Disc evolution and the relationship between Lacc and L* in T Tauri stars

We investigate the evolution of accretion luminosity L-acc and stellar luminosity L-* in pre-main-sequence stars. We make the assumption that when the star appears as a Class II object, the major phase of accretion is long past and the accretion disc has entered its asymptotic phase. We use an approximate stellar evolution scheme for accreting pre-main-sequence stars based on Hartmann, Cassen & Kenyon. We show that the observed range of values k = L-acc/L-* between 0.01 and 1 can be reproduced if the values of the disc mass fraction M-disc/M-* at the start of the T Tauri phase lie in the range 0.01-0.2, independent of stellar mass. We also show that the observed upper bound of L-acc similar to L-* is a generic feature of such disc accretion. We conclude that as long as the data uniformly fill the region between this upper bound and observational detection thresholds, then the degeneracies between age, mass and accretion history severely limit the use of this data for constraining possible scalings between disc properties and stellar mass.