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

2. 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

3. 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 / 3
2-d (e.g., cylindrical collapse) : = 1
1-d (e.g., disk like collapse): = 0 R ρ
For enough collapse, cooling is necessary!

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

5. 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 H2

6. 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

7. 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 )

8. 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

9. Nakamura
and Umemura
(2000)
Fragment
Mass
Nakamura Umemura

10. “IMF”
Double peak
NU IMF

11. 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

12. 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）

13. 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

14. 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.

15. “IMF”
Double peak ?
Single peak?
NU IMF

16. 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 > 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.

17. 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

20. Cooling Processes (Equilibrium)

21. Cooling Diagram (Equilibrium)

22. For given T, ye

31. Tsuribe (2003)

34. Omukai (2003)