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Prof. Dr. Shahram Abbassi

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Department of Physics and Astronomy, Western University, London, ON N6A 3K7, Canada
Interests: theoretical astrophysics; accretion disks; GRBs; star-formation; astrophysical instabilities

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Dear Colleagues,

This Special Issue in Symmetry is devoted to plasma in astrophysical environments and the theoretical and computational frameworks used to describe it. A central theme is how symmetries and related invariants constrain plasma dynamics and how departures from symmetry arise through instabilities, turbulence, shocks, and magnetic reconnection. We welcome contributions on magnetohydrodynamic and kinetic processes relevant to accretion flows and disks, winds and jets, compact-object magnetospheres, and high-energy transients, including neutrino-dominated accretion and GRB-related systems. Submissions may include analytical developments, numerical simulations, and observationally motivated diagnostics that connect plasma microphysics to global structure and emission. The goal is to bring together diverse approaches and provide a coherent view of plasma processes across astrophysical scales.

Prof. Dr. Shahram Abbassi
Guest Editor

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33 pages, 2134 KB

Open AccessArticle

Symmetry and Symmetry Breaking in Pulsar Spin-Down Dynamics: Fractional Calculus, Non-Integer Braking Indices, and the Resolution of the Crab Pulsar Puzzle

by Farrukh Ahmed Chishtie and Sree Ram Valluri

Symmetry 2026, 18(4), 684; https://doi.org/10.3390/sym18040684 - 20 Apr 2026

Viewed by 436

Abstract

The rotational evolution of pulsars is governed by torque mechanisms whose mathematical structure encodes fundamental symmetries of the underlying physics. We demonstrate that the standard spin-down equation

\dot{f} = - s f - r f^{3} - g f^{5}

derives from [...] Read more.

\dot{f} = - s f - r f^{3} - g f^{5}

derives from a discrete antisymmetry requirement, namely invariance of the torque under reversal of rotation sense, which restricts the frequency dependence to odd integer powers. We show that physically motivated plasma processes systematically break this symmetry, introducing fractional frequency exponents: viscous Ekman pumping at the crust–superfluid boundary layer (

f^{3 / 2}

), magnetohydrodynamic turbulent dissipation via Kolmogorov and Sweet–Parker cascades (

f^{10 / 3}

f^{11 / 3}

), non-linear superfluid vortex dynamics (

f^{5 / 2}

), and saturated r-mode oscillations (

f^{7 - 2 β}

). The central result is an exact analytical resolution of the long-standing Crab pulsar braking index puzzle: the observed

n = 2.51 \pm 0.01

, which has defied explanation for nearly four decades, emerges naturally from the superposition of magnetic dipole radiation (

\dot{f} \propto f^{3}

) and boundary layer Ekman pumping (

\dot{f} \propto f^{3 / 2}

), with analytically derived coefficients yielding a dipole-component surface field

B_{p} = 6.2 \times 10^{12}

G—higher than the standard

\sqrt{P \dot{P}}

estimate of

3.8 \times 10^{12}

G, because that formula conflates dipole and non-dipole torques, but lower than applying the Larmor formula to the full spin-down rate (

7.6 \times 10^{12}

G), since

32.7 %

of the total torque is non-radiative boundary-layer dissipation. We develop the Riemann–Liouville fractional calculus formalism for these equations, showing that fractional derivatives break time-translation symmetry through intrinsic memory effects, with solutions expressed in terms of Mittag-Leffler and Fox H-functions that interpolate continuously between exponential (fully symmetric) and power-law (scale-free symmetric) relaxation. Lambert–Tsallis

W_{q}

functions with non-extensive parameter q encoding broken statistical symmetry enable equation-of-state-independent inference of neutron star compactness and tidal deformability. Our framework establishes a unified symmetry-based classification of pulsar spin-down mechanisms and predicts frequency-dependent braking indices evolving at rate

d n / d t \sim 2 \times 10^{- 4}

yr⁻¹, yielding

Δ n \approx 0.01

over 50 years—testable with current pulsar timing programmes. The formalism provides a coherent theoretical foundation connecting plasma microphysics at the neutron star interior to macroscopic observables in electromagnetic and gravitational wave channels. Full article

(This article belongs to the Special Issue Symmetry in Plasma Astrophysics)

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