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 st ars. 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 accre tion column, so that most of the stellar photosphere is free to radiat e to space. This boundary condition is similar to the limiting case co nsidered by Palla & Stahler for intermediate-mass stars. We argue that for a wide variety of disk mass accretion rates, material will be add ed to the star with relatively small amounts of thermal energy. Protos tellar evolution calculated assuming this ''low-temperature'' limit of accretion generally follows the results of Stahler because of the the rmostatic nature of deuterium fusion, which prevents protostars from c ontracting below a ''birthline'' in the H-R diagram. Our calculated pr otostellar radii tend to fall below Stahler's at higher masses; the ad ditional energy loss from the stellar photosphere in the case of disk accretion tends to make the protostar contract. The low-temperature di sk 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 r adius of the protostellar core is large enough or if rapid disk accret ion (such as might occur during FU Ori outbursts) adds significant amo unts of thermal energy to the star. These possibilities cannot be rule d out by either theoretical arguments or observational constraints at present, so that individual protostars might evolve along a multiplici ty of birthlines with a modest range of luminosity at a given mass. Ou r results indicate that there are large uncertainties in assigning age s for the youngest stars from H-R diagram positions, given the uncerta inty in birthline positions. Our calculations also suggest that the re latively low disk accretion rates characteristic of T Tauri stars belo w the birthline cause low-mass stars to contract only slightly faster than normal Hayashi track evolution, so that ages for older pre-main-s equence stars estimated from H-R diagram positions are relatively secu re.