W.B. Sparks, B.C. Whitmore, R.A. Lucas, F. Macchetto, J. Biretta
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA.
Keywords: Distance scale
The position of M87 (NGC 4486) in the core of the Virgo cluster provides an important advantage over other Virgo cluster galaxies for distance measurements, and for the determination of the Hubble constant. For example, a large uncertainty in the Freedman et al. (1994) estimate of using Cepheid variables is the question of where M100 is relative to the cluster core. Hence, although the scatter in the period-luminosity relation for Cepheid variables is seven times smaller than the width of the luminosity function for globular clusters, the formal uncertainty in our estimate of is actually smaller. The incredible number of clusters in M87 also provides an important advantage allowing statistical uncertainties of less than 0.1 mag in determining the mean of the distribution. Finally, the high spatial resolution of HST provides a vast improvement in the ability to distinguish globular clusters from both foreground and background objects.
The globular cluster luminosity function (hereafter GCLF) has proven to be remarkably similar for a wide range of galaxies. It can be well described by a Gaussian profile with a mean mag and a width mag. However, the turnover in the GCLF has only been measured clearly in the Milky Way and M31. While a few heroic ground-based observations of galaxies in the Virgo cluster have reached just beyond the turnover (van den Bergh et al. 1985 , Cohen 1988, Harris et al. 1991), observations with the Hubble Space Telescope are now capable of observing roughly two magnitudes deeper than ground-based measurements, making the measurements of the GCLF potentially one of the most accurate methods of determining distances. The crucial assumption, of course, is that the GCLF is indeed ``universal'', a hypothesis that needs further verification.
M87 was observed with HST using the Wide Field and Planetary Camera 2 (WFPC-2) with both the F555W and F814W filters, see Whitmore et al. (1995). We define the completeness threshold as the magnitude at which 50 % of objects are missed, and this occurs at mag within 16 of the center of M87, and at 26.2 mag for the outermost region between 79 and 114.
Fig. 1 shows the GCLF in the Johnson V passband for 1032 globular clusters in M87, after correction for incompleteness. The mean of the distribution is with a width mag, as determined by fitting a Gaussian profile in the range from 20.8 mag to 25.55 mag, and this fit is also shown in the figure.
By dividing the sample in various ways, Whitmore et al. (1995) deduce a final best value for the mean of , and dispersion = 1.40 mag. The GCLF in M87 is well described by a Gaussian profile with these parameters. Proceeding from this secure result to a value for requires additional assumptions. The first step is a determination of , the intrinsic value of the mean absolute V magnitude of a Gaussian describing the GCLF. Using the Milky Way and M31, Secker (1992) finds a value of mag while Sandage & Tammann (1995) find a value of mag. The primary reason for the difference is the use of a new RR Lyra calibration scale by Sandage & Tammann. Metallicity differences between globular clusters in spirals and ellipticals may result in values of which are about 0.2 mag fainter for ellipticals. We adopt a value of mag, which covers the range from mag (Sandage & Tammann 1995, assuming no corrections between spirals and ellipticals) to mag (Secker 1992, with a 0.2 mag correction between spirals and ellipticals).
This, therefore, yields a distance modulus of to the Virgo cluster, corresponding to a distance of 16.75 Mpc.
We next adopt the technique of using the well determined value of mag (e.g., van den Bergh 1992, de Vaucouleurs 1993, Jerjen & Tammann 1993, Freedman et al. 1994) to estimate the distance modulus to the Coma cluster. This cluster is roughly six times further than the Virgo cluster, hence uncertainties introduced by peculiar local velocities have a much smaller effect on our estimate of the Hubble constant. The resulting distance modulus of the Coma cluster is mag, corresponding to a distance of 92.5 Mpc. Adopting a value of 7188 km s for the velocity of the Coma cluster (Jerjen & Tammann 1993) results in a value for the Hubble constant of
Whitmore et al. (1995) present the detailed error budget.
The Hubble Space Telescope offers several important advantages for measuring the globular cluster luminosity function for distant galaxies. These include a detection limit which is two or three magnitudes deeper than ground-based observations, the high resolution necessary to distinguish point-like clusters from the foreground and background galaxies, and the ability to use very small apertures which reduces the effect of the background galaxy and allows measurements to be made much nearer the center of the galaxy where the density is highest.
Similarly, M87 has several advantages over other galaxies in the measurement of the GCLF and the determination of the Hubble constant. These include an incredibly dense population of clusters which provides high statistical accuracy and minimizes the effects of background contamination, and the position in the core of the Virgo cluster which removes the uncertainty of whether the galaxy is in front of or behind the cluster.
We have combined these attributes by using HST to measure over a thousand clusters in M87, with a limiting magnitude which is more than two magnitudes beyond the turnover in the luminosity function. We find the GCLF is well fit by a Gaussian profile with a value of mag and a width of 1.40 mag. Adopting a value of mag results in a distance modulus of to the Virgo cluster. Bootstrapping our way to the Coma cluster leads to an estimate of Mpc for the Hubble constant.
At present, the largest uncertainties are introduced by the local calibrators and the question of the universality of the GCLF.
Support for this work was provided by NASA through grant number GO-5477.01-93A from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555.
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Figure: The M87 GCLF for the full WFPC-2 sample, showing a Gaussian fit to the data.
W. B. Sparks, B. C. Whitmore, R. A. Lucas, F. Macchetto, J. BirettaSparks et al.HST Observations of Globular Clusters in M87 and an Estimate of