Kelvin-Helmholtz instabilities at the sloshing cold fronts in the Virgo
  cluster as a measure for the effective ICM viscosity
  Sloshing cold fronts (CFs) arise from minor merger triggered gas sloshing.
Their detailed structure depends on the properties of the intra-cluster medium
(ICM): hydrodynamical simulations predict the CFs to be distorted by
Kelvin-Helmholtz instabilities (KHIs), but aligned magnetic fields, viscosity,
or thermal conduction can suppress the KHIs. Thus, observing the detailed
structure of sloshing CFs can be used to constrain these ICM properties. Both
smooth and distorted sloshing CFs have been observed, indicating that the KHI
is suppressed in some clusters, but not in all. Consequently, we need to
address at least some sloshing clusters individually before drawing general
conclusions about the ICM properties. We present the first detailed attempt to
constrain the ICM properties in a specific cluster from the structure of its
sloshing CF. Proximity and brightness make the Virgo cluster an ideal target.
We combine observations and Virgo-specific hydrodynamical sloshing simulations.
Here we focus on a Spitzer-like temperature dependent viscosity as a mechanism
to suppress the KHI, but discuss the alternative mechanisms in detail. We
identify the CF at 90 kpc north and north-east of the Virgo center as the best
location in the cluster to observe a possible KHI suppression. For viscosities
$\gtrsim$ 10% of the Spitzer value KHIs at this CF are suppressed. We describe
in detail the observable signatures at low and high viscosities, i.e. in the
presence or absence of KHIs. We find indications for a low ICM viscosity in
archival XMM-Newton data and demonstrate the detectability of the predicted
features in deep Chandra observations.
