2025MNRAS.541.1145L

Gravitational instability (GI) is typically studied in cooling-dominated discs, often modelled using simplified prescriptions such as $\beta$-cooling. In this paper, we investigate the onset and evolution of GI in accretion discs subject to continuous mass injection, combining 1D and 3D numerical simulations. We explore an alternative self-regulation mechanism in which mass replenishment drives the system toward marginal stability $Q\sim 1$. In this regime, the disc establishes a steady-state disc-to-star mass ratio, balancing the mass transported to the central object with that added to the disc. Our 3D simulations reveal that the general scaling predicted from the linear theory are respected, however there are important difference compared to the cooling case in terms of morphology and pattern speed. Unlike the flocculent spirals seen in cooling-driven instability, the power is concentrated towards the dominant modes in infall-driven spirals. Additionally, spiral waves generate at the mass injection location, and propagate at constant pattern speed, unlike in the cooling case. This suggests a fundamental difference in how mass-regulated and cooling-regulated discs behave and transport angular momentum.