We develop a parallel cosmological hydrodynamic simulation code designed for the study of formation and evolution of cosmological structures. The gravitational force is calculated using the TreePM method and the hydrodynamics is implemented based on the smoothed particle hydrodynamics. The ini- tial displacement and velocity of simulation particles are calculated according to second-order Lagrangian perturbation theory using the power spectra of dark matter and baryonic matter. The initial background temperature is given by Recfast and the temperature uctuations at the initial particle position are as- signed according to the adiabatic model. We use a time-limiter scheme over the individual time steps to capture shock-fronts and to ease the time-step tension between the shock and preshock particles. We also include the astrophysical gas processes of radiative heating/cooling, star formation, metal enrichment, and supernova feedback. We test the code in several standard cases such as one-dimensional Riemann problems, Kelvin-Helmholtz, and Sedov blast wave instability. Star formation on the galactic disk is investigated to check whether the Schmidt-Kennicutt relation is properly recovered. We also study global star formation history at different simulation resolutions and compare them with observations.

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.

We trace the dynamical evolution of dark matter (DM) content in NGC 6397, one of the native Galactic globular clusters (GCs). The relatively strong tidal field (Galactocentric radius of ~ 6 kpc) and short relaxation timescale (~ 0.3 Gyr) of the cluster can cause a significant amount of DM particles to evaporate from the cluster in the Hubble time. Thus, the cluster can initially contain a non-negligible amount of DM. Using the most advanced Fokker-Planck (FP) method, we calculate the dynamical evolution of GCs for numerous initial conditions to determine the maximum initial DM content in NGC 6397 that matches the present-day brightness and velocity dispersion profiles of the cluster. We find that the maximum allowed initial DM mass is slightly less than the initial stellar mass in the cluster. Our findings imply that NGC 6397 did not initially contain a significant amount of DM, and is similar to that of NGC 2419, the remotest and the most massive Galactic GC.

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum space) version of the FP model or when the initial condition is extreme (e.g., a very large cluster mass and a small cluster radius). To avoid such a problem, we have developed a new integration scheme for a two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI) method given in the Douglas-Rachford split form. We find that our ADI method reduces the computing time by a factor of ~2 compared to the fully implicit method, and resolves problems of numerical instability.