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,
and
.
q | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
![]() | 3.91 | 2.81 | 2.75 | 2.94 | 2.85 | 3.08 | 3.17 |
Parameter | Photometric element |
q | ![]() |
i | ![]() |
L1/(L1+L2) | ![]() |
L1/(L1+L2) | ![]() |
g1=g2 | 0.32 |
A1=A2 | 0.5 |
![]() | ![]() |
![]() | 2.7718 |
x1B | 0.750 |
x2B | 0.810 |
x1V | 0.600 |
x2V | 0.680 |
T1 | 6600 K |
T2 | ![]() |
r1(pole) | ![]() |
r1(point) | ![]() |
r1(side) | ![]() |
r1(back) | ![]() |
r2(pole) | 0.2915 |
r2(point) | 0.4187 |
r2(side) | 0.3041 |
r2(back) | 0.3367 |
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 for each value of
q are listed in Table 4 (click here) and plotted in Fig. 2. A minimum of
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
. 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.