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