formed to the (Mv, (B–V)) plane to enable comparison with the observations. The accuracy of the necessary transformations, derived from atmosphere models, is crucial, because the steep slope of the main sequence means that any systematic errors in the colors are amplified at least 5-fold in the derived distance modulus. Because most theoretical models fail to match the sun exactly, a direct application of similar models to metal-poor stars is not advisable. Moreover, it is clear from recent high-resolution spectroscopic observations that the abundance pattern in halo subdwarfs differs from that among disk dwarfs. Oxygen, calcium, neon, and other a-rich elements have enhanced abundances relative to iron in halo subdwarfs, reflecting the greater contribution made by Type II supernovae to chemical evolution at early epochs. It is only recently that these detailed differences have been taken into account in model calculations.

Thus, both of these approaches have significant drawbacks: sparse sampling of the (Mv, (B–V)) plane by the empirical data, and zeropoint uncertainties in the theoretical tracks. Given these problems, most recent studies (e.g., ref. 1) have adopted a semiempirical, hybrid approach, using the few subdwarfs with well calibrated distances to determine systematic corrections to the theoretical isochrones, and then matching the corrected, calibrated isochrones against the cluster data. These corrections generally comprise an offset of a few hundredths in the (B–V) colors of the models, with the assumption that the same correction is appropriate at all luminosities. Thus, Bolte and Hogan (1) used the local subdwarfs (primarily the nearest subdwarf, Groombridge 1830 or HD 103095) to estimate that the colors predicted by the Bergbusch and Vandenberg (8) isochrones were too blue by 0.02 magnitudes. Applying this systematic offset to the appropriate-abundance isochrones, Bolte and Hogan matched the theoretical tracks against observations of the classical metal-poor cluster M92 and derived a best-fit age of 15.8±2 Gyr.

Hipparcos and the Local Subdwarfs

Ground-based, parallax measurements can achieve an accuracy of better than 1 mas—but only through the painstaking acquisition of numerous well calibrated CCD frames, extending deep enough to include observations of a sufficient number of faint, distant, positional-reference stars. The nearby F and G subdwarfs, whose parallaxes are essential for main-sequence fitting, have magnitudes of 8 to 10—observable photographically, but not with CCDs, and photographic plates cannot achieve the necessary precision. The Hipparcos satellite was designed to achieve milliarsecond-precision astrometry for stars at these magnitudes and to obtain absolute parallaxes for over 110,000 stars, including almost every star brighter than ninth magnitude.

Hipparcos achieved this goal by using two small telescopes to image widely separated regions of sky onto the same focal plane. In ground-based parallax measurement, one can measure only the parallactic motion of a nearby star relative to the positions of fainter background stars in the same field. Those stars share that same parallactic motion, albeit at a much lower level. Hence, statistical corrections must be applied to the derived relative parallax to correct to an absolute scale. Hipparcos, by measuring the angular separation of stars more than 58° apart on the sky, and at very different parallactic angles, was able to circumvent this problem.

The satellite was launched in 1989 and, despite being left in a highly elliptical orbit through a technical failure, was able to obtain almost 3 years of data. Those raw observations, essentially tens of millions of measured angular separation between pairs of stars from the input catalogue specified in 1985, were then reduced and analyzed separately by two consortia. The final catalogue was completed in late 1996 and will be released to the general community in June 1997 (9). However, astronomers who had requested observations of stars for specific projects (the “1982 PIs”) were given access to subsets of the data in January 1997.

As part of the “1982 PI” release, I received astrometric data for some 2,400 stars from the Lowell observatory proper motion catalogue—stars brighter than 11.5 and with proper motions of at least 0.27 as per year. Among those stars were more than 700 that had photometric and spectroscopic observations by Carney et al. (10) as part of their investigation of local Galactic structure—including more than 100 subdwarfs with abundances [Fe/H]<-1, stars suitable for calibrating globular cluster distances through main-sequence fitting (ref. 10, hereinafter CLLA). However, many of those stars lie at distances of more than 100 pc. where even Hipparcos parallaxes are of relatively low precision. Combining low-precision parallax data in a statistical analysis can lead to significant systematic bias: in any volume-limited sample, there are more stars with small parallax than large parallax, so if a subsample is defined, either implicitly or explicitly, by a parallax limit, then observational uncertainties in the measured parallax will lead to a larger number of stars scattering into the sample from a larger distance than are scattered out of the sample. Hence, the average distance, and the mean luminosity, of the parallax-limited subsample is underestimated.

This statistical bias was quantified originally for a uniform space distribution by Lutz and Kelker (11). Hanson (12) extended the analysis to different spatial distributions and deals with the effect of introducing a magnitude limit (as is the case in the Hipparcos sample). These biases should be corrected for in any statistical analysis, such as main-sequence fitting, but the corrections can amount to more than half a magnitude for a parallax precision less than 20%. Given these concerns, our present analysis is limited to a total of 18 subdwarfs with abundances (from CLLA) of less than -1.3 dex and with parallaxes measured to a precision of better than 12%. The statistical corrections involved are no more than 0.12 mag for an individual star and 0.02 mag in the mean.

Cluster Distances

We have matched the local subdwarf-calibrating stars against fiducial (V, (B–V)) sequences derived for a number of the better-studied globular cluster systems. Rather than rely on theoretical models to determine the color corrections required to adjust each star to match a given cluster abundance, we have limited the analysis to subdwarfs whose abundance is within ±0.25 dex of each cluster in the sample. The cluster abundances were taken from the compilation by Zinn and West (13). This technique limits the calibration to only 7–9 stars per cluster, but the distribution in absolute magnitude is sufficient so that the cluster distances can be determined to a formal distance of ˜5% (±0.1 magnitude). Results for three well studied clusters are shown in Fig. 1, and full details of this first analysis are given by Reid (14).

The most important result is that the distances to the most metal-poor clusters ([Fe/H] ~ -2.0) have been underestimated by at least 10–15% in previous analyses. NGC 6397, long known as the nearest cluster to the sun, turns out to be fully 25% more distant than the conventional estimate, lying at a 2.8 kpc distance. To some extent, this reflects differences between the older, ground-based parallaxes and the new Hipparcos data but is also due partly to an underestimate of the color corrections required to match previously available theoretical isochrones to the observations. Rather than 0.02 mag, the latter corrections amount to at least 0.05 mag for the extreme, metal-poor subdwarfs. [Much smaller corrections are required to match the isochrones predicted by the most recent models calculated by D’Antona et al. (15).)

An immediate consequence of the increased distance to these clusters is that one infers a higher luminosity for the



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement