The Effect of Synchrotron Losses on Multiple Diffusive Shock Acceleration

Don Melrose , Ashley Crouch, PASA, 14 (3), 251
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Conclusions

We present the results of numerical calculations that show the effect of synchrotron losses on diffusive shock acceleration (followed by adiabatic decompression) at multiple shocks. Our main results can be summarized as follows.

  • Synchrotron losses are most important, during the acceleration process, when the electrons are in the compressed-B region just downstream from the shock. Synchrotron losses imply a synchrotron cutoff, tex2html_wrap_inline734, to the distribution of accelerated particles; DSA cannot cause any particle to be accelerated to tex2html_wrap_inline800.
  • It is shown analytically that two procedures for treating the combination of synchrotron losses and DSA are equivalent. In one treatment, the effects of synchrotron losses are included in the momentum change in each cycle of a particle crossing the shock from upstream to downstream and back. In the other procedure, used in our numerical calculations, synchrotron losses are first neglected to find the distribution of electrons resulting from DSA alone, and then the synchrotron losses are allowed to modify this distribution. The two procedures are equivalent provided that the time for which the synchrotron losses are allowed to operate in the latter `sequential' procedure is identified as the time (7).
  • Just below the synchrotron cutoff, the distribution of particles injected at an initial shock and subjected to DSA at many shocks without further injection tends to form a plateau distribution (f(p) independent of p), which corresponds to an energy spectrum tex2html_wrap_inline780.
  • The distribution below the synchrotron cutoff due to the cumulative effect of injection at every shock tends to a distribution tex2html_wrap_inline370 with tex2html_wrap_inline372 at tex2html_wrap_inline696, with the distribution becoming somewhat flatter such that the slope has a peak (with tex2html_wrap_inline814) just below tex2html_wrap_inline364 (at tex2html_wrap_inline818 for strong shocks). Such a distribution, if the source were homogeneous (which it is not due to the shocks), would correspond to a flat synchrotron spectrum (tex2html_wrap_inline820) becoming a weakly inverted spectrum (tex2html_wrap_inline822) with a peak just below a sharp cutoff due to synchrotron losses.

We conclude that it is possible in principle for multiple DSA coupled with synchrotron losses to account for a flat synchrotron spectrum. This may be a viable explanation for the flat synchrotron spectra observed in some Galactic Centre sources. A more detailed investigation of this possibility is warranted.


Next Section: Acknowledgments
Title/Abstract Page: The Effect of Synchrotron
Previous Section: Interpretation
Contents Page: Volume 14, Number 3

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