Figure rotation of dark haloes in cold dark matter simulations

We investigate the figure rotation of dark matter haloes identified in Λ cold dark matter (CDM) simulations. We find that when strict criteria are used to select suitable haloes for study, five of the 222 haloes identified in our z = 0 simulation output undergo coherent figure rotation over a 5 h^-1Gyr period. We discuss the effects of varying the selection criteria and find that pattern speeds for a much larger fraction of the haloes can be measured when the criteria are relaxed. Pattern speeds measured over a 1 h^-1Gyr period follow a lognormal distribution, centred at Ω_p = 0.2 h rad Gyr^-1 with a maximum value of 0.94 h rad Gyr^-1. Over a 5 h^-1Gyr period, the average pattern speed of a halo is about 0.1 h rad Gyr^-1 and the largest pattern speed found is 0.24 h rad Gyr^-1. Less than half of the selected haloes showed alignment between their figure rotation axis and minor axis, the exact fraction being somewhat dependent on how one defines a halo. While the pattern speeds observed are lower than those generally thought capable of causing spiral structure, we note that coherent figure rotation is found over very long periods and argue that further simulations would be required before strong conclusions about spiral structure in all galaxies could be drawn. We find no correlation between halo properties such as total mass and the pattern speed.