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

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.