F

I mod

where superscript "mod" refers to WD intrinsic model quantities, a is the orbital semi-major axis, and A is interstellar passband extinction in magnitudes, with subscripts 1 and 2 for the binary components. The polar normal intensities /1ph and I|h are computed by an interpolation routine approximating the radiation by a stellar atmosphere.

Utilization of a stellar atmosphere, or an approximation to it, requires a good temperature estimate for one star from spectra or color indices, or derivation of both temperatures from two light curves as described in Sect. 5.1.2.3. As stated in Wilson's EB temperature-distance theorem, calibrated light curves in two passbands are needed and are, in principle, sufficient to determine both temperatures and the distance. Note that the light curve model involves and reproduces mean surface temperature, temperature at a definite reference point (usually, the pole), at any local surface point, and observed (aspect-dependent) temperature.

Distances derived from EBs can be very accurate and can be determined for nearby galaxies [cf. Wilson (2004)]. However, we should keep in mind that they depend on extinction, A, and they could also be contaminated by third light. The light, l3, of a third star or planet makes a system appear brighter and thus apparently nearer, and also influences EB solutions in other ways. It dilutes all variations (eclipses, tides, reflection, etc.) and thus reduces light curve amplitudes.

Interstellar extinction dims light curves so as to increase distance estimates, whereas its associated reddening decreases temperature estimates. Reduced theoretical temperatures reduce predicted absolute fluxes and thus decrease distance estimates. Thus, in regard to distance determined from this light curve analysis approach, extinction and reddening partly offset one another and, accordingly, the overall effect of extinction on distance determination is less than one might suppose (Wilson 2008, Sect. 7). Wilson (2008) also investigated the possibility of determining A through the least-squares analysis. Although this is indeed possible given absolutely scaled light curves in three passbands, it is not very practical as the sensitivity with respect to the calibration of the light curves is typically strong. Small deviations in the calibration lead to significantly different A values.

In addition to these interstellar extinction or third light problems specific to the analysis and observation of a particular binary, Wilson (2008, Section 5) carefully discusses the radiative model, photometric response functions, absolute photometric calibration, and photometric transformations as sources of systematic errors of the overall procedure.

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