The effects of disk self-gravity and radiative cooling on the formation of gaps and spirals by young planets

We have carried out two-dimensional hydrodynamical simulations to study the effects of disk self-gravity and radiative cooling on the formation of gaps and spirals. (1) With disk self-gravity included, we find stronger, more tightly-wound spirals and deeper gaps in more massive disks. The deeper gaps are due to the larger Angular Momentum Flux (AMF) of the waves excited in more massive disks, as expected from the linear theory. The position of the secondary gap does not change, provided that the disk is not extremely massive ($Q \gtrsim 2$). (2) With radiative cooling included, the excited spirals become monotonically more open (less tightly-wound) as the disk's cooling timescale increases. On the other hand, the amplitude and strength of the spirals decrease when the cooling time increases from a small value to $\sim 1/\Omega$, but then the amplitude starts to increase again when the cooling time continues to increase. This indicates that radiative dissipation becomes important for waves with $T_{cool}\sim$ 1. Consequently, the induced primary gap is narrower and the secondary gap becomes significantly shallower when the cooling time becomes $\sim 1/\Omega$. When the secondary gap is present, the position of it moves to the inner disk from the fast cooling cases to the slow cooling cases. The dependence of gap properties on the cooling timescale (e.g. in AS 209) provides a new way to constrain the disk optical depth and thus disk surface density.