Formation Processes of Early Cosmological Objects Ryoichi Nishi (Niigata University)

Scenario Scenario of Formation of Early Cosmological Objects Gravitational Collapse of Proto Clouds Cooling and Formation of Disk like Clouds Fragment into Cylindrical Clouds Cylindrical Collapse Fragmentation of Cylindrical Star Formation from the Core シナリオ Scenario

Necessity of Cooling For enough collapse, cooling is necessary! M Effective of gravity 　　E = EＰ + EＧ ~ PR３ ｰ GM２ / R 　　　 ~ R３（P ｰ GM２/３ρ４/３） 　　P = Kρ　 3-d contraction (e.g., spherical collapse): 　　　　　Effective 　　of gravity 4 / 3 2-d (e.g., cylindrical collapse) : = 1 1-d (e.g., disk like collapse): = 0 R ρ For enough collapse, cooling is necessary!

Cooling Processes of Primordial Gas Primordial Gas: H, He, (D), T > 105.5 K: free-free emission 104 K < T < 105.5 K: line emission of H and He T < 104 K: line emission of H2 For star formation, H2 formation is necessary.

H2 formation processes: H－ process: H + e－ 　　　H－ + γ H－ + H　　　　H2 + e－ H2＋ process: H + H＋ H2＋ + γ H2＋ + H H2 + H＋ 3-body processes (n > 108 cm-3): 3H H2 + H H2 + 2H 2H2

Low Mass Clouds (Tv < 104 K) Nishi and Susa (1999), Susa (2003) Estimation of H2 fraction Comparing important time scales H2 formation time, H2 dissociation time recombination time, cooling time key process Relic electron (ye ～10－3.5） H2 fraction Cooling Diagram

Massive Clouds (Tv > 104 K) Susa et al. (1998), Nishi et al Massive Clouds (Tv > 104 K) Susa et al. (1998), Nishi et al. (1998), Yamada and Nishi (1998, 2001), Yamada (2003), etc. Shock Heating at the Bounce Epoch Ionization H2 Formation via Non-Equilibrium Process 　　　　　 (H2 / H=10-3～10-2 )

Collapse and Fragmentation of Cylindrical Clouds (Uehara et al Collapse and Fragmentation of Cylindrical Clouds (Uehara et al. 1996, Nakamura and Umemura 1998, 2000) Cylindrical clouds formed via gravitational instability is unstable to gravitational collapse. After collapse, collapse becomes showered by pressure gradient. Fragmentation Important to determine the mass of star forming core

Nakamura and Umemura (2000) Fragment Mass Nakamura Umemura

“IMF” Double peak NU IMF

Minimum Fragment Mass (Uehara et al. 1996) Existence of Minimum Fragment Mass 　　　It should be written by physical constants Dimensional Analysis： 　　Gravity：G，mｐ, Radiation (Cooling)：h，c 　　　Mfrag ~ mpl3 / mp2 ~ Mch 　 mpl ~ (hc/G)1/2 : Planck mass 　　　　　mp : Proton mass 　　　　　Mch : Chandrasekhar mass

Physical Process At the fragmentation epoch, T becomes Tvir : 　kBT = 1/2 μmp G λ μ:mean molecular weight 　tcool = tdyn tcool : cooling time scale Optically thick line cooling is important. Fragmentation condition:　　　　tdyn = tff 　 tdyn : Collapse time scale tff : Free fall time （time scale for fragmentation）

Minimum Fragment Mass tcool ~ ET / Λ ET ~ λ/ (μmp) kBT Λ ~ 2πRσT4 (Δν/ν)αc σ = 2π5kB4 / 15h3c2 Δν/ν= (kBT / mpc2)1/2 : Doppler broadening tff = 1 / (2πGρ0)1/2 　　　　 Mfrag ~ 2πRλ ~ Mch αc: number of effective lines

Effects of Dark Matter Formation Process of Early Cosmological Objects 　　　Dark Matter Potential is Important. Cylindrical Clouds 　　　　　　　Formed via Dark Matter Potential 　　　　　　　　　　（e.g., Abel et al.) But Dark Matter cannot collapse much, since Dark Matter does not cool.

“IMF” Double peak ? Single peak? NU IMF

Summary Formation of early cosmological objects start after collapse of the dark matter halo with the virial temperature higher than about 1000K. z < 25～30, M > 105-6 Msun Understanding for the Formation Process of First Stars have greatly progressed. Initial mass of protostar is not different from the case of present-day star formation. Probably, strongly top-heavy IMF.

Stellar Mass Scale Accretion Phase (High Accretion Rate) Omukai-san (Star Formation) Saigo-san (Accretion Rate) Tsuribe-san (Effect of Rotation) Mizusawa-san (H2 Line Emission) Kamaya-san (HD Line Emission) Initial Mass Function Nakamura-san

Cooling Processes (Equilibrium)

Cooling Diagram (Equilibrium)

For given T, ye

Tsuribe (2003)

Omukai (2003)