A Kinematic Measurement of the Effective Viscosity of the Intracluster Medium: The Cold Front of A3667 Seen by XRISM

Abstract

Constraints on the effective viscosity of the intracluster medium (ICM) come almost exclusively from imaging: the power spectrum of X-ray surface brightness fluctuations, and the morphology of Kelvin-Helmholtz rolls at cold fronts. Both indicate a viscosity below the isotropic Spitzer value. XRISM/Resolve opens a complementary, purely kinematic route, in which the viscosity is inferred from the thickness of the viscous shear layer that develops at a sliding contact discontinuity. We apply it to the prototypical cold front of A3667. The interface is the classical Rayleigh problem, in which momentum diffuses to a depth d in a time T, giving a kinematic viscosity \nu ~ d^2/(4T). The XRISM velocity map shows a line-of-sight velocity jump of 535 km/s across the front, completed within the 100 kpc-wide region immediately inside it, the only region with an anomalously broad line. Hence d ~< 100 kpc. Adopting interaction times set by the sizes of the interacting regions divided by this velocity, we obtain dynamic viscosities of 5.2 x 10^3 and 3.3 x 10^3 g/cm/s for the cool and the hot side of the front, or 6.4 and 0.72 times the Spitzer value. Because d is limited by the angular resolution of XRISM, and the viscosity scales as its square, these are upper limits. The kinematic constraint is consistent with, and independent of, the imaging results.