skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
ORCiD logo [1];  [2];  [1]
  1. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)
  2. 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) (SC-24)
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. doi: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. doi: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 = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share: