The Effect of Shear Viscosity on Spectra, Elliptic Flow, and HBT Radii

Abstract

I calculate the first correction to the thermal distribution function of an expanding gas due to shear viscosity. With this modified distribution function I estimate viscous corrections to spectra, elliptic flow, and HBT radii in hydrodynamic simulations of heavy ion collisions using the blast wave model. For reasonable values of the shear viscosity, viscous corrections become of order one when the transverse momentum of the particle is larger than 1.7 GeV. This places a bound on the $p_{T}$ range accessible to hydrodynamics for this observable. Shear corrections to elliptic flow cause $v_{2}(p_{T})$ to veer below the ideal results for $p_{T} \approx 0.9$ GeV. Shear corrections to the longitudinal HBT radius $R^{2}_{L}$ are large and negative. The reduction of $R_{L}^2$ can be traced to the reduction of the longitudinal pressure. Viscous corrections cause the longitudinal radius to deviate from the $\frac{1}{\sqrt{m_T}}$ scaling which is observed in the data and which is predicted by ideal hydrodynamics. The correction to the sideward radius $R^{2}_{S}$ is small. The correction to the outward radius $R^{2}_{O}$ is also negative and tends to make $R_{O}/R_{S} \approx 1$.