Vacuum Polarization Effects in Baryon-Loaded Magnetar Bursts and Implications for X-ray Polarization

TL;DR

The paper tackles vacuum polarization effects in magnetar bursts where fireballs are loaded with baryons, requiring a three-component plasma model. It develops a comprehensive framework incorporating vacuum corrections into the dielectric response, derives the normal modes, and identifies a vacuum resonance condition that depends on the total pair density, enabling MSW-like mode conversion and nonadiabatic Landau-Zener transitions. The authors apply the framework to analytic trapped and expanding fireball scenarios, predicting energy-dependent X-ray polarization signatures that depend on the baryon loading parameter $f$ and magnetic field $B$, with potential probes from current or future X-ray polarimeters. These predictions offer a way to diagnose fireball composition and dynamics in magnetar bursts, linking fundamental QED effects to observable polarization signals.

Abstract

Magnetars provide natural laboratories for strong-field quantum electrodynamics processes, such as vacuum polarization, which gives rise to vacuum resonance together with the plasma response. We develop a general framework to describe vacuum resonance in a three-component plasma consisting of ions, electrons, and positrons, as expected in baryon-loaded magnetar bursts. By introducing a parametrization of the plasma composition, we establish the general criterion for the occurrence of vacuum resonance in such plasmas. Our analysis encompasses both Mikheyev-Smirnov-Wolfenstein-like adiabatic mode conversion and nonadiabatic eigenmode transition, highlighting their dependence on the plasma composition. Applying this framework to baryon-loaded fireballs in magnetar bursts, we estimate the characteristic X-ray polarization signatures. Detection of these polarizations will provide observational signatures of vacuum polarization as well as baryon loading in magnetar fireballs.

Figures (6)

• Figure 1: Schematic picture of baryon-loaded fireballs in magnetar bursts; a trapped fireball (right) and an expanding fireball (top). The coexistence of the two fireballs is not required.
• Figure 2: Electron-positron density dependence of $\bar{K}_\pm$, defined as $K_\pm$ normalized by the maximum value of $K_+$ in the large $\sigma n_e$ limit. Solid lines correspond to $K_+$, and dashed lines to $K_-$. Different colors indicate different values of $f$ (see Eq. \ref{['eq:f']}). The curves for $f = 10^{-5}$, $10^{-1}$, $0.5$, $1-10^{-1}$, and $1-10^{-5}$ are further normalized by a factor of $1.6\times 10^6$, $1.6\times 10^2$, $2.5\times 10^1$, $1.0\times 10$, and $8.3$, respectively. The inset shows curves around the vacuum resonance in a linear scale.
• Figure 3: Observed spectrum from a trapped fireball and pair number densities. (Top panel) The black line shows the total observed spectrum, the red dotted line indicates the observed X-mode photons, and the blue dashed line indicates the observed O-mode photons. The lower portion shows the nonadiabatic transition probability. The green vertical line marks $\omega_{\rm cri}$. (Bottom panel) The magenta line shows the number density at which X-mode photons are emitted from the plasma, and the black line shows $n_{e,{\rm res}}$ where vacuum resonance occurs. The red and blue arrows indicate the propagation of photons and their typical modes in terms of X/O, rather than $\pm$.
• Figure 4: $\omega_{\rm cri}$ (green line) and $\omega_{\rm adi}$ (purple line) for different baryon loading, ${\mathcal{F}}_{\rm trap}$. The legends $Bx$ represents the model with $B = 10^{x}\,{\rm G}$.
• Figure 5: Observed spectrum from an expanding fireball. Each line has the same meaning as the top panel of Fig \ref{['fig:trapped']}.