Vacuum polarization effects on radiative opacities in a strong magnetic field

We study the electromagnetic properties of plasmas allowing for the polarization effect of the vacuum induced by the presence of a strong external magnetic field. Adopting the cold-plasma polarization tensor to account for the electron component, we find that the polarization properties and transport of x-ray radiation can be severely altered by the magnetic vacuum effects. The effect becomes important at relatively high frequencies, $\frac{\omega }{{\omega }_p}\gtrsim {\left(\frac{15\pi }{\alpha }\right)}^{\frac{1}{2}}$ $\frac{B_c}{B}$ where ${\omega }_p={\left(4\mathrm{}\pi n_e\frac{e^2}{m}\right)}^{\frac{1}{2}}$ is the plasma frequency of the electron component, $\alpha$ is the fine-structure constant, and $B_c=\frac{m^2{c}^3}{e\hslash }\simeq 4.4\times {10}^{13}$ G is the electrodynamic critical field. For typical pulsar magnetic fields, $B\sim 0.1$ $B_c$, and x-ray frequencies, this condition is satisfied even for relatively high plasma densities $n_e\sim {10}^{23}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Whenever the above inequality is fulfilled the vacuum effect dominates the polarization properties of the normal modes of the medium, giving rise to a significant change in the medium opacity. The Thomson, bremsstrahlung, and cyclotron opacities are thus significantly altered from their usual cold-plasma values. The largest departures are found in the vicinity of the electron gyrofrequency, where the vacuum induces a strongly anisotropic resonant behavior on the ordinary mode (which is nonresonant in the usual cold-plasma circumstances). This property may be significant in analyzing the polarization and spectral character of the cyclotron feature in Hercules X-1 and other accreting x-ray pulsars.