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Register a new userPlanetesimal fragmentation and giant planet formation II: dependencies with planetesimal relative velocities and compositions
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Added by
Irina Luciana San Sebasti\\'an
Publication date
2019
fields
Physics
and research's language is
English
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Most of planet formation models that incorporate planetesimal fragmentation consider a catastrophic impact energy threshold for basalts at a constant velocity of 3 km/s during all the process of the formation of the planets. However, as planets grow the relative velocities of the surrounding planetesimals increase from velocities of the order of m/s to a few km/s. In addition, beyond the ice line where giant planets are formed, planetesimals are expected to be composed roughly by 50 percentage of ices. We aim to study the role of planetesimal fragmentation on giant planet formation considering planetesimal catastrophic impact energy threshold as a function of the planetesimal relative velocities and compositions. We improve our model of planetesimal fragmentation incorporating a functional form of the catastrophic impact energy threshold with the planetesimal relative velocities and compositions. We also improve in our model the accretion of small fragments produced by the fragmentation of planetesimals during the collisional cascade considering specific pebble accretion rates. We find that a more accurate and realistic model for the calculation of the catastrophic impact energy threshold tends to slow down the formation of massive cores. Only for reduced grain opacity values at the envelope of the planet, the cross-over mass is achieved before the disk time-scale dissipation. While planetesimal fragmentation favors the quick formation of massive cores of 5-10 Earth masses the cross-over mass could be inhibited by planetesimal fragmentation. However, grain opacity reduction or pollution by the accreted planetesimals together with planetesimal fragmentation could explain the formation of giant planets with low-mass cores.
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The equation of state calculated by Saumon and collaborators has been adopted in most core-accretion simulations of giant-planet formation performed to date. Since some minor errors have been found in their original paper, we present revised simulations of giant-planet formation that considers a corrected equation of state. We employ the same code as Fortier and collaborators in repeating our previous simulations of the formation of Jupiter. Although the general conclusions of Fortier and collaborators remain valid, we obtain significantly lower core masses and shorter formation times in all cases considered. The minor errors in the previously published equation of state have been shown to affect directly the adiabatic gradient and the specific heat, causing an overestimation of both the core masses and formation times.
Forming gas giant planets by the accretion of 100 km diameter planetesimals, a typical size that results from self-gravity assisted planetesimal formation, is often thought to be inefficient. Many models therefore use small km-sized planetesimals, or invoke the accretion of pebbles. Furthermore, models based on planetesimal accretion often use the ad hoc assumption of planetesimals distributed radially in a minimum mass solar nebula fashion. We wish to investigate the impact of various initial radial density distributions in planetesimals with a dynamical model for the formation of planetesimals on the resulting population of planets. In doing so, we highlight the directive role of the early stages of dust evolution into pebbles and planetesimals in the circumstellar disk on the following planetary formation. We have implemented a two population model for solid evolution and a pebble flux regulated model for planetesimal formation into our global model for planet population synthesis. This framework is used to study the global effect of planetesimal formation on planet formation. As reference, we compare our dynamically formed planetesimal surface densities with ad-hoc set distributions of different radial density slopes of planetesimals. Even though required, it is not solely the total planetesimal disk mass, but the planetesimal surface density slope and subsequently the formation mechanism of planetesimals, that enables planetary growth via planetesimal accretion. Highly condensed regions of only 100 km sized planetesimals in the inner regions of circumstellar disks can lead to gas giant growth. Pebble flux regulated planetesimal formation strongly boosts planet formation, because it is a highly effective mechanism to create a steep planetesimal density profile. We find this to lead to the formation of giant planets inside 1 au by 100 km already by pure planetesimal accretion.
According to the sequential accretion model, giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. In order to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. We compute the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. We compute the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate mass planets that have not started yet their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have either masses below 10 ME or above several Jupiter masses. To form giant planets before the dissipation of the disc, small planetesimals (~ 0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate mass planets. Other processes must therefore be at work in order to explain the population of extrasolar planets presently known.
We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result --- a radial planetesimal distribution --- can be used as initial condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratio sufficiently such that particle gas interactions can no longer prevent planetesimal formation on small scales. The location of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject of ongoing research, thus they are implemented via free parameters. This enables us to study the influence of the disk properties on the formation of planetesimals, predicting their time dependent formation rates and location of primary pebble accretion. We show that large $alpha$-values of $0.01$ (strong turbulence) prevent the formation of planetesimals in the inner part of the disk, arguing for lower values of around $0.001$ (moderate turbulence), at which planetesimals form quickly at all places where they are needed for proto-planets. Planetesimals form as soon as dust has grown to pebbles ($simmathrm{mm}$ to $mathrm{dm}$) and the pebble flux reaches a critical value, which is after a few thousand years at $2-3,$AU and after a few hundred thousand years at $20-30,$AU. Planetesimal formation lasts until the pebble supply has decreased below a critical value. The final spatial planetesimal distribution is steeper compared to the initial dust and gas distribution which helps to explain the discrepancy between the minimum mass solar nebula and viscous accretion disks.
Many massive objects have been found in the outer region of the Solar system. How they were formed and evolved has not been well understood, although there have been intensive studies on accretion process of terrestrial planets. One of the mysteries is the existence of binary planetesimals with near-equal mass components and highly eccentric orbits. These binary planetesimals are quite different from the satellites observed in the asteroid belt region. The ratio of the Hill radius to the physical radius of the planetesimals is much larger for the outer region of the disk, compared to the inner region of the disk. The Hill radius increases with the semi major axis. Therefore, planetesimals in the outer region can form close and eccentric binaries, while those in the inner region would simply collide. In this paper, we carried out $N$-body simulations in different regions of the disk and studied if binaries form in the outer region of the disk. We found that large planetesimals tend to form binaries. A significant fraction of large planetesimals are components of the binaries. Planetesimals that become the components of binaries eventually collide with a third body, through three-body encounters. Thus, the existence of binaries can enhance the growth rate of planetesimals in the Trans-Neptunian Object (TNO) region.
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