1 Introduction

An intrinsic colour calibration is a relation defining, either in some colour-colour plane, or in some N-dimensional space if the calibration requires Ncolour indices, the locus occupied by stars. The calibration is called "intrinsic'' because it holds for the colours which emerge from the stellar atmosphere but not for the observed colours, which are altered while passing through the interstellar medium. Knowledge of an intrinsic colour calibration allows one, at least in principle, to derive the reddening of a given star by comparing the observed colours with the colours predicted by the calibration. This may fail if the effect of reddening is to shift the point representative of a star along the curve, i.e. if the reddening vector is parallel to the intrinsic locus. This occurs for instance in the $\left( (B-V),(U-B)\right)$ plane for F, G, K stars where the reddening vector in the $\left( (B-V),(U-B)\right)$ plane is almost parallel to the intrinsic locus of Main Sequence stars.

Determining the reddening of an individual star is important for several reasons. First, estimation of reddening is necessary if we want to obtain a photometric distance of the star. Second, it is necessary for the derivation of atmospheric parameters of the star, such as effective temperature, surface gravity and metallicity. These parameters can be derived from suitable colours, provided the reddening is properly taken into account. For example the (V-K) colour may be accurately calibrated onto $T_{\rm eff}$ (Alonso et al. 1996, 1999; Di Benedetto 1998), but using (V-K) rather than (V-K)₀ will result in an underestimate of the temperature. Finally the knowledge of the reddening gives important information on the interstellar medium along the line of sight towards the star.

For F, G and K stars the calibration of $uvby\beta$ colours by Schuster & Nissen (1989) has proved to be both a very powerful and accurate tool for estimating the reddening and has become the "standard'' procedure for its determination. The possibility of deriving such a calibration was foreseen in the very design of the Strömgren photometric system and was already exploited by the calibrations of Crawford (1975) and Olsen (1983) which preceded the Schuster & Nissen calibration and are superseded by it. The calibration is possible because the system provides two indices, (b-y) and $\beta$, which mainly depend on effective temperature; however while (b-y) depends on reddening the $\beta$ index is reddening-independent. Therefore there exists a functional relation $(b-y)_0= f(\beta)$ which allows us to calibrate the reddening of the observed (b-y). This is accomplished by the Schuster & Nissen calibration in which terms in m1 allow us to take into account the metallicity dependence of (b-y), while terms in c1 allow us to take into account its dependence on surface gravity (luminosity). Although very powerful, Strömgren photometry requires a considerable investment in telescope time, due to the large number of filters (6) and to their relatively narrow width.

The HK objective-prism/interference filter survey (Beers et al. 1985, 1992) provides, at present, the largest sample of stars suited for the study of the galactic structure. The survey is kinematically unbiased and therefore it is ideal for studying both kinematics and dynamics of the Galactic Halo. Besides being the main source of extremely metal-poor stars, ${\rm [Fe/H]}< -3.0$, it provides a large number of stars in the range $\rm -0.5 \le [Fe/H] \le -2.0$ which are well suited to study both the thick-disc and the halo thick-disc transition. The medium dispersion follow-up survey, which provides radial velocities and metallicities, has been extended by Beers and collaborators in both northern and southern hemispheres and the results will be soon available (see Beers 1999 for a summary). At the same time photometric campaigns are being carried out to complement spectroscopic data. Norris et al. (1999) provide UBVdata for $\sim 2500$ stars, Preston et al. (1991) for about 1800 stars, Doinidis & Beers (1990, 1991) for about 300 stars and Bonifacio et al. (2000) for about 300 stars. Strömgren photometry is provided for 89 stars by Schuster et al. (1996), and for $\sim 500$ stars by Anthony-Twarog et al. (2000), although the latter data do not include the $\beta$ index and therefore cannot be used to derive reddenings from the Schuster & Nissen calibration.

From the above summary it is clear that the Schuster & Nissen calibration is of little use in determining reddenings for HK stars and would require further observational efforts to obtain also $uvby\beta$ data. So far reddenings for these stars have been determined from maps, those of Burstein & Heiles (1982) in the first place, and, more recently, those of Schlegel et al. (1998). However it is possible to determine reddenings from available data by developing a suitable Schuster & Nissen - type calibration. The indices involved in the Schuster & Nissen calibration are mostly measures of the following quantities: slope of the Paschen continuum (b-y), metallicity (m1), Balmer jump (c1), H$\beta$ ($\beta$). Johnson photometry provides the slope of the Paschen continuum (B-V) and the Balmer jump (U-B), the line index KP defined in Beers et al. (1999) is sensitive to metallicity, while the index HP2 is a pseudo-equivalent-width of H$\delta$. It is therefore reasonable to expect that a Schuster & Nissen - type calibration, involving (B-V), (U-B), HP2 and KP may be derived. In the following we show that this is indeed the case and that reddening may be derived from it with an accuracy comparable to that of the Schuster & Nissen calibration.