Pebble accretion

Pebble accretion is the accumulation of particles, ranging from centimeters up to meters in diameter, into planetesimals in a protoplanetary disk that is enhanced by aerodynamic drag from the gas present in the disk. This drag reduces the relative velocity of pebbles as they pass by larger bodies, preventing some from escaping the body's gravity. These pebbles are then accreted by the body after spiraling or settling toward its surface. This process increases the cross section over which the large bodies can accrete material, accelerating their growth. The rapid growth of the planetesimals via pebble accretion allows for the formation of giant planet cores in the outer Solar System before the dispersal of the gas disk. A reduction in the size of pebbles as they lose water ice after crossing the ice line and a declining density of gas with distance from the Sun slow the rates of pebble accretion in the inner Solar System resulting in smaller terrestrial planets, a small mass of Mars and a low mass asteroid belt.

Description In a protoplanetary disk, the probability of accretion of pebbles ranging in size from centimeters to a meter is ≤10% on planets up to about 20 Earth masses. A protoplanetary disk is made up of a mix of gas and solids including dust, pebbles, planetesimals, and protoplanets. Gas in a protoplanetary disk is pressure supported and as a result orbits at a velocity slower than large objects. The gas affects the motions of the solids in varying ways depending on their size, with dust moving with the gas and the largest planetesimals orbiting largely unaffected by the gas. Pebbles are an intermediate case, aerodynamic drag causes them to settle toward the central plane of the disk and to orbit at a sub-Keplerian velocity resulting in radial drift toward the central star. The pebbles frequently encounter planetesimals as a result of their lower velocities and inward drift. If their motions were unaffected by the gas only a small fraction, determined by gravitational focusing and the cross-section of the planetesimals, would be accreted by the planetesimals. The remainder would follow hyperbolic paths, accelerating toward the planetesimal on their approach and decelerating as they recede. However, the drag the pebbles experience grows as their velocities increase, slowing some enough that they become gravitationally bound to the planetesimal. These pebbles continue to lose energy as they orbit the planetesimal causing them to spiral toward and be accreted by the planetesimal.

Small planetesimals accrete pebbles that are drifting past them at the relative velocity of the gas. Those pebbles with stopping times similar to the planetesimal's Bondi time are accreted from within its Bondi radius. In this context the Bondi radius is defined as the distance at which an object approaching a planetesimal at the relative velocity of the gas is deflected by one radian; the stopping time is the exponential timescale for the deceleration of an object due to gas drag, and the Bondi time is the time required for an object to cross the Bondi radius. Since the Bondi radius and Bondi time increase with the size of the planetesimal, and the stopping time increases with the size of the pebble, the optimal pebble size increases with the size of the planetesimal. Smaller objects, with ratios of stopping times to Bondi times less than 0.1, are pulled from the flow past the planetesimal and accreted from a smaller radius which declines with the square root of this ratio. Larger, weakly coupled pebbles are also accreted less efficiently due to three body effects with the radius accreted from declining rapidly between ratios of 10 and 100. The Bondi radius is proportional to the mass of the planetesimal so the relative growth rate is proportional to mass squared resulting in runaway growth. The aerodynamic deflection of the gas around the planetesimal reduces the efficiency of pebble accretion resulting in a maximum growth timescale of 100 km. Larger planetesimals, above a transition mass of roughly Ceres mass in the inner Solar System and Pluto mass in the outer Solar System, accrete pebbles with Stokes numbers near one from their Hill radii. The "Stokes number" in this context is the product of stopping time and the Keplerian frequency. As with small planetesimals the radius from which pebbles accrete declines for smaller and larger pebble sizes. The optimal pebble size for large planetesimals measures in cm's due to a combination of the accretion radius and the radial drift rates of the pebbles. As objects grow their accretion changes from 3-D, with accretion from part of the thickness of the pebble disk, to 2D with accretion from full thickness of pebble disk. The relative growth rate in 2-D accretion is proportional to the mass 2 / 3 {\displaystyle ^{2/3}} leading to oligarchical growth and the formation of similar sized bodies. Pebble accretion can result in doubling of mass of an Earth-massed core in as little as 5500 years, reducing the timescales for growth of the cores of giant planets by 2 or 3 orders of magnitude relative to planetesimal accretion. The gravitational influence of these massive bodies can create a partial gap in the gas disk altering the pressure gradient. The velocity of gas then becomes super-keplerian outside the gap stopping the inward drift of pebbles and ending pebble accretion. Detailed simulations, based on first-principle calculations, indicate that in typical protoplanetary disks the formation time of giant planets via pebble accretion is a few to several million years, comparable to that obtained from planetesimal accretion calculations.

… excerpt ends here. Continue reading the full article.