The effectiveness of oscillation frequencies in constraining stellar model parameters

Timothy M. Brown, J. Christensen-Dalsgaard, Barbara Weibel-Mihalas, Ronald Lynn Gilliland

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1013-1034
Number of pages22
JournalAstrophysical Journal
Volume427
Issue number2
StatePublished - Jun 1 1994

Fingerprint

stellar models
oscillation
oscillations
helium
stellar structure
opacity
stars
astrometry
settling
heavy elements
estimates
stellar mass
data quality
equation of state
photometry
parameter
sun
convection
equations of state
decomposition

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Brown, T. M., Christensen-Dalsgaard, J., Weibel-Mihalas, B., & Gilliland, R. L. (1994). The effectiveness of oscillation frequencies in constraining stellar model parameters. Astrophysical Journal, 427(2), 1013-1034.
Brown, Timothy M. ; Christensen-Dalsgaard, J. ; Weibel-Mihalas, Barbara ; Gilliland, Ronald Lynn. / The effectiveness of oscillation frequencies in constraining stellar model parameters. In: Astrophysical Journal. 1994 ; Vol. 427, No. 2. pp. 1013-1034.
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Brown, TM, Christensen-Dalsgaard, J, Weibel-Mihalas, B & Gilliland, RL 1994, 'The effectiveness of oscillation frequencies in constraining stellar model parameters', Astrophysical Journal, vol. 427, no. 2, pp. 1013-1034.

The effectiveness of oscillation frequencies in constraining stellar model parameters. / Brown, Timothy M.; Christensen-Dalsgaard, J.; Weibel-Mihalas, Barbara; Gilliland, Ronald Lynn.

In: Astrophysical Journal, Vol. 427, No. 2, 01.06.1994, p. 1013-1034.

Research output: Contribution to journalArticle

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AB - 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.

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Brown TM, Christensen-Dalsgaard J, Weibel-Mihalas B, Gilliland RL. The effectiveness of oscillation frequencies in constraining stellar model parameters. Astrophysical Journal. 1994 Jun 1;427(2):1013-1034.