Supernova and Cosmic rays Notes

https://www.aanda.org/articles/aa/pdf/2018/10/aa32879-18.pdf

The magnetic field turbulence created upstream and at the shock by various instabilities is transferred downstream where it is eventually damped due to the lack of the turbulence driving (Pohl et al. 2005).

The immediate downstream magnetic field is transported inside the SNR with the plasma flow and evolves following the induction equation for ideal MHD.

The remnant expanded in a medium with small dense clouds that survive the passage of the shock
and provide target material for cosmic rays. However, this scenario also has diverticulitis large amount of mass in clouds required for a fit of the high energy spectrum in this scenario requires pre-exiting clouds unaffected by the stellar wind of the progenitor star, which is rather implausible as the stellar wind would form kevin-helmholtz and rayleigh-taylor instabilities destroying the outer layers of the clouds. This would be followed by the formation of steams of gas, which would stongle emit x-rays when interacting with the forward shock.

Cosmic ray production in supernovae
https://arxiv.org/pdf/1801.08890.pdf

4.5 Effect of CR acceleration on remnant dynamics, plasma heating, and thermal X-ray production

If CRs are produced efficiently (i.e., > 10% of the shock bulk flow kinetic energy is placed in relativistic particles), the backpressure of CRs will influence the remnant hydrodynamics since relativistic particles produce less pressure for a given energy density than non-relativistic ones.
The energy placed in CRs comes from the thermal plasma so the shocked temperature is less than expected for test-particle acceleration.
Furthermore, the efficient production of CRs can result in an increase in the shock compression ratio from standard Rankine-Hugoniot values.
The change in temperature and density of the shocked plasma will modify the X-ray line emission. This effect has been studied extensively with a code coupling the remnant hydrodynamics with efficient CR production (see Ellison et al. 2012, Patnaude et al. 2017, and references therein). The effect of CR production influences the non-equilibrium ionization X-ray emission in observable ways.


4.6 Magnetic field amplification (MFA)
? the correlation between magnetic field amplifiation and cosmic rays pressure 
? MFA need high cosmic rays pressure (proton is important)
Bykov et al. (2014) giving the pressure in magnetic turbulence versus shock speed u0, as obtained with Monte Carlo techniques including the resonant CR-streaming instability and two non-resonant CR-current instabilities (i.e., Bell 2005, Bykov et al. 2013). The Monte Carlo results show that the efficiency of MFA, as defined by the pressure in turbulence, saturates at ∼ 10 − 15% of the far upstream bulk flow ram pressure.
https://arxiv.org/pdf/1105.0130.pdf (Magnetic fields in cosmic particle acceleration sources)




4.7 Cosmic ray escape in Fermi acceleration
diffusion coefficient which is an increasing function of CR momentum and the fact that all real shocks are finite in extent. In this case, at some p, $D(p)/u_{sh} ∼ R_{sh}$, where $R_sh$ is the shock radius, and the CR can no longer be confined independent of any plasma physics details (see Drury 2011, for a discussion of effects of the background ISM field)

A consequence of escape is that, if SN shocks are producing galactic CRs by Fermi acceleration, an outside observer would see at each particular moment just a relatively narrow spectrum of the escaped particles centered at some maximum momentum $p_{max}(t)$. However, since $p_{max}$ evolves with the SNR expansion, the time integrated CR spectrum can be an extended power law (e.g., Ptuskin & Zirakashvili 2005).

The escaping CR spectrum is clearly broadened when super-diffusion is taken into account. This broadening will influence the pion decay emission and measurements of γ-ray spectra produced by CRs escaping a SNR adjacent to a molecular cloud can be used to constrain super-diffusive transport models.



Observational Signatures of Particle Acceleration in Supernova Remnants

https://link.springer.com/article/10.1007%2Fs11214-012-9919-8



Acceleration time to x TeV for electron
https://www.aanda.org/articles/aa/full_html/2018/04/aa30002-16/aa30002-16.html#R8

TeV PWN  size >> x-ray PWN

Efficiency of pulsar spin down energy to cosmic ray energy






Within the hypothesis of a hadronic origin of gamma-rays, the gamma-ray flux is proportional to the number densities of the ambient matter and relativistic protons, while the X-ray flux is proportional to the number density of electrons. If the matter distribution varies significantly throughout the SNR, we need fine parameter tuning among the matter distribution, the electron injection rate, and the proton injection rate, in order to produce the tight correlation. Therefore, a more natural explanation is that the matter density is uniform, and that the injection rates of electrons and protons are proportional to each other

There remains the possibility (Malkov et al. 2005) that the density increases steeply outwards (SNR hitting a shell) to the point where most of the γ-ray emission is produced outside the remnant

compute the distribution of CRs in ahead the front shock. https://ui.adsabs.harvard.edu/abs/2015A%26A...577A..12F/abstract