Early in the reionization process , the intergalactic medium ( IGM ) would have been quite inhomogeneous on small scales , due to the low Jeans mass in the neutral IGM and the hierarchical growth of structure in a cold dark matter Universe .
This small-scale structure acted as an important sink during the epoch of reionization , impeding the progress of the ionization fronts that swept out from the first sources of ionizing radiation .
Here we present results of high-resolution cosmological hydrodynamics simulations that resolve the cosmological Jeans mass of the neutral IGM in representative volumes several Mpc across .
The adiabatic hydrodynamics we follow are appropriate in an unheated IGM , before the gas has had a chance to respond to the photoionization heating .
Our focus is determination of the resolution required in cosmological simulations in order to sufficiently sample and resolve small-scale structure regulating the opacity of an unheated IGM .
We find that a dark matter particle mass of m _ { dm } \lesssim 50 ~ { } M _ { \odot } and box size of L \gtrsim 1 Mpc are required .
With our converged results we show how the mean free path of ionizing radiation and clumping factor of ionized hydrogen depends upon the ultraviolet background ( UVB ) flux and redshift .
We find , for example at z = 10 , clumping factors typically of 10 to 20 for an ionization rate of \Gamma \sim 0.3 - 3 \times 10 ^ { -12 } s ^ { -1 } , with corresponding mean free paths of \sim 3 - 15 Mpc , extending previous work on the evolving mean free path to considerably smaller scales and earlier times .