Time evolution of a viscous protoplanetary disk with a free geometry: toward a more self-consistent picture

Observations of protoplanetary disks show that some characteristics seem recurrent, even in star formation regions that are physically distant such as surface mass density profiles varying as $r^{-1}$, or aspect ratios about 0.03 to 0.23. Accretion rates are also recurrently found around $10^{-8} - 10^{-6}~\mathrm{M_{\odot}~yr^{-1}}$ for disks already evolved (Isella et al., 2009, Andrews et al., 2009, 2010). Several models have been developed in order to recover these properties. However, most of them usually simplify the disk geometry if not its mid-plane temperature. This has major consequences for modeling the disk evolution over million years and consequently planet migration. In the present paper, we develop a viscous evolution hydrodynamical numerical code that determines simultaneously the disk photosphere geometry and the mid-plane temperature. We then compare our results of long-term simulations with similar simulations of disks with a constrained geometry along the Chiang & Goldreich (1997) prescription (dlnH/dlnr = 9/7). We find that the constrained geometry models provide a good approximation of the disk surface density evolution. However, they differ significantly regarding the temperature time evolution. In addition, we find that shadowed regions naturally appear at the transition between viscously dominated and radiation dominated regions that falls in the region of planetary formation. We show that $\chi$ (photosphere height to pressure scale height ratio) cannot be considered as a constant, consistently with Watanabe et al. (2008). Comparisons with observations show that all disk naturally evolve toward a shallow surface density disk ($\Sigma \propto r^{-1}$). The mass flux across the disk stabilizes in about 1 million year typically.Comment: 43 pages, 16 figures Accepted in Astrophysical Journa

Dynamical Evolution of the Debris Disk after a Satellite Catastrophic Disruption around Saturn

The hypothesis of a recent origin of Saturn's rings and its mid-sized moons is actively debated. It was suggested that a proto-Rhea and a proto-Dione might have collided recently, giving birth to the modern system of mid-sized moons. It is also suggested that the rapid viscous spreading of the debris may have implanted mass inside Saturn's Roche limit, giving birth to the modern Saturn's ring system. However, this scenario has been only investigated in very simplified way for the moment. This paper investigates it in detail to assess its plausibility by using $N$-body simulations and analytical arguments. When the debris disk is dominated by its largest remnant, $N$-body simulations show that the system quickly re-accrete into a single satellite without significant spreading. On the other hand, if the disk is composed of small particles, analytical arguments suggest that the disk experiences dynamical evolutions in three steps. The disk starts significantly excited after the impact and collisional damping dominates over the viscous spreading. After the system flattens, the system can become gravitationally unstable when particles are smaller than $\sim$ 100 m. However, the particles grow faster than spreading. Then, the system becomes gravitationally stable again and accretion continues at a slower pace, but spreading is inhibited. Therefore, the debris is expected to re-accrete into several large bodies. In conclusion, our results show that such a scenario may not form the today's ring system. In contrast, our results suggest that today's mid-sized moons are likely re-accreted from such a catastrophic event.Comment: 12 pages, 8 figures, accepted for publication in A

LIDT-DD: A new self-consistent debris disc model including radiation pressure and coupling collisional and dynamical evolution

In most current debris disc models, the dynamical and the collisional evolutions are studied separately, with N-body and statistical codes, respectively, because of stringent computational constraints. We present here LIDT-DD, the first code able to mix both approaches in a fully self-consistent way. Our aim is for it to be generic enough so as to be applied to any astrophysical cases where we expect dynamics and collisions to be deeply interlocked with one another: planets in discs, violent massive breakups, destabilized planetesimal belts, exozodiacal discs, etc. The code takes its basic architecture from the LIDT3D algorithm developed by Charnoz et al.(2012) for protoplanetary discs, but has been strongly modified and updated in order to handle the very constraining specificities of debris discs physics: high-velocity fragmenting collisions, radiation-pressure affected orbits, absence of gas, etc. In LIDT-DD, grains of a given size at a given location in a disc are grouped into "super-particles", whose orbits are evolved with an N-body code and whose mutual collisions are individually tracked and treated using a particle-in-a-box prescription. To cope with the wide range of possible dynamics, tracers are sorted and regrouped into dynamical families depending on their orbits. The code retrieves the classical features known for debris discs, such as the particle size distributions in unperturbed discs, the outer radial density profiles (slope in -1.5) outside narrow collisionally active rings, and the depletion of small grains in "dynamically cold" discs. The potential of the new code is illustrated with the test case of the violent breakup of a massive planetesimal within a debris disc. The main potential future applications of the code are planet/disc interactions, and more generally any configurations where dynamics and collisions are expected to be intricately connected.Comment: Accepted for publication in A&A. 20 pages, 17 figures. Abstract shortened for astro-p

On the Impact Origin of Phobos and Deimos I: Thermodynamic and Physical Aspects

Phobos and Deimos are the two small moons of Mars. Recent works have shown that they can accrete within an impact-generated disk. However, the detailed structure and initial thermodynamic properties of the disk are poorly understood. In this paper, we perform high-resolution SPH simulations of the Martian moon-forming giant impact that can also form the Borealis basin. This giant impact heats up the disk material (around $\sim 2000$ K in temperature) with an entropy increase of $\sim 1500$ J K$^{-1}$ kg$^{-1}$. Thus, the disk material should be mostly molten, though a tiny fraction of disk material ($< 5\%$) would even experience vaporization. Typically, a piece of molten disk material is estimated to be meter sized due to the fragmentation regulated by their shear velocity and surface tension during the impact process. The disk materials initially have highly eccentric orbits ($e \sim 0.6-0.9$) and successive collisions between meter-sized fragments at high impact velocity ($\sim 3-5$ km s$^{-1}$) can grind them down to $\sim100 \mu$m-sized particles. On the other hand, a tiny amount of vaporized disk material condenses into $\sim 0.1 \mu$m-sized grains. Thus, the building blocks of the Martian moons are expected to be a mixture of these different sized particles from meter-sized down to $\sim 100 \mu$m-sized particles and $\sim 0.1 \mu$m-sized grains. Our simulations also suggest that the building blocks of Phobos and Deimos contain both impactor and Martian materials (at least 35%), most of which come from the Martian mantle (50-150 km in depth; at least 50%). Our results will give useful information for planning a future sample return mission to Martian moons, such as JAXA's MMX (Martian Moons eXploration) mission.Comment: 11 pages, 6 figures. Accepted for publication in Ap

Long-term & large-scale viscous evolution of dense planetary rings

We investigate the long-term and large-scale viscous evolution of dense planetary rings using a simple 1D numerical code. We use a physically realistic viscosity model derived from N-body simulations (Daisaka et al., 2001), and dependent on the disk's local properties (surface mass density, particle size, distance to the planet). Particularly, we include the effects of gravitational instabilities (wakes) that importantly enhance the disk's viscosity. We show that common estimates of the disk's spreading time-scales with constant viscosity significantly underestimate the rings' lifetime. With a realistic viscosity model, an initially narrow ring undergoes two successive evolutionary stages: (1) a transient rapid spreading when the disk is self-gravitating, with the formation of a density peak inward and an outer region marginally gravitationally stable, and with an emptying time-scale proportional to 1/M_0^2 (where M_0 is the disk's initial mass) (2) an asymptotic regime where the spreading rate continuously slows down as larger parts of the disk become not-self-gravitating due to the decrease of the surface density, until the disk becomes completely not-self-gravitating. At this point its evolution dramatically slows down, with an emptying time-scale proportional to 1/M_0, which significantly increases the disk's lifetime compared to the case with constant viscosity. We show also that the disk's width scales like t^{1/4} with the realistic viscosity model, while it scales like t^{1/2} in the case of constant viscosity, resulting in much larger evolutionary time-scales in our model. We find however that the present shape of Saturn's rings looks like a 100 million-years old disk in our simulations. Concerning Jupiter's, Uranus' and Neptune's rings that are faint today, it is not likely that they were much more massive in the past and lost most of their mass due to viscous spreading alone.Comment: 18 pages, 18 figures, 2 tables. Accepted for publication in Icaru

Saturn's Exploration Beyond Cassini-Huygens

For its beautiful rings, active atmosphere and mysterious magnetic field, Saturn is a fascinating planet. It also holds some of the keys to understanding the formation of our Solar System and the evolution of giant planets in general. While the exploration by the Cassini-Huygens mission has led to great advances in our understanding of the planet and its moons, it has left us with puzzling questions: What is the bulk composition of the planet? Does it have a helium core? Is it enriched in noble gases like Jupiter? What powers and controls its gigantic storms? We have learned that we can measure an outer magnetic field that is filtered from its non-axisymmetric components, but what is Saturn's inner magnetic field? What are the rings made of and when were they formed? These questions are crucial in several ways: a detailed comparison of the compositions of Jupiter and Saturn is necessary to understand processes at work during the formation of these two planets and of the Solar System. This calls for the continued exploration of the second largest planet in our Solar System, with a variety of means including remote observations and space missions. Measurements of gravity and magnetic fields very close to the planet's cloud tops would be extremely valuable. Very high spatial resolution images of the rings would provide details on their structure and the material that form them. Last but not least, one or several probes sent into the atmosphere of the planet would provide the critical measurements that would allow a detailed comparison with the same measurements at Jupiter. [abridged abstract

A method for coupling dynamical and collisional evolution of dust in circumstellar disks: the effect of a dead zone

Dust is a major component of protoplanetary and debris disks as it is the main observable signature of planetary formation. However, since dust dynamics is size-dependent (because of gas-drag or radiation pressure) any attempt to understand the full dynamical evolution of circumstellar dusty-disks that neglect the coupling of collisional evolution with dynamical evolution is thwarted because of the feedback between these two processes. Here, a new hybrid lagrangian/eulerian code is presented that overcomes some of these difficulties. The particles representing "dust-clouds" are tracked individually in a lagrangian way. This system is then mapped on an eulerian spatial grid, inside the cells of which the local collisional evolutions are computed. Finally, the system is remapped back in a collection of discrete lagrangian particles keeping constant their number. An application example on dust growth in a turbulent protoplanetary disk at 1 AU is presented. First the growth of dust is considered in the absence of a dead-zone and the vertical distribution of dust is self-consistently computed. It is found that the mass is rapidly dominated by particles about a fraction of millimeter in size. Then the same case with an embedded dead-zone is investigated and It is found that coagulation is much more efficient and produces, in a short time scale, 1cm-10cm dust pebbles that dominate the mass. These pebbles may then be accumulated into embryos sized objects inside large-scale turbulent structures as shown recently (see e.g. Johansen et al., 2007).Comment: 29 pages, 10 figures, Accepted for publication in Ap