2 Period

The orbital period listed in the GCVS (Kholopov 1985) is P = 2.6060653 days. However, we are dealing here with a semi-detached system which, by definition, has a variable period due to mass transfer. During most photometric observations done in 1984-1987 by Dr. Zdenek Kviz, the period remained fairly constant, since it was possible to obtain a well-defined lightcurve with P=2.6061082 days. This value was obtained using the reciprocal $\theta_1$ test of Renson (1978) - see also Manfroid et al. (1991) - which had been defined above all for Ap stars (which vary with small amplitudes) but proved very efficient for a precise determination of the period of eclipsing binaries. The ephemeris we have adopted is:

$$\begin{eqnarray} \mbox{HJD}(\mbox{Min I})& = & ~~~(2\,446\,109.6922 ~~ \pm {\it ... ...\ & & + (2.6061082 ~~ \pm {\it 0.0000020}) \times E. \nonumber\end{eqnarray}$$ (1)

The orbital period has varied, as shown by the times of minima registered over decades by amateur astronomers. The O-C values so obtained, and published in the BSAG Bulletin (e.g. Locher 1997) are shown in Fig. 1 together with a parabolic fit which gives:

$$\begin{eqnarray} {\rm O-C} & = & - (0.0050 ~~ \pm {\it 0.0014}) \\ & & - (1.0... ...& + (2.433 \pm {\it 0.143} \ 10^{-9} (\mbox{HJD}-t_0)^2 \nonumber \end{eqnarray}$$ (2)

where t₀ = 2446109.6922 . The typical error on the epochs of primary minima in Fig. 1 is a few minutes (0.002 - 0.005 d). Therefore the fit only represents a mean trend, upon which are superposed sudden period changes that cannot be accounted for by measurement errors (see especially the very steep rise just before JD 2450000).

  

Figure 1: O-C diagram of TZ Eri from observations made by amateurs and published in the BSAG Bulletin (two points are defined by Geneva photometry). A parabolic fit is superposed, showing the regular increase in the period. Short arrows define the intervals of photometric measurements; long arrows define the interval of radial-velocity observations

Although the period changes are interesting by themselves, they are rather a nuisance in our context, because the radial-velocity measurements, which were made recently, have to be put in phase with the photometric ones, which are much older. For this reason we have not used the above formula for O-C, but we have simply used additional photometric measurements kindly made by Marc Künzli in November 1996 with the same equipment. He has made 36 new multicolour measurements, several of which during the primary minimum. Using the code EBOP16 (Etzel 1989) and the adopted ephemeris, we adjusted the $\Delta\theta$ parameter (phase correction for the position of the primary minimum) for these recent data, as well as for the old data alone. The difference is:

$$\Delta\phi = -0.01734\pm 0.00020$$ (3)

and represents the phase correction to be applied to the 1996 data, to fit them into the adopted ephemeris. Although the $V\rm _r$ observations have been made one year earlier than the new photometric ones, we neglect the slight period change that may have occurred in between, compared to the change that has taken place between the old photometric measurements and the $V\rm _r$ ones. Therefore, the above phase shift was applied as such to the $V\rm _r$ data.