Accretion in Protoplanetary Disks: The Imprint of Core Properties

In this Letter, we present a theoretical scenario to explain the steep correlation between disk accretion rates and stellar masses observed in pre-main-sequence stars. We show that the correlations and spread observed in the two best-studied regions, ρ Oph and Taurus, can be reproduced by a simple model of single-star formation from a rotating collapsing core and the viscous evolution of the circumstellar disk. In this model, the rate of rotation of the parent core sets the value of the ``centrifugal radius'' within which the infalling matter is loaded onto the surface of the disk. As a consequence, the disk accretion rate measured long after the dispersal of the parental core bears the imprint of the initial conditions of star formation. The observed trend results naturally if, at the onset of the collapse, cores of all masses rotate with the same distribution of angular velocities, measured in units of the breakup rotation rate.