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Register a new userDiagnosing Cosmic Ray Modified Shocks with H {alpha} Polarimetry
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A novel diagnostic of cosmic-ray modified shocks by polarimetry of H $alpha$ emissions is suggested. In a cosmic-ray modified shock, the pressure of cosmic rays is sufficiently high compared to the upstream ram pressure to force the background plasma to decelerate (measured in the shock rest frame). Simultaneously, a fraction of the hydrogen atoms co-existing in the upstream plasma collide with the decelerated protons and undergo charge-exchange reactions. As a result, hydrogen atoms with the same bulk velocity of the decelerated protons are generated. We show that when the shock is observed from edge-on, the H $alpha$ radiated by these upstream hydrogen atoms is linearly polarized with a sizable degree of a few per cent as a result of resonant scattering of Ly $beta$. The polarization direction depends strongly on the velocity modification; the direction is parallel to the shock surface for the case of no modification, while the direction is parallel to the shock velocity for the case of a modified shock.
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The non-linear back reaction of accelerated cosmic rays at the shock fronts, leads to the formation of a smooth precursor with a length scale corresponding to the diffusive scale of the energetic particles. Past works claimed that shocklets could be created in the precursor region of a specific shock width, which might energize few thermal particles to sufficient acceleration and furthermore this precursor region may act as confining large angle scatterer for very high energy cosmic rays. On the other hand, it has been shown that the smoothing of the shock front could lower the acceleration efficiency. These controversies motivated us to investigate numerically by Monte Carlo simulations the particle acceleration efficiency in oblique modified shocks. The results show flatter spectra compared to the spectra of the pressumed sharp discontinuity shock fronts. The findings are in accordance with theoretical predictions, since the scattering inside the precursor confines high energy particles to further scattering, resulting in higher energies making the whole acceleration process more efficient.
Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles, $p_{max}$, decreases with time, as is the case for the Sedov-Taylor phase of expansion of a shell Supernova Remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time $t$, particles with momenta larger than $p_{max}(t)$ leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at Earth. In this paper we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov-Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at Earth.
Particle acceleration at non-relativistic shocks can be very efficient, leading to the appearance of non-linear effects due to the dynamical reaction of the accelerated particles on the shock structure and to the non-linear amplification of the magnetic field in the shock vicinity. The value of the maximum momentum $p_{max}$ in these circumstances cannot be estimated using the classical results obtained within the framework of test particle approaches. We provide here the first attempt at estimating $p_{max}$ in the cosmic ray modified regime, taking into account the non-linear effects mentioned above.
Supernova remnants (SNRs) are believed to accelerate particles up to high energies through the mechanism of diffusive shock acceleration (DSA). Except for direct plasma simulations, all modeling efforts must rely on a given form of the diffusion coefficient, a key parameter that embodies the interactions of energetic charged particles with the magnetic turbulence. The so-called Bohm limit is commonly employed. In this paper we revisit the question of acceleration at perpendicular shocks, by employing a realistic model of perpendicular diffusion. Our coefficient reduces to a power-law in momentum for low momenta (of index $alpha$), but becomes independent of the particle momentum at high momenta (reaching a constant value $kappa_{infty}$ above some characteristic momentum $p_{rm c}$). We first provide simple analytical expressions of the maximum momentum that can be reached at a given time with this coefficient. Then we perform time-dependent numerical simulations to investigate the shape of the particle distribution that can be obtained when the particle pressure back-reacts on the flow. We observe that, for a given index $alpha$ and injection level, the shock modifications are similar for different possible values of $p_{rm c}$, whereas the particle spectra differ markedly. Of particular interest, low values of $p_{rm c}$ tend to remove the concavity once thought to be typical of non-linear DSA, and result in steep spectra, as required by recent high-energy observations of Galactic SNRs.
We present a semi-analytical kinetic calculation of the process of non-linear diffusive shock acceleration (NLDSA) which includes the magnetic field amplification due to cosmic ray induced streaming instability, the dynamical reaction of the amplified magnetic field and the possible effects of turbulent heating. The approach is specialized to parallel shock waves and the parameters we chose are the ones appropriate to forward shocks in Supernova Remnants. Our calculation allows us to show that the net effect of the amplified magnetic field is to enhance the maximum momentum of accelerated particles while reducing the concavity of the spectra, with respect to the standard predictions of NLDSA. This is mainly due to the dynamical reaction of the amplified field on the shock, which noticeably reduces the modification of the shock precursor. The total compression factors which are obtained for parameters typical of supernova remnants are $R_{tot}sim 7-10$, in good agreement with the values inferred from observations. The strength of the magnetic field produced through excitation of streaming instability is found in good agreement with the values inferred for several remnants if the thickness of the X-ray rims are interpreted as due to severe synchrotron losses of high energy electrons. We also discuss the relative role of turbulent heating and magnetic dynamical reaction in driving the reduction of the precursor modification.
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