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3. Photometric solution

Photometric solutions of DD Mon were obtained by using the 1992 version of the Wilson-Devinney program (Wilson 1992). The present observations were combined into 60 and 55 normal points in V and B, and the number of the individuals in each normal point was taken as the weight of each point. DD Mon is a single-lined spectroscopic binary (SB1) (Yamasaki et al. 1990), and so the spectroscopic orbit can not provide the mass ratio q directly. A search for a reliable mass ratio q via the photometric solution is very necessary. As the B observations at secondary minimum is slightly deficient, the single V light curve was employed in deriving the mass ratio q. According to the spectrum F5 of DD Mon (Yamasaki et al. 1990), we adopted the temperature of 6600 K for star 1 (star eclipsed at Min.I). The gravity-darkening g1=g2=0.32, the bolometric albedo A1=A2=0.5, and the limb-darkening coefficients x1=0.78,x2=0.84(B) and x1=0.60,x2=0.68(V) were assumed. The solutions for several assumed values of mass ratio q (q=0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) were obtained. The adjustable parameters were: the inclination i, the mean temperature of star 2, T2, the monochromatic luminosity of star 1, L1, and the dimensionless potentials of star 1 and star 2, tex2html_wrap_inline884 and tex2html_wrap_inline886.

   

q0.30.40.50.60.70.80.9
tex2html_wrap_inline8943.912.812.752.942.853.083.17
Table 4: The mass ratio q and corresponding residual tex2html_wrap_inline890

   

ParameterPhotometric element
qtex2html_wrap_inline898
itex2html_wrap_inline902
L1/(L1+L2)tex2html_wrap_inline906
L1/(L1+L2)tex2html_wrap_inline910
g1=g20.32
A1=A20.5
tex2html_wrap_inline884tex2html_wrap_inline918
tex2html_wrap_inline8862.7718
x1B0.750
x2B0.810
x1V0.600
x2V0.680
T16600 K
T2tex2html_wrap_inline934K
r1(pole)tex2html_wrap_inline938
r1(point)tex2html_wrap_inline942
r1(side)tex2html_wrap_inline946
r1(back)tex2html_wrap_inline950
r2(pole)0.2915
r2(point)0.4187
r2(side)0.3041
r2(back)0.3367
Table 5: Photometric solutions for DD Mon

For all mass ratios the calculation started at mode 2 (detached mode). In the calculation we found that the solution converged to mode 5 (semi-detached mode) when q = 0.3, 0.4, 0.5 and 0.6, and the solution converged to mode 2 when q = 0.7, 0.8 and 0.9. The resulting sums of weighted square deviations tex2html_wrap_inline964 for each value of q are listed in Table 4 (click here) and plotted in Fig. 2. A minimum of tex2html_wrap_inline964 is achieved at q=0.5. Therefore, we chose the initial value of q to be 0.5 and made it an adjustable parameter. Then we performed a differential correction until it converged and found that the mass ratio q converged to tex2html_wrap_inline976. Finally, we fixed the mass ratio q=0.45, and used the two-colour B and V observations to derive the photometric parameters of DD Mon as listed in Table 5 (click here). Figure 3 shows the theoretical light curves (solid lines) computed with these parameters. Our solution reveals that the system is a semi-detached binary with the secondary component filling its Roche lobe.


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