Photon Splitting in Strongly Magnetized Cosmic Objects—Revisited

Abstract

We reassess the importance of photon splitting to spectral formation in cosmic X-ray and $\gamma$-ray sources with magnetic fields of several $10^{12}$ gauss. Our analysis is based on the recent numerically accurate evaluation of the full relativistic expression for photon splitting at neutron star magnetic field strengths (Mentzel et al. 1994). Using these results we demonstrate that Adler's (1971) widely used approximation formula for photon splitting underestimates the correct splitting rate by {\em several} orders of magnitude, at these magnetic field strengths. Even down at X-ray energies of a few tens of keV magnetic photon splitting is found to be an efficient photon conversion process, producing mean free paths as short as several tens of centimeters for fields on the order of $5 \times 10^{12}$ gauss. We conclude that previous analyses of the contributions of magnetic photon splitting to spectral formation based on Adler's approximation formula are physically unreliable, and, in particular, that photon splitting must be included in realistic modelings of spectra of both strongly magnetized cosmic X-ray and $\gamma$-ray sources.