Supernova (SN) explosions can potentially affect the structure and evolution of circumnuclear disks in active galactic nuclei (AGN). Some previous studies have suggested that a relatively low rate of SN explosions can provide an effective value of alpha viscosity between 0.1 and 1 in AGN accretion disks within a 1 pc scale. In order to test this possibility, we provide some analytic scalings of the evolution of an SN remnant embedded in a differentially rotating smooth disk. We calibrate our estimates using three-dimensional hydrodynamical simulations where the gas is modeled as adiabatic with index γ. Our simulations are suited to include the fact that a fraction of the momentum injected by the SN escapes from the disk into the corona. Based on these results, we calculate the contribution of SN explosions to the effective alpha viscosity, denoted by α SNe, in a model AGN accretion disk, where accretion is driven by the local viscosity α. We find that for AGN galaxies with a central black hole of and a disk with viscosity α = 0.1, the contribution of SN explosions may be as large as , provided that . On the other hand, in the momentum conservation limit, which is valid when the push by the internal pressure of the SN remnant is negligible, we find .

We evaluate the thermal torques exerted on low-mass planets embedded in gaseous protoplanetary discs with thermal diffusion, by means of high-resolution three-dimensional hydrodynamics simulations. We confirm that thermal torques essentially depend on the offset between the planet and its corotation, and find a good agreement with analytic estimates when this offset is small compared to the size of the thermal disturbance. For larger offsets that may be attained in discs with a large pressure gradient or a small thermal diffusivity, thermal torques tend toward an asymptotic value broadly compatible with results from a dynamical friction calculation in an unsheared medium. We perform a convergence study and find that the thermal disturbance must be resolved over typically 10 zones for a decent agreement with analytic predictions. We find that the luminosity at which the net thermal torque changes sign matches that predicted by linear theory within a few percents. Our study confirms that thermal torques usually supersede Lindblad and corotation torques by almost an order of magnitude for low mass planets. As we increase the planetary mass, we find that the ratio of thermal torques to Lindblad and corotation torques is progressively reduced, and that the thermal disturbance is increasingly distorted by the horseshoe flow. Overall, we find that thermal torques are dominant for masses up to an order of magnitude larger than implemented in recent models of planetary population synthesis. We finally briefly discuss the case of stellar or intermediate-mass objects embedded in discs around AGNs.

We study the dynamical evolution of Jupiter and Saturn embedded in a gaseous, solar-nebula-type disc by means of hydrodynamics simulations with the FARGO2D1D code. We study the evolution for different initial separations of the planets' orbits, ∆a SJ , to investigate whether they become captured in mean motion resonance (MMR) and the direction of the subsequent migration of the planet (inward or outward). We also provide an assessment of the planet's orbital dynamics at different epochs of Saturn's growth. We find that the evolution of initially compact orbital configurations is dependent on the value of ∆a SJ . This implies that an evolution as that proposed in the Grand Tack model depends on the precise initial orbits of Jupiter and Saturn and on the timescales for their formation. Capture in the 1:2 MMR and inward or (nearly) stalled migration are highly favoured. Within its limits, our work suggests that the reversed migration, associated with the resonance capture of Jupiter and Saturn, may be a low probability evolutionary scenario, so that other planetary systems with giant planets are not expected to have experienced a Grand Tack-like evolutionary path.

Using time-dependent linear theory, we investigate the morphology of the gravitational wake induced by a binary, whose center of mass moves at velocity V cm against a uniform background of gas. For simplicity, we assume that the binary's components are on circular orbits about their common center of mass. The consequences of dynamical friction is twofold. First, gas dynamical friction may drag the binary's center of mass and cause the binary to migrate. Second, drag forces also induce a braking torque, which causes the orbits of the binary components to shrink. We compute the drag forces acting on one component of the binary due to the gravitational interaction with its own wake. We show that the dynamical friction force responsible to decelerate the binary's center of mass is smaller than it is in the point-mass case because of the loss of gravitational focusing. We show that the braking internal torque depends on the Mach numbers of each binary component about their center of mass, and also on the Mach number of the center of mass of the binary. In general, the internal torque decreases with increasing the velocity of the binary relative to the ambient gas cloud. However, this is not always the case. We also mention the relevance of our results on the period distribution of binaries. Subject headings: binaries: general -black hole physics -hydrodynamics -ISM: general -waves 1 The evolution of binaries in stellar clusters due to the dynamical interactions with other stars has received considerable attention (e.g.,

We evaluate the torque acting on a gravitational perturber on a retrograde circular orbit in the midplane of a gaseous disk. We assume that the mass of this satellite is so low it weakly disturbs the disk (type I migration). The perturber may represent the companion of a binary system with a small mass ratio. We compare the results of hydrodynamical simulations with analytic predictions. Our two-dimensional (2D) simulations indicate that the torque acting on a perturber with softening radius R soft can be accounted for by a scattering approach if R soft < 0.3H, where H is defined as the ratio between the sound speed and the angular velocity at the orbital radius of the perturber. For R soft > 0.3H, the torque may present large and persistent oscillations, but the resultant time-averaged torque decreases rapidly with increasing R soft /H, in agreement with previous analytical studies. We then focus on the torque acting on small-size perturbers embedded in full three-dimensional (3D) disks and argue that the density waves propagating at distances H from the perturber contribute significantly to the torque because they transport angular momentum. We find a good agreement between the torque found in 3D simulations and analytical estimates based on ballistic orbits. We compare the radial migration timescales of prograde versus retrograde perturbers. For a certain range of the perturber's mass and aspect ratio of the disk, the radial migration timescale in the retrograde case may be appreciably shorter than in the prograde case. We also provide the smoothing length required in 2D simulations in order to account for 3D effects.