## Traditional Distance Estimation

Traditional distance estimation is an a posteriori step that follows the light curves analyses in Sect. 4.4.4.1. Here we summarize the underlying idea. As pointed out in Chap. 1 (page 22) the distance D or parallax n of a binary can (in favorable cases) be derived if both light and radial velocity curves are available. Although the orbit size, relative dimensions, and temperature difference are the results of a simultaneous least-squares analysis, it is useful to remember that these quantities strongly relate to the data sources as listed by Wilson (2008):

1. The orbit size, i.e., the semi-major axis a, and thus the linear scale of the system follow from the radial velocity curves.

2. The star dimensions relative to a (i.e., their mean radii) follow from the form of the light curve that establishes a one-dimensional family of mean surface temperatures [T1; T2] through the two eclipse depths.

3. If one mean temperature is obtained from spectra or color indices (as is usually the case), the other temperature follows implicitly from the [T1; T2] family through the least-squares analysis. Together with the surface gravity distribution, irradiation from the other star, and possibly spots, a temperature distribution can be computed. If this distribution is entered into an atmosphere model, or a simplified model involving a blackbody law with limb darkening, we obtain the emission per unit surface area on both stars. 4. The above information determines the absolute passband luminosities, as well time-dependent observable flux for any assumed distance.

The traditional way to compute the distance from the four data types above in most "distance deriving" publications prior to 2007 is described in Sect. 4.4.4.1 and finds D from the unreddened distance modulus, for instance in the Johnson system introduced in Sect. 2.1.1

where D is the distance in parsecs, and R = AV/EB-V is the ratio of the passband extinction, AV, of the V light by the interstellar medium to the color excess EB-V. Note that the apparent magnitude of the binary needs to be known in a standard system, e.g., Johnston UBV or Str omgren uvby. Differential photometry alone is not sufficient. If distance were derived at all, we further note the following.

1. The distance derivation using the separate follow-up step is strictly valid only for spherical stars as otherwise the local physics is not treated properly.

2. Formal standard errors of the derived distance are not provided, although other kinds of error estimates may be given.

Therefore, below we argue in favor of Wilson's (2008) self-consistent approach that exploits photometric light curves in standard physical units.

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