2014ApJ...781...44W

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_eff) ∼ g^p R^p) to determine the masses and metallicities of red giant branch stars in open clusters NGC 6791 and NGC 6819 from the global oscillation parameters Δν (the large frequency separation) and ν_max(frequency of maximum oscillation power). The Δν and ν_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 Δν and ν_max, with lower intrinsic uncertainties, and (3) the mass dependence in the Δν - ν_max relation for red giant branch stars.