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Using molecular dynamics simulation, we calculate fluctuations and responsefor steadily sheared hard spheres over a wide range of packing fractions $\phi$and shear strain rates $\gamma$, using two different methods to dissipateenergy. To a good approximation, shear stress and density fluctuations arerelated to their associated response functions by a single effectivetemperature $T_{eff}$ that is equal to or larger than the kinetic temperature$T_{kin}$. We find a crossover in the relationship between the relaxation time$\tau$ and the the nondimensionalized effective temperature$T_{eff}/p\sigma^3$, where $p$ is the pressure and $\sigma$ is the spherediameter. In the solid response regime, the behavior at fixed packing fractionsatisfies $\tau\gamma\propto \exp(-cp\sigma^3/T_{eff})$, where $c$ dependsweakly on $\phi$, suggesting that the average local yield strain is controlledby the effective temperature in a way that is consistent with sheartransformation zone theory. In the fluid response regime, the relaxation timedepends on $T_{eff}/p\sigma^3$ as it depends on $T_{kin}/p\sigma^3$ inequilibrium. This regime includes both near-equilibrium conditions where$T_{eff} ~ T_{kin}$ and far-from-equilibrium conditions where $T_{eff} \neT_{kin}$. We discuss the implications of our results for systems with softrepulsive interactions.

Ratio of effective temperature to pressure controls the mobility of sheared hard spheres