The Age of the Sculptor Dwarf Spheroidal Galaxy from Imaging with WFPC2¹

Dwarf spheroidal galaxies are enigmatic objects, characterized by extremely low surface brightnesses and often high mass‐to‐light ratios. The Milky Way has some nine such companions, ranging in luminosity from 2 × 10⁵ to 2 × 10⁷ L_⊙. Hierarchical models of formation depict the Galaxy as having formed by accreting smaller clumps of matter. Dwarf spheroidal galaxies may be the evolved remnants of these elementary building blocks and therefore tracers of the earliest epochs of star formation. Yet the star formation histories of the dwarf spheroidal satellites of the Milky Way are diverse (Da Costa 1998; Mateo 1998): there are relatively simple systems, such as Draco, which is dominated by an old population of stars and is well‐described by single burst of star formation, and there are systems with complex histories, such as Carina, which has a substantial intermediate‐age population with a smaller fraction of older stars (Hurley‐Keller, Mateo, & Nemec 1998 and references therein). Both Carina and Draco possess predominantly red horizontal branches, despite the fact that they are very metal poor—that is, they exhibit the second parameter effect. Although this is a clear characteristic, there are blue stars in Sculptor too (Kaluzny et al. 1995). The fact that the bulk of Draco's stars appears to be within 2 billion years of the oldest globular clusters (Grillmair et al. 1998) indicates that if age is the second parameter, horizontal‐branch structure must depend very sensitively on it.

The Sculptor dwarf spheroidal galaxy is a significantly flattened galaxy located toward the Milky Way's south pole. Stellar photometry in this galaxy reached the horizontal branch in the work of Kunkel & Demers (1977) and the main sequence in the Da Costa (1984) study. With a total luminosity exceeding 10⁶ L_⊙, it is larger than either Carina or Draco, although Sculptor is metal poor (on average [Fe/H] = -1.8 ± 0.1; Mateo 1998). Unlike Carina, neither Sculptor nor Draco has stars significantly exceeding the luminosity of the red giant branch tip (Frogel et al. 1982). This lack of upper asymptotic giant branch (AGB) stars leads to the expectation that Sculptor also lacks a significant intermediate‐age population. The carbon stars found by Aaronson & Mould (1985) and Azzopardi (1994) are at or below the red giant branch tip in luminosity.

Sculptor is of particular interest because it may possess some neutral hydrogen. Carignan et al. (1998) discovered two or more sizable clouds of H i inside the tidal radius and within the velocity range of the dwarf galaxy. Sculptor is apparently unique in this respect, although it should be noted that the H i velocity distribution of this region is quite complex (Putman et al. 1998; M. Putman 1999, private communication). The location of our Hubble Space Telescope Wide Field Planetary Camera 2 (WFPC2) field with respect to the Sculptor dwarf and Carignan's cloud is shown in Figure 1. It was chosen so that the photometry would go as deep as possible, undisturbed by confusion and crowding effects, rather than for proximity to this diffuse gas.

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In this paper we apply the WFPC2 to Sculptor in order to measure the properties of the dwarf galaxy's main‐sequence turnoff. The photometry we obtain reaches to 3 or 4 mag below the turnoff and allows us to compare the Sculptor dwarf spheroidal galaxy with its smaller northern counterpart in Draco.

A field well outside the core of Sculptor was selected in order to avoid image crowding problems. The images were taken on 1997 December 13 by the WFPC2 instrumentation aboard the Hubble Space Telescope. The observations comprise two 1200 s and two 1300 s images taken with the F555W filter and four 1300 s images taken with the F814W filter (see Table 1). The field of view is located 141 from the center of the Sculptor dE, or a projected distance of 330 pc for a line‐of‐sight distance of 80 kpc. The raw observations were preprocessed via the WFPC2 standard pipeline calibration. Bad pixel and vignetting masks were then applied to the images, and intensity corrections were made for field distortions (Stetson et al. 1998).

Apparent magnitudes were derived from the standard WFPC2 point‐source functions developed for the H₀ Key Project using the DAOPHOT/ALLFRAME ensemble of programs (see Stetson 1994 for a complete description of this software). To reduce the effects of cosmic rays, the exposures in each filter were combined together to produce the median of the four individual images in F555W and F814W. The initial star list was produced from by combining all eight frames. The WFPC2 mosaic of the combined observations is included in Figure 2. The detected stars were subtracted from the combined image, and a second detection pass was carried out to pick out point sources obscured by the skirts of brighter stars. After the convergence of the ALLFRAME program, obvious detections of background galaxies were removed from the final star list by hand. Stellar image quality constraints further eliminated spurious detections. Including contributions from Sculptor and the Galaxy, 400 stars were obtained from the three combined WF frames and 20 stars from the PC frame. Stars with V<27.5 are listed in Table 2. Fiducial stars for astrometry are listed in Table 3.

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In order to transform our photometry to the standard system, it is necessary to include the stellar light out to radial distances of 0 5 from the centroid of the point‐source image. To this purpose, 20–30 bright, isolated stars were selected from each chip for the production of growth curves. The template growth curves and aperture corrections were constructed and applied to the rest of the photometry using DAOGROW and associated programs (Stetson 1990). Note that we have used standard transformations between F555W, F814W, and V, I (Hill et al. 1998). Holtzman et al. (1995) found that synthetic photometry of models with metal abundances [Fe/H] = -2.0 and 0.0 were indistinguishable for 0.0<V−I<1.0 in the two‐color diagrams one can form from these magnitudes. Because the field is sufficiently uncrowded, aperture photometry was performed on a sample of bright stars from the final star list. Comparison with the ALLFRAME‐derived magnitudes indicates that there is good chip‐to‐chip agreement between the two methods.

Figure 3 is a color‐magnitude diagram like that of a globular cluster, and the natural comparison is with the metal‐poor clusters of our Galaxy. The anticipated contamination of the field by foreground stars is negligible. The Galactic model of Bahcall and Soneira predicts some 20 foreground Galactic stars in our field for m_V <28 (Ratnatunga & Bahcall 1985). The majority of these will be halo M dwarfs and will lie redward of the Sculptor main sequence.

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In Figure 3 we overlay the fiducial of the M68 main sequence, as derived from Walker (1994). We shift the fiducial to the distance of Sculptor, taking distance moduli of 14.8 and 19.5 mag for M68 and Sculptor, respectively (Djorgovski 1992; Kunkel & Demers 1977). Using the method of Schlegel, Finkbeiner, & Davis (1998), we determined a reddening adjustment of E(V−I) = 0.04 from the DIRBE sky maps. The metal abundance of M68 is [Fe/H] = -2.09 (Djorgovski 1992). A change of 0.1 dex in [Fe/H] produces a change of 0.006 in V−I at M_V = 4.0 in the Yale isochrones (Green, Demarque, & King 1987). Although the overlaid fiducial sequence for M68 lies toward the blue side of the Sculptor main sequence and giant branch base, the offset is within the photometric calibration uncertainties of 0.03 mag (Stetson et al. 1998). These results are consistent with the proposition that there is no difference between the average ages of M68 and the stellar population of Sculptor.

In order to put quantitative limits on what "no difference" signifies, Yale isochrones for metallicity Z = 2 × 10^-4 and helium abundance Y = 0.23 were shifted to a common turnoff color and magnitude and fitted to the Sculptor main sequence for ages of 13, 15, and 17 Gyr in Figure 4. According to Da Costa & Armandroff (1990), Yale isochrones are satisfactory fits to cluster giant branches, provided the Frogel, Persson, & Cohen (1983) horizontal‐branch distance scale is adopted, which is the case here. Within the range of the small number statistics in our sample, the 13 and 17 Gyr isochrones lie outside the limits of probable fits to the red giant branch of Sculptor. Main‐sequence fits, using VandenBerg et al. (1999) and Padova isochrones (Bertelli et al. 1994) of comparable metal and helium abundance, are generally in good agreement with this result. Including uncertainties in the metallicity determination, and requiring that our conclusion be independent of the choice of evolutionary model, we find an age of 15 ± 2 Gyr for Sculptor. We emphasize that it is the ±2 that we are interested in determining in this way, rather than the absolute age.

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The age of the system is the most direct result of this new deep look at Sculptor, but we should keep in mind the possibility that the stellar population varies radially (Da Costa et al. 1996), as is seen in the Small Magellanic Cloud (SMC; Hatzidimitriou, Cannon, & Hawkins 1993), in NGC 147 (Han et al. 1997), and in Andromeda I (Armandroff et al. 1993). We have estimated an age of 15 ± 2 Gyr for the bulk of the main‐sequence stars. This age is comparable to the ages of the oldest Galactic globular clusters. However, the star formation histories of most dwarf galaxies are actually more complex (Carignan 1999) than the simple stellar population model of Renzini & Buzzoni (1986), and it is possible that this is true of Sculptor as well.

The main‐sequence luminosity function (MSLF) is a simple gauge of the lifetime star formation history, although in a composite population the MSLF can be degenerate over a very wide range of age/metallicity combinations. Kaluzny et al. (1995) show that there are no main‐sequence stars with m_V<21.0 in the central area of the galaxy. Calculations based on the Yale luminosity functions (Green et al. 1987) were carried out to compare the predictions of three possible star formation histories of Sculptor with the MSLF. The small number statistics of our present data permit a range of star formation histories to be taken as plausible fits to the data. The absence of stars brighter than V = 21.0 rules out star formation more recent than 2 Gyr ago. A continuous star formation model is therefore inappropriate to the central regions of the galaxy at least. A spread in chemical composition in Sculptor (Da Costa 1984) would arise naturally from an extended history of star formation.

While the placement of our field of view far from the center of Sculptor averts the problems associated with crowding, it severely restricts the number of stars brighter than the main‐sequence turnoff. The result is a sparsely populated giant branch and a statistically difficult number of stars in the blue straggler region of the color‐magnitude diagram. This inhibits our ability to draw meaningful conclusions about the contribution of intermediate‐age populations. We simply make the point that it is possible that star formation has been active in Sculptor steadily or sporadically over its lifetime, and not simply in its initial burst, presumably until the event which resulted in its gas dispersal. But we note that star formation activity inferred from the MSLF is an upper limit on the true level of activity; the chance occurrence of a background quasar or a halo white dwarf in our field would lead to an overestimation of the amount of star formation during the last 5 Gyr. It is also possible that some or all of the stars in the 22d magnitude bins in Figure 3 are blue stragglers formed from stellar mergers rather than from a separate burst of star formation.

If significantly more than 10% of the star formation in Sculptor occurred more recently than the SMC globular cluster NGC 121 was formed (11.5 Gyr ago according to Stryker, Da Costa, & Mould 1985), we would expect to see a few upper AGB carbon stars in the galaxy.

If the 22d magnitude main‐sequence stars are in fact ordinary Sculptor main‐sequence stars, the star formation history which is apparent in Sculptor is reminiscent in a very small way of what is played out fully in the Fornax dwarf (Grillmair et al. 1999; Stetson 1997). The range of star formation histories exhibited by dwarf spheroidal galaxies may run continuously from systems such as Draco, in which activity was strongly peaked in the past, to objects with a basically steady star formation rate which ceased recently, such as Fornax. Where exactly Sculptor is in this continuum remains to be seen.

Clearly, more data are required to pursue these matters further. A detailed comparison of histories of Sculptor and Fornax (and other systems) is possible and well motivated. Such a study would require adequate spatial sampling of these galaxies, which are large compared with the WFPC2 field. Ground‐based imaging is particularly important for capturing wide fields where relatively rare younger stars are to be found.