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The fastest-spinning neutron stars in low-mass X-ray binaries, despite havingundergone millions of years of accretion, have been observed to spin well belowthe Keplerian break-up frequency. We simulate the spin evolution of syntheticpopulations of accreting neutron stars in order to assess whether gravitationalwaves can explain this behaviour and provide the distribution of spins that isobserved. We model both persistent and transient accretion and consider twogravitational-wave-production mechanisms that could be present in thesesystems: thermal mountains and unstable $r$-modes. We consider the case of nogravitational-wave emission and observe that this does not match well withobservation. We find evidence for gravitational waves being able to provide theobserved spin distribution; the most promising mechanisms being a permanentquadrupole, thermal mountains and unstable $r$-modes. However, based on theresultant distributions alone it is difficult to distinguish between thecompeting mechanisms.

Population Synthesis of Accreting Neutron Stars Emitting Gravitational Waves