Changing the ${\nu }_{\max }$ Scaling Relation: The Need For a Mean Molecular Weight Term

Abstract

The scaling relations that relate the average asteroseismic parameters $\Delta \nu$ and ${\nu }_{\max }$ to the global properties of stars are used quite extensively to determine stellar properties. While the $\Delta \nu$ scaling relation has been examined carefully and the deviations from the relation have been well documented, the ${\nu }_{\max }$ scaling relation has not been examined as extensively. In this paper we examine the ${\nu }_{\max }$ scaling relation using a set of stellar models constructed to have a wide range of mass, metallicity, and age. We find that as with $\Delta \nu$, ${\nu }_{\max }$ does not follow the simple scaling relation. The most visible deviation is because of a mean molecular weight term and a ${\Gamma }_1$ term that are commonly ignored. The remaining deviation is more difficult to address. We find that the influence of the scaling relation errors on asteroseismically derived values of $\log g$ are well within uncertainties. The influence of the errors on mass and radius estimates is small for main sequence and subgiants, but can be quite large for red giants.

arXiv comment15 pages, 14 figures, accepted for publication in ApJ

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