The Effects of Viscosity on Spectra, Elliptic Elow, and HBT Radii

I calculate the first viscous correction to the thermal distribution function of an expanding gas. With this modified distribution function I calculate viscous corrections to spectra, elliptic flow, and HBT radii in hydrodynamic models of heavy ion collisions. 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. Viscous corrections to elliptic flow cause $v_{2}(p_{T})$ to veer below the ideal results for $p_{T} \approx 0.9$ GeV. Viscous 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. 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 $R_{O}/R_{S} \approx 1$.