HALO SPIN PARAMETER IN COSMOLOGICAL SIMULATIONS

Using a cosmological ACDM simulation, we analyze the differences between the widely-used spin parameters suggested by Peebles and Bullock. The dimensionless spin parameter lambda proposed by Peebles is theoretically well-justified but includes an annoying term, the potential energy, which cannot be directly obtained from observations and is computationally expensive to calculate in numerical simulations. The Bullock's spin parameter lambda' avoids this problem assuming the isothermal density profile of a virialized halo in the Newtonian potential model. However, we find that there exists a substantial discrepancy between lambda and lambda' depending on the adopted potential model (Newtonian or Plummer) to calculate the halo total energy and that their redshift evolutions differ to each other significantly. Therefore, we introduce a new spin parameter, lambda '', which is simply designed to roughly recover the value of lambda but to use the same halo quantities as used in lambda'. If the Plummer potential is adopted, the lambda '' is related to the Bullock's definition as lambda '' = 0.80 x (1 + z)(-1/12)lambda'. Hence, the new spin parameter lambda '' distribution becomes consistent with a log-normal distribution frequently seen for the lambda' while its mean value is much closer to that of lambda. On the other hand, in case of the Newtonian potential model, we obtain the relation of lambda '' = (1 + z)(-1/8)lambda'; there is no significant difference at z = 0 as found by others but lambda' becomes more overestimated than lambda or lambda '' at higher redshifts. We also investigate the dependence of halo spin parameters on halo mass and redshift. We clearly show that although the lambda' for small-mass halos with M-h < 2 x 10(12)M(circle dot) seems redshift independent after z = 1, all the spin parameters explored, on the whole, show a stronger correlation with the increasing halo mass at higher redshifts.