Electron heating in hot accretion flows

Prateek Sharma, Eliot Quataert, Gregory W. Hammett, James McLellan Stone

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159 Scopus citations


Local (shearing box) simulations of the nonlinear evolution of the magnetorotational instability in a collisionless plasma show that angular momentum transport by pressure anisotropy (p⊥ ≠ p∥, where the directions are defined with respect to the local magnetic field) is comparable to that due to the Maxwell and Reynolds stresses. Pressure anisotropy, which is effectively a large-scale viscosity, arises because of adiabatic invariants related to p⊥ and ∥ in a fluctuating magnetic field. In a collisionless plasma, the magnitude of the pressure anisotropy, and thus the viscosity, is determined by kinetic instabilities at the cyclotron frequency. Our simulations show that ∼50% of the gravitational potential energy is directly converted into heat at large scales by the viscous stress (the remaining energy is lost to grid-scale numerical dissipation of kinetic and magnetic energy). We show that electrons receive a significant fraction [∼(Te/T i)1/2] of this dissipated energy. Employing this heating by an anisotropic viscous stress in one-dimensional models of radiatively inefficient accretion flows, we find that the radiative efficiency of the flow is greater than 0.5% for M ≳ 10-4MEdd. Thus, a low accretion rate, rather than just a low radiative efficiency, is necessary to explain the low luminosity of many accreting black holes. For Sgr A* in the Galactic center, our predicted radiative efficiencies imply an accretion rate of ≈3 × 10-8 M yr-1 and an electron temperature of ≈ 3 × 1010 K at ≈10 Schwarzschild radii; the latter is consistent with the brightness temperature inferred from VLBI observations.

Original languageEnglish (US)
Pages (from-to)714-723
Number of pages10
JournalAstrophysical Journal
Issue number2 I
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Accretion, accretion disks
  • Galaxy: center
  • MHD
  • Plasmas


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