The effectiveness of oscillation frequencies in constraining stellar model parameters

Recent observational advances suggest that it may soon be possible to measure the frequencies of p-mode oscillations on distant Sun-like stars. We investigate the potential utility of such oscillation frequencies in determining the fundamental stellar structure parameters of these stars, in the case in which frequencies may be measured for both members of a visual binary system. To utilize all of the observations presumed to be available in an optimal way, we develop a formalism based on singular value decomposition (SVD) to relate errors in observed quantities to those in model parameters. As a particularly interesting example, we consider the a Cen system as it would be seen from distances between 1.3 pc (its true distance) and 100 pc. We find that for the nearest case, adding oscillation frequency separations with plausible errors to the available astrometric, photometric, and spectroscopic data allows one to reduce the formal errors in estimates of the helium abundance, heavy-element abundance, and mixing length by roughly a factor of 2. Estimates of the stellar masses and the system's age and distance are not markedly improved, mostly because of the very high quality astrometric data that can be obtained on such a nearby object. If the system were located at a significantly larger distance, the addition of oscillation information would allow drastic reductions in the formal error applicable to all of the stellar parameters except the helium abundance. These results suggest that accurately measured oscillation frequencies for visual binaries might allow tests of stellar structure theory at a level of precision that has hitherto been obtainable only for a few eclipsing binaries. Reducing the observational errors in photometry or astrometry by a factor of 3 does not provide the same level of improvement, especially for relatively distant systems. We show that the extra information contained in the oscillation frequencies for a reasonable set of modes would easily allow one to distinguish between models using opacity laws obtained from the Los Alamos Opacity Library and from the more recent Livermore OPAL tables. Different formulations of the equation of state (without and with Coulomb effects) lead to models that are marginally distinguishable, while models with and without helium settling from the convection zone are not distinguishable, given observations with errors as large as we assume.