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
bbp00033
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
bbp00033
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
