## 3. Analysis of the data## 3.1. Period search
The Hipparcos data (set C) represent the longest coverage, and
although they are seriously sampled, they offer the best impression of
the long-term stability of the mean level of brightness (Fig. 1).
It can be seen that the brightness changes are dominated by the
short-term variations, occurring on the time scale of several days.
The linear fit of the Hipparcos data spanning 915 days, displayed
in Fig. 1, sets the upper limit of 0.04 mag to a possible
secular trend. However, it is quite probable that the slope of the
fitting line is purely due to the sampling. The standard deviation of
this fit 0.05 mag is quite large and we will show that it is
caused by the orbital modulation. The
In the first step separate period searches were carried out for the
data sets A1, B, C using the PDM (Phase Dispersion Minimization)
program, based on the method of Stellingwerf (1978) and written by
Dr. J. Horn at the
Ondejov Observatory. This
program enables not only an automatic search for the best period
within a given interval, but also an interactive examination of the
resultant data foldings for the respective period lengths. The PDM
method evaluates the significance of the period by the parameter
which lies in the range 0-1. The
lower , the better defined period.
The period near 8.8 days was found in all three sets. The best
value always laid below 0.4,
suggesting a well defined period. The Hipparcos data can therefore be
interpreted as the constant long-term level of brightness with
variations due purely to the modulation with We found that the amplitude of the modulation slightly decreases
from the First, the folded data of set B were allowed to converge to
set A1 in SPEL. The systematic shift, determined this way, proved
to be only marginally sensitive to the exact value of the period
length. The refined period was determined again from the new set,
combined of A1 and the corrected B. In the next step the Hipparcos
data were included to the set A1+B and converged in SPEL again to
evaluate their shift. In the last step the sets A1, B and C were
solved simultaneously in PDM; the final period length of
8.8451741 days was determined this way. The significance
parameter still suggests a plausibly
defined period. The final values of the shifts of set B and
set C with respect to set A1 were determined to be
mag(
## 3.2. Character of the orbital modulationThe binary nature of V 1080 Tau was convincingly proven from spectroscopy by Martín (1993). This system comprises the main-sequence hot star and evolved cool star. The smooth modulation of brightness (Fig. 2), allows us to infer that the light variations may be caused by the proximity effects in the close binary. Only the reflection effect and ellipticity can play a role since no eclipses are apparent in Fig. 2. The folded light curve of V 1080 Tau displays a scatter which cannot be entirely attributed to the observational inaccuracies. For example the maxima of the light curve observed by B93a,b display unequal height for the respective cycles. As a result, it gives rise to enhanced scatter at some orbital phases of the folded data although this scatter is intrinsic. We will also show that there are some differences between set A1 and set B which are separated by a long gap. Due to the low amplitude of the variations these cycle-to-cycle changes smear the course of the modulation caused by the geometrical effects. Nevertheless, it is still instructive at least to constrain the role of the proximity effects in V 1080 Tau. The light curve can be still analyzed under some reasonable assumptions. The spectroscopic parameters (A3V primary and the evolved secondary of the type G to early K) put the basic constraints. The secondary, less luminous than the primary, is evolved off the main sequence while the primary is still a main-sequence star. This situation is typical for Algols which underwent mass transfer between the components. It can offer a natural explanation for the overluminosity of the secondary in V 1080 Tau. It also yields an additional constraint on the mass ratio because almost all Algols are observed in the phase after the mass ratio reversal. In order to further lower the number of parameters to be searched for, the fractional radius of the secondary can be set equal to the radius of its Roche lobe, as typical for Algols. We generated a set of synthetic orbital light curves for the
above-mentioned parameters using the code Further we examined the possibility that the modulation is
double-wave with the real orbital period
days (Fig. 2b) and
obtained much better agreement (Fig. 3). The system parameters
are summarized in Table 2. The three models brake the interval of
the possible temperatures of both components and also
The relation of the brightness variations in the red spectral
region, in which the cool secondary is prominent, and in the blue
region, where the hot primary dominates, can be emphasized by the
color index (Fig. 4). The
curve, folded according to
Eq. (1), displays a double-wave course with the minimum at phase
0.5 deeper than that at phase 0.0. The synthetic color indices,
corresponding to models 1, 2, 3, are superposed. It can readily
be seen that while model 1 and 2 give the same sense of the
color variations as the observed data (apart from the phases 0.4-0.6,
see below), model 3 is ruled out because it yields an opposite
sense. In conjunction with the residuals of the respective models,
mentioned above,
We note that the
Because the double-wave light curve (Figs. 2b and 3) does not
enable to resolve unambiguously the superior and the inferior
conjunction of the primary, an additional constraint is needed. Three
measurements of the radial velocities (RVs) of the cool secondary (88,
94 and -64 km s © European Southern Observatory (ESO) 2000 Online publication: August 17, 2000 |