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Fast electrons at slow shocks

Microphysics of slow collisionless shocks in nonthermal sources of radiation

A. Bohdan, M. Pohl, T. Teschke, P. J. Morris, Insti-tut für Physik und Astronomie, Universität Potsdam

In Short

• We conduct kinetic simulations of non-relativisticshocks to study the acceleration of electrons atsupernova remnants

• Our main objective is to establish whether ornot our understanding of electron acceleration atmildly relativistic shocks also applies to shockswith realistic velocities.

• Our simulations are scientifically important be-cause they address the unsolved problem of elec-tron injection. It is vital that we understand thiscritical ingredient in the theory of particle accelera-tion at shocks because it determines the level ofcosmic-ray feedback and hence the nonlinearity ofthe system.

Deciphering the acceleration mechanisms ofcharged particles is essential to our understandingof many physical phenomena and of high interestin astroplasma physics. It is widely accepted thatshocks, such as those formed by the interaction ofsupernova ejecta with the interstellar medium, canefficiently accelerate charged particles. The pres-ence of freshly accelerated electrons is inferred bythe association of radiation at radio, X-ray, and γ-rayfrequencies to shocks. It is usually assumed thatthese particles are accelerated by diffusive shock ac-celeration. Here, electrons undergo repeated shockcrossings and gain energy each time. However, thispicture is not yet complete, with a crucial unsolvedproblem that of particle injection. For diffusive shockacceleration to operate, particles must see the shockas a sharp discontinuity in the plasma flow. In reality,the shock has a finite width though that is commen-surate with the gyroradius of the incoming ions. Thecomparatively small electron mass, and thereforegyroradius, necessitates some pre-acceleration witha large energy gain to increase their gyroradii beforethey can be accelerated further.

Energetic charged particles couple to their envi-ronment through electromagnetic turbulence that ispartially self-produced. We conduct large particle-in-cell (PIC) simulations of collisionless shocks with aview to elucidate the processes that provide electronacceleration. PIC simulations are the appropriate

tool to study particle injection into shock accelera-tion because injection at collisionless shocks is akinetic problem that cannot be addressed with MHDor other fluid techniques. PIC simulations alone cantrack the impact of electron-scale fluctuations on theion dynamics through self-consistent treatment ofboth electrons and ions. Three-dimensional studiescan currently be conducted only with low resolutionand for very idealized parameters [1], and so weconcentrate on two-dimensional simulations.

We study electron pre-acceleration for conditionsat young-supernova-remnant shock waves, but theresults are applicable to any high-Mach-number non-relativistic perpendicular shock, e.g. the bow shockof Saturn [2]. A number of mechanisms are respon-sible for electron acceleration in the shock transition.The electrostatic Buneman instability is excited ifthe thermal velocity of the cold upstream electronsis smaller than the relative speed between incom-ing electrons and reflected ions, and is illustrated inFigure 1b. Shock surfing acceleration occurs whenelectrons are accelerated by these waves [3]. Mag-netic reconnection (Figure 1b) in the shock rampresults in acceleration of electrons via a number ofchannels discussed in [4]. Electrons also undergostochastic Fermi-like acceleration [5].

We have previously studied the efficiency of shock-surfing acceleration for a variety of simulation setupsand physical parameters. The energy gain alwaysarises from the electrostatic field of a Buneman wavewith which the electron travels for some time [6].

We recently showed that the relative contributionof each electron pre-acceleration mechanism was in-dependent of the shock velocity [7], yet our earlier re-sults from this project indicate preferential heating ofelectrons over ions for our slowest simulated shockvelocity of vsh ∼ 0.05c. We have already establishedthe importance of the Buneman instability regardingelectron acceleration via shock-surfing acceleration,therefore it is crucial that it is properly captured in oursimulations. This is challenging because the Bune-man instability occurs on spatial scales proportionalto the velocity difference between the incoming elec-trons and reflected ions that cause it, which in turn isproportional to the shock velocity. Thus we need toresolve smaller scales in our slow shock simulations,which is computationally demanding.

It is therefore possible that our simulation resolu-tion needs to be increased for slow shock simula-tions to properly resolve the Buneman instability orany additional small-scale structures. These couldotherwise cause numerical heating or modify the

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Figure 1: The structure of a slow (vsh = 0.053c) shock with in-plane magnetic field configuration. (a) shows the electron densityrelative to the original upstream density, while (b) and (c) show magnified views of magnetic reconnection and Buneman waves,respectively.

physical behaviour of electrons at the shock. Wetherefore wish to explore the effect of employing ahigher resolution on electron heating for slow shocksimulations.

These simulations are necessary to address ourmain question of whether or not our understanding ofelectron acceleration at mildly relativistic shocks alsoapplies to shocks with realistic, physically motivated,velocities. In detail, our objectives are:

• Does the simulation resolution need to be in-creased in order to properly capture the Bune-man instability for slow shocks?

• Can an insufficient simulation resolution pro-duce numerical heating effects, or otherwisemodify the physical behaviour of particles at theshock?

• Can we resolve new sub-structures present inthe shock foot for higher-resolution simulationsof slow shocks?

• What is the effect on the obliquity angle on thestructure of a slow shock and how does it in-fluence the instabilities present in the transitionregion? Does such a shock behave in the sameway as those with faster shock velocities?

• For oblique slow shocks, what is the rate ofreflected electrons? What is their energy distri-

bution and how do they modify the region up-stream of the shock?

WWWhttp://www.physics.uni-potsdam.de/index.php

More Information[1] Matsumoto, Y., Amano, T., Kato, T. N., et al.,

2017, PRL 119, 105101 doi:10.1103/Phys-RevLett.119.105101

[2] Masters, A., Sulaiman, A. H., Sergis, N., etal. 2016, ApJ, 826, 48. doi:10.3847/0004-637X/826/1/48

[3] Bohdan, A., Niemiec, J., Pohl, M., et al.2019, ApJ, 885, 10 doi:doi:10.3847/1538-4357/ab43cf

[4] Bohdan, A., Pohl, M., Niemiec, J., et al. 2020,ApJ, 893, 6 doi:doi:10.3847/1538-4357/ab7cd6

[5] Bohdan, A., Niemiec, J., Kobzar, O., et al. 2017,ApJ, 847, 71 doi:10.3847/1538-4357/aa872a

[6] Bohdan, A., Niemiec, J., Pohl, M., et al. 2019,ApJ, 878, 5 doi:10.3847/1538-4357/ab1b6d

[7] Bohdan, A., Pohl, M., Niemiec, J. et al. 2020,ApJ in press, arXiv:2008.05920

Project PartnersJ. Niemiec, A.Ligorini; IFJ PAN Cracow, Poland

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http://www.physics.uni-potsdam.d e/index.phphttp://dx.doi.org/10.1103/PhysRevLett.119.105101http://dx.doi.org/10.1103/PhysRevLett.119.105101http://dx.doi.org/10.3847/0004-637X/826/1/48http://dx.doi.org/10.3847/0004-637X/826/1/48http://dx.doi.org/doi:10.3847/1538-4357/ab43cfhttp://dx.doi.org/doi:10.3847/1538-4357/ab43cfhttp://dx.doi.org/doi:10.3847/1538-4357/ab7cd6http://dx.doi.org/10.3847/1538-4357/aa872ahttp://dx.doi.org/10.3847/1538-4357/ab1b6d

Microphysics of slow collisionless shocks in nonthermal sources of radiation