Atmospheric Transmission and Instrumental Response

As mentioned in Section 3.1.9, the correction for the effects of the atmospheric transmission and of the instrumental response in the observed spectrum of a target object, is achieved by ratioing this spectrum to that of a suitable standard star after dividing the latter by a black body with the appropriate temperature. Due to the possibility of time variability of the atmospheric transmission and also since looking at different airmasses implies a different atmospheric transmission, there is the need to try to match the observations of the object and standard stars in airmass and to make them close in time. A real problem that must be overcome is the choice of appropriate standard stars. Given that the aim of this observing run was to obtain high resolution spectra of hydrogen line profiles, one would, in principle, want to avoid stars with spectral types for which strong hydrogen lines are present, i.e. early type stars. To avoid this one could try to use later type stars instead of early type. However, the spectra of the former will contain even more line features than those of the latter, compromising the veiling measurements. Whatever the choice, the observed spectrum of the standard stars would have to be processed in order to remove the absorption lines before being used for the correcting the effects of the atmospheric transmission and of the instrumental response. The better option seemed then to be the early type stars, for which only the hydrogen line had to be removed rather than many lines as for the later type stars.

The absorption profile of hydrogen lines in stellar photospheres is expected to be the Voigt profile that results from the domination of Doppler broadening in the line core and of a damping profile on the line wings. To the line wings of the hydrogen lines there is also a very important contribution from the Stark broadening which leads to a line profile similar to that of radiation damping but with a larger damping coefficient. Also contributing to the line profiles is stellar rotation which distorts the profiles away from the Voigt function.

To remove the hydrogen absorption lines from the spectra of the observed standard stars a function consisting of the sum of a Gaussian (Doppler profile) and a Lorentzian (damping profile) was tried to be fitted to the observed profile. In practice it was quite difficult to obtain reasonably good fits in a such a way. In view of this, a different approach was taken that in practice gives much better results. Cubic spline interpolation of the data points was used to fit the absorption profile. Dividing the spectrum by the result of the interpolation eliminates the unwanted feature. The resulting spectrum contains the atmospheric transmission only and it is normalized to unity. Normalizing the spectrum of a standard in this way means that the information on the instrumental response is now also gone! Since this component is needed so that it can be removed from the observed spectrum of the object it must be restored. In order to do it the normalized atmospheric spectrum is then multiplied by another cubic spline fit. This time the fit is performed only making use of the data points at either end of the observed spectrum of the standard, away from the line to be removed. Using this procedure, one is assuming that the instrumental response across the wavelength range of the absorption feature is linear and the slope is determined by the fit. Looking at the spectra we acquired, one sees that this is a reasonable assumption for the wavelength region where the line to be removed lies. This procedure was implemented in IDL. A couple of examples are shown in Figure 3.4. There, the observed spectrum of the standard star is displayed with the spline fit used to eliminate the absorption feature and the final result of this procedure.

As one can see from Figure 3.4 the hydrogen line occupies most of the observed spectral range and defining the continuum is not an easy task. A larger spectral range, like that in the spectra taken during UT1295, is therefore desirable.

The standard stars with their hydrogen lines removed were used to correct for the atmospheric transmission and for the instrumental response.

Figure 3.5 shows the result of using the standards BS1459 and BS1392 to correct for the atmospheric transmission and instrumental response in the Pa Beta spectrum of GI Tau. One can see that the ratio of the two GI Tau spectra is, within the errors, equal to one.

Figures 3.4 and 3.5 are typical results and illustrate the results of this procedure. Similar results are obtained with other standard stars both at Pa Beta and Br Gamma.

The standard stars used for correction of the atmospheric transmission and instrumental response are listed in table 3.2.