### Abstract

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 [∼(T_{e}/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^{-4}M_{Edd}. 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 × 10^{10} K at ≈10 Schwarzschild radii; the latter is consistent with the brightness temperature inferred from VLBI observations.

Original language | English (US) |
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Pages (from-to) | 714-723 |

Number of pages | 10 |

Journal | Astrophysical Journal |

Volume | 667 |

Issue number | 2 I |

DOIs | |

State | Published - Jan 1 2007 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

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

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## Cite this

*Astrophysical Journal*,

*667*(2 I), 714-723. https://doi.org/10.1086/520800