Transcript Formation Process of First Stars

Formation Processes of Early
Cosmological Objects
Ryoichi Nishi (Niigata University)
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
Clouds
Star Formation from the Core
Necessity of Cooling
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
M
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 >
4
10
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. 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
“IMF”
Double peak
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
αc: number of effective lines
σ = 2π5kB4 / 15h3c2
Δν/ν= (kBT / mpc2)1/2 : Doppler broadening
tff = 1 / (2πGρ0)1/2
Mfrag ~ 2πRλ ~ Mch
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?
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)
nH2
1
for 
 nH2
k nH ne
nH2
0
dis 
 nH2
k nH2 nH 
 
for
nH2  nH2
eq
  ,
d is
rec
coo l
nH2  nH2
eq
For given T, ye
dis
Tsuribe (2003)
Omukai (2003)