Asteroseismology of evolved stars in six star clusters observed by Kepler/K2

In this study, we have explored the frequency separations, $\Delta \nu$ and $\delta {\nu }_{02}$, the height and width of the oscillation power excess, $H_{\mathrm{Gauss}}$ and $\delta {\nu }_{\mathrm{env}}$, as a function of the frequency of maximum power ${\nu }_{\max }$ by analyzing 187 evolved stars in six star clusters observed by the Kepler/K2 missions. We have also examined the asteroseismic relation in the Christensen-Dalsgaard diagram. Given the importance of scaling relations, the dependency of asteroseismic scaling relations on physical quantities must be verified to reduce systematic errors through the exploration of observational data obtained from various sources. In this context, the star cluster provides a valuable means to assess the age and metallicity. Focusing on evolved stars with $30\mu \mathrm{Hz}<{\nu }_{\max }<220\mu \mathrm{Hz}$, we have exploited the mass effect without the need for deriving the individual stellar mass. We have found that the considered relations appear to be associated with the age of star clusters, thereby the mass of the stars in a given evolutionary status for star clusters with different ages. By separately considering red giant branch stars and red clump stars, we have found that red clump stars appear more sensitive to the cluster age compared with red giant branch stars. It has been suggested that conclusions regarding the dependency of metallicity should be drawn with due care as outcomes are subject to how to treat metallicity. Finally, we conclude by briefly pointing out implications of our findings on asteroseismic inferences.