Disk accretion and the stellar birthline

We present a simplified analysis of some effects of disk accretion on the early evolution of fully convective, low-mass pre-main-sequence stars. Our analysis builds on the previous seminal work of Stahler, but it differs in that the accretion of material occurs over a small area of the stellar surface, such as through a disk or magnetospheric accretion column, so that most of the stellar photosphere is free to radiate to space. This boundary condition is similar to the limiting case considered by Palla & Stahler for intermediate-mass stars. We argue that for a wide variety of disk mass accretion rates, material will be added to the star with relatively small amounts of thermal energy. Protostellar evolution calculated assuming this ''low-temperature'' limit of accretion generally follows the results of Stahler because of the thermostatic nature of deuterium fusion, which prevents protostars from contracting below a ''birthline'' in the H-R diagram. Our calculated protostellar radii tend to fall below Stahler's at higher masses; the additional energy loss from the stellar photosphere in the case of disk accretion tends to make the protostar contract. The low-temperature disk accretion evolutionary tracks never fall below the deuterium-fusion birthline until the internal deuterium is depleted, but protostellar tracks can lie above the birthline in the H-R diagram if the initial radius of the protostellar core is large enough or if rapid disk accretion (such as might occur during FU Ori outbursts) adds significant amounts of thermal energy to the star. These possibilities cannot be ruled out by either theoretical arguments or observational constraints at present, so that individual protostars might evolve along a multiplicity of birthlines with a modest range of luminosity at a given mass. Our results indicate that there are large uncertainties in assigning ages for the youngest stars from H-R diagram positions, given the uncertainty in birthline positions. Our calculations also suggest that the relatively low disk accretion rates characteristic of T Tauri stars below the birthline cause low-mass stars to contract only slightly faster than normal Hayashi track evolution, so that ages for older pre-main-sequence stars estimated from H-R diagram positions are relatively secure.