Using six high resolution dissipationless simulations with a varying box size in a flat LCDM universe , we study the mass and redshift dependence of dark matter halo shapes for M _ { vir } = 9.0 \times 10 ^ { 11 } -2.0 \times 10 ^ { 14 } , over the redshift range z = 0 - 3 , and for two values of \sigma _ { 8 } = 0.75 and 0.9 .
Remarkably , we find that the redshift , mass , and \sigma _ { 8 } dependence of the mean smallest-to-largest axis ratio of halos is well described by the simple power-law relation \langle s \rangle = ( 0.54 \pm 0.02 ) ( M _ { vir } / M _ { * } ) ^ { -0.050 \pm 0.003 } , where s is measured at 0.3 R _ { vir } and the z and \sigma _ { 8 } dependences are governed by the characteristic nonlinear mass , M _ { * } = M _ { * } ( z, \sigma _ { 8 } ) .
We find that the scatter about the mean s is well described by a Gaussian with \sigma \sim 0.1 , for all masses and redshifts .
We compare our results to a variety of previous works on halo shapes and find that reported differences between studies are primarily explained by differences in their methodologies .
We address the evolutionary aspects of individual halo shapes by following the shapes of the halos through \sim 100 snapshots in time .
We determine the formation scalefactor a _ { c } as defined by Wechsler et al .
( 45 ) and find that it can be related to the halo shape at z = 0 and its evolution over time .