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Jumping the Gap: The Formation Conditions and Mass Function of 'Pebble-Pile' Planetesimals

Hopkins, Philip F. (2016) Jumping the Gap: The Formation Conditions and Mass Function of 'Pebble-Pile' Planetesimals. Monthly Notices of the Royal Astronomical Society, 456 (3). pp. 2383-2405. ISSN 0035-8711. http://resolver.caltech.edu/CaltechAUTHORS:20141222-150904506

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Abstract

In a turbulent proto-planetary disk, dust grains undergo large density fluctuations and under the right circumstances, these grain overdensities can overcome shear, turbulent, and gas pressure support to collapse under self-gravity (forming a “pebble pile” planetesimal). Using a simple analytic model for the fluctuations predicted in simulations, we estimate the rate-of-formation and mass function of self-gravitating, rapidly-collapsing planetesimal-mass bodies formed by this mechanism. The statistics of this process depend sensitively on the size/stopping time of the grains, disk surface density, and turbulent Mach numbers. However, when it occurs, we predict that the resulting planetesimal mass function is broad and quasi-universal, with a slope dN/dM ∝ M^(-(1-2)), spanning a size/mass range ~ 10-10^4 km (10^(-9)-5M_⊕). Collapse to planetesimal through super-Earth masses is possible. The key condition is that grain density fluctuations reach large amplitudes on large scales, where gravitational instability proceeds most easily (collapse of small grains is strongly suppressed by turbulent vorticity). We show this leads to a new criterion for “pebble-pile” formation: Ƭs ≳0.05 ln (Q^(1/2)/Z_d)/ln(1+10ɑ^(1/4))~0.3ψ(Q,Z,ɑ) where Ƭ_s=t_s Ω is the dimensionless particle stopping time. In a MMSN, this requires grains larger than ɑ = (50, 1, 0.1)cm at r = (1, 30, 100)au. So at large radii (beyond the ice line), this may easily occur and seed core accretion. At small radii, it would depend on the existence of large “boulders.” However, because density fluctuations depend super-exponentially on T_s (inversely proportional to disk surface density), lower-density disks are more unstable. In fact, we predict that cm-sized grains at ~ 1 au will form pebble piles in a disk with ~ 10% the MMSN density, so planet formation at ~ au may generically occur “late” as disks are evaporating. We also predict that conditions become progressively more favorable for pebble-pile formation around lower-mass, cooler stars.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1401.2458arXivDiscussion Paper
http://dx.doi.org/10.1093/mnras/stv2820DOIArticle
https://mnras.oxfordjournals.org/content/456/3/2383PublisherArticle
ORCID:
AuthorORCID
Hopkins, Philip F.0000-0003-3729-1684
Additional Information:© 2015 The Author. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2015 November 29. Received 2015 September 15; in original form 2014 January 10. First published online December 31, 2015. We thank Eugene Chiang, Jessie Christiansen, Jeff Cuzzi, Karim Shariff, Kees Dullemond, and Joanna Drazkowska for many helpful discussions during the development of this work. We also thank our anonymous referee, for a very helpful report and a number of excellent suggestions. Support for PFH was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF1-120083 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the NASA under contract NAS8-03060.
Group:TAPIR
Funders:
Funding AgencyGrant Number
NASA Einstein FellowshipPF1-120083
NASANAS8-03060
Subject Keywords:accretion, accretion discs hydrodynamics instabilities turbulence planets and satellites: formation protoplanetary discs
Record Number:CaltechAUTHORS:20141222-150904506
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20141222-150904506
Official Citation: Philip F. Hopkins Jumping the gap: the formation conditions and mass function of ‘pebble-pile’ planetesimals MNRAS (March 01, 2016) Vol. 456 2383-2405 doi:10.1093/mnras/stv2820 First published online December 31, 2015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53116
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:23 Dec 2014 16:48
Last Modified:17 Aug 2017 19:28

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