Detection Prospects of Fast-merging Gravitational Wave Sources in M31

Abstract: It is widely accepted that quite a number of double compact objects (DCOs) in the Milky Way can be identified by future space-based gravitational wave (GW) detectors, while systematic investigations on the detection of the GW sources in nearby galaxies are still lacking. In this paper, we present calculations of potential populations of GW sources for all types of DCOs in the Local Group galaxy M31. For M31, we use an age-dependent model for the evolution of the metallicity and the star-formation rate. By varying assumptions of common-envelope ejection efficiencies and supernova-explosion mechanisms during binary evolution, we make predictions on the properties of DCOs that can be detected by the Laser Interferometer Space Antenna (LISA). Our calculations indicate that a few (a dozen) DCOs are likely to be observed by LISA during its 4 (10) yr mission. We expect that the sources with black-hole components are more likely to be firstly identified during a 4-yr mission since these binaries have relatively large chirp masses, while the systems with white-dwarf components dominate the overall population of detectable GW sources during a 10-yr mission. LISA can only detect very tight fast-merging systems in M31, corresponding to the peak of orbital period distribution from $\sim 2$ min for double white dwarfs to $\sim 20$~min for double black holes.