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.

15 pages, 14 figures, accepted for publication in ApJ

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• The Helium Abundance of NGC 6791 from Modeling of Stellar Oscillations
• Testing the intrinsic scatter of the asteroseismic scaling relations with Kepler red giants
• Mitigating the mass dependence in the $\Delta \nu$ scaling relation of red-giant stars
• Determining the Best Method of Calculating the Large Frequency Separation For Stellar Models
• Solar cycle variation of ${\nu }_{\max }$ in helioseismic data and its implications for asteroseismology
• Comparison of the Asteroseismic Mass Scale of Red Clump Giants with Photometric Mass Estimates
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• Scaling relations for solar-like oscillations: a review
• Mixing-length calibration from field stars. An investigation on statistical errors, systematic biases, and spurious metallicity trends