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5. Discussion

(1) In our photometric analysis, HL Aur is found to be a near-contact binary system. The primary component is in contact or almost in contact with its Roche lobe and the secondary is inside but very close to its Roche lobe. The values of the filling factor of Roche lobe tex2html_wrap_inline1303 and tex2html_wrap_inline1305 are derived to be 0.9970 and 0.9442 from solution 1, and 1.00 and 0.9483 from solution 2, respectively.

(2) The surface temperature difference between the two components is computed to be about tex2html_wrap_inline1307 and the temperature of the secondary is derived as tex2html_wrap_inline1309, corresponding to a spectral type of G3-4 (de Jager & Nieuwenhuijzen 1987).

(3) Knowing the period, relative radii,and mass ratio we obtain the mean density of the two components as tex2html_wrap_inline1311 and tex2html_wrap_inline1313 (see Table 7 (click here)) via the formula of Mochnacki (1981). For zero-age main sequence stars with spectral types F4 and G4, the average density should be about 1.1 and 1.6, and for terminal-age main sequence stars with the same spectral types it should be 0.45 and 0.65, respectively. Therefore, the two components are approximately the same value as the terminal-age main sequence stars of the same spectral types, respectively. It means that the two components are slightly evolved and located near the terminal-age main sequence.

Table 7: The mean density of the component stars and relative parameters of HL Aur

(4) According to the statistical study by Zhai et al. (1989) the ratio of mean density for the two components is close to unity in near-contact binary systems, this is in marked contrast with the classical Algol systems for which the density ratio of the two components are usually near a value of tex2html_wrap_inline1327 0.30. The above-obtained density ratio between the two components of HL Aur is consistent with the general evolutionary picture for near-contact binary systems (Zhai et al. 1989).

(5) From our photometry the luminosity of the primary component makes some 4/5 of the total output of the system. Differential magnitude measurements between the comparison and standard stars give a colour index B-V of HL Aur as 0.42 during the maximum. If we consider that the coordinates of this system are close to the Galactic equator, and the de-reddened B-V value is smaller than 0.42, then, from the density -colour diagram for near-contact semi-detached binaries with spectral types A-F (Zhai et al. 1989; Mochnacki 1981) we see that the primary component of this system is most likely located near the terminal age main sequence.

From the criteria described above we may conclude that the system is a near-contact binary with the primary component just filling or close to its Roche lobe and the secondary near its Roche lobe, but from the O-C diagram of the times of minimum rapid mass transfer does not appear to have occurred in this system. According to the criteria given by Shaw (1990, 1994) the secondary component could be more evolved than the primary, but in our view the components of HL Aur seem to be in nearly the same evolutionary stage. Because the mass transfer has just started , the mass transferred from the primary to the secondary component is apparently not sufficient to speed up the evolutionary process of the secdonary, which appears still to be located near the terminal-age main sequence.

The criterion needs further study and test by future photometric and spectroscopic observations.


This research has been supported by the Major National Scientific Projects and the Astronomical Council of the Chinese Academy of Sciences. The authors would like to thank Dr. L.Z. Shen for helpful discussions. Thanks are also given to the United Laboratory for Optical Astronomy, China for providing the necessary observing time at the telescope.

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