Astrophysical Problems Solved by Light Curve Methods

Several important astrophysical problems have been solved with major help from light curve solution methods, e.g., the Algol Paradox [cf. Pustylnik (2005) for a historical review], the structure of W UMa stars, bolometric albedos of convective envelopes, and undersized subgiants [cf. Wilson (1994)]. Progress in understanding intriguing binaries such as e Aurigae20 and j3 Lyrae has been made by including gas streams and disks in light curve modeling (see Sect.

The improvement of light curve solution methods has contributed to our understanding of physical processes in stars. The earliest work by Russell was applied immediately to the determination of absolute parameters of stars, the precision of which improved as analytic techniques kept pace with observational techniques.

A breakthrough occurred with the introduction of Roche geometry. An example of improved astrophysical understanding through EB light curve analysis is the successful modeling of W UMa stars as over-contact systems. These very abundant binaries are excellent laboratories for convection in stars. Their fast orbital motion makes them attractive candidates for gravitational wave astronomy. In the early days these objects, as all EBs, were modeled as ellipsoids. The problem was that light curve solutions found detached configurations21 but W UMas have long been known to be main sequence objects with mass ratios much different from unity. Yet the components have very nearly equal surface temperature as shown both by light curves and spectra. Individual main sequence stars of unequal mass cannot have equal surface temperatures, so Kuiper (1941, 1948) argued that they must be over-contact binaries with energy exchange. This is because energy exchange is not

20 Apparently s Aurigae's variability was first noticed in the eclipse of 1821 by Johann Fritsch, who seems not to have published the discovery but just passed it along in some way. The first quantitatively observed eclipse was that of 1848, with pre-eclipse observations at least back to 1846. The 1848 observations by Argelander seem not to have been published until 1903 (Astron. Nachr. Vol. 164, p. 83) by Ludendorff. The early history of this star is discussed by M. Giissow (1936, Veroff. Univ. Sternwarte Berlin-Babelsberg, Vol. 11, No. 3).

21 Note that ellipsoidal models could, in principle, produce solutions with overlapping ellipsoids.

possible in detached systems. W UMas are well suited to equipotential representation; isomorphism with the Roche model is excellent, which is not true of an ellipsoidal representation. The gravity effect is also important and nicely taken care of as the surface potential gradient. The overall result has been that many inconsistencies and strange results were eliminated by Roche equipotential models [cf. Lucy (1968), Mochnacki & Doughty (1972a, b), Wilson & Devinney (1973), and Lucy (1973)].

The successful modeling of Algol systems as semi-detached gave quantitative reinforcement to the already accepted solution of the Algol paradox: The hotter, more massive primaries were clearly main sequence stars, but the less massive secondaries had radii much too large to be on the main sequence (i.e., they were evolved subgiants or giants). This finding contradicted the well-accepted picture that more massive stars evolve faster than less massive stars (see page 137 for the resolution of the Algol paradox). For a still profitable discussion of Algols, their history, evolution, relation to other binaries, and circumstellar environment refer to Batten (1989). The next stage in the study of Algols is to understand the evolution subsequent to mass transfer episodes through observation of binaries with major circumstellar mass flows. Examples might be the disk-enshrouded binary j3 Lyrae [see Hubeny & Plavec (1991) and Sects. and], the unusual binary V356 Sagittarii with its opaque ring of recently transferred matter (Wilson & Caldwell 1978), KU Cygni with its thick, dusty accretion disk (Olson 1988), AXMonocerotis with scattering clouds in its environment (Elias et al. 1997), and many symbiotic stars.

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