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 sta rs. We investigate the potential utility of such oscillation frequenci es in determining the fundamental stellar structure parameters of thes e stars, in the case in which frequencies may be measured for both mem bers of a visual binary system. To utilize all of the observations pre sumed to be available in an optimal way, we develop a formalism based on singular value decomposition (SVD) to relate errors in observed qua ntities to those in model parameters. As a particularly interesting ex ample, we consider the alpha Cen system as it would be seen from dista nces between 1.3 pc (its true distance) and 100 pc. We find that for t he nearest case, adding oscillation frequency separations with plausib le errors to the available astrometric, photometric, and spectroscopic data allows one to reduce the formal errors in estimates of the heliu m abundance, heavy-element abundance, and mixing length by roughly a f actor of 2. Estimates of the stellar masses and the system's age and d istance are not markedly improved, mostly because of the very high qua lity astrometric data that can be obtained on such a nearby object. If the system were located at a significantly larger distance, the addit ion of oscillation information would allow drastic reductions in the f ormal error applicable to all of the stellar parameters except the hel ium abundance. These results suggest that accurately measured oscillat ion frequencies for visual binaries might allow tests of stellar struc ture theory at a level of precision that has hitherto been obtainable only for a few eclipsing binaries. Reducing the observational errors i n photometry or astrometry by a factor of 3 does not provide the same level of improvement, especially for relatively distant systems. We sh ow that the extra information contained in the oscillation frequencies for a reasonable set of modes would easily allow one to distinguish b etween models using opacity laws obtained from the Los Alamos Opacity Library and from the more recent Livermore OPAL tables. Different form ulations of the equation of state (without and with Coulomb effects) l ead to models that are marginally distinguishable, while models with a nd without helium settling from the convection zone are not distinguis hable, given observations with errors as large as we assume.