Migration of Earth-size planets in 3D radiative discs

In this paper, we address the migration of small mass planets in 3D radiative disks. Indeed, migration of small planets is known to be too fast inwards in locally isothermal conditions. However, thermal effects could reverse its direction, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. This effect has been seen for masses larger than 5 Earth masses, but the minimum mass for this to happen has never been probed numerically, although it is of crucial importance for planet formation scenarios. We have extended the hydro-dynamical code FARGO to 3D, with thermal diffusion. With this code, we perform simulations of embedded planets down to 2 Earth masses. For a set of discs parameters for which outward migration has been shown in the range of $[5, 35]$ Earth masses, we find that the transition to inward migration occurs for masses in the range $[3, 5]$ Earth masses. The transition appears to be due to an unexpected phenomenon: the formation of an asymmetric cold and dense finger of gas driven by circulation and libration streamlines. We recover this phenomenon in 2D simulations where we control the cooling effects of the gas through a simple modeling of the energy equation.Comment: 17 pages, 20 figures, accepted. MNRAS, 201

The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores

The basic structure of the solar system is set by the presence of low-mass terrestrial planets in its inner part and giant planets in its outer part. This is the result of the formation of a system of multiple embryos with approximately the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the protoplanetary disk. What was the origin of this dichotomy in the mass distribution of embryos/cores? We show in this paper that the classic processes of runaway and oligarchic growth from a disk of planetesimals cannot explain this dichotomy, even if the original surface density of solids increased at the snowline. Instead, the accretion of drifting pebbles by embryos and cores can explain the dichotomy, provided that some assumptions hold true. We propose that the mass-flow of pebbles is two-times lower and the characteristic size of the pebbles is approximately ten times smaller within the snowline than beyond the snowline (respectively at heliocentric distance $r<r_{ice}$ and $r>r_{ice}$, where $r_{ice}$ is the snowline heliocentric distance), due to ice sublimation and the splitting of icy pebbles into a collection of chondrule-size silicate grains. In this case, objects of original sub-lunar mass would grow at drastically different rates in the two regions of the disk. Within the snowline these bodies would reach approximately the mass of Mars while beyond the snowline they would grow to $\sim 20$ Earth masses. The results may change quantitatively with changes to the assumed parameters, but the establishment of a clear dichotomy in the mass distribution of protoplanets appears robust, provided that there is enough turbulence in the disk to prevent the sedimentation of the silicate grains into a very thin layer.Comment: In press in Icaru

How primordial is the structure of comet 67P/C-G? Combined collisional and dynamical models suggest a late formation

There is an active debate about whether the properties of comets as observed today are primordial or, alternatively, if they are a result of collisional evolution or other processes. We investigate the effects of collisions on a comet with a structure like 67P/C-G. We develop scaling laws for the critical specific impact energies required for a significant shape alteration. These are then used in simulations of the combined dynamical and collisional evolution of comets in order to study the survival probability of a primordially formed object with a shape like 67P/C-G. The effects of impacts on comet 67P/C-G are studied using a SPH shock physics code. The resulting critical specific impact energy defines a minimal projectile size which is used to compute the number of shape-changing collisions in a set of dynamical simulations. These simulations follow the dispersion of the trans-Neptunian disk during the giant planet instability, the formation of a scattered disk, and produce 87 objects that penetrate into the inner solar system with orbits consistent with the observed JFC population. The collisional evolution before the giant planet instability is not considered here. Hence, our study is conservative in its estimation of the number of collisions. We find that in any scenario considered here, comet 67P/C-G would have experienced a significant number of shape-changing collisions, if it formed primordially. This is also the case for generic bi-lobe shapes. Our study also shows that impact heating is very localized and that collisionally processed bodies can still have a high porosity. Our study indicates that the observed bi-lobe structure of comet 67P/C-G may not be primordial, but might have originated in a rather recent event, possibly within the last 1 Gy. This may be the case for any kilometer-sized two-component cometary nuclei.Comment: Astronomy & Astrophysics, accepted pending minor revision

The Survival Rate of Ejected Terrestrial Planets with Moons

During planet formation, a gas giant will interact with smaller protoplanets that stray within its sphere of gravitational influence. We investigate the outcome of interactions between gas giants and terrestrial-sized protoplanets with lunar-sized companions. An interaction between a giant planet and a protoplanet binary may have one of several consequences, including the delivery of volatiles to the inner system, the capture of retrograde moons by the giant planet, and the ejection of one or both of the protoplanets. We show that an interesting fraction of terrestrial-sized planets with lunar sized companions will likely be ejected into interstellar space with the companion bound to the planet. The companion provides an additional source of heating for the planet from tidal dissipation of orbital and spin angular momentum. This heat flux typically is larger than the current radiogenic heating of the Earth for up to the first few hundred million years of evolution. In combination with an atmosphere of sufficient thickness and composition, the heating can provide the conditions necesary for liquid water to persist on the surface of the terrestrial mass planet, making it a potential site for life. We also determine the possibility for directly detecting such systems through all-sky infrared surveys or microlensing surveys. Microlensing surveys in particular will directly measure the frequency of this phenomenon.Comment: 4 pages, 2 figures, Accepted to ApJ

A Method to Constrain the Size of the Protosolar Nebula

Observations indicate that the gaseous circumstellar disks around young stars vary significantly in size, ranging from tens to thousands of AU. Models of planet formation depend critically upon the properties of these primordial disks, yet in general it is impossible to connect an existing planetary system with an observed disk. We present a method by which we can constrain the size of our own protosolar nebula using the properties of the small body reservoirs in the solar system. In standard planet formation theory, after Jupiter and Saturn formed they scattered a significant number of remnant planetesimals into highly eccentric orbits. In this paper, we show that if there had been a massive, extended protoplanetary disk at that time, then the disk would have excited Kozai oscillations in some of the scattered objects, driving them into high-inclination (i > 50 deg), low-eccentricity orbits (q > 30 AU). The dissipation of the gaseous disk would strand a subset of objects in these high-inclination orbits; orbits that are stable on Gyr time scales. To date, surveys have not detected any Kuiper Belt Objects with orbits consistent with this dynamical mechanism. Using these non-detections by the Deep Ecliptic Survey (DES) and the Palomar Distant Solar System Survey we are able to rule out an extended gaseous protoplanetary disk (R_D > 80 AU) in our solar system at the time of Jupiter's formation. Future deep all sky surveys such as the Large Synoptic Survey Telescope (LSST) will all us to further constrain the size of the protoplanetary disk.Comment: 10 pages, Accepted to A

Planets Formed in Habitable Zones of M Dwarf Stars Probably are Deficient in Volatiles

Dynamical considerations, presented herein via analytic scalings and numerical experiments, imply that Earth-mass planets accreting in regions that become habitable zones of M dwarf stars form within several million years. Temperatures in these regions during planetary accretion are higher than those encountered by the material that formed the Earth. Collision velocities during and after the prime accretionary epoch are larger than for Earth. These factors suggest that planets orbiting low mass main sequence stars are likely to be either too distant (and thus too cold) for carbon/water based life on their surfaces or have abundances of the required volatiles that are substantially less than on Earth.Comment: 11 pages, 1 figure, Astrophysical Journal Letters, in pres