What is the Mass of a Gap-Opening Planet?

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. Combing 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 $M_{\rm p}^2/\alpha$, where $M_{\rm p}$ is the mass of the gap-opening planet and $\alpha$ 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 $\alpha=10^{-3}$, the derived planet mass in all cases are roughly between 0.1-1 $M_{\rm J}$.Comment: 40 pages (single column), 14 figures, 2 tables, ApJ publishe

Quantum Dynamical Phase Transition in a Spin-Orbit Coupled Bose Condensate

Spin-orbit coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different experimentally controllable parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on an external perturbation to induce resonant couplings between the magnetized phases, and predict the novel quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the strength of external perturbation is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a quantum dynamical phase transition, with the critical point behavior being exactly solvable. From the numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.Comment: 9 pages, 4 figures, plus supplementary materia

Inner Super-Earths, Outer Gas Giants: How Pebble Isolation and Migration Feedback Keep Jupiters Cold

The majority of gas giants (planets of masses $\gtrsim10^2 M_\oplus$) are found to reside at distances beyond $\sim1$ au from their host stars. Within 1 au, the planetary population is dominated by super-Earths of $2-20 M_\oplus$. We show that this dichotomy between inner super-Earths and outer gas giants can be naturally explained should they form in nearly inviscid disks. In laminar disks, a planet can more easily repel disk gas away from its orbit. The feedback torque from the pile-up of gas inside the planet's orbit slows down and eventually halts migration. A pressure bump outside the planet's orbit traps pebbles and solids, starving the core. Gas giants are born cold and stay cold: more massive cores are preferentially formed at larger distances, and they barely migrate under disk feedback. We demonstrate this using 2D hydrodynamical simulations of disk-planet interaction lasting up to $10^5$ years: we track planet migration and pebble accretion until both come to an end by disk feedback. Whether cores undergo runaway gas accretion to become gas giants or not is determined by computing 1D gas accretion models. Our simulations show that in an inviscid minimum mass solar nebula, gas giants do not form inside $\sim$0.5 au, nor can they migrate there while the disk is present. We also explore the dependence on disk mass, and find that gas giants form further out in less massive disks.Comment: Accepted to Ap