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Electron Heating by the Ion Cyclotron Instability in Collisionless Accretion Flows. II. Electron Heating Efficiency as a Function of Flow Conditions
In the innermost regions of low-luminosity accretion flows, including Sgr A*
at the center of our Galaxy, the frequency of Coulomb collisions is so low that
the plasma is two-temperature, with the ions substantially hotter than the
electrons. This paradigm assumes that Coulomb collisions are the only channel
for transferring the ion energy to the electrons. In this work, the second of a
series, we assess the efficiency of electron heating by ion velocity-space
instabilities in collisionless accretion flows. The instabilities are seeded by
the pressure anisotropy induced by magnetic field amplification, coupled to the
adiabatic invariance of the particle magnetic moments. Using two-dimensional
(2D) particle-in-cell (PIC) simulations, we showed in Paper I that if the
electron-to-ion temperature ratio is < 0.2, the ion cyclotron instability is
the dominant mode for values of ion beta_i ~ 5-30 (here, beta_i is the ratio of
ion thermal pressure to magnetic pressure), as appropriate for the midplane of
low-luminosity accretion flows. In this work, we employ analytical theory and
1D PIC simulations (with the box aligned with the fastest growing wavevector of
the ion cyclotron mode) to fully characterize how the electron heating
efficiency during the growth of the ion cyclotron instability depends on the
electron-to-proton temperature ratio, the plasma beta, the Alfven speed, the
amplification rate of the mean field (in units of the ion Larmor frequency) and
the proton-to-electron mass ratio. Our findings can be incorporated as a
physically-grounded sub-grid model into global fluid simulations of
low-luminosity accretion flows, thus helping to assess the validity of the
two-temperature assumption.Comment: 18 pages, 6 figures, 6 tables, 2 appendices, submitted to ApJ. Paper
I appeared on Monday November 24t
Production of magnetic energy by macroscopic turbulence in GRB afterglows
Afterglows of gamma-ray bursts are believed to require magnetic fields much
stronger than that of the compressed pre-shock medium. As an alternative to
microscopic plasma instabilities, we propose amplification of the field by
macroscopic turbulence excited by the interaction of the shock with a clumpy
pre-shock medium, for example a stellar wind. Using a recently developed
formalism for localized perturbations to an ultra-relativistic shock, we derive
constraints on the lengthscale, amplitude, and volume filling factor of density
clumps required to produce a given magnetic energy fraction within the
expansion time of the shock, assuming that the energy in the field achieves
equipartion with the turbulence. Stronger and smaller-scale inhomogeneities are
required for larger shock Lorentz factors. Hence it is likely that the magnetic
energy fraction evolves as the shock slows. This could be detected by
monitoring the synchrotron cooling frequency if the radial density profile
ahead of the shock, smoothed over clumps, is known.Comment: 24 pages, 3 figure
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