6 D₄₀₀₀ measurements

Table 1 lists the final D₄₀₀₀ measurements and the associated random errors. Some sample spectra, exhibiting a diversity in spectral types, metallicities and gravities, are displayed in Fig. 3, whereas in Fig. 4 we show the break behaviour with effective temperature for the whole sample. It is clear from these plots that temperature is the main parameter governing D₄₀₀₀. The effect of metallicity is clearly noticeable in panel 3(b) and by the position of globular cluster stars in Fig. 4. Also, some gravity dependences are also observed, especially between hot dwarf-giants and supergiants, and between cold dwarfs and giants.

The definition of the D₄₀₀₀ given in Eq. (1) resembles that of a color. However, the peculiar combination of $\nu$ and $\lambda$ translates into the introduction of a wavelength weighting of the flux (Eq. 3). In order to facilitate the computation of the break, we have studied the effect of a redefinition of the index, namely

 

$${B}_{4000} \equiv \frac{{\displaystyle \int_{4050\,(1+z)}^{... ...nt_{3750\,(1+z)}^{3950\,(1+z)}} f_\lambda \; {\rm d}\lambda}.$$ (9)

Comparing this and the previous definition of D₄₀₀₀ (Eq. 3) for all the stars in run 6, we find that no single star deviates more than a 1% from the theoretical predicted ratio

$$\left. \frac{{ D}_{4000}}{{ B}_{4000}} \right\vert _{f_{\lambda}={\rm cte}} = 1.1619,$$ (10)

obtained for a constant $f_\lambda$. Therefore the above ratio can be safely used to convert between both break definitions.

  

Figure 5: D4000 as a function of $\theta\equiv 5040/T_{\rm eff}$ for the sample, together with the derived fitting functions. Stars of different metallicities are shown with different symbol types, with sizes giving an indication of the surface gravity (in the sense that low-gravity stars, i.e. giants, are plotted with larger symbols). Concerning the fitting functions, in the low $\theta$ range, the solid line corresponds to dwarf and giant stars, whereas the dashed line is used for supergiants. For lower temperatures, thick and thin lines refer to giant and dwarf stars respectively. For each of these groups in the mid-temperature range, the different lines represent the metallicities ${\rm [Fe/H]}=+0.5,0, -0.5,-1,-1.5,-2$, from top to bottom