Photometric solutions were obtained by means of the WD program which includes a new reflection treatment, the option of using non-linear limb-darkening laws and the ability to adjust spot parameters. All the observations were used in computing the solutions. The convergence of the minimization procedure was obtained by means of the method of multiple subsets (Wilson & Biermann 1976).
parameters | 1962's obs. | 1982's obs. | 1999's obs. | ||
color | V | B | V | B | V |
L1/(L1+L2) | 0.8621
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0.8637
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0.8636
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0.8616
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0.8648
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x1=x2 | 0.640 | 0.780 | 0.640 | 0.780 | 0.640 |
q=m2/m1 | 0.1306
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0.1273
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0.12889
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||
i | 86.60
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87.12
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86.78
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||
A1=A2 | 0.500 | 0.500 | 0.500 | ||
g1=g2 | 0.320 | 0.320 | 0.320 | ||
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1.9908
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1.9834
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1.9821
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||
f | 0.69 | 0.72 | 0.74 | ||
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0.005321 | 0.004657 | 0.003768 |
component | 1 | 2 | 1 | 2 | 1 | 2 |
T(K) | 5900 | 5836 ![]() |
5900 | 5811 ![]() |
5900 | 5852 ![]() |
r(pole) | 0.5277
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0.2182
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0.5335
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0.2217
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0.5380
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0.2179
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r(side) | 0.5872
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0.2286
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0.5963
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0.2332
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0.6031
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0.2293
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r(back) | 0.6100
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0.2762
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0.6202
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0.2914
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0.6265
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0.2893
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The adopted parameters in the solutions are described as follows: a temperature of
5900 K for Star 1 (the star eclipsed at Min.I), Claret et al.'s (1990) values of
the limb darkening coefficient (
x1=x2=0.640), Lucy's (1967) values of the
gravity darkening coefficients (
g1=g2=0.320) and Rucinski's (1969) values
of the albedo (
A1=A2=0.500), which corresponds to the spectral type
of G0 for FG Hya. The adjustable parameters were the orbital inclination, i, the
mean temperature of Star 2, T2, the potential of the components,
and
,
and the monochromatic luminosity of Star 1, L1(the Planck function was used in computing the luminosity).
Solutions were made for a series of fixed values of the mass ratio q=m2/m1(0.10, 0.15, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.50, 2.00,
2.50, 3.00, 4.00, 5.00 and 6.00). Assuming that initially it was a detached system,
the differential corrections started from mode 2, but the converged
solutions were always obtained at the contact mode 3. The resulting sum
of the square deviations of the converged solutions for each value
of q indicates that the fitting is best for q=0.15. At this point, the set of the
adjustable parameters was expanded to include q. The mass ratio converged to a
value of q=0.1289 in the final solution. This solution indicates that FG Hya is an A-type W UMa binary, in agreement with the results published by
Mochnacki & Doughty (1972), Twigg (1979), Lafta & Grainger (1986),
Jabbar et al. (1986) and Yang et al. (1991). The photometric parameters are
listed in Table 5, where Star 1 indicates a more massive component and Star 2
is one of less mass. The computed light curve by using the parameters in Table 5
is shown as the solid line in Fig. 3. As shown in Fig. 3, the fit between
the theoretical light curve and the observations is very good.
In order to compare the present solution with the previous ones, the light curves in B and V bands obtained by Binnendijk (1963) in 1961-62 and Yang et al. (1991) in 1982 were also re-analyzed in the same way. The results are also listed in Table 5, from which one can see that the solutions obtained from different observations are in agreement with each other despite the considerable change in the shape of the light curves.
We tried also to analyze the light curves obtained by Mahdy et al. (1985),
but a reasonable solution could not be found. In the course of finding a solution
by means of the DC program of the WD code, we found all obtained converged
solutions difficult to interpret. The solutions
indicated either orbital inclinations that were too small or mass ratios
substantially larger than the spectroscopically determined one. When spot
models were attempted, the solutions indicated that FG Hya would have to be
classified as a W-type system. It is possible that FG Hya is an example
of a small mass ratio binary that fluctuates between the A- and W-type
configuration, depending upon its current state of spot coverage. This
is certainly not without precedence, as the similar system V677 Cen
(Kilmartin et al. 1987) was found to possess equal temperatures for
both components, i.e., on the boundary between A-type and W-type. Other
W UMa binaries (e.g., TZ Boo, VW Cep) have displayed significantly changing
depths of eclipses such that the normally less deep secondary eclipse was
sometimes deeper than the primary one. Therefore we abandoned our attempt
to find a final solution
from Mahdy et al.'s observations. We suspect that either their observations
are in question or the distortion of the light curves is so much because of
the substantial spot that it is difficult to find a true solution.
Copyright The European Southern Observatory (ESO)