Coevolution of Dust Growth and Gravitational Instability in Massive Protostellar Disks

Massive protostellar disks are expected to sustain high accretion rates through gravitational instability, while dust growth may modify their opacity, cooling efficiency, and stability. Conversely, the time-dependent and nonaxisymmetric structures produced by gravitational instability may regulate the local conditions for dust growth. However, the coupled evolution of dust growth and gravitational instability in massive protostellar disks has not yet been explored self-consistently. We present two-dimensional hydrodynamic simulations that follow gas dynamics, dust growth, and opacity-dependent radiative cooling in a massive protostellar disk. We find that dust grains rapidly grow to millimeter-centimeter sizes shortly after disk formation, substantially reducing the infrared opacity. The enhanced cooling promotes disk fragmentation and produces more frequent accretion-driven luminosity outbursts than in a model without dust growth, with durations and peak luminosities comparable to those observed in massive protostars. Dust growth is broadly regulated by the fragmentation-limited size in dense disk regions, whereas newly formed outer disk regions and low-density regions deviate from this limit because of finite collision timescales and dust transport. These results suggest that dust growth may facilitate episodic accretion and fragmentation, while gravitationally unstable disk structures in turn regulate the dust growth process.