3 Photometric solution

Photometric solutions were obtained by means of the latest version of the WD program (Wilson 1992) which includes a new reflection treatment, the option of using non-linear limb-darkening laws and the ability to adjust spot parameters. The individual observations were combined into 54 normal points in each colour and the two light curves were employed simultaneously in computing solutions. The convergence of the minimization procedure was obtained by means of the method of multiple subsets (Wilson & Biermann 1976).

We adopted a temperature of 5600 K for star 1 (star eclipsed at Min. I), which corresponds to spectral type of G5V. The other adopted parameters were: Claret et al.'s (1990) values of the limb darkening coefficient (x₁=x₂=0.84 for B, 0.66 for V), Lucy's (1967) values of the gravity darkening coefficient (g₁=g₂=0.32) and Rucinski's (1969) values of the albedo (A₁=A₂=0.50). Adjustable parameters were the orbital inclination, i, the mean temperature of star 2, T₂, the potential of the components, $\Omega_{1}$ and $\Omega_{2}$ , and the luminosity of star 1, L₁ (the Planck function was used in computing the luminosity).

In order to search for an appropriate photometric mass ratio to compare with the spectroscopic mass ratio, solutions were made for a series of fixed values of the mass ratio q=m₂/m₁ (0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.20, 1.60, 2.00, 2.50 and 3.00). Assuming a detached system initially, the differential corrections started from the mode 2, but the converged solutions were always obtained at the contact mode 3. The resulting sums, $\Sigma$, of the weighted square deviations of the converged solutions for each value of q are plotted in Fig. 2. The best fit is for q=2.50. At this point, the set of the adjustable parameters was expanded to include q. The mass ratio converged to a value of q=2.36799 in the final solution. This solution indicates that YY Eri is a W-type W UMa binary, in agreement with the results published by Binnendijk (1965), Maceroni et al. (1982), Nesci et al. (1986) and Maceroni et al. (1994). The photometric parameters are listed in Table 4, where star 1 indicates more massive component and star 2 is of less mass. The fit of the computed light curves is shown in Fig. 1 in solid lines.

  

Figure 2: Variance of the computed fit as a function of the mass ratio q

  

Figure 3: As Fig. 1, but with dark spot included in the photometric model

  

Table 4: photometric solutions of YY Eri

While the overall fit of the computed light curves is quite satisfactory, Fig. 1 shows obvious distortions in the observed light curves that seems to be due to surface inhomogeneities of the components. Unequal quadrature light level, namely, the O'Connell effect, is known in many eclipsing binaries and several suggestions have been made to explain this effect by various authors. For YY Eri, the observed distortion, with Maximum II being fainter than Maximum I, may result from a cool region on either component. It has been assumed that the spot is on the star 1 or the star 2 and the several groups of dark spots or hot spots have been tested. While a converged solution with the hot spot(s) could be not found, the best fit to the observed light curves was found with dark spot on the star 1 or the star 2. The solutions with the dark spot (co-latitude, $q\rm _{s}$, longitude, $f\rm _{s}$, angular radius, $r\rm _{s}$, all in degrees, and the temperature factor $T_{\rm s}/T_{*}$, with T_* the local effective temperature of the surrounding photosphere) are also listed in Table 4. The solution labeled Dark 1 is with a dark spot on the primary (more massive) star and the solution labeled Dark 2 with a dark spot on the secondary star. The solution labeled Dark 1 turns out to be slightly better quality than the other. The fit of the computed light curves corresponding to the solution in Table 5 with the dark spot on the primary star is shown in Fig. 3 in solid lines.

  

Table 5: Parameters of the V light curve properties of YY Eri