Circumbinary Chaos: Using Pluto's Newest Moon to Constrain the Masses of Nix & Hydra

The Pluto system provides a unique local laboratory for the study of binaries with multiple low mass companions. In this paper, we study the orbital stability of P4, the most recently discovered moon in the Pluto system. This newfound companion orbits near the plane of the Pluto-Charon binary, roughly halfway between the two minor moons Nix and Hydra. We use a suite of few body integrations to constrain the masses of Nix and Hydra, and the orbital parameters of P4. For the system to remain stable over the age of the Solar System, the masses of Nix and Hydra likely do not exceed 5e16 kg and 9e16 kg, respectively. These upper limits assume a fixed mass ratio between Nix and Hydra at the value implied by their median optical brightness. Our study finds that stability is more sensitive to their total mass and that a downward revision of Charon's eccentricity (from our adopted value of 0.0035) is unlikely to significantly affect our conclusions. Our upper limits are an order of magnitude below existing astrometric limits on the masses of Nix and Hydra. For a density at least that of ice, the albedos of Nix and Hydra would exceed 0.3. This constraint implies they are icy, as predicted by giant impact models. Even with these low masses, P4 only remains stable if its eccentricity e < 0.02. The 5:1 commensurability with Charon is particularly unstable, Combining stability constraints with the observed mean motion places the preferred orbit for P4 just exterior to the 5:1 resonance. These predictions will be tested when the New Horizons satellite visits Pluto. Based on the results for the Pluto-Charon system, we expect that circumbinary, multi-planet systems will be more widely spaced than their singleton counterparts. Further, circumbinary exoplanets close to the three-body stability boundary, such as those found by Kepler, are less likely to have other companions nearby.Comment: 12 pages, 7 figure

Formation of the Terrestrial Planets from a Narrow Annulus

We show that the assembly of the Solar System terrestrial planets can be successfully modelled with all of the mass initially confined to a narrow annulus between 0.7 and 1.0 AU. With this configuration, analogues of Mercury and Mars often form from the collisional evolution of material diffusing out of the annulus under the scattering of the forming Earth and Venus analogues. The final systems also possess eccentricities and inclinations that match the observations, without recourse to dynamical friction from remnant small body populations. Finally, the characteristic assembly timescale for Earth analogues is rapid in this model, and consistent with cosmochemical models based on the $^{182}$Hf--$^{182}$W isotopes. The agreement between this model and the observations suggests that terrestrial planet systems may also be formed in `planet traps', as has been proposed recently for the cores of giant planets in our solar system and others.Comment: 37 pages, 16 figures. to appear in Ap

Particle-Gas Dynamics with Athena: Method and Convergence

The Athena MHD code has been extended to integrates the motion of particles coupled with the gas via aerodynamic drag, in order to study the dynamics of gas and solids in protoplanetary disks and the formation of planetesimals. Our particle-gas hybrid scheme is based on a second order predictor-corrector method. Careful treatment of the momentum feedback on the gas guarantees exact conservation. The hybrid scheme is stable and convergent in most regimes relevant to protoplanetary disks. We describe a semi-implicit integrator generalized from the leap-frog approach. In the absence of drag force, it preserves the geometric properties of a particle orbit. We also present a fully-implicit integrator that is unconditionally stable for all regimes of particle-gas coupling. Using our hybrid code, we study the numerical convergence of the non-linear saturated state of the streaming instability. We find that gas flow properties are well converged with modest grid resolution (128 cells per pressure length \eta r for dimensionless stopping time tau_s=0.1), and equal number of particles and grid cells. On the other hand, particle clumping properties converge only at higher resolutions, and finer resolution leads to stronger clumping before convergence is reached. Finally, we find that measurement of particle transport properties resulted from the streaming instability may be subject to error of about 20%.Comment: 33 pages, accepted to ApJ

Dust Settling Instability in Protoplanetary Discs

The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the midplane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the midplane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the midplane. This work presents a range of linear calculations and non-linear simulations, performed with FARGO3D, to assess conditions for DSI growth. We expand on previous linear analyses by including particle size distributions and performing a detailed study of the amount of background turbulence needed to stabilize the DSI. When including binned size distributions, the DSI often produces converged growth rates with fewer bins than the standard SI. With background turbulence, we find that the most favorable conditions for DSI growth are weak turbulence, characterized by $\alpha \lesssim 10^{-6}$ with intermediate-sized grains that settle from one gas scale-height. These conditions could arise during a sudden decrease in disc turbulence following an accretion outburst. Ignoring background turbulence, we performed a parameter survey of local 2D DSI simulations. Particle clumping was either weak or occurred slower than particles settle. Clumping was reduced by a factor of two in a comparison 3D simulation. Overall, our results strongly disfavor the hypothesis that the DSI significantly promotes planetesimal formation. Non-linear simulations of the DSI with different numerical methods could support or challenge these findings

Migration then assembly: Formation of Neptune mass planets inside 1 AU

We demonstrate that the observed distribution of `Hot Neptune'/`Super-Earth' systems is well reproduced by a model in which planet assembly occurs in situ, with no significant migration post-assembly. This is achieved only if the amount of mass in rocky material is $\sim 50$--$100 M_{\oplus}$ interior to 1 AU. Such a reservoir of material implies that significant radial migration of solid material takes place, and that it occur before the stage of final planet assembly. The model not only reproduces the general distribution of mass versus period, but also the detailed statistics of multiple planet systems in the sample. We furthermore demonstrate that cores of this size are also likely to meet the criterion to gravitationally capture gas from the nebula, although accretion is rapidly limited by the opening of gaps in the gas disk. If the mass growth is limited by this tidal truncation, then the scenario sketched here naturally produces Neptune-mass objects with substantial components of both rock and gas, as is observed. The quantitative expectations of this scenario are that most planets in the `Hot Neptune/Super-Earth' class inhabit multiple-planet systems, with characteristic orbital spacings. The model also provides a natural division into gas-rich (Hot Neptune) and gas-poor (Super-Earth) classes at fixed period. The dividing mass ranges from $\sim 3 M_{\oplus}$ at 10 day orbital periods to $\sim 10 M_{\oplus}$ at 100 day orbital periods. For orbital periods $< 10$ days, the division is less clear because a gas atmosphere may be significantly eroded by stellar radiation.Comment: 41 pages in preprint style, 15 figures, final version accepted to Ap

Sterilizable geiger-mueller tubes for space applications final report

Gas and heat sterilizable Geiger-Mueller tubes for space application

Kinematics of solid particles in a turbulent protoplanetary disc

We perform numerical simulations of solid particle motion in a shearing box model of a protoplanetary disc. The accretion flow is turbulent due to the action of the magnetorotational instability. Aerodynamic drag on the particles is modelled using the Epstein law with the gas velocity interpolated to the particle position. The effect of the magnetohydrodynamic turbulence on particle velocity dispersions is quantified for solids of different stopping times t_s, or equivalently, different sizes. The anisotropy of the turbulence is reflected upon the dispersions of the particle velocity components, with the radial component larger than both the azimuthal and vertical components for particles larger than ~ 10 cm (assuming minimum-mass solar nebula conditions at 5 AU). The dispersion of the particle velocity magnitude, as well as that of the radial and azimuthal components, as functions of stopping time, agree with previous analytical results for isotropic turbulence. The relative speed between pairs of particles with the same value of t_s decays faster with decreasing separation than in the case of solids with different stopping time. Correlations in the particle number density introduce a non-uniform spatial distribution of solids in the 10 to 100 cm size range. Any clump of particles is disrupted by the turbulence in less than one tenth on an orbital period, and the maximally concentrated clumps are stable against self-gravitational collapse.Comment: 11 pages, 9 figures. Accepted for publication in MNRA

Modification of Angular Velocity by Inhomogeneous MRI Growth in Protoplanetary Disks

We have investigated evolution of magneto-rotational instability (MRI) in protoplanetary disks that have radially non-uniform magnetic field such that stable and unstable regions coexist initially, and found that a zone in which the disk gas rotates with a super-Keplerian velocity emerges as a result of the non-uniformly growing MRI turbulence. We have carried out two-dimensional resistive MHD simulations with a shearing box model. We found that if the spatially averaged magnetic Reynolds number, which is determined by widths of the stable and unstable regions in the initial conditions and values of the resistivity, is smaller than unity, the original Keplerian shear flow is transformed to the quasi-steady flow such that more flattened (rigid-rotation in extreme cases) velocity profile emerges locally and the outer part of the profile tends to be super-Keplerian. Angular momentum and mass transfer due to temporally generated MRI turbulence in the initially unstable region is responsible for the transformation. In the local super-Keplerian region, migrations due to aerodynamic gas drag and tidal interaction with disk gas are reversed. The simulation setting corresponds to the regions near the outer and inner edges of a global MRI dead zone in a disk. Therefore, the outer edge of dead zone, as well as the inner edge, would be a favorable site to accumulate dust particles to form planetesimals and retain planetary embryos against type I migration.Comment: 28 pages, 11figures, 1 table, accepted by Ap

Rapid growth of gas-giant cores by pebble accretion

The observed lifetimes of gaseous protoplanetary discs place strong constraints on gas and ice giant formation in the core accretion scenario. The approximately 10-Earth-mass solid core responsible for the attraction of the gaseous envelope has to form before gas dissipation in the protoplanetary disc is completed within 1-10 million years. Building up the core by collisions between km-sized planetesimals fails to meet this time-scale constraint, especially at wide stellar separations. Nonetheless, gas-giant planets are detected by direct imaging at wide orbital distances. In this paper, we numerically study the growth of cores by the accretion of cm-sized pebbles loosely coupled to the gas. We measure the accretion rate onto seed masses ranging from a large planetesimal to a fully grown 10-Earth-mass core and test different particle sizes. The numerical results are in good agreement with our analytic expressions, indicating the existence of two accretion regimes, one set by the azimuthal and radial particle drift for the lower seed masses and the other, for higher masses, by the velocity at the edge of the Hill sphere. In the former, the optimally accreted particle size increases with core mass, while in the latter the optimal size is centimeters, independent of core mass. We discuss the implications for rapid core growth of gas-giant and ice-giant cores. We conclude that pebble accretion can resolve the long-standing core accretion time-scale conflict. This requires a near-unity dust-to-gas ratio in the midplane, particle growth to mm and cm and the formation of massive planetesimals or low radial pressure support. The core growth time-scale is shortened by a factor 30-1,000 at 5 AU and by a factor 100-10,000 at 50 AU, compared to the gravitationally focused accretion of, respectively, low-scale-height planetesimal fragments or standard km-sized planetesimals.Comment: Version accepted for publication in A&