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 simulations 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 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 Caffau 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.
We propose a model in which intermediate-mass black holes (IMBHs) with mass of ~10000 Msun are formed in early dark matter halos. We carry out detailed stellar evolution calculations for accreting primordial stars including annihilation energy of dark matter particles. We follow the stellar core evolution consistently up to gravitational collapse. We show that very massive stars, as massive as 10000 Msun, can be formed in an early dark matter halo. Such stars are extremely bright with Log L/Lsun > 8.2. They gravitationally collapse to form IMBHs. These black holes could have seeded the formation of early super-massive blackholes.
We use 5000 cosmological N-body simulations of 1(Gpc/h)^3 box for the concordance LCDM model in order to study the sampling variances of nonlinear matter power spectrum. We show that the non-Gaussian errors can be important even on large length scales relevant for baryon acoustic oscillations (BAO). Our findings are (1) the non-Gaussian errors degrade the cumulative signal-to-noise ratios (S/N) for the power spectrum amplitude by up to a factor of 2 and 4 for redshifts z=1 and 0, respectively. (2) There is little information on the power spectrum amplitudes in the quasi-nonlinear regime, confirming the previous results. (3) The distribution of power spectrum estimators at BAO scales, among the realizations, is well approximated by a Gaussian distribution with variance that is given by the diagonal covariance component. (4) For the redshift-space power spectrum, the degradation in S/N by non-Gaussian errors is mitigated due to nonlinear redshift distortions. (5) For an actual galaxy survey, the additional shot noise contamination compromises the cosmological information inherent in the galaxy power spectrum, but also mitigates the impact of non-Gaussian errors. The S/N is degraded by up to 30% for a WFMOS-type survey. (6) The finite survey volume causes additional non-Gaussian errors via the correlations of long-wavelength fluctuations with the fluctuations we want to measure, further degrading the S/N values by about 30% even at high redshift z=3.
We critically examine how well the evolution of large-scale density perturbations is followed in cosmological $N$-body simulations. We first run a large volume simulation and perform a mode-by-mode analysis in three-dimensional Fourier space. We show that the growth of large-scale fluctuations significantly deviates from linear theory predictions. The deviations are caused by {it nonlinear} coupling with a small number of modes at largest scales owing to finiteness of the simulation volume. We then develop an analytic model based on second-order perturbation theory to quantify the effect. Our model accurately reproduces the simulation results. For a single realization, the second-order effect appears typically as ``zig-zag patterns around the linear-theory prediction, which imprints artificial ``oscillations that lie on the real baryon-acoustic oscillations. Although an ensemble average of a number of realizations approaches the linear theory prediction, the dispersions of the realizations remain large even for a large simulation volume of several hundred megaparsecs on a side. For the standard $Lambda$CDM model, the deviations from linear growth rate are as large as 10 percent for a simulation volume with $L = 500h^{-1}$Mpc and for a bin width in wavenumber of $Delta k = 0.005h$Mpc$^{-1}$, which are comparable to the intrinsic variance of Gaussian random realizations. We find that the dispersions scales as $propto L^{-3/2} Delta k^{-1/2}$ and that the mean dispersion amplitude can be made smaller than a percent only if we use a very large volume of $L > 2h^{-1}$Gpc. The finite box size effect needs to be appropriately taken into account when interpreting results from large-scale structure simulations for future dark energy surveys using baryon acoustic oscillations.
