Comparing our observations with previous light curves of BH Vir, we can easily see that only a small
decrease in the system brightness occurred around phase 0.65 where the systematic deviations by 0.023 mag
(V) and 0.022 mag (B) are slightly greater than the intrinsic errors in 1991 although the light curves
of the system in 1991 have the missing phases in the beginning of the secondary minimum. The basic
astronomical and physical properties of BH Vir were summarized by Zeilik et al. (1990). The
spectral classification of Abt (1965) is in agreement with that of Koch (1967) as for
the secondary component (G2V) but there is a difference of about two sub-types in the case of the primary
(G0V vs. F8IV-V). From our observations we can determine that the colour index (B-V) of BH Vir during
primary eclipse is about
.
This value is in good agreement with the finding of Koch
(1967) and Scaltriti et al. (1985). Therefore we adopted a temperature for star
2 (star eclipsed at Min II) of 5500 K. The other adopted parameters were: gravity-darkening exponents,
g1,
g2 = 0.32, the bolometric albedo of two components, A1, A2= 0.5. The linear limb darkening
laws were used and the source of the values given by Al-Naimiy (1978). The reflection
effect was computed with the detailed model of Wilson (1990). As the spectroscopic mass ratio
was found to be
q=m2 / m1 = 1.02 by Abt (1965), and q=0.968 by Zhai et al.
(1990), we assumed a series of q values (0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2) to find the
preliminary photometry mass ratio with the grid method. The adjustable parameters employed were: the
orbitral inclination (i), the dimensionless potentials of star 1 and star 2, (
and
),
the mean temperature of star 1 (T1), and the monochromatic luminosity of star 1 (L1). The relative
brightness of the secondary star was calculated by the blackbody radiation model.
Because BH Vir seems to be leaving the Main Sequence (see Zhai et al. 1990), the components are
reasonably detached their Roche Lobes. It is very important for us to estimate the critical ages for
circularization and synchronization for BH Vir. From Zhai et al. (1990) results the absolute
parameters of BH Vir are
,
,
,
,
.
Using the time scales given by Claret & Cunha
(1997), we have found the critical ages for circularization and synchronization for BH Vir
that
yr,
yr,
yr and
yr. According to stellar evolutionary theory, we have
estimated that the system is older than
yr. These results reveal that both components are
essentially Main-Sequence stars, and they should be synchronized.
Firstly, a convergence test for the solution was carried out using a normal Roche model without spots. The
(O-C)i)2-q curve is shown in Fig. 1, where
(O-C)i)2 is the sum of weighted squares of residuals between the theoretical light curve and
the observations. A minimum of
(O-C)i)2 is achieved at q=1.0. At this
point, we adopted a dark, circular spot model for the active regions on the primary star and expanded the
adjustable parameters to include q. The mass ratio converged to q=0.967 in the final solution, which
is in very good agreement with the spectroscopic and photometric value determined by Zhai et al.
(1990). Figure 2 shows the O-C residuals.
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Figure 3: Light curves of BH Vir in 1991. Open circles represent the observations. Solid lines are theoretical light curves calculated from the parameters in Tables 2 and 3 |
Date | 1963/64 | 1991 |
L1/ (L1 + L2) (V) |
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L1/ (L1 + L2) (B) |
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X1 (V) | 0.64 | 0.64 |
X1 (B) | 0.77 | 0.77 |
X2 (V) | 0.66 | 0.66 |
X2 (B) | 0.81 | 0.81 |
i |
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g1 | 0.32 | 0.32 |
g2 | 0.32 | 0.32 |
q |
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A1 | 0.5 | 0.5 |
A2 | 0.5 | 0.5 |
T1 (K) |
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T2 (K) | 5500 | 5500 |
r1 (pole) |
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r1 (point) |
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r1 (side) |
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r1 (back) |
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r2 (pole) |
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r2 (point) |
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r2 (side) |
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r2 (back) |
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Data | star | latitude | longitude | ang.radius |
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1963/1964: | 1 |
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0.71 | 2.5% |
1 |
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0.72 | 2.3% | |
2 |
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0.71 | 7.6% | |
1991: | 2 |
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0.650 | 2.4% |
Notes: ph = photosphere; hem = hemisphere.
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