ABSTRACT 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 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.
ABSTRACT Recently, high angular resolution imaging instruments such as SPHERE and GPI have discovered many spiral-arm-like features in near-infrared scattered-light images of protoplanetary disks. ...Theory and simulations have suggested that these arms are most likely excited by planets forming in the disks; however, a quantitative relation between the arm-to-disk brightness contrast and planet mass is still missing. Using 3D hydrodynamics and radiative transfer simulations, we examine the morphology and contrast of planet-induced arms in disks. We find a power-law relation for the face-on arm contrast (δmax) as a function of planet mass ( ) and disk aspect ratio (h/r): . With current observational capabilities, at a 30 au separation, the minimum planet mass for driving detectable arms in a disk around a 1 Myr, 1 star at 140 pc at low inclinations is around Saturn mass. For planets more massive than Neptune masses, they typically drive multiple arms. Therefore, in observed disks with spirals, it is unlikely that each spiral arm originates from a different planet. We also find that only massive perturbers with at least multi-Jupiter masses are capable of driving bright arms with as found in SAO 206462, MWC 758, and LkH 330, and these arms do not follow linear wave propagation theory. Additionally, we find that the morphology and contrast of the primary and secondary arms are largely unaffected by a modest level of viscosity with . Finally, the contrast of the arms in the SAO 206462 disk suggests that the perturber SAO 206462 b at ∼100 au is about in mass.
High-contrast imaging instruments such as GPI and SPHERE are discovering gap structures in protoplanetary disks at an ever faster pace. Some of these gaps may be opened by planets forming in the ...disks. In order to constrain planet formation models using disk observations, it is crucial to find a robust way to quantitatively back out the properties of the gap-opening planets, in particular their masses, from the observed gap properties, such as their depths and widths. Combining 2D and 3D hydrodynamics simulations with 3D radiative transfer simulations, we investigate the morphology of planet-opened gaps in near-infrared scattered-light images. Quantitatively, we obtain correlations that directly link intrinsic gap depths and widths in the gas surface density to observed depths and widths in images of disks at modest inclinations under finite angular resolution. Subsequently, the properties of the surface density gaps enable us to derive the disk scale height at the location of the gap h, and to constrain the quantity Mp2/ , where Mp is the mass of the gap-opening planet and characterizes the viscosity in the gap. As examples, we examine the gaps recently imaged by VLT/SPHERE, Gemini/GPI, and Subaru/HiCIAO in HD 97048, TW Hya, HD 169142, LkCa 15, and RX J1615.3-3255. Scale heights of the disks and possible masses of the gap-opening planets are derived assuming each gap is opened by a single planet. Assuming = 10−3, the derived planet masses in all cases are roughly between 0.1 and 1 MJ.
Two longstanding problems in planet formation include (1) understanding how planets survive migration, and (2) articulating the process by which protoplanetary disks disperse-and in particular how ...they accrete onto their central stars. We can go a long way toward solving both problems if the disk gas surrounding planets has no intrinsic diffusivity ("viscosity"). In inviscid, laminar disks, a planet readily repels gas away from its orbit. On short timescales, zero viscosity gas accumulates inside a planet's orbit to slow Type I migration by orders of magnitude. On longer timescales, multiple super-Earths (distributed between, say, ∼0.1-10 au) can torque inviscid gas out of interplanetary space, either inward to feed their stars, or outward to be blown away in a wind. We explore this picture with 2D hydrodynamics simulations of Earths and super-Earths embedded in inviscid disks, confirming their slow/stalled migration even under gas-rich conditions, and showing that disk transport rates range up to and scale as , where is the disk surface density and Mp is the planet mass. Gas initially sandwiched between two planets is torqued past both into the inner and outer disks. In sum, sufficiently compact systems of super-Earths can clear their natal disk gas in a dispersal history that may be complicated and non-steady but which conceivably leads over Myr timescales to large gas depletions similar to those characterizing transition disks.
Abstract
Vortices are readily produced by hydrodynamical instabilities, such as the Rossby wave instability, in protoplanetary disks. However, large-scale asymmetries indicative of dust-trapping ...vortices are uncommon in submillimeter continuum observations. One possible explanation is that vortices have short lifetimes. In this paper, we explore how radiative cooling can lead to vortex decay. Elliptical vortices in Keplerian disks go through adiabatic heating and cooling cycles. Radiative cooling modifies these cycles and generates baroclinicity that changes the potential vorticity of the vortex. We show that the net effect is typically a spin down, or decay, of the vortex for a subadiabatic radial stratification. We perform a series of two-dimensional shearing box simulations, varying the gas cooling (or relaxation) time,
t
cool
, and initial vortex strength. We measure the vortex decay half-life,
t
half
, and find that it can be roughly predicted by the timescale ratio
t
cool
/
t
turn
, where
t
turn
is the vortex turnaround time. Decay is slow in both the isothermal (
t
cool
≪
t
turn
) and adiabatic (
t
cool
≫
t
turn
) limits; it is fastest when
t
cool
∼ 0.1
t
turn
, where
t
half
is as short as ∼300 orbits. At tens of astronomical units where disk rings are typically found,
t
turn
is likely much longer than
t
cool
, potentially placing vortices in the fast decay regime.
ABSTRACT 3D modifications to the well-studied 2D flow topology around an embedded planet have the potential to resolve long-standing problems in planet formation theory. We present a detailed ...analysis of the 3D isothermal flow field around a 5 Earth-mass planet on a fixed circular orbit, simulated using our graphics processing unit hydrodynamics code PEnGUIn. We find that, overall, the horseshoe region has a columnar structure extending vertically much beyond the Hill sphere of the planet. This columnar structure is only broken for some of the widest horseshoe streamlines, along which high altitude fluid descends rapidly into the planet's Bondi sphere, performs one horseshoe turn, and exits the Bondi sphere radially in the midplane. A portion of this flow exits the horseshoe region altogether, which we refer to as the "transient" horseshoe flow. The flow continues as it rolls up into a pair of up-down symmetric horizontal vortex lines shed into the wake of the planet. This flow, unique to 3D, affects both planet accretion and migration. It prevents the planet from sustaining a hydrostatic atmosphere due to its intrusion into the Bondi sphere, and leads to a significant corotation torque on the planet, unanticipated by 2D analysis. In the reported simulation, starting with a radial surface density profile, this torque is positive and partially cancels with the negative differential Lindblad torque, resulting in a factor of three slower planet migration rate. Finally, we report 3D effects can be suppressed by a sufficiently large disk viscosity, leading to results similar to 2D.
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 submicron 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 ∼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 submicron 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.
The wide, deep cavities of transition disks are often believed to have been hollowed out by nascent planetary systems. PDS 70, a ∼5 Myr old transition disk system in which a multi-Jupiter-mass planet ...candidate at 22 au coexists with a ∼30 au gas and ∼60 au dust-continuum gap, provides a valuable case study for this hypothesis. Using the PEnGUIn hydrodynamics code, we simulate the orbital evolution and accretion of PDS 70b in its natal disk. When the accreting planet reaches about 2.5 Jupiter masses, it spontaneously grows in eccentricity and consumes material from a wide swathe of the PDS 70 disk; radiative transfer post-processing with DALI shows that this accurately reproduces the observed gap profile. Our results demonstrate that super-Jupiter planets can single-handedly carve out transition disk cavities, and indicate that the high eccentricities measured for such giants may be a natural consequence of disk-planet interaction.
Circumplanetary disks (CPDs) may be essential to the formation of planets, regulating their spin and accretion evolution. We perform a series of 3D hydrodynamics simulations in both the isothermal ...and adiabatic limits to systematically measure the rotation rates, sizes, and masses of CPDs as functions of , the ratio of the planet mass to the disk thermal mass. Our ranges from 0.1 to 4; for our various disk temperatures, this corresponds to planet masses between one Earth mass and four Jupiter masses. Within this parameter space, we find that isothermal CPDs are disky and bound within ∼10% of the planet's Bondi radius , with the innermost in full rotational support. Adiabatic CPDs are spherical (and therefore not actually "disks"), bound within , and mainly pressure-supported, with rotation rates scaling linearly with extrapolation suggests full rotational support of adiabatic envelopes at . Fast rotation and 3D supersonic flow render isothermal CPDs significantly different in structure from-and orders of magnitude less massive than-their 1D isothermal hydrostatic counterparts. Inside a minimum-mass solar nebula, even a maximally cooled, isothermal CPD around a 10 Earth-mass core may have less than one Earth mass, suggesting that gas giant formation may hinge on angular momentum transport processes in CPDs. Our CPD sizes and masses appear consistent with the regular satellites orbiting solar system giants.
Abstract
High-resolution imaging of protoplanetary disks has unveiled a rich diversity of spiral structure, some of which may arise from disk-planet interaction. Using 3D hydrodynamics with
β
cooling ...to a vertically stratified background, as well as radiative-transfer modeling, we investigate the temperature rise in planet-driven spirals. In rapidly cooling disks, the temperature rise is dominated by a contribution from stellar irradiation, 0.3%–3% inside the planet radius but always < 0.5% outside. When cooling time equals or exceeds dynamical time, however, this is overwhelmed by hydrodynamic
PdV
work, which introduces a ∼10%–20% perturbation within a factor of ∼2 from the planet’s orbital radius. We devise an empirical fit of the spiral amplitude
Δ
(
T
)
=
(
M
p
/
M
th
)
c
(
f
PdV
e
−
t
arm
/
t
c
+
f
rad
)
to take into account both effects. Where cooling is slow, we find also that temperature perturbations from buoyancy spirals—a strictly 3D, nonisothermal phenomenon—become nearly as strong as those from Lindblad spirals, which are amenable to 2D and isothermal studies. Our findings may help explain observed thermal features in disks like TW Hydrae and CQ Tauri, and underscore that 3D effects have a qualitatively important effect on disk structure.
PDF
