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4. The rotation parameters

 

4.1. The rotation period

 

Strassmeier et al. (1993) list a rotation period for tex2html_wrap_inline2121 Gem of tex2html_wrap_inline2123 days. Henry et al. (1995) analyse long-term photometric data and interpret them in a two-spot model. They obtain for each spot a different period, most of them shorter than the orbital period, which is interpreted by them as differential rotation. They give a rotation period of the star tex2html_wrap_inline2125 days. Jetsu (1996) analysed the same data as Henry et al. (1995). He finds that the data of tex2html_wrap_inline2127 Gem's light minima indicate the presence of active longitudes, which means a unique period. His period is tex2html_wrap_inline2129 days. This period is identical (within the quite large errors) with the orbital period given in Eq. (5 (click here)). It thus seems that tex2html_wrap_inline2131 Gem's rotation is in fact synchronized with its orbit; this is consistent also with the finding above, that the orbit is circular. We adopt in the following tex2html_wrap_inline2133.

4.2. The rotation velocity

 

 figure445
Figure 3:   Power spectrum of tex2html_wrap2171 from the mean spectrum 1993-95, compared to that of a pure rotation profile computed with a linear limb-darkening of tex2html_wrap_inline2135. tex2html_wrap_inline2137 for the model profile is 27.1tex2html_wrap2173

For the projected rotational velocity tex2html_wrap_inline2141, Eaton (1990) gives 27tex2html_wrap2175, a value used by Hatzes (1993) and Henry et al. (1995). Strassmeier et al. (1993) give v sin i = 25tex2html_wrap2177 and remark that this value is better than the one given by Eaton.

Since tex2html_wrap_inline2151 is a very important observable concerning the constraints to be derived in the next section and a sensitive input parameter for the forthcoming surface imaging, a redetermination seems to be necessary. For this, we use the Fourier transform of the SOFIN spectra (see e.g. Unsöld 1955; Gray 1988, p. 2-1ff).

A mean spectrum is created from all 29 SOFIN spectra. For this, each spectrum has been shifted to tex2html_wrap_inline2153 using the orbital parameters of Solution 4 in Table 3 (click here). In order to minimize distortions due to noise and occasional spot features, a tex2html_wrap_inline2155-clipping has been done (in 3 iterations remove for each wavelength those points that are deviating more than tex2html_wrap_inline2157 times the standard deviation from the mean). The power-spectrum obtained from the whole wavelength range is dominated by the minima and maxima caused by the many blended lines. Only the features, whose main components are tex2html_wrap2179 and tex2html_wrap2181, are sufficiently unblended to be used.

Figure 3 (click here) shows the power-spectrum obtained from Fe I 6173 Å. It is compared to that of a pure rotational profile computed with a linear limb-darkening coefficient tex2html_wrap_inline2159 (obtained by interpolating to tex2html_wrap_inline2161K, logg=2.5, tex2html_wrap_inline2165Å in the tables given by Al-Naimiy 1978). It is obvious, that the second minimum is already heavily distorted by blending effects, so only the first minimum can be used (the same is true for tex2html_wrap2183). The mean projected rotational velocity determined from the two lines is
 equation464
This is consistent with the value given by Eaton (1990) and will be used in what follows.


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