Tearing Instability in Gyrotropic Magnetohydrodynamics: Effects of Equilibrium Pressure Anisotropy
- 1University of São Paulo
- 2National Institute for Space Research
Abstract
Weakly collisional plasmas are widespread in astrophysics and can sustain pressure anisotropy, yet most analytical tearing-mode scalings assume an isotropic equilibrium. We develop a linear theory of resistive tearing in nonideal gyrotropic MHD for a force-free Harris current sheet characterized by perpendicular plasma- β β ₀ and parallel-minus-perpendicular beta difference Δ β ₀ . In the ideal outer region, anisotropy changes the far-field decay rate and the matching parameter Δ ′ and sets the upper wavenumber cutoff for the localized tearing instability, α ≡ k a < α c = A / R 0 , where A = 1 − Δ β 0 / 2 , R 0 = 1 + 1 2 [ ( γ ∥ + γ ⊥ − 2 ) β 0 + γ ∥ Δ β 0 ] , and γ ∥ and γ ⊥ are the parallel and perpendicular polytropic indices specifying the gyrotropic pressure closure. In the resistive inner layer, anisotropy enters the leading momentum balance through A . We derive low- and high-wavenumber asymptotic branches. By matching them at their crossover, we identify the fastest-growing mode and find the maximum growth rate scaling γ max τ A ∼ A 1 / 2 R 0 − 1 / 4 S − 1 / 2 , where S is the Lundquist number and τ A is the Alfvén crossing time. Thus, the classical Lundquist-number exponent is retained, while the prefactor depends on the equilibrium anisotropy, plasma- β , and gyrotropic closure. The numerical eigenvalues support the low-wavenumber branch and are consistent with the high-wavenumber branch when Δ ′ is obtained by direct numerical integration of the ideal outer equation. Within the localized-mode and pressure-positive domain, positive Δ β ₀ generally suppresses tearing and broadens the inner layer, whereas negative Δ β ₀ enhances growth and shifts the fastest mode to a larger wavenumber. By identifying how prescribed equilibrium pressure anisotropy modifies both ideal outer matching and resistive inner-layer dynamics, this work provides a controlled extension of classical tearing theory within the gyrotropic MHD regime.
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BibTeX
@article{kowal2026tearing,
title = {{Tearing Instability in Gyrotropic Magnetohydrodynamics: Effects of Equilibrium Pressure Anisotropy}},
author = {Grzegorz Kowal and Gabriel L. Ferreira-Santos and Diego A. Falceta-Gonçalves},
journal = {The Astrophysical Journal},
year = {2026},
month = oct,
doi = {10.3847/1538-4357/aea20b},
url = {https://iopscience.iop.org/article/10.3847/1538-4357/aea20b},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Tearing Instability in Gyrotropic Magnetohydrodynamics: Effects of Equilibrium Pressure Anisotropy
AU - Grzegorz Kowal
AU - Gabriel L. Ferreira-Santos
AU - Diego A. Falceta-Gonçalves
PY - 2026
DA - 2026/10/13
JO - The Astrophysical Journal
DO - 10.3847/1538-4357/aea20b
UR - https://iopscience.iop.org/article/10.3847/1538-4357/aea20b
AB - Weakly collisional plasmas are widespread in astrophysics and can sustain pressure anisotropy, yet most analytical tearing-mode scalings assume an isotropic equilibrium. We develop a linear theory of resistive tearing in nonideal gyrotropic MHD for a force-free Harris current sheet characterized by perpendicular plasma- β β ₀ and parallel-minus-perpendicular beta difference Δ β ₀ . In the ideal outer region, anisotropy changes the far-field decay rate and the matching parameter Δ ′ and sets the upper wavenumber cutoff for the localized tearing instability, α ≡ k a < α c = A / R 0 , where A = 1 − Δ β 0 / 2 , R 0 = 1 + 1 2 [ ( γ ∥ + γ ⊥ − 2 ) β 0 + γ ∥ Δ β 0 ] , and γ ∥ and γ ⊥ are the parallel and perpendicular polytropic indices specifying the gyrotropic pressure closure. In the resistive inner layer, anisotropy enters the leading momentum balance through A . We derive low- and high-wavenumber asymptotic branches. By matching them at their crossover, we identify the fastest-growing mode and find the maximum growth rate scaling γ max τ A ∼ A 1 / 2 R 0 − 1 / 4 S − 1 / 2 , where S is the Lundquist number and τ A is the Alfvén crossing time. Thus, the classical Lundquist-number exponent is retained, while the prefactor depends on the equilibrium anisotropy, plasma- β , and gyrotropic closure. The numerical eigenvalues support the low-wavenumber branch and are consistent with the high-wavenumber branch when Δ ′ is obtained by direct numerical integration of the ideal outer equation. Within the localized-mode and pressure-positive domain, positive Δ β ₀ generally suppresses tearing and broadens the inner layer, whereas negative Δ β ₀ enhances growth and shifts the fastest mode to a larger wavenumber. By identifying how prescribed equilibrium pressure anisotropy modifies both ideal outer matching and resistive inner-layer dynamics, this work provides a controlled extension of classical tearing theory within the gyrotropic MHD regime.
SN - 0004-637X
SN - 1538-4357
ER -