3 Photometric data and variability of the components

Geneva 7-colour photometric measurements of TZ Eridani were obtained from Dec. 10, 1983 to Dec. 10, 1996, using the Swiss 70 cm telescope at the European Southern Observatory (ESO), La Silla, Chile. During this period, 429 measurements of weight $q \geq 1$ have been obtained (see Rufener 1988, for the definition of the weight q). These data are listed in Table 1, including the 36 additional photometric measurements obtained in Nov.-Dec. 1996 (see Sect. 2).

The magnitudes in each of the seven filters are obtained from the visual magnitude V and the six colour indices in the following manner:

i = V - [V - B] + [i - B]

with i representing one of the seven filters U, B, V, B₁, B₂, V₁, G. Remember that the Geneva [U - B] and [B - V] indices are not normalized to zero for an A0V star as it is the case for the Johnson UBV indices. It is possible to calculate the magnitude of the primary (mass gainer) by subtracting the flux of the secondary (mass loser), at the bottom of the primary eclipse, from the flux of the both components measured together (outside the eclipses). This calculation has been made for each of the seven Geneva magnitudes. In order to minimize the effects of a possible long-term variability (see the end of this section), only the data obtained in December 1983 and January 1984 have been used. The results are given in Table 2.

It is interesting to compare the observed uncertainties with the mean precision of the measurements made in Geneva photometry. Rufener (1988, Fig. 2) has shown the shape of the mean relation $\sigma_{V}$ vs. V obtained for the non-variable stars, in particular the progressive increase of $\sigma_{V}$with increasing V, for stars fainter than $V \simeq 9$. The same relation can be applied to the seven Geneva magnitudes. Figure 2 of this paper shows a new calculation of this relation, based on the up to date version of our photometric database. On the same figure are plotted the observed values for TZ Eri given in Table 2. A correction has been applied to the uncertainties of the magnitudes for the secondary, because the measurements obtained during the totality of the primary eclipse had shorter integration time than the other ones (4 minutes instead of 12 minutes). The conclusion is that the uncertainties on the measurements of TZ Eri are in agreement with the expected precision. Thus, the components do not exhibit a short-term variability, i.e on a time-scale shorter than about 20 orbital periods.

  

Table 2: The seven Geneva apparent magnitudes of TZ Eri (measures of December 1983 and January 1984)

  

Figure 2: Variation of the mean precision $\sigma$ with the magnitude, in the case of Geneva photometric measurements. The solid thick line refers to the mean value and the solid thin lines to the 1 s.d. level. Dots and small squares concern respectively the seven magnitudes of TZ Eri A+B outside eclipses and of the secondary (during the totality of the primary eclipse). Big squares represent the estimated values of $\sigma$ for the secondary which ought to have resulted from a "normal'' integration time of the measurements, i.e. 12 minutes (normal) instead of 4 minutes (during the primary eclipse)

The long-term photometric behaviour of both components has been analysed by comparing our photometric data obtained at 4 epochs, corresponding to the intensive monitoring of the eclipses: Dec. 1983 to Jan. 1984, Jan. 1985, Nov. 1987 and Nov.-Dec. 1996. Table 3 gives the mean values of V, [B-V] and [U-B] at each of these epochs for the both components. It appears that:

1.

The secondary exhibited a long-term luminosity increase (0.06 in V) between Dec. 1983 and Dec. 1996. The colour variations are large, especially in [U-B], but not significant due to the large standard deviation.

2.

The primary did not show any long-term variation in magnitude or in colours.

The observed variations of TZ Eri secondary are similar to those studied by Olson & Etzel (1993) in six cool subgiant secondaries of totally eclipsing Algol systems. They noted that the fluctuations increase with decreasing orbital period, or with increasing rotational velocity, suggesting that rotationally induced magnetic activity could be the origin of these brightness variations.

In order to minimize the effects of the long-term variation of the secondary luminosity, only the data obtained before HJD 2447200 (Feb. 1988) have been used for the eclipse analysis (see Sect. 6).

  

Table 3: Long-term behaviour of the components of TZ Eri in V magnitude and Geneva colours [B-V] and [U-B]. Only the variation of the secondary in V is significant