## 5. Fundamental parameters for the binary and its componentsSince the two maxima in the light curve of TV Pic are not the same, we cannot derive the physical elements (radii and masses) of the component stars in the classical way. One solution is to construct a specific model for the light curve by including a spot on one or both stars. It is therefore instructive to investigate first the constraints placed on that model by the observations, before additional degrees of freedom are introduced. The fact that the spectra were not taken exactly at quadrature
implies that the velocity semi-amplitudes and
are slightly larger than the observed velocity
differences. We assume a sinusoidal velocity curve, and apply a
correction of 1.01; hence, we estimate
km s where where is the radius of a sphere with the
same volume as the primary Roche lobe, and In view of the large light amplitude due to ellipticity and of the
absence of deep eclipses, it follows, conservatively, that
. This is because the ellipticity of the system
cannot cause a sufficiently large light amplitude at smaller
inclinations, while the (grazing) eclipse of the primary becomes much
to deep for inclinations exceeding the upper limit given above.
Moreover, the width of the shoulders of the light curve shows that the
primary must be nearly filling its Roche lobe; a 5% smaller radius
produces unacceptably broad shoulders. These bounds to the inclination
also set bounds to the separation and on their masses (Table 3). If the period is given in days and the mass in solar masses, this formula will yield the separation in solar radii. Even before carrying out a more precise determination of the inclination by detailed light curve modelling, we are finding that the masses of the stars are too small for (near-) main-sequence stars of the inferred spectral types. If we anticipate the inclination of - derived in Sect. 6.2, we deduce a dynamical estimate of for the primary - between the spectroscopic and the photometric estimates - and for the secondary; the value of 3.5 obtained spectroscopically for the latter is very uncertain.
When a star fills its Roche lobe, synchronous rotation requires If the star is smaller, the right-hand side of this equation gives
an upper limit to the required apparent rotational velocity. We thus
derive km s If we assume that the primary fills its Roche lobe and is rotating
synchronously, then from the above equation we obtain the slightly
smaller mass ratio © European Southern Observatory (ESO) 1998 Online publication: February 16, 1998 |