Main Sequence Constraints

The EB parameter estimation problem often suffers from a lack of uniqueness. Reducing parameter space may help but needs to be justified and carried out carefully. Some degrees of freedom can be eliminated by making an assumption about the morphological type of a binary star, e.g., that it is semi-detached or a contact binary. With more EB software becoming available, the set of special assumptions is increasing. Prsa & Zwitter (2005b) introduced main sequence constraints (MSC) assuming that either or both components are main sequence stars. Because a significant percentage of all stars are on the main sequence, there is a fair chance that this assumption is correct. In principle, applying MSCs to one component or both components of the modeled binary means imposing relations among mass, luminosity, temperature, and radii of main sequence stars (see, e.g., Malkov 2003 for such relations specific to EBs) which in turn relates to the computation of absolute dimensions. Consequentially, given a single parameter (e.g., a component's effective temperature), all other parameters (its mass, luminosity, and radius) are calculable. This in turn implies that in the case of circular and nearly circular orbits, the effective potential of the constrained component is fully determined.

However, the situation is not as ideal as described above. The main sequence is not a line in the Hertzsprung-Russell diagram (luminosity or absolute magnitude versus spectral type, stellar temperature or color index: Basically brightness plotted against color) but rather a strip with a non-zero width. Depending on the position selected, rather different values for the derived absolute quantities could follow. Prsa & Zwitter (2005b) account for the width of the main sequence by treating the main sequence relations not as strict constraints but rather as a user-defined penalty cost terms.

Although MSCs break the degeneracy, at best they could be used for testing whether either or both stars can plausibly be main sequence stars: Depending on the behavior of the standard deviation of the fit, such a hypothesis can be accepted or rejected. MSCs are of a different nature than morphological constraints and may lead to a circular argument: EBs provide absolute parameters for stars, which can then be used to establish various calibrations. MSCs, on the other hand, use calibrations. Thus, main sequence constrained solutions must never be used to establish calibrations of any kind.

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