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Universal scaling relations in scale-free structure formation

Guszejnov, Dávid and Hopkins, Philip F. and Grudić, Michael Y. (2018) Universal scaling relations in scale-free structure formation. Monthly Notices of the Royal Astronomical Society, 477 (4). pp. 5139-5149. ISSN 0035-8711.

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A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dM ∝ M^(−2) which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters, and even dark matter haloes. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M^(−2) and a column density distribution with a power-law tail of dA/dln Σ ∝ Σ^(−1). In the case where structure formation is controlled by gravity the two-point correlation becomes ξ2D ∝ R^(−1). Furthermore, structures formed by such processes (e.g. young star clusters, DM haloes) tend to a ρ ∝ R^(−3) density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation, and detailed ‘full physics’ hydrodynamical simulations. We find that these power laws are good first-order descriptions in all cases.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Guszejnov, Dávid0000-0001-5541-3150
Hopkins, Philip F.0000-0003-3729-1684
Additional Information:© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2018 April 10. Received 2018 March 7; in original form 2017 July 18. We would like to thank Michael S. Fall and Christopher F. McKee for their invaluable comments. Support for PFH, DG, and MYG was provided by an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G, and NSF Collaborative Research Grant #1411920 and CAREER Grant #1455342. Numerical calculations were run on the Caltech compute cluster ‘Zwicky’ (NSF MRI award #PHY-0960291) and allocation TG-AST130039 granted by the Extreme Science and Engineering Discovery Environment (XSEDE) supported by the NSF.
Group:TAPIR, Astronomy Department
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:turbulence, stars: formation, ISM: structure, galaxies: star clusters: general, galaxies: star formation, cosmology: theory
Issue or Number:4
Record Number:CaltechAUTHORS:20180705-141511132
Persistent URL:
Official Citation:Dávid Guszejnov, Philip F Hopkins, Michael Y Grudić; Universal scaling relations in scale-free structure formation, Monthly Notices of the Royal Astronomical Society, Volume 477, Issue 4, 11 July 2018, Pages 5139–5149,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87561
Deposited By: George Porter
Deposited On:06 Jul 2018 14:57
Last Modified:09 Mar 2020 13:18

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