Nixon, C.J. orcid.org/0000-0002-2137-4146, Pringle, C.C.T. orcid.org/0000-0001-9908-626X and Pringle, J.E. orcid.org/0000-0002-1465-4780 (2024) On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos. Journal of Plasma Physics, 90 (1). 905900101. ISSN 0022-3778
Abstract
Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma β∼1. Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at β≫1. This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of β≫1. We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as R2/3m. We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of Rm∼1010. We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), 2024. Published by Cambridge University Press. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | astrophysical plasmas |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Astrophysics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 31 Jan 2024 15:29 |
Last Modified: | 31 Jan 2024 15:29 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/s002237782300140x |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208447 |