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Stellar distance is an important basic parameter in stellar astrophysics.Stars in a cluster are thought to be formed coevally from the same interstellarcloud of gas and dust. They are therefore expected to have common properties.These common properties strengthen our ability to constrain theoretical modelsand/or to determine fundamental parameters, such as stellar mass, metalfraction, and distance when tested against an ensemble of cluster stars. Herewe derive a new relation based on solar-like oscillations, photometricobservations, and the theory of stellar structure and evolution of red giantbranch stars to determine cluster distance moduli through the globaloscillation parameters $\Delta\nu$ and $\nu_{\rm max}$, and photometric data\textit{V}. The values of $\Delta\nu$ and $\nu_{\rm max}$ are derived from\textit{kepler} observations. At the same time, it is used to interpret thetrends between \textit{V} and $\Delta\nu$. From the analyses of this newlyderived relation and observational data of NGC 6791 and NGC 6819 we devise amethod in which all stars in a cluster are regarded as one entity to determinethe cluster distance modulus. This approach fully reflects the characteristicof member stars in a cluster as a natural sample. From this method we derivetrue distance moduli of $13.09\pm0.10$ mag for NGC 6791 and $11.88\pm0.14$ magfor NGC 6819. Additionally, we find that the distance modulus only slightlydepends 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.

Asteroseismic Study on Cluster Distance Moduli for RGB Stars in NGC 6791 and NGC 6819