The properties of the secondary star

Observationally, little is known about the basic parameters (masses, temperatures, radii) of stars as late as the RR Cae secondary. It is therefore at the same time important and difficult to assess the reliability of the present results. A comparison with similar late type stars should be helpful.

Probst (1983) conducted IR photometry of RR Cae. Although the IR band is dominated by the secondary the contribution of the primary is not quite negligible. Taking the veiling factor of 0.6 at 6100  Å (Sect. 2.4) and assuming the components to radiate like black bodies with the best fit temperatures (Table 3) a colour correction is calculated. Then, the values measured by [Probst (1983)] translate into colours of J-H=0.63and H-K=0.35 for the secondary of RR Cae. Comparing them with the colours of the sample of late type stars investigated by [Leggett et al. (1996)] it is found that only the UV Cet type star DX Cnc has similar colours: DX Cnc is slightly bluer in J-H (0.58) and has practically the same value of H-K (0.36). According to [Henry et al. (1996)] DX Cnc has a spectral type of M6.5. Thus, the RR Cae secondary should have a similar, possibly a bit later but definitely not earlier spectral type. This is consistent with the rough estimate obtained in Paper I.

Leggett et al. (1996) fitted an atmosphere model for late type stars of [Allard & Hauschildt (1995)] to the spectrum of DX Cnc and found a temperature of 2700 K. The best fit temperature of the RR Cae secondary is in agreement with this value accounting for its probably slightly later spectral type. But note that the WD models cannot determine a really reliable temperature T_2 for the RR Cae secondary for two reasons: (1) The temperatures for both stars are strongly correlated. Even assuming an absurdly high or low temperature T_1 for the white dwarf a satisfactory model fit is possible if T_2 is modified accordingly. The formal error of T_1 quoted by [Bragaglia et al. (1990)] of 140 K translates into an uncertainty (at the same level of confidence) of roughly half that value for T_2. (2) The WD routine uses black body radiation for the RR Cae secondary. It is well known that the spectral energy distribution for late type stars can differ drastically from that of a black body. Therefore, the temperature determined here must be regarded as a brightness temperature in the range around 6700 Å (the effective wavelength of the R band in which the observations were taken) and can differ significantly from the effective temperature.

The spectral type and colours are, of course, determined by the surface temperature. Therefore, an agreement between both stars in one quantity implies an agreement in the others, as observed. This is different for the radius. Here, a comparison between the RR Cae secondary and DX Cnc shows disagreement: While [Leggett et al. (1996)] derive a radius of 0.1167 +- 0.0014 R_solar for DX Cnc from the temperature and the known distance, the best fit radius for the RR Cae secondary is considerably larger, 0.189 R_solar. The radius depends on the internal structure and thus on the chemical composition of the star. Systems such as RR Cae - a white dwarf and a red dwarf in a close orbit - are probably the result of a common envelope evolution which occurred when the progenitor of the white dwarf was on the red giant or asymptotic giant branch. During this phase the secondary must be expected to have accreted nuclearly processed material. Its deep reaching convection zone could easily have caused a thorough mixing of this metal rich matter. As a consequence the inner structure and the radius of the RR Cae secondary could be different from that of a normal late type main sequence star.

In the absence of model calculations for the structure of very low mass stars with elevated metallicity a comparison with the solar composition and zero metallicity models of [Burrows et al. (1996)] might shed some light on the present case: For a mass as low as the RR Cae secondary their models yield radii which are only 63% of the radius found here (unless the star is extremely young which can be excluded in view of the cool white dwarf in RR Cae). The zero metallicity model yields even smaller radii. Thus, an elevated metallicity in fact leads to a larger radius. In the absence of both, an empirical determination of the metallicity of the RR Cae secondary and suitable models for high metallicity late type dwarfs it must remain unclear whether this effect can explain as large a radius as observed.