The usefulness and limits of coronagraphy in the presence of pinned speckles

In this Letter we study the utility and limitations of ground-based coronagraphy with adaptive optics (AO). In very high AO correction regimes, residual speckles are pinned on the diffraction rings of the Airy pattern. We show that this effect is due to small errors in the complex wave in the focal plane, amplified by the coherent part of the wave. The statistics of these speckles are fairly well described by a modified Rician distribution. The variance of the speckles, at high flux and at photon-counting levels, finds simple expressions. The total variance can be partitioned into two contributions: one that can be suppressed by a coronagraph and one that cannot. Different regimes can be identified. These results enable us to analyze when a coronagraph can defeat the noise variance, and they provide a criterion for the effectiveness of such instruments.