1204.1766 (Banibrata Mukhopadhyay)

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

Banibrata Mukhopadhyay

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be ~ h_bar/4 pi k_B, when h_bar and k_B are Planck's and Boltzmann constants respectively. 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 have a significant turbulent viscosity, generating heat and hence entropy in the flow. Certain optically thin, hot, accretion flows, of temperature >~ 10^9 K, are 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 only for such hot flows when the source of energy is due to the underlying thermonuclear reactions only, but not due to the viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow. Finally, our finding questions the finite value of Shakura-Sunyaev viscosity in hot accretion flows and argues for its decrease with increasing density and/or temperature.

View original: http://arxiv.org/abs/1204.1766