3 Absolute elements

Although spectroscopic observations are not available for this binary the UBV photoelectric observations can be used for obtaining the tentative absolute elements. Using the derived luminosities (Table 1, Col. 6), the differential magnitudes, $\Delta m$, at the quadrature and the standard values of the magnitudes of the comparison star in the UBV passbands (Sect. 2), we derived the following magnitudes and colours of the individual components: Hotter component V=8.84, B-V=0.32, U-B=-0.06, Cooler component V=9.47, B-V=0.45, U-B=0.07.

  

Table 3: YY CMi: Comparison of elements from various studies

Assuming no interstellar reddening, the (B-V) of the primary corresponds to a temperature of $7030\, \pm \,100$ K which in turn corresponds to a spectral type of F1V [3, (Allen 1976]; [20, Popper 1980]; [23, Schmidt-Kaler 1982)]. The above temperature agrees quite well with that of the fixed temperature $7000 \, \pm \, 100$ K used for the primary component in the analysis. The (B-V) of 0.45 for the secondary component corresponds to a spectral type of F5V (6450 K) and its derived temperature of 6145 K (Table 1, Col. 6) suggests a spectral type of F8V [3, (Allen 1976]; [20, Popper 1980]; [23, Schmidt-Kaler 1982)]. This small discrepancy of about 300 K between the spectral types derived from the colour (B-V) and effective temperature for the secondary component could be attributed to the uncertainties in the model atmospheres incorporated in the W-D programme, appropriate for each spectral type. Keeping in view the bigger sizes (radii) of both the components (see the following) we adopted a spectral type of F1V-IV for the primary and F5V-IV for the secondary component. Our improved solution based on UBV photometry gives an earlier spectral type for the primary compared to other authors.

Since no spectroscopic studies exist for this system, neither the spectral types nor the individual masses of the components are presently available. Hence it is difficult to get reliable absolute elements for the components. However, to get tentative dimensions and masses of the components, we assumed the primary F1V component to obey the spectral type-mass relation of the normal main sequence stars [4, (Andersen 1991)]. From this assumption one gets a mass of $1.56\ m_\odot$ for the primary component. From the presently derived mass-ratio, $m_{\rm c}/m_{\rm h}=q=0.89$ and the assumed mass of $1.56\ m_\odot$ for $m_{\rm h}$,one gets a mass of $1.39\ m_\odot$ for the secondary component.

Using Kepler's 3rd law

$$A^3=74.55(m_{\rm h}+m_{\rm c})P^2$$ (1)

and with a period of $1\hbox{$.\!\!^{\rm d}$}0940197$ [2, (Abhyankar 1962b)], one gets $A=6.41\ R_\odot$ as the separation of the components. From the derived average fractional radii $[r=(r_{\rm pole}+r_{\rm side}+r_{\rm back})/3]$ of 0.393 and 0.371 for the primary and secondary components respectively, one gets $Ar_{\rm h}=R_{\rm h}=2.52\ R_\odot$ and $Ar_{\rm c}=R_{\rm c}=2.38\ R_\odot$. The above derived radii of the primary and secondary components, $R_{\rm h}$ and $R_{\rm c}$, are larger than those of $2.07\ R_\odot$ and $1.70\ R_\odot$ of normal F1V and F5V stars respectively [4, (Andersen 1991)]. This may be due to the evolution of both the primary and secondary components which are overfilling their Roche lobes $(r^*_{\rm h}=0.385, r^*_{\rm c}=0.363$ for q=0.89; [19, Plavec & Kratochvil 1964)] by 3%. The system parameters are as given in Table 3 along with the elements and parameters given by [7, Giuricin & Mardirossian (1981)] and [18, Niarchos et al. (1998)].

The bolometric corrections are from [20, Popper (1980)]. According to [6, Buser & Kurucz (1978)] a star with a (B-V) colour of 0.32 and $\log\ g$ of 3.83 should have a temperature of about 7000 K. This agrees quite well, within the errors of assumed parameters, with the temperatures of $7000 \, \pm \, 100$ K used by us for the primary component in our analysis.