Although the SDSS is primarily intended to facilitate the investigation of galaxies and quasars, the largest number of objects recorded in the photometric survey will be stars. There will be of order 7 x 107 stars with signal-to-noise ratios above 5 in at least three bands in the survey. Some of those stars will be indispensable for other aspects of the survey, in particular for the determination of Galactic absorption, the establishment of the astrometric coordinate frame, providing template spectra for the spectroscopic survey, and for correcting the telluric absorption features in the spectroscopic data at near-infrared wavelengths. We will obtain many stellar spectra for a variety of purposes, and those spectra, with their high resolution and accurate ( ~ 20 km s -1 ) radial velocities, will also yield a large catalog for various kinds of statistical and Galactic-structure studies. Both the spectroscopic and imaging catalogs will, moreover, reveal a large number of astrophysically interesting objects. The size and depth of the photometric catalog is such that the data bases for most of these studies improve on existing ones by large factors, and for those requiring accurate photometry, good temperatures (from r'-i' ), or gravity and abundance measurements (using u' data), by factors of order 100 or greater.
An indication of what we expect to see can be gleaned from Figure 3.6.1, which shows the numbers and mix of stars predicted at the north Galactic pole from the model of Bahcall and Soneira (1984); the total counts and the color distributions predicted by this model were fixed by direct comparison with then-available stellar surveys. Since our survey region is mostly above Galactic latitude 30°, the majority of the faint stellar objects we will find will be halo stars and very faint stars in the disk. The limits of our survey allow a thorough investigation of the stellar content and distribution in the halo: main-sequence stars of solar luminosity will be detected to a distance of 40 kpc, and horizontal-branch stars to 250 kpc, so that the survey will contain an essentially complete census of the halo for objects brighter than the Sun. All of the rare halo objects with distinctive colors in the survey area will be found, such as super-horizontal-branch (SHB) stars, hot subdwarfs, and planetary nebulae. For objects of the luminosity of Population II giants, we will have good photometry at distances of 500 kpc, and so can look at the intergalactic population in the Local Group. Thus, the stellar sample derived from our survey will provide unexcelled constraints for deriving a new detailed model for our Galaxy's stellar populations.
Expected differential star counts at the North Galactic Pole. (From Bahcall and Soneira 1984). The mean over the 104 square degree survey region is about 1.5 times higher.
Except for a small number of standard stars of various kinds, the spectroscopic observations will not include stars as primary targets. However, many fields will have excess fibers because of the clustering properties of galaxies, which can be used to observe other objects, such as candidate X-ray stars, white dwarfs, blue horizontal branch stars, dwarf carbon stars (Green 1996), and cataclysmic variables. In addition, the efficiency of the quasar target selection is likely to be much above 70% (Section 3.3.2), which will give roughly 20 more stars per field, mostly of unusual colors. Thus on the average, we might expect to obtain spectra of 30 stars (in addition to standards) per field. While in no way giving complete samples over the whole survey area, these observations will yield high-quality spectra of large numbers of rare and interesting stars.
The survey will reach to one old-disk scale height, about 300 pc, for stars brighter than absolute magnitude about 14.9, 16.2, 16.0, 15.4 and 13.8 in u' , g' , r' , i' , and z' respectively. For an exponential height distribution, this is an equivalent volume of about 0.2 cubic scale heights in the plane, or ~ 5 x 106pc3. We expect to find an enormous number of M dwarfs; for example, in the bolometric magnitude range 8-13 ( Mi' <~ 14.0 , later than about M0), there will be about a million such stars (cf. the luminosity function in Liebert and Probst 1987). Some significant fraction of these are young enough to display observable chromospheric activity, and some we will catch flaring; we address the general question of variable stars below. Comparison with the ROSAT catalog will identify many X-ray sources associated with chromospheric activity among this population (Rosner et al. 1985, and further discussion below). To illustrate this point, consider that the ROSAT All-Sky Survey will have detected about 200 M dwarfs with X-ray luminosities fainter than about 1028 ergs s -1 and about 600 of the much rarer objects with luminosities of order 1029 ergs s -1 (the numbers of the latter are larger because of the larger sampling volume). The corresponding distances are of order 15 and 50 pc, respectively, and we will have accurate photometry and astrometry for all of these sources.
The spectrum of the very cool dwarf PC0025+0447. The surface temperature is near 2,000 K and the mass probably near 0.04 M0 The H alpha line has an equivalent width of about 250 Å, which is the largest seen to date in any star, and probably is an indicator of extreme youth.
Of particular interest of course is the faint end of the main sequence and below, and it is here that the data obtained with the z' filter will be particularly exciting. The lowest luminosity main sequence dwarfs have Mi' ~ 15.0m and Mz' ~ 13.5m (Schneider et al. 1991; Leggett 1992; Tinney 1993; Tinney et al. 1993; Kirkpatrick et al. 1993), and these have colors so red that they will be quite distinctive in the SDSS color system (we expect r' - i'~ 2.5m, i'-z' ~ 1.5m ). The coolest main sequence stars known are PC0025+0447 (Schneider et al. 1991 - see Figure 3.6.2) whose spectral type is M9.5 (Kirkpatrick, Henry and Liebert 1993) and whose effective temperature is ~ 2000 K, the (perhaps even cooler) object found as a companion to a white dwarf by Zuckerman and Becklin (1987), and 2MASPJ0345432+254023, discovered in 2MASS test observations by Kirkpatrick et al. (1996) (see also the discussion in Section 2.3).
Stars with r'-z' colors larger than 2.2m , which includes essentially all M stars, will be more easily detected in the z' filter than in the i' filter. Stars like PC0025+0447 can be detected to a distance of ~ 200 pc in the northern survey and we should find several thousand of them. Since this distance is nearly one scale height for the galactic disk stars and since the survey is made at the North Polar Cap, the data should provide a reliable luminosity function for faint red stars well below the hydrogen burning limit. The southern survey will yield a much larger number of faint M stars and a very large number of proper motions.
Most of the stars below the hydrogen burning limit, the so-called brown dwarfs, will be detected only in the z' filter (cf. Nakajima et al. 1995 and the discussion in Section 2.3) and will need follow up observations and comparison with the results of near-infrared sky surveys like the Two-Micron All Sky Survey (Section 2.3) to confirm their identification. Moreover, such stars will not be detected at all unless they are very young, and young stars are likely to have very strong H alpha emission as is the case for PC0025+0447 (cf. Figure 3.6.2). This gives these stars a very characteristic color signature; they have very red i' - z' colors but r' - i' colors which are not particularly red because of the strong H alpha emission.
Cool dwarfs have similar colors to cool giants; but the cool star counts are unlikely to be contaminated by cool giants because of the finite thickness of the disk. The luminosities of AGB stars are 108 - 109 higher than those of the lowest main sequence stars, so that a late M giant with the same apparent magnitude as PC0025+0447 would be at a distance of 800 kpc. Whether there is a significant population of these short-lived stars in the Galactic halo or in intergalactic space in the Local Group remains to be seen; such objects would also be extremely interesting.
White dwarfs with colors like early G stars and bluer are quite distinctive in the u'-g', g'-r' diagram (see Figure 3.3.1) because of their weak Balmer discontinuities. Such stars will be found to distances of order 600 pc and in large numbers, of the order of 105 or more. Separating them from halo subdwarfs at similar temperatures, which have similar colors and will be much more numerous, will be a difficult task, but the proper motions obtained in the southern survey will allow this separation. The extremely faint cool white dwarfs cannot be reliably found without proper motions, and we address this question below.
Very hot white dwarfs are much more luminous and much rarer spatially, but can be seen to greater distances. From the numbers found in the Palomar Green survey (Green 1980), which covered 1,430 square degrees to B=16.5 , we estimate that there will be about 8,000 white dwarfs with surface temperatures greater than 104 K to our limit, and about 2,500 brighter than 20.5, at which brightness the photometry is accurate enough to allow reddening determinations; the distances at this brightness are still greater than 500 pc, so the bulk of the absorbing material must still be in the foreground.
Ordinary G and K dwarfs will be cataloged to distances of the order of 5 kpc. Studies of the height dependencies of chemical abundances (through the excellent handle on UV excess with our 5-filter system) and of the vertical structure of the disk (including any additional extended component, e.g., the "thick disk" of Gilmore and Reid (1983), though complete characterization depends on follow-up radial velocity studies, for which the SDSS telescope is very well-suited) can be done with high precision. We will be able to identify dwarfs to two scale heights (at which distance one sees about half the stars one will see in the exponential distribution to arbitrarily faint levels) down to about M6, and we will be able to determine the old disk main sequence luminosity function and its variation with height exquisitely well.
Schmidt (1975, see also Bahcall et al. 1983) has estimated the mass density represented by the halo stars by looking at a complete proper-motion selected sample. Of these stars, the local density in the mass range 0.55-0.65 Msolar is about 6 x 10-6 pc-3 . These stars correspond to F and G subdwarfs, which are photometrically distinctive (though not very different from white dwarfs in the same temperature range). We will see 2 x 106 such objects to g' = 20.5 (about 10 kpc), to which level they can easily be recognized, and 107 to our limit. Though the reddening cannot be determined from a single photometric measurement on a single subdwarf, because the UV depression as one increases the metallicity is roughly parallel to the reddening trajectory in the color-color diagrams, one can get a good statistical handle on the reddening with 200 such stars with good photometry per square degree. Most of the objects in this color range will be subdwarfs even at fainter levels (though at the very faintest levels, "contamination" by quasars probably becomes significant!), and one can get very good information on the metallicity-radius relation for the halo. The blanketing depression in the u' band is about 0.05 magnitudes at a metallicity about 10-2 solar for stars with temperatures like the Sun; we have a very sensitive temperature indicator in our r'-i' color (see, for example, Bessel and Wickramasinghe 1979), and should be able to determine individual metallicities of very metal-poor subdwarfs to of order 2 x 10-3 .
The survey will be a gold mine for rare but intrinsically brighter halo objects, which we will see to any reasonable limit for the size of the halo. Subdwarfs at MV = 5.5 are already 40 kpc away at the limit, which corresponds to horizontal branch stars ( MV = +1 ) at a distance of 300 kpc. Again from the survey of Green, we expect about 3,000 subdwarf O and B stars to g'=20.5 ; these stars have completely distinctive colors, provide a reddening point for each star, and we will obtain spectra for them as a matter of course. How many more of them there will be to the limit of the survey is not known; the distances are already of order 80 kpc at this brightness level. The numbers at fainter levels of these and cooler horizontal branch stars, which we discuss in the next paragraph, will allow excellent determinations of the form of the stellar halo at very great distances.
Lower temperature horizontal branch stars and the rare denizens in the same temperature range of the super-horizontal branch like the objects +39° 4926 (Kodaira et al. 1970) and HD46703 (Luck and Bond 1984), and the W Virginis stars are marked by their very low surface gravities and correspondingly large Balmer discontinuities. Our filter system is ideally constituted for finding these stars. There will be of order 105 yellow horizontal branch stars in the survey, of which about 104 will be RR Lyrae variables (see, for example, Saha 1985). A few hundred SHB stars will be found, and should finally define with some certainty at least where in the HR diagram they go, and for how long these short-lived phases last.
There is considerable controversy about the ages of the halo stars and, in particular, whether there is an age gradient and/or dispersion in the halo. We should be able with these data to investigate the horizontal branch morphology, which is a sensitive indicator of age, with great precision. Preston et al. (1991), for example, report that the blue horizontal branch stars cataloged by them (Beers et al. 1988, Preston et al. 1990) exhibit a small but measurable change of the average color with their distance from the Galactic center. This color gradient is most readily interpreted as a gradient in age, with the outer Galactic halo being younger than the inner one by a few Gyr. The catalog on which Preston et al. based their analysis has a limiting magnitude mB~16 , which corresponds to a distance limit of 5 kpc, and only a few percent of the sky was covered. The northern survey will vastly increase the size and the depth of the sample, making the determination of the age gradient much more reliable.
Finally, there are stars with bizarre colors because of strong emission, the most characteristic class being the planetary nebulae. The frequencies are very uncertain, but we may expect of the order of 100 of them; their usefulness for understanding the chemical evolution of Population II stars is clear.
By the time all the sundry overlaps are taken into account, we will survey about 40% of the sky in the northern survey twice, and of course all of the southern survey many times. Though in the north two observations are hardly enough to characterize a variable object, the other photometric data will help enormously. A star with 5-color photometry like an early G giant with two images which differ by a few tenths of a magnitude with appropriate color changes can hardly be anything but an RR Lyrae star. A star which is hot and bright in one frame and looks like an M dwarf in another can hardly be anything but a flare star; we should in this rather scatter-shot way vastly increase the known number of these objects. In any case, preliminary classifications and a finding list of interesting objects will be generated as a matter of course. We will find halo Miras, RV Tauri stars, dwarf novae, W Virginis stars, and get some indication of the presence and frequency of Population II W Ursae Majoris variables, though many of these will need follow-up work to characterize fully.
In the south, the situation is very much better, and one will get excellent handles on the population of RR Lyraes to very great distances (400 kpc!), W UMa stars, Pop II dwarf novae, flare stars, and W Virginis stars, and quite possibly other variable objects in the halo population of which we know nothing at present. Of course, we will not be able to compete with the variability studies of the microlensing surveys towards the Galactic Center and the LMC (cf., Alcock et al. 1995; Kaluzny et al. 1995).
If we realize our goal of 50 mas absolute positions (Chapter 10) we will be able to find high-proper-motion objects in our overlap areas with ease. Since the star counts will be dominated by halo objects, the relative reference frame, for which we can probably do at least a factor of 5 better, or about 10 mas, will be quite good for disk stars. If the average lapse between stripe overlaps is one year, we can find objects reliably whose proper motions are of order 50 mas/year at the 4 sigma level, or about 10 mas 1- sigma . With relative velocities of 30 km/s, we can thus obtain proper motions to about 200 pc. White dwarfs and faint red dwarfs brighter than about 14th absolute magnitude will appear brighter than 20.5 (the brightness at which one has about 2% photometry and sufficiently good positional accuracy) at that distance. Thus the faint end of both the main sequence and the white dwarf sequence will be accessible to us via proper motions over some significant fraction of the sky covered by the northern survey. The controversial faint cool end of the white dwarf sequence (see, for example Greenstein and Liebert 1990, Liebert et al. 1988) is populated by stars with effective temperatures of 4,000 K and cooler and absolute V magnitudes of 16 and fainter. We will have a complete proper-motion and photometric sample of these objects from our overlap region to about 80 pc, which should contain about 1,000 stars, and will thus provide by far the best and largest (by two orders of magnitude) data set for these red degenerate stars. The space density of these old objects provides data on the cooling theory and, eventually, a completely independent handle on the star formation history in the disk (Tamanaha et al. 1990).
In the south we will do considerably better because of the fixed transit nature of that survey and the statistics afforded by repeated measurement. If we scan the strip 36 times and realize 20 mas accuracy absolute, we will have a 1-sigma proper-motion limit of 1 mas/year for objects brighter than about r'=21 . This will allow the measurement of halo motions to several kpc and the application of statistical parallaxes to a much larger class of halo objects than heretofore possible; this sample will, because of its greater depth, contain nearly as many faint cool white dwarfs as the northern survey (though the ones found in the north will be brighter, and therefore more easily studied in detail).
Of particular interest from the southern survey is the number of supernovae, particularly those of type Ia, which will be observed. There is evidence that Type Ia supernovae are very good standard candles, with the blue and visual absolute magnitude at maximum reaching m(max) ~ 18.8 + 5 log (z/0.1) (where z is the redshift of a supernova; van den Bergh, McClure, and Evans 1987; Hamuy et al. 1996; Riess, Press, and Kirshner 1996). The scatter is believed to be as small as 0.25 magnitude, and possibly less, especially after correction for the variation in peak absolute magnitude with light curve shape (Phillips 1993). Thus these are ideal objects to determine the geometry of the Universe observationally (cf., Perlmutter et al. 1996). Their light curves seem to be almost identical, making their identification unambiguous if the light curves are properly sampled.
The supernova rates are uncertain, but according to van den Bergh et al. (1987) the rate ~ 0.3 h1002 per 1010 Lsolar per century seems to be reasonable for SN Ia. Combining this rate with the luminosity density in the Universe ~ 2 x 108 h100 Lsolar Mpc-3 (Kirshner, Oemler and Schechter 1979) the expected SN Ia rate is ~7,000 (z/0.1)3 per year out to a redshift z over the whole sky.
The southern survey area of about 300 square degrees will be covered many times by the Survey Telescope for about 5 months every year. This should lead to a discovery of about ~ 20 type Ia supernovae every year with z < 0.1 , with good light curves extending down to at least 4 magnitudes below the maximum, and ~ 200 SN Ia with z < 0.2 covered to at least 2 magnitudes below the maximum. A comparable number of supernovae of other types will be discovered. To take full advantage of these objects will require more regular photometric follow-up of their light curves, as will be possible using such dedicated telescopes as the Katzman Automatic Imaging Telescope (cf., http:/astro.berkeley.edu:80/~bait/kait.html), which will require that we recognize and announce supernova discoveries to the community quickly. Follow-up spectroscopy on larger telescopes will of course also be necessary to confirm and classify supernovae candidates; we do not plan to do spectroscopy of supernovae on a regular basis with the SDSS.
These results will be useful in many ways. First, the local supernova rate should be established with high precision. The classification of supernovae will be based on a much better sample than now, and in particular the usefulness of SN Ia as standard candles for use in cosmological tests will be better established (Perlmutter et al. 1996). These data will firmly anchor the z = 0 point of the Hubble diagram for supernovae.
It is likely that the X-ray source identification programs pursued by the several existing X-ray telescope missions (including ROSAT and ASCA) will be nowhere near completion by the time we begin to obtain data (cf., Section 2.1). Our digital data base, based on multiple color photometry, will therefore be of instant utility to scientists involved in these identification programs. Other X-ray missions, including XMM and AXAF, will also find our data base to be extremely useful for both source identifications and as a "finder telescope" for interesting objects. As an illustration, recall that at a soft X-ray flux limit of approximately 10-14 ergs s -1 cm -2 , the Einstein Medium Sensitivity Survey showed that roughly 1/4 of all X-ray point sources turn out to be stars; even at higher galactic latitudes more characteristic of our survey, the stellar log N -log S curves do not bend over significantly at flux levels of 10-15 ergs s -1 cm -2 (comparable to the typical deeper ROSAT exposures), so that stars will continue to bedevil the extragalactic X-ray astronomers for some time to come.
Stellar X-ray observations divide into two distinct categories: the first entails observations of stars which are already well-identified optically (or at other wavelengths); these are the pointed observations (the "Pointed Surveys" in the following), which constitute the vast majority of guest observations on the Einstein and ROSAT observatories. The second category consists of unidentified point X-ray sources, some fraction of which are stars; this category includes objects found in the ROSAT All-Sky Survey as well as serendipitously in pointed fields (especially pointings with very long exposure times, viz., >10 ksec for ROSAT).
Of relevance to the present discussion is the fundamental fact that because stars show a wide range of X-ray properties, it is essential to assemble sufficiently large samples of such objects that their statistical properties can be well-characterized. Typical examples include (i) the determination of stellar X-ray luminosity functions as a function of optical stellar properties (cf. Micela et al. 1990; Schmitt et al. 1990ab; Barbera et al. 1993; Micela et al. 1996; Giampapa et al. 1996); and (ii) the implications of these results for the stellar contribution to the galactic diffuse soft X-ray background, again as a function of optical stellar properties (e.g. Rosner et al. 1981; McCammon and Sanders 1990; Micela et al. 1991; Kashyap et al. 1992). The pointed surveys are typically far too sparse to answer questions such as these; and thus most of the effort has been focused on stellar objects found serendipitously in either the pointed or All-Sky surveys. An obvious prerequisite for such studies is the optical characterization of the stellar X-ray sources, i.e. the identification of optical stellar counterparts to the otherwise unidentified X-ray sources. (It is essential to recall that the vast majority of stellar X-ray sources will not have any catalogued optical counterpart, so that the question of whether a given X-ray point source is a star in our galaxy, or is an extragalactic object, can only be established by comparison with optical images of the X-ray fields.)
Now, for the reasons given above, there has been substantial interest in the construction of X-ray point source catalogs from data sets such as the pointed surveys; one recent example is the so-called "WGACAT" point source catalog for the publically-archived pointed ROSAT fields, constructed by N. White and collaborators. As one might expect, only a very small fraction of the sources in this catalog have optical counterparts as of this date; and this difficulty is much more severe for catalogs such as that based on the ROSAT All-Sky Survey because of the far larger data volume.
The magnitude of the identification task is readily appreciated by roughly estimating the number of stars that may be found in such serendipitious surveys. Consider, for example, the Extended Medium Sensitivity Survey (Gioia et al. 1990); roughly speaking, at a soft X-ray flux limit of approximately 10-14 ergs s -1 cm -2 , 1/4 of all X-ray point sources are stars; even at high galactic latitudes, the stellar log N -log S curves do not bend over significantly at flux levels of 10-15 ergs s -1 cm -2 (c.f. Kashyap et al. 1992), the typical deeper ROSAT exposure limit. One of the standard data sets from ROSAT has a sensitivity that is comparable to (actually, somewhat more sensitive than) the Extended Medium Sensitivity survey, namely the data set consisting of all pointed PSPC images in the existing public archives with effective exposure times in excess of 1 ksec; the total number of such fields is ~ 4,000 (n.b.: the ROSAT All-Sky Survey is considerably larger, albeit somewhat less sensitive). In any case, the number of unidentified stellar sources that one has to deal with then lies in the several thousands (an estimate based on the mean exposure time).
In the case of the longer exposures, the number of unidentified sources becomes much larger; to illustrate the problem, consider the magnitude of the task for two examples of deeper ROSAT exposures, namely the Lockman Hole and the Pleiades. The first is a classic target for extragalactic X-ray studies because of the relative paucity of obscuring galactic material in that field, and a particularly long exposure ( ~ 122 ksec) of this field was carried out using the ROSAT PSPC (G. Hasinger/MPI). The second example is the very crowded field of the central Pleiades, for which we obtained a relatively deep ( > 20 ksec) PSPC image (in AO-1; Micela et al. 1996). In Table 3.6.1, we show the number of X-ray point sources found in these two fields (based on the ROSAT WGACAT catalog); in the case of the Pleiades field, virtually all of these objects are stars, and even in this well-known field, there remains a substantial number of objects which are as yet optically unidentified.
| Field | Detection Method | # of sources | # of sources | Total |
|---|---|---|---|---|
| | | <20' | >20' | # |
| Pleiades | WGACAT | 64 | 63 | 127 |
| Lockman | WGACAT | 53 | 49 | 102 |
The SDSS digital data base, based on 5-color photometry, is of obvious and immediate utility for addressing this problem of identifying optical counterparts. The photometry is sufficient to identify the spectral type of stellar objects down to the sensitivity limit (roughly, the equivalent of V ~ 22-23 ); and by combining this information with the already-known stellar X-ray luminosity functions as a function of spectral type and luminosity class, it is possible to separate stars from extragalactic objects rather efficiently. Current and future X-ray missions, including Astro D, XMM, and AXAF, will also find the SDSS data base to be extremely useful for source identification, especially as the stellar X-ray sources become dominated by late spectral type dwarf stars at X-ray fluxes substantially fainter than 10-14 ergs s -1 cm -2 (i.e. such stars are very readily separated by the SDSS photometry).
There are obvious possibilities for specialized stellar surveys to be carried out during bright time, and after the main SDSS survey is complete. (As a result, such work would not be funded by the Survey, and the incremental costs would have to be supported by other means.) Nevertheless, it is useful to point out that the Survey telescope is a powerful instrument for stellar studies if used in ways other than in the Survey proper. As a specific example, note the possibility of a Galactic disk survey, which might consist of several 30°x2.5° stripes, obtained at several values of Galactic longitude. Such a survey would be an extremely powerful tool for studying the scale height distributions of stars (and measuring the Galactic potential), and strongly constraining Galactic models. Another example, the observing of a complete photometric stellar catalogue of the northern sky, is discussed in detail in Appendix B.
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