Transcript Formation and Evolution of Infalling Disks Around Protostars

Star Formation Triggered
By First Supernovae
Fumitaka Nakamura (Niigata Univ.)
Questions

What is the typical mass of the first stars?

Can primordial cloud cores break up into multiple
fragments?
Binary formation?

Can first supernovae trigger subsequent star
formation?

What is the typical mass of the stars formed by
shock compression?
low mass star formation? (e.g., HE0107-5240)
What is the typical mass of first stars?


Typical mass of fragments ~ 100M8
No fragmentation for the polytrope gas with g = 1.1.
(e.g., Tsuribe’s talk)
HII region
30 pc
Size of HII region ~ 100 pc
Free-fall time of fragments ~ 106yr
↓
Positive feedback of UV radiation
↓
Enhanced H2 formation
(Bromm, Coppi, Larson 1999)

If a truly first star is massive, it emits strong UV radiation, which
should affect subsequent evolution of other prestellar fragments.
Positive feedback of UV radiation

Enhanced H2 formation


H  e  H  h
(Nakamura & Umemura 2002)
H   H  H 2  e
Formation of HD molecules

D  H 2  HD  H
D  H 2  HD  H

Threshold H2 abundance
xH2 > 3 x 10-3
HD
H2
LiH
(Nakamura & Umemura 2002)
HD cooling is more dominant for T < 100 ~ 200 K
Thermal Property of Primordial
Gas for HD Controlled Case
Temperature

HD controlled collapse
g ~ 5/3
sphere

H2 controlled collapse
g ~ 1.1
cylinder
g~1
density
Machida et al. (in prep.)
Fragmentation !
Omukai 2000
For HD dominant clouds, EOS is almost isothermal.
Thus, there is a possibility for the fragments to break up into multiple cores.
Fragment mass ~ 10-40 M8.
Summary part 1: typical mass
of first generation stars



Truly first stars may be very massive as ~100 M8.
But, many first generation stars may have masses of
10~40 M8.
Effect of HD cooling !
Massive binary stars may be common product.
Fragmentation !
HD cooling
Can First Supernovae Trigger
Subsequent Star Formation?
Supernovae of first stars
SNR
Shock-cloud interaction
(e.g., Shigeyama & Tsujimoto 1998)
Fragmentation of cooling shells
Complete mixing
Compression of cloud cores
No mixing
Cloud destruction?
Induced SF?
Induced star formation?
Evolution of SNR
adiabatic
1. Free expansion
2. Sedov-Taylor
cooling
3. Pressure-driven expansion
Step 1: 1D calculation
We follow the evolution of the SNR shell with the thin-shell approximation.
・Dynamical evolution : analytic model
・Thermal evolution : radiative cooling + time-dependent chemical evolution
Step 2: 2D hydrodynamic simulation
Then, we follow fragmentation of the cooling shell with the thin-disk approximation.
Evolution of SNR: Step 1
Radius and expansion velocity
Machida et al. (in prep.)
Evolution of density
Evolution of temperature
Formation of Self-Gravitating Shells

The cooling shell is expected to become self-gravitating
by the time 106 - 107 yr.
Ｔｆｆ
Ｔcool
Ｔdyn
Formation of self-gravitating
Shell
↓
Tff = Tdyn
Ｔexp
Texp is sufficiently longer
than Tff and Tdyn at the
final stage.
Fragmentation of Cooling
Shells: Step 2

Fragmentation of a self-gravitating sheet




Thin-disk approximation
isothermal EOS
Power law velocity fluctuations
2D hydro simulation
Nakamura & Li (in prep.)
Fragmentation of Cooling Shells

Mass fraction of dense regions reaches ~0.7.
→ star formation efficiency may be high.
M: Mach number of the
velocity perturbations

Dense cores are rotating very rapidly.
Fragmentation Condition of SNR
The shell should be self-gravitating before blow out.
Expansion velocity should be larger than the sound speed.
Summary part2: Star Formation
Triggered by First Supernovae
Supernovae of first stars
SNR
Shock-cloud interaction
Fragmentation of cooling shells
Complete mixing
No mixing
Z ~ 10-3Z8
HD cooling
Metal cooling
Compression of cloud cores
Induced SF
Formation of low-mass metal-free stars
Formation of massive metal-free stars
Similar to present-day SF
~1M8.
~1M8.
~10-40M8.
Effect of Mixing
The temperature goes down to 20-40 K.



Dense cores are rotating very rapidly.
→ binary formation
Dense cores may fragment into small cores with masses of ~ 1 M8.
The efficiency of star formation may be high.
Shock-Cloud Interaction
Shock can trigger gravitational collapse before KH instability
grows significantly.
The density can become greater
Polytrope gas, 2D axisymmetric, no self-gravity
than 104 cm-3 for nearly
isothermal case.
Nakamura, McKee, & Klein (in prep.)
Fragmentation into 1M8 cores is
expected due to efficient H2
cooling by three-body reaction.