Super-Eddington Atmospheres That Do Not Blow Away

We show that magnetized, radiation-dominated atmospheres can support steady state patterns of density inhomogeneity that enable them to radiate at far above the Eddington limit without suffering mass loss. The inhomogeneities consist of periodic shock fronts bounding narrow, high-density regions, interspersed with much broader regions of low density. The flow of radiation avoids the dense regions, which are therefore weighed down by gravity, while gas in the low-density regions is slammed upward into the shock fronts by radiation force. As the wave pattern moves through the atmosphere, each parcel of matter alternately experiences upward and downward forces, which balance on average. We calculate the density structure and phase speed of the wave pattern and relate these to the density contrast and the factor by which the net radiation flux exceeds the Eddington limit. The presence of a magnetic field is essential for the existence of these flows since magnetic tension shares the competing forces between regions of different densities, preventing the atmosphere from blowing apart. There appears to be a broad family of modes propagating in arbitrary directions with respect to the direction of the mean magnetic field and exhibiting a range of density contrasts. While the transition from low to high density occurs through a strong shock, the gas must pass through a slow magnetosonic critical point in order to return to the low-density state. The flux of radiation escaping from the atmosphere exceeds the Eddington limit by a factor of order the square root of the ratio between maximum and minimum density. In principle, this factor can be as large as the ratio of magnetic pressure to mean gas pressure. Although the magnetic pressure must be large compared to the mean gas pressure in order to support a large density contrast, it need not be large compared to the radiation pressure. These highly inhomogeneous flows could represent the nonlinear development of the "photon bubble" instability discovered by Gammie. If they occur in nature, these structures could have an impact on our understanding of luminous systems such as accreting compact objects and very massive stars.