The optical properties of galaxies are at the core of this proposal. The survey will result in a catalog of 5 x 107 galaxies with good surface photometry in five bands and high-quality moderate-resolution spectroscopy from 3900-9200 Å for the brightest one million of these. The survey will thus result in an enormous improvement in our understanding of the properties of the ensemble of galaxies and their environment. Examples of problems which can be addressed (Section 3.4.5) are the correlations between galaxy morphologies, colors, and spectral properties, the density-morphology relation, which (in all its nasty detail) lies at the heart of relating the distribution of galaxies to the large-scale distribution of matter, the calibration of distance indicators and the investigation of the dependence of their zero-points on detailed morphology and environment, the luminosity function of galaxies with a sample large enough to investigate its detailed dependences on morphology and environment, the statistical incidence of almost any known class of peculiarity, either morphological or spectroscopic, the incidence of interaction and its dependence on environment, such environmental questions as the multiplicity function for groups and its dependence on group morphology, and the dynamics, morphology, and population of binary systems and small groups. In addition, there are several new areas of galaxy studies which will be made possible by the unique features of the data base produced by this survey. These include searches for very compact and for very extended low surface brightness galaxies, the use of the u' -band and z' -band data and the analysis of the detailed spectra as an adjunct to the image morphology. The discussion here is very far from exhaustive; we have selected a few of what we consider to be the most exciting possibilities.
The homogeneity of the spectroscopic survey is of very great concern, as it to a very large extent determines the ultimate usefulness of the spectroscopic sample. The photometric survey will go several magnitudes fainter than the spectroscopic survey so that, in the end, how well the spectroscopic sample is defined depends not on any limitations imposed by the photometric data but on how well we can define our selection criteria, as discussed in Sections 5 and 3.1.2.4.
Many of us feel that the photometric sky survey alone more than justifies this project. Almost all research on the statistical properties of nearby galaxies has until very recently been based on the Palomar Sky Survey and the ESO-B Survey and on the catalogs obtained from these and other photographic plate archives (de Vaucouleurs, de Vaucouleurs and Corwin 1976; Zwicky et al. 1960-68; Lauberts 1982; Sandage and Tammann 1981; Nilson 1973; Lauberts and Valentijn 1989; de Vaucouleurs et al. 1991). All of these catalogs have been selected by eye examination of plate material and suffer from incompletenesses and inhomogeneities at many levels. Some recent work has used digital catalogs produced at other wavelengths, most notably the IRAS Point Source Catalog (1988), and very recently, catalogs of galaxies have been produced over large areas from digital scans of photographic plates, with calibration from CCD sequences (Maddox et al. 1990a; Collins et al. 1989; Picard 1991), but the photometric errors and systematic offsets are much larger than for CCD work. The advantage to extragalactic astronomy of the proposed sensitive, uniform, photometrically and astrometrically accurate, digital sky survey cannot be overstated. In this chapter, we describe the nature of the data, both photometric and spectroscopic, we will obtain for galaxies, and the science we hope to do with it.
The photometric pipeline with which we will process the photometric images is described in some detail in Section 14. Here we describe a few of the aspects specific to galaxy science.
The first issue that comes up is identifying the galaxies themselves, in particular distinguishing them from the much more numerous stars. The two-dimensional image of every object that is identified by the object finder will be fit to three models: a star (i.e., the point-spread function, or PSF), a pure exponential profile (Freeman 1975) of arbitrary inclination, convolved with the PSF, and a pure de Vaucouleurs (1948) profile of arbitrary inclination, convolved with the PSF. It is feasible, in fact, to fit composite models (i.e., bulge + disk); it is not clear yet, however, how stable the results are, or whether the computer time this would entail is prohibitive. In any case, star-galaxy separation can be done in essentially an optimum way: a galaxy is any object whose goodness of fit to the galaxy models is superior to the PSF fit. We are currently carrying out extensive tests of this approach with model and real images. These fits will be done on the images in all five colors individually and will work with excellent data, since we plan to use only the finest seeing conditions (we expect images of order 1 arcsecond FWHM for the photometric survey; see Chapters 5 and 13). We thus expect the survey to be much more complete than previous catalogs for objects such as very compact galaxies and galaxies with bright starburst and nonthermal nuclei, since the nuclei will have quite different colors from the main body of the galaxy, and the object will be more extended in some bands than in others.
The resulting galaxy counts in different colors will be invaluable for studies of galaxy evolution, large scale structure (section 3.1) and the distribution of Galactic extinction (Section 3.7). Table 3.4.1 shows the number of galaxies per steradian per magnitude interval in the J Band, which is close to the photographic band; J = B - 0.1m = g' + 0.4m . These counts are averaged from several sources, as summarized in Figure 15 of Kron (1980) and Figure 8 of Yoshii and Takahara (1988). Thus in pi steradians we expect a total of 106 galaxies to J = 18.7m (corresponding roughly to our spectroscopic limit of r' ~ 18.2 ) and about 5 x 107 galaxies to J = 22.5m , which represents roughly the 5-sigma detection limit for extended objects (galaxies) in the survey.
| J | g' | A | dlogA/dm |
|---|---|---|---|
| 16 | 15.6 | 1.49 x 104 | 0.55 |
| 17 | 16.6 | 5.16 x 104 | 0.53 |
| 18 | 17.6 | 1.70 x 105 | 0.51 |
| 19 | 18.6 | 5.29 x 105 | 0.45 |
| 20 | 19.6 | 1.34 x 106 | 0.38 |
| 21 | 20.6 | 3.06 x 106 | 0.35 |
| 22 | 21.6 | 6.73 x 106 | 0.37 |
| 23 | 22.6 | 1.65 x 107 | 0.41 |
The model-fitting algorithm will classify as galaxies extended objects within our own Galaxy, such as planetary nebulae and highly evolved stars with circumstellar envelopes. There are likely to be few enough of these in the survey region ( <~ 100 ) that they are an infinitesimal perturbation on the galaxy counts (although they are very interesting on their own account; see Section 3.6) and in any case can be distinguished on the basis of their colors.
Of course, model fits will not deal properly with the roughly 2 million objects in our sample which will be saturated (i.e., brighter than r' ~ 14 ). Because we expect at most a few tens of (well-known) galaxies to saturate in this survey, identifying saturated objects as stars is not a terribly difficult problem. However, very bright stars have quite extended wings and diffraction spikes, as well as bleed trails, and the object finder must not split these up into thousands of faint and highly clustered galaxies. We have developed code which characterizes the extended wings of the PSF, and subtracts it off the brightest objects; Figure 4.14 shows the effect. Those parts of the object for which this subtraction is not effective will be masked; our tests show that the number of spurious objects that remain is negligible.
One of the more problematic aspects of galaxy photometry is deblending: how to deal with multiples of objects whose isophotes overlap. This is of course of concern for star-galaxy separation, because of the possibility that overlapping stellar images can be taken as a pair of galaxies, and the difficulties of doing model-fitting and photometry for a galaxy with superposed star, or a pair of galaxies. This is currently the focus of most of our work on the photometric pipeline, but we have demonstrated that our sector array approach to 2-D photometry (Section 14) does an impressive job of rejecting stars and cosmic rays in the outer parts of galaxies. In addition, we have developed software to fit local maxima in extended images to a PSF and subtract them if the fit is good, which should be able to remove stars very close to the center of a galaxy. The much more difficult problem of deblending a close pair of galaxies brings up astrophysical questions as well. Most people would agree that NGC 5194 and NGC 5195, the two galaxies which make up M51, the Whirlpool Nebula, should indeed be considered two galaxies. At the opposite extreme, the nucleus of Arp 220 is double on the scale of 1" in the near-IR (Graham et al. 1990), but few would argue that this should therefore be considered two galaxies. Where between these two extremes should one draw the line? The answer to this question, which in practice will be a function of redshift, will have repercussions on any number of galaxy statistics, from large-scale structure, to luminosity functions, to number counts.
A related area of concern is the analysis of crowded fields. While these are less of a problem at high Galactic latitudes than at low we will scan through several globular clusters and must be able to recognize when we have done so. Crowded field algorithms for the analysis of star images such as those described by Lupton (1986) and Stetson (1987) would be prohibitively expensive in terms of processing time, and so our approach is to make the code robust enough to recognize when to throw up its hands and mark a region as too confused for further analysis. Of course, most such regions (e.g., globular clusters) will indeed be known about a priori.
Finally, galaxies are extended objects, and thus a galaxy whose center is close to the edge of a CCD strip will not necessarily have its entire image on the frame. In particular, the overlap between adjacent strips is 1' (Chapter 5), and thus the photometry of objects that are bigger than this will not be complete. The fraction of galaxies of size d that are affected by this is clearly of the order of d/D , where D = 13.5' is the CCD field width. Integrating this over the diameter distribution of galaxies shows that there will be roughly 3000 galaxies over the survey area which will be affected by this. As we describe in Section 3.1.2.4, we will target for spectroscopy all galaxies in the sample with diameters greater than 1' , so that we need not worry about performing accurate photometry for those objects at the edge of a scan, at least for the purposes of target selection. We hope eventually to create a merged pixel map of the entire sky (Section 14.3.5.10), from which proper photometry of overlap objects can be done.
Morphological typing of galaxies is important in a number of applications. For example, the relative mix of galaxy types depends quite strongly on the local number density (Dressler 1980, 1984). One needs to have a quantitative calibration of the morphology-density relation that includes the fact that the luminosity functions of ellipticals and spirals are different and hence that the relative mix varies with the limiting absolute magnitude. Whether or not the observed trends continue into very low density regions is not known, though there are suggestions to the affirmative, and this survey will finally bring into existence a sample big enough to answer questions like this one (cf. the discussion in section 3.1.3). It is clear that the question "do the galaxies trace the mass?" is an a priori exceedingly ill-posed one, since different kinds of galaxies live in different kinds of places, and the only way to clarify the situation is to address the detailed morphological mix and its relationship to the density. Studies of the color-morphology relation (Humason, Mayall and Sandage 1956; Bothun, Schommer and Sullivan 1982; Giovanelli and Haynes 1983; Roberts and Haynes 1994) show that galaxies of a given morphological type have a very wide range in B-V , and may well have systematically different colors (and therefore have different kinds of stellar populations and mass-to-light ratios) in different kinds of environments. We know as well that the luminosity functions of different kinds of galaxies are different (Sandage et al. 1985; Binggeli et al. 1988), and all these effects must be considered carefully to answer the much-better posed but still very difficult question "Does the baryonic matter associated with galaxies trace the mass?" We thus consider both the morphological and the color data to be an absolutely necessary part of the survey for large-scale structure studies (cf., the discussion in Section 3.1.3.6), without which the much more laboriously obtained redshift data are much less useful.
Hubble's (1926) morphological classification scheme for galaxies has proved to be an exceedingly powerful tool for studies of galaxies. His "tuning fork" diagram has been shown to be, to first order, a sequence of bulge to disk ratios, from the diskless elliptical galaxies to the bulgeless late type spirals. This classification scheme has also been shown to have considerable physical significance. Disks are bluer than bulges, since they have continuous star formation while bulges do not, so that the global color of a galaxy (bulge + disk) is roughly correlated with its morphological type. Further, disks are dynamically `cold', are very thin in the z direction and are supported by rotation, while bulges are dynamically hot, have comparable dimensions in all three coordinates and are supported by the random motions of their stars. These shapes contain fundamental information about the formation history of a galaxy and about the nature of the density fluctuations in the early universe from which the galaxies formed.
The shapes and sizes of galaxies are, however, affected by other things than formation. Galaxies evolve: they merge with neighbors; they accrete gas from smaller neighbors and from continued infall; they lose gas to star formation, to galactic winds and to ram pressure sweeping by intergalactic gas. The colors, size, and shape of a galaxy are related to its dynamical and star-formation history. Ideally we would like to do a study of color, luminosity, and morphology as a function of cosmic time from the formation epoch to the present. We clearly cannot do this with the present survey, with which we will be able to extract some morphological information to redshifts of about 0.2, but we will be able to characterize in detail the current morphological mix and its dependence on environment for comparison with the necessarily small samples of very distant objects obtained with large telescopes (cf. Appendix A). It is not currently possible to do this in any reliable way with any existing database.
As described above, the photometric pipeline will not do a detailed morphological analysis of the objects detected in the images, but will confine itself to two-dimensional model fits to stellar, exponential, and de Vaucouleurs profiles. Our long-term plan is to develop what we call an "atlas-image pipeline", in which we would carry out detailed morphological and photometric analyses of the brighter several million objects in the sample. This can be done after the fact, because the results of these analyses are not needed for the running of the survey itself (e.g., we do not need this information for galaxy target selection), and because the photometric pipeline cuts out atlas images of every detected image, precisely for the purpose of such a posteriori analyses.
As we develop and test such software, and think about the sort of galaxy science that can be done with the images, it is useful to have examples of galaxies with known morphologies as they will appear at different redshifts. These are very useful to see, for example, how a morphological classifier becomes biased with redshift, and thus to see how well we can distinguish spirals and ellipticals as we approach the photometric limit of the images. We have used a series of images in g and r of Hercules cluster ( z = 0.036 ) galaxies taken by Dressler, Gunn, and Schneider. This cluster contains galaxies of all morphological types at a common distance. The appearance which these galaxies would have at larger redshifts in our survey (from 0.072 to 0.288 in g' , and from 0.216 to 0.814 in r' ) have been simulated by reducing the scale of each image by the appropriate amount, applying the effect of redshift on the magnitude (i.e. the opposite of the K-correction), convolving with a point spread function obtained from the stellar imaging, repixelling, and adding noise appropriate for our effective exposure time and quantum efficiency. These redshifted images are also shown in Figure 3.4.1. The luminosities of these objects are such to put them all beyond the spectroscopic limit at z > 0.2 ; as the images show, for z < 0.2 , spirals and ellipticals can still easily be distinguished, and finer gradations in morphological type can be made in most cases.
We have started to investigate several approaches to the quantitative analysis of morphology, in addition to the exponential and de Vaucouleurs model fits described above. One such is to look at galaxies in theta , log r space; in such a space, logarithmic spiral arms will be straight lines. Frei (1994) has developed code to do such an analysis, and was able to quantify the multiplicity of the arm pattern, its brightness amplitude, and the width of the arms. We hope to modify this code to run in an efficient and stand-alone mode to analyze the literally millions of galaxy images which are of high enough signal-to-noise ratio to allow such an analysis.
Another approach developed by M. Edwards and R. Lupton is to investigate the possibility of fractal structure in spiral galaxy disks using our digital images of nearby spiral galaxies. The results to date are very promising; evidence for fractal structure has indeed been found (a result of great interest on its own). Edwards has devised a method for computing the Hausdorff (1919) measure of a galactic isophote and has shown that it depends on the morphological type and on the bulge to disk ratio. Very roughly, the Hausdorff measure is the ratio of the length of a closed isophote at some scale epsilon to the area enclosed by that isophote. A smooth curve can be successively approximated by polygonal segments of scale epsilon which converge to a finite total length, that of the curve, as epsilon --> 0 . The same procedure carried out on a fractal curve produces a length which increases without bound. The Hausdorff measure thus characterizes the behavior of a curve at scale epsilon . This measure shows a transition between higher and lower values as the isophote intensity is increased and can therefore be used as a measure of the bulge to disk ratio. The method can also be generalized to deal with low resolution, noisy data and can thus be used to compare galaxy properties over a wide range of distance using the SDSS imaging data.
We continue our discussion of galaxy morphology below in Section 3.4.5, but let us first quantify the nature of the spectroscopic data we will obtain for galaxies.
A mosaic of nine Hercules cluster galaxy fields. The galaxies are shown as they will appear in the survey in g' at the Hercules redshift of 0.036. The panels which have visibly higher noise are noisier than the survey data will in fact be; they were taken with the PFUEI imager on the Hale Telescope with a very bright sky at large zenith angle. The others are four-shooter images taken under very much better conditions; all are in the g band.
The galaxies of panel a as they would appear at a redshift of 0.072. Most of the structure in the bright galaxies remains.
The galaxies of panel a as they would appear at a redshift of 0.144. The detail in the spiral structure of the bright galaxies is disappearing, but the bulges and disks are still quite distinct, as are the faint extensions in the interacting pair (6,7).
The galaxies of panel a as they would appear in g' at redshift of 0.216. At this distance most of the bright galaxies are near the survey limit. Second panel: z= 0.288, and almost all of the galaxies have dropped out of the sample. Also shown are simulated r' -band images at redshifts of 0.288, 0.407, 0.586, and 0.814. All these images are to the same scale.
The goal of this project is to obtain redshifts for 106 galaxies, which involves, of course, obtaining spectra for all of the galaxies. The details of the expected spectral coverage, sensitivity and resolution are discussed in Chapter 11.
Simulated galaxy spectra. The models are a g' = 17.6 elliptical galaxy and a g' = 19.7 spiral, showing the signal input and the output spectra. See text for details.
What might the spectra from the survey look like? It turns out to be quite difficult to answer this question in detail, because data of the quality which will be obtained in this survey (spectral coverage, signal to noise ratio and resolution) simply do not exist at present for large representative samples of either stars or galaxies. Figure 3.4.2 shows our partial answer. Spectra of two model galaxies are shown, crudely synthesized following approximately the prescription of Bruzual (1983) from the stellar spectra in the atlas of Jacoby, Hunter and Christian (1984). These spectra cover the wavelength range of 4000 Å to 6000 Å (the blue channel) at a resolution of 1000, half that of the SDSS spectrographs (although the velocity dispersion broadening in a typical galaxy spectrum more than makes up for the difference). The bottom two panels show a model spiral at z=0.2 with g'= 19.7 , i.e. well beyond the survey magnitude limit. This model galaxy has Bruzual's star formation parameter µ = 3 , and corresponds to the star formation history expected for a middle spiral galaxy. The top two panels are for a galaxy with µ = 5, (i.e. early star formation, as would occur in an E or S0 galaxy), with g' = 17.6 and z = 0.1. The top panel of each pair gives the spectral distribution before detection by the telescope, i.e. the `input', noiseless spectrum. The lower panel shows the spectrum as observed by the SDSS, i.e. with noise added and as it would appear after sky subtraction (accounting for the spikes in the simulated spectra). The intensity difference between the two is due to the loss incurred by the finite fiber diameter. The bottom-most spectrum in Figure 3.4.2 is one of the most difficult types of spectra from which to obtain a redshift. The galaxy is faint, the hydrogen and other lines are weak and the 4000 Å break is weak. However, it is more than good enough to obtain a redshift and velocity dispersion accurate to about 20 km s-1 , and it represents the expected results from a galaxy more than a magnitude fainter than our average limit. The spectrum of the brighter object illustrates another factor, that one does not do as well as one might expect for brighter galaxies because a smaller fraction of light is captured by the fiber.
An absolutely integral part of this survey will be the acquisition of a large library of stellar spectra taken with the SDSS spectrographs, either during the test year, during the time when the Moon is up, or both. These spectra will act as templates for calculating the redshifts and velocity dispersions of the galaxies and also as raw material for population synthesis modeling. It is important to realize that the excellent five color imaging data which will be obtained from the photometric survey will allow the spectra to be photometrically calibrated. Fiber spectroscopy always carries with it the question of how well centered the fibers really are on the object during the exposure; we will attempt to address this problem by taking four very short and heavily binned exposures with the telescope offset slightly in the four cardinal directions (in elevation and azimuth). These data used in conjunction with the image data should tell us unambiguously for each object where the center of the fiber is, and furthermore allow us to make corrections for chromatic differential refraction to do quite accurate spectrophotometry (see Chapters 5 and 11 for a fuller discussion.)
The spectrophotometry and the high signal to noise ratios for the spectra of even the faintest galaxies in the spectroscopic sample may allow the redshifts and velocity dispersions to be calculated by direct fitting of the stellar spectra to the galaxy spectra in wavelength space (e.g., Rix and White 1992; Connolly et al. 1995), instead of using the Fourier quotient or Fourier cross-correlation techniques which have become standard in this field (Sargent et al. 1977; Tonry and Davis 1979; Statler 1995). Direct fitting, if it can be done, has several advantages: it makes use of the information in the continuum slope and in the spectral breaks, and it allows the variation of the signal to noise ratio across the spectra to be properly taken into account. The algorithms we are developing are described in Chapter 14.
If appropriately calibrated, The spectroscopic data produced by the SDSS will give an invaluable source to study the stellar content of galaxies and their evolution. There exist only a few dozen galaxies for which good spectroscopic data with this wide spectral coverage and moderately high dispersion exist; the SDSS data will increase this by several orders of magnitude. The K -correction, which is a basic ingredient in studying distant galaxies, has been calculated from only a few galaxies in each morphological class (Coleman, Wu and Weedman 1980; Kennicutt 1992).
The spectroscopic data from SDSS will allow stellar synthesis models to a level of sophistication not previously possible: for example, the coverage to 9000Å will allow us the determination of the fraction of early and late M-stars, and fine resolution will tell us about A and F stars. The understanding of stellar populations is crucial for the study of galaxy evolution. Particularly interesting will be the spectral synthesis and star-forming history of irregular galaxies, which are now believed to be the most rapidly evolving population, responsible for the excess of blue galaxies at faint magnitudes (Glazebrook et al. 1995).
Our redshift survey will reach beyond z = 0.15 , corresponding to a look-back time of 2 Gyrs; this may be enough to see the effects of evolution (indeed, Maddox et al. 1990 find evidence for galaxy evolution in the number counts at the magnitude limit of the redshift survey). The effects we will be looking for are subtle, but we will have excellent data for large numbers of objects.
A number of elementary statistical characteristics of galaxies, such as the luminosity function, the color distribution, the frequency of morphological and profile types, the frequency of characteristic surface brightnesses and the various correlations among galaxy global properties remain poorly determined. This is because there is no large catalog of galaxy image profiles in more than one band for normal field galaxies chosen in some unbiased way. The SDSS will completely change this situation by providing excellent multi-color photometry for an enormous sample of galaxies. The use of the u' and z' filters in the photometric survey will be an especially important contribution, since little galaxy photometry has been done at these wavelengths. The U - B colors of galaxies span a wide range and are critically diagnostic of star formation, and, in the images, of the presence of even small amounts of obscuring dust.
Studies of the galaxy luminosity function and other properties and of evolution effects can be made both on the larger photometric sample of 5 x 107 galaxies and on the spectroscopic sample. The large sample of galaxies to our imaging limit could be subdivided into groups of similar apparent magnitude and apparent size to test for redshift effects and to test how different sample selection changes the apparent galaxy relationships.
The measurement of redshifts allows the physical properties of galaxies, such as their diameters and luminosities, to be determined. To date, the determination of distribution functions such as the galaxy luminosity function have of necessity been quite crude because the statistically reliable samples have been small. Thus, the assumption is often made that the form of the luminosity function is the same in rich clusters as in the field and that different types of giant galaxies have the same shape of luminosity function. It is unlikely that such uniformity actually prevails (e.g. Sandage, Binggeli and Tammann 1985) and it is important to determine how the luminosity function does vary. Figure 3.4.3 shows the best determination to date of the galaxy luminosity function in optical bands (Loveday et al. 1992). These data indeed show that the spiral and elliptical luminosity functions are quite distinct. Although the luminosity function is well-determined near the knee, it is uncertain at the bright end, and even more so at the faint end; indeed, the slope of the luminosity function at the faint end has been a point of a great deal of controversy (cf. Efstathiou et al. 1988 and references therein). This has been a great source of uncertainty in the modeling of the faint galaxy counts and tests for evolution (cf., Koo, Gronwall, and Bruzual 1993; Koo and Kron 1992; Gronwall and Koo 1995). With a total sample of 106 galaxies one can subdivide the sample into many groups according to the spectral type, surface brightness, local environment etc. and still have excellent statistics for determining the shape of the luminosity function and its normalization in luminosity and in amplitude. Similarly, one can construct bivariate luminosity functions, with the second independent variable being color, diameter (e.g. Sodré and Lahav 1993), or even flux in a waveband other than the optical. With a sufficiently large number of galaxies, it will be possible to search for features in the luminosity function (aside from the characteristic roll-over at bright luminosities). Such features might be especially evident in the distribution of diameters for disk galaxies grouped according to spectral type, which might be suggestive of physical processes that operate only above some threshold, for example in the surface density of gas in the disk.
Luminosity function of a magnitude-limited sample of 1769 galaxies. Note the large statistical errors at faint and at bright luminosities. Note also the difference between the luminosity functions of elliptical and spiral galaxies. The curves drawn are fits to a Schechter (1976) curve. From Loveday et al. (1992).
When we start to contemplate the full multivariate distribution function of galaxies as a function of all relevant observable properties, what we are really doing is looking for the underlying physical correlations between these properties. A full understanding of these correlations would go a long way towards putting the morphological classification of galaxies on a firm physical basis, and would supply invaluable clues for galaxy formation models and the origin of the range of galaxy morphologies. One well-developed technique for quantifying these correlations is Principal Component Analysis, or PCA (cf., Murtagh and Heck 1987). Previous PCA studies performed on samples of bright galaxies (e.g., Whitmore 1984; Efstathiou and Fall 1984; Han 1995) have shown the existence of at least two significant dimensions both for disk and elliptical galaxies, although the parameters included in the analysis are different for the two classes of galaxies (Okamura et al. 1989, Kormendy and Djorgovski 1989). The dimensionality and the shape of the manifold must ultimately reflect the physics of galaxy formation and evolution.
However, the small size of the samples used (20-150 galaxies) and the limited range of data for each galaxy leaves many important questions unanswered:
The SDSS will produce excellent data to investigate these questions. The spectroscopic sample, in particular, will include 106 galaxies with superb morphological, spectroscopic, and photometric data, residing in a wide range of environments. The number of galaxies with uniform data available is unprecedented, of course. The complete redshift survey will allow local (i.e., several Mpc) density to be included in the PCA analysis. The spectra will allow a host of spectral diagnostics to be developed, including absorption and emission line strengths and ratios, which can also be correlated with the morphological and photometric properties of the galaxies. It will also become possible to analyze subsamples under different environments in order to see the universality of the manifold. Finding either universality or change among the subsamples would give important clues to the understanding of galaxy formation. Finally, new correlations between distance-dependent and distance-independent quantities will give rise to new distance indicators, which will of course be very useful in peculiar velocity studies (Section 3.1.4).
We can of course apply PCA to the much larger number of galaxies in the deeper photometric sample, although the number of available parameters for each object will be smaller, both because of absence of redshifts and spectra, and because the images will not be as detailed. Distance independent parameters such as colors, surface brightness, and concentration index can be included in the analysis.
This work offers many opportunities for further investigations. For example, photometry from large-scale surveys in other bands, such as the near-infrared (the Two Micron All Sky Survey; cf., Section 2.3), the radio continuum (the FIRST survey; Becker, White, and Helfand 1995; cf., Condon 1992), and the ROSAT X-ray data (cf., Section 2.1) can be included in the PCA analysis, yielding insights into the physical processes that give rise to these forms of emission. On the longer term, this work could evolve to more sophisticated tools than PCA, using eigenvalue techniques such as the Karhunen-Loève (K-L) Transform (for recent astronomical applications, cf., Connolly et al. 1995; Vogeley and Szalay 1996; Tegmark, Taylor, and Heavens 1996).
It has long been argued (Disney 1976; McGaugh, Bothun, and Schombert 1995; Sprayberry, Impey, and Irwin 1996) that existing galaxy surveys are strongly biased against finding low surface brightness galaxies, an argument made stronger by the recent discovery of appreciable numbers of large galaxies with central surface brightnesses of muV > 25 mag per square arc-sec (Schombert and Bothun 1988; Schombert et al. 1992; Dalcanton 1995; Impey et al. 1996) and galaxies with dramatically large HI mass to optical luminosity ratios (e.g., Carignan and Beaulieu 1989; Impey et al. 1990). The low surface brightness population is very important to quantify, because it may represent an appreciable fraction of the baryonic content of the universe, and have much to tell us about thresholds for star formation and the fragility of disks (cf., Impey and Bothun 1989; Schombert et al. 1990). Indeed, given our standard picture of hierarchical clustering and merging in the universe, it is unclear how such low-surface brightness disks can possibly survive. The low-luminosity end of the galaxy luminosity function is quite uncertain, as mentioned above, and tying it down will require a full inventory of low surface brightness systems. Indeed, the discovery of objects like Malin 1 (Impey and Bothun 1989) shows us that there exist populations of low surface brightness galaxies with appreciable integrated luminosities; it is unknown if there are enough of these to appreciably contribute to the galaxy luminosity function at the bright end (McGaugh 1996). It has been suggested that the faint blue galaxies seen in deep photometric surveys are going through a starburst and have faded to low surface brightnesses today (e.g., McGaugh 1994; Ferguson and McGaugh 1995); such a scenario can be constrained only by characterizing the low surface brightness population at the present.
Very little is known about the large-scale distribution of low-surface brightness objects. Although it does not appear that moderate surface brightness galaxies (i.e., those with mean surface brightnesses high enough to appear in the UGC, although still faint with respect to "ordinary" galaxies) fill the voids traced by brighter galaxies (Bothun et al. 1986; Thuan, Gott, and Schneider 1987; Eder et al. 1989), they do show lower-amplitude clustering on small scales than do "ordinary" galaxies (Bothun et al. 1993; Mo, McGaugh, and Bothun 1994; Sprayberry et al. 1995). The fragility of their disks would argue that they should not be found in dense environments (Bothun et al. 1993), although surveys in clusters have found many galaxies of low surface brightness (e.g., Bothun, Impey, and Malin 1991; Ulmer et al. 1996). At the brighter surface brightness limits of the SDSS spectroscopic survey (cf., Section 3.1.2.4), one can search for differences in the density fields traced by galaxies of different surface brightnesses.
Objects like Malin I present further mysteries. It is one of several low surface brightness galaxies known with a dwarf Seyfert nucleus. It is completely unclear how such a seemingly fragile system can form and feed a massive black hole in its center. These objects are rich in HI but deficient in CO, and have blue colors with very weak star formation (Schombert et al. 1990). With only a handful of such galaxies known, it is difficult to come up with models to explain this series of seemingly paradoxical results.
The SDSS should be superb for finding low surface brightness galaxies. The drift-scan mode means that we should be able to flatfield with high precision: if we can flat-field to a (pessimistic) 1% in normal staring mode, then we should be able to do a factor of N1/2 better in drift-scan mode, where N=2048 is the number of pixels across the CCD. Thus we should have systematic problems 9 magnitudes below sky, or at about µV = 30.7 mag per square arcsec; in any case, we should be limited by photon statistics for any reasonable object. Thus we find that if we assume a Gaussian profile for these objects, the 5 sigma detection limit of galaxies with a scale length of 16" is r' = 19.5 (a factor of 10 fainter than Malin 1!), with a central surface brightness of 27.5 mag arcsec -2 . If they have exponential profiles (e.g., McGaugh, Schombert, and Bothun 1995), our efficacy will be somewhat lower. Dalcanton (1995) has used the drift scan data of Schneider, Schmidt, and Gunn (1989) to demonstrate the advantages of this approach to find low surface brightness objects; her survey is perhaps the deepest yet over substantial areas of the sky. We should be able to go to a surface brightness limit two magnitudes fainter still when the multiple scans of the Southern Stripe (Section 5.5) are stacked (cf., Section 14.3.5.10).
Low surface brightness galaxies are not the only very diffuse extended objects which can be detected in this work; we will also detect a large number of the diffuse, extended high latitude reflection nebulae (e.g., Guhathakurta and Tyson 1989), and high-redshift clusters of galaxies (Dalcanton 1996; Zaritsky et al. 1996; cf., Chapter 3.2). Algorithms for finding and distinguishing among these objects are going to be tricky, and this remains work for the future. Photometric measurements of the larger low surface brightness galaxies will be biased low by the determination of the local background sky in the automated reduction of the SDSS images, so that much work will be involved in carrying out simulations and going back to the raw data to calibrate and correct for this effect.
Most elliptical galaxies have red colors (B-V = 1.0) reflecting their old stellar populations (Faber et al. 1989). However, a small fraction (about 5% of elliptical galaxies in a magnitude limited sample) have colors considerably bluer than this, with B - V <= 0.8 . These galaxies also tend to contain more cold interstellar matter (detected via far infrared, CO and HI emission; Lees et al. 1991) and to be of lower luminosity than the redder galaxies. Is the color-luminosity relation for ellipticals due to metallicity effects or is it indicative of slow continuous star formation? What are the interrelations among metallicity, color and luminosity? Are the blue ellipticals really ellipticals? The combination of excellent colors, the u' band flux densities, the high quality surface brightness/morphology information and the high dispersion spectra (which include information on absorption line strengths, on velocity dispersions and on emission line strengths) for a large number of early type galaxies should allow definitive answers to these questions. They are important for several reasons: what really is the star formation history of the typical elliptical galaxy? How is this affected by environment? How reliable are elliptical galaxies as standard candles and how well can their distances be calibrated? How does star formation work in an elliptical galaxy, which provides a very different environment than does the disk of a spiral galaxy? How did these galaxies form, and what does this tell us about the early structure of the Universe? Can galaxies have formed as recently as recently than z ~ 1 - 2 , which some currently fashionable cosmological models predict? This is only one of the many possible studies of galaxies which will be enabled by a catalog of well determined morphologies.
The SDSS will obtain high resolution photometric images in five colors of several thousand galaxies larger than 2 arcminutes; most of these will be spirals. This will provide a large sample which will allow quantitative studies of spiral structure and allow such quantities as the strength of the spiral pattern to be measured as a function of color. The density wave theory of spiral structure predicts that the spiral pattern should be strong in the dynamically cold material and much weaker in the dynamically hot material (the old disk stars). However, near infrared (2 µm ) images of M51 show that the arm-interarm brightness contrast is greater at K than in the visible (Rix and Rieke 1993). The great contrast in the visible can be attributed to the effects of dust and young stars, but it is difficult to explain the infrared result. The images discussed herein should allow this question to be investigated for a very large number of spiral galaxies of many different types and allow us to infer whether the arms are adequately described by more-or-less classical density wave theory or not, and what are the conditions (mass of the galaxy, presence of a satellite, etc). which give rise to spiral structure in the young and old material.
It is well known that low-level quasar-like activity is found in the nuclei of large numbers of galaxies, and it is estimated that as many as 50% of nearby galaxies show some signs of non-thermal activity in their centers (e.g., Filippenko and Sargent 1985; Ho, Filippenko, and Sargent 1995; Ho 1996), although only ~ 2 % of optically selected galaxies are of classical Seyfert type 1 or 2 (Blandford et al. 1990). Thus the SDSS spectroscopic survey can be expected to find of the order of 20,000 classical Seyfert galaxies, several times the number currently known (although many might be classified as quasars depending on their luminosity), with superb photometry and spectroscopy for each, and more than an order of magnitude more weaker AGNs.
Active galaxies manifest themselves in a large number of ways. The optical spectra of AGNs often show broad emission lines. Seyfert 2 galaxies have lines with FWHM of order 500 km s -1 (appreciably broader than the rotation speeds of all but the most massive galaxies), while Seyfert 1 galaxies show widths of up to many thousands of km s -1 .
The SDSS spectra will cover a large range of wavelengths, allowing one to search for many emission lines diagnostic of nuclear activity; the spectral range from [O II]3726, 3729 Å to [S III]9069 Å is potentially observable at low redshifts. Line-ratio diagnostics such as have been developed by Baldwin, Phillips, and Terlevich (1981), Veilleux and Osterbrock (1987) and Osterbrock et al. (1992) will select complete samples of AGNs; indeed, the quality and quantity of the SDSS spectra will be such that these diagnostics will be refined substantially. Similarly, the survey will be sensitive to rare types of AGNs: those with uncommon emission lines or emission line ratios. At the ~ 2 Å resolution of the SDSS spectrographs, one can distinguish AGNs by their line widths, and for the higher signal-to-noise ratio spectra, one can search for quite low amplitude AGN components (cf., Filippenko and Sargent 1985). To do this properly, especially for AGNs with luminosities small compared to that of their host galaxies, will require careful subtraction of the underlying stellar continuum spectrum (cf., Filippenko and Sargent 1988), which will require specialized software to be developed as the survey progresses.
The scientific returns from such an analysis are obvious. Models for the formation of emission lines in the narrow and broad line regions of AGNs (cf., Davidson and Netzer 1979; Netzer and Ferland 1984) are rarely faced with high quality spectra covering essentially the entire optical window. Having line strengths and widths for such a range of lines for many thousands of spectra will test these models to their limit, and inspire the next generation of models. We plan to stack the spectra of many individual AGNs of a given class to obtain generic spectra at very high signal-to-noise ratio, which can be used to search for very faint emission lines (cf., Francis et al. 1991; Lawrence and McCarthy 1996). We can also use the more sophisticated tools of PCA and the K-L Transform (see above) to find the set of eigenspectra that span the space of observed spectra (cf., Francis et al. 1992; Connolly et al. 1995). In addition, these studies will be the first complete inventory of active galaxies in our neighborhood. The luminosity function of AGN (or even more interesting, the mass function of the putative black holes at the centers of these galaxies) at the present is wildly uncertain; existing samples are small and are based on inaccurate and ill-defined criteria. This survey will measure the luminosity function directly, and thus yield insights into the evolution of QSO's and their connection to the AGN population. In particular, the increase in the comoving density of quasars as a function of redshift z suggests that inactive or weakly fueled black holes abound in nearby galaxies; the luminosity function of local AGN to faint levels will yield important insights into this question.
Comparison of the spectroscopic and morphological properties of these galaxies may yield insights into the starburst-AGN connection (cf., Filippenko 1992) (especially if emission lines like H alpha can be decomposed into broad and narrow components), and unified models for AGN. In particular, it remains a mystery why Seyfert galaxies are associated with spirals, while radio galaxies are exclusively found in elliptical galaxies (cf., Balick and Heckman 1982 and the recent discussion in Bahcall et al. 1996).
The optical continuum of AGNs is another distinguishing property. It is usually power-law in form, fnu ~ nu-0.7 . However, in galaxies in which the AGN is comparable or weaker than the stellar light of the host galaxy, it can be difficult to separate the non-stellar and stellar continuum, especially in the presence of reddening. If the non-thermal continuum of the AGN population can be measured, models of the ionizing background at low redshifts will be strongly constrained (cf., the discussion in Williams and Schommer 1993).
AGNs manifest themselves photometrically as well. In many galaxies, they appear as an unresolved nucleus in the stellar profile, becoming more prominent in the blue (cf., Maoz et al. 1995). Unresolved nuclei are not a unique indicator of activity, however, as many elliptical galaxies are now being found with unresolved cusps, even at HST resolution (cf., Lauer et al. 1995). However, a galaxy with a central region dramatically bluer than the galaxy as a whole is a good AGN candidate.
The Southern photometric survey, with its multiple scans of a single strip, will yield large numbers of candidate AGNs through their variability. This will yield an AGN sample selected completely independently of its spectral or color characteristics, and may be an ideal way to discover previously unrecognized classes of AGN (cf., Trevese et al. 1989). This survey will almost certainly discover new types of spectral variability of AGNs with careful measurements on long time baselines.
Finally, AGNs manifest themselves by their emissions in other wavebands, in particular the radio. The VLA 1.4 GHz FIRST survey (Becker, White, and Helfand 1995; cf., Appendix A) is covering the same area as the Northern SDSS area. At the 1 mJy flux limit of this survey, the radio source population is nearly an equal mixture of high-redshift radio galaxies, and nearby star-forming galaxies (it is the latter population that exhibits a tight correlation between the radio and far-infrared luminosity; cf., Condon 1992; Crawford et al. 1996). Thus those radio galaxies that are optically bright enough to be spectroscopic targets will be mostly star-forming galaxies, while the high-redshift population will be identified photometrically, to be followed up on larger telescopes. Estimates are that 60% of the radio sources will have optical counterparts brighter than the Northern photometric survey limit.
From the ROSAT survey (Section 2.1), we will have soft X-ray fluxes, or limits thereon, for all the spectroscopic targets, allowing detailed comparison of the X-ray and optical properties of AGN. The presence of a galaxy with spectral lines indicative of an AGN within the positional error box of a ROSAT source should make the identification of that source unambigous, of course!
By assembling a uniform sample of AGNs with emission-line strengths and photometric and morphological data for each, it will be possible to explore the full range of AGN phenomena, and in particular, to find correlations between properties which point to physical processes which unify the plethora of AGN types. This database will become particularly powerful when combined with the surveys in other wavebands mentioned above. With such a complete accounting of the AGN sample, we will be able to calculate accurate luminosity functions in many wavebands, which is tremendously important for modeling the X-ray background (e.g., Fabian and Barcons 1992) and the evolution of quasars (e.g., Crampton 1992), among other things.
It has become increasingly clear in the last decade that the faint number counts of galaxies are inconsistent with no-evolution or even passive evolution models (e.g. Tyson 1988), and it has been suggested from galaxy number counts that the evolution is evident even at bJ = 18 (Maddox et al. 1990b). That is, number evolution of galaxies may indeed be apparent within the redshift survey sample (cf. Figure 3.1.4). Redshift surveys of faint galaxies have failed to detect the signature of evolution in the shape of the redshift histogram, although the amplitude, and emission-line strength, does show signs of evolution (Colless et al. 1990). Models to explain this have invoked starbursts, dramatic merging, and a positive cosmological constant (cf. Koo and Kron 1992); it is now becoming clear that irregular galaxies have undergone much more dramatic evolution recently than have ordinary spiral and elliptical galaxies (Glazebrook et al. 1995; Fukugita et al. 1996). The SDSS photometric and redshift survey will of course not go as deep as one would like to probe evolutionary effects at the highest redshifts; this is really the domain of surveys on much larger telescopes, such as DEEP (Mould 1993; cf. Appendix A), and of course imaging surveys from HST. However, there are a number of aspects of the evolution problem that the SDSS is well suited to tackle, especially in the Southern survey.
With detailed number counts in several bands to the photometric limits of the survey, one can put firm constraints on models for galaxy evolution, at least at relatively low redshifts. The Southern photometric survey will probe to redshifts of order unity, and will give the best data for evolutionary probes. Matching the photometric catalog with catalogs drawn from sky surveys in other wavebands, from X-ray to radio (cf. Appendix A) will allow models of the evolution of flux in these wavebands to be developed and tested.
The faint galaxy count data have been interpreted as implying the existence of a new population of blue galaxies appearing at B = 21 or so (e.g. Lilly et al. 1991), which seems to show weaker clustering than do the red galaxies, at least at fainter magnitudes (Efstathiou et al. 1991). This will be testable directly from the southern photometric data; although it does not go as faint as does the data of Efstathiou et al., it covers a much greater area and number of galaxies, and we will be able to measure correlations in narrow magnitude and color slices. However, Koo et al. (1993) have argued that our knowledge of the luminosity function as a function of passband and morphological type at the present is so uncertain that one can fit all existing data to models with very little evolution, and without needing to invoke a new population. The SDSS photometric and redshift surveys will tie down the luminosity function of nearby galaxies once and for all (see above), and will allow detailed modeling along the lines of Koo et al., but at a far more sophisticated level.
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