  We study relaxation and rheology of dense athermal suspensions of
frictionless particles close below the jamming density. Our key quantity, the
relaxation time---determined from the exponential decay of the energy after the
shearing has suddenly been switched off---is argued to be a determining factor
behind the algebraic divergence of various quantities as the jamming density is
approached from below. We also define and measure the ``dissipation time'',
which is obtained directly in shearing simulations and find that it behaves
similarly to the relaxation time. Comparing shear viscosity with the expression
for the dissipation time we identify a non-divergent factor that explains the
need for correction terms in the scaling analyses of the shear viscosity.
