PHOTON BUBBLES - OVERSTABILITY IN A MAGNETIZED ATMOSPHERE

Linear stability theory is used to study the formation of "photon bubbles" in a convectively stable scattering atmosphere supported against gravity entirely by radiation pressure. A WKB analysis shows that internal waves in an isothermal magnetized atmosphere are overstable, when the magnetic pressure of a vertical magnetic field satisfies B2/8-pi > (M0/2-gamma)p(rad). Here M0 << 1 is the ratio of the sound crossing time to the photon diffusion time in the atmosphere and gamma is the ratio of specific heats. The unstable waves are buoyant, rising with a group velocity approximately c0M0, where c0 is the isothermal sound speed, and have maximum growth rate approximately kc0M0(0.4) when kh >> M0(-1/2). Here k is the wavenumber, and h is the isothermal scale height. The most unstable waves correspond to the formation of long vertical fingers of radiation where the density is depleted relative to the surroundings. The instability mechanism is the small conductive transfer of heat from high-density to low-density regions in the wave, while the wave's propagation is maintained by much larger radiative heat transfer across the magnetic field. A simple model is developed for the two-dimensional structure of a plasma mound formed by laminar accretion onto the magnetic poles of a neutron star, in which upward photon diffusion balances downward photon advection with the plasma. It is shown that the vertical pressure and density structure is the same as in an isothermal atmosphere. Application of the stability theory to this model suggests photon bubbles would form in a polar accretion mound under the conditions expected in accretion-powered pulsars within a few tenths of a millisecond. Because long-wavelength modes have the largest rise speeds, eventual dominance by a few large bubbles is suggested, and possible connections between bubble formation and short-time variability in accretion-powered pulsars is briefly discussed, as well as a possible connection of the photon bubble phenomenon to the rapid time variability observed in the Rapid Burster and in quasi-periodic oscillator sources.