A&A 429, 887-894 (2005)
DOI: 10.1051/0004-6361:20041694
S. M. Percival1 - M. Salaris1 - M. A. T. Groenewegen2
1 - Astrophysics Research Institute, Liverpool John Moores
University, Twelve Quays House, Egerton Wharf, Birkenhead, CH41 1LD, UK
2 -
Instituut voor Sterrenkunde, PACS-ICC, Celestijnenlaan 200B,
3001 Leuven, Belgium
Received 20 July 2004 / Accepted 6 September 2004
Abstract
Hipparcos parallax measurements of stars in the Pleiades notoriously result in
a cluster distance of 118 pc, which is approximately 10% shorter than the
"classical'' result obtained from earlier main sequence (MS) fitting studies.
In an earlier paper we developed a purely empirical MS-fitting method
in an attempt to address this problem. This work produced
conflicting results for the Pleiades between the (B-V) and (V-I) colour
indices, indicating that the cluster's photometric metallicity is
substantially lower than its generally accepted spectroscopic metallicity
of
.
We were able to reconcile the discrepancy by
assuming
,
the appropriate metallicity indicated from
(B-V)/(V-I) colour-colour plots, and the distance moduli obtained from the
two colour indices were in agreement with the
Hipparcos result, within the 1
errors.
With the release of the 2MASS All Sky Catalogue, we now apply our MS-fitting method to the Pleiades using the infrared colours in addition to the optical bands, in order to test the plausibility of our earlier result.
Using the full field dwarf sample
and fitting in the V/(V-K) and K/(J-K) colour planes, we find
that assuming a substantially subsolar metallicity does not produce distances
in agreement with the (B-V) and (V-I) results. However the infrared plus
(V-I) distances are in mutual agreement when adopting the spectroscopic
metallicity. By considering only the field dwarfs with
,
i.e. brighter than the magnitude where the Pleiades (B-V)colours start to be anomalous (Stauffer et al. 2003, AJ, 126, 833), the infrared and
optical colour indices all yield consistent distances using the
spectroscopic [Fe/H].
The concordant distances thus obtained
from the V/(B-V), V/(V-I), V/(V-K) and K/(J-K) planes yield a mean of
pc, in excellent agreement with both the pre-Hipparcos
MS-fitting results, and the most recent determinations from other methods.
We conclude that there are two distinct, and unrelated, issues affecting the
Pleiades: 1) the Hipparcos parallax is in error by 10%, as previously
claimed; 2) the (B-V) colours of the lower MS are anomalous, and we caution
against using the (B-V) index for MS-fitting to the Pleiades and similarly
young open clusters.
Key words: Galaxy: open clusters and associations: general - Galaxy: open clusters and associations: individual: Pleiades - stars: Hertzsprung-Russell (HR) and C-M diagrams - stars: distances
The distance to the Pleiades has been controversial ever since the Hipparcos
mission (Perryman & ESA 1997) measured parallaxes of individual stars in the cluster
- the mean distance to the cluster determined from individual star parallaxes
was found to be approximately 10% shorter than distances previously
determined from main sequence (MS) fitting methods.
Specifically, the parallax measurements yield a distance of 118.34 pc,
corresponding to a distance modulus of
(m-M)0 = 5.37
(van Leeuwen 1999 and references therein), whereas MS-fitting
generally yields
(around 132 pc) or even longer
(e.g. Mermilliod 1981; Vandenberg & Poll 1989; Mitchell & Johnson 1957; Eggen 1986; Nicolet 1981; Crawford & Perry 1976).
After the release of the Hipparcos results, several authors attempted to
address this discrepancy using various methods based on semi-empirical
MS-fitting techniques, and all found distance moduli in agreement with the
earlier MS-fitting results (Stello & Nissen 2001; Soderblom et al. 1998; Pinsonneault et al. 1998).
On the other hand Castellani et al. (2002), who used purely theoretical
isochrones in their fits, were able to retrieve the Hipparcos parallax
distance by assuming a substantially subsolar metallicity for the cluster.
Concerns were raised that most of the distance determinations in the
literature use methods which have some model dependence which may introduce
unquantified systematic errors, hence in an earlier paper
(Percival et al. 2003, hereafter PSK03) we developed a purely empirical
MS-fitting method. This method employs a sample of 54 local field stars,
all with precise Hipparcos parallaxes, and with homogeneous metallicity
determinations on a scale consistent with that of the open clusters being
studied. These field stars were used to construct a template MS which was
fit to several open clusters, including the Hyades and the Pleiades
(PSK03; Percival & Salaris 2003).
Fitting in both the (B-V) and
colour planes
, this method
precisely reproduces the Hipparcos distance to the Hyades, yielding
.
Applying the same method to the Pleiades, we found
that the (B-V) fits yield
whilst (V-I) gave
(corresponding to 141.9 and 130.6 pc respectively).
Not only are these results much longer than the Hipparcos parallax
distance, they are also mutually inconsistent.
The location of the MS in a colour-magnitude diagram (CMD) is, of course,
dependent on metallicity and hence MS-fitting methods rely on matching the
metallicity of the template MS to that of the cluster. In PSK03 we used the
generally accepted spectroscopic metallicity for the Pleiades in our
"standard'' fits, specifically
(this value, plus
error bar is taken from the catalogue of Gratton 2000 and is based on
the HRS determination of Boesgaard & Friel 1990). Since the (B-V) and
(V-I) colour indices have different sensitivities to metallicity, the
discrepancy found between the (B-V) and (V-I) MS-fitting results suggests
that the spectroscopic metallicity is not the appropriate one to use when
applying MS-fitting to the Pleiades. Assuming that both the (B-V) and
(V-I) colours are normal for some metallicity, PSK03 used colour-colour
diagrams to demonstrate that the photometric metallicity of the Pleiades is
consistent with
,
and hence argued that this is the
appropriate metallicity to use for MS-fits to the cluster. Repeating the
MS-fits using this lower metallicity, PSK03 found that consistent distances
were obtained between the two colour planes. Furthermore, the concordant
distances derived at this assumed metallicity are much shorter than those
obtained from the solar abundance fits, and are thus consistent with the
Hipparcos parallax distance (see PSK03 for full details, and summary in
Sect. 3.3, Table 1).
Hence, in PSK03 we concluded that our analysis did not support any
mismatch between the MS-fitting and Hipparcos distances for the Pleiades
and that the widely discussed discrepancy is just an artifact due to the
cluster's (B-V) and (V-I) colours (and hence, photometric metallicity),
which are inconsistent with the spectroscopic metallicity.
However, the three most recent studies of the Pleiades, which use
alternative
distance determination methods, once again find long distances in general
agreement with the earlier MS-fitting results. Pan et al. (2004) examined data
for Atlas (the second brightest star in the Pleiades), a wide binary which
is resolved using optical interferometry. Combining orbital data
with an assumed mass-luminosity relation, they determine a distance of
133 < D < 137 pc, with a firm lower bound of D > 127 pc. The results
are slightly model-dependent, since the masses of the two components must be
taken from model isochrones - however a 10% uncertainty on the mass only
leads to a 3% uncertainty on the final derived distance, due to the
precision of the orbital parameters. Meanwhile, Munari et al. (2004) studied
the eclipsing binary HD 23642. From extensive new observations in Johnson
B and V (to obtain light curves) and high resolution spectra (yielding
radial velocities) they modelled the system and found a distance of
pc. These results are also slightly model dependent as the
temperature of the primary star must be determined independently - this is
done by comparing photometry in many different systems (from the
literature) to synthetic spectra.
Most recently, Soderblom et al. (2004) have measured trigonometric parallaxes
for three G and K dwarfs in the Pleiades, using the Fine Guidance Sensors on
HST. Their net parallax result of
milliarcsec, corresponding to
a distance of
pc, is in excellent agreement with both Pan et al. (2004)
and Munari et al. (2004).
Hence the problem of the Pleiades distance discrepancy still exists - whilst empirical MS-fitting using the (B-V) and (V-I) colours now yields a distance in agreement with the Hipparcos one (by assuming the photometric metallicity rather than the spectroscopic one), other methods continue to find distances in agreement with the earlier, pre-Hipparcos, results.
It should be pointed out at this stage however that there is a known problem with the Pleiades, which may or may not be related to the distance discrepancies (we hope to clarify this point later). This is that the lower main sequence stars (the K dwarfs) fall well below the position expected for a solar metallicity system in the V/(B-V) colour-magnitude diagram. Hence these stars are either underluminous, or have (B-V) colours which are too blue for their (spectroscopic) metallicity. As discussed in detail by Stauffer et al. (2003) (hereafter S03), this fact has been known for many years, but has largely been ignored, and certainly not explained. S03 present new spectroscopic observations of several Pleiades K dwarfs and, by comparison with similar observations of K dwarfs in Praesepe, they show that the unusual blue colours in the Pleiades arise from anomalous spectral energy distributions (SEDs) - at least for the two Pleiades K dwarfs that they study. This anomaly, which S03 ascribe to rapid stellar rotation and "spottedness'', causes the Pleiades stars to be approximately 10% brighter in the B-band than their Praesepe counterparts, whilst the V-band flux is unaffected. These spectroscopic measurements indicate that the (B-V) colours of the Pleiades K dwarfs should be about 0.1 mag bluer in (B-V) than the "standard'' solar sequence, in agreement with the broadband observations.
Comparison of the shape of the MS for the two clusters shows that in the
V/(B-V) CMD the two sequences start to diverge at
,
in the sense that the Pleiades MS becomes increasingly bluer (or fainter)
than the Praesepe MS towards fainter magnitudes (see S03, their Fig. 4).
Crucially, this divergence occurs right in the middle of the magnitude
range of the field dwarfs used in our empirical MS-fitting work, which have
.
However, similar comparisons in the V/(V-I)
and V/(V-K) planes show that the two sequences have identical shapes in
the full magnitude range of our field dwarfs. This fact is very important
for our study, as it implies that only the (B-V) index is affected by an
anomaly, and that MS-fitting using (V-I) and (V-K) should give reliable
(and consistent) results using the spectroscopic [Fe/H] for the cluster.
We note here that when
applying a MS-fitting method, for a fixed metallicity, the bluer (or more
subluminous) the cluster MS, the longer the derived distance will be -
hence the PSK03 results for (B-V) and (V-I), at
,
are consistent with the observations of S03.
With the release of the 2MASS All Sky Catalogue, we are now able to test our empirical MS-fitting method using the infrared colours in addition to the optical bands. We now know (from S03) that MS-fitting using (B-V) colours may give spurious results for the Pleiades, therefore it is important to apply the method using the (V-K) colours to see whether they yield a distance which is consistent with the (V-I) result, since both indices appear to be unaffected by any colour anomalies in the magnitude range of interest. Also, if concordant distances are obtained, we vitally need to know whether they are consistent with the Hipparcos parallax distance, or the longer distance determined from other methods. The 2MASS data also allows us to utilise the (J-K) colours. Whilst we have no specific information on the SEDs of the Pleiades K dwarfs in this part of the spectrum, the (J-K) index should be much less sensitive to differences in metallicity than either (V-I) or (V-K), and is also much less affected by extinction. Using the K/(J-K) CMD also ensures that the photometry is completely homogeneous between cluster and field stars and thereby minimizes systematic errors. Using (J-K) and (V-K) colour indices in addition to (V-I) helps to constrain the cluster metallicity (and reddening) since the sensitivities are different for each colour index and consistent distances must be obtained from all the colour planes used if the results are valid. This should enable us to determine once and for all whether the discrepancy between the MS-fitting distance and the Hipparcos parallax distance for the Pleiades is real.
As in PSK03, the method can be tested on the Hyades since fits using the
(V-K) and (J-K) must also be able to reproduce the Hipparcos distance
modulus for the cluster. We can also use M 67 as a comparison cluster for the
Pleiades since it has a similar spectroscopic metallicity
(
according to Gratton 2000), its
(B-V)/(V-I)colour-colour plot is consistent with solar metallicity field dwarfs (PSK03)
and its distance is not disputed (see Sect. 3.2).
The layout of the rest of the paper is as follows: Sect. 2 lists the sources of data used in this work; Sect. 3 gives a brief overview of the empirical MS-fitting method, and presents the results of its application to the Hyades, M 67 and the Pleiades, and Sect. 4 contains a discussion of the results and some general conclusions.
The empirical MS-fitting method used here is described in detail in PSK03, to
which we refer the interested reader. In outline, the method utilizes a
sample of 54 local unevolved (MS) field stars, with metallicities in the
range
for which PSK03 obtained new
photoelectric photometry. All the stars in the sample have
Hipparcos parallax measurements with errors less than 12%, Hipparcos
catalogue entries were also carefully checked to avoid the inclusion of any
binaries, and metallicities were determined from their Strömgren
indices. JHK data were
extracted from the 2MASS all-sky point source catalogue
using a star-by-star
coordinate search. Combining the 2MASS magnitudes with the parallax data
yields the absolute magnitudes, MJ, MH and MK, which are then
corrected for Lutz-Kelker bias, as described in PSK03. We note here the 2MASS
JHK data have already been retrieved and utilized by Sarajedini et al. (2004) in
a MS-fitting study of several open clusters, and appear in their Table 2.
2MASS data for the Hyades were retrieved for all stars listed in
Perryman et al. (1998) as single, definite cluster members, again using a
coordinate search. Data for the Pleiades were obtained in a similar manner,
individual MS stars having been identified from the Mermilliod's WEBDA
database (and see PSK03)
and known binaries removed (Raboud & Mermilliod 1998; Bouvier et al. 1997). For M 67, the single
star sequence was taken from Table 5 of Sandquist (2004), individual stars
and their coordinates were then identified by cross-correlating with the
data of Montgomery et al. (1993).
Since the field star and cluster data from 2MASS are all in the same
photometric system, for which the K filter used is actually (K short), no photometry conversions were necessary.
Before MS-fitting can be performed, the [Fe/H] dependence of the colour
index used must be determined so that the field star template can be matched
to the metallicity of the cluster - here we use (V-K) and (J-K). This
procedure is fully described in PSK03, where it was applied to (B-V) and
(V-I), and it is also utilized by Sarajedini et al. (2004) to determine the
metallicity dependence of (V-K). Firstly, the slope of the relevant
portion of the MS is estimated using the Hyades MS as a guide, then using
this slope, each field star is "shifted'' along this vector to an
absolute magnitude of MV=6.0. The colour of each star at MV=6.0
(i.e.
(V-K)MV=6.0) is then plotted against [Fe/H] to determine the
metallicity dependence of the colour index (see top panel of
Fig. 1). Using this procedure we find
,
in complete agreement with
Sarajedini et al. (2004), who find
.
When working with the (J-K) colour index we will be using the K/(J-K)CMD and hence the procedure is modified to find the (J-K) colour at
MK=4.0 (this roughly corresponds to MV=6.0 for the field star
sample in that it falls near the middle of the range of magnitudes for
the sample).
The precise metallicity dependence of (J-K) is harder to determine since the
colour range of the field star sample is very small and the resultant
plot is dominated by intrinsic
scatter. In fact, the total colour range of the field dwarf sample, at
their observed colours, is only 0.25 in (J-K) compared with 0.91 in (V-K).
A formal fit to the field star data yields a metallicity dependence of
although most of this dependence comes from the stars with
(see bottom panel of Fig. 1).
Fitting the subsolar and supersolar metallicity
ranges separately we find
for
,
whilst
is
virtually negligible for
.
We note here that this
difference in metallicity dependence for the two metallicity regimes
is in qualitative agreement with the theoretical isochrones of
Girardi et al. (2000)
and
Pietrinferni et al. (2004)
. However, the errors on these fits
are of the same order
of magnitude as the slopes, due to the relatively large scatter in
the colours and, in fact, tests using the Hyades show that the metallicity
dependence in (J-K) is actually consistent with zero (see
Sect. 3.1).
![]() |
Figure 1:
Metallicity dependence in (V-K) and (J-K). Top panel
- best fit relationship for the (V-K) data,
![]() ![]() ![]() |
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The Hyades fiducials were determined by fitting a polynomial (cubic) to all
the available single star data, reddening was assumed to be zero and the
metallicity was taken to be
(cluster
metallicities are taken from Gratton 2000, as explained in PSK03).
Shifting the field star sample to
and fitting to the
cluster fiducial in the V/(V-K) plane gives a best-fit distance modulus of
,
where the 1
error accounts
for photometry errors for the field stars, errors on magnitudes due to their
parallax errors, and error due to the cluster metallicity, all added in
quadrature.
![]() |
Figure 2: Fits to the Hyades MS. All 3 plots show the Hyades single star data (open triangles) and polynomial fit to the MS line, both shifted in magnitude by the best-fit distance modulus, and the field star data at their absolute magnitudes (filled circles). Top panel - V/(V-K) CMD, using best-fit distance modulus of (m-M)0=3.33; middle and bottom panels - K(J-K) CMDs, showing shifted and unshifted field stars using best-fit distance moduli of (m-M)0=3.40 and (m-M)0=3.35 respectively. |
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In the K/(J-K) plane, applying the maximum possible metallicity dependence
(
)
to the field stars yields a
best-fit distance modulus of
which is
marginally inconsistent with the Hipparcos parallax result of
.
Since the mean metallicity of the field star
sample is
and the Hyades is at
(i.e. near the top end of the range of metallicities
for the field stars), a relatively small error in the estimation of
the metallicity dependence can become significant when the field stars are
shifted. Hence it appears that the estimate of
is slightly
too high. Repeating the MS-fit assuming no metallicity dependence in (J-K)(i.e.
)
results in a best-fit distance
modulus of
(random errors only), in complete
agreement with the Hipparcos result. The uncertainty on the level of
metallicity dependence in the (J-K) index induces a systematic error of
0.06 mag on the Hyades distance modulus since the colours of the stars
are being "shifted'' on average 0.2 dex in metallicity, with an uncertainty
of 0.078 in
,
and the slope of the MS in
the K/(J-K) CMD is approximately 4.
It is important to realise however that the assumed level of metallicity
dependence makes negligible difference to the MS-fitting results for the
Pleiades. This is because the metallicity of the Pleiades is very close to
the mean of the field star sample (we assume
in our standard fits). When
building the MS template, individual field stars are being shifted both ways
in the CMD, i.e. from lower to higher and from higher to lower metallicity,
to match the metallicity of the cluster. Since the mean metallicity of the
field stars is well matched to the cluster metallicity, most of the effects
of the uncertainty on the metallicity dependence cancel out in this process
(see Sect. 3.3).
Fiducials for M 67 were determined in the same way as for the Hyades, by
fitting a polynomial to all the available single star data. The cluster
metallicity was taken to be
(Gratton 2000) and
a reddening value of
E(B-V)=0.04 was taken from Twarog et al. (1997).
Relative extinctions and
reddenings were calculated according to Cardelli et al. (1989), so that
AK=0.114AV,
E(V-K)=2.75E(B-V) and
E(J-K)=0.52E(B-V). After
correcting the cluster fiducial for extinction and reddening, and shifting
the field stars to the cluster metallicity, the best-fit distance modulus in
the V/(V-K) plane was found to be
.
We note that this
is in complete agreement with the results of Sarajedini et al. (2004) who find
(corresponding to
(m-M)0=9.62, with
E(B-V)=0.04) from a (V-K) MS-fit of our field dwarf sample to the M 67
data of Montgomery et al. (1993).
![]() |
Figure 3: Fits to dereddened and extinction corrected M 67 MS - symbols as for Fig. 2. Top panel - V/(V-K) CMD, using best-fit distance modulus of (m-M)0=9.65; middle and bottom panels - K(J-K) CMD, showing shifted and unshifted field stars, using best-fit distance moduli of (m-M)0=9.63 and 9.61, respectively. |
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The Pleiades fiducials were determined in the same way as for the Hyades, by
fitting a polynomial to all the single star data. As in PSK03, reddenings
for individual stars were taken from Breger (1986) (for those with no
listing an average of
E(B-V)=0.04 was used) and Gratton's metallicity of
was assumed in the standard fits.
Applying reddening and extinction corrections as before and shifting the
field stars to the cluster metallicity, the best-fit distance modulus in
V/(V-K) is
,
where the 1
error includes an
uncertainty of 0.02 mag in E(B-V), as for M 67.
In the K/(J-K) plane, the best-fit yields
- it
is important to note that in this plane, the results are the same, to within
0.01 mag, whether or not a metallicity dependence is assumed in (J-K).
![]() |
Figure 4: Fits to dereddened and extinction corrected Pleiades MS - symbols as for Fig. 2. Top panel - V/(V-K) CMD, using best-fit distance modulus of (m-M)0=5.67; middle and bottom panels - K(J-K) CMD, shifted and unshifted field stars respectively, both using best-fit distance modulus of (m-M)0=5.61. |
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In response to the findings of S03, we returned to the (B-V) data and
tested the effect of imposing a cut at MV=6.0, the point at which the
V/(B-V) MS appears to diverge from the "standard'' sequence. Using only
field stars with
MV < 6.0 in the fit, the best-fit distance modulus is
,
a reduction of 0.09 mag compared to the result from
the full sample (PSK03). Significantly, imposing the same cut in the
V/(V-I), V/(V-K) and K/(J-K) planes produces the same results as those
obtained from the full sample.
We recall here that PSK03 found that by assuming
,
the V/(B-V) and V/(V-I) CMDs yielded
distance moduli in agreement with the Hipparcos parallax result (specifically,
(m-M)0=5.46 and 5.39 respectively, using the full field dwarf sample).
In order to test the plausibility of this cluster abundance, we performed the
V/(V-K) and K/(J-K) fits again, this time using
,
keeping the same reddening as for the standard fits.
The V/(V-K) fit yields
whilst the K/(J-K) fits
yield
for
and
when no metallicity dependence is assumed (i.e.
the same result as for
).
Imposing a cut at MV=6.0, as before, has exactly the same effect on the
results as for the
fits, i.e. the V/(B-V) distance
modulus is reduced by 0.09 mag, to
(m-M)0=5.37, whilst the results from
the other colour indices remain unchanged.
All these results are summarised in Table 1.
Table 1: Summary of MS-fitting results for the Pleiades.
If we accept that the K dwarfs in the Pleiades really are too blue in (B-V) for their spectroscopic metallicity, as indicated by S03, then we should not expect the (B-V) and (V-I) MS-fitting results to be the same if the full MS is used (i.e going fainter than MV=6.0). In fact, we should treat with caution any models which claim to find concordant distances in these two planes, since the colours of the lower MS (the K dwarfs) are obviously anomalous for any value of [Fe/H], whether solar or otherwise.
Excluding the (B-V) results using the whole field dwarf sample, the distance
moduli obtained from the "standard'' fits in all the other colour planes
(i.e. V/(V-I), V/(V-K) and K/(J-K)) are in agreement with each other
within their 1
errors - and all are discrepant by at least
3
with the Hipparcos result. The average of the (V-I), (V-K)
and (J-K) fits is
,
corresponding to
pc.
Imposing a cut at MV=6.0 and including the (B-V) results, the average
of the fits in all four colour planes is
,
or 133.8 pc.
Assuming
(as we did in PSK03), whilst bringing
the (B-V) and (V-I) results into agreement with the Hipparcos parallax
distance, does not yield consistent results in (V-K) and (J-K). The
V/(V-K) distance modulus is still discrepant with the Hipparcos one at
the 2
level, whilst the (J-K) result is slightly more ambiguous
because of the uncertainty on the metallicity dependence for this colour index.
However, even using the maximum dependence, the result of
is still discrepant by more than 1
from the
Hipparcos distance modulus.
In summary, each of the four CMDs used here has a different slope on the MS
and a different sensitivity to the effects of reddening and metallicity.
We can find no combination of
and E(B-V) which produces distance moduli which are
consistent across all four colour planes simultaneously when the full
magnitude range of our field dwarf sample is used. However, imposing a cut
at MV=6.0 brings all the distance moduli into agreement when assuming
the generally accepted metallicity of
,
and average
reddening of
E(B-V)=0.04. Furthermore, the average of the best-fit
distance moduli yields a Pleiades distance of
pc, in complete
agreement with the results obtained from binaries in the cluster
(Munari et al. 2004; Pan et al. 2004) and the most recent parallax determination from HST
(Soderblom et al. 2004).
When applying the MS-fitting method to any cluster to derive its distance,
using the local field stars as a template, we are assuming that we are
comparing like with like - practically, this is the only sensible assumption
we can make. The Pleiades is known to be anomalous in several respects -
we know it is very young (100 Myr) and has fast rotating stars,
which may be affecting
the (B-V) colours, whilst the field stars have unknown ages but are likely
to be much older (typically a few Gyr).
Spectroscopic metallicity determinations rely on some assumptions, one
of which is a temperature scale. The spectroscopic determination used here
(and generally regarded as the most reliable one) is from
Boesgaard & Friel (1990), who used the temperature scale of Boehm-Vitense (1981).
This temperature scale is based on (B-V) colours - i.e. from an observed
colour, a temperature is inferred. Boesgaard & Friel determined
temperatures for the Pleiades stars using (B-V), Strömgren b-y and
H
photometry, all essentially in the same (blue) portion of the optical
spectrum, as detailed in Boesgaard et al. (1988). They themselves noted that
the (R-I) data was also examined for
use in determining the temperatures but go on to say that it was "rejected
on the basis that all calibrations gave consistently lower temperatures than
those obtained using the three other indices''. We remark that this is
consistent with the observation that the late-type MS stars in the Pleiades
have (B-V) colours which are
anomalously blue when compared to indices in other parts of the spectrum,
in that a bluer colour indicates a higher temperature.
The problem of determining which colour index yields the most appropriate temperature is not just confined to the Pleiades. In a study of photospheric abundances in active binaries, Morel et al. (2004) state that there is a tendency for the (V-R) and (V-I) indices to yield systematically lower temperatures than (B-V). As was the case for the Pleiades, Morel et al. (2004) regard the (V-R) and (V-I) colour temperatures as being "spuriously low''. On the other hand, in a study of the effect of chromospheric activity on the mean colour of late-type stars, Amado (2003) find evidence for a blue excess in both the (U-B) and (B-V) indices for active stars when compared with quiescent ones of the same spectral type. In fact, Amado (2003) cautions against the use of the (B-V) index when determining fundamental parameters (e.g. temperature) for late-type active (i.e. young) stars and suggests that near-infrared colours should be better temperature indicators for these stars. It is beyond the scope of this work to predict what effect this may have on the derived spectroscopic metallicity for the Pleiades and other young clusters, but it should be borne in mind when assuming a metallicity for MS-fitting.
Reddening estimates are also generally determined from a star's colours, assuming that they are normal for their particular spectral type. Most of the Breger (1986) reddenings for the Pleiades stars are derived from broadband (B-V) or Strömgren b-y indices, both of which are in the potentially anomalous part of the spectrum. If the B flux is too strong for the late-type (lower MS) stars, and hence the colours too blue at a fixed spectral type, this would seem to indicate that the derived reddenings would be under-estimated. This would only serve to make the Pleiades problem worse in that assuming a higher reddening would yield an even longer distance. However the referee has pointed out that the Pleiades reddening (and metallicity) measurements are in fact heavily weighted towards stars of early spectral types (mostly B, A and F), and so the canonical reddening and metallicity values may not be greatly affected by the anomaly displayed by the K dwarfs.
Acknowledgements
We warmly thank the referee John Stauffer for a constructive report and some helpful comments and suggestions. S.M.P. would like to thank P.A.J. for financial and emotional support during a difficult time. This research has made extensive use of the WEBDA, HIPPARCOS and 2MASS databases.