Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

Abstract

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be ~ mu hbar/4pi k_B, when hbar and k_B are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In addition, certain optically thin, hot, accretion flows, of temperature >~ 10^9K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.

16 pages including 4 figures; version modified substantially including new figures (removing some old figures) and effects of magnetic field; to appear in Physics Letters B

References in corpus (8)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• X-ray Properties of Black-Hole Binaries
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The QCD equation of state with dynamical quarks
• The QCD transition temperature: results with physical masses in the continuum limit
• The QCD transition temperature: results with physical masses in the continuum limit II.
• Beyond eta/s = 1/4pi
• The bound on viscosity and the generalized second law of thermodynamics

Cited by in corpus (6)

• A pure hydrodynamic instability in shear flows and its application to astrophysical accretion disks
• Fate of an Accretion Disc around a Black Hole when both the Viscosity and Dark Energy is Effecting
• Violation of Universal Lower Bound for the Shear Viscosity to Entropy Density Ratio in Dark Energy Dominated Accretion
• Origin of hydrodynamic instability from noise: from laboratory flow to accretion disk
• Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation
• Forced linear shear flows with rotation: rotating Couette-Poiseuille flow, its stability and astrophysical implications