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:
-
[1];
- 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}
}
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