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The Problem With Pebbles Being Unstable

The process of building up planets in protoplanetary disks has been a large challenge in the field of astrophysical and planetary sciences. Planetary systems begin as large molecular clouds of gas and dust that collapse under their own gravity due to an outside disturbance. We can easily observe gas nebulas, measure their composition, and calculate certain parameters for what the eventual star may be. Once the star is forming, we can observe the disk and partially see gaps in the disk, that we assume to be the planetesimals that are “eating” up material around them. Unfortunately, we are unable to resolve individual meter sized rocks that are far away, so knowing how they get from grain/meter sized to kilometer sized in a very short time frame is very difficult to understand. We have to first look at what this protoplanetary disk is made of. Primarily it is filled with a mix of gas and dust particles, and as these dust particles accumulate they will begin to gain more mass. Due to the increasing mass, this dust or rock will experience a battle of forces between gravity, and a drag force coming from the gas. Since the gas has negligible mass relative to the dust, it does not feel this drag and continues at a constant angular velocity. The dust, on the other hand, will feel a force from the drag and lose some of its angular momentum which would imply it to fall radially inward toward the star. If this were all that was to happen all of the planets we have today would have gotten to around the size of a meter and then been vaporized as they got too close to the sun! This poses the question of how do planets jump this size gap without getting pulled into and vaporized by the sun or taking an immense amount of time.

Many studies have been done on observations of exoplanetary systems that are still in development. The figure to the left shows the size of these “pebbles” relative to their position in the disk, in units of cm and AU (Laibe et al. 2012). The closer the distance to the star, the density of material will increase, and because of the pile up of material at the midplane, the pebbles can accrete into planetesimals through a rapid rate of growth. One way to think of what may happen is to look at the disk from the outside and imagine what is happening to the gas and dust inside. Since the dust is heavier, it will also feel a force that will cause it to migrate closer to the midplane of the disk. As this happens, material can “pile up” and start to accrete (Guillaume et al. 2013). A good visual is to think of smoke or ash in the air here on earth after a volcano erupts. The ash goes straight up, but is more massive than the atmosphere and eventually falls down to the ground. This process has three stages that ends with the final one being a very efficient rapid accretion of dust and grains to form planetesimals, perhaps gravitational instabilities between the pairs of grains would cause a rapid accretion to jump to kilometer-sized bodies. Liu et al. 2019 explains that the “streaming instability is a key mechanism for planet formation” by making clusters of pebbles that will eventually gain enough self gravity to start accreting to finally form planetesimals and planets. In the plot above by Liu et al. 2019, it is shown the mass of a planetesimal growing rapidly on a timescale of around a million years, and also moving to a closer semi-major axis (distance from the sun) showing the extremely rapid process of this instability.

References: Guillaume Laibe, Growing dust grains in protoplanetary discs – II. The radial-drift barrier problem, Monthly Notices of the Royal Astronomical Society, Volume 437, Issue 4, 01 February 2014, Pages 3037–3054, https://doi.org/10.1093/mnras/stt1928

Revisiting the “radial-drift barrier” of planet formation and its relevance in observed protoplanetary discs,G. Laibe, J.-F. Gonzalez and S. T. Maddison,A&A, 537 (2012) A61,DOI: https://doi.org/10.1051/0004-6361/201015349

Growth after the streaming instability - From planetesimal accretion to pebble accretion Beibei Liu, Chris W. Ormel and Anders Johansen A&A, 624 (2019) A114 DOI: https://doi.org/10.1051/0004-6361/201834174