Based on the ephemeris (1), the observations of 1994 were combined into a single orbital cycle and the light curves of HL Aur in both V and B are shown in Fig. 2 (click here). The light curve of the system is essentially symmetric, although the average light level seems to be slightly brighter at phase 0.75 than at 0.25. The primary-ecilpse depth is 0.98 in V and 1.06 in B, the secondary-eclipse depth is 0.47 in V and 0.45 in B.
Figure 2: BV light curves and the synthetic light curves based on the
photometric solutions of HL Aur. The synthetic light curves are shown with
solid lines
In the following photometric analysis, the observations are further
combined into 59 normal points in V and 51 points in B, respectively.
The new, 1992 version of the Wilson-Devinney computing code
(Wilson & Devinney 1971; Wilson 1990) is
employed to perform the photometric solution of the B and V light curves
simultaneously. In the Roche model, from the calibration of the statistical
relations between stellar spectral/luminosity classes and effective
temperature (de Jager & Nieuwenhuijzen 1987)
the temperature of component 1 was fixed at 
,
corresponding to spectral type F4 (Götz & Wenzel 1961).
The gravity-darkening coefficients are adopted to be 
(Lucy
1967), and the bolometric albedo to be 
(Rucinski
1969) in accordance with the assumed stellar convective envelope.
From the tables in Al-Naimiy (1978) the limb-darkening
coefficients are taken to be 
, 
for the V band and
, 
for the B band. The adjustable parameters are: the
inclination i, the polar temperature of the secondary component 
, the
nondimensional surface potentials 
and 
, the luminosity
of the primary (component 1) star 
and the mass ratio 
.
Unfortunately, no photometric or spectroscopic information on the mass
ratio q is available. In search of an approximate mass ratio, we carried
out test solution by assuming mass ratio 
, 0.50, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 1.05, 1.45, 2.0, and
2.5.
The test solution for each assumed 
value started from the
detached model (mode 2), but after a few runs in the iteration, the system
converged into a semi-detached configuration with component 1 in contact
with the inner critical equipotential surface of the binary system. Then
computing mode 4 was used instead of mode 2 until a final convergent
solution was reached. Figure 3 (click here) represents the sum of the weighted
residuals, 
for each assumed mass ratio 
.
It is found that the mass ratio of the system is most likely somewhere around
q=0.75, at which the test solution gives the smallest residuals in the
diagram. With this probable mass ratio we started again and
let it be adjusted freely along with
other adjustable parameters. In the last few runs the parameters
, 
and 
in both V and B bands are also made
adjustable. However, 
, 
and 
seem to be not
adjustable and no convergent values could be found for them. The
final test converged into two slightly different solutions with nearly the same
parameters and the same 
value at q= 0.722 for HL Aur, depending
on the last mode (2 or 4) of the W-D program we used. Solution 1 indicates
that the system
is a detached binary with 
very close to 
while
solution 2 tells us that the system has a semi-detached configuration with the
primary in contact with its Roche lobe. The two solutions are set out in
Table 6 (click here). The theoretical light curves based on solution 2 is shown
in Fig. 2 (click here) and the configuration of the system is given in
Fig. 4 (click here). Almost the same theoretical light curve and configuration
as those in Figs. 2 (click here) and 4 (click here) could be found for HL Aur
based on solution 1. Figure 2 (click here) displays a good, full-orbit fitting
between the theoretical and observed light curves.
Table 6: Photometric solutions of HL Aur
Figure 3: The behaviour of 
as a function of the mass ratio q
Figure 4: The configuration of HL Aur