Asteroseismic Searching for Environmental Influence in Star Clusters Observed by Kepler/K2

In this paper, we investigate asteroseismic scaling-relations of evolved stars in star clusters observed by Kepler/K2, aiming to address the issue of whether observed stellar oscillations are influenced by environmental factors, as there are interesting phenomena relating to the stellar pulsations observed in star clusters. Specifically, we compare statistical properties of distributions including ∆ν, ν_max, H_Gauss, δν_env, and δν₀₂ derived from red giant branch (RGB) and red clump (RC) stars in two pairs of star clusters: NGC 2682-NGC 6819 and NGC 1817-NGC 6811. We have found that the slopes of relations between ν_max and ∆ν and between H_Gauss and ν_max associated with RC stars in the more compact star clusters, NGC 2682 and NGC 1817, are in common less steep compared with those for NGC 6819 and NGC 6811. It is also found that the slopes of the relation between δν_env and ν_max from RC stars in the more compact star clusters are in common steeper compared with those for the others. For the relation between δν₀₂ and ∆ν obtained from RGB stars, the slope resulting from NGC 2682 and NGC 6819 is indistinguishable. The Kolmogorov–Smirnov tests conducted on RC stars in the pairs of NGC 2682 and NGC 6819, as well as NGC 1817 and NGC 6811, indicate that all the seismic quantities considered in this paper are drawn from different distributions. We conclude, therefore, that the properties of star clusters should be considered when asteroseismic data obtained from stars within star clusters are interpreted.