Stellar mergers are important processes in stellar evolution, dynamics, and transient science. However, it is difficult to identify merger remnant stars because they cannot easily be distinguished from single stars based on their surface properties. We demonstrate that merger remnants can potentially be identified through asteroseismology of red giant stars using measurements of the gravity mode period spacing together with the asteroseismic mass. For mergers that occur after the formation of a degenerate core, remnant stars have over-massive envelopes relative to their cores, which is manifested asteroseismically by a g~mode period spacing smaller than expected for the stars mass. Remnants of mergers which occur when the primary is still on the main sequence or whose total mass is less than $approx! 2 , M_odot$ are much harder to distinguish from single stars. Using the red giant asteroseismic catalogs of Vrard et al. 2016 and Yu et al. 2018, we identify $24$ promising candidates for merger remnant stars. In some cases, merger remnants could also be detectable using only their temperature, luminosity, and asteroseismic mass, a technique that could be applied to a larger population of red giants without a reliable period spacing measurement.
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