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The HR Diagram and the Galactic distance scale after Hipparcos
I. Neill Reid
Palomar Observatory, 105í24, California Institute of Technology, Pasadena, CA 91125, eímail:
inr@astro.caltech.edu
ABSTRACT
The completion and publication of the Hipparcos astrometric catalogue has
revitalised studies in many fundamental areas of Galactic structure and stellar
evolution. This article reviews the impact of the new parallax results on our
understanding of the location of the mainísequence as a function of abundance, of
the luminosity calibration of primary distance indicators and of the Galactic distance
scale. Many of these issues remain to be resolved.
Subject headings: Stars: subdwarfs, parallaxes, RR Lyraes; Globular clusters:
distances; Galactic structure

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1. Introduction
Calibration of the extragalactic distance scale rests on our ability to determine accurate
locations in the observational HertzsprungíRussell diagram for specific types of stars at particular
stages in their evolution. Whether one uses Cepheids, RR Lyraes, planetary nebulae or type
I supernovae as links in the distance chain, the underlying assumptions are that in matching
similar types of stars in different stellar systems, one is comparing like with like; and that if the
calibrators are not identical, systemic variations can be traced to systematic trends with changes
in physical characteristics. Given that those criteria are satisfied, in principle all distanceíscale
investigations can determine relative distances between different external galaxies. However,
determining absolute distances requires absolute luminosities for individual calibrators. Thus, the
accuracy with which one can derive parameters such as the Hubble constant, H 0 , depends on the
accuracy with which one can measure distances within the Galaxy so as to calibrate the various
distance indicators.
Trigonometric parallax measurements offer the only method of directly measuring distances
to almost all single stars or muliple star systems. The application of CCD detectors to astrometry
(Monet, 1988) has shown that subímilliarcsecond (mas) precision can be achieved from the
ground. However, the need for adequate reference stars within the small field of view allowed by
current CCDs limits observations to faint apparent magnitudes (VÖ 14), and hence to nearby
stars of low intrinsic luminosities. Moreover, the accuracy of the final parallax is dependent on the
transformation from relative to absolute reference frames.
The ESA Hipparcos satellite was designed to address this issue. Full details of the scope
of this mission and the subsequent analysis are given by van Leeuwen (1997) and Kovalevsky
(1998). Two 13ícm diameter optical telescopes were used to image 1 squareídegree regions of the
sky, separated by 58 o , onto the same focal plane. A photodiode timed stellar transits across a
reference grid as the satellite rotated on its axis. Groundíbased parallax observations are limited
to small angular fields of view, and reference stars share the same parallactic motion as the target
í hence the necessity for correction from relative to absolute systems. Hipparcos measured angular
separations of stars with significantly different parallax factors, allowing direct determination of
absolute parallaxes in the final astrometric solution.
Hipparcos was a targeted mission, rather than a sky survey, with programme objects limited
generally to surface densities of eight per square degree. Photonícounting statistics rendered
impracticable observations of sources fainter than 13th magnitude. The final catalogue includes
positions, proper motions and parallax measurements, as well as BV photometry, for 118,000
stars, including nearly every star brighter than 7th visual magnitude, but for only 45,000 stars
with 9 ! V ! 11 and 4,000 stars between 11th and 13th magnitude.
These data have formed the basis for a large number of investigations over the last two years
(160 refereed publications as of May, 1998). The present article does not aim at a comprehensive
review of all issues raised in those papers. Rather, our intention is to consider the impact of the

-- 3 --
Hipparcos results on investigations of the distance scale. This leads us to focus on two issues:
the location of the mainísequence as a function of age and chemical abundance, based partly
on observations of nearby stars and partly on distance estimates to clusters; and direct distance
measurements of primary distance indicators. We consider how these reícalibrations affect distance
estimates to the Magellanic Clouds and M31, but carry extragalactic distance scale arguments no
further.
2. Astrometric accuracy and systematic biases
2.1. Measurement precision
The formal precision of the astrometry for an individual star depends primarily on the number
of observations and the signalítoínoise of each observation. Scans were made with the satellite
rotational axis precessing at 6.4 revolutions yr \Gamma1 at an angle of 43 o to the direction to the Sun.
As a result, stars at ecliptic latitudes fi ? 47 o (particularly those at fi ¦ 47 o ) were observed more
frequently than those at lower latitudes, with a corresponding ¦ 50% increase in accuracy (ESA,
1997). Figure 1 illustrates the typical distribution of formal uncertainties (oe ï(ff) ; oe ï(ffi) ; oe ‹ ) as a
function of apparent magnitude.
Data reduction was undertaken independently by two consortia, NDAC and FAST, with the
final catalogue consisting of the merged astrometric parameters. Both undertook extensive tests
and comparisons to verify the accuracy of the satellite astrometry, particularly the reliability of
the absolute zeropoints in ï and ‹. Those tests are discussed by Arenou et al (1995), Lindegren et
al (1995) and Lindegren (1995) for the initial 30ímonth analysis, and in the first and third volumes
of the Hipparcos catalogue (ESA, 1997). In brief, the positional data show clear evidence for
distortions in the FK5 groundíbased frame at the 60í100 milliarcsecond level, while a comparison
of the proper motions against groundíbased data, which have longer time baselines and comparable
accuracy, confirms random uncertainties of ffl H (ï) ¦ 1 \Gamma 2 mas. Similarly, comparisons of the
Hipparcos parallax data against the most accurate available groundíbased measurements (by
the US Naval Observatory) generally confirm the 1í2 mas quoted uncertainties of individual
observations, as does Lindegren's (1995) analysis of the distribution of negative parallaxes.
Determining the reliability of the absolute zeropoints, notably in parallax, is a more complex
issue. Coíordinates are on the J2000 system (epoch 1991.25), referenced to the International
Celestial Reference System (ICRS) via secondary standards (no extragalactic reference sources
were observable by Hipparcos). The zeropoint for the properímotion system is tied to the
extragalactic frame through reference sources with absolute motions, either directly from VLBI
or indirectly, from photographic surveys (see Johnson, 1999, this volume). The zeropoint of the
Hipparcos parallaxes, ‹H , was tested by matching against independent parallax estimators (e.g.
photometric parallax), primarily for distant stars where oe ‹ (other) !! oe ‹ (H). In particular,
Hipparcos data for 46 Magellanic Cloud stars (‹ ‹ 0:02 mas) give ï
‹ = \Gamma0:16 \Sigma 0:26 mas and

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oe ‹ = 1:72 \Sigma 0:18 mas. Arenou et al conclude that the overall results are consistent with a global
zeropoint error of ! 0:1 mas in ‹H . However, this does not exclude larger deviations on smaller
angular scales, as discussed further below.
These tests of the parallax zeropoint rest primarily on relatively faint stars, since few
stars brighter than 7th magnitude have highíaccuracy groundíbased parallaxes. Harris et al
(1997) and Gatewood et al (1998) present comparisons based on 23 and 63 stars respectively. A
weighted mean of their results (Hanson, priv. comm.) gives ‹H \Gamma ‹ other = 0:30 \Sigma 0:24mas, where
the uncertainty is the standard error of the mean. While this is consistent with the absolute
zeropoint defined at fainter magnitudes, they fail to provide a stringent test of the presence of any
magnitudeídependent systematics.
2.2. Systematic biases in parallax determination
LutzíKelker bias
The measured parallax provides the best (trigonometric) estimate of the distance to a
particular star system. If, however, one considers that same object in a statistical sense í as a
representative of the disk main sequence, for example í then one must allow for possible systematics
introduced by the sampleíselection criteria adopted. This potential for bias in statistical analysis
of parallaxíselected datasets was noted early this century by Russell and is also discussed by
Trumpler & Weaver (1953). Lutz & Kelker (1973) provide the first quantitative description of this
effect.
Under the standard assumption that the measured parallax, ‹ o , is an unbiased estimate of
the true parallax, ‹, the conditional distribution C o (‹ o j‹) has a mean value ‹. However, we are
aiming to determine ‹ given ‹ o , and are therefore concerned with the conditional distribution
C(‹j‹ o ). In that case,
C(‹j‹ o ) ¦ C o (‹ o j‹) \Lambda ND (‹) (1)
where ND (‹) is the true parallax distribution of stars in dataset D. Note that ND (‹) is often not
identical with the parallax distribution of the parent Galactic stellar population, since D is usually
preíselected based on a combination of magnitude, color and proper motion. The dependence on
ND (‹) leads to systematic bias in the mean parallax if one selected a subísample, S, from dataset
D on the basis of ‹ o .
LutzíKelker corrections
\DeltaM LK = hM true \Gamma M o i = h5log
‹
‹ o
i (2)
provide a means of correcting this bias in the absolute magnitude plane. The bias is not present
if there is no selection based on ‹ o , as in the methods of mean parallaxes (e.g. averaging open
cluster parallaxes) or reduced parallaxes (cf. Feast & Catchpole's (1997) Cepheid analysis and

-- 5 --
Feast (2000)). The LK bias, however, is always present when one averages absolute magnitudes,
since the latter cannot be calculated if ‹ o is negative.
Lutz & Kelker computed \DeltaM LK for the specific case of a uniform distribution, ND (‹) / ‹ \Gamma4 ,
and are limited to oe ‹
‹ ! 0:175. Hanson (1979) showed that common observational selection effects
(magnitude limits, proper motion limits) lead to less steep powerílaw density distributions, and
used series expansion to derive general solutions for ND (‹) / ‹ \Gamman . This results in both smaller
LK corrections, and reliable corrections for higher values of oe ‹
‹ (see also Koen, 1992).
With an apparent magnitude limit of V ¦ 12, the Hipparcos dataset is magnitudeílimited for
stars with M true ? 5:0. In that case, the powerílaw exponent n of the density distribution and the
resultant LutzíKelker bias are reduced significantly (Lutz, 1983), since imposing a magnitude limit
modifies ND (‹) without direct reference to ‹ o . The situation is analagous to observations toward
an opaque molecular cloud at ‹MC : no stars have ‹ ! ‹MC , reducing the number of stars with
smaller ‹, and the probability that, for any given star, ‹ ! ‹ o . This emphasises that there is no
unique \DeltaM LK for a given star: the correction depends on context. If one modifies ND (‹) based on
parallaxíindependent criteria before selecting the ‹ídefined subsample, one also modifies \DeltaM LK .
Effects on small angular scales
The surface density of Hipparcos targets was set to match the limits of the observing mode.
As a result, the same objects were generally observed on successive scans of a particular region.
This leads to correlations in the derived astrometric data over scales of up to ‹2 degrees (twice
the field of view). One notable effect is that the precision of the mean parallax of stars with
separations within this r'egime is oe ‹
n 0:35 rather than oe ‹
n 0:5 (Lindegren, 1988).
These correlations may lead to systematic bias in ‹H at those angular scales. A comparison
between the results from NDAC and FAST (Hipparcos catalogue, ESA, 1997; vol 3, ch 16 & 17)
shows that differences of up to ¦ 2 mas can occur within 2 \Theta 2 degree regions near the ecliptic,
corresponding to potential offsets of ‹ 1 mas in the final, merged catalogue. This result does not
contradict the finding that the global zeropoint in ‹H is reliable at the 0.1 mas level, but it serves a
cautionary note for studies which require subímilliarcsecond accuracy over 1í2 degree scalelengths.
Temporal effects in parallax measurement
In simple terms, the aim of the Hipparcos data reduction is to solve the following equations
of condition for each target:
X = X 0 + ïX (T \Gamma T 0 ) + FX ‹ (3)
Y = Y 0 + ï Y (T \Gamma T 0 ) + F Y ‹ (4)
where (X, Y) are the observations, (X 0 ; Y 0 ) the coíordinates, (ï X ; ï Y ) the proper motions and
(F X ; F Y ) the parallax factors. If observations are not wellídistributed in time, the unknowns are
correlated. Hipparcos observations span the period January, 1990 to March, 1993, but no data
were obtained between September and November, 1992, due to the loss of a gyro and subsequent
reíconfiguration of the control system. As a result, January to March scans are available at four

-- 6 --
epochs, but September to November at only two. This imbalance leads to correlation coefficients,
ae, of up to \Sigma0:6 (Hipparcos catalogue, ESA, 1997; volume 1, ch 3.2), particularly in ae(‹; ff).
Groundíbased parallax analyses almost always achieve ae ! 0:1 since one of the usual criteria is
equal numbers of morning and evening observations. The existence of such high correlations does
not guarantee bias, but the data are clearly vulnerable to such effects.
3. Distances to open clusters
The typical Galactic open cluster is populated by from a few tens to a few hundred stars,
the product of a single staríforming region, spanning a narrow range in age and in chemical
composition. Several fiducial clusters fall within the range of Hipparcos (Mermilliod et al, 1997;
van Leeuwen et al, 1997). Since open clusters have a small lineíofísight depth and since cluster
membership can be decided based on photometric, proper motion or radial velocity criteria,
individual parallax measurements can be combined without incurring significant LutzíKelker bias,
although other systematic sources of error may be present. In particular, the small angular size of
the more distant clusters renders the astrometry susceptible to the smallíscale systematic problems
outlined in section 2. Indeed, Lindegren (1988) identified observations of open cluster stars as a
powerful diagnostics of the extent of biases on small angular scales.
3.1. The Hyades
The metalírich Hyades is near enough to permit groundíbased trigonometric and, in resolved
binaries, orbital parallax measurements, as well as statistical convergentípoint analysis of the
proper motions and radial velocities. The most recent latter study, by Schwann (1991), derived
a mean modulus of 3.40\Sigma0:04 mag. (47.9\Sigma0:9 pc.) based on 145 stars with proper motion
measurements from the FK5/FK4Sup, N30 and PPM catalogues. Perryman et al (1998) have
analysed the Hipparcos astrometry, complemented by additional radial velocity data. Conventional
convergentípoint analyses derive the cluster distance from the equation
ï
d = \Sigma N
i ( V S sinÖ i
ßï i
) = N (5)
where ß = 4:74, V S is the cluster space velocity, ï i the individual proper motions toward the
convergent point and Ö i the angular distance between each star and the convergent point. As
Perryman et al point out, the exact location of the last parameter depends on the extent to
which one allows for random cluster motions (oe cl ¦ 0:2 to 0.4 kms \Gamma1 ) in defining the membership
list. The Hipparcos data provide full positional and velocity information, and allow iterative
membership analysis. Following that approach, Perryman et al derive a distance of 46.34\Sigma0.27
pc. ((míM)=3.33) to the center of mass defined by 134 stars within a radius of 10 parsecs of the
cluster center.

-- 7 --
The main source of the 3.4% discrepancy between the Hipparcos result and Schwan's analysis
is the value adopted for the cluster space motion: Schwan's datum is V S = 46:6kms \Gamma1 , based on
Detweiler et al (1984), while Perryman et al derive V S = 45:72kms \Gamma1 from CORAVEL data, a 2%
difference. Most of the remaining discrepancy rests with the proper motions, and those differences
are also responsible for the larger mean distance derived by Torres et al (1997) based on precise
orbital parallax determination. Thus, the new Hyades distance determination is fully consistent
with previous observations.
3.2. The Pleiades and other clusters
The same consistency with previous work is not apparent in initial analyses of the distance
to the Pleiades cluster, which offered potentially the most significant result of the Hipparcos
mission. The concensus of preíHipparcos studies located the Pleiades at a distance of ¦ 130pc.,
(míM) 0 =5.6 mag. However, both van Leeuwen & HanseníRuiz (1997) and Mermilliod et al (1997)
derive a mean parallax from Hipparcos observations of ï ‹ = 8:6 \Sigma 0:24 mas, or r=116\Sigma3 pc. and
(míM) 0 =5.33\Sigma0:05 mag., placing the (solaríabundance) Pleiades mainísequence ¦0.2 magnitudes
fainter than the relation defined by nearby field stars (h[F e=H]i ¦ \Gamma0:15 dex). Such a result can
be accommodated within standard stellar evolution models, but only at the expense of invoking
substantial anomalies, such as a helium abundance YMS ¦ 0:35, and casting severe doubt on the
global utility of distance determination by mainísequence fitting.
Pinsonneault et al (1998) reíexamine this issue and show that plotting parallax against
the ae(‹; ff) correlation (see section 2) for individual Pleiads reveals a clear trend, with stars
having higher ae(‹; ff) also having larger ‹ (their figure 18). As noted in section 2, observations
with high ae(‹; ff) correlation indices may also have biased parallax determinations. Since the
relevant Pleiads are also predominantly bright stars near the cluster center, carrying most of the
weight in deriving ï ‹, the small angularíscale correlation inherent in Hipparcos astrometry leads
one to expect correlated bias. Given that Pleiads with ae(‹; ff) ! 0:2 give ï
‹ = 7:49 \Sigma 0:50mas,
(míM) 0 =5.63\Sigma0:14 mag, and that there is an absence of any [Fe/H]¦ 0 field stars which reproduce
the van Leeuwen/Mermilliod mainísequence (Soderblom et al, 1998), it is reasonable to reject the
initial Pleiades distance estimates as likely to be biased. The current best estimate of the distance
of the Pleiades remains at (míM) 0 =5.6 magnitudes, or 132 parsecs (although see van Leeuwen,
1999, for a dissenting viewpoint).
Mermilliod et al (1997) and Robichon et al (1997) estimate distances to other nearby
clusters, including Coma, Praesepe, IC 2602 and ff Persei. Most are significantly more distant
than the Pleiades and, in general, the Hipparcos distance moduli are consistent with previous
determinations. An exception is the sparse, nearby cluster Coma Berenices, where Pinsonneault
et al find a discrepancy of ¦ 0:2 magnitudes with respect to isochroneífitting, and trends in
(‹; ae(‹; ff)) similar to those in the Pleiades.

-- 8 --
In summary, Hipparcos astrometry does not provide the major challenge to stellar evolution
theory suggested by the preliminary analyses. Systematic biases, correlated over scales of ! 1
degree, limit the reliability of results derived for most open clusters. To echo Pinsonneault et al,
it seems more prudent to regard these comparisons as tests of smallíscale zeropoint errors, rather
than as measurements of cluster distances.
4. The HR diagram defined by field stars
The technique of distance determination through mainísequence fitting rests on the
hypothesis that the absolute magnitude (luminosity) of normal, single stars of a given color
(effective temperature) is a monotonic function of metallicity. Hipparcos provides the first
opportunity for a thorough empirical test of that hypothesis.
4.1. The abundance scale
In principle, fine analysis of highíresolution optical spectra, coupled with accurate temperature
determination, provides the best basis for measuring stellar metallicity. However, it is only recently
that such studies have been extended to significant numbers of even moderately faint stars. As a
result, most investigations of abundance distributions are based on a variety of loweríresolution
spectroscopic or photometric techniques, each anchored to the highíresolution scale through a
limited (and noníunique) set of standards. The latter step can lead to systematic zeropoint offsets
between different studies, particularly given the relativelyírecent revision in the accepted value of
the solar iron abundance (Bi'emont et al, 1991).
Advances in atmosphere modelling are opening the door for the first quantitative abundance
analyses of lateítype (K, M) dwarfs, notably using metal hydride bandstrengths (Allard et al,
1997; Gizis, 1997). However, most investigations continue to concentrate on F, G and earlyíK
stars on the upper mainísequence. Sandage & Eggen (1959) originally devised ffi(UíB), the
ultraviolet excess index, as a means of using Johnson broadband photometry to measure relative
lineíblanketing shortward of 4000 Ú A. Intermediateíband systems, such as Strèomgren or Geneva
photometry, have refined that measurement to some extent, while spectroscopic calibrations center
on Fe, CH, CN and Mg features in the 4000í5300 Ú A range (Rose, 1991; Carney et al, 1994; Jones
et al, 1996).
Two of the most extensive abundance catalogues are Schuster et al's (1993) Strèomgreníbased
dataset and Carney et al's (1994: CLLA) spectroscopic calibration. Schuster & Nissen (1989: SN)
derive relations, tailored for mainísequence stars, between the (bíy), c 1 and m 1 indices and [Fe/H],
while the CLLA calibration is based on high dispersion, but low signalítoínoise, spectra covering
¦ 50 Ú A centerd on the Mgb triplet. Abundances are derived by crossícorrelating the latter spectra
against observations of standard stars. Jones et al (1996) adopt a similar approach, basing their

-- 9 --
calibration on the CLLA system, while Flynn & Morell (1997) have devised an abundance index
for G and K dwarfs which combines Geneva photometry with a Cousins (RíI)íbased temperature
scale.
All of these calibration (save the last) are tied to standards with highíresolution abundance
analyses which predate the revision in [Fe/H] fi . This leads to an offset between those abundance
scales and metallicities defined in the more recent highíresolution studies by Axer et al (1994:
AFG) and Gratton et al (1997a: GCC), while there are further systematic differences between the
individual datasets. Reid (1998) finds
[F e=H]GCC ¦ [F e=H]AFG ¦ [F e=H] SN + 0:15 ¦ [F e=H]CLLA + 0:3
with dispersions of oe ¦ 0:2 dex. The offsets in the latter two scales become less pronounced at
nearísolar abundances. There is also evidence for a color term (temperature scale difference)
between the Schuster & Nissen and Carney et al calibrations, while Axer et al clearly underestimate
logg for a number of Hipparcos stars (see also Nissen et al, 1997). Clementini et al (1999) generally
confirm these offsets,
[F e=H]GCC = [F e=H] SN + 0:102 \Sigma 0:012
[F e=H]GCC = (0:935 \Sigma 0:032)[F e=H]CLLA + 0:181 \Sigma 0:173
while comparison with data from Ryan & Norris (1991) gives
[F e=H]GCC = [F e=H]RN + 0:40 \Sigma 0:04
Since the Jones et al scale is based on CLLA standards, one expects similar systematic errors in
their abundances.
4.2. The HR diagram of the local disk
Stars within the immediate Solar Neighbourhood can be used to probe the general properties
of the disk, since the overall velocity dispersion permits stars born at Galactic radii from 3 to 13
kpc to migrate through the Solar Radius. However, one of the early results from the Hipparcos
survey was an indication that a significant fraction of the stars included in the most recent
incarnation of the Nearby Star catalogue (CNS3: Jahreiss & Gliese, 1991) are not, in fact, within
the nominal distance limits. analysis of the final catalogue confirms that ¦ 40% of the CNS3
stars observed by Hipparcos lie beyond 25 parsecs. This has obvious implications for statistical
investigations which require unbiased, volumeílimited samples. For example, figure 2 plots
Hipparcos data for 106 nominallyísingle stars from the ''Gídwarf'' sample which are used by Wyse
& Gilmore's (1995) to analyse the disk abundance distribution. Approximately 10 percent of the
stars lie well above the mainísequence, and are likely to be evolved subgiants rather than dwarfs,
while a further 5í10 stars are probably previouslyíunrecognised binaries. To date, no comparable
study has been undertaken based on a volumeílimited sample drawn from the Hipparcos catalogue.

-- 10 --
While the Wyse/Gilmore stars do not constitute a volumeílimited sample, these observations
can be used to examine the variation in mainísequence location with changing abundance. Wyse
& Gilmore use Strèomgren photometry (from Schuster & Nissen, 1989) to estimate metallicities.
Dividing the stars into four subsets, figure 2 compares the (M V , (BíV)) distribution against
1íGyr and 5íGyr isochrones for solar abundance and [Fe/H]=í0.4 dex as computed by Bertelli
et al (1994). Ignoring evolved stars, the relative ranking is consistent with expectations, with
M V generally becoming fainter with decreasing [Fe/H] SN at a given color. However, there is a
systematic offset with respect to the isochrones, in the sense that the loweríabundance stars are
brighter than expected given the Strèomgren metallicity estimates. This is consistent with the
abundanceíscale comparisons given in the previous section.
The data plotted in figure 2 are consistent with the hypothesis of a monotonic change in
the location of the mainísequence with varying metallicity. Moreover, the comparison with the
isochrones suggests that most disk stars have abundances within \Sigma0:2 dex of the solar value (see
also figure 4 of Pinsonneault et al, 1998). Jimenez et al (1998) find a comparable systematic offset
between the loweríabundance (í0.6 ! [F e=H] ! \Gamma0:4) stars in the Flynn & Morell sample and
their [Fe/H]=í0.5 isochrones. The implication is that previous studies, such as Wyse & Gilmore's
analysis, overestimate the extent of the metalípoor tail to the disk abundance distribution, an
inference consistent with Reid's (1998) analysis of Hipparcos data for Lowell properímotion
stars. Definitive results await more extensive observations, particularly detailed abundance
determinations, of an Hipparcosíbased volumeílimited sample.
4.3. The HR diagram for halo subdwarfs
The low space density of the local halo coupled with the apparent magnitude limits of the
Hipparcos survey lead to the final catalogue including only a few tens of metalípoor subdwarfs
or subgiants with parallaxes of even moderate accuracy. As a result, those data offer only weak
constraints on theoretical calculations. Cayrel et al (1997) compare the observed (M bol , log T eff )
distributions for stars with \Gamma1:8 ! [F e=H] ! \Gamma1:2, with temperatures taken from Alonso et al
(1996), against (asíyet unpublished) isochrones computed by Lebreton and Vandenberg 1 They
find a systematic offset of 0.01 in logT eff , in the sense that the models are too hot. Adjusting the
isochrones, Cayrel et al deduce an age of ¦ 14 Gyrs for the field halo, although it should be noted
that that result rests on the location of two subgiants.
Figure 3 matches D'Antona et al's (1997) theoretical isochrones for 12 Gyríold populations
against data for subdwarfs from the AFG and GCC analyses, restricting the latter to stars with
no known binary companion having \Deltam ! 4 mag., with oe ‹
‹ ! 0:15 and with [Fe/H]! \Gamma0:7.
1 As discussed further in section 5, the D'Antona et al (1997) models predict a similar (M bol , log T eff ) relation
for mainísequence stars with MV ? MV (TO)1 .

-- 11 --
As with the disk stars, the overall trend matches theoretical expectations. At metallicities
exceeding [Fe/H] = í1.7 there is reasonable agreement between the observations and the predicted
isochrones, a circumstance also noted by Chaboyer et al (1998). There is a suggestion that the
lowestíabundance subdwarfs are more luminous (redder?) than expected, but this may reflect
smallínumber statistics or an inherent selection effect rather than intrinsic stellar properties.
These data can also be used to estimate \DeltaY
\DeltaZ , the proportional increase in helium and heavy
element abundance due to stellar nucleosynthesis í an important quantity in determining the
primordial helium abundance, Y P . Helium abundance cannot be measured directly for stars on the
lower mainísequence, but can be inferred by matching the observed distribution in the (M bol , log
T eff ) plane against theoretical isochrones. Based on preíHipparcos data for nearby disk Gídwarfs,
Fernandes et al (1996) deduce that \DeltaY
\DeltaZ ? 2. Pagel and Portinari (1