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Register a new userOligarchic planetesimal accretion and giant planet formation II
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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.
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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.
In the standard model of core accretion, the formation of giant planets occurs by two main processes: first, a massive core is formed by the accretion of solid material; then, when this core exceeds a critical value (typically greater than 10 Earth masses) a gaseous runaway growth is triggered and the planet accretes big quantities of gas in a short period of time until the planet achieves its final mass. Thus, the formation of a massive core has to occur when the nebular gas is still available in the disk. This phenomenon imposes a strong time-scale constraint in giant planet formation due to the fact that the lifetimes of the observed protoplanetary disks are in general lower than 10 Myr. The formation of massive cores before 10 Myr by accretion of big planetesimals (with radii > 10 km) in the oligarchic growth regime is only possible in massive disks. However, planetesimal accretion rates significantly increase for small bodies, especially for pebbles, particles of sizes between mm and cm, which are strongly coupled with the gas. In this work, we study the formation of giant planets incorporating pebble accretion rates in our global model of planet formation.
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.
Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplanetary disk. We compute, through numerical simulations, the gas and dust evolution, including dust growth, fragmentation, radial drift and particle accumulation at a pressure bump. We also consider the formation of planetesimals by streaming instability and the formation of a moon-size embryo that grows into a giant planet by the hybrid accretion of pebbles and planetesimals. We find that pressure maxima in protoplanetary disks are efficient collectors of dust drifting inwards. The condition of planetesimal formation by streaming instability is fulfilled due to the large amount of dust accumulated at the pressure bump. Then, a massive core is quickly formed (in $sim 10^4$ yr) by the accretion of pebbles. After the pebble isolation mass is reached, the growth of the core slowly continues by the accretion of planetesimals. The energy released by planetesimal accretion delays the onset of runaway gas accretion, allowing a gas giant to form after $sim$1 Myr of disk evolution. The pressure maximum also acts as a migration trap. Pressure maxima in protoplanetary disks are preferential locations for dust traps, planetesimal formation by streaming instability and planet migration traps. All these conditions allow the fast formation of a giant planet by the hybrid accretion of pebbles and planetesimals.
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.
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