[Paper Review] On the corona of magnetars

Yuri Lyubarsky, David Eichler|ArXiv.org|Jun 25, 2007

Pulsars and Gravitational Waves Research1 references3 citations

TL;DR

This paper proposes that the persistent hard X-ray and soft gamma-ray emission from magnetars arises from a hot, extended corona formed by collisional Landau level excitations and pair production in the superstrong magnetic field, rather than collisionless instabilities. Electrons accelerated along magnetic field lines lose energy via collisional processes, escape the surface with high energy, and produce a power-law spectrum (photon index 1 < α < 2) via Comptonization and bremsstrahlung, explaining the observed nonthermal emission up to MeV energies.

ABSTRACT

Slow dissipation of non-potential magnetic fields in the magnetosphere of the magnetar is assumed to accelerate particles to hundreds MeV along the magnetic field lines. We consider interaction of fast particles with the surface of the magnetar. We argue that the collisionless dissipation does not work in the atmosphere of the neutron star because the two-stream instability is stabilized by the inhomogeneity of the atmosphere. Rather, the dominant dissipation mechanism is collisional Landau levelexcitations followed by pair production via the deexcitation gamma-rays ultimately leading to electrons with the energy below the Landau energy. We show that, because of the effects of the superstrong magnetic field, these electrons could emerge from the surface carrying most of the original energy so that a hot corona arises with the temperature of 1 - 2 MeV. This extended corona is better suited than a thin atmosphere to convert most of the primary beam energy to non-thermal radiation and, as we show, most of the coronal energy release is radiated away in the hard X-ray and the soft gamma-ray bands by Comptonization and bremsstrahlung. The radiation spectrum is a power-law with the photon index $1

Motivation & Objective

• To explain the origin of persistent nonthermal hard X-ray and soft gamma-ray emission observed from soft gamma-repeaters and anomalous X-ray pulsars.
• To resolve the inconsistency of collisionless two-stream instability models, which can only account for ~25% of observed hard-band luminosity.
• To investigate whether collisional processes in the superstrong magnetic field can produce a hot, extended corona capable of radiating most of the beam energy in the hard band.
• To assess the role of Landau level excitations and pair production in enabling electron escape and energy deposition at high altitudes.

Proposed method

• Analyzes particle beam interaction with the neutron star atmosphere under ultrastrong magnetic fields (B ~ 10^15 G), focusing on collisional dissipation mechanisms.
• Models electron energy loss via collisional Landau level excitations followed by deexcitation gamma-ray emission and pair production.
• Uses relativistic kinetic equations to describe Comptonization, incorporating relativistic invariants and angular dependence of scattering.
• Derives the steady-state photon distribution function using a modified Kompaneets-type equation adapted to magnetized plasmas.
• Solves the transport equation for photon spectra in the steady state, showing that power-law solutions with α > 1 are possible due to antisymmetry in scattering kernels.
• Applies the Fredholm alternative to prove existence of nontrivial solutions for α = 1, indicating formation of a hard power-law spectrum.

Experimental results

Research questions

• RQ1 Can collisional processes in the magnetar atmosphere produce a hot corona capable of radiating the observed hard X-ray and soft gamma-ray emission?
• RQ2 Why is the two-stream instability ineffective in the inhomogeneous atmosphere of a neutron star, and what alternative dissipation mechanism dominates?
• RQ3 How does the superstrong magnetic field alter electron dynamics and energy loss, enabling high-energy electrons to escape and form a corona?
• RQ4 What determines the spectral index of the nonthermal emission, and can it reproduce the observed power-law with 1 < α < 2?
• RQ5 Why is the observed emission extended into the MeV band, and how does this challenge previous models based on resonant scattering?

Key findings

• The two-stream instability is suppressed in the inhomogeneous neutron star atmosphere, invalidating collisionless dissipation as the primary mechanism.
• Collisional Landau level excitations and subsequent pair production dominate energy loss, enabling electrons to retain high energy and escape the surface.
• Electrons with energy below the Landau level energy (ε_B ≈ 1–2 MeV) can escape upward, forming a hot corona at T ≈ 1–2 MeV.
• Comptonization and bremsstrahlung in the corona produce a nonthermal power-law spectrum with photon index 1 < α < 2, matching observations.
• The model accounts for the fact that most of the beam energy is radiated in the hard X-ray and soft gamma-ray bands, resolving the luminosity discrepancy of prior models.
• The extended corona is better suited than a thin atmosphere to convert beam energy into observable nonthermal radiation, explaining the persistent MeV-band emission.