No Title

Abstract

The luminosity of the red-giant branch tip (TRGB) is a highly precise standard candle for Population II stars; for stellar populations more metal-poor than [Fe/H] $\simeq -0.7$ , the TRGB luminosity is at $M_I = -4.2 \pm 0.1$ , visible as a sharp upturn in the luminosity function (eg. Lee et al. 1993a). With the high resolution and depth of the Hubble Space Telescope, the keystone Virgo and Fornax galaxies should be within reach.

We have used WFPC2 on HST to obtain deep I-band images of a Virgo dE galaxy, VCC1104, to test the feasibility of this technique at the $\sim 15-20$ Mpc distance range. Our target galaxy, a nucleated dE, is moderately metal-poor ([Fe/H] $\sim -1.3$ according to integrated colors), and its radial velocity and central location in Virgo maximize the probability that it belongs to the `core' of Virgo defined by the gE and dE,N galaxies. Our composite I-band image succeeds in cleanly resolving the red giant branch, and clearly shows the expected step-function luminosity function upturn at the RGB tip. From this we derive $(m-M)_o = 30.83\pm 0.18$ ( $d= 14.7 \pm 1.2$ Mpc), and clearly supports the larger values of H_o that have been derived using other independent techniques.

Introduction

The distance to the Virgo cluster has long been sought, due to its extreme importance in the extragalactic distance scale and the determination of the Hubble constant H_o (and thus possible ages for the universe itself). As such the Virgo cluster has been the focus of numerous studies, both ground-based and HST-based (eg. Pierce et al. 1994, Freedman et al. 1994; see also van den Bergh 1996).

Related to this problem is the range of derived values of H_o that have arisen through use of many different `standard candles' to derive distances; values as low as 55 km/sec/Mpc to over 80 km/sec/Mpc are commonplace in the literature (eg. van den Bergh 1996). Thus it is important to refine as many techniques as possible to reduce the uncertainty in H_o.

The TRGB Method

The I magnitude of the tip of the red giant branch (TRGB) has been used as a distance indicator for many nearby galaxies from ground-based photometry and out to $\sim 10$ Mpc using the HST (Sakai et al. 1996, 1997). This technique requires only that the resolved stellar population is (a) old (>2-3 Gyr) and (b) relatively metal-deficient ([Fe/H]<-0.7: see Lee et al. 1993a). Under these conditions, the absolute magnitude of the TRGB is $M_I\approx -4$ , with little dependence in [Fe/H], making it an ideal population II distance indicator. This technique has a firm physical footing, as the tip corresponds to the point of core helium ignition in low-mass halo stars.

For targets such as Virgo and Fornax, the TRGB method has several key advantages over the use of Cepheids for distance determination:

non-variable stars, so no repeat measurements necessary
target galaxy likely in core of cluster, unlike spirals
fewer steps of the extragalactic distance scale ladder :
[-] subdwarf parallaxes $\rightarrow$ globular clusters (RR Lyraes) $\rightarrow$ TRGB distance
intrinsically as precise as Cepheids ( $\sim \pm 0.1$ mag)
no internal reddening problems

These conditions are readily met in dwarf elliptical (dE) galaxies. Although giant spiral and elliptical galaxies do have old metal-poor populations, they are not the dominant population, as it is in dE's. The TRGB method has been successfully tested in the dE's in the Local Group (NGC 147/185/205; see Baade 1944, and more recently Lee et al. 1993a,b).

The Virgo cluster of galaxies is the nearest large reservoir of dE galaxies, thus making them ideal targets for a comparison of the TRGB method with other techniques (eg. Cepheids, surface brightness fluctuations, PNLF, GCLF). Furthermore, the nucleated dE's (or dE,N's) are known to preferentially lie in the densest regions of clusters (Ferguson & Sandage 1989); thus dE,N's provide us with a natural probe of the cluster core region.

VCC 1104

VCC 1104 is a dE4,N galaxy (M_V=-16.2) located 43 $^{\prime}$ from M87 (see Figure 1). This (and evidence presented above) suggests this galaxy is likely in the Virgo cluster core.

Although we expect dE's to (in general) have intermediate-[Fe/H] populations, we have used WIYN UBV images of VCC 1104 to derive (U-B) and (B-V) color profiles (Figure 2). Comparing the colors with those of Milky Way globular clusters (Figure 3) indicates that the metallicity of the dominant stellar population in VCC 1104 is [Fe/H] $\sim -1.3\pm 0.3$ . In addition, the luminosity of VCC 1104 is intermediate between that NGC 185 (M_V=-15.5, [Fe/H]=-1.3) and NGC 205 (M_V=-16.6, [Fe/H]=-0.85); again suggesting [Fe/H] $\sim -1$ .

Data Reduction & Analysis

In June 1997 we obtained a deep series of WFPC2 F814W images (I : 12 images with a total exposure time of 32200 s) of VCC 1104. The cleaned, combined image (Fig. 4) clearly resolves the primary stellar population(s) in this galaxy. DAOPHOT II photometry was performed on the stars in the WF2/3/4 frames that are in the outer parts of the galaxy so as to avoid image crowding. Background objects (faint galaxies plus a few foreground stars), have been removed statistically using half of the WF4 field as a control field. The 50% completeness level, f(I)=0.5 is at $I \sim 27.4$ , as determined from artificial star tests.

We calibrated the photometry using WIYN I-band images and the prescription given in Holtzmann et al. (1995), and our I-band LF is illustrated in Fig. 5. The position of the TRGB was estimated using two independent methods: (a) The Sobel edge-detection filter, E(I), in its continuous form (Sakai et al. 1996) is applied to $\Phi(I)$ , a continuous probability distribution function defined by the Gaussian-smoothed LF. A peak at $I_{\rm Sobel} = 26.68\pm0.02$ mag marks the TRGB (Fig. 6). (b) Modifying the maximum-likelihood algorithm of Secker & Harris (1993), we construct a model LF which includes contributions from the RGB stars (a truncated exponential) and a background population, corrected for detection completeness and photometric error. The TRGB position is a free parameter in this model, and we obtain $I_{\rm ML} = 26.65\pm0.06$ mag, consistent with the Sobel filter results. Thus we have detected stars over 0.5-mag fainter than the RGB tip in VCC 1104, illustrating that the TRGB method is indeed feasible for Virgo cluster galaxies.

Distance to VCC 1104

From the I_TRGB value, we have computed a distance assuming $M_{I,tip} = -4.20\pm 0.10$ . This value is based on Figure 6, where the globular cluster RGB's from Da Costa & Armandroff (1990) have been recalibrated in accordance to the distances of the GC's using recent Hipparcos parallaxes (Gratton et al. 1997). This value also accounts for the even brighter tip magnitudes which have been suggested by recent theoretical work (Cassisi & Salaris 1997).

Our derived distance modulus for VCC 1104 is 30.83 $\pm$ 0.18, or a distance of 14.7 $\pm$ 1.2 Mpc, making this the most distant galaxy for which the TRGB method has been applied. Our result is similar to that derived by Cepheid-variable studies of Virgo spirals (Pierce et al. 1994, Freedman et al. 1994) and that using most other standards candle (eg. Mould et al. 1995), and strongly supports the larger values of H_o ( $\sim 70-85$ km s^-1 Mpc^-1) that have been derived recently by numerous other studies (using a variety of other techniques).