Numerical Studies of Photon Bubble Instability in a Magnetized, Radiation‐dominated Atmosphere

Abstract

An initially static, plane-parallel, radiation pressure supported exponentialatmosphere in a strong magnetic field is found to be unstable tothe growth of buoyant low-density regions or "photon bubbles" inlinear stability analysis. Here we present a series of numericalstudies of the photon bubbles in such an atmosphere carried out using aquasi--two-dimensional radiation hydrodynamical code. When a single-modeperturbation is applied to the atmosphere, we find that the growth ofthese bubbles is in good agreement with the linear theory. When theevolution becomes nonlinear, the growth of the photon bubbles is found tobe an efficient mechanism of energy transport. The presence of thelow-density regions helps to increase the photon diffusion speed bya factor of several, while the buoyancy of the bubbles serves totransport energy via advection. Multimode studies, consisting of aperturbation with the linear combination of two single modes and a randomperturbation, suggest that there is a tendency toward merger of thephoton bubbles in their transport properties. The small wavenumbermodes eventually dominate in radiation pressure, while the largewavenumber modes, although having higher growth rates, also saturatemore quickly, and their contribution to the energy transport canbe truncated. A grid study and the multimode calculations indicatethat the energy transport through the atmosphere is well representedas long as the photon bubble mode with optical depth of ~10 over awavelength is well resolved. Possible applications of the photon bubbleinstability includes the settling layer in the accretion column of aneutron star undergoing super-Eddington accretion. The enhanced energytransport may manifest itself in the emergent spectrum from the accretingpulsars and in the short-time variability in the light curves.