Cosmic rays (CRs) leave their sources mainly along the local magnetic field present in the region around the source and in doing so they excite both resonant and non-resonant modes through streaming instabilities. The excitation of these modes leads to enhanced scattering and in turn to a large pressure gradient that causes the formation of expanding bubbles of gas and self-generated magnetic fields. By means of hybrid particle-in-cell simulations, we here demonstrate that, by exciting this instability, CRs excavate a cavity around their source where the diffusivity is strongly suppressed. This phenomenon is general and is expected to occur around any sufficiently powerful CR source in the Galaxy. Our results are consistent with recent γ-ray observations where emission from the region around supernova remnants, stellar clusters and pulsar wind nebulae have been used to infer that the diffusion coefficient around these sources is ∼ 10 − 100 times smaller than the typical Galactic one.
Cosmic rays are thought to escape their sources streaming along the local magnetic field lines. We show that this phenomenon generally leads to the excitation of both resonant and non-resonant streaming instabilities. The self-generated magnetic fluctuations induce particle diffusion in extended regions around the source, so that cosmic rays build up a large pressure gradient. By means of two-dimensional (2D) and three-dimensional (3D) hybrid particle-in-cell simulations, we show that such a pressure gradient excavates a cavity around the source and leads to the formation of a cosmic ray dominated bubble, inside which diffusivity is strongly suppressed. Based on the trends extracted from self-consistent simulations, we estimate that, in the absence of severe damping of the self-generated magnetic fields, the bubble should keep expanding until pressure balance with the surrounding medium is reached, corresponding to a radius of ∼10–50 pc. The implications of the formation of these regions of low diffusivity for sources of Galactic cosmic rays are discussed. Special care is devoted to estimating the self-generated diffusion coefficient and the grammage that cosmic rays might accumulate in the bubbles before moving into the interstellar medium. Based on the results of 3D simulations, general considerations on the morphology of the γ-ray and synchrotron emission from these extended regions also are outlined.
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