CHAPTER 14 GALAXY PROFILES AND PARAMETERS 14.1 INTRODUCTION In this chapter we describe how to obtain the surface brightness distributions and the seeing-free photometric and structural parameters of elliptical galaxies which may or may not overlap, from two-dimensional images. The modules can also be used to model star images which may or may not overlap, as well. The surface brightness distributions are averages around elliptical contours expressed as a function of semimajor axis. The central location, inclination, and eccentricity of each elliptical contour are allowed to be independent of each other and can be solved for as a function of semimajor axis by the method of Fourier coefficients if desired. Thus one can look for twisting of isophotes and variations of ellipticity. Alternately, these quantities can be held constant and simple contour averages made. This approach is less desirable, but is sometimes necessary if the center of the galaxy lies off the frame. The photometric and structural parameters, e.g., central surface brightness, effective surface brightness, Hubble radius parameter, effective radius parameter, etc., are derived from nonlinear least squares fits (with image smearing taken into account) of one-dimensional files representing the contour averaged surface brightness. The surface brightness distribution of an isolated galaxy is easily solved for, however the images of most galaxies are contaminated by overlapping images of nearby stars and other galaxies, especially if one is working in a rich cluster of galaxies. Bad pixels and ghost images must also be dealt with. Briefly, one proceeds with the following recipe, which is explained in more detail in the later sections of this chapter. The editing options EC (EDITCIRCLE), EP (EDITPOINT), and ER (EDITRECT) allow one to remove bad areas of the 2-dimensional image (SAD file) when starting the analysis. We use these options to edit out everything but the brightest galaxy, or the galaxy of interest. Then by using the options EA (ANNULUS), PR (PROFILE), and/or SG (SMOOTHGAL) (described in more detail below), we arrive at a first approximation to the two-dimensional surface brightness distribution of that galaxy. By subtracting this first approximation model with option FG (FAKGAL), other objects which were contaminated by the light from this galaxy can now more accurately be modeled by further use of these same options. Stars and ghost images are similarly modeled and subtracted. A helpful option at this stage is SA (SADMASK), which operates with with a mask file to quickly remove areas know to be bad or which contain objects in the frame, too small to be modeled. In general, one proceeds from the brightest object to the fainter ones. You may not wish to model the very faintest galaxies since less accurate surface brightness parameters and radius parameters will result. However, these fainter objects are sometimes located where their modeling and subtraction will improve the results for another more desirable galaxy. The fainter objects are still useful for obtaining aperture derived Page 2 integrated magnitudes with option BB (BBEN). Once the initial models for the objects have been determined and subtracted, the frame should look reasonably clear except for the unmodeled fainter and less offensive objects. The first object can be remodeled in a second iteration. Severely overlapping images may require several iterations before a final model is obtained. The surface brightness distribution as derived from iterative modeling is still affected by atmospheric seeing. In order to derive the actual galaxian surface brightness parameter and radius parameter, this smearing must be accounted for. In the nonlinear least squares fitting routine, RG (RADGAL), a stellar profile is used as a smearing function to convolve the fitting function before the actual fit is made. Finally, the photometric parameters are calibrated by placing them on some photometric system, and the structural parameters are transformed to units of arc seconds. These conversions operations are done with options ED (EDITDATA1) and E3 (EDITDATA3). Galaxies' models too faint to be accurately fit with RG can be integrated to yield magnitudes with option E3, command I. Galaxies too faint to be modeled can be photometered with option BB. 14.2 CONSTRUCTING A FINDING CHART Before any modeling work on a frame can begin, it is helpful to have a finding chart. Option AC can be used here to produce a contour plot. However, if the flat fielded exposure of the frame of interest contains an enormous galaxy which overlaps other galaxies, it may be necessary to subtract out this galaxy before constructing the contour plot. Once the frame has been selected, use option GA to determine the sky level and the sigma of the exposure in a blank area. The lowest contour intensity level should be set at approximately the sky plus 7 sigma. The hightest contour level should be set equal to the center of the brightest interesting object. Intermediate contour levels, say 4 of them, should be spaced in a geometric progression between the lowest and highest levels. Some trial and error may be necessary before finding the right intensity levels. Experiment on a small area of the map, as this option is slow. Write the plot to a file but do not put a frame around the plot. The plot file can then be sent to one of the supported plot devices. Observe the offsets, scale, and rotations recommended in Chapter 15 of this volume. The option FI (FIND) can be used to automatically create a list of objects and their positions in the frame, or one can do this manually with option CT (CENTR). 14.3 CONSTRUCTING A MASK FILE When operating on the galaxy images in a frame, one will find that certain areas need to be repeatedly excluded at each stage of the iterative process. These areas might be stars that have saturated, bad pixels, cosmic ray events, and faint galaxies that are not to be modeled and subtracted. It is thus convenient Page 3 to have a mask file which can quickly set those areas to zero in the working frame. At some point, one can edit all such areas in a frame and set them equal to zero with the options EC (EDITCIRCL), EP (EDITPOINT), and ER (EDITRECT), for circles, single pixels, and rectangles, respectively. This is then used repeatedly as a mask frame in the option SA. 14.4 MODELING THE GALAXIES AND STARS One begins this iterative procedure by making a first approximation to the brightest object in the field. In order to do this in a way which is reasonably free of contamination, one should edit out areas of the less brighter objects which overlap the program object. The editing options EC, EP, and ER can be used for this purpose. If a mask file has been constructed, that can be used with option SA. Keep a copy of the original file of course. The preferred way to make the model is with option PR (PROFILE). See the file PR.DOC for an example of how to do this. Option PR will yield a character file of type 1 with columns of values for distance along the major axis, x and y central location of each elliptical contour, inclination, eccentricity, and surface brightness. It also integrates the surface brightness, but option RG should be used for the final integrated value. An alternative way to obtain some of the information that option PR provides, is available through the option EA (ANNULUS). This option simply uses fixed values of central location, inclination, and eccentricity for each contour. It does not solve for these quantities; they must be input by the user. Option EA is useful when an object lies off the edge of the frame and no detailed solution for the model is possible. For each model, one should estimate a sky level which needs to be subtracted from the file when writing data back to the frame at latter stages in the modeling. To do this, display the surface brightness values in a plot on a graphics terminal. One is prompted for this plot in both option PR and EA. Press R and the crosshairs will appear. Position the crosshairs at the left and right boundaries of the section of the plot to be replotted, pressing the <CR> after each position. A sky value can be read by pressing C to turn on the crosshairs, and then the <CR> to read a value. Press Q to turn off the crosshairs. The plot will also indicate if certain values at large distances from the center, are bad. If this is the case, use the EDT editor to delete those outer contours. Option SG (SMOOTHGAL) is useful for recomputing the run of surface brightness with distance from the center of an object. The operation which it provides is available in option PR, but it is possible that the user may wish to smooth the outer profile parameters by polynomial fitting at some later time, without going throught the entire solution again. This option operates on the 2-dimensional SAD file and the character file containing the previous solution for a given object. Another use of the option is to recompute the surface brightness distribution after some change has been made to the SAD file, such as removing addditional contamination. Here again, a saving results by not having to run option PR over Page 4 again. Although options PR, EA, and SG provide plotting of all profile parameters against distance from the center of the object, it is possible to request only plotting of a particular data file by using option DA (DISPANN). One simply enters the name of the file in response to the prompt and selects what set of parameters is to be plotted. 14.5 GHOSTS, THE LED EFFECT, AND THE LEFT SIDE OF THE CCD Occasionally, a CCD frame with suffer from one or more artifacts which produce unwanted images in the area to be analyzed. Ghost images, resulting from reflections of bright stars from the dewar window or other optical surfaces, can be modeled in a way similar to galaxies and stars. A ghost image will usually have a donut appearance, circular symmetry, a central hole, and uniform surface brightness out to some limiting radius. In this case, option PR will not work; the derivative will be positive and the central region will not offer a solution. Here we must use option EA, assuming an eccentricity of 0.0, and an estimated central location. If the ghost image is free of ovelapping objects, the first model will be sufficient. Usually, however, more than one iteration is required. On some frames, an LED effect will be evident. This is caused by excessive current throught the on-chip amplifier on the CCD. For long exposures, some CCD systems turn off the CCD amplifier to avoid this problem. If it is present, there will be a bright radiating source in one of the corners of the CCD (upper right on the RCA CCD). This source cannot be modeled with either options PR or EA. One must model the LED effect by selecting several dark frames of the same exposure as the program frame, averaging them, and then subtracting a constant background level. This model should be set to zero everywhere except in the region of the LED effect, and subtracted from each program frame as required. Since the effect is repeatable, only one model need be kept. The leftmost columns on some CCDs have a higher background level due to some unknown cause. To model this effect, which may be slightly different on each exposure, model and subtract stars and galaxies near the left edge of the frame. If the effect is strong, these models will be only a first approximation. Next use option AV to compute average values for each column. The averaging process will neglect edited areas which were set to zero. These average values can be written to a frame. At some point, say column 20 or so, the effect fades into the background. Subtract this background from the frame and set the columns to the right of that point, exactly equal to zero. This frame is then subtracted from the program frame to rid it of the troublesome columns on the left side. 14.6 THE SECOND AND HIGHER ITERATIONS Let us assume that you have modeled a few of the brighter objects (galaxies and stars) and have data files of type 1 for each of these objects. These models were created by editing out Page 5 contamination from overlapping objects. The files themselves may have required additional editing to remove the outer contours which may have been too noisy or contaminated. In this stage you will obtain a better approximation to each object by subtracting away contamination, rather than editing it out. With option FG (FAKGAL) one can subtract an image from the working SAD file. To start this process, the SAD file must be exactly the same as the original frame (no edited areas). Option FG will prompt for the sky, which was determined with the cursor, and for a scale factor. Enter -1 for the scale factor since we must subtract. Do this operation for the second brightest object and then observe the frame on the TV display. There will be less contamination from this object. Repeat this for all the other objects fainter than the second, and then run option PR on the brightest object once more. There should be an improvement. If the brightest object is now subtracted, and the second brightest written back to the frame (set the scale factor equal to +1 in option FG), the second brightest object can be more accurately modeled. This process is continued until all of the brigher objects in the frame have been modeled a few times. You are done when, by subtracting all objects, a uniform field results. Several iterations may be required for rich fields. Some of the processing can be done by batch; simply create a command file with all of the information required by the option prompts, contained in the file. 14.7 THE STELLAR POINT SPREAD FUNCTION In order to fit surface brightness formulas to the surface brightness data, a proper accounting of atmospheric seeing must be made. It is thus necessary to model the stellar point spread function. While the original exposures are two-dimensional files, the surface brightness data is in the form of one-dimensional files. The point spread function will also be in this form. In modeling the objects in the field, one will have modeled several stars as well as the galaxies. Usually, the stars in the center of the frame will not be different than those at the edges, but one should verify this before adding the stellar profiles together. Since the stellar profiles, as produced by option PR, already exist, one only has to average a few of these profiles in order to obtain a good point spread function. Option ED allows one to perform mathematical operations on profile data. With this option, we first add the surface brightness, inclination, and eccentricity values of all the stellar files, and then divide each of these parameters by the number of files. Two files may be operating on each time, with several parameters being operated on at once. The positions of the stars are unimportant for deconvolution, hence no operation is performed on x and y. Likewise, the integrated surface brightness is also ignored. The averaged files will still have a sky background which must be removed. The sky is estimated in the same way as described above in section 14.4. Here however, access to the plotting prompt is obtained by use of option DA. This sky value is then subtracted from the file with Page 6 option ED. See the file [-.MIIPS.SAMPLES]POINT_SPREAD.DAT for an example of how a stellar point spread function looks, and plot it with option DA. 14.8 STRUCTURAL AND PHOTOMETRIC PARAMETERS Once an object has been modeled with options PR or EA, one will have a data file of type 1 where the surface brightness averaged around elliptical contours is presented as a function of distance outward along the major axis of each contour. This one-dimensional file can be used to obtain the photometric and structural parameters of the particular object. It is necessary to take account of the blurring of the light passing through the earth's atmosphere and the imaging optics which make the galaxy image appear to be larger than its true size, and to possess a dimmer central surface brightness than it actually has. The data file for the stellar point spread function, derived as indicated above, is used in conjuction with a nonlinear least squares fitting routine to derive the galaxy's parameters. Parameters from several different surface brightness formulas can be solved for with the option RG, e.g., the modified Reynolds Hubble formula, the de Vaucouleurs formula, etc. The command HE RG will provide online help in the form of an actual example solution. Alternately, one could TYPE the file RG.DOC in the [-.MIIPS.DOC] directory, to see this. A sample file of the data type needed for using option RG (data file type 1) is given in the [-.MIIPS.SAMPLES] directory. This file, GALAXY_PROFILES.DAT, contains a large galaxy, ID=70, extending out to 243 pixels, and a small galaxy, ID=170, extending out to 50 pixels. A solution should be tried with the point spread functions given in the sample file POINT_SPREAD.DAT in the same directory. This file contains three objects, with ID=STARS, 138, and STARS2, which extend out as far as 17 pixels. The object STARS represent an average of severage stars whose point spread functions were measured by option PR. 14.9 CALIBRATING THE FILES For the files of surface brightness distribution (type 1), the following calibrations will be necessary. 1) The surface brightness values will be noisy at large distances from the center of the object, and some smoothing by binning will be necessary if plots are to be made. The binning is not necessary in order to use option RG. 2) Since the inclination angle is measured on the frame, and the frame may be tilted relative to north on the sky, a constant may have to be added. 3) The radius is in pixels and should be converted to arc seconds. 4) The surface brightness values are in ADU and should be converted to magnitudes for plots and tables. These calibrations are carried out with option ED in successive steps. The binning can be done with a step size proportional to the radius (command B1) and in the log domain. Before converting to magnitude units, the sky (as determined from Page 7 option RG) must be subtracted. It is most convenient to do all the computations in batch mode where the command file contains the necessary answers to the prompts and the calibration constants. Start with a small amount of binning and then plot the file with option DA to see the effect. The file of galaxy parameters (type 3) also needs to be calibrated. Here a conversion from ADU to magnitudes, and a conversion from pixels to arc seconds must be made. The conversion to magnitudes is given simply by m=-2.5log(ADU)+constant. Certain options, e.g. CG, will ask for the constant when plotting error bars. Option E3 (EDITDATA3) is designed to files of galaxy parameters. Similar operations, ie., addition, multiplication, etc., can be done on several columns simultaneously. In this regard, it is similar to option ED. 14.10 PLOTS OF THE SURFACE BRIGHTNESS DISTRIBUTIONS AND PARAMETERS Option DA can be used to plot the surface brightness distrbution in the units which exist in a single file of type 1. No error bars can be included with this option however. This option is most useful for looking at the raw data, before any calibrations or binning have been done. When it is desirable to include a fitting function formula and error bars in a plot of measured surface brightness in magnitude units, one should use option CG. The data file should have already been converted to magnitude units, and have been binned (see above). The fitting function must exist as a data file of type 1 in units of magnitudes and should have been convolved with the appropriate point spread function. The files [-.MIIPS.SAMPLES]GALAXYPROFILESMAG.DAT and [-.MIIPS.SAMPLES]GALAXYPROFILESMAGDEVAUC.DAT are examples of data and reconstructed profiles using the de Vaucouluers formula, of two galaxies, ID 70 and 170. The command file [-.MIIPS.SAMPLES]GALAXYPROFILESMAG.COM illustrates how the binning and calibration were carried out for ID 170 under batch operation. Option FG is used to create the reconstructed, or artificial, data file, making use of the parameters which were solved for with option RG, and the point spread function. After this stage, option ED is used to convert to magnitudes and arc seconds. The command file [-.MIIPS.SAMPLES]GALAXYPROFILESDEVAUC.COM illustrates how the reconstruction was accomplished in batch mode for the galaxy with ID=170. Try plotting the data for these galaxies with option CG, command TD. Answer the prompts with the following parameters: readout noise and gain = default, sky and sigma of sky = 491 0.05 for ID 70 (sky and sigma of sky = 491 0.1 for ID 170), and calibration constant = 27.4212. Option CG can also be used to plot color as a function of radius, along with the predictions of two fitting formulas, the de Vaucouleurs formula and the modified Hubble formula (Abell and Mihalas 1966, A.J.). Here one requires several files, two files for the blue and red data, two files for the modified Hubble formula at blue and red wavelengths, and two files for the de Page 8 Vaucouleurs formula at two wavelengths. An example of this usage is given in CG.DOC. Option DG (DISPGAL) is used to plot the photometric and structural parameters (character file of type 3) and perform various kinds of fits. One could, for example, plot log(radius parameter) against magnitude, fitting two intersecting straight lines to the bright and faint ranges. One can also plot luminosity functions, surface brightness parameter against magnitude, color delta against magnitude, etc. In certain instances, a histogram of the residuals about a fitted line can be made. The file DG.DOC gives two examples of the usage of option DG. Also, the directory [-.MIIPS.SAMPLES] contains the files GALAXY_PARAMETERS_BLUE.DAT and GALAXY_PARAMETERS_RED.DAT which can be used to get familiar with option DG.