We present a novel method for particle splitting in smoothed particle hydrodynamics simulations. Our method utilizes the Voronoi diagram for a given particle set to determine the position of fine daughter particles. We perform several test simulation
s to compare our method with a conventional splitting method in which the daughter particles are placed isotropically over the local smoothing length. We show that, with our method, the density deviation after splitting is reduced by a factor of about two compared with the conventional method. Splitting would smooth out the anisotropic density structure if the daughters are distributed isotropically, but our scheme allows the daughter particles to trace the original density distribution with length scales of the mean separation of their parent. We apply the particle splitting to simulations of the primordial gas cloud collapse. The thermal evolution is accurately followed to the hydrogen number density of 10^12 /cc. With the effective mass resolution of ~10^-4 Msun after the multi-step particle splitting, the protostellar disk structure is well resolved. We conclude that the method offers an efficient way to simulate the evolution of an interstellar gas and the formation of stars.
We investigate the condition for the formation of low-mass second-generation stars in the early universe. It has been proposed that gas cooling by dust thermal emission can trigger fragmentation of a low-metallicity star-forming gas cloud. In order t
o determine the critical condition in which dust cooling induces the formation of low-mass stars, we follow the thermal evolution of a collapsing cloud by a one-zone semi-analytic collapse model. Earlier studies assume the dust amount in the local universe, where all refractory elements are depleted onto grains, and/or assume the constant dust amount during gas collapse. In this paper, we employ the models of dust formation and destruction in early supernovae to derive the realistic dust compositions and size distributions for multiple species as the initial conditions of our collapse calculations. We also follow accretion of heavy elements in the gas phase onto dust grains, i.e., grain growth, during gas contraction. We find that grain growth well alters the fragmentation property of the clouds, and that this still does not approach to the value in the local universe. The critical conditions can be written by the gas metallicity Zcr and the initial depletion efficiency fdep,0 of gas-phase metal onto grains, or dust-to-metal mass ratio, as (Zcr/10^{-5.5} Zsun) = (fdep,0/0.18)^{-0.44} with small scatters in the range of Zcr = [0.06--3.2]x10^{-5} Zsun. We also show that the initial dust composition and size distribution are important to determine Zcr.
We study the formation of low-mass and extremely metal-poor stars in the early universe. Our study is motivated by the recent discovery of a low-mass (M < 0.8 Msun) and extremely metal-poor (Z <= 4.5 x 10^{-5} Zsun) star in the Galactic halo by Caffa
u et al. We propose a model that early supernova (SN) explosions trigger the formation of low-mass stars via shell fragmentation. We first perform one-dimensional hydrodynamic simulations of the evolution of an early SN remnant. We show that the shocked shell undergoes efficient radiative cooling and then becomes gravitationally unstable to fragment and collapse in about ten million years. We then follow the thermal evolution of the collapsing fragments using a one-zone code. Our one-zone calculation treats chemistry and radiative cooling self-consistently in low-metallicity gas. The collapsing gas cloud evolves roughly isothermally, until it cools rapidly by dust continuum emission at the density 10^{13}-10^{14} /cc. The cloud core then becomes thermally and gravitationally unstable and fragments. We argue that early SNe can trigger the formation of low-mass stars in the extremely metal-poor environment as Caffau et al. discovered recently.
