The relationship between accretion disc age and stellar age and its consequences for protostellar discs

We show that for young stars which are still accreting and for which measurements of stellar age t*, disc mass Mdisc and accretion rate Graphic are available, nominal disc age Graphic is approximately equal to the stellar age t*, at least within the considerable observational scatter. We then consider theoretical models of protostellar discs through analytic and numerical models. A variety of viscosity prescriptions including empirical power laws, magnetohydrodynamic turbulence and gravitational instability were considered within models describing the disc phenomena of dead zones, photoevaporation and planet formation. These models are generally poor fits to the observational data, showing values of tdisc which are too high by factors of 3–10. We then ask whether a systematic error in the measurement of one of the observational quantities might provide a reasonable explanation for this discrepancy. We show that for the observed systems only disc mass shows a systematic dependence on the value of tdisc/t*, and we note that a systematic underestimate of the value of disc mass by a factor of around 3–5 would account for the discrepancy between theory and observations.