1 Introduction

The calibration of the scale of effective temperatures of stars (i.e. relations which link $T_{{\rm eff}}$, [Fe/H] and explicitly or implicitly log(g) with observable features such as photometric colours and indices or spectral features) is a necessary tool in many astrophysical fields for interpreting observations or relating them with theory. Affected topics range from stellar physics to cosmology. Four general areas can be readily mentioned:

The interpretation of the observed HR diagram (e.g., V: B-V) in terms of theoretical isochrones ( $L{:}\ T_{{\rm eff}}$); In this case, the morphology of red giant branch and lower main sequence is appreciably altered by changes of $\sim 100-200$ K in the effective temperature-colour calibration adopted (e.g. Bell 1992; Cassisi et al. 1999).

Another important area affected by $T_{{\rm eff}}$ calibrations is the determination of chemical abundances from spectroscopic analysis. As a rather conspicuous example of "cosmological'' consequences, an erroneous temperature scale for dwarfs could lead to incorrect conclusions regarding the primordial lithium abundance (e.g. Spite et al. 1998; Bonifacio & Molaro 1997 versus Ryan et al. 1996). Regarding giants, the influence of temperature on the strength of molecular bands in cool stars is well known and it is equally important for the determination of neutral element abundances; temperature indicators independent of metallicity and only weakly influenced by interstellar reddening are therefore needed (e.g. Sneden et al. 1992).

The analysis of the physics of stellar atmosphere models also requires the use of empirical temperatures to avoid the risk of a vicious circle (e.g., Bell & Gustaffson 1989).

Finally, in the synthesis of stellar populations, the use of colours and spectral atlases requires an accurate determination of atmospheric parameters and of the effective temperature in particular (e.g. Vazdekis et al. 1996). As a consequence the calibration of $T_{{\rm eff}}$ with colour and metallicity is also relevant in these types of (extra)galactic studies.

In conclusion, analyses in several astrophysical fields require now stringent internal accuracies of the effective temperatures, typically of the order of 1%.

The calibration of the temperature scale of giant stars of Population I with semi-empirical approaches has been addressed in several works (e.g. Ridgway et al. 1980), however the extension to Population II has been only fully and homogeneously accomplished by means of theoretical methods (e.g. Bessell et al. 1998). The calibrations we present here cover temperature and metallicity in the ranges: 3500 K $\leq T_{{\rm eff}} \leq$ 8000 K; -3.0 $\leq [{\rm Fe/H}] \leq +0.5$. Therefore, the present study extends previous semi-empirical works towards the metal-poor domain providing calibrations with a smaller dependence on atmosphere models.

This work is part of a long term programme aimed at a complete and uniform revision of the $T_{{\rm eff}}$ scale of the different regions of the HR diagram. It is based on temperatures derived with the InfraRed Flux Method (IRFM, Blackwell et al. 1990), scaled to direct $T_{{\rm eff}}$, and on good quality photoelectric photometry. The subprogramme concerning giant stars in which the present work is included has been extensively explained in (Alonso et al. 1999; Paper II).