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

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Abstract
An initially static, plane-parallel, radiation pressure supported exponential atmosphere in a strong magnetic field is found to be unstable to the growth of buoyant low-density regions or "photon bubbles" in linear stability analysis. Here we present a series of numerical studies of the photon bubbles in such an atmosphere carried out using a quasi-two-dimensional radiation hydrodynamical code. When a single-mode perturbation is applied to the atmosphere, we find that the growth of these bubbles is in good agreement with the linear theory. When the evolution becomes nonlinear, the growth of the photon bubbles is found to be an efficient mechanism of energy transport. The presence of the low-density regions helps to increase the photon diffusion speed by a factor of several, while the buoyancy of the bubbles serves to transport energy via advection. Multimode studies, consisting of a perturbation with the linear combination of two single modes and a random perturbation, suggest that there is a tendency toward merger of the photon bubbles in their transport properties. The small wavenumber modes eventually dominate in radiation pressure, while the large wavenumber modes, although having higher growth rates, also saturate more quickly, and their contribution to the energy transport can be truncated. A grid study and the multimode calculations indicate that the energy transport through the atmosphere is well represented as long as the photon bubble mode with optical depth of ~10 over a wavelength is well resolved. Possible applications of the photon bubble instability includes the settling layer in the accretion column of a neutron star undergoing super-Eddington accretion. The enhanced energy transport may manifest itself in the emergent spectrum from the accreting pulsars and in the short-time variability in the light curves.