6 Rotation and metallicity

The rotational velocity of the primary deduced from the standard calibration of the width of the correlation dip measured with CORAVEL (Benz & Mayor 1984), is

$$v\sin i = 38.1 \pm 2.2\ \rm km\,s^{-1}$$ (5)

which is slightly faster than the synchronous rotation value, since with a radius $R=1.70\ R_\odot$ (see Sect. 6), the expected equatorial velocity of the primary is 33.0 kms^-1. It is not exceptional for Algol gainers to rotate faster than synchronously as shown by Koch et al. (1965). However, the difference being only $2.3 \sigma$, we cannot firmly conclude that a departure from synchronism exists in TZ Eri. On the other hand, $v\sin i$may be overestimated, due to several factors. First, the rotational velocity is so large that we hardly reach the continuum of the correlation function, which can bias the fit. Second, the profile is fitted by a Gaussian, while the rotational profile itself does not have this shape, even if it is convoluted by a Gaussian instrumental profile (the calibration was intended for slow rotators, with $v\sin i$ generally slower than $\sim$20 km s^-1). Third, the calibration has been devised above all for cool, solar-type stars (although it does include a temperature term) and we apply it to a late A star, i.e. at the very border of its validity. Fourth, the $v\sin i$ determination is based on the hypothesis of a solar-type macroturbulence; this is probably not valid in a semi-detached short period system and, thus the value given in (5) could be an overestimate.

We did not attempt to derive the projected rotational velocity of the secondary component by using the correlation dip obtained with the NTT spectrum, because a new calibration would have been needed which is beyond the scope of this paper, and the correlation dip of the secondary is in any case very shallow.

It is interesting to notice that the "surface'' or equivalent width of the CORAVEL autocorrelation dip of the primary is the same as for single late-A stars. We have $W=2.31\pm 0.14$ kms^-1, while HD 2628, type A7III and $\rm [Fe/H]=-0.02$, has W=2.41 and HD 110379, type F0V and $\rm [Fe/H]=-0.07$, has W=2.49. This implies that the metallicity of TZ Eri is close to the solar value, in agreement with the result obtained in Sect. 4 on the basis of the photometric analysis.