2017ApJ...838..151T

We investigate the dust structure of gravitationally unstable disks undergoing mass accretion from the envelope, envisioning its application to Class 0/I young stellar objects (YSOs). We find that the dust disk quickly settles into a steady state and that, compared to a disk with interstellar medium (ISM) dust-to-gas mass ratio and micron-sized dust, the dust mass in the steady state decreases by a factor of 1/2 to 1/3, and the dust thermal emission decreases by a factor of 1/3 to 1/5. The latter decrease is caused by dust depletion and opacity decrease owing to dust growth. Our results suggest that the masses of gravitationally unstable disks in Class 0/I YSOs are underestimated by a factor of 1/3 to 1/5 when calculated from the dust thermal emission assuming an ISM dust-to-gas mass ratio and micron-sized dust opacity, and that a larger fraction of disks in Class 0/I YSOs is gravitationally unstable than was previously believed. We also investigate the orbital radius r_P within which planetesimals form via coagulation of porous dust aggregates and show that r_P becomes ∼20 au for a gravitationally unstable disk around a solar mass star. Because r_P increases as the gas surface density increases and a gravitationally unstable disk has maximum gas surface density, r_P∼20 au is the theoretical maximum radius for planetesimal formation. We suggest that planetesimal formation in the Class 0/I phase is preferable to that in the Class II phase because a large amount of dust is supplied by envelope-to-disk accretion.