4 Hipparcos photometry and ellipticity effect

The Hipparcos spacecraft has observed HR 7428 from December 1989 till March 1993.

The Hipparcos $H{_{\rm p}}$ photometric system is characterised by a response curve including B and V band and therefore not immediately comparable to classical UBV photometry.

Figure 6: Top: Hipparcos' magnitudes of HR 7428 through the period between 1989 and 1993, where the dashed line is the light curve solution accounting for the proximity effects. Bottom: Difference between Hipparcos magnitudes and the synthetic light curve.

The photometric data are shown in Fig. 6, where $H{_{\rm p}}$ magnitudes are plotted versus orbital phase computed with our new ephemeris. Notwithstanding the scatter of points, a photometric double wave appears well defined, with two maxima nearly at the quadratures and two minima nearly at the conjunctions. However, the behaviour is clearly asymmetric, the first maximum being brighter, with a peak at about phase 0.2. This behaviour is very similar to that observed by Strassmeier et al. (1989) from 1983 to 1984. These asymmetries were supposed to be connected to rotational modulation of starspots unevenly distributed on the surface of the K primary star. In a detailed study Hall et al. (1990a) show that the starspot wave, detected after removal of the variability produced by the ellipticity effect, is not permanent, and sometimes two different waves are simultaneously present.

To better define the starspot wave, we have calculated the light curve, dominated by the ellipticity effect, in absence of starspots, using the system parameters we derived in the previous sections.

Assuming a system inclination of 67 $\hbox{$^\circ$ }$, we found a full amplitude of about 0 $\hbox{$.\!\!^{\rm m}$ }$02, that is a bit smaller than the 0 $\hbox{$.\!\!^{\rm m}$ }$033 value found by Hall et al. (1990a), and than the 0 $\hbox{$.\!\!^{\rm m}$ }$04 value found by Strassmeier et al. (1989). A better agreement can be found with a higher inclination (near the maximum value of 75 $\hbox{$^\circ$ }$) and a larger radius of the cool star (46 $R{_\odot }$) or with the minimum system separation allowed by the errors in $a_{\rm h}\sin ^3i$.

The residual asymmetry that appears in the difference between Hipparcos data and the ellipticity light curve solution may result from the presence of starspots, as suggested by Hall et al. (1990a).