Spectral Breaks as a Signature of Cosmic Ray Induced Turbulence in the Galaxy

We show that the complex shape of the cosmic ray (CR) spectrum, as recently measured by PAMELA and inferred from Fermi-LAT $\gamma$-ray observations of molecular clouds in the Gould belt, can be naturally understood in terms of basic plasma astrophysics phenomena. A break from a harder to a softer spectrum at rigidity $R\simeq 10\mathrm{GV}$ follows from a transition from transport dominated by advection of particles with Alfvén waves to a regime where diffusion in the turbulence generated by the same CRs is dominant. A second break at $R\simeq 200\mathrm{GV}$ happens when the diffusive propagation is no longer determined by the self-generated turbulence, but rather by the cascading of externally generated turbulence (for instance due to supernova bubbles) from large spatial scales to smaller scales where CRs can resonate. Implications of this scenario for the cosmic ray spectrum, grammage, and anisotropy are discussed.

Figure 1

Spectrum of CR protons from our calculations (solid line) compared with the results from observations of $\gamma$-ray emission from clouds in the Gould belt [2] (shaded region) and with PAMELA measurements [1].

Figure 2

Diffusion coefficient induced by streaming instability of CRs and cascading from a large spatial scale of 50 pc.

Figure 3

Grammage obtained in our calculations (solid line) compared with the leaky box fit proposed in Ref. 20 (dashed and dotted lines are the fit for $\delta =0.5$ and $1/3$ respectively).