Spectrum convolution

The average resolution power of ELODIE (42000) corresponds to a FWHM of 7.14 km.s^-1 for the line-width. The actual FWHM of spectral lines is the convolution of the intrinsic line-width by this instrumental line-width. It turns out that the resulting line-width varies from star to star, but is most of the time between 10 and 13 km.s^-1 for old F,G, and K stars. For a young star the FWHM can be much higher. The resulting resolution is measured by the FWHM of the cross-correlation function of the radial velocity determination ($2.35\sigma_{V_r}$, where $\sigma_{V_r}$ is the standard deviation of the cross-correlation function of the star given by the ELODIE reduction software). As the template mask used for the correlation has a large number of lines, the accuracy on the radial velocity is much smaller than $\sigma_{V_r}$.For the temperature range of our stars, $\sigma_{V_r}$is usually smaller than 5.5 km.s^-1. In this case, to compare spectra at the same resolution, all the spectra (target and reference stars) were convolved by a gaussian of standard deviation : $\sqrt{5.5^{2}-\sigma_{Vr}^{2}}$km.s^-1.

Unfortunately for some hot stars ($T_\mathrm{eff} \gt$ 6100 K), the $\sigma_{V_r}$ reaches values higher than 5.5 km.s^-1. In this case TGMET is performed with versions of the library degraded to lower resolutions.

  

Figure: Order 94 of HD 4306 ($T_\mathrm{eff}$ = 4975 K, $\log g$ = 2.01, [Fe/H] = -2.72, S/N = 89) before and after atmospheric lines removal. The circles are showing the wavelengths of the telluric lines as identified in the Rolland's table. The broad line at 656.28 nm is $H_{\alpha}$.