Science, Faculty of
Physics and Astronomy, Department of
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Hogg, David William
Master of Science - MSc
University of British Columbia
Difficulties with direct comparisons of corrected observational data and model predictions are discussed in the context of faint galaxy number counts and redshift distributions. By simulating images, based on various model universes, and reducing the images via a variety of algorithms, concerns regarding surface brightness biases, systematic and random photometry errors, and incompleteness corrections can be explored. Two software tools have been developed to aid in this investigation, a faint object photometry package (bigphot), and an image simulator. The simulations suggest that attempts to extend number count observations as deep as possible via incompleteness corrections are suspect. Models in which number evolution of the galaxy population has a (1 + z)η redshift dependence on the normalization of the luminosity function (ϕ* in the Schechter function) suggests a value of η between 1 and 3.
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FAINT GALAXY OBSERVATIONS AND MODEL PREDICTIONSByDAVID WILLIAM HOGGB.Sc., McGill University, 1987A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Geophysics and AstronomyWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIASeptember 1992®David Wiffiam Hogg, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying •of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of 1QcpAy5Ic5 cJ Aoiom,The University of British ColumbiaVancouver, CanadaDate Oc+erDE-6 (2/88)AbstractDifficulties with direct comparisons of corrected observational data and model predictions are discussed in the context of faint galaxy number counts and redshift distributions.By simulating images, based on various model universes, and reducing the images via avariety of algorithms, concerns regarding surface brightness biases, systematic and random photometry errors, and incompleteness corrections can be explored. Two softwaretools have been developed to aid in this investigation, a faint object photometry package(bigphot), and an image simulator. The simulations suggest that attempts to extendnumber count observations as deep as possible via incompleteness corrections are suspect.Models in which number evolution of the galaxy population has a (1 + z) redshift dependence on the normalization of the luminosity function (4,* in the Schechter function)suggests a value of i between 1 and 3.11ContentsABSTRACTLIST OF TABLESLIST OF FIGURESACKNOWLEDGEMENTS1 Introduction3 Image Simulator- description3.1 Introduction3.2 Magnitude calibration3.3 Galaxy generation3.4 Star generationUviviiiix12 Faint galaxy observations2.1 Galaxy Detection2.2 Photometry2.2.1 Introduction2.2.2 Isophotal Photometry2.2.3 Growth curve photometry2.2.4 Fixed aperture photometry2.3 Incompleteness Corrections2.4 Star/Galaxy separation4466891111131515161621‘U3.5 Convolution3.6 Sky and noise4 Simulations 254.1 Galaxy number counts 254.1.1 Model comparison 254.1.2 Simulation parameters 304.1.3 Simulation results 344.2 Galaxy redshift distributions 485 Conclusions 52REFERENCES 54A Image Simulator- User’s ManualA.1 IntroductionA.2 Setting the observing conditionsA.3 Parameters of the simulated UniverseA.4 Miscellaneous optionsA.5 Contrived Simulation OptionsA.6 Review of Command-line arguments57575759616264B Bigphot User’s ManualB.1 IntroductionB.2 Object detection algorithmsB.3 Object photometry routinesB.3.1 Fixed circular aperture photometry (-p 2)B.3.2 Growth curve photometry (-p 3)B.3.3 Isopliotal photometry (-p 4)242466666770707071ivB.4 Sky determination techniques.72B.5 Splitting and Masking facilities 74B.5.1 Masking 74B.5.2 Splitting 75B.6 Output formats 76B.7 Review of command-line arguments 77VList of Tables2.1 Star-galaxy counts 144.1 Simulation parameters 314.2 Simulation conditions for number counts 334.3 Simulation conditions for redshift survey 49viList of Figures2.1 Galaxy Visibility 52.2 Gaussian vs. Moffat PSF 83.1 E/S0 spectra 223.2 Sb spectra 234.1 B3 CCD image 264.2 B3 COD image 274.3 No evolution model comparison 284.4 Luminosity evolution model comparison 294.5 Number evolution model comparison 304.6 Filter transmission curves 334.7 Tyson incompleteness corrections 364.8 Number evolution with = 1, 1.5,2.0 374.9 Number evolution with i = 3.0,4.0 384.10 Number evolution, Tyson data 394.11 Number evolution, Lilly data 404.12 Tyson and Lilly data magnitude error 434.13 Susceptibility of results to sky algorithms 444.14 Number counts and photometry algorithms 454.15 Magnitude error for various photometry algorithms 46vii4.16 Redshift distribution.51vu’AcknowledgementsI would like to thank Paul Hickson, my supervisor. Congratulations Paul, for getting thelargest optical telescope on Canadian soil operational! It was an interesting experience inwhich to have participated. I look forward to seeing reams of data.I look forward to receiving my handmade rug, Mom.I would also like to thank Phil for always being available to listen to my ideas. Actually,for always being available after September 4, 1991, at 9:52 pm (8 lb., 0 oz.).Thanks also to my friends in the department, who make life far more interesting.Finally, I thank my wife Heidi, for putting up with me.IixChapter 1IntroductionStatistical observations of faint galaxies such as number counts and redshift distributionshave led to interesting results. Comparisons of number count observations to no-evolutionmodels (models where galaxy properties are constant with time and are determined fromthe local galaxy population) indicate an observed excess of as much as twice the number ofgalaxies predicted by B3 = 20.5 (Maddox et al. 1990) with the excess becoming larger atfainter blue magnitudes. Observations at longer wavelengths are less discrepant in comparison to the no-evolution model predictions. The obvious solution to this discrepancy,luminosity evolution of the galaxy population, is not entirely satisfactory. Luminosityevolution alone appears to favour cosmologies which provide a greater co-moving volumeof space with redshift than an = 1, A = 0 cosmology provides (1, is the present meandensity of the universe divided by the closure density and A is the cosmological constant)In addition, such models prefer high redshifts for the epoch of galaxy formation, a potential problem for bottom-up scenarios of structure formation in the universe such as colddark matter (Rees 1991). The introduction of co-moving number density evolution canprovide rough agreement with the large numbers of observed galaxies in an = 1, A = 0universe, an issue explored further in chapter 4 of this work. Finally, the observed red-shift distribution of galaxies follows the no-evolution model predictions quite well. The1The excess depends on one’s normalization of the counts at the brighter - more difficult to determine- end of the counts, as well as one’s choice of cosmology.1absence of a high redshift tail in the redshift distribution is a problem for some modelswhich incorporate evolution to explain the counts (Guiderdoni and Rocca-Volmerange1990).Interpretation of statistical observations of faint galaxies is complicated by their dependence on several factors: intrinsic galaxy brightness, galaxy distance, cosmology, andgalaxy evolution. Thus, models are necessary for comparison with the observations. Interpretation of results appears particularly difficult for the observational cosmologist, whowants information on the geometry of the Universe - clearly a second order effect in thepresence of strong evolution of the galaxy population. Nevertheless, cosmological information may still be obtained within the confines of certain assumptions. For example,if the co-moving number density of galaxies is assumed to be constant, the asymptoticvalue that the counts reach can still provide information on geometry of the Universe. Theobserved excess at faint magnitudes is so huge that no amount of luminosity evolutionwill replicate the counts in an ft = 1, A = 0 universe (Fukugita et ai. 1990).Additional complications arise that are best explored by examining the details of howthe observations are made. Models lend themselves naturally to predicting the numberof galaxies and their luminosities. Observations, on the other hand, provide the numberof objects detected, and measured magnitudes. Factors such as incompleteness (and subsequent corrections applied to the data), random and systematic photometry errors, andsurface brightness selection effects can all play a role in distorting the observed distribution. Effis et al. (1984) discussed these issues in terms of an observational map. Theyemphasize the mapping of source properties to image properties is highly nonlinear, anddependent on the detail of the observations. Phiffipps et al. (1990) also discuss theseissues as related to surface brightness bias.Unlike previous efforts to explore the above complications, this work explores the relationship between model predictions and observations by simulating images, based on2various model universes, and subsequently reducing the images using a variety of faintobject detection and photometry algorithms that are used to reduce actual observations.This approach lends itself naturally to examine the aforementioned observational complications, as both the actual and observed galaxy distributions are known for the simulatedimages.To carry out this exploration, two tools have been developed: an image simulator anda faint object photometry package (hereafter called bigphot). Both tools are designedto be used in conjunction with UNIPS (UNix Image Processing System - written by P.Hickson). The operating environment of UNIPS is UNIX. It it thus relatively easy toexplore a wide range of model and observational parameters simply by creating scriptsthat automatically produce images, and carry out the subsequent data reduction, withparameters being controlled via command line arguments.Chapter 2 discusses the issues which this work addresses. Chapter 3 describes theimage simulator. Chapter 4 presents the results of simulations as applicable to observedgalaxy number counts and redshift distributions. The number count simulations areintended to replicate the observations described in Lilly et al. (1991) and Tyson (1988)while the redshift distribution is based on observations used for the LDSS deep redshiftsurvey (Colless et a.l. 1990). Chapter 5 presents conclusions. Appendices A and B areusers manuals for the image simulator and bigphot respectively.3Chapter 2Faint galaxy observations2.1 Galaxy DetectionFaint galaxy observations may contain false detections and will certainly suffer incompleteness. Generally, the observations are carried out in such a way that the probabilityof false detections is very low. However, incompleteness is always present at some leveland is not necessarily simply a function of the apparent magnitude of the objects. Faintgalaxies may be resolved to some extent making the probability of detecting such objectsagainst the night sky a function of both the observed galaxy proffle and its apparentluminosity.Figure 2.1 illustrates how such a bivariate incompleteness function might lead to interpretation difficulties when ignored. Galaxy scale length is plotted vs. absolute Bmagnitude in the rest frame of the galaxy. The contours are lines of constant visibility, where visibility is defined as the volume of space within which a galaxy would bedetectable. The dashed and dotted lines indicate observed relationships of absolute Bmagnitude with scale length based on nearby galaxies.Figure 2.1 was generated by considering a grid of points in the B magnitude - scalelength plane. For each point a galaxy proffle was generated, assuming an rhI4 profile forB/SO galaxies and an exponential disk for Sb galaxies. The profile was then convolvedwith a Moffat function, and the magnitude of the galaxy measured out to a fixed isophote.41Sb galaxy, no evolution0.80.6UC. C.• 0.4bCo 00.20—0.2,Figure 2.1: This figure plots contours of constant galaxy visibility, where visibffity is thevolume of space within which a galaxy would be detected.The dashed line for the Sb galaxies represents an absolute B magnitude - scale lengthrelationship derived from observations published by Kent (1985). The dotted line forboth the Sb and E/SO galaxies aie similar relationships used by Guiderdoni and RoccaVohnerange (1991). The dashed line for the E/SO galaxies is a relationship taken fromKormendy (1985).The maximum redshift considered here is 1.7. The bottom left-hand corner representsgalaxies visible to at least a redshift of 1.7 for the Sb galaxies and to a redshift of 0.7for the E/SO galaxy. The upper right-hand corner contour reflects a redshift of 0.05.Contours are equally spaced in redshift (not volume). The k corrections were taken fromRocca-Volinerange and Guiderdoni (1988).—22 —21 —20 —19Absolute B magnitude5The photometry and observing conditions reflect the conditions described in Lilly et al.(1991). The galaxy was considered detectable if the measured magnitude reflected at leasta 3cr detection. This process was repeated by stepping through redshift space from 0.05to 1.7.Figure 2.1 shows that the brightest galaxies may not be the most visible, due tothe fact that more luminous galaxies are larger. Galaxy visibility is determined by thedetafls of the observing conditions, the data reduction steps, the actual surface-brightnessdistribution of galaxies, as well as the extent of crowding on the image. All of these issuescan be addressed by reducing simulated images for various model universes.2.2 Photometry2.2.1 IntroductionThe photometry of faint galaxies is a tricky task. Unlike stellar photometry, where profile-fitting is clearly the preferred algorithm, no one algorithm is an immediately obviouschoice. Faint object photometry packages generally employ one of the following threealgorithms:1. Isopliotal methods, where all contiguous pixels above some isophotal level are summedto obtain the object flux (after subtracting some estimate of the sky level in thosepixels). Variants of this method are found in FOCAS (Jarvis 1981), APM (Irwinand Tumble 1984) and AOLP (Scharein 1984).2. Fixed aperture photometry, where the object flux within some fixed aperture (usually circular) is summed.3. Growth curve photometry, where a light growth curve of the object being photometered is measured (usually using a series of concentric circular apertures centered onthe object) and the growth curve itself is used to determine the aperture size to be6used for the photometry. Variants of this method have been used by Kron (1980a),Infante (1987), and Yee (1991).Each of the preceding algorithm choices have advantages and disadvantages. Thefollowing three sections discuss the issues pertinent to a given photometry algorithm whichcontribute to systematic and random photometry errors. It is these issues which result inthe differences between observed magnitudes and total (model prediction) magnitudes.It should be noted that Guiderdoni and Rocca-Volmerange (1991) did attempt toconsider the effects of isopliotal magnitudes in their model predictions. By assumingthat the galaxies are represented by an rh/4 or exponential profile for nearby galaxies anda Gaussian profile for distant galaxies, they could determine an isophotal magnitude byintegrating the profile to a set isophotal level. However, such a scheme cannot address thedetectability of objects in the presence of sky noise and crowding. In addition, modeffingthe PSF of unresolved objects with a. Gaussian underestimates any systematic magnitudeerror with magnitude which effects both the predicted magnitudes and incompleteness.A Gaussian profile underestimates the amount of flux in the wings of an actual PSF. AMoffat function, fit to actual CCD data, is used as the PSF in the simulations presentedin chapter 4.The left-hand panel in figure 2.2 shows a Gaussian and Moffat profile with the sameFWHM, normalized to contain the same amount of flux. The central panel is a plot ofmagnitude error versus magnitude intended to replicate the conditions of the B, imagesfound in Tyson (1988), where the PSF is described by a Gaussian (dashed line) and aMoffat function (solid line). The right-hand panel shows incompleteness for unresolvedobjects in an uncrowded field observed with similar conditions to Tyson (1988), for botha Gaussian (dashed line) and Moffat function (solid line). Isophotal photometry, similarto the method described in Tyson (1988) was carried out to obtain the magnitude errorand incompleteness shown in figure 2.2.710080a 60p.4020LJ0 1 2 3 20 22 24 26 26 26.5 27 27.5 28radIus fl apparent magnitude BJ apparent magnitudeFigure 2.2: The solid line represents a Gaussian PSF, the dashed line a Moffat functionPSF2.2.2 Isophotal PhotometryIsophotal photometry has been used by several groups examining galaxy number counts.Tyson used FOCAS for his faint blue galaxy work (Tyson 1988), and subsequent workershave also published isophotal determined magnitudes to allow for comparison.It is well recognized that isophotal magnitudes are susceptible to systematic errors.The angular diameter of an object is given as S = s(1 + z)2/dL, where s is the objectsmetric size and dL is the luminosity distance (the distance at which the objects apparentand intrinsic luminosities are related by the inverse square law). Thus, surface brightnessis not conserved with redshuft since area oc 92 cc (1 + z)4. This (1 + z)4 surface brightnessdimming means a systematic underestimate of the object’s flux as a function of redshiftoccurs if one measures the light within a fixed isophote. However, a minimum area criterion is usually employed to avoid the problem of the faintest galaxies’ surface-brightnessproffles sinking below the isophotal limit. In addition, an isophotal threshold is chosenthat is considered sufficiently faint to avoid systematically underestimating the light fromthe faintest objects.The isophotal technique’s criterion for evaluating a pixel as containing light from anS..0VCC8object is necessarily dependent on the signal to noise ratio of the object. This can beparticularly troublesome for colour measurements where the noise properties and objectsignal will differ between frames. A greater fraction of the object’s flux will be measuredin the higher signal-to-noise frame leading to erroneous colours. This can lead to colouramplification of the fainter objects in an image. Note that this colour amplification isdependent on the relative signal-to-noise between images taken in different wavebands.Proponents of isophotal techniques point out that using the isophotal contour as one’saperture can mean a smaller sky contribution, and therefore a higher signal-to-noise ration, if the galaxy is not well approximated by a circular (or effiptical) aperture. Theexpectation of circular or elliptical symmetry for a faint object is especially suspect whendoing photometry on gravitationally lensed objects, or tidally disrupted objects undergoing interactions of some sort. However, It has also been pointed out that the resultingisophotal images of faint galaxies, even those which in fact do contain a great deal ofelliptical or circular symmetry, do not reflect their true light distribution. The shape ofthe region defined by the isophotal region will depend on the image noise and the gradientof the galaxy proffle at the isophotal threshold (Kron 1980b). This edge effect in isophotalmethods is caused by pixels at the isophotal limit being included due to noise fluctuations(see Irwin 1985).2.2.3 Growth curve photometryThe growth curve determined aperture photometry method’s earliest proponent was Kron.His concerns about the isophotal magnitude methodology led him to use a circular aperture centered on the object with a radius equal to twice the light growth curve firstmoment, defined by:—f1xg(x)dxrl= 00J1 g()dx9where g(x) is the light distribution as a function of radius from the object centroid. Thelight distribution function is the total light in each annulus (the differential light growthcurve).This choice of aperture reflects a compromise between getting all of the light (largerapertures) and getting higher signal-noise (smaller apertures since the objects light usuallyhave a central concentration). The choice of an aperture of 2ri is shown by Kron to includeabout 91% of an object’s light regardless of the object’s redshift (ie. an invariance to the(1 + z)4 surface brightness dimming problem) and whether or not seeing is included(Kron 1980a).Thus, the growth curve technique appears to measure a roughly constant fraction ofan object’s light, regardless of the object’s morphology, redshift, or seeing. Kron pointsout that the growth curve method will result in greater random errors than the isophotaltechnique, since the number of pixels measured for faint objects will be greater relativeto the number considered using the isophotal technique. However, the reduction in therandom errors using the isophotal technique may simply be at the expense of an increase inthe systematic errors. It should be noted that the growth curve method has the appealingfeature of considering only the object’s light growth curve, and makes no explicit referenceto the noise properties in the image.Unfortunately, the desired benefit of measuring a constant fraction of an object’s lightis not realized in practice for faint objects. In addition to the increased random errorsdue to a large number of pixels being considered (in fact for the faintest objects, twicethe first moment of the light distribution may be beyond the maximum aperture size setby the user), the very definition of r1 becomes extremely susceptible to the sky noise.Frequently the growth curve aperture obtained is the maximum allowable aperture set bythe user, for low S/N objects. This makes the photometry have large random errors (dueto the inclusion of a lot of sky in the large aperture), and be susceptible to contamination10from neighbours.2.2.4 Fixed aperture photometryThe simplest of techniques, measuring the light within a fixed aperture, is susceptible tomany systematic errors that the growth curve technique was designed to avoid. A differingfraction of an object’s total light will be measured with a fixed aperture if there aredifferences in seeing or galaxy morphology. There will also be a systematic underestimateof an object’s flux as its redshift increases since the metric scale that the aperture subtendswill be a function of redshift. However, the fixed aperture method does have the benefitof being simple. If the aperture size is compensated for seeing, and the colour gradient ofthe measured galaxy is small, accurate colours should be obtainable using this technique.2.3 Incompleteness CorrectionsIncompleteness corrections are used to extend number count observations to fainter magnitudes than would be otherwise possible with a given data set. There will always be thedesire to extend the observations to fainter magnitudes by attempting tocorrect for thesytematic loss of objects and light at the faint limit of a survey. Two distinct problemsarise when attempting to carry out such corrections; one applicable to any attempt tocorrect for incompleteness, the other unique to data containing resolved galaxies. It isnoted that at the faint limit of the counts published by Tyson (1988), corrections on theorder of a factor of 10 in the counts have been appplied to the data. It is imperative thatsuch corrections be beleivable if the corrected data are to be used in model comparisons.Incompleteness corrections for galaxy number counts have generally been carried outin the following way:1. Produce an object proffle from brighter galaxies on the frame. No specific attemptappears to be made to consider the surface brightness of the galaxies.112. Scale the profile to represent a desired magnitude and add objects to the frame.3. Reduce the frame with several such simulated objects and determine the requiredcorrections from the number of objects added to the frame, in a particular magnitudebin (the magnitude here being the actual magnitude of the simulated object), thatare detected.Such corrections can only result in an increase (or no change) in the counts at a givenmagnitude. This technique, in addition to ignoring surface brightness, ignores the factthat the measured magnitude of an object does not correspond to the true magnitude ofthe object. This effect appears only to have been considered by people working on theluminosity function of globular clusters (see Drukier et al. 1988, Stetson 1991).Stetson (1991) provides an excellent description of the problem, where he uses DAOPHOTto obtain the globular cluster luminosity function. A plot of magnitude error (measured-actual) as a function of actual magnitude for stellar photometry using DAOPHOT willshow a systematic measured magnitude error. A bias towards measuring objects toobright appears toward the faint limit, which Stetson attributes to two effects:1. Stars with magnitudes close to the flux limit that are measured too faint will simplybe lost, while those measured too bright are not.2. Stars may be superimposed on another undetected faint star whose flux will be addedto the detected star. The relative importance of the undetected object increases asthe detected objects flux becomes smaller, resulting in a systematic brightening ofthe faintest objects.Note that for the counts themselves, the last effect acts counter to the tendency to miss(ie. not detect) a greater fraction of the objects at fainter magnitudes. In additionto the above effects, a rising luminosity function or number count law in the presenceof random errors can result in a distortion of the measured distribution. If the galaxy12number count relation has a positive slope, there are more galaxies at fainter magnitudesand even a symmetric distribution of photmetric errors will result in more faint galaxiesbeing scattered to brighter magnitudes than bright galaxies being scattered to faintermagnitudes.Among the possible effects the above issues can cause is an observed number countexcess over the actual distribution in some magnitude bins. Recall that the traditionalmeans of carrying out incompleteness corrections described above can only result in anincrease (or no change) between observed and corrected data.It should be noted that the effects discussed above in relation to stellar photometrywith DAOPHOT may not occur in the same manner for all photometry methods. Indeed,simulations of Tyson’s data presented in chapter 4 indicate a systematic underestimateof the objects flux with magnitude using isophotal photometry.Lilly et al. (1991) chose to extend their observations oniy out to magnitudes where theincompleteness corrections extended up to a factor of 2. Tyson (1988) adopted a differentapproach to the incompleteness corrections altogether. Tyson generated simulated imagesand adopted the input number-magnitude relation that best replicated the obtained rawcounts.2.4 Star/Galaxy separationOne issue of interest in many faint object photometry packages that is absent in thisdiscussion is object classification. This absence is partly a consequence that the originalmotivation behind this work stemmed from considering analysis of data expected to beproduced by the UBO/Laval 2.7m Liquid Mirror Telescope, where the object classificationwill be based on spectral energy distributions rather than morphology. In addition, thiswork is specifically aimed at considering photometry of the very faintest galaxies, wherethe ability to distinguish between stars and galaxies is the most difficult and where the13B magnitude stars/deg2/mag galaxies/deg2/mag % stars20 410 200 6721 529 796 4022 658 2.0 * io 2523 795 6.3 * 1O 1124 940 2.0 * iO 4.525 1096 6.3 * iO 1.726 1265 1.3 * iO 1.027 1450 2.0 * io 0.7Table 2.1: Star-galaxy counts based on the BahcaJl & Soniera model for a high-galacticlatitude field.number of stars is neglibible compared to the galaxy population. Table 2.1 indicates thenumber of stars and galaxies per square degree per B magnitude bin. The star counts arefrom Bahcall and Soniera (1980) at the galactic pole and the galaxy counts are based onthe results of Tyson (1988). The final column gives the percentage of stars and galaxiesin that magnitude bin that are stars.The simulations presented in chapter 4 are based on data number counts obtained byLilly et al. (1991) and Tyson (1988) and redshift distribution obtained by Colless et al.(1990). All faint objects were assumed to be galaxies in Tyson and Lilly observations.Colless et al. obtained spectra (for the redshift determination) of all objects for objectidentification.14Chapter 3Image Simulator - description3.1 IntroductionThe UNIPS image simulator generates CCD images of stars, galaxies, and noise. It wasoriginally written for UNIPS (UNIX Image Processing System - written by P. Hickson) byP. Rickson, and subsequently modified and extended by D.Hogg. This chapter describesthis modified version.The cosmology assumed has f, = 1, A = 0 with a default Rubble constant of H0 =50 km Mpc’(although the Rubble constant can be changed by the user).The following is a summary of the simulator’s tasks, in the order that they are performed:1. Determine magnitude calibration constant2. Make galaxies3. Make stars4. Convolve image with PSF5. Add sky and Poisson noise to imageThe user can tailor the simulation by the use of a variety of command line arguments.This includes the selection of a ifiter (from 82 on-line ifiter transmission curves), observingconditions (PSF FWRM, exposure time, telescope diameter, plate scale, etc.) as wellas properties of the objects themselves. The simulator outputs both an image and, if15desired, ifies listing information regarding both the simulation conditions and positionsand properties of objects in the frame. Refer to appendix A for the image simulator user’smanual.3.2 Magnitude calibrationAs a means of determining a magnitude zero point, -2.5xlog(electrons detected for magnitude zero), an AOV star is observed with the selected observing conditions through thespecified bandpass. The star is assumed to be magnitude zero, regardless of the bandpasschosen. The spectrum is taken from Gunn and Stryker (1983).3.3 Galaxy generationThree general types of model universes may be simulated with respect to the galaxypopulation:No evolution model : Parameters describing galaxies remain constant with look-backtime: co-moving number density, luminosity function, and galaxy spectra.Luminosity evolution model : Galaxy spectra evolve, galaxies becoming brighter withlook-back time. A constant co-moving number density of galaxies is assumed.The local galaxy poulation is assumed to be described by a Schechter luminosityfunction (also the case for the no-evolution model).qf(L) =where L is absolute luminosity, in B, and cb(L) dL dV specifies the number of galaxiesin the volume dV with luminosities in the range between L and L + dL. The threeSchechter function parameters, L*, q!, and a, specify the form of the function.The luminosity evolution is then simulated by using the atlas of synthetic spectradescribed in Rocca-Volmerange and Guiderdoni (1988). The Rubble types provided16in the atlas and used in the simulations are referred to as Sa, Sb, Sc, Sd, Irr (irregular), E/SO hot, and burst. A complete description of the model inputs used togenerate the spectral atlas is given in Guiderdoni and Rocca-Volmerange (1987).The atlas provides galaxy spectra as a function of age and Rubble type. The red-shift of galaxy formation and the present galaxy redshift determines the galaxy age,where the age-redshift relation is given byt = +Figure 3.1 and figure 3.2 plot representative spectra for E/SO hot and Sb galaxies.Number evolution model : Galaxy spectra and the co-moving number density ofgalaxies change with look-back time in this model. The mass function is assumedto be described by the Schechter function (where M is the galaxies mass).4, 4,*(M/M*)ae_M/M*lOne of the three Schechter parameters (qS*, M*, or c) is evolved with a (1 + z)’?dependence. A second parameter is kept constant while a third is evolved withredshift to maintain a constant total co-moving mass (This parameterization is alsodescribed in Guiderdoni and Rocca-Volmerange 1991).This parameterization leads to three possible models:1. 4,atar() = q*(O)(l + z)’, constant L.2. M*(z) = M*(O)(1 + z)”, constant q.3. 4t(z) =c1*(O)(1 + z)’7, constant M*.Luminosity evolution of the merging galaxy population is also carried out usingthe atlas of spectra described above. The local luminosity function is specified viaSchechter paramaters, and the B* values are converted to M* (in solar masses)17via present day mass-to-light ratios given in Rocca-Volmerange et al. (1988). Theevolving mass Schechter function then determines a given galaxy’s mass, with thespectral atlas providing the corresponding luminosity based on age, hubble type,and mass of the galaxy.Note that the models used to generate the spectral atlas do not specifically considermerging in the luminosity evolution scenario.Intially, the co-moving volume, V, that the image subtends within a specified maximum redshuft (Zmaz with a default of 4) is determined=— 1 (see Weinberg 1972)3 \H0) J /l+Zmg,jwhere is the solid angle subtended by the image c is the speed of light.For the luminosity evolution and no-evolution models, the number of galaxies to beadded to the image is obtained by integrating the local luminosity function (the Schechterfunction) over all absolute luminosities from Lmjn to infinity and multiplying by theavailable volume:Ngaio = v x {gtyper(te + 1,type typeThe subscript type refers to the Rubble type; fitype is the fraction of galaxies of that Rubbletype, and r is the incomplete gamma function.For the number evolution models, the number of galaxies to be added to the image isgiven byJ4Ngais = > (X gt4(z)P(at(z) + 1, M€(Z)117)where M refers to galaxy mass. Although all three Schecliter parameters a(z), M*(z) andare depicted as being a function of redshift, only two of the three parameters willvary with redshift, depending on the chosen model choice as described previously. Thefraction of galaxies of a given Rubble type is assumed to remain constant with redshift.18For each of the galaxies, a redshift is chosen. The redshift distribution reflects thecurrent model assumption of co-moving number density, and is generated from a uniformlydistributed random number through a change of variables and/or a rejection method (seePress et al. 1989). For the number evolution model, the probability distribution ofredshifts, f(z), can be described byf(z) ç(z)r(1 + a(z), M*(z))where V is the co-moving volume anddV / 1 2 32(l+z)/For the no-evolution and luminosity evolution models absolute B magnitudes are chosen such that the luminosity distribution is described by the Schechter function. A rejection method is employed to generate the desired Schechter function distribution from auniformly distributed random number. The apparent b magnitude of the galaxy is thendetermined byb=B+5*loglo(dL)—5where the luminosity distance is calculated bydL=-[(z+1)—/z+1j.For the number evolution models, a galaxy mass is chosen such that the distributionis described by the appropriate Schechter function. The spectral atlas provides absoluteflux, FM in photons/s/M0,as a function of Rubble type and age. The apparent flux, fin photons/s/cm2is then given by: f = (FM x M)/(4ird?).The scale length (in kpc), r0 of the Galaxy is a function of the absolute B magnitudeand morphology. Note that the absolute B magnitude used refers to the present day,restframe absolute B magnitude for all models. The following are the default parameters:19• E/SO (Kormendy 1985): r 10—0.429*B--9.78• Sa and Sb (Kent 1985):Disk scale length: Te=10—0.362*B—7.O0Bulge scale length: r0 =10—03*B—7.69Where the bulge-to-total light ratio has a Gaussian distribution with a mean of 0.4and sigma of 0.2, with the proviso that the ratio is 0.• Sc and Sd (Kent 1985):Disk scale length: re=10—0.58*B--11.35Bulge scale length: r0 = 100.15Where the Bulge-to-total light ratio has a Gaussian distribution with a mean of 0.1and sigma of 0.1, with the proviso that the ratio is 0.For each of the above scale-length - absolute magnitude relations a dispersion in scale-length is simulated by specifying a sigma in log r. This is typically set to 0.2 for diskgalaxies and 0.1 for E/S0’s (a tighter relation).The scale length in pixels is then determined:206265= —(z + 1)2Swhere s is the plate scale in arcseconds/pixel.The position of galaxy centroids are found from a random, uniform distribution acrossthe image.If the object is an elliptical galaxy, its profile, prior to convolution with the seeingPSF, is assumed to follow the de Vaucouleurs rhI4 law:I=I3exp(7.662(1 — (TP)l/4)20where I is the number of electrons at pixel i and r, is the effective distance from theobject centroid calculated from the pixels actual distance from the object centroid (r),the objects position angle 4, and the inclination angle. The inclination angle, 8, is takenfrom a uniform distribution in cos(6). I is the surface brightness at r, = r0 and is relatedto the total number of electrons by:= 7.22irr1A spiral and irregular galaxies are assumed to have an exponential disk:I: = Ide 1.68as well as a spheroidal component described by the r114 law. The relative component oflight in disk to bulge is based on the relation given previously. The value of ‘d is relatedto the total number of electrons via:2irrI.zThe flux calculated for the centre of a pixel is assumed to represent the flux integratedover the entire pixel. The total flux of the object, summed over all pixels, is normalizedsuch that the relations between I and I, given above hold.3.4 Star generationThe observed stellar population is simulated to approximate the observed stellar countsand colour distribution as a function of apparent magnitude as given by the Bahcailand Soniera model for the North Galactic Pole. Three stellar spectra are used : GOV,MOV and a GOIlI, which represents the disk stars, spheroid dwarf stars, and spheroidgiant stars respectively. The relative fraction of stellar type and number of stars as afunction of magnitude is based on the Bahcall and Soniera model. The stellar spectrahave 50 A resolution and are based on Sviderskiene (1988).21E/SO GalaxyFigure 3.1: Spectra for an E/SO galaxy. The x-acis is wavelength in A, the y-axis is f.A present day spectrum for an B/SO galaxy is taken as shown in the bottom panel. They-axis is arbitrary, although the relative values between panels (for the same type) reflectsthe assumed evolutionary brightening of the spectra. Theoretical atmosphere models areused to generate the spectra below 1220 A.22Sb GalaxyFigure 3.2: Spectra for an Sb galaxy. The x-axis is wavelength in A, the y-axis is Apresent day spectrum for an Sb galaxy is taken as shown in the bottom panel. The y-axisis arbitrary, although the relative values between panels (for the same type) reflects theassumed evolutionary brightening of the spectra. Theoretical atmosphere models are usedto generate the spectra below 1220 A.23The stellar population only includes stars with apparent visual magnitudes between18 and 30, although a facility exists to add a number of brighter stars if desired.The stars’ centroids are distributed randomly across the image.3.5 ConvolutionThe default PSF is a Moffat function:1(r) = I(1 + ()2)_where R = FWHM/l.l and j3 = 2.85. These parameters are based on fitting the Molfatfunction to CCD data (Yee 1991).A Gaussian PSF is also available, which allows for much faster convolutions as itemploys an FFT.3.6 Sky and noiseThe sky level is based on the spectrum of the night sky at Palomar taken from Turnrose1974. Finally, random, Poisson noise is added with a variance equal to the sky level plusthe square of the detector readout noise.24Chapter 4Simulations4.1 Galaxy number countsThis section presents results from the reduction of simulated data in B3 and I. The dataare intended to replicate the faint galaxy number count observations described in Tyson(1988) and Lilly et aL (1991). All of the simulations use number evolution models.Figure 4.1 and figure 4.2 are examples of portions of simulated images in B3. HereafterTyson data will refer to data described in Tyson (1988) and Lilly data will refer to dataas described in Lilly et at (1991).Note that the same model universe is being simulated for both figure 4.1 and figure 4.2(although for a different field). The Lilly data as shown here is much less crowded due tothe superior sampling and seeing as compared to the Tyson data.4.1.1 Model comparisonFigures 4.3, 4.4, and 4.5 are comparisons of the simulator output with published modeloutputs from the literature. Note that the simulation models in these figures reflect whatthe simulator adds to the image, not what is observed to be in the image. Unless statedotherwise, all models assume H0 = 50 km s1 Mpc’and S20 = 1. The agreement betweenthe model in use for this work with models published in the literature is reasonable,with the primary reason for any differences likely due to the adopted spectral energy25Figure 4.1: A sample portion of a CCD image in Bj. The plate scale is 0.6 arcseconds/pixel. This image is intended to replicate the observing conditions described inTyson 1988. The model universe being observed has number evolution with a value of= 2. The value of ç = 0.029h3Mpc3.26Figure 4.2: A sample portion of a CCD image in B. The plate scaIe is 0.11 arcseconds/pixel. This image is intended to replicate the observing conditions described inLilly et a1. 1991. The model universe being observed has number evolution with a valueof = 2. The value of qY 0.029h3Mpc3.27Q5t0060a34to0distributions.The no-evolution model comparison is based on data from Yoshui and Takahara (1988).The parameters for this model include a type independent luminosity function with a =—1.1, B = —21.1, and 4,* = 0.0184h3 Mpc3. The Rubble type proportions used byYoshui and Takahara were based on Tinsley (1980): 0.321 E/S0, 0.281 Sab, 0.291 Sbc,0.045 Scd, 0.061 Sdm. The simulation comparison had a Rubble type mix of: 0.16 E/S0hot, 0.16 burst, 0.28 Sa, 0.29 Sb, 0.05 Sc, 0.05 Sd, 0.01 Irr. The models are reasonablycomparable, with the greatest difference arising in the B3 passband below magnitudes ofabout 25. This difference likely arises primarily from a difference in the adopted present-day spectral energy distributions between this simulation (see figure 4.3) and that ofYoshii and Takahara (1988), shortward of the Balmer break. Note that there is littledifference between models in the I band.22 24 26 285-3 • I. .122Figure 4.3: No-evolution model comparison:[solid line, B3]: Model from Yoshui and Takahara (1988)[dotted line, B3]: Simulator output.[solid line, I]: Model from Yoshli and Takahara (1988)[dotted line, I]: Simulator output.24I26 28286tb(sI’)0,0)c4bfl022 24 26 28IFigure 4.4: Luminosity evolution model comparison:[solid line, B]: Model from Yoshli and Peterson (1991)[dotted line, B]: Simulator output[solid line, I]: Model from Yoshii and Peterson (1991)[dotted line, I]: Simulator outputThe luminosity evolution comparison model is taken from Yoshui and Peterson (1991).The adopted parameters here include a type independent luminosity function with paramaters a = —1.1, B, = —21.1, 4* = 0.0156h3Mpc3,and a redshift of galaxy formationof 10. The proportion of Rubble types adopted by Yoshui and Peterson (1991) were: 0.38B/SO, 0.16 Sab, 0.25 Sbc, 0.10 Scd, 0.11 Sdm. The simulation comparison has a Rubbletype mix of 0.19 E/S0 hot, 0.19 burst, 0.16 Sa, 0.25 Sb, 0.1 Sc, 0.1 Sd, 0.01 Irr. Hereagain the difference between models is likely to be primarily a difference in the modelingof the UV spectral energy distributions.The number evolution models come from Guiderdoni and Rocca-Volmerange (1991).The type dependent luminosity function and Rubble type distribution is the same as foundin table 4.1 in the next section. The redshift of formation assumed in the simulations is 5for all types, as compared to those adopted by Guiderdoni of 5 E/S0, 3 for early spirals,I I I29Figure 4.5: Number evolution (merger) model comparison:[solid line, B3]: Model from Guiderdoni and Rocca-Volmerange (1991)[dotted line, B1]: Simulator output[solid line, I]: Model from Guiderdoni and Rocca-Volmerange (1991)[dotted line, I]: Simulator outputand 2 for late spirals and irregulars. Number evolution with = 1.5 (using the M*c5*model described in Guiderdoni and Rocca-Volmerange 1991) is modelled. The differencein the B1 band at the faint end is due to attempts at modelling isophotal magnitudes byGuiderdoni and Rocca-Volmerange (where the simulator model here is outputting totalmagnitudes).4.1.2 Simulation parametersThe next section presents results of simulating Lilly and Tyson data. This section describes the default parameters used in the generation and subsequent reduction of thesimulated images. Unless specified otherwise, the parameters used to generate images inthe next section are as described in this section.Default parameter values of c and B,. are given as a function of morphological typein the following table (as in Guiderdoni and Rocca-Volmerange 1990).Si I30Morphological type B c % of total ‘sE/S0 -21.10 -1.00 35Sa -20.90 -1.00 7Sb -20.90 -1.00 18Sc -20.90 -1.00 17Sd -20.45 -1.00 15Irr -20.45 -1.00 8Table 4.1:The morphological type distribution of the galaxies is chosen to reflect the the percentages given in the last column in the above table.The following lists more default parameters used to generate the galaxy population:• H0—50 km/s/Mpc•= 0.029h3Mpc• z=5 is epoch of galaxy formation for all Rubble types• The surface brightness distribution is specified by assuming all elliptical galaxieshave an r’ proffle, and all spiral galaxies have an exponential disk with a bulgecomponent described by an rh/4 proffle. The following are the assumed absolute Bmagnitude - scale length relations adopted:ellipticallog(r0)= —0.429 * B — 9.78, dispersion: 0.05Sa and Sbbulge: log(r0)= —0.383 * B — 7.69, dispersion: 0.20disk: logfr) = —0.362 * B — 7.69, dispersion: 0.20bulge-total light ratio: 0.4, dispersion: 0.231Sc,Sd, and Irrbulge: log(r0)= 0.15, dispersion: 0.20disk: log(re) = —0.58 * B — 11.35, dispersion: 0.20bulge-total light ratio: 0.1, dispersion: 0.1For each of the above surface brightness relations a Gaussian dispersion (in log(scalelength in kpc) for the absolute magnitude- scale length relations) is present. The dispersion values listed in the above list are the standard deviations of the dispersion.Additional simulation conditions adopted are summarized in table 4.2. Figure 4.6shows the transmission curves of the two filters used in these simulations. Note that thefilter curves as given represent the adopted overall efficiency (atmosphere, filter, telescope,detector). The final column of table 4.2 provides the survey area for the simulated data.The simulated survey area is about 1/3 larger than the actual Lilly survey and about 7times smaller than the actual Tyson survey. The original Lilly survey covered only 1/30ththe area of sky covered in the Tyson survey.All number evolution simulations, unless otherwise stated, use the following parameterization for the Schechter function:c1,star(z) = ç(o)(1 + z)’1, constant a.Observations of the simulated images were carried out using bigphot. Unless otherwisestated, isophotal photometry was performed. The isophotal thresholds for the photometryas given by Lilly et al. and Tyson are:B3 = 28.7 mag arcsec2 (Tyson 1988)I = 25.9 mag arcsec2 (Tyson 1988)B3 = 29.1 mag arcsec2 (Lilly et al. 1991)I = 27.5 mag arcsec2 (Lilly et al. 1991)In practice, isophotal thresholds are specified by considering all pixels with an object32B filter I filter0.5,,,0_0.4- / 0.4- -o .. • 00.3- / 0.3 - -C .a- .‘ 0.2 - .• -0.1- 0.1 - I -.. -‘.3500 4000 4500 5000 5500 8000 9000 10wavelength (A) wavelength (A)Figure 4.6: Filter transmission curves used in simulations.Simulation exposure plate scale diameter of seeing fwhm survey areatime (s) (arcsec/pixel) mirror (m) (arcseconds) (sq. arcseconds)Tyson B3 and I 9600 0.6 4.0 1.2 94,300Lilly B3 and I 7500 0.11 3.6 1.0 31,700Table 4.2: Simulation conditions for the Lilly and Tyson data.33flux (pixel value - sky estimate) more than some threshold (specified in terms of theestimated sky noise). The sky level is determined by the sky determination algorithmemployed in FOCAS, and described in appendix B.The requirements for regarding a detection as real are a minimum of 6 connectedpixels above the given threshold levels for the Tyson data. The Lilly data has photometryperformed on a detection with the proviso that if the isophotal diameter sank below 2”.O,circular aperture photometry was carried out with a 2”.O diameter. In practice, mostof the objects have aperture photometry in the Lilly data as the isopliotal diameter isusually less than 2.”O.The simulation of noise in the images is carried out in such a way that both a spatially correlated (via undetected objects) and an uncorrelated (Gaussian random noise)component are present. Tyson filtered his data prior to detection and photometry with a5 x 5 symmetric filter with amplitudes of 1-3-5-3-1. The noise characteristics of Tyson’sdata before and after ifitering are described in Tyson (1988) and the simulations reflectattempts to replicate these conditions. The same ifitering operation is applied in thereduction of the Tyson data simulated images. Lilly et al. (1991) did not provide a greatdeal of detail regarding the noise characteristics, system efficiency, or exposure times.The Lilly simulations thus have noise properties, exposure time, and overall efficiencyssuch that obtained counts reach a similar depth to the published raw counts. No ifiteringoperations are applied to the Lilly data in accordance with the description in Lffly et al.(1991).4.1.3 Simulation resultsThis section presents results from observing various number evolution model universesunder various observing conditions and using different photometry and detection algorithms. The sensitivity of the results to parameters that describe the galaxy population34(a, M*, 4, i, morphological type distribution, surface brightness distribution) as well asissues dependent on the adopted object detection and photometry algorithms are presented.Figure 4.8 and figure 4.9 show results for the number evolution models with variousvalues of . In each row of these figures, 4 plots are presented showing number counts(log(gala.xies/deg2/O.5 mag)) for Tyson and Lilly data in B3 and I. The banners aboveeach set of plots indicates parameters that differ from the default simulation parametersgiven in the last section. For each plot 4 lines are plotted. The solid line indicates theraw observed counts obtained from reducing the simulated images. The long dashed lineindicates objects that the simulator added to the image. The solid points indicate theobservations obtained by Tyson or Lilly et al. (as appropriate). The short dashed lineindicates the corrected data as given by Tyson or Lilly et al..Figure 4.7 shows the results of reducing an image whose galaxies are described bythe N(m) relation given by Tyson as his corrected counts. Note that the raw counts soobtained are also in rough agreement with the raw counts obtained for various number evolution models. Utilizing incompleteness corrected counts beyond the completeness limitfor model comparisons appears unreliable. The discrepancy at the turnover in the countsbetween the Tyson raw counts and those obtained via the simulations presented here maybe a consequence of being unable to simulate the noise properties of the original imageprecisely. Nevertheless, it is clear from a comparison with figure 4.8 and figure 4.9 that theobservations appear relatively insensitive to model differences beyond the completenesslimit.Figure 4.8 and figure 4.9 also illustrate that defining the completeness limit is uncertain. Due to the very poor sampling and seeing of the Tyson data, it appears that almostall of the faint galaxies are unresolved and the completeness limit is thus reasonably welldefined (although incompleteness shows up as bright as B3 25 due to the very bad35crowding on the images). The Lffly data, with superior sampling and seeing, containspartially resolved objects which may remain undetected to very bright magnitudes. Thetrue incompleteness is dependent both on the intrinsic surface brightness distributions ofthe Universe and the details of how the observations were made.Under the model assumptions described in the last section, the best fit for numberevolution occurs with a value of 2 —* 3. However, other values (such as = 1.5) arenot excluded. A value of = 4, the predicted value in the CDM scenario for matter (notnecessarily luminous) on galaxy scales (Hickson 1992), appears to produce insufficientlyvisible galaxies (recall that the current model requires the total co-moving mass to beconstant) in B3. However, a reasonable fit is obtained in the red. Recall that the physicsthat were used to generate the atlas of evolving synthetic spectra used in these situationsdid not specifically consider merging.Figure 4.10 and figure 4.11 show the sensitivity of the number evolution models to6It)o5V0btJ03Figure 4.7: Tyson incompleteness corrections. The solid lines are the observed raw countsof an image where the actual N(m) relation present in the image is given by long dashedline. The short dashed line is the corrected counts and the filled circles the raw counts asfound by Tyson.22 24 26 28 20 22 24 26B1 I36I-.aq Cb 00 E i-I 0 Ilog(#gals/deg2/O.5mag)log(#ga1s/deg/O.5mag)(31(31C)(31C)(3’0)Co(31(3)w6V6If)V036VIf05V03Figure 4.9: Number evolution models. The bottom row of results are based on simulationswith a value of O.0156h3Mpc3 instead of the default value of ç& = O.029h3Mpc.I B I38SIf,V600V000)000003600VSIf)o5000)•0S.-.Figure 4.10: Number evolution models with = 2 for Tyson data. The banners aboveeach panel indicate the parameter(s) changed between the simulation presented and thedefault simulation in the upper-left panel.I B IB IB3 I B I39to(0IDo50C)06543to(0EID05toV0V(04toto06543Figure 4.11: Number evolution models with i = 2 for Lilly data. The banners aboveeach panel indicate the parameter(s) changed between the simulation presented and thedefault simulation in the upper-left panel.40redshift of galaxy formation, q, M*, a, Rubble type mix, and the surface brightnessdistribution. All simulations in these figures have i = 2. The upper left hand panel ofeach figure has simulation parameters for the galaxy population as described in the lastsection. A short description above each other panel in the figures indicates the parameterthat was varied from the simulations plotted in the upper left-hand panel. The upper rightpanel has a redshift of formation for all Rubble types of 30 (z1 = 30) in comparison to thedefault z1 = 5. The middle left panel has a zero redshift value of cb*(0) = 0.036 h3 Mpc3in comparison to the default value of 4*(0) = 0.029 li3 Mpc3. The middle right panelhas an adopted morphological type mix of 0.14 E/S0 hot, 0.14 burst (effipticals) , 0.13Sa, 0.23 Sb, 0.22 Sc, 0.01 Irr, 0.14 burst (in comparison to the default values 0.175, 0.175,0.07, 0.18, 0.17, 0.15, 0.08 respectively). The bottom left panel has an adopted value ofa = _1.5,M* = —20. for spirals and irregulars and a = _0.7,M* —19.6 for effipticalsin comparison to the default values listed in table 4.1. The bottom right panel has anadopted surface brightness distribution of:ellipticals and bulges of all spirals : log(r0) —0.23 * B — 4.1, dispersion: 0.05disk of spirals and irregulars : 1ogfr) = —0.2 * B — 3.46, dispersion: 0.20bulge-total light ratio:0.4, dispersion: 0.2 (Sa and Sb)0.1, dispersion: 0.1 (Sc and Sd)0.1, dispersion: 0.2 (Irregulars)The model dependency on the parameter variations is more pronounced in B3. Notealso that the Lilly data are more sensitive to changes in the surface brightness distributionof the galaxy population, as expected due to the data’s superior sampling and seeing.It is clear that none of the models presented here account for both the Lilly and Tysonobservations in both B, and I. The I band counts of Lilly et aT. fit several number evolution41model universes. The observations currently do not extend to faint enough magnitudes,where the difference among the models is most pronounced. The I band counts of Tysonare not reproduced well by any of the current models. This may be due to a differencein the simulated images’ noise properties, as compared to the data obtained by Tyson,or to some unknown difference in the reduction process. The B, counts also exhibit adiscrepancy between the Tyson and Lilly data sets. The Tyson blue data suggest a valuefor i 2 — 3 while the Lilly data suggest a value of i 1 — 2.Although these simulations suffer from uncertainties due to unknown properties ofthe original data and reduction process, they do ifiustrate problems with comparisons ofcorrected observations with model predictions. First, incompleteness corrections introduce a great deal of uncertainty in the results. Second, the completeness limit may bedifficult to define, being dependent on the details of the observations, the reduction of theobservations, and the actual surface brightness distribution of the galaxies.Figure 4.12 plots magnitude error (total magnitude - measured magnitude) as a function of total magnitude for the Tyson and Lilly number evolution simulations with q = 2,in B3. Although the mean magnitude error as a function of magnitude is comparablein the two data sets, the Lilly data were published only to B3 ‘-‘-‘ 27, while Tyson extended his data to B, —‘ 28. The Tyson data are subject both to a underestimate ofan object’s flux as a function of magnitude as well as the overestimation of an object’sflux due to contamination from neighbouring objects. The Lilly data, which are largelya consequence of aperture photometry, suffer from confusion at the faint limit, althoughthe effect is only beginning by B1 = 27. Figure 4.13 shows how the obtained numbercounts vary with the chosen sky level and sky noise algorithm employed. The results arereasonably insensitive to the adopted method, with the exception of the mode estimator method, 2*median1*mean. This method, employed in the faint object photometrypackage PPP (Yee 1991), underestimates the sky level systematically, fortuitously pro420a).42tos-I0ci)a)-d---ItoFigure 4.12: Magnitude error (total magnitude - measured magnitude)total magnitude for Tyson and Lilly images in 133.as a function ofviding counts closer to what is present in the image. This is not a consequence of themode estimator doing an effective job of removing the effects of undetected objects, asthe estimate is systematically below the sky brightness added to the images (excludingundetected objects).To illustrate the effects of adopting different detection and photometry algorithms(not necessarily just those used by Lilly et al. or Tyson) on the obtained number counts,the number evolution = 2 model was reduced via a variety of methods. The observingconditions for the Lilly data were used as the data were better sampled and thereforemore typical of faint galaxy observations.Tyson data42Lifly data—443 II 11111111111 11111 II 11111• I 3 I I I I I I --L.I -f: •— s_s..... S —liii, II I I 1111111 liii I 11111131 I22 24 26 28 22 24 26 28total magnitude total magnitudeIIIllIIIIIIi.1i_ti hIhIhIIIhIIhII!--Mr --- -I I I I I I I I I 1 I I I I I I I I I0—4 22 24 26 28total magnitude22 24 26 28total magnitude43Figure 4.13: left panel: Sky level set to input values.middle left panel: Sky level is mean of sample from 2.1 sigma clipping.middle right panel: Sky level is median of sample.right panel: Sky level is 2*median1*mean of sample.Figure 4.14 and figure 4.15 present results of reducing the data with 3 different techniques, each employing 4 different sky determination algorithms. For each row of eachfigure, the left panel has the sky noise and sky level set to the input value. The middleleft panel has the sky level set to the input value, and utilizes the FOCAS sky algorithmto determine the sky noise. The middle right panel uses sky level as the mean of a 2.1sigma clipped sample and the sky noise the sigma of a 5 sigma clipped sample. The rightpanel sets the sky level as the median of the sample and the sky noise as the the sigmaof the sample. For the object photometry, an annulus of inner radius 20 pixels and outerradius 25 pixels was used to obtain the sky sample.The isophotai technique, presented in the top row of each figure, required an objectto have at least 6 contiguous pixels in order to be considered real. Note that the growthcurve and aperture photometry results used a local maximum detection criterion where alocal maximum with a central pixel at least 4o above the sky was required for detection.The result is a more complete detection with the local maximum criterion to some level,and then a precipitous lack of detections beyond that magnitude as the object flux level no22 24 26 28 22 24 26 28 22 24 26 28B magnitude B magnitude magnitude44Isophotalto0CltoC)02totbto0toSto05Cltoa)02toto0toStq05Ntoa)t02toto.23Figure 4.14: Each panel in each row of thisalgorithm. See the text.figure uses a different sky determinationGrowth CurveFixed Aperture45Figure 4.15: Each panel in each row of this figure uses a different sky determinationalgorithm. See the text.4IsophotalI-.00)0)—2-I I I I I I I I I I_.• I I I I I I I I I I I I I I I I I I I; I I I I I I2.•.:.•0- -... . . . . .— ,., ..,,t’ —..‘ —.i, 4I:I I I I I I I I .:i:2 24 26 28 22 24 26 28 22 24 26 28 22 24 26 28total magnitude total magnitude total magnitude total magnitudeGrowth Curve0a)a).4-,-4 1111111 II.I:_ iii i 1.i 111111 111 I.I.I 11111111 I2 :- ... . .. .:-. -0 — c .j.. —: •.. .... .I III II II 1111 I II I I IIII• I I III II I I II I liii2 24 26 28 22 24 26 28 22 24 26 28 22 24 26 28total magnitude tota’ magnitude total magnitude B magnitudeFixed ApertureS..04)a).4-,—2.,.1, I. I,.. .124 26 28 22 24 26 28 22 24 26 28 22 2426 28total magnitude tota’ magnitude total magnitude total magnitude46longer rises 4u above the noise. The isophotal detection criterion, which considers pixelswhich are 2.5 above the noise to be object pixels, suffers incompleteness at brightermagnitudes, due to the necessity of having 6 contiguous pixels for a detection. Notethat the Lilly et al. observations, which largely used aperture photometry, relied on anisophotal detection criterion.Included in the reduction process for both the isophotal and aperture photometrypresented here is an attempt to reduce the contaminating influence of nearby objects.This is done by either splitting of objects detected via the isophotal technique or maskingsuspected contaminating pixels (see Appendix B for a description). However, the growthcurve technique suffers badily from measuring faint objects too bright, due to the tendencyof the growth curve-determined aperture to be very large (often the maximum allowedaperture set by the user). Thus, the growth curve-obtained number counts detect anexcess of galaxies, a consequence of the systematic overestimate of an object’s flux inthe presence of rising number counts. The fixed aperture photometry (with an aperturediameter equal to the FWHM of the seeing), underestimates the brightest object’s fluxand is suseptible to the effects of contaminating objects at the faint end. Nevertheless, thefixed aperture technique does a reasonably good job of faithfully reproducing the countsto B, ‘-‘ 26.474.2 Galaxy redshift distributionsThe redshift distribution of faint galaxies has been obtained by Broadhurst et al. (1988)and Colless et al. (1990) in the blue (B3). Their datasets are comprised of redshifts forgalaxies with 20 < B3 < 22.5. The redshift distributions obtained in this magnitudeinterval appear to be consistent with both no-evolution models and number evolutionmodels of the type described in this work (see Guiderdoni and Rocca-Volmerange 1991).Luminosity evolution, however, of a universe with a constant co-moving number density ofgalaxies results in a high redshift tail which is not seen in the present surveys (Guiderdoniand Rocca-Volmerange 1990). It has also been suggested that selection effects mightaccount for the absence of this high redshift tail (Yoshii and Peterson 1991).Unfortunately, the advent of CCD’s has not entirely eliminated the need for observations based on photographic plate work. The very small field of view obtainable withCCD imaging is insufficient for redshift surveys at B3 ‘— 21.’ Both the LDSS deep red-shift survey (Colless et aL 1990) and the Durham/AAT redshift survey (Broadhurst etal. 1988) are based on galaxies slected from photographic plates.The image simulator described in chapter 3 simulated CCD observations, where thedetector is assumed to be perfectly linear. Photographic observations cannot be simulatedaccurately under this assumption as they are both nonlinear and suffer reciprocity failure.The response (or characteristic) curve typical for a photographic plate is nonlinear atboth high and low light levels. In addition, a minimum threshold exposure is required fordetection (see Walker 1989). For the simulations of photographic plate work presentedhere, the detector is assumed to be perfectly linear down to some minimum exposurelevel. Any pixels (which are of the size of the inicordensitometer spot size), which haveflux levels below this minimum exposure level are set to the minimum level, with a Poisson1For 150 galaxies with 21 < B, < 22.5, one needs to search - 3.0E6 square arcseconds of sky - aformidable task with CCD’s48exposure plate scale diameter of seeing fwhm survey area efficiencytime (s) (arcsec/spot) mirror (m) (arcseconds) (sq. degrees)4200 0.25 4.0 1.5 7.2 0.02Table 4.3: Summary of conditions adopted for simulation of the LDSS redshift survey.noise component. Reciprocity failure and plate saturation is not simulated. Although thissimulation is approximate, it is useful as an illustration of potential difficulties with galaxyredshift surveys where the sample selection is based on photographic plates.The LDSS deep redshift survey (Colless et al. 1990) has been simulated. In orderto obtain roughly the same number of galaxies (Colless et al. observed 149 objects), atotal of 7.2 square degrees of sky was simulated. The COSMOS plate measuring machineapplied to AAT UK Schmidt photographs in the blue as described in Shanks et al. 1984is the basis for the adopted observing parameters summarized in table 4.3.Figure 4.16 shows the results of several simulated redshift surveys. The dashed curve isa no-evolution model prediction (Guiderdoni and Rocca-Volmerange 1990). The solid linehistogram shows galaxies that the image simulator added to the images and the dashedline histogram shows those that were detected to be in the images. The top and middlerows represent luminosity evolution model outputs where qS’ = 0.0156 h3 Mpc3. The toprow represents a redshift for the epoch of galaxy formation of 10 and the middle row aredshift of 5. In addition, the top row utilizes the default surface brightness distributiondescribed in chapter 4, while the middle row forces all galaxies to be point sources. Thelast row represents a number evolution model with i = 2. Each panel in each row represents a different minimum exposure level for a pixel to react. The left hand panel ineach row represents no minimum level. The central panel represents a minimum of 35,000photons/pixel over the course of the exposure is required. The left panel represents aminimum of 42,500 photons/pixel for the top and bottom rows and 37,500 photons/pixel49for the middle row. These values represent representitive values for the toe of the characteristic curve (the point where the measured density above fog becomes nonzero) ofphotographic plates (see Walker 1989).These plots suggest that redshift surveys could be subject to a selection effect, reducingthe detection of the higher redshift tail in the redshift distribution. These simulations,although rather uncertain both due to the fact that the actual AAT plate characteristicsare not used here, as well as the simple method adopted of simulating a photographicplate, point out that the details of the photographic plate galaxy survey need to beconsidered to assess the importance of selection effects.50o 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8III III II III III II II II III III II III6--6i:Z20 iiiIiiiIiiiIiiiI 08- 86- 6j:°HIIIIIHI IIIIIIIIIIIIII08--8iiiif1S0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8redshift redshift redshiftFigure 4.16: Redshift distribution for luminosity evolution models (top and middle rows),and number evolution model (last row).51Chapter 5ConclusionsGalaxy number count models differ the most at faint magnitudes. Thus, observationsshould reach the faintest possible limits in order to provide more information regardingthe nature of the Universe. However, the simulations presented here suggest that extending one’s observations via incompleteness corrections is dangerous. For example, theturnover in Tyson’s corrected B3 counts should not be used to make inferences aboutthe galaxy population (such as the epoch of galaxy formation) since the observationsappear insensitive to model differences at the faint limit. Lilly et al. adopted the moreconservative approach of extending the corrections only to magnitudes where the countcorrections did not exceed a factor of two. However, even corrections to this level need tobe considered in the light of the details of the observations. The presence of systematicand random photometry errors cause the measured magnitudes to differ from the actualmagnitudes and should be considered explicitly in the corrections. Finally, the details ofthe observations and the actual surface brightness distribution of the galaxies will affectthe completeness even at quite bright magnitudes. Finally, the redshift distribution ofgalaxies, although carried out using CCD’s, still depends on galaxy catalogues derivedfrom photographic survey work. Simulations suggest that these surveys might be biasedby selection effects.The process adopted in this work of comparing raw data to simulated images is not free52of problems. Additional uncertainties arise since the properties of the simulated images(such as noise) may differ from that utilized to produce the original galaxy statistics(the number counts and redshift distribution). These uncertainties could be lessenned byhaving the data on hand. Additional difficulties with the models will ultimately need tobe addressed before one can expect a good fit in all wavelength bands to the number countand redshift distributions. For example, the merger model used here adopts assumptionsabout the luminosity evolution and surface brightness evolution of galaxies which do notspecifically include the effects of merging. Nevertheless, these results do suggest thatcaution is necessary both in the reduction of data and in its interpretation.53Bibliography[1] Bahcall, J.N., Soniera, R.M.,Ap.J.Supp.,44, 73 (1980)[2] Broadhurst, T.J., Effis, R.S., Shanks, T., MNRAS, 235, 827 (1988)[3] Colless, Matthew, Ellis, Richard S., Taylor, Keith, Hook, Richard N., MNRAS ,244,408 (1990)[4] Da Costa, G.S., ASP Conference series Astronomical CCD observing and ReductionTechniques, ed. Steve B. Howell, Vol 23, 90 (1992)[5] Drukier, Gordon A., Fahiman, G.G., Richer, Harvey B., A.J.,95, 1415 (1988)[6] Effis, G.F.R., Perry, J.J., Sievers, A.W., A.J., 89, 8 (1984)[7] Fukugita, M., F. Takahara, K. Yamashita, Y. Yoshui, Ap.J. 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Physica Scripta, 21, 652 (1980a)[20] Kron, Richard G.,Ap.J.Supp.,43, 305 (1980b)[21] Lilly, S.J., Cowie, L.L., Gardner, J.P., Ap.J., 369, 79 (1991)[22] Maddox, S.J., Sutherland, W.J., Efstathiou, G, Loveday, J, Peterson, B.A., MNRAS,247,lp (1990)[23] Phiffipps, 5, Davies, J.I., Disney, M.J.,MNRAS, 242, 235 (1990)[24] Press, Wiffiam H., Flannery, Brian P., Teukolsky, Saul A., Vetterling, Wiffiam T.,Numerical Recipes in C, Cambridge University Press, Cambridge (1989)[25] Rees, M.J., Physica Scripta,T36, 97 (1991)[26] Rocca-Volmerange,B., Guiderdoni, B., A.A. Supp., 75, 93 (1988)[27] Rocca-Volmerange,B., Guiderdoni, B., MNRAS, 247,166 (1990)[28] Scharein, R, Master’s thesis UBC (1984)[29] Stetson, Peter, B., ASP conference proceedings The Formation and Evolution of StarCLusters, ed. Kenneth James, 13, 88 (1991)[30] Sviderskiene, Z., Bulletin of the Vilnius Observatory, 80 (1988)55[31] Tinsley, B.M., Ap.J., 241, 41(1980)[32] Turnrose, Barry, E., P.A.S.P., 86, 545 (1974)[33] Tyson, J.A., A.J., 96, 1 (1988)[34] Valdes, Francisco, NOAO memo Faint Object Classification and Analysis System(1982)[35] Walker, Gordon, Astronomical Observations, Cambridge University Press, Cambridge (1989)[36] Yee, H.K.C., F.A.S.P., 103, 396 (1991)[37] Yoshui, Yuzuru , Bruce A. Peterson, Ap.J., 372,8 (1991)[38] Yoshii, Yuzuru , Fumio Takahara, Api., 326, 1 (1988)56Appendix AImage Simulator - User’s ManualA.1 IntroductionThis manual describes the operation of the UNIPS image simulator. The image simulatoris written in ‘C’ and requires several program and data files. Once installed in your pathand compiled, invoking the program without any command line arguments (ie. ‘simim’)will result in the usage statement being sent to the stderr.The only mandatory argument that must be supplied to simim is the name of a blankimage, which has the dimensions of ones desired image. A blank image can be producedby using the UNIPS command ‘mkimage’.The default model assumed by the simulator is luminosity evolution.The following outlines the possible command-line options available for the image simulator. The # symbol following a command-line flag indicates an argument is expected.A.2 Setting the observing conditions-d # : Set aperture diameter of telescope where # is in meters. Default is 3.6 m.-g : Set COD gain in electrons/adu. Default is 10 e/adu.-q : Set system efficiency. Default is 0.5. This, in conjunction with any selected filtertransmission curve, defines the efficiency of the entire system: atmosphere, telescope57optics, and COD quantum efficiency.-r : COD read noise per pixel. Default is 0.-s : Plate scale in arcseconds/pixel. Default is 0.33.-t : Exposure time in seconds. Default is 3600 s.-f # : Set the seeing conditions (FWHM in arcseconds). Default is 1.0 arcsecond withthe PSF being a MofFat function.-b # : Specify a filter transmission curve with a bandwidth (in A, default is 1000),and central wavelength (in A, default 5500). This will assume a filter with 100%transmission within the filter and 0% transmission outside of it. This option maynot be used in conjunction with the -c option.-e : If #=0, a list of all available online filter transmission curves will be output tostdout. An identification number will precede each filter’s description, which canthen be used with the -c option to use the specified ifiter in a simulation.If the -e option is invoked with a non-zero argument, the filter transmission curveof the selected filter is output to stdout. It is recommended that the chosen filtercurve be examined prior to use.For example, for a list of all available online filters in file ‘flitlist’, type:simim blankimage -e 0 > ifitlistFor a look at the transmission curve of filter 61, type:simim blankimage -e 61“blankimage” does not need to exist, but the argument must be supplied.-c : Use the filter transmission curve with ID number.(see the -e option). Thisoption may not be used with the -b option.58A.3 Parameters of the simulated Universe-me : Set the redshift of formation for all galaxy types to this value. The default is 5for all types.-mh : Set the Rubble parameter, h (h = II/100 with H0 in km/s/Mpc). Defaultvalue is h=0.5.-mu : Minimum apparent v magnitude of all star’s on frame (default 20.) andmaximum apparent v magnitude of all star’s on frame (default 30.).-my : min..mag, maxmag, Bmax. Minimum apparent magnitude (default 20)and maximum apparent magnitude (default 30) in the selected passband, and maximum restframe absolute B magnitude (default -14) of all galaxies in image.-mm : maximum redshift of galaxies (default = 3).-mn : Set the value of q at z=0 in h3 Mpc3 (default = 0.0156h3Mpc3).-md : No spectral evolution of galaxies with redshift if this flag is used (ie. this flagselects the no-evolution model). This flag is meaningless if used in conjunction withthe -mb flag.-mo : The # argument is the name of a file which contains information to change thefraction of galaxy morphological types, the scale-length distributions of the galaxies,the redshift of galaxy formation, and the values for the Schechter parameters B,4, and a at zero redshift. Any or all of these may be changed at one time. Thefollowing is a sample file which contains the default parameter settings (the actualvalues used if the -mo flag is not used) for all of these items:59alpha.:-1.0 -1.0 -1.0 .1.0 .1.0 -1.0phiatar:0.0156fraction:0.35 0.42 0.60 0.77 0.92 1.00bat at:-21.10 .20.90 -20.90 -20.90 -20.45 -20.45galpan:-0.429 .9.78 0.05-0.383 .7.69 0.20 -0.362 .7.00 0.20 0.4 0.20.000 0.150 0.20 .0.580 -11.35 0.20 0.1 0.10.000 0.150 0.40 .0.580 -11.35 0.40 0.1 0.2zfor:5. 5. 5. 5. 5. 5.The fraction, bstar, phistar, zfor, and alpha entries are ordered to correspondto E/S0, Sa, Sb, Sc, Sd, Irregular galaxies respectively. Note that the values for thephistar entries are expected in units of h3 Mpc3, where h is Rubble’s constantin units of 100 km s1 Mpc’(ie. the provided number will be multiplied by theselected value of h).The galpars entry has one line corresponding to E/S0, Sa and Sb, Sc and Sd,Irregulars, in that order (total of 4 lines). The first and second number on eachline corresponds to the slope and intercept respectively of the spheroid scale-length,absolute B magnitude relation (log(r) = slope*B+intercept, where r is the scale-length in kpc). The third number on each line corresponds to the sigma of thevariation in log(r) (Gaussian distribution assumed).The 4th, 5th, and 6th entries of each line corresponds to the slope, intercept, andsigma for the exponential disk (where the 1st, 2nd, and 3rd entries would be corresponding to the bulge). The final two entries on each line (excluding the E/S0 line)correspond to the mean bulge to total light ratio and the sigma about that meanrespectively.Note that other options exist (-me and -mn) that can be changed via the -mooption as well (ie. don’t use both).60-mb : This flag selects the number evolution model. The first argument determineswhich Schechter parameters to evolve. The second argument spcifies the value for. The number preceeding each item below is the required first argument for thatform of evolution parameterization.1 q58t(z) = 4*(O)(1 + z), constant a.2 M*(z) = M*(O)(1 + z), constant &.4 l,star() = (O)(1 + z)”, constant M*.-mp : The flag allows one to specify a minimum threshold (for photographic platesimulations) in photons/pixel. If the flux level is below this threshold, the pixelvalue will be set to this level, with a Poisson noise component.A.4 Miscellaneous options-v : Verbose mode.-p : Produce the two output files, SSTN..# and SPAR..#. SPAR# contains information of the conditions of the current simulation and SSTN_# contains informationon the stars and galaxies in the simulated image.The first line of the SSTN_# file contains the magnitude calibration constant (-2.5*log( electrons for a magnitude zero star)). Each successive line contains information for each object added to image. A description of each output line follows:x y type objectilux spheroid_scaledength disk_scalelength galaxy.iedshiftWhere the objectJlux is in electrons. The type field indicates the object is a:9 - star, 0 - E/S0, 1 - Sa, 2 - Sb, 3 - Sc, 4 - Sd, 5 - Irr61-j : Field number (default 0). The number supplied here is a seed to the randomnumber generator which determines the positions, types, and magnitudes of theobjects placed on the image. Consecutive simulations with the same field numbershould be equivalent to consecutive observations of the same field. Thus, multi-filterobservations of the same field is possible.-k # : The is a seed for the random number generator that produces image noise.-a : Do not add sky nor noise to image. This may be used to add objects to actual dataframes.-1 : This flag causes the PSF to be a Gaussian (the default is a Moffat function). Thisis much faster than the Moffat convolution as the 2-D Gaussian convolution isperformed via 2, l-D FFT’s.-h # : This selects a galaxy spectra for output to stdout. The first argument specifiesthe galaxy spectral type (l-esflh,2-Sa,3-Sb,4-Sc,5-Sd,6-burst,7-Irr) and the secondthe age of the galaxy (in Gyrs - must be an integer 0-19).-n : Generate # bright stars on image. Here bright means within one magnitudeof saturating the chip. The second argument specifies the full-well capacity of theCCD. This is only used for determining the bright star’s magnitude. Chip saturationis not simulated.-x : Debug flag, outputs information used in debugging.A.5 Contrived Simulation Options-oa : Produce an image with only: #=1 stars: #=2 galaxies: #=3 sky.-ou : Make all galaxies unresolved.62-oz : Set the redshift of all galaxies to this redshift.-00 : Set all galaxies to this morphology where (1-es0h,2-Sa,3-Sb,4-Sc,5-Sd,6-burst,7-Irr.)-ob : Set cos(8) of all galaxies to this value (0.4 - 1.), where is the inclination angleof the galaxy with respect to the line of sight.-or : Set absolute B magnitude of all galaxies to this value.-od # : Produce only # objects on image where the following arguments specifythe x and y pixel coordinates of those objects. For example, too produce an imagewith only two objects at x=30 y=29 and x=33 y=40: -od 2 30 29 33 40-Os : Place all objects on a grid with the first argument specifying the objectseparation in pixels. The second argument is the minimum apparent magnitudeallowed for background objects which will be distributed randomly around the imageto provide for an element of spatially correlated noise.-on : Set the random background noise to have a variance of #.-01 : Set the scale length of all galaxies to the first argument (in pc). Thesecond and third arguments are distances from the galaxy centroid (in pc) at whichthe surface brightness of the galaxy will be listed in the file ‘Color’.-oc : Input a galaxy number count relation to be used to generate the galaxies onthe image. Specify, up to 20 lines, on each line the magnitude and the log10 of thenumber of galaxies per square degree per 0.5 magnitude interval. is the file name.63A.6 Review of Command-line argumentsOptions are enclosed in square brackets, where the only non-optional item is the name ofa blank image.simim: blanicimage[-v verbose model[-b # # bandwidth A (default 1000)/central lambda A (def 5500)][-c # convolve with ifiter # m. (see -e option)][-d # use telescope diameter of # m (default 3.6)][-e # (if #==0 list au filters/else list data of selected filter mj[-f # seeing FWHM in arcsec (default 1.0 arcsec)][-g # gain in electrons/adu][-p # print output ifies SSTN.#,SPAR#][-q # use quantum efficiency qe (default 0.5)][-r use read noise of # per pixel (default 0)][-s use scale of # arsec/pixel (default 0.33)][-t /fr use exposure time of # sec (default 3600)][-a do not add sky,read noise to image][-j # look at field number field (default 0)][-1 convolve with gaussian (default is a mofl’at)][-k # seed for background][-h # # stdout spectra type #(1-esoh,2-sa,3-sb,4-sc,5-burst,6-irr),age #(Gyrs)][-x debug flag][-n # # generate n bright stars in image, fwell capacity in e-][-me # redshift of formation for all galaxies][-rrth use Rubble parameter h = H/100 (default 0.5)][-mu # # min_mag max.mag for stars][-my min_mag max.mag max_Bmag for galaxies][-md no galaxy spectral evolution][-mb # # Merger model, eta value][-mo # where is name of file for galaxy params.][-urn # phi star of galaxies][-mm # Maximum galaxy redshift][-mp Minimum photons/pixel for photograph to be above fog][-oa # if 1, stars only. if 2, gals only. if 3, noise only][-ou Make all galaxies unresolved][-oz # redshift of all galaxies][-on # set background noise to # sigma gaussian noise][-ol # # scalelen leni len2][-oo # object type for all galaxies][-os obj separation for grid, mm mr mag for bgnd obj][-ob # Set cosine of inclination angle (0.4 - 1.0)][-or # Absolute B magnitude of galaxy]64[-od # ..? specifying object positions][-oc ifie for number-magnitude relation for galaxies]65Appendix BBigphot User’s ManualB.1 IntroductionBigphot is a photometry package written primarily for assessing faint object photometryalgorithms under various conditions. Using bigphot one can replicate many of the currentfaint object photometry algorithms (such as FOCAS Jarvis et al. (1981), PPP Yee (1991),VIC Infante (1987), Kron (1980a)) simply by supplying appropriate command-line flagsto bigphot.Bigphot is intended to be used in conjunction with UNIPS (UNix Image Processingpackage, written by P. Hickson). Because UNIPS uses Unix as its operating environment,it becomes relatively easy to compare various algorithms and input parameters on randomand systematic errors for various simulated observing conditions (see manual for UNIPSIMAGE SIMULATOR, appendix A) by employing Unix shell scripts to fully automatethe data reduction. Bigphot itself is designed to operate without intervention once theappropriate reduction options have been specified.To get bigphot’s usage statement, include the necessary bigphot directory(s) in yourpath and type ‘bigphot’ with no command-line options.66B.2 Object detection algorithmsFaint object photometry generally employs one of two mechanisms for detecting objects.One method employs scanning the image for any local maxima (a pixel with a valuegreater than its surrounding 8 neighbours), and requiring the estimated object flux insome region around the maxima to be above some threshold above sky for inclusion in theobject catalogue. A second technique searches for all individual pixels with an estimatedobject flux above some threshold above sky and subsequently groups all connected pixelstogether to form objects. Pixels are considered connected if another detected pixel liesadjacently or diagonally. Generally a minimum area criterion (minimum number of pixels)is specified in order for the object to be included in the object catalogue. These twodetection methods will be refered to as a local maxima and a pixel detection methodrespectively.The -d flag allows the user to select one of 5 different detection strategies based onone or both of the above detection algorithms. (The -1 flag also allows the user to skipall detection algorithms and perform photometry only on objects specified in an inputfile) The syntax for specifying the detection algorithm is -d dtype, where the followingchoices for dtype are valid:-d 1 : Object detection involves searching for local maxima which have an estimatedobject flux in the 9 pixels centered on the local maxima > thresh*skynoise. Thealgorithm for deterniining sky noise and the sky level is controlled by the -sg option(see section B.4).Subsequent to the object detection, all detections within a specified radius (in pixels)are merged together and replaced by a mean x and y position.The -1 thresh merge-radius flag is used to specify the detection threshold andradius for merging objects.67-d 2 : This is a pixel detection method. Pixels are considered detected if they containan estimated object flux > thresh*sky-noise. All such detected pixels are thenassigned to an object. The details of the sky level and noise are the same as usedin the FOCAS detect routine.The -op thresh minsz flag is used to specify the detection threshold and theminimum size (minsz), in pixels, that an object must have to be included in thecatalogue of detections.The object detection may be carried out using a detection ifiter. The -if filter-sizefilter-file flag allows one to specify the filter in a file. The filter must have the samex and y dimensions with a maximum length of 5 pixels. For example:-if 5 fdetwhere the file fdet contains:0121012321234321232101210The detection filter is then applied to each line of the image prior to object detection.If the -if option is not specified, no filter is used.-d 3 : This is another pixel detection method, which employs different sky determinatonstrategies. Pixels are checked to see if they have an object flux above thresh*skynoise. The sky level and noise used are based on the -sg flag.The -op thresh minsz option specifies thresh and a minimum size (minsz) in pixelsfor an object to be included in the catalogue.-d 4 : This option uses both the local maximum (-d 1) and pixel detection ( describedunder -d 2) algorithms to look for objects. If a local maximum detection falls within68the region defined by an object detected using the pixel detection algorithm, thelocal maximum detection is ignored. Thus, using both techniques will produce alist of objects found via the pixel detection algorithm or via the local maximumcriterion alone.The -od option, if used, will turn off the FOCAS style determined sky after thepixel detection algorithm is run and the -sg option will determine the sky and skynoise to be used for the subsequent local maximum detection algorithm. If the -odoption is not used, the sky and sky noise determined in the pixel detection algorithmis used for the local maximum detections.The use of both detection routines can be used to determine which objects to attempt object splitting on, if desired. This is discussed further in the section on‘masking and splitting’.-d 5 : This option uses both the local maximum (-d 1) and pixel detection (describedunder -d 3) algorithms. The -sg option determines the sky and sky noise methodto be used for both algorithms.This option can also be used to determine which objects should be subjected to anobject splitting algorithm.Following object detection the objects centroid is determined more accurately via anobject centering algorithm. A description of the centering algorithm can be found inDa Costa 1992. The -f flag aflows the FWHM of the PSF to be specified. This value,if provided, is used to determine the region to be examined for determining an object’scentroid. If the -f flag is not used, a default value of 15 pixels is employed.It is possible to carry out only object detection (and no photometry) by specifyingthe-p 0 option. This will cause only a list of x and y object positions to be sent to thestandard output.69B.3 Object photometry routinesThe choice of object photometry is dictated by the -p ptype flag, where valid values ofptype are 0,1,2,3, or 4.B.3..1 Fixed circular aperture photometry (-p 2)Fixed circular aperture photometry simply adds up the estimated object flux within somespecified radius of an objects centroid. If a pixel has a fraction of its area, n, withinthe chosen aperture, then the object flux within that pixel times n reflects the assumedcontribution to the object flux. The -ga option spcifies the chosen aperture radius inpixels.The sky estimate is defined by the -sp option. The ccd gain in electrons/adu (-cccd-gain), is required only if the objects estimated signal-to-noise is desired.The default is to have the masking facifity active which is described in section B.5.1.The masking facility can be disabled using the -gm option.Sample command-line for aperture photometry:bigphot image -p 2 -d dtype -ffwhm -c ccd-gain -ol thresh merge-radius -ga aperture-radius-sp skymode irad orad> outputB.3.2 Growth curve photometry (-p 3)Growth curve photometry uses a light growth curve of the object to determine the size ofthe aperture to be used for the object’s photometry. To produce a light growth curve aseries of concentric circular apertures centered on the object centroid are used to obtainthe object’s estimated object flux as a function of radius. The -gr rinc rmin rmax flagis used to specify the minimum and maximum aperture radii and the radius increment(rinc) in pixels. These values may be floating point.The light growth curve obtained can then be used in one of two ways to chose an70appropriate aperture. If the -gc option is not used, the chosen aperture radius is twicethe first moment of the light growth curve where the light curve’s first moment is definedby:— >rxf(r)ri—where f(r) is the object flux as a function of radius from the object centroid. If the -gcoption is use, the chosen aperture is determined from several criteria which are based onthe form of function which describes the object flux as a function of aperture radius (seeYee 1991 for a description of similar criteria):1. If the slope of the function increases for three consecutive aperture radius increments, the aperture at the second last radius is the adopted aperture.2. If the slope is negative for two consecutive aperture increments, the last radius isadopted.3. If the change in the slope of the function does not change for two consecutive radiusincrements, the second last aperture radius is adopted.The sky estimate is defined by the -sp option. The ccd gain in electrons/adu (-c ccdgain), is required only if the objects estimated signal-to-noise is desired.The default is to have the masking facility active which is described in section B.5.1.The masking facility can be disabled using the -gm option.Sample command-line for growth curve photometry:bigphot image-p 3 -d dtype -f fwhxn -c ccd-gain -ol thresh merge-radius-gr rinc rmin rmax -sp skymode irad orad> outputB.3.3 Isophotal photometry (-p 4)Isophotal photometry simply adds up the object flux out to a specified isophote. Theisophote is determined via the -op flag at the object detection stage, where detected71pixels are found and grouped into objects. Only objects detected using a pixel detectionalgorithm (ie. not the local maxima algorithm) can be photometered using this technique.The sky determination technique to be used for the photometry is chosen by the -spflag.The -of flag allows one to specify a minimum number of pixels an object must have forisophotal photometry to be carried out. If the object has fewer than the number of pixelsspecified (the argument of -of # - # being an integer), then circular aperture photometryis carried out with an aperture radius defined by the -ga flag.Sample command-line for isopliotal photometry:bigphot image-p 4 -d dtype -f fwhm -c ccd-gain -op thresh minsz-sg skymode sky-pixel-size> outputB.4 Sky determination techniquesThe technique to be used to estimate sky level and sky noise needs to be specified bothfor object detection and object photometry.The object detection step is preceded by the generation of a sky level and sky noiseimage. These images are at a lesser resolution than the actual image. The -sg sky-flagsky-pixel-size flag allows spcification of both the sky determination algorithm as well asthe size in pixels of one sky-pixel in the sky noise and sky level images. For example, ifsky-pixel-size is 8 (the default value), the image pixel values in an 8*8 region will be sentto a sky determination routine for an estimated sky level and sky noise of that region.Note that the pixel detection algorithm described for detection type 2 (-d 2 and -d 4)does not use these algorithms for sky determination, although the -sg option is still usedto specify the size of a sky-pixel. Here the sky determination is carried out as describedin section 5.1 of Valdes (1982).The sky determination for the object photometry is specified by the -sp sky-flag irad72orad flag. Pixels found in a circular annulus between irad and orad of the object centroidare sent to a sky determination routine. This circular annulus is divided into 4 equalsegments and a sky level is determined for each segment individually. An average of thetwo segments with the lowest sky level is then the adopted sky. This procedure, which isan attempt to lessen the effects of contaminating nearby objects, can be disabled by the-sb flag. If the -sb flag is chosen, the sky level is simply based on the pixels found withinthe entire annulus. If the value of sky-flag in the -sp option is 0, then the sky values usedduring the photometry stage will be the sky-level and sky-noise images determined viathe -sg flag.The sky-flag argument in both the -sp and -sg options determines which of the following algorithms are chosen:sky-flag = 1 : This method for sky determination is very similar to what is found inPPP. The sky level is calculated as 2*median1*mean of a sample that has hadoutliers more than 5 sigma away rejected iteratively. The sky noise returned is thesigma of that sample.sky-flag = 2 : This method returns the median as the sky level and the (.15866*n)element in the ascending order sorted array of n pixel values as the sky noise.sky-flag = 3 : This method is similar to that found in Infante (1987). The mean of asample which is found by rejecting all pixels num * sigma (of sample) away. numcan be set by -so num option. Default for num=2.1 . The sky noise is the sigma ofa sample with 5 sigma outliers from the mean rejected.sky-flag = 4 : This method is similar to that used in FOCAS. The sky level is the meanof a sample which is produced by removing all pixels more than 2 sigma away fromthe mode. The mean is also corrected by subtracting the average difference between73mode and mean for all sky-pixels (as described above). The sky noise is that in a 5sigma truncated sample about the mean.sky-flag 5 : This method returns the mode of the sample (no rejection of outliers),and the sky noise is the sigma of this sample.B.5 Splitting and Masking facilitiesThe masking and splitting facilities are applicable to the aperture photometry (includinggrowth curve photometry) and isophotal photometry techniques respectively. The defaultis for them both to be active, although the masking facility can be turned off via the -gmflag and the splitting facility can be turned off via the -ic flag.B.5.1 MaskingMasking can be employed in an attempt to lessen the effects of nearby contaminatingobjects. This masking procedure is based on a description found in Yee (1991). Prior toaperture photometry, any objects whose centroid’s lie within twice the maximum allowedaperture radius (set using the -gr flag, or within twice the adopted aperture radius whenperforming aperture photometry) of the centroid of the current object are considered tobe possible sources of contamination. The pixels lying along the line joining the twoobjects are obtained and the minimum along this line is determined. All pixels withina radius defined by this minimum plus some specified number of pixels (specified by the-ge flag and whose default is 3) from the contaminating object’s centroid are masked.If the contaminating object’s central pixel has an object flux > mu1t*skynoise (wheremult is specified by the -gn flag and whose default value is 700), then all pixels in theregion bounded by a line perpendicular to the line connecting the object centroids andpositioned at the minimum plus some specified number of pixels are masked.A sub-image is formed in the masking stage which has dimensions just large enough to74incorporate the maximum aperture to be used for this objects photometry. If the numberof pixels to be masked exceeds some fraction of the sub-image area (specified by the -gfflag, where -gf 2 means more than 1/2 of the image (default=2)) then the masking isperformed once more with the extra number of pixels (-ge) set to zero for this object.This remasking option can be disabled using the -gb flag.Those pixels that are marked for masking are replaced by values obtained from non-masked pixels assuming circular symmetry about the object.B.5.2 SplittingObjects that were detected via a pixel detection algorithm can have the splitting algorithmapplied to them in attempt to seperate out objects that may have merged at the detectionisophote. If the -d 2 or -d 3 options were used for detection, all objects will have objectsplitting attempted. If the -d 4 or -d 5 options were used for detection, only those objectswhich had more than one local maximum detection within the object’s isophote will besent to the splitting algorithm.The splitting algorithm increases the detection isophote and examines the resultingimage for a separation of the object. This is an iterative process, where the detectionthreshold (pixels above skylevel+thresh*skynoise) is increased by:threshnew = thresh0zd * (1 + thiric)up to the maximum sky value in the image. The value of thinc (default 0.2), is specifiedby the -01 option. The intial value of thresh and the chosen sky-level and sky-noise aredetermined by the -sp option. All objects that separate out and are comprised of morethan the minimum pixel requirement (set using the -op flag), are considered real. Thetotal flux of the original merged object is distributed amongst the split objects using theratio of the objects’ fluxes after splitting.75B.6 Output formatsBigphot outputs results to stdout. Error messages are output to stderr and generallycause execution to end. Warnings are output to the file Berror.tmp.If no photometry is performed (-p 0), only the x and y object centroid coordinates areoutput. If photometry is performed, the default is to have:x-position y-position object-flux object-size sky-level sky-noise detection-pathThe object-flux is given in adus (assuming that is what the original image is in). Thesky-level and sky-noise are the sky values used during the photometry step. The detection-path indicates what sort of photometry was performed on this object in order to arriveat this flux:o : If aperture photometry was selected for all objects, this will be the detection path.Otherwise, this indicates growth curve photometry was performed. Object-size willreflect the aperture radius in pixels.1 : Indicates isophotal photometry, with the splitting algorithm applied to the objectwithout success. The object-size here will indicate the number of pixels belongingto the object.2 : This object had aperture corrections applied to it. Object-size here indicates theaperture used prior to aperture corrections being applied.3 : Indicate isophotal photometry, with this object resulting from a succesful split.4 : Isophotal photometry, no splitting performed. Object-size indicates the number ofpixels comprising the object.5 : Indicates isophotal photometry, although one local maximum detection was detectedwithin the object. No splitting was attempted.76The -m flag can be used to change the above default output formats. The -m 2option outputs only x and y object coordinates. The -m 3 option outputs all of the aboveinformation, in the same order as above, with the addition of the estimated signal-to-noise for objects with a detection-path of 0 or 2 (aperture photometry). The -m 4 optionoutputs x,y, and the object-flux.B.7 Review of command-line argumentsThe usage statment for bigphot can be obtained by typing bigphot with no command-linearguments. Options are enclosed in square brackets, where the only non-optional item isthe name of the image file. The following is Bigphot’s usage statement, with additionaldescriptions. The # indicates an argument expected following this flag.Bigphot usage statement:bigphot: image[-f # (fwhm)] FWHM in pixels of the PSF[-m # (output format)] Specifies the output format.[-c # (gain in e/adu)] CCD gain, used only for S/N calculation.[-a # (dtype)] Detection type[-p # (ptype)] Photometry type[-1 # (list of objects)] Supply a filename with a list of object positions.[-oc (centering off)] Disable object centering.[-od (skydet off)] Do not generate additional sky image for local maximum detection followingpixel detection algorithm.[-oi z (separ increment)] Increment in threshold for splitting.[-os (mm pix for separ)] Minimum area in pixels for an object to be included following splitting.[-op # # (obj thresh, minsz)] Detection threshold and minimum size for an object to be includedin catalogue.[-ol (cmax thresh, merge radius)] Detection threshold and radius for objects to bemerged within.[-of # (miii pixels to use aperture)] If, for a -p 4 and -d 2 or 3 detection, the numberof pixels is less than #, use circular aperture photometry.[-sg # # (gskyflg, SKY pixel size)] Sky detection algorithm flag andsky-pixel size.[-ss # (set sky level)] Set the sky level.[-sn # (set sky noise)] Set the sky noise.[-so (sky sigma for sky3)][-sb (use only one sky buffer)]77[-sp # # # (pskyfig, irad, orad)][-gr # # # (rinc rmin rmax)][-ge # (extra pixels for mask)][-gd # (dmiilt)][-gb (no remasking)][-gi r/fr (apert correction)][-gn & (nrrrult)][-ga # (aperture radius)][-gf # (1/mask fraction for remasking)][-gc (growth curve determination)][-gt (no apert corrections)][-gm (no masking)][-ic (no splitting)][-in (nupdate)][-if # # (filter x size, filter file)][-ia # (sa)][-ib # (sb)][-ie # (ecc max for zero)][-ir r//z (restlir)][-ip # (pkthr)][-x & (debug mode)] Outputs information for debugging purposes.[-z (verbose memalloc mode)] Used for tracking memory allocation.78
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Astronomy
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Faint galaxy observations and model predictions
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