Cosmic-ray acceleration during the impact of shocks on dense clouds

Thomas W Jones, Hyesung Kang

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


As part of an initial effort to understand the properties of diffusive shock acceleration in nonuniform environments we have carried out an extensive set of simulations of the dynamical interactions between plane nonradiative shocks and dense gas clouds initially in static equilibrium with their environments. These time dependent calculations are based on the two-fluid model for diffusive cosmic ray transport, and include the dynamically active energetic proton component of the cosmic rays as well as passive electron and magnetic field components. We have modeled shock-cloud impacts for both plane-parallel (one-dimensional) clouds and small two-dimensional clouds of circular cross section. Shock impact on a cloud creates new and sometimes complex shock structures, including a shock inside the cloud that is stronger than the incident shock, a reflected bow shock and in two dimensions a fairly strong tail shock. Except when the incident shock is itself already dominated by cosmic ray pressure, however, we find that the presence of the cloud adds little to the net acceleration efficiency of the original shock and can, in fact, reduce slightly the net amount of energy transferred to cosmic rays after a given time. Similarly, we find in two-dimensional cloud simulations that the always-weak bow shock and the shock inside the cloud are less important to acceleration during the interaction than the tail shock. When the incident shock is dominated by cosmic ray pressure both of these conclusions are changed, since the bow shock, by compressing the large preexisting cosmic ray pressure, becomes an effective site for acceleration augmentation. In those cases individual clouds may augment the energy transferred to cosmic rays by an amount several times the quantity ρau2saVc, where ρa is the density of the ambient medium, usa is the velocity of the incident shock, and Vc is the preimpact volume of the cloud. Using the passive electron and magnetic field elements of our simulations we modeled the synchrotron emissivity distribution associated with the two-dimensional clouds. The emissivity is controlled largely by growth of magnetic field in the shear layer around the cloud. None of the shocks generated, including the bow shock and the tail shock are strongly highlighted in the synchrotron emission of these models. The lifetime of a dense cloud after impact is probably only a few cloud crushing times, or significantly less than the time required to drag the cloud into its surrounding flow. This will limit the time during which such clouds might be visible as "hot spots" inside supernova remnants, for example.

Original languageEnglish (US)
Pages (from-to)560-573
Number of pages14
JournalAstrophysical Journal
Issue number2
StatePublished - Jan 10 1993


  • Acceleration of particles
  • Cosmic rays
  • Hydrodynamics
  • Shock waves

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