalization is weird The effect of wrong units by a multiplicative con stant as sometimes the case if the units are in Counts sec only makes the normalization of y rather screwy But it is the relative weights between the pixels that gov ern convergence which is not affected by an uncertainty in y normalization Item D Convolution PSF and optional CCD Diffusion Kernel The observed PSF image in FITS format is required only if one wants to convolve a model with the PSF or fit a PSF to a star Otherwise it is op tional The diffusion kernel is also optional and is mostly associated with oversampled HST PSFs that are created using the TinyTim software for CCD imagers such as WFPC WFPC2 STIS and ACS The reason charge dif fusion kernel is considered when using TinyTim is that physically in CCDs the neighboring pixels are not com pletely insulated from one another because the potential wells are not infinitely deep Therefore when incoming photons excite the release of electrons in a substrate the electrons may travel into neighboring pixels The effect of this diffusion causes an image to be slightly blurred This blurring is entirely a detector artifact and adds to the blurring caused by telescope and atmospheric optics If the PSFs are created through natural stars or if the TinyTim
4. Changes the input file name to v fits h 300 440 330 470 See Item H Changes the 4 corners of the fitting box 1 369 4 395 3 1 1 Change the initial x y position to 369 4 395 3 and allow both to vary If you have more than one model and for instance you want to change parameters for model lt number gt you have to first designate it by typing m lt number gt Then all parameters you specify to change will only affect that component So for example to change the magnitude 3rd parameter of object 4 to 19th magnitude you have to first enter m 4 then 3 19 0 20 Right now the program does not check to see if the parameters you entered make any sense or even if they re valid numbers Adding a Non Classical Fitting Parameter e g Co Fourier Mode Coordinate Rotation Trunca tion The menu items by default only show the so called classical parameters commonly associated with 2 D galaxy fitting However there are additional free parameters that can add even more flexibility to GAL FIT the diskyness boxyness parameter Co the Fourier modes bending modes coordinate rotation and profile truncation To minimize clutter these parameters would only appear in the menu when they are specified to be fit by being given a value This simplifies the use of GAL FIT Partly the scheme is to underscore the fact these parameters are higher order corrections to a model As such they should only be turne
5. 0 050000 0 012500 0 050000 0 012500 Table 1 An example of the WFPC2 CCD charge diffusion kernel The charge diffusion convolution is applied only after the model image has been convolved and rebinned see next Item down to the original resolution of the HST im agers Note that if the science data has been drizzled to a platescale other than the original instrumental pixel scale it makes no sense to apply the diffusion kernel see Item E for further explanation Also note that observed HST PSFs are sometimes slightly broader than the PSF s generated by TinyTim which may be caused by a small amount of spacecraft jitter NOTE If the PSF image is sitting on top of a non zero sky background then the sky should be removed Or else when convolved with a model the region inside the convolution box would seem to be elevated compared to the region outside of the bor The PSF does not have to normalized GALFIT will do so automatically A DC offset will also appear if the PSF size is too small because the image cuts the PSF off in the wings However in this case the sky pedestal is not the problem Instead one should enlarge the PSF size Item E PSF Fine Sampling Factor When the PSF is not Nyquist sampled the Fourier transform is not uniquely invertible Therefore in principle all data should be Nyquist sampled i e FWHM 2 pixels for convolution purposes If one does not have a Nyquist sampled science image sometimes one
6. 1 From the Unix Linux Prompt To facilitate fitting with minimal interaction once you have a pre formatted text file shown in Figure 17 the typical GALFIT session is just a single step On the com mand line type gt galfit input_file_name The example shown below Figure 17 fits a galaxy with a PSF a S rsic exponential disk and a Nuker model while holding the sky level constant at 2 counts ADU 7 3 2 From Within GALFIT Prompt The second way to run GALFIT is by typing at the UNIX LINUX command prompt gt galfit If you don t have a prepared input file ignore the first question by hitting return This brings you to the GAL FIT prompt where you can edit object and image param eters manually The GALFIT prompt looks like Enter item initial value s fit switch es gt Below I will not bother to re show the prompt all com mands issued are assumed to come after that generic prompt At the GALFIT prompt you can read in one or more template files To do so simply type t file_name or followed by a return Be careful about reading in two or more input files while additional models will be added to the pre existing file the parameters A P i e input data image output file name noise file etc will take on values of the newest input file Note most of the time you won t use this option anyway but you can 19 7 4 OPTIONAL Interactive Command Line Options While in GALFIT a k a R
7. 200 Radius 50 0 50 100 150 200 50 Radius Fic 9 Hyperbolic tangent powerlaw spiral angular rotation functions with outer spiral radius of rout 100 pix a Examples of a pure hyperbolic tangent spiral a 0 with different bar radii rin b Examples with different bar radii and asymptotic powerlaw a as indicated the Fourier modes that modify the ellipsoid To create Note that the bar term in the coordinate rotation highly intricate and asymmetric spiral structures Fourier should be regarded only as a mathematical construct to modes can be used in conjunction with coordinate rota grant the rotation function as much flexibility as possi tion ble This construct can reflect reality but it does not have to and it often does not For instance mathe The bar radius rin is a mathematical construct matically a negative rin radius Figure 9b is perfectly 12 50 0 50 50 0 50 50 0 50 Fic 10 Examples of pure i e with powerlaw a 0 or without logarithmic function hyperbolic tangent coordinate rotation modifying a elliptical profile with axis ratio q 0 4 Note that all the figure panels share the same parameters as shown up top external to the figures The spiral model has no bar The numbers within each panel shows the amount of total winding units in degrees at the spiral rotation radius of 50 pixels Notice that outside r 50 pixels the rotation angle becomes constant due
8. GALFIT the concept of using Fourier modes to modify an ellipse is fundamentally the same as using the axis ratio param eter q to modify a circle into an ellipse the latter is what all 2 D image fitting algorithms do Indeed the axis ratio parameter q is a special case of the Fourier modes In both instances only the shape of the model changes whereas the structural parameters size concentration index magnitude retain their original meaning It is worth emphasizing that coordinate stretching by Fourier mode is a self similar remapping This means that the form and meaning of the radial profile func tions being modified do not change by this remapping i e our prior intuitions about the meaning of the pa rameters e g S rsic index n size etc in traditional 2 D fitting still apply For instance each model compo nent still has a single peak and radially the profile falls off according to one of the fitted functions such as S rsic exponential Nuker etc in every direction from the peak the peak does not have to be the geometric center if the component is lopsided The decline is monotonic so it is still meaningful to talk about e g an average light profile e g S rsic with say an average S rsic concen tration index n no matter what the galaxy may look like azimuthally In this manner irregular galaxies can be parameterized because even they have an average light profile For instance when the aver
9. after finding an optimal solution with the classical ellip soid model Otherwise strong residuals can always be locally Taylor expanded into Fourier modes which would have high amplitudes Likewise high order modes are quite sensitive to the presence of neighboring objects such as stars overlapping galaxies They ought to be removed either by masking or simultaneous fitting Bending Modes Bending modes allows for curvature in the model when the amount of curvature is less than half a circle The coordinate transformation x y gt 2 y is obtained by only perturbing the y axis in a rotated frame in the following way 14 Yon J 26 Tscale where x g scale is the scale radius of a model i e reg for S rsic rs for exponential etc Some examples of this perturbation are shown in Figure 8 Note that m 1 resembles quite closely to the axis ratio param eter g However the m 1 bending mode is actu ally a shear term the effect of which is most easily seen when it operates on a purely boxy profile Co 2 Fig ure 6a shearing it into a more disky shape see Fig ure 8d The bending modes can be modified by Fourier modes or diskyness boxyness to change the higher or der shape of the overall model This kind of coordinate transformation again preserves the original meaning of the radial profiles Here the object size parameter refers to the unstretched size i e projected onto the original x y Carte
10. between different components by providing this file An example of the format is found in the file EXAM PLE CONSTRAINTS When constraints are imposed it is unclear what the errorbars mean if anything Further more it may prematurely force the solution to wander off into a corner of the parameter space from which it is dif ficult to wander out So use constraints at own risk See 11 regarding parameter constraints for more details Item H Fitting Region The image region to fit GALFIT will cut out a section of the image specified by xmin xmax ymin ymax from the original image and then minimize x only over that region The fitting region should be large enough to include a significant amount of background sky especially if the sky is a free parameter in the fit Item I Convolution Box Size The convolution box size and the PSF image size are the two most impor tant factors in determining the running speed of GALFIT Convolution can take up 80 of total execution time for a small image There is one box for each model com ponent centered on the model so that all components will have their centers convolved with the PSF This is much more efficient than convolving the entire image Of course if one wants to convolve the entire image one can still set the convolution box to the fitting region size or even larger but this is often not the most efficient way to go In principle the box size should be just big enough
11. brightness magnitude He use sersic2 function at the effective radius corresponding to Xe The integrated magnitude is the standard definition Frot Metot 2 5logig G magzpt O exp where terp is EXPTIME from the image header Each S rsic function can thus potentially have 7 classical free parameters in the fit e Ye Mtot Te N q PA The non classical parameters Co Fourier modes bending modes and coordinate rotation may be added as needed There is no restriction on the number of Fourier modes and bending modes but each S rsic component can only have a single set of Co and coordinate rotation parameters The Exponential Disk Profile The exponential profile has some historical significance so GALFIT is ex plicit about calling this profile an exponential disk even though an object which has an exponential profile need not be a classical disk Historically an exponential disk has a scale length r which is not to be confused with the effective radius re used in the S rsic profile For situations where one is not trying to fit a classical disk it would be less confusing nomenclature wise to use the S rsic function for n 1 and quote the effective radius re But because the exponential disk profile is a special case of the S rsic function for when n 1 see Figure 1 there is a relationship between re and rs given by re 1 678r For n 1 only 6 The functional form of the exponenti
12. can obtain a rea sonably accurate oversampled i e more finely sampled PSF through observational e g dithering or numeri cal e g TinyTim techniques For HST images there is a software that can generate oversampled PSF s The other alternative is to combine dithered sub exposures of bright stars during an observation or by interpolating to get an intrinsic PSF by using multiple stars in the same image e g with globular clusters GALFIT can deal with situations where the PSF pro vided is more finely sampled than the data i e the PSF has a finer pizel scale arcsec piz than the data GAL FIT will internally produce models at the same sampling factor as the input PSF perform convolution and finally rebin the results to the data pixel scale The PSF fine sampling factor for Item E can only be an integer value It is a ratio between the platescale arc sec piz of the PSF and the DATA observed under the same seeing condition i e optics convolved with atmo sphere If they have the same platescale seeing the factor is 1 A TECHNICAL MEMO REGARDING HST CCD DATA i e for WFPC2 STIS WFPC and ACS but not NICMOS If the PSF being used is created from nat ural stars or if the TinyTim PSF is 1 time sampled there is no need to apply the CCD diffusion kernel However if the PSF is created by TinyTim and it is N times over sampled N 1 TinyTim provides a diffusion kernel for you but it does not actually apply
13. except by the computer memory and the com putation speed 8 1 The Image Parameters A P Item A Input Data Image The input data image is a FITS file It must be a single image and not an image block If the user does not provide an input image or if the input image is not found then a model image will be created using the input parameters having an exposure time of one second Item B Output Image Block The output im age block is a 3 D image cube in FITS created using CFITSIO Pence 1999 The image data cube has 3 lay ers blahblah fits 1 blahblah fits 2 and blahblah fits 3 The first image is the postage stamp sized region speci fied in Item I see below Image 2 is the final model of the galaxy in that region Image 3 is the residual image formed by subtracting 2 from 1 Image 0 is blank The final parameters obtained in the fit are stored in the FITS header of image 2 If you are dumping the final parameters into a table using a script this is an easier place to obtain them instead of trying to dissect fit log Note that if Item Z see below is set to 1 for any component that component will still be optimized but the model for that component will not be constructed in the output image 2 The residual image 3 will also reflect that fact since image 3 is created by subtracting image 2 from 1 Item C Input Weight Sigma Image A sigma image is a map of the standard deviations o
14. inner or outer regions or both Those trun cation functions may even be modified by Fourier modes bending modes and or the diskyness boxyness parame ter The degree of complexity that is allowed may seem a bit dizzying at first But just because such complexity is allowed does not mean that using them all simultane ously from the start is a good idea Proper use of these capabilities requires some training and human supervi sion to produce the most physically meaningful solution 8 3 1 Diskyness and Boxyness The effect of diskyness boxyness parameter on a per fect ellipse is shown in Figure 6 The diskyness boxyness parameter can be used with Fourier modes though it is not advisable because of parameter degeneracy issues Item CO Diskyness Boxyness Amplitude Co When Co lt 0 the ellipsoid appears disky and when Co gt 0 it appears boxy The following specifies its use in the input file c0 0 1 or on the command line c0 0 1 8 3 2 Fourier Modes The Fourier modes allow the possibility to create com plex shapes Figure 2 Just like diskyness boxyness Fourier modes are higher order corrections to a model As such it is not wise to turn them on when most of the other parameters are still rough because far away from an optimum solution large initial residuals would look like high power Fourier modes This is especially true for the m 2 mode which is quite degenerate with the axis ratio q The recomme
15. m x n Il 1 Pa z Y Tens Yen Vbreak n AT soft n gt an OPA n where Tpreak is the break radius where the profile is 99 of the original i e un truncated model flux at that ra dius The parameter Ar og is the softening length so that r rpreak Arsott is where the flux drops to 1 that of an un truncated model at the same radius the sign depends on whether the truncation is inner or outer The inner truncation function P tapers a light profile in the inner regions of a light profile whereas the outer truncation function 1 P tapers a light profile in the wings The behavior of the hyperbolic tangent function is ideal for truncation because it asymptotes to 1 at the break radius r gt rpreak and 0 at the softening radius r lt soft and vice versa for the complement function Thus when multiplied to a light profile f r the functional behavior exterior of the break radii region have intuitively obvious meanings For example as shown in Figure 14a if a S rsic function with n 4 is truncated in the wings shown in red the core has exactly an n 4 profile interior to the rpreak radius marked in vertical dashed line which is a free parameter to fit Likewise an n 4 profile truncated in the core green has exactly an n 4 profile exterior to the outer break radius Thus when one sums two functions of different S rsic indices n Figure 14b the asymptotic profiles of the wing and core retain
16. the menu or template file B1 0O 1 Shear term B2 0 1 banana term Just like the Fourier modes one can fit for an unre stricted number of bending modes and any number may be skipped However only the first 3 are the most use ful and the first mode B1 shear can be somewhat degenerate with the axis ratio of a model or the second Fourier mode when the amplitude is low So care should be taken when fitting the B1 mode 8 3 4 Coordinate Rotation As shown in Section 5 coordinate rotation allows for the creation of spiral structures There are two types of coordinate rotation allowed a tanh and log tanh The prefix a and log refer to the asymptotic behavior of the angular rotation function beyond r gt rout O r x r or O r x log r The suffix tanh refers to the fact that at small radii the powerlaw logarithmic functions are trun cated by a hyperbolic tangent This is useful because the tapering of the tanh function toward r 0 allows for the creation of a natural bar Note that unlike ellipsoid models a spiral model is actually a 3 dimensional struc ture that can be inclined and tilted However it is an infinitely thin model when viewed at 90 inclination Item RO Coordinate rotation function type The options are power for a tanh rotation or log for log tanh rotation Item R1 Inner bar radius The radius at which O r flattens off to 0 thus creating the appearance of a bar see F
17. the spiral structure cannot yet be modeled even though it is possible to do so by allowing for kinks in the rotation function Lastly the spiral structure cannot wind back onto itself because that would require the rotation function to be multi valued While it is possible 13 amp tanh spiral R 20 a 0 3 Radius pix Radius pix Radius pix 9 incl 0 05x 0 incl 45 sky_ Opa incl 45 9 Y 60 50 0 50 50 0 50 50 0 50 Fic 11 Examples of powerlaw hyperbolic tangent a tanh coordinate rotation modifying a face on tilt 0 deg elliptical profile with axis ratio q 0 4 The parameters of the rotation functions are shown on the top and right hand side of the diagram The top panels show the spiral rotation angle as a function of radius for the panels in the same column to do so it is not yet implemented O r bout tanh Tins Touts Binet O28 x ow i log af 1 28 Like the a tanh rotation function the log tanh func Coordinate Rotation II Logarithmic Hyper bolic Tangent log tanh The winding rate of spiral arms in late type galaxies is often thought to be logarithmic with radius rather than powerlaw Thus GALFIT also allows for a logarithmic hyperbolic tangent coordinate rotation function which is defined as tion has a hyperbolic tangent part that regulates the bar length and the speed of rotation withi
18. their original meaning and there is very little log tanh spiral 15 9 0 gy 0 incl 50 0 50 crosstalk outside of the truncation region denoted by vertical dashed lines in Figure 14 The use of the truncation functions is highly flexi ble There can be an unrestricted number of inner and outer truncation functions for each light profile model Furthermore multiple light profile models can share the same truncation functions This is useful for instance when trying to fit a dustlane inner truncation in a fairly edge on galaxy that may affect both the bulge and the disk components Just as with light profile mod els the truncation functions can be modified by Fourier modes bending modes etc independent of the higher order modes for the light profile they are modifying 50 0 50 50 0 50 Fic 13 Logarithmic hyperbolic tangent spiral log tanh angular rotation examples all face on 6jn 1 0 and an 0 deg The top left panel shows the meaning of the rotation parameter values at the corners of each box Like with the a tanh spirals the log tanh spiral can be tilted and rotated to any sky projection angle or combined with Fourier modes to produce lopsided or multi armed spiral structures not shown and with truncation function to produce an inner ring or an outer taper The top left panel figure for all practical purposes is a pure logarithmic spiral with a winding scale radius Rws 5 pixels
19. to the rotation function being a hyperbolic tangent thereby creating the appearance of a flattened disk even though there is not a separate disk component involved in the model sensible because of the way Eqs 27 and 28 for logarith mic spiral below are defined a negative rj just means that the spiral rotation function has a finite rotation an gle at r 0 relative to the initial ellipsoid out of which it is constructed When there is clearly no bar the rin parameter can become quite negative in this case one should probably just hold rin fixed to 0 Furthermore often times one may not wish to create a bar and a spi ral out of one smoothly continuous function for various reasons e g they may have different widths the spiral may not extend into the center or the spiral may start off in a ring In these situations one can detach the bar from the spiral by using a truncation function see 6 and 8 3 5 by instead creating a bar with a sep arate S rsic Ferrer or other functions When this is done a bar radius is still useful mathematically in the coordinate rotation function but it may bear no physical relation to the physical bar Limitations of the spiral rotation formulation While the a tanh rotation function works surprisingly well for many spiral galaxies there are several limita tions to the simple formulation One limitation is that the spiral rotation functions are smooth so kinks in
20. you hit p or n you will receive a prompt in your iteration window not the green one You must answer the question in the iteration window before it would go on Usually GALFIT will decide when to quit fitting on its own But if GALFIT iterates over 100 times an arti ficial limit it will also quit You can set the maximum number of iterations you want this to happen by hitting n and specifying the number of iterations Normally GALFIT should converge between 10 to 30 iterations 10 OUTPUT FILES Once GALFIT finishes fitting it will store the final parameter information into 2 text files The first file fit log summarizes all the final parameters and error bars for the fit This file just keeps getting appended and does not get removed The errors quoted in fit log are based on diagonalizing and projecting the covariance matrix Thus the errors are purely statistical some would say meaningless because the errors are often dom inated by systematics due to the real galaxies not being idealized profiles The columns of numbers in the out put file are in the same order as the parameter numbers Parameters whose values are held fixed are enclosed in square brackets e g 6 27 whereas constrained param eters are in curly braces e g 1 24 If there is any pa rameter enclosed in between stars as of Version 3 0 1 e g 0 15 it may have caused numerical convergence issues such that even if GALFIT
21. 0 1 1 azim Fourier mode 3 amplitude amp phase angle Z 0 output option 0 resid 1 Don t subtract Object number 3 0 expdisk object type 1 48 5180 51 2800 11 position x y 3 20 0890 1 integrated magnitude 4 5 1160 1 R_s disk scale length pix 9 0 7570 1 axis ratio b a 10 60 3690 1 position angle PA deg Up 0 Left 90 CO 0 05 0 diskyness boxyness Z 0 output option 0 resid 1 Don t subtract Object number 4 0 nuker object type 1 48 5180 51 2800 11 position x y 3 20 0890 1 mu Rb mag arcsec 2 4 5 1160 1 Rb pix 5 4 2490 1 alpha 6 1 1000 1 beta 7 0 3000 1 gamma 9 0 7570 1 axis ratio b a 10 60 3690 1 position angle PA deg Up 0 Left 90 Z 0 output option 0 resid 1 Don t subtract Object number 5 0 sky object type 1 1 3920 1 sky background at center of fitting region ADUs 2 0 0000 0 dsky dx sky gradient in x 3 0 0000 o dsky dy sky gradient in y Z 0 output option 0 resid 1 Don t subtract Fic 17 Example of an input file The object list is dynamic and can be extended as needed 32 Radius APPENDIX A HYPERBOLIC TANGENT ROTATION FUNCTION The hyperbolic tangent tanh rin Tout inci OPF r portion of the a tanh Eq 27 and pow tanh Eq 28 rotation function is given by Equation 5 below The constant CDEF is defined such that the rotation angle at the
22. FoR GALFIT 3 0 4 AND MORE RECENT VERSIONS Preprint typeset using IAT X style emulateapj v 7 8 03 GALFIT USER S MANUAL CHIEN Y PENG For GALFIT 3 0 4 and more recent versions ABSTRACT GALFIT is a tool for extracting information about galaxies stars globular cluster stellar disks etc by using parametric functions to model objects as they appear in two dimensional digital images In simplest use GALFIT allows one to fit an ellipsoid model to light profiles in an image For more complicated situations it can model highly detailed shapes that are curved irregular lopsided ringed truncated or have spiral arms One can mix and match these features within a single component model or can add them to other components to create complex shapes This document describes how to run GALFIT and explains its features but it is not complete without two companion papers Peng Ho Impey amp Rix 2010 AJ 139 2097 and Peng Ho Impey amp Rix 2002 AJ 124 266 which illustrate how the features can be used on real galaxies There have been a number of upgrades since the original 2002 publication because GALFIT continues to evolve Thus this document supersedes both of the articles whenever there are differences Subject headings 1 INTRODUCTION A way to characterize the structure of objects in an image is to model their light distribution using analytic functions For the functions to be useful they gener ally have to have free p
23. ITS image without prompt ing EXPTIME GAIN or ATODGAIN RDNOISE and NCOMBINE If these keywords are not found for some reason GALFIT assumes the default values of 1 7 and 5 2 1 respectively which for historical reasons only correspond to values for the WFPC2 camera on HST As of Version 3 0 1 the RDNOISE parameter is not used Together with the photometric zeropoint in the input menu file given by the user EXPTIME is used to cal culate the magnitude or surface brightness of a model If for some reason an image has units of flux counts sec the EXPTIME parameter value should be 1 sec ond rather than the total or average exposure time Side note it should be noted that it is highly inadvisable to analyze images where the ADUs are in flux units rather than count units because the sky in flux units virtually always appears deceptively small and insignificant The GAIN and NCOMBINE parameters are only used by GALFIT to calculate the o image the o x y in Eq 1 for pixel weighting if the user does not provide one In the example you ran above GALFIT generated a image internally Further details will be discussed in Section 8 1 regarding images However here is the basic idea GALFIT converts the image ADUs into elec trons using the GAIN parameter such that at each pixel ADUxGAIN electrons per pixel Therefore if the ADU has units of counts then the GAIN has to have a unit of e7 ADU This signal term i e
24. PSF is created to be 1 time oversampled one can ignore the CCD diffusion kernel because the kernel is already included However if you created a twice or more sub sampled PSF using TinyTim and your data image is only one time sampled then you may want to provide the diffusion Kernel see below The peak flux of the PSF image should be at the geo metric center when the number of pixels on a side is odd However if the number of pixels N on a side is even the 22 peak should be located at pixel position N 2 1 Ifthe peak is anywhere else the model that GALFIT generates will be systematically offset in position by the difference from the predefined center This is important to keep in mind when the convolution box is small you may want to make sure to refit the image with a large convolution box after the solution has first converged As mentioned above the input PSF can be accompa nied by a CCD charge diffusion kernel which is simply a text file It is usually only needed if one has created an oversampled HST PSFs using TinyTim If the PSF has unit sampling the diffusion is applied by TinyTim auto matically so GALFIT will not re apply it even if a kernel is specified The appropriate charge diffusion kernel can be found under the COMMENTS section in the PSF image header created by TinyTim Here is a typical ex ample of what the diffusion kernel input file should look like 0 012500 0 050000 0 012500 0 050000 0 750000
25. T will output a parameter called FLAGS which lists all the flags that have been tripped during the iterations To see what the flags mean type on the command line galfit help Most of the flags will not affect the fit they are just gathered into one place so the user may be aware of which ones were tripped The most important flags to watch out for are numbered 1 and 2 as well as the A ones 11 HINTS ON DIFFICULT FITTING The above information is all that one needs to know to run GALFIT This section discusses some rules of thumb when dealing with complicated analysis For simple one or two component models GALFIT can usually perform its duty without any interaction But once in a while one may come across a galaxy that re quires some amount of interaction to achieve a reasonable fit Unfortunately this situation is often blamed on pa rameter degeneracies when in fact it may be due to some other reasons To be sure there are times when degen eracy and local minima are to blame However many of the problems people encounter are caused by either bad priors or bad initial guesses that cause parameters to take on extreme values With bad priors no amount of manipulation or parameter restarts is going to instill more meaning to the analysis There is also another widely held belief that numeri cal degeneracy is mostly caused by the number of pa rameters a notion which is overly simplistic To see why cons
26. age peak of an irregu lar galaxy is not located at the geometric center it has a high amplitude m 1 Fourier mode i e lopsidedness Other high order modes can be used to quantify higher degrees of asymmetry on top of lopsidedness The phase angles of the Fourier modes are also useful information to keep in mind Modes with the following phase angles have the following symmetry properties e Symmetry about a central point a 0 regardless of other mode phase and amplitude e For all modes m there is reflection symmetry at m 0 180 For m even this symmetry is about both the major and minor axes Whereas for m odd the reflection symmetry is only about the major axis e For odd modes of m there is additional reflection symmetry about the minor axis at m 90 An irregular galaxy has angles that are out of phase oes whereas regular galaxies have angles that are more in degrees 10 phase i e reflectionally symmetric around either mi nor or major axis Therefore it is possible to quantify various forms and degree of asymmetry by constructing indices based on the amplitude and phase angles of the Fourier modes The most intuitively obvious asymmetry index is the m 1 mode which captures the lopsided ness Az of a galaxy i e the positioning of the bright est central region relative to the fainter outer region of a galaxy Ar lail 23 Asymmetric galaxies are also
27. al profile is D r Xo exp 7 Fot 2rr2Doq R Co m 8 The 6 free parameters of the profile are x y total mag nitude rs Opa and q The Gaussian Profile The Gaussian profile is an other special case of the S rsic function for when n 0 5 see Figure 1 but here the size parameter is the FWHM instead of re The functional form is T 3 Frot 2ro7Xoq R Co m 10 The Modified Ferrer Profile Intensity 0 20 40 60 80 100 Radius Fic 2 The modified Ferrer profile The black reference curve has parameters rout 100 a 0 5 8 2 and No 1000 The red curves differ from the reference only in the a parameter as indicated by the red numbers Likewise the green curves differ from the reference only in the 8 parameter as indicated by the green numbers The Empirical King Profile 1000 100 a o 10 1 0 1 0 20 40 60 80 100 Radius Fic 3 The empirical King profile The black reference curve has parameters re 50 rt 100 a 2 Xo 1000 The red curves differ from the reference curve only in the a parameter as indicated by the red numbers Likewise the green curves differ from the reference only in the re parameter as indicated by the green numbers The Moffat Profile 1000 100 Intensity 10 0 20 40 60 80 100 Radius F c 4 The Moffat profile The black reference curve has parameters n 2 FWHM 20 and Xo 1000 The othe
28. angle at r 0 Therefore in GALFIT at r 0 the rotation function reaches 0 0 Figure 12 Lastly it is also important to keep in mind that the meaning of the bar radius just as described in the section for a tanh rotation function is a mathematical construct 6 THE TRUNCATION FUNCTION Truncation functions allow for a possibility to create rings outer profile cut offs dustlanes or a composite profile in the sense that the inner region behaves as one function and the outer behaves as another The trunca tion function can modify both the radial profile and az imuthal shape A ring can be created by truncating the inner region of a light profile Likewise when a galaxy has spiral arms that do not reach the center it can be viewed as being truncated in the inner region 6 1 General Principle In GALFIT each truncation function can modify one or more light profile models Also any number of light profile can share the same truncation function The trun cation function in GALFIT is a hyperbolic tangent func tion see Eq 7 in Appendix B Schematically a trun cated component is created by multiplying a radial light profile function fo x y by one or more truncation functions Pm or 1 P depending on whether the type is an inner or an outer truncation see Eq 7 of Appendix B in the following way EO oa G70 Leis Yc i di OPA i X 29 m Il Pn x Y Tem Yeym gt Tbreak m gt AT soft m dm OPA
29. another layer of complexity in its use If the analysis is to be complex it ought to be because an object is physically complicated not because the code is complicated to use Moreover the ability to do complicated analysis should not make it burdensome for fitting a single component These crite ria mean that GALFIT does only one thing which is to fit functions It does not help users do a lot of other things 1 NRC Herzberg Institute of Astrophysics 5071 West Saanich Road Victoria British Columbia Canada V9E 2E7 Chien Y Peng gmail com 2 http users obs carnegiescience edu peng work galfit galfit html that are useful for analyzing large surveys like helping users extract a point spread function determining the initial parameters of the fit figuring out the image size to fit locating galaxies in an image masking out neighbor ing objects determining the sky pedestal level a priori etc even though all these things are crucial for doing a correct analysis Instead the user must take care of all those pre and post processing parameter value con version book keeping outside of GALFIT Doing so greatly simplifies the use of GALFIT It gives users more control over the analysis Because each of the aforemen tioned steps requires some degree of mastery by not try ing to do everything for users allows GALFIT to be less a black box than it might seem otherwise Even though GALFIT does not perform critical pr
30. arameters e g size luminosity which one can adjust to model a wide variety of differ ent shapes GALFIT is an image analysis algorithm that can model profiles of galaxies stars and other astronom ical objects in digital images If successful the features of interest are summarized into a small set of numbers such as size luminosity and profile central concentration which one can compare against other objects for doing science One common application of this technique is to measure global morphology by using a single compo nent ellipsoidal model Another use is to take apart a galaxy into different constituents like bulge disk bar or to separate overlapping galaxies by using two or more component models This document details the features available for use in GALFIT and how to use them Design Considerations Fitting functions to an image and interpreting what the results mean can be challeng ing even to skilled analysts because astronomical objects come in many sizes shapes and degrees of complexity In addition what one wishes to get out of the data de pends on the science goal Therefore there is often not one universal way to do an analysis that will satisfy ev eryone s needs Deciding what to do and interpreting what the results mean require one to draw on scientific technical and often artistic skills and intuition The analysis being potentially complex the design premise of GALFIT tries to avoid adding
31. behave In a similar vein 6 Know when to hold em i e the parameters fixed If a fit is converging on something non sensical one can temporarily hold some of the parameters fixed to more sensible values in the main input template file as opposed to the constraint file They do not have to be precise One can set them free later when the other parameters have converged This technique is useful when parameters like the S rsic index and size to haywire because of nearby sources PSF or profile mismatches sky determi nation issues or for other reasons Note that if one has to do this often it is because the initial guesses are very far from reality for at least one of the components or there is something else in the image that should be either be fitted simultane ously or masked out For instance large residuals around bright unresolved sources can often cause an underlying S rsic model to take on extreme val ues of n or re Parameter constraint files are NOT good to use Often times people use parameter constraints to make sure that the parameters fall within a sensible range However keep in mind that 1 The reason that parameters may get nonsensical is that other things in the image are affecting the fit Thus the solution should be to remove the offending objects 2 Parameters that hit the boundary walls are bad parameters and should not be trusted used 3 When a parameter hits a boundary often times it hamp
32. by component num ber N Just like the previous this parameter is added on to the end of a light profile model to indicate it is truncated in the wings by component number N When a profile is truncated only in the outskirts the flux nor malization parameter is the central surface brightness If used in conjunction with inner truncation the luminosity parameter is the surface brightness at fout The truncation function itself can have the following free parameters some of which are optional If not ex plicitly listed in the template file or GALFIT menu the optional parameters take on the value of the light profile component to which the truncation function is associ ated See Appendix B for details on the how the trun cation function depends on the following parameters Item TO Truncation type The options are ra dial for all light profiles except edgedisk For edgedisk only the only options are length and or width The truncation type also has options Type 1 vs Type 2 as well as Type a vs Type b for spiral rotations only as explained below Type 1 and Type a are default and have no special designations whereas Type 2 and Type b are represented for example by radial2 and radial b Item T1 x y position optional The centroid of the truncation function can be different from the light profile model When not specified i e when T1 does not exist in the menu the centroid position
33. characterized by overall de viation from an ellipse thus another intuitively useful quantity to measure is the sum of the Fourier amplitudes N Ag X lea 24 Asymmetric galaxies by definition have high Ag How ever it is possible for galaxies with both high Ag and Az to be reflectionally symmetric the degree of reflectional symmetry may be an indicator for how well the galaxies is relaxed Reflection asymmetry is given by the index Ar AR J meven l m sin am se Epm oda lam sin nme 25 where m is in degrees In this formulation the higher the reflectional asymmetry the higher the index Apr Used together these three descriptors provide highly use ful ways to quantify the degree galaxies are irregular For instance high values of Ag and Ar most likely imply high global asymmetry in the intuitive sense Whereas a high value of Ap with low Ap implies high regularity but large deviation from an ellipse such as edge on disky galaxies or a disky boxy ellipticals Caveat in using Fourier modes Because Fourier modes are high order corrections to some intrinsic shape care should be taken when fitting them For instance Fourier modes can be high order corrections to a perfect circle q 1 or an ellipse q lt 1 In most instances it is the perturbation on an ellipsoid shape that is the most interesting Therefore with the possible exception of the first mode high order Fourier modes should be used only
34. create an image block subcomps fits where each image slice after the first data is the indi vidual components used in the fit Alternatively one can do these things on the command line by doing galfit o1 lt file gt galfit o2 lt file gt galfit 03 lt file gt model only standard img block subcomps 8 2 Classical Object Fitting Parameters 0 10 and Z GALFIT allows for a simultaneous fitting of arbitrary number of components simply by extending the following object list 0 10 Z for each component Items 1 10 are the initial rough guesses at the object parameters and they don t have to be accurate But of course the more complicated a fit is i e the more number of components the better the initial guesses should be so GALFIT doesn t wander off to never never land The 2nd column in Items 3 10 are initial guesses for the parameter and the 3rd column is where one can hold the parameters fixed 0 or allow them to vary 1 Note that items 1 and 2 e Yc are on the same line except for fitting the sky Below is a more detailed explanation of what each of the parameters means Item 0 Object name The valid entries are sersic devauc nuker expdisk moffat gaussian sky psf Items 1 2 X and Y positions of the galaxy in pixels For the sky Items 1 and 2 are on consecutive lines instead of the same line For the sky Item 1 is the DC offset in it ADUs and Item 2 is the gradient in the X directio
35. ction Window Sometimes it is useful to quit out of a fit early and save results pause a fit extend the number of maximum iterations default 100 etc The interaction window lets you do this There are three options In the regular option there is no interaction possible In the both option a green xterm window will pop up to show you what commands one can issue to GALFIT during fitting The commands see 6 are issued by typing a single letter in the green window not in the fitting window except when the fit is paused or when one is entering new number of iterations In the curses mode one can issue the same com mands as the both option But all the interaction is done in the fitting window instead of a separate window For Mac OS X users only To use the both mode you must run GALFIT in X11 xterm mode otherwise it would complain about not being able to open a window If not in X11 set this parameter to regular 23 Item P Options If this option is set to 0 GALFIT will run normally Once it finishes running it will create the standard image block data model residual of the best fit If the option is set to 1 GALFIT will create a model image based on your input parameters and imme diately quit If the option is set to 2 GALFIT will create an image block data model residual based on the cur rent fitting parameters and quit If the option is set to 3 GALFIT will
36. ctor software and choose the option to output a segmentation image The segmentation image is a mask of all the objects that are detected by SExtractor where instead of fluxes 10 11 12 13 29 the pixel values correspond to unique ID numbers of objects To convert the segmentation image into an object mask for GALFIT all one has to do is to locate the object of interest to fit and unmask it by replacing the object ID with zero values using e g IRAF imreplace See a bright convolution PSF region in the model That usually means one or more of the following 1 the convolution box Item I is too small en large it 2 the convolution PSF image size Item D is too small extract a larger PSF image size or 3 the PSF has a sky pedestal that is not re moved properly Be sure not to confuse 2 with 3 a PSF image that cuts off the wings may look like it has a sky pedestal but confusing the difference will lead to bad consequences To confirm visually that the sky is subtracted off completely make sure first that the PSF image is large enough to include the wing then multiply it by a large value do not take for granted that close to zero means there is no sky especially when the image ADU is in counts second Take a look at the individual subcomponents It is useful to scrutinize individual model subcompo nents to make sure that they make sense instead of just looking at the parameter
37. d on after a solution has first converged for the classical parameters The non classical parameters will only appear when the user assigns to them a value even a value of 0 For instance c0 0 111 F3 0 0 11 rO power Deleting A Non Classical Parameter These non classical parameters can be deleted by setting both the values and the toggle flags equal to 0 To disable coordi nate rotation set RO equal to none For instance c0 0 O Removing diskyness boxyness F7 0 0 0 O Removing 7th Fourier mode rO none Disabling coord rotation Once a parameter is deleted or the value is held fixed to 0 it will go back into hiding unless called upon Deleting an Object To delete an object use the x key followed by the object number For example x 3 deletes the 3rd model from the fit Start Fitting Once you re done with enter ing changing all the parameters to start fitting hit q 8 GALFIT MENU ITEMS This section describes the menu items Figure 17 in a little more detail The GALFIT menu is separated into two sections the image parameters the top half of the menu i e Items labeled A P and the object fitting pa rameters the bottom half i e Items numbered 0 10 and Z There is only one set of image parameters A P but there can be an arbitrary number of object parameters depending on what you want to fit simultaneously In principle there is no limit to the number of fitted com ponents
38. ditions can affect the output parameter values or the physical inference of the components Indeed practically the only solution to true numerical degeneracies is to start the fit with different initial conditions or by choosing a more appropriate function for the desired science task Even though real degeneracies may be present between some parameters it is useful to think carefully about whether the science goals are negatively affected Here is a concrete example if a goal is to extract the total luminosity or size of a galaxy bar then the issue of de generacy is moot even if one chooses to use both the Co and the Fourier modes For even though Co and Fourier modes are mutually degenerate they are not degener ate with the size and luminosity parameters The use of high order modes would benefit in this scenario by re covering more of the flux As another example as shown Figure 16 sometimes the spiral arm parameters may be degenerate for various reasons Even so the use of a spi ral component can help to stabilize the measurements of bulge and disk components 12 RULES OF THUMB FOR IMAGE FITTING AND FREQUENTLY ASKED QUESTIONS There are certain rules of thumb i e good practices to understand when doing image fitting analysis Some of these originate from questions I received in the course of user support over the years others based on techni cal knowledge of the how the Levenberg Marquardt algo rithm works while others
39. e analysis for peo ple the project website does provide all the information necessary for users to learn the background necessary to perform proper analysis The above considerations mean the GALFIT interface has the smallest essential set of controlling parameters needed to perform reliable photometry located in a con cise menu text file There are no other hidden program knobs to fine tune behavior The only things which are not immediately visible to users are fundamental data that ought to be present in FITS image headers expo sure time instrumental gain readnoise and number of images combined to produce the data They are essen tial for doing quantitative science therefore one should reasonably expect or provide them in all FITS images just as importantly that they correspond correctly to the data units To provide additional controls an user may define a constraint file The bare essential inter face allows users to focus attention on the analysis itself rather than on tweaking the program knobs in order to produce a reliable outcome To emphasize the above philosophy this manual starts by getting new users quickly going on running GALFIT by the next page A new user should then immediately 3 correspond correctly means that the exposure time must correspond to the image data units e g an image in flux units has an exposure time of 1 second not total exposure time The gain factor directly converts
40. eaning for the normalization e function default see documentation below e function central surface brightness e function2 surface brightness at radius parame ter 4 e g effective radius for S rsic FWHM for Gaussian r for exponential etc e function for truncation only surface brightness at the break radius i e 99 flux radius The S rsic Profile The S rsic powerlaw is one of the most frequently used to study galaxy morphology and has the following functional form The Sersic Profile Intensity 0 20 40 60 80 100 Radius Fic 1 The S rsic profile Notice that the larger the S rsic index value n the steeper the central core and more extended the outer wing A low n has a flatter core and more sharply truncated wing Large S rsic index components are very sensitive to uncer tainties in the sky background level determination because of the extended wings U r De exp z 4 2 Ne is the pixel surface brightness at the effective radius Te The parameter n is often referred to as the concentra tion parameter When n is large it has a steep inner pro file and a highly extended outer wing Inversely when n is small it has a shallow inner profile and a steep trun cation at large radius The parameter re is known as the effective radius such that half of the total flux is within re To make this definition true the dependent variable K is coupled to n thus it is not a
41. ective radius Ter So fmoa r Der oe S rsic profile now has the following explicit form fmoa T Zer exp E 31 For the S rsic exponential and Nuker profiles this corresponds to functions as written in Sec tion 4 For example a e function flux parameter is the surface brightness Xbreak at the break radius rpreak This is the most useful situation when a truncation results in a large scale galaxy ring so that the surface brightness parameter corresponds closely to the peak of the light profile model When the truncation is not concentric with the light profile model this kind of normalization is not very intuitive For radial truncation Tpreak is parameter 4 whereas for ra dial2 rpreak is parameter 4 for outer truncation and parameter 5 for inner truncation When ser sic3 option is chosen the rpreak parameter comes automatically from the first truncation component that a certain light profile model is associated In our example of the S rsic profile fmoa r Trea AES For example a S rsic profile now has the following explicit form fmoa Ubreak i z 9 32 F Figure 15 demonstrates just some of the possibilities allowed when fitting truncations In addition to the reg ular ellipsoid shape the higher order modes like disky ness boxyness parameters bending modes and Fourier modes can also modify the shape of the truncation func tions One ca
42. ellipsoid model has been found Fourier Modes Few galaxies look like perfect el lipsoids and one can better refine the azimuthal shape by adding perturbations in the form of Fourier modes The Fourier perturbation on a perfect ellipsoid shape is defined in the following way N r x y rolz y 5 am cos m 0 n 22 In the absence of Fourier modes in the parenthesis the ro z y term is the radial coordinate for a traditional ellipse and 0 arctan y yc xe q defined in Equation 21 am is the Fourier amplitude for the mode m Defined as such am is the fractional deviation in radius from a generalized ellipse of Eq 21 The number of modes N is up to the user to decide and the user may also choose to skip certain modes See Figure 7 for some examples of how Fourier modes modify a circle and an ellipse into other shapes The phase angle m is the angle of a mode m rel ative to the PA of the generalized ellipse That is to say the phase angle is 0 degrees in the direction of the semi major axis of the generalized ellipse rather than up increasing counter clockwise Notice that the phase angle is complete within a range of 180 m lt dm lt 180 m which is referred to as the cardinal angle The phase angle in GALFIT is always reported to users in the cardinal range Unlike the classical shape parameters q and PA the Fourier modes will only appear in the menu when the user wants to fit th
43. elp when fitting very difficult cases If the suggestions above do not work after all of this one is more than welcome to email me cyp nrc cnre gc ca and I d be happy to give it a go to see what the problem might be REFERENCES Elson R A 1999 Stellar Dynamics in Globular Clusters in 10th Canary Islands Winter School of Astrophysics Globular clusters p 209 248 Eds C Martinez Roger P Fourrion F Sanchez Cambridge Contemp Cambridge University Press Krist J E amp Hook R N 1997 in HST Calibration Workshop with a New Generation of Instruments eds S Casertano et al Baltimore STScI p 192 Lauer T R Ajhar E A Byun Y I Dressler A Faber S M Grillmair C Kormendy J Richstone D amp Tremaine S 1995 AJ 110 2622 Pence W 1999 ASP Conf Ser Vol 172 487 Peng C Y Ho L C Impey C D amp Rix H W 2002 AJ 124 266 Peng C Y Ho L C Impey C D amp Rix H W 2010 AJ 139 2097 Press W H Teukolsky S A Vetterling W T amp Flannery B P 1997 Numerical Recipes in C Cambridge Cambridge Univ Press 31 IMAGE PARAMETERS A gal fits Input data image FITS file B imgblock fits Output data image block C none Sigma image name made from data if blank or none D psf fits Input PSF image and optional diffusion kernel E 1 PSF fine sampling factor relative to data F none Bad pixel mask FITS i
44. em see EXAMPLE INPUT for how to do so Otherwise they will remain out of view to avoid clutter Each mode has 2 free parameters am and om and the number of modes the user can add is unre stricted However the most useful modes are low order ones m 1 3 6 Also m 2 should rarely be used if one is already fitting the traditional axis ratio q for an ellipse since q and m 2 are fairly degenerate with each other Initially the parameters of the Fourier modes can be all set to 0 even if the final values greatly deviate from 0 Properly Interpreting Fourier Mode Parameters A common but incorrect first impression is to regard the Fourier modes as a shapelet decomposition technique In shapelet decomposition of an image an object is bro ken down into some number of basis functions i e fixed 2 D geometric patterns that are mathematically orthogo nal functions The amplitude of a shapelet basis function is the flux of that component By combining the right shape and number of basis functions anything in the image can be modeled However GALFIT does not do shapelet decomposition In GALFIT the Fourier modes modify the coordinate system from a rectilinear grid into something more exotic By stretching shrinking it in the radial direction by an amount that depends on the az imuthal angle the result is that the azimuthal shape of a component is modified but the radial profile is not Another way to think about it is that in
45. erally would not hurt to let GALFIT do so unless the data ADUs have mysterious units that are not easily con verted into electrons through the GAIN parameter So please make sure that the image header units are such that ADUx GAIN electrons and that the ob ject does not dominate the field of view Please see Section 8 1 for a more detailed discussion on the o image The next three sections describe the analytic functions available in GALFIT for fitting light profiles The func tions are divided into three categories the regular radial profile 4 the azimuthal shape 5 and the trunca tion function 6 4 THE RADIAL PROFILE FUNCTIONS The radial profile functions control the radial fall off in flux e g the S rsic Nuker exponential models among others GALFIT allows for some of the most frequently used functions in literature and more will likely be added in the future The normalization parameter for the radial profiles can be specified by the user by adding an integer to the end of the name of the functional name e g sersic2 gaus sian1 etc The default normalization which is not in dicated using a number depends on the functional form and is discussed in the individual sections below For instance the default normalization for a S rsic profile is total luminosity whereas for a Ferrer s profile it is cen tral surface brightness Aside from the default option the numerical suffix has the following m
46. ers the convergence of other parameters as well possibly making those equally unreliable The only constraints that are good to use are the ones in the GALFIT main menu template file or the off set constraints in the constraint file For instance it is fine to use the offset constraint to hold the centroids between two components e g bulge amp disk fixed relative to each other But in gen eral boundary constraints are rather finicky to use In my personal experience I have never needed to use constraint files except to keep relative centroids fixed So users please be aware and inspect the re sults carefully Use object masking One should always consider masking out objects that are not being fitted espe cially if an area is too dusty or irregular in shape For example the jet in M87 will give GALFIT prob lems because even though they are local features the knots are much brighter than the diffuse un derlying star light Masking is especially impor tant when fitting high order modes such as Fourier modes because by definition higher order modes are sensitive to small perturbations To create a mask I have a program which can help If one needs to mask a lot please visit the Frequently Asked Question section on the GALFIT website or use SExtractor On my website I provide programs to expedite the process of creating masks A better way to mask out a lot of objects e g stars is to use the SExtra
47. es of the truncation function When softening length Argof is used a free parameter it is defined as Argoft Tbreak Tsoft Tbreak
48. es only one value differs from the reference as shown in the legend Eq 19 The other free parameters are the core radius re and the truncation radius r in addition to the ge ometrical parameters Outside the truncation radius the function is set to 0 Thus the total number of classical free parameters is 8 x yY Xo Te Tt Q q Opa The Moffat Profile The profile of the HST WFPC2 PSF is well described by the Moffat function Other than that the Moffat function is less frequently used than the above functions for galaxy fitting The functional profile and the total flux equations are respectively a ae U r r Domraq n 1 R Co m In GALFIT the size parameter to fit is the FWHM where the relation between rg and FWHM is D r 13 Frot 14 FWHM 15 Soe t an The 7 free parameters are Y Mot i e total magni tude instead of po FWHM instead of ra the concen tration index n q and Opa The Nuker Profile The Nuker profile Figure 5 was introduced by Lauer et al 1995 to fit the nuclear profile of nearby galaxies and it has the following form I r 2 E 16 The flux parameter to fit is 4p the surface brightness of the profile at r which is defined as I texpAxAy The Nuker profile is a double powerlaw where in Eq 16 B is the outer power law slope y is the inner slope and a controls the sharpness of the transition The motivation for using this
49. f the data image as defined by Equation 1 which is derived based on assumptions about Poisson more precisely Gaussian statistics It is used to give relative weights to the pixels during the fit and it should not be arbitrary More pre cisely a x y should be one standard deviation of counts at pixel position x y for a noiseless underlying parent distribution i e image That means that in principle a x y can be known precisely only if we have an infinite signal to noise image of the source Because we never have this the sigma image is always an approximation This rather subtle point can be made more clear by way of a simple example an image taken of a constant sky background sky has only one value of o across the entire image and that value sky The propor tionality factor depends on the units of the ADU The pixel to pixel fluctuation one sees in a sky image comes about because each pixel value is randomly drawn from a Poisson distribution with the same o for all the pizels appropriate to a given mean sky value So in this exam ple the sigma image for GALFIT should be a single value across the whole image For data having real objects it is somewhat more difficult to obtain the underlying a x y because the flux distribution is no longer con stant Nonetheless this concept suggests an approach to take for creating a sigma image which is described below If the sigma image is not provided If a sigma i
50. free parameter The classic de Vaucouleurs profile that describes a number of galaxy bulges is a special case of the S rsic profile when n 4 thus amp 7 67 As explained below both the ex ponential and Gaussian functions are also special cases of the S rsic function when n 1 and n 0 5 respec tively As such the S rsic profile is a common favorite when fitting a single component The flux integrated out to r oo for a S rsic profile is Fot 2ar2Dee nk 2 T 2n q R Co m 3 The term R Co m is a geometric correction factor when the azimuthal shape deviates from a perfect ellipse As the concept of azimuthal shapes will be discussed in Sec tion 5 we will only comment here that R Co m is sim ply the ratio of the area between a perfect ellipse with the area of the more general shape having the same axis ra tio q and unit radius The shape can be modified by Fourier modes m being the mode number or disky ness boxyness For instance when the shape is modified by diskyness boxyness R Co has an analytic solution given by R Co Teta 6 BUN 2 1 1 Co 2 where is the Beta function In general when the Fourier modes are used to modify an ellipsoid shape there is no analytic solution for R m and so the area ratio must be integrated numerically In GALFIT the flux parameter that one can use for the S rsic function is either the integrated magnitude Metot use sersic function or the surface
51. he next step If the x decreases significantly GALFIT will keep going When the solution no longer improves by some criterion it will stop on its own In GALFIT the indicator of goodness of fit is the normalized or reduced y i e x2 66 nx ny Yy faata x LY Noor 2 yc olx y eel ides y 1 e Xv summed over all na and ny pixels where Npor is the degree of freedom number of pixels number of free parameters As shown in Equation 1 x minimization requires there to be two input images the input data faata 2 y and the image a x y The model image fmodei 2 y is generated by GALFIT internally on the fly as it tries to find the best match to the data the user specifies what models are to be used in the fit o x y is often called either as the sigma image or the weight image i e one standard deviation of counts at each pixel which is re lated to the Poisson noise In times when the o y image is not available to the user GALFIT has a way to automatically generate one internally based on Poisson statistics of the data This is the only time when the im age header information is used For GALFIT to compute a sigma image reliably the input data image has to be in the following specific form and there need to be some information in the image header What Header Keywords GALFIT Wants and Why There are only 4 standard header keywords that GAL FIT normally scans for in a F
52. hieve the same value for the fraction E More specifically as shown in Figure 13 a low a can be reproduced by both a high y and a low 8 Another example of numerical degeneracy is between the axis ratio q the second Fourier mode m 2 and the first bending mode m 1 i e shear all of which can simulate ellipticity Likewise a combination of the m 2 and m 4 Fourier modes can reproduce the same features as the diskyness boxyness parameter Co A third example is in trying to fit a spiral structure When spiral arms are diffuse and have low inter arm con trast it may be difficult for GALFIT to lock onto a so lution In this situation a model with a large amount of winding of thin spiral arms might reduce the residual just as well as a thick arm with fewer windings Some other examples of numerical degeneracy include high S rsic index values with the sky level or the size central concentration of a truncated model that has a long softening radius Note that in every one of the above examples degeneracies happen because numeri cally different parameters are similar in their ability to model some behavior Therefore it is worthwhile to keep in mind that some of these parameters should not be used together haphazardly even though one is allowed to do so in GALFIT The bottom line is that true numerical degeneracies often cannot be solved by using better priors and they represent situations where different starting con
53. ider a situation where there are a million stars that are non overlapping The three million parameters needed to fit those stars using a Gaussian profile or the 7 million needed for using a S rsic model are completely non degenerate Contrast this to a single Nuker model of 9 parameters when ry is sufficiently small which would be degenerate in the powerlaw parameters a 8 and y 27 TRADITIONAL MODEL NEW MODEL Fic 16 Examples of bad priors or numerical degeneracy on image analysis a a 3 component traditional ellipsoid fit to NGC 289 and a single component fit to a neighboring object Note that none of the components corresponds to a bulge due to the strong spiral arm residuals b a bulge disk bar and spiral arm fit of the same galaxy The fitted bulge comes out naturally to have an axis ratio of 0 8 and is an exponential bulge It is important for users to learn to tell the difference be tween situations caused by bad priors from those caused by true numerical degeneracies when attempting to per form complex analysis because the solutions to those problems are quite different 11 1 What are Bad Solutions Caused by Bad Priors A prior is bad when an user wants GALFIT to per form analysis by using models that are ill suited to the task The most common example is when one tries to do a two component decomposition allegedly to extract a bulge and a disk on a galaxy which clearly has three or more compone
54. igure 7 As Section 5 explains the bar radius is an useful mathematical construct and may or may not have any bearing on the physical bar Item R2 Outer radius The radius beyond which the function 6 r behaves either like a pure power law or a pure logarithm see Figure 7 Item R3 Total angular rotation out to outer radius The total angular rotation Oout at the outer transition radius 06 Oout r Tout or O r Ooutlog r rout i Item R4 Asymptotic powerlaw rate a tanh or scale parameter log tanh For a tanh this pa rameter is the parameter in 0 x r For the log tanh function it is the winding scale parameter rws in 6 x log r rws Item R9 Inclination angle to line of sight A face on spiral can be inclined relative to the line of sight to appear more elliptical Zero degrees is face on whereas 90 degrees is edge on Note that a 90 degree solution is not allowed because it corresponds to an infinitesimally thin model Item R10 Position angle in the plane of the sky An inclined spiral can be rotated in the plane of the sky to match the position angle of the galaxy A zero degree PA is usually parallel to the x axis in contrast to the standard definition of the PA of an ellipsoid model 8 3 5 Profile Truncation As discussed in Section 6 the profile truncation func tion can modify both the radial profile and the azimuthal shape of an object when the truncation is allowed to have
55. is the same as the individual light profile models see Figure 15c Item T2 Break radius For an inner truncation this corresponds to the radius where the flux is 99 of the amplitude of the original model i e at rout For an outer truncation this corresponds to the inner radius where the flux is 99 of the amplitude of the original model Item T3 Softening length Type 1 soften ing radius Type 2 This parameter is the length be yond Tpreak over which the flux drops to 1 of the flux normally at that radius Type 1 models have softening length as the free parameter so that the smaller the soft ening length value the sharper the truncation Whereas Type 2 models have softening radius so that the closer in value T2 is to T3 the sharper the truncation Item T9 Axis ratio optional The truncation function can have its own elliptical axis ratio parameter independent of the light profile see Figure 15 When T9 does not exist in the menu it takes on the value of the light profile model Item T10 Position angle optional The trun cation function can have its own position angle parameter independent of the light profile see Figure 15 When T10 does not exist in the menu it takes on the value of the light profile model Type a vs Type b truncations For spiral galax ies the truncation parameter normally follows the tip 26 and tilt of the coordinate system because it is generally more intuitive to e
56. it The reason is that the kernel should only be applied after you bin the PSF down to 1 time sampling So what do you do about the diffusion kernel if your data are drizzled to 2x sampled so you want to keep your TinyTim PSF on the same grid One obvious solution is to just transform i e interpo late the diffusion kernel the new plate scale and apply that If you decide to do this you can apply the kernel outside of GALFIT instead of inside since the data and the PSF have the same sampling factor This will make GALFIT run faster as it doesn t have to apply the same kernel each time Item F Bad Pixel Mask Sometimes one may want to exclude pixels from a fit This bad pixel map can be either a FITS file or an ASCII text file If the file is an ASCII it should have 2 columns listing x and y coordinates without a comma separator of all the bad pixels If you want to mark out an irregularly shaped region and have a list of polygon vertices you can run a program called fillpoly to create points inside the poly gon See GALFIT website on Frequently Asked Technical Questions to get a copy The output file can then be read directly into Item D If the dust map is a FITS image the bad pixels should have a value of gt 0 while good pixels have a pixel value of 0 Item G Parameter Coupling Parameter con straint coupling file ASCII is optional Parameters can be held fixed to within a certain range or can be cou pled
57. its own set of shape parameters The profile truncation is also a little unusual in the sense that it is a pseudo component in the GALFIT menu it is designated as an object component just like a S rsic or a Gaussian in contrast to Fourier or bend ing modes which only modify the component they im mediately follow This is done so that multiple compo nents can be truncated by the same functions of identical parameters without resorting to complicated constraint files For instance this allows a bar a spiral arm and a ring when represented as three individual components to be joined seamlessly when truncated at the transition region by just one function For this to work the com ponent being truncated has to be associated with a trun cation component and this is done by attaching one or both of the following to the end of a regular light profile component Item Ti Inner truncation by component num ber N The light profile is truncated in the inner region 25 by component number N This has the effect of making a ring out of a regular light profile whose outer region be yond rout is unaffected by truncation When an object is truncated in the inner region the flux normalization parameter changes to surface brightness normalized at T Tout aS Opposed to the total luminosity or central surface brightness This is done because the flux is near peak near that location thus is more intuitive Item To Outer truncation
58. ixels or larger than the image size it probably indicates that profile trun cation parameters are not meaningful Rather it more likely reveals the fact that there is a mismatch between the light profile model and the actual galaxy profile 7 RUNNING GALFIT There are two ways to run GALFIT by either provid ing a template file on the command line or through an interaction menu Providing a template file to GALFIT on the command line is the easiest way In the future an interaction menu may not be available Once GALFIT starts going it does not care when and how you quit To quit abruptly hit control c at anytime at your plea sure but note that the results will not be saved In this section I will describe several ways to run and quit 7 1 GALFIT Optional Flags When starting GALFIT on the command line several flags are available and the list of flags are summarized using the command gt galfit help The options are noskyest See Section 8 1 Item C skyped n skyrms n outsig ol See Section 8 1 Item P 02 03 7 2 The Template File GALFIT is completely menu driven and the menu can either come via a text file template easy this is the way to go or it can be filled in manually tedious not a good way to go The menu items will be more fully described in 8 Figure 17 below shows an example of the GALFIT input template file When you start GALFIT without a tem plate file you wil
59. l see a similar screen except the entries are blank You can enter everything interactively on the command line of GALFIT this can be quite tedious if you have a long object list but it is certainly possible 7 4 will show you how After the menu Item P the length of the list is flexible and depends on how many components you want to fit You can add or remove the number of components as you deem necessary In the input file things after hash marks are com ments and are always ignored by the program Blank lines are also ignored and the column alignment you see is optional purely aesthetic There is pretty much no error checking to catch problems in the input file so one should stick to the following format pretty closely For example in the input file do not modify 3 xxx note the spaces to look like 3 xxx bad spacing GAL FIT does not care how the columns are aligned vertical alignment is only for aesthetics as long as they are in the proper sequence The order of the rows is also ar bitrary for the image parameters and within each object block because each row has a unique ID except for the objects In fact the image parameters A P can appear anywhere in any row Everything else about the format should be pretty intuitive If there are errors in the in put file GALFIT may not complain about them and may simply crash 7 3 The Easiest Way to Run GALFIT Reading in a Template File 7 3
60. mage is not provided or the name is unrecognized then it is generated internally by GALFIT based on the GAIN or ATODGAIN and RDNOISE parameters taken from the image header see 2 1 If you let GALFIT do this the data image ADUs and the image gain should have units such that GAIN x ADU total electrons collected at each pixel The background sky is important for estimating the sigma image because it is a source of noise As far as statistics are concerned there is no distinction between thermal background due to the telescope environment and that due to a natural sky brightness To determine what the sky RMS noise is GALFIT first computes a filtered median after removing 20 outliers of bright and faint data points For this to work the image should in principle have have 60 of empty regions not occupied by a source of any kind From empty regions the RMS is computed and added in quadrature to the flux variance of the data after removing the estimated sky background Schematically therefore the RMS image is obtained in the folowing manner o y y Faata y sky GAIN osky y 33 In Eq 33 the readnoise term is absorbed by the esti mation of the sky RMS oxx z y in ADU so the RD NOISE parameter is not used The user has the option to provide an estimated sky pedestal and sky RMS by specifying on the command line respectively galfit skyped ADUs lt file gt galfit skyped ADUs skyr
61. mage or ASCII coord list G none File with parameter constraints ASCII file H 1 93 1 93 Image region to fit xmin xmax ymin ymax I 100 100 Size of the convolution box x y J 26 563 Magnitude photometric zeropoint K 0 038 0 038 Plate scale dx dy arcsec per pixel 0 both Display type regular curses both P 0 Options O normal run 1 2 make model imgblock amp quit INITIAL FITTING PARAMETERS For object type the allowed functions are nuker sersic expdisk devauc king psf gaussian moffat ferrer and sky Hidden parameters will only appear when they re specified CO diskyness boxyness Fn n integer Azimuthal Fourier Modes RO R10 PA rotation for creating spiral structures ee nn a a a a a m e m e e par par value s fit toggle s parameter description eee ee a a a Object number 1 A TRUE point source 0 psf Object type 1 50 00 50 00 11 position x y 3 18 000 1 total magnitude Z 0 Output option 0 residual 1 Don t subtract Object number 2 0 sersic object type 1 48 5180 51 2800 11 position x y 3 20 0890 1 integrated magnitude 4 5 1160 1 R_e half light radius pix 5 4 2490 1 Sersic index n de Vaucouleurs n 4 9 0 7570 1 axis ratio b a 10 60 3690 1 position angle PA deg Up 0 Left 90 F1 0 0001 0 0000 1 1 azim Fourier mode 1 amplitude amp phase angle F3 0 0001 0 000
62. mathematical bar radius rin the rotation angle reaches 20 degrees This definition is entirely empirical The above Figure shows a pure tanh rotation function where the rotation angle reaches a maximum out near r frout Beyond rout the rotation angle peaks out at ouz This function is multiplied with either a logarithmic or a powerlaw function to produce the desired asymptotic rotation behavior seen in more realistic galaxies see Section 5 CDEF 0 23 constant for bar definition 1 2 x CDEF 1 00001 2 Qout CDEF 2 Tout B 2 tanh A 3 Tout Tin r y Ar Ay circular centric distance 4 tanh rin rout incl OSF r 0 5x tanh 1 1 5 Tout B HYPERBOLIC TANGENT TRUNCATION FUNCTION The hyperbolic tangent truncation function tanh 2 Yc Tbreak soft q 0pa see Section 6 is very similar to the coordinate rotation formulation in Appendix A except for different constants that define the flux ratio at the truncation radii at r Tbreak the flux is 99 of the untruncated model profile whereas at r rsoy the flux is 1 With this definition Equation 7 is the truncation function B 25 1 98 bres 6 Tbreak Tsoft r P tanh ze Yc break Tsoft q Opa 0 5 x tanh le B B 1 7 Note that the radius r is a generalized radius as opposed to a circular centric distance i e one which is perturbed by Co bending modes or Fourier mod
63. ms ADUs lt file gt The sky pedestal here is an estimated value Even though this should in principle be the same as the sky parameter one is allowed to fit for the o image must be generated before fitting is done therefore does not have the benefit of hindsight Note that when providing the sky RMS the sky pedestal must also be provided The user also has the option to not allow GALFIT to estimate the sky pedestal by specifying galfit noskyest lt file gt This is not the same thing as setting skyped 0 on the command line When the sky is not estimated the sky RMS is determined from the image RDNOISE parame ter and added in quadrature sum with the noise of the flux pixel value scaled directly to electrons using the GAIN parameter This is useful if the user wants to see how much the uncertainty in the sigma image affects the fitting results To see the o image generated by GALFIT one can spec ify the following on the command line galfit outsig lt file gt GALFIT will then produce a file called sigma fits Details to keep in mind when providing a sigma image There are several important things to keep in mind if one intends to create one s own sigma image Indeed many of the odd behaviors reported back to me about GALFIT were by people who supplied their own version of the sigma image which were not appropriate in the sense of Equation 1 Such odd behaviors include simple fits that last for hundreds
64. n Item 3 For S rsic de Vaucouleurs and exponential disk this is the integrated magnitude of a galaxy For Nuker and the King profile this is the surface brightness mag square arcsec calculated using the pixel scale from Item K For fitting the sky this is the sky gradient in the Y direction Item 4 Scalelength of the fitted galaxy in PIXELS not arcseconds The scale length is measured along the semi major axis Item 5 For S rsic it is the concentration index n For Nuker it is the powerlaw a For King it is the truncation radius beyond which the fluxes are 0 For all other functions it is ignored Item 6 For Nuker it is the powerlaw 8 and for King it is the powerlaw a For all other functions this param eter is ignored Item 7 For Nuker it is the powerlaw y Item 9 The axis ratio is defined as semi minor axis over the semi major axis for a circle this value is 1 for an ellipse this value is less than 1 Item 10 The position angle is 0 if the semi major axis is aligned parallel to the Y axis and increases toward the counter clockwise direction 4 Best fit does not necessarily mean a good fit 24 Item Z If you want this model to not be subtracted in the final image set this to 1 If you want to subtract this model from the data set this to 0 When this parameter is set to 0 for all the objects you will get a residual image The default is 0 Note that this does not affect whether this component i
65. n The most intuitive flux nor malization for a truncated is the total luminosity Un fortunately both the total luminosity and the derivative of the free parameters with respect to the total luminos ity are especially time consuming to work out computa tionally and there are generally no closed form analytic solutions to the problem Therefore the alternative is to allow for different ways to normalize a component flux The user may choose whichever one is more intuitive given the situation and the science task at hand The default way depends on the truncation type e Inner truncation the flux is normalized at the break radius For a ring model this represents the outer radius of the ring near the peak flux e Outer truncation flux normalized at the center 17 Truncation Examples 50 0 50 50 0 50 50 0 50 Fic 15 Examples of truncation functions acting on a single component light profile of various shapes a Inner truncation of a round profile creating a ring b The truncation function can be modified by Fourier modes just like the light profile c The truncation function can be offset in position relative to the light profile d The truncation function can act on a spiral model e The truncation can tilt in the same way as the spiral f The truncation function can be modified by Fourier modes while acting on a spiral model g A round light profile is being truncated in the wing by a pentagonal Fourier mode 5
66. n also use the truncation function on a spi ral model on models with Fourier and bending modes and diskyness boxyness models some of which are shown in Figure 15d e f amp i When a truncation function acts on a spiral component it can do so either in the plane of the disk Type a or in the plane of the sky Type b e g radial b While the default is in the plane of the disk the parameters are more intuitive in Type b cases when the disk is tilted and rotated 6 3 Caveats about using the truncation function The use of truncation functions should be carefully su pervised because unexpected things can happen such as the size or the concentration index of a component can grow without bound This behavior is due to the fact that there are degeneracies between the sharpness of truncation and the steepness size of the galaxy There fore truncation functions should only be used on objects that clearly have truncations When two functions are joined by using a truncation function the cross talk region is located in between the two truncation radii it is worth bearing in mind the defi nition that at the break and softening radii the fluxes are 99 and 1 that of the same model without truncation respectively In other words the larger the truncation length the larger the cross talk region Therefore when one or more of the parameters rpreak break AT soft OF soft is either too small K few p
67. n roy Be yond Tout the asymptotic rotation rate is that of the logarithm function which has a winding scale radius 14 Logarithmic Tanh Spiral 500 400 300 0 deg 200 100 0 50 100 150 Radius Logarithmic Tanh Spiral 500 400 300 0 deg 200 100 0 50 100 150 Radius Fic 12 Logarithmic hyperbolic tangent spiral angular rotation functions a Examples of different bar radius and where the outer hyperbolic spiral radius is rout Tin 10 pix The lower horizontal dashed line shows the rotation angle at the bar radius rin b Examples with different bar radii and winding scale radii rws as indicated illustrating the degree of flexibility of the spiral rotation rate The rotation angle at rout is fixed to 150 degrees as shown by the upper horizontal dashed line The left most black curve is close to being a pure logarithmic function recasted so that at r 0 the rotation angle 0 0 of rws the larger the winding scale radius the tighter the winding Thus like the a tanh spiral the log tanh spiral rotation function also has 6 free parameters Bout Tin Tout Oe Aa Note that in terms of ca pabilities the a tanh function can often reproduce the log tanh function and more Therefore the a tanh is probably a more useful rotation function in practice Note that GALFIT does not allow for a pure logarith mic spiral because such a function has a negative infinity rotation
68. n statistics without adding a sky RMS term This is a useful way to see how sensitive the results are due to the accuracy of the o image as well as the crude sky determination The user can also tell GALFIT what sky and RMS to use by specifying galfit skyped value skyrms value lt filename gt If the user wants to supply a sigma image the user may override GALFIT see 8 1 GALFIT will then ig nore the RDNOISE GAIN and NCOMBINE informa tion But it is worth emphasizing that doing so is 3 advisable only for users who are clear about the notion of a sigma image Indeed one of the prob lems most commonly reported could be avoided if users simply allowed GALFIT to create an internal sigma im age instead of providing one without making sure it is appropriate as explicitly defined by Equation 1 GAL FIT is not very sensitive to the correctness of a sigma image as long as it obeys the Poisson statistics even roughly Even if the normalization of the sigma image is off greatly only the y calculation is affected but not the convergence on a solution Most mistakes in the sigma image are pretty glaring the sigma images have zero or negative values have the wrong pedestal level are not Poisson in scaling or do not look anything like the data If you feel you ought to provide a o image please first read Section 8 1 and refer to the GALFIT website on Fre quently Asked Questions and Advisory Otherwise it gen
69. nd easiest way to run GALFIT is to have a pre formatted template file like the one shown in Figure 17 also look for the EXAMPLE INPUT file in the GALFIT source directory Skip to 8 to see what the menu parameters mean In the galfit EXAMPLE directory there is a simple example that one can try out immediately After GALFIT has been compiled and aliased linked to run the example go into that directory and simply type galfit galfit feedme In fact please do so now before reading any further If there is a problem at this stage now is the time to re quest assistance If the example runs properly the resid ual image imgblock fits 3 should look flat at the center where there used to be a galaxy One should display imgblock fits 1 imgblock fits 2 and imgblock fits 3 and examine their image headers to understand what infor mation is produced Note that imgblock fits 0 is blank The example only fits one S rsic model to a real galaxy It is simple enough that just one will remove all signifi cant residuals down to the noise level In general if the galaxy is more complex one can add more components to reduce the residuals There is no limit as to the num ber of components or the mix of functional types one can use in a fit For this particular example however adding more components is not useful because a single S rsic al ready removes all the galaxy light adding another model will cause one of the components to be highly su
70. ndation for using Fourier modes is to first run GALFIT without them Once a so lution has been found the Fourier modes may be used to improve the fit and to quantify the degree of deviation from an optimum model Item FN Fourier mode amplitude and phase angle Each Fourier mode has two free parameters the amplitude and phase angle as given in Equation 22 The mode amplitude is in units of the fractional radius whereas the phase angle has units of degrees The phase angle is zero in the direction of the semi major axis of the best fitting ellipse and is reported only in the cardinal range To activate Fourier modes one can specify something like the following which enable the 3rd and 2nd Fourier modes Fourier mode m 3 Fourier mode m 2 Note that holding the amplitude fixed to 0 for any mode will effectively turn off that Fourier mode making it dis appear from the menu One can employ an unrestricted number of Fourier modes and some may be skipped However only the first 6 10 modes are useful The higher the mode one uses the more likely that the fit is sensitive to neighboring objects 8 3 3 Bending Modes Bending modes allow the possibility for the model to shear and bend like a banana see 5 Figure 3 which are otherwise not possible to model using Fourier modes Item BN Bending Modes The free parameters are the model amplitude am defined in Equation 26 The bending modes appear like the following in
71. ng radius radial2 Sometimes instead of softening length Arsott it is more useful for the fit parameter to be a softening radius fsoft especially when one desires to hold the parameter fixed That is also allowed in GAL FIT as a Type 2 truncation function designated e g as radial2 The default option does not have a numerical suffix Inclined default radial vs Non inclined radial b Truncations A spiral rotation function is an infinitesimally thin planar structure Nevertheless it should be thought of as a 3 D structure in the sense that the plane of the spiral can be rotated through 3 Eu ler angles not just in position angle on the sky When a truncation function is modifying a spiral model it is therefore sometimes useful to think about the truncation in the plane of the spiral model When Fourier modes and radial truncations are modifying a spiral structure the default radial is for the modification to take place in the plane of the spiral structure However there are some instances when that may not be ideal for some rea son e g a face on spiral may actually be ellipsoidal In those situations one can choose radial b which would allow a truncation function to modify the spiral structure in the plane of the sky even though the spiral structure can tip and tilt as needed And yes the truncation function can be Type 2b i e radial2 b as well Flux normalizatio
72. nts e g bulge disk bar spiral ring etc The solution here is one which finds the best compromise between the substructures so that neither model compo nent may represent any physical feature in particular Here the notion that one is performing bulge to disk decomposition with two components is a flawed prior Another common situation is when a two component fit might settle on features which are closest to the initial parameter guesses because features like a ring bar or spiral are spatially localized This situation is often re ferred to as a local minimum solution and it mostly hap pens when some of subcomponents are strongly localized features However it is important to keep in mind that even if a code can break out of such a local minimum the meaning would still be vague because the model repre sents a compromise of sorts Figure 16 top shows such a situation where the prior is a 3 component fit intended to extract a bulge disk bar However even with 3 compo nents it is clear that at least the bulge component bears no visual resemblance to a bulge and is instead strongly affected by the spiral residuals Contrasting that to Fig ure 16 bottom where spiral structures are fitted away the bulge comes out more sensibly to q 0 8 and n 1 Another situation where the prior is inappropriate is when one tries to fit more components than is present in a galaxy e g a 2 component fit onto a one component galaxy Becau
73. nvision truncation in a face on con figuration However if for some reason it is easier to conceive truncation in the plane of the sky instead of in the plane of the disk then the Type b truncations are allowed All the parameters thereby refer to the values as measured in the plane of the sky rather than in the plane of the disk For non spiral galaxies there is no difference between Type a and Type b As shown in Figure 15 the truncation function as a pseudo component can be modified by disky ness boxyness Fourier and bending modes These terms can be added onto the end of any truncation function component and identically affect all profiles that are linked to it 9 THE GREEN POP UP Garrit WINDOW If Item O is set to both a green GALFIT window will pop up to indicate that the fit is ongoing At any time you can quit output a menu file pause the fit or change the number of iterations by hitting the keys q o p or n respectively in the green pop up window At the first convenient moment i e after the current iteration GALFIT will do what you asked The pop up window has memory so if you hit a key multiple times e g out of frustration it will be reissued at the earliest convenience To get rid of the memory kill the green window The output menu file option o is simply a pre formatted file that you can feed back into GALFIT It stores parameters in the current fit iteration If
74. of iterations wild swings in parameter values between each iteration extremely large small 2 values or convergence on solutions that make no sense These issues may be avoided if one keeps in mind the following when supplying a sigma image 21 e Visual Inspection Before using a sigma image please display it to see that it bears some resem blance to the data modulo weird scaling since af ter all the o image is derived directly from the data It is known that some algorithms e g Mul tidrizzle output a weight image that is either an exposure time map or a map of the number of images combined Either kind of those weight image is incorrect and has been known to cause GALFIT to go haywire e Units The o image should have the same units as the input data image If the data pixels are in counts sec then so must the weight image be in counts sec Otherwise the x2 value that GALFIT outputs will not make much sense even if it might not affect the solution or how GALFIT converges on it e Noise The o image is a noise map of the data However if one thinks about it it usually ought not itself be noisy Unfortunately when one creates a sigma image from a noisy image the map also looks noisy There is not much one can do about this It is important to keep in mind that often one should not have to provide his her own sigma image if the GAIN and RDNOISE parameters are in the image header and ADU x GAIN
75. onents b a composite profile made up of an n 4 nucleus truncated in the wings and an n 1 truncated in the core with truncation radii r 10 and r 20 Note that the hump in the summed model would give rise to a ring in a 2 D model variations in more detail and Section 8 3 5 will discuss how these options are specified in the GALFIT input file see also EXAMPLE INPUT Parameter sharing In the most general form each truncation function has its own set of free parame ters Y 1preak A sott q Opa However by default the z y q and Op are tied to the light profile model and are activated only when the user explicitly specifies a value for them Radial radial vs Length length or Height height Truncations The most use ful type of truncation is one which has radial symme try to first order i e where it has a center an ellip ticity an axis ratio However in the case of a perfectly edge on disk galaxy edgedisk model an additional type is allowed that truncates linearly in length or in height For instance a dustlane running through the length of the galaxy has an inner height truncation For the edgedisk profile GALFIT also allows for a radial truncation like with all other functions The one draw back to height and length truncations is that they cannot be modified by Fourier and higher order modes like the radial truncations Softening length radial vs softeni
76. parate the central point source from the host galaxy For decomposition to work well the PSF must be over sampled and there has to be a good match between the PSF model and the data 30 14 15 PSF There is no reliable solution if the mismatch is great For situations where the PSF is undersam pled One should either generate an oversampled PSF somehow or one should broaden the image out to Nyquist sampling before doing the analysis How to tell if a source is unresolved If one wants to test whether a compact source is a true point source one can convolve a narrow Gaussian with a PSF However make sure FWHM gt 0 5 pixels or else GALFIT may stop converging altogether Usu ally it s a good idea to hold the Gaussian FWHM fixed to 0 5 pixel Once a solution is found fit it again by allowing the FWHM to vary Make sure the exposure times are what you think Make sure the image header has the correct ex posure time parameter EXPTIME and value so the initial guess for the flux is not several hundred times off 16 Watch out for Nuker parameters For the Nuker profile make sure the parameters a 7 do not have the same values this can easily cause singular values and force the program to quit Initially one s best bet for a and 3 parameters is somewhere between 0 and 3 and 0 to 1 for y To get a better feel for the behaviors of the parameters take a look at Lauer et al 1995 I hope these tips will h
77. ppressed or be shifted out of the image completely Either one of these things happening will then make GALFIT crash Even though this is not a graceful way to exit the op erating philosophy is to provide no solution over a false solution when the problem is not well posed numerically After GALFIT finishes running it will produce three output files called galfit 01 fit log and img block fits To understand these files please see Sec tion 10 You now know how to run GALFIT The rest of the document will explain the parameters in the input and output files Please take a look at EXAMPLE INPUT which contains examples of things that can be done in GALFIT and visit the GALFIT website for answers to questions that may already have come up by now 3 LEAST SQUARES MINIMIZATION AND STATISTICS Least Squares Minimization GALFIT is a least squares fitting algorithm of the non linear type and uses a Levenberg Marquardt algorithm to find the opti mum solution to a fit Non linear simply means that the parameters being fitted are not only coefficients am plitude to functions but can be involved in exponents of powerlaws in fractions etc Non linear analysis re quires iterating to find the best solution whereas linear minimization involves a matrix inversion As with all least squares algorithms GALFIT deter mines the goodness of fit by calculating x and comput ing how to adjust the parameters for t
78. produced an output the entire solution may have been unreliable One must re fit the galaxy and restart fix that or other parameters to something sensible A solution should never have a parameter enclosed within stars When GALFIT finishes fitting it will also output a file called galfit N N that contains all the best fit parame ters NN is a value that keeps increasing so it will never overwrite the previous fit Note that if there are missing numbers in the galfit NN sequence the gap will even tually be filled One can modify this file and feed it back into GALFIT to refine the fit Lastly GALFIT will output a data image block which is described in Item B of 8 1 The final fit parameters and a few important input parameters are also placed into the FITS header of image 2 for convenience Like in fit log parameters whose values are held fixed are enclosed in square brackets and constrained parameters are in curly braces If a user is running GALFIT in a batch fitting mode us ing an external wrapper script GALFIT will return error number 1 if it crashes otherwise it ll output a 0 This code number can be intercepted by the calling script for example errno system galfit parfile The calling script can then decide how to proceed i e whether to move on to the next object to fit this object manually or to redo the fit by modifying the input file Also in the header of image fits 2 GALFI
79. profile is that the nuclei of many galaxies appear to be fit well in 1 D see Lauer et al 1995 by a double powerlaw However use caution when interpret ing this function because for example a low a value a S 2 can be reproduced by simultaneously a high 7 and a low 8 compare Figure 5c with the other two pan els which is a serious potential for degeneracy In all there are a total of 9 free parameters x Y Hb Ty Q B Y 4 Opa Hb 2 5 logio mag zpt 17 The Edge On Disk Profile Ifa flattened disk galaxy is viewed edge on the projected surface brightness dis tribution takes on the following form X r h o K sech 18 where No is the surface brightness profile rs is the major axis disk scale length and h is the perpendicular disk scale height and K is a Bessel function The flux pa rameter being fitted in GALFIT is the central surface brightness Xo Ho 2 5 logio s mag zpt 19 where texp is the exposure time from the image header and Az and Ay are the platescale in arcsec which the user supplies Item K in the GALFIT input file Note that if the disk is oriented horizontally the coor dinate r is the x distance as opposed to the radius of a 20 10 0 10 20 X Fic 6 Generalized ellipses with a axis ratio q 1 and b axis ratio q 0 5 pixel from the origin There are 6 free parameters in the profile model zo yo Xo Ts hs and Opa The PSF P
80. r colored lines differ only in the concentration index n as shown by the numbers The dashed line shows a Gaussian profile of the same FWHM where FWHM 2 3540 The 6 free parameters of the profile are x y the total magnitude FWHM q and Opa The Modified Ferrer Profile The Ferrer profile Figure 2 has a nearly flat core and an outer trunca tion The sharpness of the truncation is governed by the parameter a whereas the central slope is governed by parameter 6 Because of the flat core and sharp trun cation behavior it is often used to fit galaxy bars and lenses U r Xo 1 ea 11 The profile is only defined within r lt rout beyond which the function has a value of 0 The 8 free parameters of the Ferrer profile are x y central surface brightness Tout Q p q and Opa The Empirical Modified King Profile The em pirical king profile Figure 3 is often used to fit the light profile of globular clusters It has the following form El son 1999 1 J renee 1 1 a la Ter UF T A12 The standard empirical King profile has a powerlaw a 2 In GALFIT a can be a free parameter In this model the flux parameter to fit is the central surface brightness expressed in mag arcsec form i e po see D r Zo h The Nuker Profile Intensity Fic 5 The Nuker profile The black reference curve has parameters rp 10 a 2 8 2 7 Radius 0 and J 100 For the other colored lin
81. rofile For unresolved sources one can fit pure stellar PSFs to an image as opposed to narrow functions convolved with the PSF The PSF function is simply the convolution PSF image that the user provides in Item D of the GALFIT menu hence there is no pre scribed analytical functional form As the point spread function this is the only profile that is not convolved The PSF has only 3 free parameters e Ye and total magnitude Because there is no analytical form the to tal magnitude is determined by integrating over the PSF image and assuming that it contains 100 of the light If the PSF wing is vignetted there will be a systematic offset between the flux GALFIT reports and the actual value If one wants to fit this function make sure the in put PSF is close to or super Nyquist sampled The PSF shifting is done by a Sinc Kaiser interpolation ker nel which can preserve the widths of the PSF even un der sub pixel shifting This is in principle much bet ter then Spline interpolation or other high order inter polants However if the PSF is under sampled aliasing will occur and the PSF interpolation will be poor If the PSF is undersampled it is better to provide an oversam pled PSF if possible even if the data is undersampled With HST data this can be done using TinyTim Krist amp Hook 1997 or by combining stars GALFIT will take care of rebinning during the fitting Note that the alternative to fitting a PSF is
82. s optimized just whether or not it shows up in the output images This is useful for showing subcomponents in the residual image in a multi component fit 8 3 Non Classical Fitting Parameters Non classical parameters allow GALFIT to break from ellipsoidal axisymmetry They are absconded from view if they are not used in the analysis The following pa rameters are non classical diskyness boxyness Fourier modes bending modes coordinate rotation and trunca tion Another reason for keeping the non classical pa rameters from view is to emphasize the higher order na ture of these parameters This means that it is often nec essary to first let GALFIT converge on a classical ellip soidal solution before turning on the non classical ones In other words the simplest and most correct way to fathom these parameters is to consider them as higher order perturbations on the best fitting ellipse even if the perturbations can be quite large In the menu or template file the non classical parameters usually should come at the end of the component that one is inter ested in modifying The only exception is the truncation model which can appear anywhere in the object list and behaves like a separate component Note that a single component model can be altered by any one or all of the following functions simultaneously For example one can modify an ellipse into a spiral which can be perturbed by Fourier modes and truncated either in the
83. se few galaxies are modeled perfectly by a single analytic function the solution one obtains may only reflect the degree of mismatch between the model profile and the data In summary when a prior is bad restarting the fit from different initial conditions can yield an equally bad and different solution no amount of clever fine tuning or starting initial conditions can rescue the situation from ambiguity In that sense it is important to understand that bad solutions due to flawed priors are not true nu merical degeneracies The solution is to apply better pri ors and sometimes this means using more components rather than fewer Indeed often a more stable solution can be achieved by using more components if they can remove all the prominent features as for the case of Fig ure 16 In contrast for true numerically degenerate solu tions no amount of adding new components will produce a more meaningful solution 11 2 What are Bad Solutions Caused by Numerical Degeneracy or Local Minima in the xy There are situations in galaxy fitting where there are true problems with numerical degeneracy and local min ima This happens when multiple parameters can pro 28 duce similar features For instance in the Nuker profile Equation 16 when ry is sufficiently small when there is a profile mismatch or when the data are noisy the parameters a 8 7 are truly numerically degenerate be cause there is an infinite number of ways to ac
84. sian frame as opposed to a length along the curvature Coordinate Rotation I Powerlaw Hyperbolic Tangent a tanh Sometimes the isophotes of a galaxy may rotate as a function of radius as in the case of spiral galaxies To model the light profile it is now also possible to allow for coordinate rotation in GALFIT GALFIT allows for two types of coordinate rotation func tions the powerlaw spiral a tanh and the logarithmic spiral log tanh Both of these are coupled to the hyper bolic tangent in order to potentially generate a bar that extends into the center The exact functional form of the rotation function is lengthy see Appendix A but the schematic functional dependence of the powerlaw spiral on the parameters is given by the following a e r ja Oout tanh rin Touts Pinal gay r x E 7 1 2 Tout 27 Figure 9 shows a hyperbolic tangent rotation function for several different bar parameters left and a combi nation of bar parameters and the asymptotic powerlaw slope a right where r is the radial coordinate system Oout is the rotation angle roughly at rout The bar radius Tin is defined to be the radius where the rotation reaches roughly 20 degrees This angle corresponds fairly closely to our intuitive notion of bar length based on examin ing the images and is not a rigorous physical defini tion The inclination inci is the line of sight inclination of the disk where inci 0 deg is face on and Oing
85. so that the seeing does not affect your galaxy profile outside of the box something like 20 or more seeing diameters depending on how extended the PSF wing is Item J Magnitude Zeropoint The magnitude zeropoint is used to convert pixel values and fluxes into a physical magnitude by the standard definition mag 2 5log ADUs tes mag zpt 34 The exposure time is taken from the EXPTIME image header without prompting the user So please make sure the EXPTIME header reflects how the data pixel have been normalized Unfortunately it is rather common for the EXPTIME to show the total integration time but for the image ADUs to be normalized to one second One reason why this may happen especially in infrared data is that not all pixels may have the same exposure time If the EXPTIME keyword is not found GALFIT assumes the exposure time to be 1 second If you want GALFIT to generate a a x y image internally and the ADUs are in counts sec please multiply EXPTIME back to the image and update the EXPTIME header accordingly Item K Plate Scale The plate scale should be in units of arcseconds and is used only to convert fluxes into surface brightness units mag arcsec for the King and the Nuker profiles see Eq 35 Note that the sizes of objects re rs ra and FWHM in GALFIT are quoted in pixel units rather than in arcsec units ADUs p 2 5logi9 Cece exp mag zpt 35 Item O Intera
86. still are just based on personal experience 1 It is better to work with images where the pixels are in counts units rather than counts per second Now a days it is common for reduced images from telescopes to have pixel units of counts per sec ond However for image analysis it is better to work with units in counts because it is easiest to known when the sky parameter is fit incorrectly In galaxy fitting the sky parameter is one of the most important parameter to measure accurately A wrong estimate by even a count or two can lead to significantly wrong total luminosity concentra tion and size of a galaxy When the image is in counts per second a significant error in the fit of the sky may be hard to detect when it is divided by the exposure time Check to make sure the sigma image is correct If the convergence seems a bit weird large changes in parameters that do not seem to converge toward any particular answer make sure that the sigma image is reasonable If you are providing your own sigma image into GALFIT please take a look at it first to see if the objects show up in that image If they do not it is not a sigma image Please see the GALFIT page regarding why the sigma image is important to get right Start simple build up complexity When fitting multiple components start with single or two com ponents first then add more components based on need arising from visual inspection of the residuals Al
87. the following azimuthal functions For example an ellipse can be modified by bending modes Fourier modes diskyness boxyness and a spiral rotation function the combination of which would result in a rather odd looking spiral structure Generalized Ellipses The simplest azimuthal shape in GALFIT is the traditional generalized ellipse This is the starting point for all GALFIT analysis no matter how complex the final outcome is one should always begin by fitting an ellipsoid on top of which complications are introduced The radial coordinate of the generalized ellipse is de fined by r z y zad t Co 2 rengs 21 Here the ellipse axes are aligned with the coordinate axes and e Yc is the centroid of the ellipse The el lipse is called general in the sense that Co is a free parameter which controls the diskyness boxyness of the isophote When Co 0 the isophotes are pure ellipses With decreasing Co Co lt 0 the shape becomes more disky diamond like and conversely more boxy rectan gular as Co increases Co gt 0 see Figure 6 Note that Co will not appear in the menu unless the user explicitly asks for it see EXAMPLE INPUT The major axis of the ellipse can also be oriented to a position angle PA not shown Thus there are a total of 4 free parameters x0 Yo 9pa in the standard ellipse and one Co for diskyness boxyness parameter Co should not be used until a best fitting
88. the pixel values into electrons and the readnoise is in units of electrons See Section 3 2 be able to try out complex applications to hone intuition without being mired in trying to figure out what different program options do With the basic hand shakes out of the way the quickest way to learn about GALFIT is to read up to Section 2 run the first example provided in the galfit EX AMPLE direc tory and experiment with it The remaining document will then explain how GALFIT determines the goodness of fit 3 what functions are available to fit in GALFIT 4 5 6 how one can run GALFIT using an interactive menu 7 which one actually never needs to do items in the GALFIT menu 8 which is the most important section Section 9 will explain how one can interact with GALFIT through a green window once it gets going use ful but not crucial This will give the user some control over when to quit which is sometimes nice Once the fit is done the algorithm will produce several output files 10 Then Section 11 tries to offer some hints on how to deal with difficult situations Lastly for frequently asked questions that are not an swered by this document please visit the GALFIT web site which is permanently maintained at there is no space in the address http users obs carnegiescience edu peng work galfit galfit html 2 QUICK START RUNNING Gatrit FOR THE VERY FIRST TIME ON THE EXAMPLE The quickest a
89. to fit a Gaussian with a small width i e 0 4 0 5 pixels which GALFIT will convolve with the PSF This is generally not advisable if a source is a pure point source because convolving a narrow function with the PSF will broaden out the overall profile even if slight The convergence can also be poor if the FWHM parameter starts becoming smaller than 0 5 pixel However this technique can still be useful to see if a source is truly resolved The Background Sky The background sky is a flat plane that can tilt in x and y Thus it has a total of 3 free parameters The pivot point for the sky is fixed to the geometric center xo yo of the image calculated by Npic 1 2 where npig is the number of pixels along one dimension The tip and tilt are calculated relative to that center Because the galaxy centroid located at x y is in general not at the geometric center xo yo of the image the sky value directly beneath the galaxy centroid is calculated by dsk dsk sky x y sky xo yo x x0 T y yo i x y 20 5 THE AZIMUTHAL PROFILE FUNCTIONS The previous section illustrates the kind of radial pro files that are available to fit galaxies However to gener ate the shapes of a galaxy requires the use of azimuthal functions which control what a model component looks like in the sky projection e g elliptical disky boxy ir regular curvy or spiral Each profile component can be modified by any one or all of
90. truncation function h A round light profile is being truncated in the inner region by a triangular function Fourier mode 3 and in the wing by a pentagonal function i A 3 arm lopsided spiral light profile model is truncated in the wing by a pentagonal function and in the inner region by a triangular function e Both inner and outer truncation same as the case for Inner truncation However there are many situations when the default is not desirable Instead the user can choose the radius where the flux is normalized using the same scheme dis cussed in the introduction to Section 4 To be pedagogi cal we explicitly show here the normalization for just the S rsic function and allow an user to infer the analogous relation for other functions e function default e g sersic nuker king etc See above e function1 flux normalized at the center r 0 i e Xo A function which is given originally by forig 1 is now defined as fmoa r Ty fae For the S rsic profile i e called by sersicl the profile function is redefined in the following way written explicitly AA Tea exp x For the Ferrer Gaussian King Moffat this corre sponds to functions as written in Section 4 18 e function2 flux parameter is the surface brightness at a model s native size parameter parameter 4 of the light profile model For a S rsic profile called by sersic2 this means the eff
91. unning GALFIT the Hard Way Note you can bypass this entire section and go on to 8 1 if you already have your own input file The easiest way to run GALFIT is to directly edit a parameter file and feed it into GALFIT on the Unix command line as in 7 3 1 You can run GALFIT entirely via the GALFIT command line The one possible benefit of using the interaction menu is to check on your input file format which has been causing GALFIT to crash for no apparent reason If so here are the things you can do on the command line Re displaying the Menu To display or redisplay the menu after new changes have been made hit r Adding New Objects Changing Initial Parame ters Deleting Objects To add a new object on the command line hit 0 or N followed by the name of the model you want to add For example when you get the GALFIT prompt type O devauc will add a de Vaucouleurs function Initially all the pa rameters are set to 0 which you can then change To change the value of an item enter the following on the GALFIT command line in consecutive order sep arated by one or more spaces only 1 the item number alphabet without the right parenthesis 2 the initial value then 3 optionally followed by whether to hold that param eter fixed or not during the fit To hold a parameter fixed use the value 0 to fit use 1 Here are 3 examples that produce some entries shown in Figure 17 a v fits See Item A
92. values If the re sults do not make intuitive sense often times look ing at the images of subcomponents individually will reveal quite easily what GALFIT sees in the image Use the following command to produce sub components galfit 03 lt filename gt Alternatively one can set parameter P to 3 See Item P in 8 1 Why do the centroids reported by GALFIT not match up to object centers in an image If the centroid reported by GALFIT seems to be off set from the galaxy peak position then the PSF image is not centroided correctly The absolute po sition parameter depends on how well the convolu tion PSF is centered in the PSF image Nominally the PSF should be centered on pixel N 2 1 for even N number of pixels along a side and N 2 0 5 for odd number of pixels Bin down the data to save iterating time If a galaxy covering hundreds of pixels on a side is hard to fit try reducing the fitting region or bin ning down the data image to something more man ageable Once a good fit has been obtained redo the fit on the original image fitting region This a handy trick for fitting many large galaxy images because it speeds up the analysis and allows one to explore a larger parameter space or combination of components Be aware of PSF sampling and mismatch High contrast image analysis e g quasar host decom position is one of the most difficult analysis to do Often times PSF mismatch makes it difficult to re liably se
93. ways start with ellipsoidal models first When fitting Fourier modes spiral arms or other things more complicated always start out with simple el lipsoids Then take the best fit solution and add complexity to those One should never introduce Fourier modes until the very last step For in stance when fitting a spiral galaxy using coordi nate rotation with the exception of the m 1 mode I always find the best solution without Fourier modes first Once the spiral component locks on I then introduce Fourier modes to cre ate more realistic looking arms Keep a sharp eye out for small axis ratio q lt 0 1 or size r S 0 5 pix parameters in the model When either the size parameter or the axis ratio of a model grows too small at any time while GAL FIT is iterating it will not be able to converge ef fectively All the parameters would appear to be frozen even when the code continues to iterate The reason this happens is that small sizes and axis ratios often mean that the flux of the model can fit within a single pixel in one or all directions therefore there is insufficient gradient information for GALFIT to converge Note that GALFIT often will not crash when this happens The code will just seem to converge extremely slowly To solve this problem hold the problematic size or axis ra tio parameter fixed to a larger value until the other parameters have converged then release it to see whether it continues to mis
94. with back ground removed is then added in quadrature with the background RMS to determine the Poisson noise at each pixel Finally this image with units of electrons is con verted back into the same units as the data image i e in ADU There is one subtlety in this process related to the num ber of images used to create the data image because the data image might have been created by averaging or summing several subexposures If the subexposures were averaged into a final image NCOMBINE equals the number of images used in the average and the GAIN and RDNOISE need to be that for a single readout GAINp RDNOISE The RDNOISE parameter should have a unit of electrons On the other hand if the subex posures were summed then NCOMBINE should be set to 1 the GAIN value should be that for a single image GAINo and the RDNOISE should be an effective read noise often Nimages RDNOISEp When creating a o image the sigma at each pixel comes from both the source and from a uniform sky back ground summed in quadruture The sigma of the back ground is estimated directly from the RMS fluctuation in regions where there are no objects Sky estimation is automatic and though rather crude is nevertheless of ten sufficient The user can turn off sky estimation by telling GALFIT galfit noskyest lt filename gt When this happens the o image is obtained by scaling the image pixels as is directly into electrons based on Poisso

GALFIT USER`S MANUAL ABSTRACT Galfit is a tool for extracting

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