New asteroseismic scaling relations based on Hayashi track relation applied to red-giant branch stars in NGC 6791 and NGC 6819

Abstract

Stellar mass $M$, radius $R$, and gravity $g$ are important basic parameters in stellar physics. Accurate values for these parameters can be obtained from the gravitational interaction between stars in multiple systems or from asteroseismology. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. The cluster members are therefore expected to have some properties in common. These common properties strengthen our ability to constrain stellar models and asteroseismically derived $M$, $R$ and $g$ when tested against an ensemble of cluster stars. Here we derive new scaling relations based on a relation for stars on the Hayashi track ($\sqrt{T_{\mathrm{eff}}}\sim g^p{R}^q$) to determine the masses and metallicities of red giant branch stars in open clusters NGC 6791 and NGC 6819 from the global oscillation parameters $\Delta \nu$ (the large frequency separation) and ${\nu }_{\max }$ (frequency of maximum oscillation power). The $\Delta \nu$ and ${\nu }_{\max }$ values are derived from \kepler\ observations. From the analysis of these new relations we derive: (1) direct observational evidence that the masses of red giant branch stars in a cluster are the same within their uncertainties, (2) new methods to derive $M$ and $z$ of the cluster in a self consistent way from $\Delta \nu$ and ${\nu }_{\max }$, with lower intrinsic uncertainties, (3) the mass dependence in the $\Delta \nu$ - ${\nu }_{\max }$ relation for red giant branch stars.

open clusters and associations: individual (NGC 6791, NGC 6819) -- stars: late-type -- stars: fundamental parameters -- stars: interiors -- stars: oscillations -- asteroseismology

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• Li Evolution and the Open Cluster NGC 6819: A Correlation Between Li Depletion and Spindown in Dwarfs More Massive Than the F-Dwarf Li-Dip
• The Helium Abundance of NGC 6791 from Modeling of Stellar Oscillations
• A uvbyCaHbeta Analysis of the Old Open Cluster, NGC 6819
• Asteroseismic Study on Cluster Distance Moduli for RGB Stars in NGC 6791 and NGC 6819
• CCD UBV photometry of the open cluster NGC 6819
• New Insights for High-precision Asteroseismology: Acoustic Radius of KIC 6225718
• Ensemble asteroseismology of pulsating B-type stars in NGC 6910
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• Kepler Binary Stars in NGC 6819 Open Cluster: KIC 5113146 and KIC 5111815
• Early Results from APOKASC