A semi-analytic model for the temporal evolution of the episodic disc-to-star accretion rate during star formation

Abstract We develop a semi-analytic formalism for the determination of evolution stellar mass accretion rate specified density and velocity profiles that emerge from runaway collapse prestellar cloud core. In early phase, when infall matter surrounding envelope is substantial, star accumulates primarily because envelope-induced gravitational instability in protostellar disc. this we model isothermal free-fall molecular The disc gains envelope, transports to via mechanism includes episodic bursts according Toomre Q-criterion. later accreted on due torques within spiral structures disc, manner analytic theory suggests has ∝t−6/5. Our provides self-consistent by joining spherical (dominant at earlier stage) with (important stage), accounts presence appropriate times. show using simple example burst mode can provide good match observed distribution bolometric luminosities. framework reproduces key elements detailed numerical simulations aid developing intuition about basic physics as well compare observations.