High Resolution Simulation ofFirst Generation Star Formation
Tamon SUWA (U. Tsukuba)
M. Umemura (U. Tsukuba)
D. Sato (U. Tsukuba)
H. Susa (Konan U.)

Mass of the First Stars• Massive stars (≧100 MO)– Bromm, Coppi, & Larson (2002)• Clumps of ~1000MO is formed– Yoshida et al.(2006)• MZAMS～100MO– O’Shea & Norman (2007)• 12 simulations of adaptive mesh refinement (AMR)• Isolate core which suggest stellar mass of ~100MO• Low mass stars (～1MO)– Low mass stars can be formed by fragmentation ofdense (n>105cm-3) filament (Nakamura & Umemura
2001).

Problems• What is the functional form of theprimordial IMF?
• Whether or not low-mass star can beformed by fragmentation of filaments inrealistic situation?

Yoshida et al. (2006)

This work• Using uniformly high-resolution
cosmological simulation, we investigate adensity peak of our simulation box.

FIRST Cluster• Hybrid PC cluster system– 256 (16 x 16) node 2U-size
server PC• 496 CPU ＋
16 Blade-GRAPE
224 Blade-GRAPE X64– Main memory:
240 x 6GB + 16 x 10GB
= 1.6 TB
– Total performance (Host): 3.1 Tflops• Each node equip a newly-developedboard for gravity calculations,Blade-GRAPE

Blade-GRAPE• Blade-GRAPE– Embedded Special Purpose Processor for Gravity– Each board has 16MB memory• Corresponds to 256K particles at the maximum– Theoretical peak performance: 136.8 GFlops• Blade-GRAPE X64– 64 bit PCI-X version with FPGA
– newly developed in 2006

• Total performance:33 Tflops

P3M + GRAPE+SPH• Gravitational forces are solved by ParticleParticle-Particle-Mesh (P3M) scheme– PP-part is accelerated by Blade-GRAPE– Calculation with GRAPE is about 10 times fasterthan that by host CPUs

• Hydrodynamic processes are solved by
Smoothed Particle Hydrodynamics (SPH)
scheme (Springel & Hernquist 2002)

Chemical reaction &heating/cooling• 6 species of chemical elements areincluded (e-, H, H+, H-, H2, H2+)
– Minimal model of Galli & Palla (1998)• Main reaction– Low density (n<108cm-3)
Proton reaction

p + H → H2 + γ+Electron reaction

H + e− → H − + γ

H − + H → H 2 + e−
– High density (n>108cm-3)
H2 + H → H2 + p+3H → H 2 + H 3-body
2H + H 2 → 2H 2

Simulation setup• # of particles: 2×30 million （DM＋SPH）• Mass resolution:– 0.3MO (SPH)– 1.5MO (DM)• Box size: 100kpc (comoving)• Mesh Size: Lbox/256• Initial condition is
generated at z=15
using truncated Zeldvich approx.
• Cosmological parameters:
WMAP 3-year: (Ω0,Ωb, h)=(0.24, 0.04, 0.73)kpc (comoving)Mass profile of the peak

MOred: total mass
green: baryon mass
blue: DM masspc (physical)

Estimation of stellar mass
dM/dt (cs)• We estimate the stellar mass

RMM& (cs )t KH ( M ) = M•M：Mass in a radius R•tKH: Kelvin-Helmholtz time determined by mass•dM/dt (= cs3/G): Mass accretion rate
106

tKH of PopIII ZAMS

• Estimated mass of thefirst star at the peak is
M~25MO(Schaerer 2002)

105

104

yr

1

10

MO

102

103

Discussion• This low-mass is due to low-temperature(~120 K) at the center of the peak
• The reason might be under estimation ofSPH gravitation– Weak contraction force
may not balance radiative
coolingSummary• We perform a cosmological simulation of
first star generation with FIRST cluster.
• Baryon mass resolution is 0.3 MO all overthe simulation box.
• Estimated stellar mass at the center of thedensest peak is 20～30MO.
– This low-mass is due to low-temperature(~120 K) at the center of the peak.
– Physical validity of such temperature is still
controversial.