Accretion-Driven Evolution of Compact-Object Populations in Gas-Rich Environments and the Origin of Massive Gravitational-Wave Sources

The origin of the most massive gravitational-wave sources remains elusive. We show that gas accretion can be understood as a transport process in mass space, causing compact objects to migrate through a population at rates determined by the underlying growth law. Using a continuity-equation framework, we demonstrate that population evolution is governed primarily by the mass dependence of the accretion rate, $\dot m \propto m^\beta$. Accretion laws with $\beta>1$ naturally produce divergent evolution and generate extended high-mass tails, whereas $\beta<1$ leads to convergent evolution and compresses the population toward a narrower range of masses. We apply this framework to physically motivated accretion regimes and explore their consequences using analytical calculations and Monte Carlo population models. We show that sustained gas accretion can substantially broaden compact-object mass distributions, populate the high-mass end of gravitational-wave catalogs, and alter the mass-ratio distribution of compact-object binaries. In particular, collective accretion within compact binaries drives their mass ratios toward unity. Our results suggest that gaseous environments act as transport media that continuously reshape compact-object populations, providing a natural pathway toward the formation of massive mergers such as GW231123 and the high-mass tails increasingly revealed by gravitational-wave observations.