2014ApJ...786...10W

Stellar distance is an important basic parameter in stellar astrophysics. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust; therefore, they are expected to have common properties. These common properties strengthen our ability to constrain theoretical models and/or to determine fundamental parameters, such as stellar mass, metal fraction, and distance, when tested against an ensemble of cluster stars. Here we derive a new relation based on solar-like oscillations, photometric observations, and the theory of stellar structure and evolution of red giant branch stars to determine cluster distance moduli through the global oscillation parameters Δν and ν_max and photometric data V. The values of Δν and ν_maxare derived from Kepler observations. At the same time, it is used to interpret the trends between V and Δν. From the analyses of this newly derived relation and observational data of NGC 6791 and NGC 6819, we devise a method in which all stars in a cluster are regarded as one entity to determine the cluster distance modulus. This approach fully reflects the characteristic of member stars in a cluster as a natural sample. From this method we derive true distance moduli of 13.09±0.10 mag for NGC 6791 and 11.88±0.14 mag for NGC 6819. Additionally, we find that the distance modulus only slightly depends on the metallicity [Fe/H] in the new relation. A change of 0.1 dex in [Fe/H] will lead to a change of 0.06 mag in the distance modulus.