A Physical Relationship between Electron-Proton Temperature Equilibration and Mach Number in Fast Collisionless Shocks

Abstract

The analysis of Balmer-dominated optical spectra from non-radiative (adiabatic) SNRs has shown that the ratio of the electron to proton temperature at the blast wave is close to unity at v S 400 km s −1 , but declines sharply down to the minimum value of m e /m p dictated by the jump conditions at shock speeds exceeding 2000 km s −1 . We propose a physical model for the heating of electrons and ions in non-cosmic ray dominated, strong shocks (v S > 400 km s −1 ) wherein the electrons are heated by lower hybrid waves immediately ahead of the shock front. These waves arise naturally from the cosmic ray pressure gradient upstream from the shock. Our model predicts a nearly constant level of electron heating over a wide range of shock speeds, producing a relationship (T e /T p ) 0 ∝ v −2 S (∝ M −2 ) that is fully consistent with the observations.

Using optical lines to study particle acceleration at supernova remnants

“…If the equilibration occurs in a very efficient manner, the electron pressure cannot be neglected and the total gas pressure needs to include both the proton and electron contributions, namely P g = P i + P e = P i (1 + β), where β(z) ≡ T e /T i is the electron to proton temperature ratio and is taken here as a free parameter. While it is well established that electron-ion equilibration in the downstream might be only partial [24,25], in the presence of a precursor (either induced by the CRs or by the neutrals), also upstream of the shock the level of equilibration becomes an unknown. In order to solve the set of non-linear equations involving neutrals, ions, CRs and magnetic field, we adopt an iterative method that is fully described in [16].…”

Probing the effects of hadronic acceleration at the SN 1006 shock front

“…The blue curve shows the profile derived by assuming that η is proportional to the radio flux divided by B 3 / 2 , and adopting the magnetic field model MF2 of Petruk et al 2009 and by assuming the relationship between the injection efficiency and shock compression ratio adopted by Ferrand et al 2010. s cm −3 provides a very reasonable estimate for the time elapsed after the shock impact (∼ 200 yr), considering the 1 kyr age of the remnant; and iii) the temperature (kT I S M ∼ 1.4 keV) suits the expectations for the shocked ISM, as shown below. In collisionless shocks at high Mach number (shock velocity of the order of 10 3 km/s) the electron to proton temperature ratio is expected to be T e /T p 1 (Ghavamian et al 2007, Vink et al 2003. In the north-western limb of SN 1006 the shock velocity is v sh ∼ 3000 km/s and it has been calculated that T e /T p < 0.07 (Ghavamian et al 2002).…”

Observational Signatures of Particle Acceleration in Supernova Remnants

“…For these efficiencies, the acceleration process changes the shock structure and makes a precursor in the upstream region 2 (Drury and Voelk, 1981). In the precursor region, magnetic-field amplification (Lucek and Bell, 2000;Bell, 2004;Ohira and Takahara, 2010;Bykov et al, 2011b;Schure and Bell, 2011;Reville and Bell, 2011) and plasma heating (McKenzie and Völk, 1982;Ghavamian et al, 2007;Rakowski et al, 2008;Niemiec et al, 2008;Ohira et al, 2009a;Raymond et al, 2011) are thought to occur. Although there is more and more evidence that magnetic field amplification is important, the process itself is not yet fully understood.…”