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Heat conduction in rotating relativistic stars

Heat conduction in rotating relativistic stars
Heat conduction in rotating relativistic stars

In the standard form of the relativistic heat equation used in astrophysics, information propagates instantaneously, rather than being limited by the speed of light as demanded by relativity. We show how this equation none the less follows from a more general, causal theory of heat propagation in which the entropy plays the role of a fluid. In deriving this result, however, we see that it is necessary to make some assumptions which are not universally valid: the dynamical time-scales of the process must be long compared with the explicitly causal physics of the theory, the heat flow must be sufficiently steady, and the space-time static. Generalizing the heat equation (e.g. restoring causality) would thus entail retaining some of the terms we neglected. As a first extension, we derive the heat equation for the space-time associated with a slowly-rotating star or black hole, showing that it only differs from the static result by an additional advection term due to the rotation, and as a consequence demonstrate that a hotspot on a neutron star will be seen to be modulated at the rotation frequency by a distant observer.

Accretion, accretion discs, Conduction, Gravitation, Stars: rotation, Stars:- neutron
0035-8711
4207-4215
Lander, S.K.
a5710ce4-cb3b-4bad-91d3-85dbb602feb9
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Lander, S.K.
a5710ce4-cb3b-4bad-91d3-85dbb602feb9
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304

Lander, S.K. and Andersson, N. (2018) Heat conduction in rotating relativistic stars. Monthly Notices of the Royal Astronomical Society, 479 (3), 4207-4215. (doi:10.1093/mnras/sty1725).

Record type: Article

Abstract

In the standard form of the relativistic heat equation used in astrophysics, information propagates instantaneously, rather than being limited by the speed of light as demanded by relativity. We show how this equation none the less follows from a more general, causal theory of heat propagation in which the entropy plays the role of a fluid. In deriving this result, however, we see that it is necessary to make some assumptions which are not universally valid: the dynamical time-scales of the process must be long compared with the explicitly causal physics of the theory, the heat flow must be sufficiently steady, and the space-time static. Generalizing the heat equation (e.g. restoring causality) would thus entail retaining some of the terms we neglected. As a first extension, we derive the heat equation for the space-time associated with a slowly-rotating star or black hole, showing that it only differs from the static result by an additional advection term due to the rotation, and as a consequence demonstrate that a hotspot on a neutron star will be seen to be modulated at the rotation frequency by a distant observer.

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More information

Accepted/In Press date: 26 June 2018
e-pub ahead of print date: 29 June 2018
Published date: 21 September 2018
Additional Information: This article has been accepted for publication in Monthly Notices of the Astronomical Society ©: 2018 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
Keywords: Accretion, accretion discs, Conduction, Gravitation, Stars: rotation, Stars:- neutron

Identifiers

Local EPrints ID: 423430
URI: https://eprints.soton.ac.uk/id/eprint/423430
ISSN: 0035-8711
PURE UUID: 82168937-fbb5-4a41-8705-03abef868693

Catalogue record

Date deposited: 21 Sep 2018 16:30
Last modified: 13 Mar 2019 18:07

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