Astron. Astrophys. 345, 156-162 (1999)

6. The global shift

We will call "global shift" GS , the combined effect of diffusion and calibration. Its component in effective temperature is given in Table 2 and 3 for the 10 Gy models. Fig. 6 shows, as a function of mass, the variations of effective temperature for the three different metal content considered here.

Both diffusion and calibration reduce the effective temperature, but in an opposite way with respect to [Fe/H]. The effect of diffusion increases while the effect of calibration decreases with [Fe/H].

In luminosity the situation is different. The calibration procedure compensates partly the luminosity increase due to diffusion. The variation can reach 0.03 dex, depending both on mass and [Fe/H]. The mass dependence remains strong, from 0.06 dex at 0.85, to 0.01 dex at 0.6. It produces a distortion in the Mass-Luminosity relation, see Fig. 7, depending on [Fe/H], an effect which could be detected with high quality data on a reasonable set of objects.

The displacement in the HR diagram is seen as a translation towards lower effective temperatures, see Fig. 4. It produces a slight variation of the curvature of the evolutionary track, see Fig. 5, due to the time dependence of the process. Isochrones are then slightly more vertical.

Fig. 4. The main-sequence evolutionary tracks of models, evolved without diffusion (dashed) and calibrated (full). The solar bolometric magnitude is taken as .

Fig. 5. Schematic isochrones at 10 Gy for models with , -0.94, -1.24 and -1.72; dashed: model without diffusion, full: calibrated models with diffusion. : locations of stars with observed [Fe/H] within as derived from Hipparcos data.

Fig. 6. Total variation of effective temperature at 10 Gy between standard and calibrated models with respect to the mass. At evolutionary effects become significant.

Fig. 7. Mass-luminosity diagram at 10 Gy for standard (thin) and calibrated (thick) models.

Stars with observed [Fe/H] within and the most accurate fundamental parameters, studied by Lebreton et al. (1997) have been added to Fig. 5. As already said, though microscopic diffusion tends to reduce the discrepancy between the effective temperature of observed and theoretical models, the effect is not sufficient to solve the difficulty.

For , Fig. 8 shows, as a function of luminosity and effective temperature, the effective temperature difference between two isochrones at the same luminosity: the standard one experiences no diffusion and its initial abundances are equal to the observed ones, while the second one is computed using our proposed calibration.

Fig. 8. Temperature difference between two isochrones at the same luminosity as a function of luminosity, respectively for 10 Gy (full) and 8 Gy (dahed), with - wigles are due to the interpolation procedure.

© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999
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