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Published October 2019 | Submitted + Published
Journal Article Open

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

Abstract

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.

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 (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_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.

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Submitted - 1811.05583.pdf

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Additional details

Created:
August 19, 2023
Modified:
October 20, 2023