Pengfei Tang and Liping Jin
Astrophysical Journal 871, 222 Link to Article [DOI: 10.3847/1538-4357/aafb6f ]
College of Physics, Jilin University Changchun, Jilin 130012, People’s Republic of China
We construct an analytical model of gravitationally unstable protoplanetary disks consisting of three regions: the inner region where the internal dissipation dominates the heating, the intermediate region where the central protostar irradiation dominates, and the outer region where background irradiation dominates. We use this analytical model and an evolutionary numerical model of protoplanetary disks to calculate the cooling time and find out the location of the isothermal region. We investigate the effects of the isothermal region on the disk instability model for giant planet formation. We find that the fragmentation region found in previous studies is contained in the isothermal region of a disk. In this case, the cooling time criterion is not applicable for fragmentation. Therefore, the constraint on the disk instability model caused by the cooling time criterion should be relieved. The viability of the disk instability model is improved. When the isothermal region is considered, the inner boundary of the fragmentation region is extended inward to ~20 au. We also show that if the contribution of the protostar irradiation to the disk surface temperature can be included in the cooling rate, the fragmentation region defined by the cooling time criterion can be extended inward to ~26 au. We find that a disk tends to be isothermal in the region where the cooling time criterion is satisfied. We also find that at the later stage of disk instability, the inner boundary of the fragmentation region is determined by the inner boundary of the gravitationally unstable region.
and
, are depleted. We compare the results of these model calculations with the solid carbon-to-silicon fraction in the solar system. Although we find a carbon depletion gradient, there are some quantitative discrepancies: the model shows a higher value at the position of the asteroid belt and a lower value at the location of Earth. In addition, using the obtained molecular abundance distributions, coupled with line radiative transfer calculations, we make predictions for ALMA to potentially observe the effect of carbon grain destruction in nearby PPDs. The results indicate that HCN,
, and c-
may be good tracers.