Long-term Evolution of Photoevaporating Protoplanetary Disks

We perform calculations of our one-dimensional, two-zone disk model to study the long-term evolution of the circumstellar disk. In particular, we adopt published photoevaporation prescriptions and examine whether the photoevaporative loss alone, coupled with a range of initial angular momenta of the protostellar cloud, can explain the observed decline of the frequency of optically-thick dusty disks with increasing age. In the parameter space we explore, disks have accreting and/or non-accreting transitional phases lasting of $\lesssim20 %$ of their lifetime, which is in reasonable agreement with observed statistics. Assuming that photoevaporation controls disk clearing, we find that initial angular momentum distribution of clouds needs to be weighted in favor of slowly rotating protostellar cloud cores. Again, assuming inner disk dispersal by photoevaporation, we conjecture that this skewed angular momentum distribution is a result of fragmentation into binary or multiple stellar systems in rapidly-rotating cores. Accreting and non-accreting transitional disks show different evolutionary paths on the $\dot{M}-R_{\rm wall}$ plane, which possibly explains the different observed properties between the two populations. However, we further find that scaling the photoevaporation rates downward by a factor of 10 makes it difficult to clear the disks on the observed timescales, showing that the precise value of the photoevaporative loss is crucial to setting the clearing times. While our results apply only to pure photoevaporative loss (plus disk accretion), there may be implications for models in which planets clear disks preferentially at radii of order 10 AU.