Star formation in nuclear rings controlled by bar-driven gas inflow

Nuclear rings are sites of intense star formation at the center of barred spiral galaxies. A straightforward but unanswered question is what controls star formation rate (SFR) in nuclear rings. To understand how the ring SFR is related to mass inflow rate, gas content, and background gravitational field, we run a series of semi-global hydrodynamic simulations of nuclear rings, adopting the TIGRESS framework to handle radiative heating and cooling as well as star formation and supernova feedback. We find: 1) when the mass inflow rate is constant, star formation proceeds in a remarkably steady fashion, without showing any burst-quench behavior suggested in the literature; 2) the steady state SFR has a simple linear relationship with the inflow rate rather than the ring gas mass; 3) the midplane pressure balances the weight of the overlying gas and the SFR surface density is linearly correlated with the midplane pressure, consistent with the self-regulated star formation theory. We suggest that the ring SFR is controlled by the mass inflow rate in the first place, while the gas mass adjusts to the resulting feedback in the course of achieving the vertical dynamical equilibrium.