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A Stable Finite-Volume Method for Scalar-Field Dark Matter

Hopkins, Philip F. (2019) A Stable Finite-Volume Method for Scalar-Field Dark Matter. Monthly Notices of the Royal Astronomical Society, 489 (2). pp. 2367-2376. ISSN 0035-8711.

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We describe and test a family of new numerical methods to solve the Schrödinger equation in self-gravitating systems, e.g. Bose–Einstein condensates or ‘fuzzy’/ultra-light scalar field dark matter. The methods are finite-volume Godunov schemes with stable, higher order accurate gradient estimation, based on a generalization of recent mesh-free finite-mass Godunov methods. They couple easily to particle-based N-body gravity solvers (with or without other fluids, e.g. baryons), are numerically stable, and computationally efficient. Different sub-methods allow for manifest conservation of mass, momentum, and energy. We consider a variety of test problems and demonstrate that these can accurately recover solutions and remain stable even in noisy, poorly resolved systems, with dramatically reduced noise compared to some other proposed implementations (though certain types of discontinuities remain challenging). This is non-trivial because the ‘quantum pressure’ is neither isotropic nor positive definite and depends on higher order gradients of the density field. We implement and test the method in the code GIZMO.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper ItemGIZMO
Hopkins, Philip F.0000-0003-3729-1684
Additional Information:© 2019 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 2019 June 27. Received 2019 June 24; in original form 2018 November 11. Published: 25 July 2019. We thank Victor Robles, Michael Kopp, Xinyu Li, and our anonymous referee for a number of helpful discussions and suggestions. Support for PFH was provided by an Alfred P. Sloan Research Fellowship, NSF Collaborative Research grant #1715847 and CAREER grant #1455342. Numerical calculations were run on the Caltech compute cluster ‘Wheeler,’ allocations from XSEDE TG-AST130039 and PRAC NSF.1713353 supported by the NSF, and NASA HEC SMD-16-7592.
Group:TAPIR, Astronomy Department
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:elementary particles, hydrodynamics, methods: numerical, cosmology: theory, dark matter
Issue or Number:2
Record Number:CaltechAUTHORS:20190206-105628264
Persistent URL:
Official Citation:Philip F Hopkins, A stable finite-volume method for scalar field dark matter, Monthly Notices of the Royal Astronomical Society, Volume 489, Issue 2, October 2019, Pages 2367–2376,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92727
Deposited By: George Porter
Deposited On:08 Feb 2019 15:22
Last Modified:24 Oct 2019 15:57

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