Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions
Abstract
Recent X-ray observations of merger shocks in galaxy clusters have shown that the post-shock plasma is two-temperature, with the protons being hotter than the electrons. Here, the second of a series, we investigate the efficiency of irreversible electron heating in perpendicular low Mach number shocks, by means of two-dimensional particle-in-cell simulations. We consider values of plasma beta (the ratio of thermal and magnetic pressures) in the range 4 ≲ β p0 ≲ 32, and sonic Mach number (the ratio of shock speed to pre-shock sound speed) in the range 2 ≲ M s ≲ 5, as appropriate for galaxy cluster shocks. As reflected in Paper I, magnetic field amplification—induced by shock compression of the pre-shock field, or by strong proton cyclotron and mirror modes accompanying the relaxation of proton temperature anisotropy—can drive the electron temperature anisotropy beyond the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance, and allows for efficient entropy production. We determine that the post-shock electron temperature T e2 exceeds the adiabatic expectation $${T}_{e2,\mathrm{ad}}$$ by an amount $$({T}_{e2}-{T}_{e2,\mathrm{ad}})/{T}_{e0}\simeq 0.044\,{M}_{s}({M}_{s}-1)$$ (here, T e0 is the pre-shock temperature), which depends only weakly on the plasma beta over the range 4 lesssim β p0 lesssim 32 that we have explored, as well as on the proton-to-electron mass ratio (the coefficient of sime0.044 is measured for our fiducial $${m}_{i}/{m}_{e}=49$$, and we estimate that it will decrease to sime0.03 for the realistic mass ratio). Our results have important implications for current and future observations of galaxy cluster shocks in the radio band (synchrotron emission and Sunyaev–Zel'dovich effect) and at X-ray frequencies.
- Authors:
-
- Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)
- Columbia Univ., New York, NY (United States). Dept. of Astronomy
- Publication Date:
- Research Org.:
- Columbia Univ., New York, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1542022
- Grant/Contract Number:
- SC0016542
- Resource Type:
- Accepted Manuscript
- Journal Name:
- The Astrophysical Journal (Online)
- Additional Journal Information:
- Journal Name: The Astrophysical Journal (Online); Journal Volume: 858; Journal Issue: 2; Journal ID: ISSN 1538-4357
- Publisher:
- Institute of Physics (IOP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; galaxies: clusters: general; instabilities; radiation mechanisms: thermal; shock waves
Citation Formats
Guo, Xinyi, Sironi, Lorenzo, and Narayan, Ramesh. Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions. United States: N. p., 2018.
Web. doi:10.3847/1538-4357/aab6ad.
Guo, Xinyi, Sironi, Lorenzo, & Narayan, Ramesh. Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions. United States. https://doi.org/10.3847/1538-4357/aab6ad
Guo, Xinyi, Sironi, Lorenzo, and Narayan, Ramesh. Thu .
"Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions". United States. https://doi.org/10.3847/1538-4357/aab6ad. https://www.osti.gov/servlets/purl/1542022.
@article{osti_1542022,
title = {Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions},
author = {Guo, Xinyi and Sironi, Lorenzo and Narayan, Ramesh},
abstractNote = {Recent X-ray observations of merger shocks in galaxy clusters have shown that the post-shock plasma is two-temperature, with the protons being hotter than the electrons. Here, the second of a series, we investigate the efficiency of irreversible electron heating in perpendicular low Mach number shocks, by means of two-dimensional particle-in-cell simulations. We consider values of plasma beta (the ratio of thermal and magnetic pressures) in the range 4 ≲ β p0 ≲ 32, and sonic Mach number (the ratio of shock speed to pre-shock sound speed) in the range 2 ≲ M s ≲ 5, as appropriate for galaxy cluster shocks. As reflected in Paper I, magnetic field amplification—induced by shock compression of the pre-shock field, or by strong proton cyclotron and mirror modes accompanying the relaxation of proton temperature anisotropy—can drive the electron temperature anisotropy beyond the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance, and allows for efficient entropy production. We determine that the post-shock electron temperature T e2 exceeds the adiabatic expectation ${T}_{e2,\mathrm{ad}}$ by an amount $({T}_{e2}-{T}_{e2,\mathrm{ad}})/{T}_{e0}\simeq 0.044\,{M}_{s}({M}_{s}-1)$ (here, T e0 is the pre-shock temperature), which depends only weakly on the plasma beta over the range 4 lesssim β p0 lesssim 32 that we have explored, as well as on the proton-to-electron mass ratio (the coefficient of sime0.044 is measured for our fiducial ${m}_{i}/{m}_{e}=49$, and we estimate that it will decrease to sime0.03 for the realistic mass ratio). Our results have important implications for current and future observations of galaxy cluster shocks in the radio band (synchrotron emission and Sunyaev–Zel'dovich effect) and at X-ray frequencies.},
doi = {10.3847/1538-4357/aab6ad},
journal = {The Astrophysical Journal (Online)},
number = 2,
volume = 858,
place = {United States},
year = {Thu May 10 00:00:00 EDT 2018},
month = {Thu May 10 00:00:00 EDT 2018}
}
Web of Science
Works referenced in this record:
Electromagnetic ion cyclotron instability driven by ion energy anisotropy in high-beta plasmas
journal, January 1975
- Davidson, R. C.; Ogden, Joan M.
- Physics of Fluids, Vol. 18, Issue 8
Structure of perpendicular shocks in collisionless plasma
journal, January 1983
- Leroy, M. M.
- Physics of Fluids, Vol. 26, Issue 9
Shock fronts, electron-ion equilibration and intracluster medium transport processes in the merging cluster Abell 2146: The merging cluster Abell 2146
journal, May 2012
- Russell, H. R.; McNamara, B. R.; Sanders, J. S.
- Monthly Notices of the Royal Astronomical Society, Vol. 423, Issue 1
Mach number dependence of electron heating in high Mach number quasiperpendicular shocks
journal, April 2010
- Matsukiyo, Shuichi
- Physics of Plasmas, Vol. 17, Issue 4
A shock front at the radio relic of Abell 2744
journal, June 2016
- Eckert, D.; Jauzac, M.; Vazza, F.
- Monthly Notices of the Royal Astronomical Society, Vol. 461, Issue 2
Electron-Ion Temperature Equilibration in Collisionless Shocks: The Supernova Remnant-Solar Wind Connection
journal, July 2013
- Ghavamian, Parviz; Schwartz, Steven J.; Mitchell, Jeremy
- Space Science Reviews, Vol. 178, Issue 2-4
Planck intermediate results : VIII. Filaments between interacting clusters
journal, February 2013
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 550
Heating of a Confined Plasma by Oscillating Electromagnetic Fields
journal, January 1958
- Berger, J. M.; Newcomb, W. A.; Dawson, J. M.
- Physics of Fluids, Vol. 1, Issue 4
Particle simulation study of electron heating by counter-streaming ion beams ahead of supernova remnant shocks
journal, July 2012
- Dieckmann, M. E.; Bret, A.; Sarri, G.
- Plasma Physics and Controlled Fusion, Vol. 54, Issue 8
Evidence for a pressure discontinuity at the position of the Coma relic from Planck Sunyaev–Zel'dovich effect data
journal, January 2015
- Erler, J.; Basu, K.; Trasatti, M.
- Monthly Notices of the Royal Astronomical Society, Vol. 447, Issue 3
On the electron-ion temperature ratio established by collisionless shocks
journal, June 2015
- Vink, Jacco; Broersen, Sjors; Bykov, Andrei
- Astronomy & Astrophysics, Vol. 579
A Textbook Example of a Bow Shock in the Merging Galaxy Cluster 1E 0657-56
journal, February 2002
- Markevitch, M.; Gonzalez, A. H.; David, L.
- The Astrophysical Journal, Vol. 567, Issue 1
Suzaku observations of the merging galaxy cluster Abell 2255: The northeast radio relic
journal, April 2017
- Akamatsu, H.; Mizuno, M.; Ota, N.
- Astronomy & Astrophysics, Vol. 600
Magnetic pumping by magnetosonic waves in the presence of noncompressive electromagnetic fluctuations
journal, January 1986
- Borovsky, Joseph E.
- Physics of Fluids, Vol. 29, Issue 10
Planck intermediate results : X. Physics of the hot gas in the Coma cluster
journal, June 2013
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 554
Discovery of a radio relic in the low mass, merging galaxy cluster PLCK G200.9−28.2
journal, August 2017
- Kale, Ruta; Wik, Daniel R.; Giacintucci, Simona
- Monthly Notices of the Royal Astronomical Society, Vol. 472, Issue 1
Chandra observation of two shock fronts in the merging galaxy cluster Abell 2146: The merging cluster Abell 2146
journal, May 2010
- Russell, H. R.; Sanders, J. S.; Fabian, A. C.
- Monthly Notices of the Royal Astronomical Society
Particle Acceleration on Megaparsec Scales in a Merging Galaxy Cluster
journal, September 2010
- van Weeren, R. J.; Rottgering, H. J. A.; Bruggen, M.
- Science, Vol. 330, Issue 6002
XMM–Newton observations of the merging galaxy cluster CIZA J2242.8+5301
journal, January 2013
- Ogrean, G. A.; Brüggen, M.; Röttgering, H.
- Monthly Notices of the Royal Astronomical Society, Vol. 429, Issue 3
The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions
journal, July 1956
- Chew, G. F.; Goldberger, M. L.; Low, F. E.
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 236, Issue 1204, p. 112-118
The radio relic in Abell 2256: overall spectrum and implications for electron acceleration
journal, February 2015
- Trasatti, M.; Akamatsu, H.; Lovisari, L.
- Astronomy & Astrophysics, Vol. 575
Stochastic Electron Acceleration by the Whistler Instability in a Growing Magnetic Field
journal, November 2017
- Riquelme, Mario; Osorio, Alvaro; Quataert, Eliot
- The Astrophysical Journal, Vol. 850, Issue 2
Alma-Sz Detection of a Galaxy Cluster Merger Shock at half the age of the Universe
journal, September 2016
- Basu, K.; Sommer, M.; Erler, J.
- The Astrophysical Journal, Vol. 829, Issue 2
Simulations of ion Acceleration at Non-Relativistic Shocks. i. Acceleration Efficiency
journal, February 2014
- Caprioli, D.; Spitkovsky, A.
- The Astrophysical Journal, Vol. 783, Issue 2
XMM-NEWTON OBSERVATION OF THE NORTHWEST RADIO RELIC REGION IN A3667
journal, May 2010
- Finoguenov, Alexis; Sarazin, Craig L.; Nakazawa, Kazuhiro
- The Astrophysical Journal, Vol. 715, Issue 2
Electron anisotropy constraint in the magnetosheath: Cluster observations
journal, January 2005
- Gary, S. Peter
- Geophysical Research Letters, Vol. 32, Issue 13
Electromagnetic electron temperature anisotropy instabilities
journal, August 1985
- Gary, S. Peter; Madland, Christian D.
- Journal of Geophysical Research: Space Physics, Vol. 90, Issue A8
Non-Thermal Electron Acceleration in low mach Number Collisionless Shocks. i. Particle Energy Spectra and Acceleration Mechanism
journal, October 2014
- Guo, Xinyi; Sironi, Lorenzo; Narayan, Ramesh
- The Astrophysical Journal, Vol. 794, Issue 2
Non-Thermal Electron Acceleration in low mach Number Collisionless Shocks. ii. Firehose-Mediated Fermi Acceleration and its Dependence on Pre-Shock Conditions
journal, November 2014
- Guo, Xinyi; Sironi, Lorenzo; Narayan, Ramesh
- The Astrophysical Journal, Vol. 797, Issue 1
THE RADIO RELICS AND HALO OF EL GORDO, A MASSIVE z = 0.870 CLUSTER MERGER
journal, April 2014
- Lindner, Robert R.; Baker, Andrew J.; Hughes, John P.
- The Astrophysical Journal, Vol. 786, Issue 1
CLARREO shortwave observing system simulation experiments of the twenty-first century: Simulator design and implementation
journal, January 2011
- Feldman, Daniel R.; Algieri, Chris A.; Ong, Jonathan R.
- Journal of Geophysical Research, Vol. 116, Issue D10
Modified two-stream instability in the foot of high Mach number quasi-perpendicular shocks
journal, January 2003
- Matsukiyo, Shuichi
- Journal of Geophysical Research, Vol. 108, Issue A12
Simultaneous Acceleration of Protons and Electrons at Nonrelativistic Quasiparallel Collisionless Shocks
journal, February 2015
- Park, Jaehong; Caprioli, Damiano; Spitkovsky, Anatoly
- Physical Review Letters, Vol. 114, Issue 8
Electron heating and the potential jump across fast mode shocks
journal, January 1988
- Schwartz, Steven J.; Thomsen, Michelle F.; Bame, S. J.
- Journal of Geophysical Research, Vol. 93, Issue A11
Electron Heating by the ion Cyclotron Instability in Collisionless Accretion Flows. ii. Electron Heating Efficiency as a Function of flow Conditions
journal, February 2015
- Sironi, Lorenzo
- The Astrophysical Journal, Vol. 800, Issue 2
Electron Heating by the ion Cyclotron Instability in Collisionless Accretion Flows. i. Compression-Driven Instabilities and the Electron Heating Mechanism
journal, February 2015
- Sironi, Lorenzo; Narayan, Ramesh
- The Astrophysical Journal, Vol. 800, Issue 2
Heating of a confined plasma by oscillating electromagnetic fields
journal, September 1958
- Berger, J.; Dawson, J.; Frieman, E.
- Journal of Nuclear Energy (1954), Vol. 7, Issue 3-4
Planck intermediate results : XL. The Sunyaev-Zeldovich signal from the Virgo cluster
journal, December 2016
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 596
Particle Acceleration on Megaparsec Scales in a Merging Galaxy Cluster
text, January 2010
- van Weeren, R. J.; Rottgering, H. J. A.; Bruggen, M.
- arXiv
Planck intermediate results. X. Physics of the hot gas in the Coma cluster
text, January 2012
- Collaboration, Planck; Ade, P. A. R.; Aghanim, N.
- arXiv
Electron-Ion Temperature Equilibration in Collisionless Shocks: the Supernova Remnant-Solar Wind Connection
text, January 2013
- Ghavamian, Parviz; Schwartz, Steven J.; Mitchell, Jeremy
- arXiv
On the electron-ion temperature ratio established by collisionless shocks
text, January 2014
- Vink, Jacco; Broersen, Sjors; Bykov, Andrei
- arXiv
Electron Heating by the Ion Cyclotron Instability in Collisionless Accretion Flows. I. Compression-Driven Instabilities and the Electron Heating Mechanism
text, January 2014
- Sironi, Lorenzo; Narayan, Ramesh
- arXiv
Simultaneous Acceleration of Protons and Electrons at Nonrelativistic Quasiparallel Collisionless Shocks
text, January 2014
- Park, Jaehong; Caprioli, Damiano; Spitkovsky, Anatoly
- arXiv
A shock front at the radio relic of Abell 2744
text, January 2016
- Eckert, Dominique; Jauzac, Mathilde; Vazza, Franco
- arXiv
ALMA-SZ Detection of a Galaxy Cluster Merger Shock at Half the Age of the Universe
text, January 2016
- Basu, Kaustuv; Sommer, Martin; Erler, Jens
- arXiv
Stochastic Electron Acceleration by the Whistler Instability in a Growing Magnetic Field
text, January 2017
- Riquelme, Mario; Osorio, Alvaro; Quataert, Eliot
- arXiv
A Textbook Example of a Bow Shock in the Merging Galaxy Cluster 1E0657-56
text, January 2001
- Markevitch, M.; Gonzalez, A. H.; David, L.
- arXiv
Works referencing / citing this record:
Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations
journal, August 2019
- Liang, Haoming; Cassak, Paul A.; Servidio, Sergio
- Physics of Plasmas, Vol. 26, Issue 8
Two-Temperature Magnetohydrodynamics Simulations of Propagation of Semi-Relativistic Jets
journal, January 2019
- Ohmura, Takumi; Machida, Mami; Nakamura, Kenji
- Galaxies, Vol. 7, Issue 1
Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas
journal, November 2018
- Bret, Antoine; Narayan, Ramesh
- Journal of Plasma Physics, Vol. 84, Issue 6
Astrophysics with the Spatially and Spectrally Resolved Sunyaev-Zeldovich Effects: A Millimetre/Submillimetre Probe of the Warm and Hot Universe
journal, February 2019
- Mroczkowski, Tony; Nagai, Daisuke; Basu, Kaustuv
- Space Science Reviews, Vol. 215, Issue 1
Density jump as a function of magnetic field for collisionless shocks in pair plasmas: The perpendicular case
journal, June 2019
- Bret, A.; Narayan, R.
- Physics of Plasmas, Vol. 26, Issue 6