Strassmeier et al. (1993) list a rotation period for Gem
of
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
days. Jetsu (1996)
analysed the same data as Henry et al. (1995). He finds that the
data of
Gem's light minima indicate the presence of active
longitudes, which means a unique period. His period is
days. This period is identical (within the
quite large errors) with the orbital period given in Eq. (5 (click here)).
It thus seems that
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
.
Figure 3: Power spectrum of from
the mean spectrum 1993-95, compared to that of a pure rotation
profile computed with a linear limb-darkening of
.
for the model profile is 27.1
For the projected rotational velocity , Eaton (1990)
gives 27
, a value used by Hatzes (1993) and
Henry et al. (1995). Strassmeier et al. (1993) give
v sin i = 25
and remark that this value is better than the one given by
Eaton.
Since 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 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
-clipping has been done (in 3 iterations remove for each
wavelength those points that are deviating more than
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
and
, 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 (obtained
by interpolating to
K, logg=2.5,
Å 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
). The mean
projected rotational velocity determined from the two lines is
This is consistent with the value given by Eaton (1990) and will be used
in what follows.