6 Conclusion

The "reference'' temperatures taken from Smalley & Dworetsky (1995) for six stars are compatible within the errors with $T_{\rm eff}$  derived from the $T_{\rm eff}$ vs.  $(V-K)_{\rm0}$  relation taken from the grids of synthetic colours RIJKL computed by Castelli and available at the Kurucz web-site. For four out of the six stars the differences between the reference $T_{\rm eff}$  and $T_{\rm eff}$  from $(V-K)_{\rm0}$ is less than 100 K. The same is true for a sample of ISO standards which have temperatures that Di Benedetto (1998) derived with empirical methods. The accuracy is limited by the uncertainty in the correction for interstellar extinction (see Appendix A) and by the looseness of the definition of the Johnson photometric system for hot stars.

We give $T_{\rm eff}$ as a function of the colours $(V-J)_{\rm0}$, $(V-H)_{\rm0}$ and $(V-K)_{\rm0}$  (Bessell-Brett system) for various metallicities and $\log g$ appropriate for (a) BHB stars and (b) main sequence stars in Tables 2 and 3 respectively. The data in Table 3 are appropriate for the BMP (or class A) stars that make up a substantial fraction of the blue stars in the galactic halo.

We give relations by which the colours derived from V and the 2MASS magnitudes may be converted to the Johnson system so that the transformed colours may be used (with Tables 2 or 3) to derive $T_{\rm eff}$. Satisfactory agreement was found between these $T_{\rm eff}$ and those found for (a) Hyades dwarfs (b) local BHB stars (c) BMP stars and (d) BHB stars in the globular cluster M 13. We therefore conclude that this use of the 2MASS data affords a practical way of getting $T_{\rm eff}$  for blue halo stars in the magnitude range $5 \leq V \leq 15$. The accuracy is at least as good as that obtainable from $(B-V)_{\rm0}$.

While the $T_{\rm eff}$ derived by Wilhelm et al. (1999) for their BMP stars are in reasonable agreement with ours, the $T_{\rm eff}$  which they derive for their (generally hotter) BHB stars are significantly smaller than ours and the difference increases with increasing temperature. The distribution of the $T_{\rm eff}$ in their sample of BHB stars suggests that such differences are present in their whole sample of BHB stars. This is confirmed by Kinman & Miller (2002) who find that the differences between their $T_{\rm eff}$  and T_JHK  are related to their choice of $\log g$. As a consequence, the [Fe/H] that Wilhelm et al. derive for their BHB stars are, on average, $\sim$0.4 dex too metal-poor.

Acknowledgements

We are grateful to John Carpenter for a discussion of the difference between Eqs. (4) and (5) and about the possibility of errors in the 2MASS magnitudes of the brightest stars. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.