The Galaxy has a unique role to play in determining the origins of the Hubble sequence of galaxies, since although it is a typical disk galaxy we can obtain atypical observational data, allowing rather detailed models to be tested. The SDSS will provide an unprecedentedly large, uniformly observed sample of stars which can be used to investigate many aspects of star formation and Galaxy evolution. Many interesting and fundamental problems can be addressed with the photometric catalog alone, while the addition of kinematics and chemistry, available from the spectroscopic survey, provides a powerful tool for deciphering the evolution of the Galaxy and galaxy formation in general (e.g. Bahcall 1986; Binney and Tremaine 1987; Freeman 1987; Gilmore, Wyse and Kuijken 1989; Majewski 1993).
The catalog of positions, magnitudes and colors of stars resulting from the photometric survey can be used to calculate the two-point correlation function of stars. This quantity of course first acts as a check that one has not lost faint galaxies by falsely classifying them as stars -- interloper galaxies into the stellar sample will provide a signal in the correlation function on large (tens of arcmin) scales where stars should be intrinsically uncorrelated (see Figure 3.5.1, taken from Gilmore, Reid and Hewett 1985). The correlation function and other measures of the angular clustering of stars can also be used to investigate physical phenomena in the Galaxy.
Two-point correlation functions. These are compared for (a) galaxies (b) stars and (c) the star-galaxy cross-correlation from the sample of Gilmore et al. (1985). Error bars are indicated for (a) and for (b) and (c) are smaller than the points. The complete absence of structure in the stellar functions illustrates that no significant galaxy contamination is present in the stellar samples, and that the upper limit to the patchy obscuration affecting the stellar distributions is less than EB-V ~ 0.03.
The small-scale two-point angular correlation function of stars will contain real information about the physical distribution of stars, and in particular their binary nature. Other measures of small-scale clustering, such as nearest neighbor analysis, may also be applied to the data (e.g. Bahcall and Soneira 1981). Wide binaries are intrinsically interesting, and in terms of galactic structure they are also potentially important probes of dark matter. As shown by Weinberg (1990) wide binaries in principle can place strong limits on the mass of dark objects in the disk, but at present such an analysis is limited by the lack of suitable samples. Weinberg identifies the interesting separation as being 0.1 pc, which will correspond to less than a few arcminutes for most of the stellar sample. We should be able to obtain a large number of candidate binaries, and thus carry out the first real analysis limiting the mass of putative dark objects in the disk.
The other important aspect which can be addressed is the possible variation in binary properties across the sky -- Saarinen and Gilmore (1989) searched Schmidt plates covering 800 square degrees of sky to identify candidate binaries brighter than B = 12 mag with separations less than 3 arcmin, and found large variations in the local surface density of wide binaries. Such a variation may trace the tidal field of the halo.
The clustering properties of the giant stars will also reveal low surface brightness dwarf galaxies; the photometric catalog will allow systematic surveys for satellite galaxies whose strongest signature is in their resolved stellar component. The strength of automated techniques has been demonstrated by the discoveries of the Sextans and Sagittarius dwarf spheroidal galaxies by Irwin et al. (1990) and Ibata et al. (1994). The Sextans dwarf was found through analysis of the catalog of stellar positions and magnitudes resulting from an APM scan of a Schmidt plate (Irwin et al. 1990) which had previously been searched visually. The galaxy is clearly seen as a local peak in contour plots of the giant star density. The Sextans dwarf was found as an enhancement in two dimensional star count data; the contrast can be very significantly enhanced by searching a photometric data base in three dimensions, i.e. by using the magnitude as well as the position information, and exploiting the excellent photometric accuracy of the SDSS by running a matched filter through the star count data in exactly the same way as is done for clusters of galaxies as described in section 3.2.2. The filter consists of a model surface brightness distribution and luminosity function for a dwarf spheroidal galaxy. The surface brightness distribution can be described by a Plummer sphere and the luminosity function by that found for the Carina system by Mighell (1990). Color information can be folded into the matched filter as well The great size and accuracy of the photometric data base should enable thousands of these systems to be found if their mean density in the Local Group is as high as their local density. For example, a typical dwarf spheroidal at at distance of 600 kpc would have a giant branch extending to r' ~ 21 , and should easily be found. Likewise, globular clusters like the Palomar clusters, which are much less populous than dwarf spheroidals but much denser, will be found to comparable distances if they exist, and a census of objects like these in the solid angle of the survey throughout the whole Local Group can be made.
The SDSS will provide high-latitude stellar data to complement those obtained as a by-product of gravitational lens searches. The OGLE data (Szymanski et al. 1996), for example, have revealed the structure of the stellar disk in the inner regions of the Galaxy in great detail, and show the presence of a well-defined bar. Star count data from the Northern and Southern galactic hemispheres locate the Sun with respect to the Galactic midplane (Humphreys and Larsen 1995) - the SDSS can produce star counts at different colors and over a much wider range of magnitude than can be derived from photographic plates, and can both refine the Solar system displacement as well as exploit it to investigate the scale heights of different stellar populations.
It is possible that the survey will be extended to lower latitude after the galactic cap measurements are made, and if this is done the measurement of the stellar warp of the Galaxy should also be an area where the SDSS can provide significant input. The warp in the HI gas reaches 3 kpc above the plane about 12 kpc from the sun, in the north. The warp is strongest for l~100°, b~15° (alpha~20h, delta~60°). The stellar warp may or may not follow the gas -- but its behavior is of obvious importance in studying the warp itself e.g. is it long-lived, as expected in some models with non-axisymmetric halo potentials? (see Djorgovski and Sosin 1989 for a tentative detection in IRAS sources, and Binney 1992 for a review of warps).
The warp may also be exploited as a tool for studying the stellar population in the outer disk. The tilt above the plane cuts down extinction significantly, and there are windows of even lower obscuration. It is of great interest to know where the disk ends and what the metallicity and kinematics of the stars in the outer regions are (hence spectroscopy of candidate stars is desirable). The scale-length and radial structure of the thin disk are rather poorly known at present. Star counts from V, B-V CCD photometry in the anti-center by Ojha et al. (1994) led to the conclusion that the exponential scale-length is only 2.5 kpc, compared to the estimate of 5.5 +- 0.5 kpc from Pioneer 10 surface photometry of the Galaxy (van der Kruit 1986). A variation in scale-length with the age of the stars used as tracers is predicted in some models of disk star formation (e.g. Wyse and Silk 1989); again the SDSS will allow quantitative comparisons with models. It should also be noted that one way of constraining the value of the Hubble constant involves comparing the radial scale-lengths of external disk galaxies, which are dependent on distance and hence the Hubble constant, with that of the Milky Way; thus the radial structure of the disk is also relevant for large-scale structure. The data of Ojha et al. (1994) also show an abrupt fall off in stellar density beyond 6 kpc from the Sun. However, there are HII regions known beyond this radius, the most extreme being that discovered recently by de Geus et al. (1993).
The general anti-center region is also of interest to constrain models of thick disk formation -- for example the scale-length of the thick disk is poorly known at present but can be a major discriminant of theories of thick disk formation, being for example about 50% larger than that of the thin disk in some merger models (Quinn, Hernquist and Fullager 1993) but approximately equal to the thin disk in models where the thick disk is simply part of a quasi-static settling of material to the plane (Burkert, Truran, and Hensler 1992).
Consideration of the extant data suggests that the shape of the stellar halo varies as a function of distance from the Galactic center, being flatter closer to the center (within the solar circle) but nearly spherical at large distances (e.g. Bahcall and Soneira 1984; Hartwick 1987; Wyse and Gilmore 1989; Sommer-Larsen and Zhen 1990). The shape of the stellar halo, especially when combined with stellar kinematic data, tells us much about the role of gaseous dissipation during collapse and formation of the stellar halo, and is also important in comparison with predictions from cosmological simulations of dissipationless, and dissipational, galaxy formation. For example, Cold-Dark-Matter-dominated cosmologies predict that dissipationless systems are rather strongly triaxial (e.g. Dubinski 1992 and references therein).
The bright blue stars cataloged in the directions of known High Velocity Clouds will provide a useful database for follow-up high resolution spectroscopy (once the distances to the stars are established, for which photometric parallax should suffice) in order to constrain the distances to the HVCs and their kinematics, via study of absorption features if the clouds are intervening.
The photometric survey will also provide an ideal database for selection of candidate young stars in the halo. Lance (1988) carried out the most complete survey to date -- she identified 218 early-type stars (to F0) in 305 square degrees at the SGP, and interpreted her results in terms of a burst of star formation due to interaction with a satellite galaxy. Again, the SDSS should provide an ideal sample for spectroscopic identification and study of possible main sequence A stars.
Even with a relatively small number of fibers allocated to stars, the spectroscopic survey will be able to address many problems in galactic structure. The 20 km/s or so velocity accuracy should allow for thick disk/halo discrimination, and also for thin disk/thick disk discrimination, especially if the thick disk has the intermediate kinematics favored by Wyse and Gilmore (1986) and Soubiran (1993). Chemical abundance estimates should also be possible (Bryn Jones et al. 1996). The combination of kinematics and chemistry provides a powerful tool for deciphering the evolution of the Galaxy (e.g. Gilmore, Wyse and Kuijken 1989). We shall give just two examples here.
Faint blue horizontal branch (BHB) stars are efficient tracers of the distant halo, being intrinsically bright and reasonably plentiful (note that the survey will also provide a map of the `second parameter' of horizontal branch morphology through the halo, with identification of RR Lyrae stars also, thus providing an indicator of age in the stellar field population; see Suntzeff, Kinman and Kraft 1991). Their kinematics thus provide strong constraints on the dark matter distribution (e.g. Pier 1982; 1983; Sommer-Larsen and Christensen 1986; Arnold and Gilmore 1992). Further, there have been tentative identifications of `halo moving groups' in samples of BHB stars (Sommer-Larsen, Christensen and Carter 1989; Dionidis and Beers 1989; Arnold and Gilmore 1992), which may be signatures of past merging events in the formation of the halo.
An example of other problems that can be investigated spectroscopically, armed with the photometric catalog, is the amplitude of the chemical abundance gradient in the old disk. At present there are discrepant results, with field K giants showing little gradient (Lewis and Freeman 1989) while old open clusters (ages estimated to be in the range from 1 Gyr to 8 Gyr) show a negative gradient of amplitude ~ -0.1 dex/kpc (Friel 1993) similar to that seen in the youngest tracers, the HII regions (Shaver et al. 1983). These data can also be used to investigate the incidence of metal-poor stars in the disk population (Ryan and Lambert 1995) and the vertical abundance gradients in the old disk (cf. Gilmore et al. 1995; Layden 1995).
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