1. Star Formation Triggered By First Supernovae Fumitaka Nakamura (Niigata Univ.)

2. Questions What is the typical mass of the first stars? What is the typical mass of the first stars? Can first supernovae trigger subsequent star formation? Can first supernovae trigger subsequent star formation? Can primordial cloud cores break up into multiple fragments? Can primordial cloud cores break up into multiple fragments? Binary formation? Binary formation? What is the typical mass of the stars formed by shock compression? What is the typical mass of the stars formed by shock compression? low mass star formation? (e.g., HE0107-5240)

3. What is the typical mass of first stars? Typical mass of fragments ~ 100M  Typical mass of fragments ~ 100M  No fragmentation for the polytrope gas with  = 1.1. No fragmentation for the polytrope gas with  = 1.1. (e.g., Tsuribe’s talk) (e.g., Tsuribe’s talk) Size of HII region ~ 100 pc Free-fall time of fragments ~ 10 6 yr ↓ Positive feedback of UV radiation ↓ Enhanced H 2 formation 30 pc (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. If a truly first star is massive, it emits strong UV radiation, which should affect subsequent evolution of other prestellar fragments. HII region

4. Positive feedback of UV radiation Enhanced H2 formation Enhanced H2 formation HD cooling is more dominant for T < 100 ~ 200 K Threshold H2 abundance x H2 > 3 x 10 -3 (Nakamura & Umemura 2002) Formation of HD molecules (Nakamura & Umemura 2002)

5. Thermal Property of Primordial Gas for HD Controlled Case HD controlled collapse HD controlled collapse    Fragmentation ! 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 M . H2 controlled collapse H2 controlled collapse Omukai 2000 Machida et al. (in prep.) sphere cylinder density Temperature

6. Summary part 1: typical mass of first generation stars Truly first stars may be very massive as ~100 M . Truly first stars may be very massive as ~100 M . But, many first generation stars may have masses of 10~40 M . But, many first generation stars may have masses of 10~40 M . Massive binary stars may be common product. Massive binary stars may be common product. HD cooling Effect of HD cooling ! Fragmentation !

7. Can First Supernovae Trigger Subsequent Star Formation? Supernovae of first stars Complete mixingNo mixing Cloud destruction? Induced SF? Compression of cloud cores Shock-cloud interaction Induced star formation? Fragmentation of cooling shells SNR (e.g., Shigeyama & Tsujimoto 1998)

8. Evolution of SNR Step 1: 1D calculation We follow the evolution of the SNR shell with the thin-shell approximation. 1. Free expansion2. Sedov-Taylor3. Pressure-driven expansion ・ 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. adiabatic cooling

9. Evolution of SNR: Step 1 Radius and expansion velocityEvolution of density Evolution of temperature Machida et al. (in prep.)

10. Formation of Self-Gravitating Shells The cooling shell is expected to become self-gravitating by the time 10 6 - 10 7 yr. The cooling shell is expected to become self-gravitating by the time 10 6 - 10 7 yr. Ｔｆｆ Ｔ dyn Ｔ exp Ｔ cool Formation of self-gravitating Shell ↓ Tff = Tdyn Texp is sufficiently longer than Tff and Tdyn at the final stage.

11. Fragmentation of Cooling Shells: Step 2 Fragmentation of a self-gravitating sheet Fragmentation of a self-gravitating sheet Thin-disk approximation isothermal EOS Power law velocity fluctuations 2D hydro simulation Nakamura & Li (in prep.)

12. Fragmentation of Cooling Shells Mass fraction of dense regions reaches ~0.7. Mass fraction of dense regions reaches ~0.7. → star formation efficiency may be high. → star formation efficiency may be high. Dense cores are rotating very rapidly. Dense cores are rotating very rapidly. M: Mach number of the velocity perturbations

13. Fragmentation Condition of SNR The shell should be self-gravitating before blow out. Expansion velocity should be larger than the sound speed.

14. Summary part2: Star Formation Triggered by First Supernovae Supernovae of first stars Fragmentation of cooling shells Compression of cloud cores Complete mixingNo mixing Metal cooling Z ~ 10 -3 Z  HD cooling Similar to present-day SF Formation of massive metal-free stars Induced SF SNRShock-cloud interaction Formation of low-mass metal-free stars ~10-40M . ~1M .

15. Effect of Mixing Dense cores are rotating very rapidly. Dense cores are rotating very rapidly. → binary formation → binary formation Dense cores may fragment into small cores with masses of ~ 1 M . Dense cores may fragment into small cores with masses of ~ 1 M . The efficiency of star formation may be high. The efficiency of star formation may be high. The temperature goes down to 20-40 K.

16. Shock-Cloud Interaction Shock can trigger gravitational collapse before KH instability grows significantly. Nakamura, McKee, & Klein (in prep.) The density can become greater than 10 4 cm -3 for nearly isothermal case. Fragmentation into 1M  cores is expected due to efficient H2 cooling by three-body reaction. Polytrope gas, 2D axisymmetric, no self-gravity