Inclined Massive Planets in a Protoplanetary Disc: Gap Opening, Disc Breaking, and Observational Signatures

We carry out 3D hydrodynamical simulations to study planet–disc interactions for inclined high-mass planets, focusing on the disc’s secular evolution induced by the planet. We find that, when the planet is massive enough and the induced gap is deep enough, the disc inside the planet’s orbit breaks from the outer disc. The inner and outer discs precess around the system’s total angular momentum vector independently at different precession rates, which causes significant disc misalignment. We derive the analytical formulae, which are also verified numerically, for: (1) the relationship between the planet mass and the depth/width of the induced gap, (2) the migration and inclination damping rates for massive inclined planets, and (3) the condition under which the inner and outer discs can break and undergo differential precession. Then, we carry out Monte Carlo radiative transfer calculations for the simulated broken discs. Both disc shadowing in near-infrared images and gas kinematics probed by molecular lines [e.g. from the Atacama Large Millimeter/submillimeter Array (ALMA)] can reveal the misaligned inner disc. The relationship between the rotation rate of the disc shadow and the precession rate of the inner disc is also provided. Using our disc breaking condition, we conclude that the disc shadowing due to misaligned discs should be accompanied by deep gaseous gaps (e.g. in Pre/Transitional discs). ... See full text for complete abstract

Planet-driven Spiral Arms in Protoplanetary Disks. I. Formation Mechanism

Protoplanetary disk simulations show that a single planet can excite more than one spiral arm, possibly explaining the recent observations of multiple spiral arms in some systems. In this paper, we explain the mechanism by which a planet excites multiple spiral arms in a protoplanetary disk. Contrary to previous speculations, the formation of both primary and additional arms can be understood as a linear process when the planet mass is sufficiently small. A planet resonantly interacts with epicyclic oscillations in the disk, launching spiral wave modes around the Lindblad resonances. When a set of wave modes is in phase, they can constructively interfere with each other and create a spiral arm. More than one spiral arm can form because such constructive interference can occur for different sets of wave modes, with the exact number and launching position of the spiral arms being dependent on the planet mass as well as the disk temperature profile. Nonlinear effects become increasingly important as the planet mass increases, resulting in spiral arms with stronger shocks and thus larger pitch angles. This is found to be common for both primary and additional arms. When a planet has a sufficiently large mass (gsim3 thermal masses for (h/r) p = 0.1), only two spiral arms form interior to its orbit. The wave modes that would form a tertiary arm for smaller mass planets merge with the primary arm. Improvements in our understanding of the formation of spiral arms can provide crucial insights into the origin of observed spiral arms in protoplanetary disks

Gas and dust hydrodynamical simulations of massive lopsided transition discs - I. Gas distribution

Motivated by lopsided structures observed in some massive transition discs, we have carried out 2D numerical simulations to study vortex structure in massive discs, including the effects of disc self-gravity and the indirect force which is due to the displacement of the central star from the barycenter of the system by the lopsided structure. When only the indirect force is included, we confirm the finding by Mittal & Chiang (2015) that the vortex becomes stronger and can be more than two pressure scale heights wide, as long as the disc-to-star mass ratio is >1%. Such wide vortices can excite strong density waves in the disc and therefore migrate inwards rapidly. However, when disc self-gravity is also considered in simulations, self-gravity plays a more prominent role on the vortex structure. We confirm that when the disc Toomre Q parameter is smaller than pi/(2h), where h is the disc's aspect ratio, the vortices are significantly weakened and their inward migration slows down dramatically. Most importantly, when the disc is massive enough (e.g. Q~3), we find that the lopsided gas structure orbits around the star at a speed significantly slower than the local Keplerian speed. This sub-Keplerian pattern speed can lead to the concentration of dust particles at a radius beyond the lopsided gas structure (as shown in Paper II). Overall, disc self-gravity regulates the vortex structure in massive discs and the radial shift between the gas and dust distributions in vortices within massive discs may be probed by future observations.Comment: 10 pages, 7 figures, accepted for publication in MNRA

Fast Rise of "Neptune-Size" Planets (4−8REarth4-8 R_{\rm Earth}) from P∼10P\sim10 to ∼250\sim250 days -- Statistics of Kepler Planet Candidates Up to ∼0.75AU\sim 0.75 {\rm AU}

We infer the period ($P$) and size ($R_p$) distribution of Kepler transiting planet candidates with $R_p\ge 1 R_{\rm Earth}$ and $P < 250$ days hosted by solar-type stars. The planet detection efficiency is computed by using measured noise and the observed timespans of the light curves for $\sim 120,000$ Kepler target stars. We focus on deriving the shape of planet period and radius distribution functions. We find that for orbital period $P>10$ days, the planet frequency d$N_p$/d$\log$P for "Neptune-size" planets ($R_p = 4-8 R_{\rm Earth}$) increases with period as $\propto P^{0.7\pm0.1}$. In contrast, d$N_p$/d$\log$P for "super-Earth-size" ($2-4 R_{\rm Earth}$) as well as "Earth-size" ($1-2 R_{\rm Earth}$) planets are consistent with a nearly flat distribution as a function of period ($\propto P^{0.11\pm0.05}$ and $\propto P^{-0.10\pm0.12}$, respectively), and the normalizations are remarkably similar (within a factor of $\sim 1.5$ at $50$ days). Planet size distribution evolves with period, and generally the relative fractions for big planets ($\sim 3-10 R_{\rm Earth}$) increase with period. The shape of the distribution function is not sensitive to changes in selection criteria of the sample. The implied nearly flat or rising planet frequency at long period appears to be in tension with the sharp decline at $\sim 100$ days in planet frequency for low mass planets (planet mass $m_p < 30 M_{\rm Earth}$) recently suggested by HARPS survey. Within $250$ days, the cumulative frequencies for Earth-size and super-Earth-size planets are remarkably similar ($\sim 28$ and $25$), while Neptune-size and Jupiter-size planets are $\sim 7$, and $\sim 3$, respectively. A major potential uncertainty arises from the unphysical impact parameter distribution of the candidates.Comment: Accepted by Ap