4 H$_{\alpha}$ variations

The average spectrum of $\sigma$ Gemis shown in Fig. 2 which is obtained by adding together the 14 individual spectra after velocity shift corrections to the centers of H$_{\alpha}$,agreeing to $\pm$1 pixel. The center of H$_{\alpha}$ is located by fitting a Gaussian profile as illustrated in Fig. 2. Subtracting the average spectrum from the shifted, individual spectra yields the residual spectra as shown in Fig. 3. Arrows mark the centers of H$_{\alpha}$. As can be seen in Fig. 3, the residual H$_{\alpha}$ profiles show variations with phase. It is clearly in emission in scans 6 and 7 with phases around 0.25, which corresponds to the maximum of the light curves. At phases with more spots in view (scans 1, 2 and 13, 14), the residual H$_{\alpha}$ lines appear obviously in absorption.

  

Figure 3: Residual spectra obtained by abstracting the average spectrum from the individual spectra after velocity shift corrections. Phases are from Table 2. Arrows mark the centers of H$_{\alpha}$

Table 5 lists the values of the equivalent width (EW) and the central depth ($R_{\rm c}$) of H$_{\alpha}$ for each of the 14 individual spectra and the average spectrum of $\sigma$ Gem. These values are obtained by one Gaussian fitting. Figure 4 shows the variations of EW and $R_{\rm c}$ with phase according to Table 5. The dashed line represents the calculated V light curve. It is obvious that the equivalent width and central depth of the H$_{\alpha}$ profile show distinct anti-correlation with the light curve, (i.e., with the spot regions), though the spectroscopy covers only half of a period. The H$_{\alpha}$ equivalent width shows the smallest value at maximum brightness, and tends to increase with the appearance of spots. It agrees well with the result from the analysis of the residual H$_{\alpha}$ profiles above.

  

Figure 4: The anti-correlations of the H$_{\alpha}$ equivalent width (EW) and the central depth $R_{\rm c}$ with the distorted wave. The dotted line represents the V light curve of $\sigma$ Gem

In general, for a temperature insensitive spectral line, the appearance of spots cause changes in the shape of the line profile, but not in its equivalent width (Vogt & Penrod 1983). Thus, the variation of the H$_{\alpha}$ equivalent width in $\sigma$ Gem is probably due to chromospheric H$_{\alpha}$ emissions.

Many authors investigated the correlation between H$_{\alpha}$ core emission and spot regions in RS CVn-type stars, and got different results. Weiler (1978) found a marginal correlation between H$_{\alpha}$ emission and wave minimum for RS CVn, UX Ari and Z Her. A similar correlation holds for II Peg (Vogt 1981). In the Sun, the enhanced chromospheric emissions are from the plage regions visible in white light. If, according to the suggestion of Walter (1996), the solar analogy is valid, in case of $\sigma$ Gem there may be bright, spatially distinct plages where the enhanced H$_{\alpha}$ core emission comes from at the phase of maximum light.

 

Table 3: The variations of the H$_{\alpha}$ profile of $\sigma$ Gem

The average equivalent width of the H$_{\alpha}$ absorption profile is measured to be EW = 1042 mÅ with an average central depth of $R_{\rm c}=0.47$ for $\sigma$ Gem. Strassmeier et al. (1986) gave a value of EW = 972 mÅ  with $R_{\rm c}=0.51$ while Bopp et al. (1988) gave EW $\simeq 1100$ mÅ  and $R_{\rm c}\simeq 0.44$. The differences may be due to the variations of the active regions apart from the errors of measurements.