Mach cones in the quark-gluon plasma: Viscosity, speed of sound, and effects of finite source structure

I use the space-time distribution of energy and momentum deposited by a fast parton traversing a perturbative quark-gluon plasma as a source term for the linearized hydrodynamical equations of the medium. A method of solution for the medium response is presented in detail. Numerical results are given for different values of the shear viscosity to entropy density ratio, $\eta/s$, and speed of sound, $c_s$. Furthermore, I investigate the relevance of finite source structure by expanding the source term up to first order in gradients of a $\delta$ function centered at the fast parton and comparing the resulting dynamics to that obtained with the full source. It is found that, for the source term used here, the medium response is sensitive to the finite source structure up to distances of several fm from the source parton.