Evolution of the Bolometric Temperature and Luminosity of Young Stellar Objects

We model the broadband emission from a star-disk-envelope system to obtain expressions for the bolometric temperature T_bol and luminosity L_bol as functions of time, from the youngest class 0 protostars to stars on the zero-age main sequence. The model predicts evolution, driven by infall and contraction luminosity, in terms of position on the log T_bol-log L_bol diagram, a close analog of the H-R diagram. The evolutionary tracks depend on the envelope initial conditions, the main-sequence mass of the star, and the envelope dissipation timescale. The model L_bol rises due to infall and then falls due to contraction, while T_bol increases steadily toward the main sequence due to central heating and envelope dissipation. In order to smoothly join the protostellar and pre-main-sequence phases it is necessary to model the termination of infall as gradual rather than sudden. This change reduces the peak infall luminosity for the collapse of a singular isothermal sphere by a factor 4, bringing predicted infall luminosities into better agreement with observations. For stars of main-sequence mass 0.5 M_☉, the model decrease in L_bol from its peak value of ~3 L_☉ at T_bol ~ 250 K (class I) to ~0.4 L_☉ at T_bol ~ 3000 K (class II/III) closely matches the observed decrease in median L_bol for young stellar objects in Chamaeleon, Corona Australis, Lupus, Ophiuchus, and Taurus. The model should be useful for estimating the distributions of mass and age, and for describing the birth history, of stars younger than 1 Myr in well-studied complexes.