Strength Of Gravitational Instability Research Articles

The role of the drag force in the gravitational stability of dusty planet-forming disc – II. Numerical simulations

ABSTRACT Young protostellar discs are likely to be both self-gravitating, and to support grain growth to sizes where the particles decoupled from the gas. This combination could lead to short-wavelength fragmentation of the solid component in otherwise non-fragmenting gas discs, forming Earth-mass solid cores during the Class 0/I stages of young stellar object evolution. We use three-dimensional smoothed particle hydrodynamics simulations of two-fluid discs, in the regime where the Stokes number of the particles St > 1, to study how the formation of solid clumps depends on the disc-to-star mass ratio, the strength of gravitational instability, and the Stokes number. Gravitational instability of the simulated discs is sustained by local cooling. We find that the ability of the spiral structures to concentrate solids increases with the cooling time and decreases with the Stokes number, while the relative dynamical temperature between gas and dust of the particles decreases with the cooling time and the disc-to-star mass ratio and increases with the Stokes number. Dust collapse occurs in a subset of high disc mass simulations, yielding clumps whose mass is close to linear theory estimates, namely 1–10 M⊕. Our results suggest that if planet formation occurs via this mechanism, the best conditions correspond to near the end of the self-gravitating phase, when the cooling time is long and the Stokes number close to unity.

Accretion bursts in magnetized gas-dust protoplanetary disks

Aims. Accretion bursts triggered by the magnetorotational instability (MRI) in the innermost disk regions were studied for protoplanetary gas-dust disks that formed from prestellar cores of a various mass Mcore and mass-to-magnetic flux ratio λ. Methods. Numerical magnetohydrodynamics simulations in the thin-disk limit were employed to study the long-term (~1.0 Myr) evolution of protoplanetary disks with an adaptive turbulent α-parameter, which explicitly depends on the strength of the magnetic field and ionization fraction in the disk. The numerical models also feature the co-evolution of gas and dust, including the back-reaction of dust on gas and dust growth. Results. A dead zone with a low ionization fraction of x≲10−13 and temperature on the order of several hundred Kelvin forms in the inner disk soon after its formation, extending from several to several tens of astronomical units depending on the model. The dead zone features pronounced dust rings that are formed due to the concentration of grown dust particles in the local pressure maxima. Thermal ionization of alkaline metals in the dead zone trigger the MRI and associated accretion burst, which is characterized by a sharp rise, small-scale variability in the active phase, and fast decline once the inner MRI-active region is depleted of matter. The burst occurrence frequency is highest in the initial stages of disk formation and is driven by gravitational instability (GI), but it declines with diminishing disk mass-loading from the infalling envelope. There is a causal link between the initial burst activity and the strength of GI in the disk fueled by mass infall from the envelope. We find that the MRI-driven burst phenomenon occurs for λ = 2–10, but diminishes in models with Mcore ≲ M⊙, suggesting a lower limit on the stellar mass for which the MRI-triggered burst can occur. Conclusions. The MRI-triggered bursts occur for a wide range of mass-to-magnetic flux ratios and initial cloud core masses. The burst occurrence frequency is highest in the initial disk formation stage and reduces as the disk evolves from a gravitationally unstable to a viscous-dominated state. The MRI-triggered bursts are intrinsically connected with the dust rings in the inner disk regions, and both can be a manifestation of the same phenomenon, that is to say the formation of a dead zone.

Accretion bursts in low-metallicity protostellar disks

Aims. The early evolution of protostellar disks with metallicities in the Z = 1.0 − 0.01 Z⊙ range was studied with a particular emphasis on the strength of gravitational instability and the nature of protostellar accretion in low-metallicity systems. Methods. Numerical hydrodynamics simulations in the thin-disk limit were employed that feature separate gas and dust temperatures, and disk mass-loading from the infalling parent cloud cores. Models with cloud cores of similar initial mass and rotation pattern but distinct metallicity were considered to distinguish the effect of metallicity from that of the initial conditions. Results. The early stages of disk evolution in low-metallicity models are characterized by vigorous gravitational instability and fragmentation. Disk instability is sustained by continual mass-loading from the collapsing core. The time period that is covered by this unstable stage is much shorter in the Z = 0.01 Z⊙ models than in their higher metallicity counterparts thanks to the higher rates of mass infall caused by higher gas temperatures (which decouple from lower dust temperatures) in the inner parts of collapsing cores. Protostellar accretion rates are highly variable in the low-metallicity models reflecting the highly dynamic nature of the corresponding protostellar disks. The low-metallicity systems feature short but energetic episodes of mass accretion caused by infall of inward-migrating gaseous clumps that form via gravitational fragmentation of protostellar disks. These bursts seem to be more numerous and last longer in the Z = 0.1 Z⊙ models than in the Z = 0.01 Z⊙ case. Conclusions. Variable protostellar accretion with episodic bursts is not a particular feature of solar metallicity disks. It is also inherent to gravitationally unstable disks with metallicities up to 100 times lower than solar.

Accretion in giant planet circumplanetary discs

During the final growth phase of giant planets, accretion is thought to be controlled by a surrounding circumplanetary disk. Current astrophysical accretion disk models rely on hydromagnetic turbulence or gravitoturbulence as the source of effective viscosity within the disk. However, the magnetically-coupled accreting region in these models is so limited that the disk may not support inflow at all radii, or at the required rate. Here, we examine the conditions needed for self-consistent accretion, in which the disk is susceptible to accretion driven by magnetic fields or gravitational instability. We model the disk as a Shakura-Sunyaev $\alpha$ disk and calculate the level of ionisation, the strength of coupling between the field and disk using Ohmic, Hall and Ambipolar diffusevities for both an MRI and vertical field, and the strength of gravitational instability. We find that the standard constant-$\alpha$ disk is only coupled to the field by thermal ionisation within $30\,R_J$ with strong magnetic diffusivity prohibiting accretion through the bulk of the midplane. In light of the failure of the constant-$\alpha$ disk to produce accretion consistent with its viscosity we drop the assumption of constant-$\alpha$ and present an alternate model in which $\alpha$ varies radially according to the level magnetic turbulence or gravitoturbulence. We find that a vertical field may drive accretion across the entire disk, whereas MRI can drive accretion out to $\sim200\,R_J$, beyond which Toomre's $Q=1$ and gravitoturbulence dominates. The disks are relatively hot ($T\gtrsim800\,$K), and consequently massive ($M_{\text{disk}}\sim0.5\,M_J$).

Control of Star Formation in Galaxies by Gravitational Instability

We study gravitational instability and consequent star formation in a wide range of isolated disk galaxies, using three-dimensional smoothed particle hydrodynamics simulations at a resolution sufficient to fully resolve gravitational collapse. Stellar feedback is represented by an isothermal equation of state. Absorbing sink particles are inserted in dynamically bound, converging regions with number density n > 103 cm-3 to directly measure the mass of gravitationally collapsing gas available for star formation. Our models quantitatively reproduce not only the observed Schmidt law, but also the observed star formation threshold in disk galaxies. Our results suggest that the dominant physical mechanism determining the star formation rate is just the strength of gravitational instability, with feedback primarily functioning to maintain a roughly constant effective sound speed.