Sub-Neptune Formation: The View from Resonant Planets

The orbital period ratios of neighbouring sub-Neptunes are distributed asymmetrically near first-order resonances. There are deficits of systems---"troughs" in the period ratio histogram---just short of commensurability, and excesses---"peaks"---just wide of it. We reproduce quantitatively the strongest peak-trough asymmetries, near the 3:2 and 2:1 resonances, using dissipative interactions between planets and their natal discs. Disc eccentricity damping captures bodies into resonance and clears the trough, and when combined with disc-driven convergent migration, draws planets initially wide of commensurability into the peak. The migration implied by the magnitude of the peak is modest; reductions in orbital period are $\sim$10\%, supporting the view that sub-Neptunes complete their formation more-or-less in situ. Once captured into resonance, sub-Neptunes of typical mass $\sim$$5$--$15 M_{\oplus}$ stay captured (contrary to an earlier claim), as they are immune to the overstability that afflicts lower mass planets. Driving the limited, short-scale migration is a gas disc depleted in mass relative to a solar-composition disc by 3--5 orders of magnitude. Such gas-poor but not gas-empty environments are quantitatively consistent with sub-Neptune core formation by giant impacts (and not, e.g., pebble accretion). While disc-planet interactions at the close of the planet formation era adequately explain the 3:2 and 2:1 asymmetries at periods $\gtrsim$ $5$--$15$ days, subsequent modification by stellar tides appears necessary at shorter periods, particularly for the 2:1.Comment: Accepted to MNRA

The End of Runaway: How Gap Opening Limits the Final Masses of Gas Giants

Gas giants are thought to form by runaway accretion: an instability driven by the self-gravity of growing atmospheres that causes accretion rates to rise super-linearly with planet mass. Why runaway should stop at a Jupiter or any other mass is unknown. We consider the proposal that final masses are controlled by circumstellar disc gaps (cavities) opened by planetary gravitational torques. We develop a fully time-dependent theory of gap formation and couple it self-consistently to planetary growth rates. When gaps first open, planetary torques overwhelm viscous torques, and gas depletes as if it were inviscid. In low-viscosity discs, of the kind motivated by recent observations and theory, gaps stay predominantly in this inviscid phase and planet masses finalize at $M_{\rm final}/M_\star\sim(\Omega t_{\rm disc})^{0.07}(H/a)^{2.73}(G\rho_0/\Omega^2)^{1/3}$, with $M_\star$ the host stellar mass, $\Omega$ the planet's orbital angular velocity, $t_{\rm disc}$ the gas disc's lifetime, $H/a$ its aspect ratio, and $\rho_0$ its unperturbed density. This final mass is independent of the dimensionless viscosity $\alpha$ and applies to large orbital distances, typically beyond $\sim$10 AU, where disc scale heights exceed planet radii. It evaluates to a few Jupiter masses at 10-100 AU, increasing gradually with distance as gaps become harder to open.Comment: Accepted to MNRA

Gap Opening in 3D: Single Planet Gaps

Giant planets can clear deep gaps when embedded in 2D (razor-thin) viscous circumstellar disks. We show by direct simulation that giant planets are just as capable of carving out gaps in 3D. Surface density maps are similar between 2D and 3D, even in detail. In particular, the scaling $\Sigma_{\rm gap} \propto q^{-2}$ of gap surface density with planet mass, derived from a global "zero-dimensional" balance of Lindblad and viscous torques, applies equally well to results obtained at higher dimensions. Our 3D simulations reveal extensive, near-sonic, meridional flows both inside and outside the gaps; these large-scale circulations might bear on disk compositional gradients, in dust or other chemical species. At high planet mass, gap edges are mildly Rayleigh unstable and intermittently shed streams of material into the gap - less so in 3D than in 2D.Comment: Accepted for publication in Ap

Stellar Winds and Dust Avalanches in the AU Mic Debris Disk

We explain the fast-moving, ripple-like features in the edge-on debris disk orbiting the young M dwarf AU Mic. The bright features are clouds of sub-micron dust repelled by the host star's wind. The clouds are produced by avalanches: radial outflows of dust that gain exponentially more mass as they shatter background disk particles in collisional chain reactions. The avalanches are triggered from a region a few AU across -- the "avalanche zone" -- located on AU Mic's primary "birth" ring, at a true distance of $\sim$35 AU from the star but at a projected distance more than a factor of 10 smaller: the avalanche zone sits directly along the line of sight to the star, on the side of the ring nearest Earth, launching clouds that disk rotation sends wholly to the southeast, as observed. The avalanche zone marks where the primary ring intersects a secondary ring of debris left by the catastrophic disruption of a progenitor up to Varuna in size, less than tens of thousands of years ago. Only where the rings intersect are particle collisions sufficiently violent to spawn the sub-micron dust needed to seed the avalanches. We show that this picture works quantitatively, reproducing the masses, sizes, and velocities of the observed escaping clouds. The Lorentz force exerted by the wind's magnetic field, whose polarity reverses periodically according to the stellar magnetic cycle, promises to explain the observed vertical undulations. The timescale between avalanches, about 10 yr, might be set by time variability of the wind mass-loss rate or, more speculatively, by some self-regulating limit cycle.Comment: Accepted to Ap

Eccentric Jupiters via Disk-Planet Interactions

Numerical hydrodynamics calculations are performed to determine conditions under which giant planet eccentricities can be excited by parent gas disks. Unlike in other studies, Jupiter-mass planets are found to have their eccentricities amplified --- provided their orbits start eccentric. We disentangle the web of co-rotation, co-orbital, and external resonances to show that this finite-amplitude instability is consistent with that predicted analytically. Ellipticities can grow until they reach of order the disk's aspect ratio, beyond which the external Lindblad resonances that excite eccentricity are weakened by the planet's increasingly supersonic epicyclic motion. Forcing the planet to still larger eccentricities causes catastrophic eccentricity damping as the planet collides into gap walls. For standard parameters, the range of eccentricities for instability is modest; the threshold eccentricity for growth ($\sim$$0.04$) is not much smaller than the final eccentricity to which orbits grow ($\sim$$0.07$). If this threshold eccentricity can be lowered (perhaps by non-barotropic effects), and if the eccentricity driving documented here survives in 3D, it may robustly explain the low-to-moderate eccentricities $\lesssim 0.1$ exhibited by many giant planets (including Jupiter and Saturn), especially those without planetary or stellar companions.Comment: Accepted to ApJ with added references and minor revision

Breeding Super-Earths and Birthing Super-Puffs in Transitional Disks

The riddle posed by super-Earths (1-4$R_\oplus$, 2-20$M_\oplus$) is that they are not Jupiters: their core masses are large enough to trigger runaway gas accretion, yet somehow super-Earths accreted atmospheres that weigh only a few percent of their total mass. We show that this puzzle is solved if super-Earths formed late, as the last vestiges of their parent gas disks were about to clear. This scenario would seem to present fine-tuning problems, but we show that there are none. Ambient gas densities can span many (up to 9) orders of magnitude, and super-Earths can still robustly emerge after $\sim$0.1-1 Myr with percent-by-weight atmospheres. Super-Earth cores are naturally bred in gas-poor environments where gas dynamical friction has weakened sufficiently to allow constituent protocores to merge. So little gas is present at the time of core assembly that cores hardly migrate by disk torques: formation of super-Earths can be in situ. The picture --- that close-in super-Earths form in a gas-poor (but not gas-empty) inner disk, fed continuously by gas that bleeds inward from a more massive outer disk --- recalls the largely evacuated but still accreting inner cavities of transitional protoplanetary disks. We also address the inverse problem presented by super-puffs: an uncommon class of short-period planets seemingly too voluminous for their small masses (4-10$R_\oplus$, 2-6$M_\oplus$). Super-puffs easily acquire their thick atmospheres as dust-free, rapidly cooling worlds outside $\sim$1 AU where nebular gas is colder, less dense, and therefore less opaque. Unlike super-Earths which can form in situ, super-puffs migrated in to their current orbits; they are expected to form the outer links of mean-motion resonant chains, and to exhibit greater water content. We close by confronting observations and itemizing remaining questions.Comment: Accepted to Ap

Strong Lefschetz property under reduction

Let n>1 and G be the group SU(n) or Sp(n). This paper constructs compact symplectic manifolds whose symplectic quotient under a Hamiltonian G-action does not inherit the strong Lefschetz property.Comment: 9 pages. Added some computation detail

To Cool is to Accrete: Analytic Scalings for Nebular Accretion of Planetary Atmospheres

Planets acquire atmospheres from their parent circumstellar disks. We derive a general analytic expression for how the atmospheric mass grows with time $t$, as a function of the underlying core mass $M_{\rm core}$ and nebular conditions, including the gas metallicity $Z$. Planets accrete as much gas as can cool: an atmosphere's doubling time is given by its Kelvin-Helmholtz time. Dusty atmospheres behave differently from atmospheres made dust-free by grain growth and sedimentation. The gas-to-core mass ratio (GCR) of a dusty atmosphere scales as GCR $\propto t^{0.4} M_{\rm core}^{1.7} Z^{-0.4} \mu_{\rm rcb}^{3.4}$, where $\mu_{\rm rcb} \propto 1/(1-Z)$ (for $Z$ not too close to 1) is the mean molecular weight at the innermost radiative-convective boundary. This scaling applies across all orbital distances and nebular conditions for dusty atmospheres; their radiative-convective boundaries, which regulate cooling, are not set by the external environment, but rather by the internal microphysics of dust sublimation, H$_2$ dissociation, and the formation of H$^-$. By contrast, dust-free atmospheres have their radiative boundaries at temperatures $T_{\rm rcb}$ close to nebular temperatures $T_{\rm out}$, and grow faster at larger orbital distances where cooler temperatures, and by extension lower opacities, prevail. At 0.1 AU in a gas-poor nebula, GCR $\propto t^{0.4} T_{\rm rcb}^{-1.9} M_{\rm core}^{1.6} Z^{-0.4} \mu_{\rm rcb}^{3.3}$, while beyond 1 AU in a gas-rich nebula, GCR $\propto t^{0.4} T_{\rm rcb}^{-1.5} M_{\rm core}^1 Z^{-0.4}\mu_{\rm rcb}^{2.2}$. We confirm our analytic scalings against detailed numerical models for objects ranging in mass from Mars (0.1 $M_\oplus$) to the most extreme super-Earths (10-20 $M_\oplus$), and explain why heating from planetesimal accretion cannot prevent the latter from undergoing runaway gas accretion.Comment: 9 pages, 6 figures, accepted to Ap

A Primer on Unifying Debris Disk Morphologies

A "minimum model" for debris disks consists of a narrow ring of parent bodies, secularly forced by a single planet on a possibly eccentric orbit, colliding to produce dust grains that are perturbed by stellar radiation pressure. We demonstrate how this minimum model can reproduce a wide variety of disk morphologies imaged in scattered starlight. Five broad categories of disk shape can be captured: "rings," "needles," "ships-and-wakes," "bars," and "moths (a.k.a. fans)," depending on the viewing geometry. Moths can also sport "double wings." We explain the origin of morphological features from first principles, exploring the dependence on planet eccentricity, disk inclination dispersion, and the parent body orbital phases at which dust grains are born. A key determinant in disk appearance is the degree to which dust grain orbits are apsidally aligned. Our study of a simple steady-state (secularly relaxed) disk should serve as a reference for more detailed models tailored to individual systems. We use the intuition gained from our guidebook of disk morphologies to interpret, informally, the images of a number of real-world debris disks. These interpretations suggest that the farthest reaches of planetary systems are perturbed by eccentric planets, possibly just a few Earth masses each.Comment: Accepted to ApJ; minor edits mad

Gravito-Turbulent Disks in 3D: Turbulent Velocities vs. Depth

Characterizing turbulence in protoplanetary disks is crucial for understanding how they accrete and spawn planets. Recent measurements of spectral line broadening promise to diagnose turbulence, with different lines probing different depths. We use 3D local hydrodynamic simulations of cooling, self-gravitating disks to resolve how motions driven by "gravito-turbulence" vary with height. We find that gravito-turbulence is practically as vigorous at altitude as at depth: even though gas at altitude is much too rarefied to be itself self-gravitating, it is strongly forced by self-gravitating overdensities at the midplane. The long-range nature of gravity means that turbulent velocities are nearly uniform vertically, increasing by just a factor of 2 from midplane to surface, even as the density ranges over nearly three orders of magnitude. The insensitivity of gravito-turbulence to height contrasts with the behavior of disks afflicted by the magnetorotational instability (MRI); in the latter case, non-circular velocities increase by at least a factor of 15 from midplane to surface, with various non-ideal effects only magnifying this factor. The distinct vertical profiles of gravito-turbulence vs. MRI turbulence may be used in conjunction with measurements of non-thermal linewidths at various depths to identify the source of transport in protoplanetary disks.Comment: Accepted to Ap