Linear analysis of the Kelvin–Helmholtz instability in relativistic magnetized symmetric flows

Journal Article · 19 June 2023 · Monthly Notices of the Royal Astronomical Society

DOI: https://doi.org/10.1093/mnras/stad1833 · OSTI ID:2422188

Chow, Anthony  ^[1]; Rowan, Michael E.; Sironi, Lorenzo; Davelaar, Jordy ; Bodo, Gianluigi ; Narayan, Ramesh

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1. OSTI

ABSTRACT We study the linear stability of a planar interface separating two fluids in relative motion, focusing on the symmetric configuration where the two fluids have the same properties (density, temperature, magnetic field strength, and direction). We consider the most general case with arbitrary sound speed cs, Alfvén speed vA, and magnetic field orientation. For the instability associated with the fast mode, we find that the lower bound of unstable shear velocities is set by the requirement that the projection of the velocity on to the fluid-frame wavevector is larger than the projection of the Alfvén speed on to the same direction, i.e. shear should overcome the effect of magnetic tension. In the frame where the two fluids move in opposite directions with equal speed v, the upper bound of unstable velocities corresponds to an effective relativistic Mach number $$M_{\rm re}\equiv v/v_{\rm {f}\perp }\sqrt{(1-v_{\rm {f}\perp }^2)/(1-v^2)} \cos \theta =\sqrt{2}$$, where $$v_{\rm {f}\perp }=[v_{\rm {A}}^2+c_{\rm s}^2(1-v_{\rm {A}}^2)]^{1/2}$$ is the fast speed assuming a magnetic field perpendicular to the wavevector (here, all velocities are in units of the speed of light), and θ is the laboratory-frame angle between the flow velocity and the wavevector projection on to the shear interface. Our results have implications for shear flows in the magnetospheres of neutron stars and black holes – both for single objects and for merging binaries – where the Alfvén speed may approach the speed of light.

• Research Organization: Columbia Univ., New York, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0023015
• OSTI ID: 2422188
• Journal Information: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 1 Vol. 524; ISSN 0035-8711
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: United States
• Language: English