I. Star Formation & Evolution in AGN Disks
Gravitational instability (GI) occurs in accretion disks where the temperature is low and the density is high. This mechanism is believed to form gas giants in the outer regions of protoplanetary disks (Boss 1997) and stars in the outskirts of AGN disks. Previous numerical studies, often based on simple gas equations of state and global Newtonian cooling functions, have concluded that fragmentation can be avoided when the cooling timescale exceeds a certain threshold. However, our 3D shearing box, radiation hydrodynamic simulations show that even with long cooling times, fragmentation can occur when the disk is dominated by radiation pressure, making star formation easier than previously thought. When the cooling timescale is short, the typical fragment mass can differ significantly from the total Jeans mass due to rapid diffusion, as radiation can no longer behave as an adiabatic fluid.
Density (left) and radiation pressure fraction (right) distributions in typical fragmentation simulations. The clumps are expected to further contract and form stars/black holes or binaries.
Once they form, the accretion of AGN stars from the disk background is also quite complex. We used RHD simulation of stellar envelopes to discuss different regimes of accretion from an isotropic background with finite density and temperature. Applying our results to realistic environments, moderately massive stars embedded in AGN disks typically accrete in the fast-diffusion regime, where not only the intrinsic luminosity contributes a reduction in effective gravity, but also feedback from other energy fluxes (gravitational & thermal, the former of which is analogous to Eddington feedback for black holes).
Left: Density, temperature and radial velocity fluctuations in quasi-steady state for our stellar accretion simulations. Right: Time evolution of angle-averaged radial profiles (density, temperature, mass accretion rate and optical depth).
Depending on the currently poorly understood compositional mixing in the radiative layer, AGN stars may or may not remain on the hydrogen-rich main sequence by recycling nuclear waste with the disk reservoir. However, the differences between the 'immortal' and 'impermanent' scenarios can be reflected in AGN disk profiles through a key parameter that represents the fraction of gas removed from the disk accretion rate per unit of surface heating. This generalization also serves as a natural bridge between Sirko & Goodman (2003)-like disk models (negligible effective removal) and Thompson et al. (2005)-like disk models (maximum effective removal).
Embedding the star in a real disk geometry with tidal source term, vertical stratification and shear flow. Paper coming soon.
II. Accretion & Migration of Gap-opening Planets
In the context of classical companion-disc interaction theory, we evolve a companion planet/star/black hole embedded in a laminar, locally isothermal accretion disk surrounding the host star/SMBH, adding viscosity to mimick the effect of turbulent advection/diffusion. A massive companion can carve a gap in the surface density profile of the disk close to its vicinity, while the perturbed density profile determines the migration torque. Although this density depletion factor can be calculated self-consistently if the gap is relatively wide and flat (Kanagawa+ 2018), we show in this paper that this estimation could break down if the gap is steep enough for very massive companions, in which case only a few low-order Lindblad resonances at the gap edges contribute effectively to the total migration torque. In conclusion, the intrinsic surface density slope of the disk delicately determines both the pace and direction of very massive planets' type II migration.
How density profile alters the resonance pattern speeds (left) and contribution to total migration torque from individual resonances (right, low m dominates due to higher local densities)
In another series of papers, we conduct 2D and 3D simulations of gas giants on fixed orbits to measure their accretion rates, deriving simple scaling relations that depend on the mass ratio and disk parameters. We highlight that, across a wide parameter space and with appropriate inner boundary conditions, the planet's accretion rate is often capped by the outer disk's accretion rate, while the inner disk becomes depleted on a viscous timescale. We also find that a the eccentricity of the disk requires much larger companion mass to excite in 3D compared to 2D. Additionally, in our investigation of the concurrent accretion and migration of gas giants , we emphasize the significance of accretion torque, demonstrating that gas giants can migrate outward under certain conditions of high viscosity.
Midplane (left) and vertical (right) density distribution / flow pattern around the companion.
III. "Unorthodox" Companion-Disk Interactions
In extreme AGN environments and specific regimes of protoplanetary disks, the traditional picture of a laminar disk with a circular companion is incomplete. In a series of studies, we explored several unconventional factors that could significantly influence conclusions about companion-disk interactions.
- Eccentricity: In the classical picture, the circum-companion disk spin is prograde with respect to the global angular momentum. However, this is not trivial since the Keplerian shear background of the disk is retrograde, and steady tidal perturbation is required to twist that background into the classical circum-companion flow within a few orbital timescales. We used 2D and 3D, adaptive mesh refinement simulations to show that when the companion is eccentric enough, the epicyclic motion could disrupt steady tidal perturbation, and establish a retrograde circum-companion disk. This finding has implications for the spin evolution of AGN-embedded black holes and in-situ formation of retrograde satellites.
- Turbulence: We show in this study that strong turbulence can also disrupt the prograde circum-companion flow, and cause stochastic spin accretion of the companion. On average, this effect tends to reduce the magnitude/dispersion of AGN-embedded Black Holes' spin towards a small residue value, consistent with LIGO-VIRGO measurements. We also find that it could lead to chaotic Type I migration .
- Wind: Recent observations indicate that in the MRI-dead zone of protoplanetary disks, accretion may be driven by MHD winds instead of turbulence. Detailed 3D non-ideal MHD simulations (e.g., Aoyama & Bai 2023) suggest that strong advection of material across a planet-induced gap, in a windy disk, could disrupt classical horseshoe flows and influence corotation torque. By incorporating phenomenological models that capture basic dynamical effects of disk winds into cost-effective 2D hydrodynamic simulations, we perform parameter surveys to examine the dependence of migration torque on accretion parameters in windy disks (paper in prep).
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We also try to look at global signatures of these iteractions that could potentially
manifest in ALMA images of substructured protoplanetary disks.
E.g. eccentric planets,
due to their radial excursion, can produce relatively wide gaps in the dust profile ,
complicating the inference of planet mass from gap widths;
In windy discs, we find that radial advection of materials enhances Rossby Wave Instability at the gap outer edges,
leading to
amplified asymmetries in the dust distribution ,
counteracting the effects of viscosity.
We plan to observe a particular source DM Tau during ALMA Cycle 11 to determine whether the asymmetry of this system is associated with disk winds.
ALMA synthetic images across the viscosity-wind strength parameter space. Colors in the middle panel show proxy for the level of substructure asymmetry (black means completely axisymmetric).
Flow pattern around the companion at larger and larger orbital eccentricities. Color indicates specific angular momentum, red=prograde and blue=retrograde.
Flow pattern around the companion that shows steady progradeness at low turbulence, and stochastic shift between prograde and retrograde at high turbulence.
IV. Preservation of Super-earths from Runaway Accretion
In my first paper, we investigate the effect of pebble isolation on the cooling process of rocky planet cores, before the quasi-steady (thermal) accretion could grow a gas envelope more massive than the core itself and trigger dynamical (runaway) accretion, the latter of which is relevant to fore-mentioned hydrodynamical simulations. We find that as pebbles are trapped in the pressure bump outside the planet core's orbit, they collide to produce small dust that enhances the opacity in the planet's vicinity. This process will effectly prolong the core's cooling process and preserve super-Earths within a few au of the star, while at larger orbital radii, cooling of the core can still be efficient enough to trigger runaway accretion, forming gas giants. This dichotomy is consistent with the inner super-Earth, outer gas giant general picture of exoplanet architecture statistics.
A schematic showing the main idea of the mechanism that we identified: abundant pebbles are trapped in the planet-induced pressure maxima -> a fraction of them fragments into dust and slip through the pressure barrier -> they pollute the planetary atmosphere and slows down gas accretion by elevating opacity.
V. Dust Accumulation at the Magnetospheric Truncation Radius of Protoplanetary Disks
In Paper I, we explored the possibility of dust being trapped at the global pressure and density maxima of the disk, specifically at the inner magnetospheric truncation radius, Rt. Within a limited parameter space where the temperature at Rt is moderate—sufficiently high to allow magnetic coupling but low enough to prevent dust sublimation— two planetesimal formation channels emerge: (i) Breakthough scenario: individual dust particles can coagulate and grow beyond the fragmentation threshold, or (ii) GI scenatio: small dust particles can accumulate until their concentration exceeds unity, triggering strong gravitational instabilities that lead to planetesimal formation. In Paper II, we found that thermal feedback due to the correlation between opacity and concentration of small dust, tends to suppress scenario (ii). These planetesimals may eventually form ultra-short-periodic Vulcan planets.
Schematic illustration of dust evolution in the global pressure maximum induced by the magnetospheric truncation, assuming a relatively low accretion rate such that gas temperature allows dust survival.
VI. Atmosphere Boundary Conditions for Giant Planet Post-formation Evolution
We updated the atmospheric boundary condition tables for gas giants to include treatments for cloud formation and irradiation. Each grid point in these tables represents a plane-parallel solution of multi-frequency radiative transfer equations, which describe the temperature-pressure profile and, notably, the internal entropy at the base of the atmosphere, given the planet's internal effective temperature and surface gravity. My collaborators have developed APPLE, that utilizes these tables to study the post-formation cooling of gas giants towards the present epoch. APPLE functions similarly to stellar evolution codes like MESA but includes updated treatments of the equation of state, convection, and helium rain, making it more suitable for studying Jupiter and Saturn-like exoplanets.
Visualization of boundary condition table statistics applied in evolution models, atmosphere base entropy as a function of effective temperature and surface gravity. Different surfaces correspond to different irradiation levels and helium abundance