Using a cosmological CDM simulation, we analyze the differences between the widely-used spin pa- rameters suggested by Peebles and Bullock. The dimensionless spin parameter λ 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 λ′ 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 λ and λ′ 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, λ′′, which is simply designed to roughly recover the value of λ but to use the same halo quantities as used in λ′. If the Plummer potential is adopted, the λ′′ is related to the Bullock’s definition as λ′′ = 0.80 × (1 + z)−1/12λ′. Hence, the new spin parameter λ′′ distribution becomes consistent with a log-normal distribution frequently seen for the λ′ while its mean value is much closer to that of λ. On the other hand, in case of the Newtonian potential model, we obtain the relation of λ′′ = (1 + z)−1/8λ′; there is no significant difference at z = 0 as found by others but λ′ becomes more overestimated than λ or λ′′ at higher redshifts. We also investigate the dependence of halo spin parameters on halo mass and redshift. We clearly show that although the λ′ for small-mass halos with Mh < 2× 1012M⊙ 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.

ABSTRACT
1. INTRODUCTION
2. THE SIMULATION
3. THE SPIN PARAMETERS
4. DISCREPANCY IN SPIN VALUE BE-TWEEN THE DIFFERENT SPIN PARAM-ETERS
    4.1 Potential Model Effect
    4.2 Virialization Effect
    4.3 Density Profile Effect
    4.4 Mass Resolution Effect of Simulation
5. EMPIRICAL CORRECTION TO λ′
6. REDSHIFT & MASS DEPENDENCES OF THE SPIN PARAMETER
7. SUMMARY & DISCUSSIONS
REFERENCES

• JIEUN AHN(School of Space Research, Kyung Hee University)
• JUHAN KIM(Center for Advanced Computation, Korea Institute for Advanced Study)
• JIHYE SHIN(Dept. of Astronomy & Space Science, Kyung Hee University)
• SUNGSOO S. KIM(School of Space Research, Kyung Hee University, Dept. of Astronomy & Space Science, Kyung Hee University)
• YUN-YOUNG CHOI(Dept. of Astronomy & Space Science, Kyung Hee University) Corresponding Author