1. Low-Mass Star Formation, Triggered by Supernova in Primordial Clouds Masahiro N. Machida (Chiba University) Kohji Tomisaka (NAOJ) Fumitaka Nakamura (Niigata University) Masayuki Y. Fujimoto (Hokkaido University )

2. Introduction Is the formation of the low mass, metal deficient star possible in early universe ? Is the formation of the low mass, metal deficient star possible in early universe ? Why do we discuss the low mass star? Why do we discuss the low mass star? They have a long life time and survive up to now They have a long life time and survive up to now They can be observed (Beers et al. 1992, Norris et al. 1999) They can be observed (Beers et al. 1992, Norris et al. 1999) Why do we discuss the metal deficient star? Why do we discuss the metal deficient star? They formed in early universe that has not been polluted They formed in early universe that has not been polluted They have an information on the early universe They have an information on the early universe Recently many metal deficient star ( [Fe/H]<-3 ) has been observed Recently many metal deficient star ( [Fe/H]<-3 ) has been observed However, not yet understood when and how such stars form However, not yet understood when and how such stars form In this study, we examine the low mass star formation processes, triggered by the first generation SNe In this study, we examine the low mass star formation processes, triggered by the first generation SNe

3. How to form the low mass star in early Universe In a present star formation, the gas cools to ～ 10K for dust and metal cooling low temperature gas ⇒ small Jeans mass ⇒ low mass star formation In a present star formation, the gas cools to ～ 10K for dust and metal cooling low temperature gas ⇒ small Jeans mass ⇒ low mass star formation In early Universe (no dust, no metal), the gas cools to about 300-500K (Nakamura & Umemura 1998) ⇒ It is difficult to form the low mass star in a primordial composition In early Universe (no dust, no metal), the gas cools to about 300-500K (Nakamura & Umemura 1998) ⇒ It is difficult to form the low mass star in a primordial composition How to form the low mass star in early Universe How to form the low mass star in early Universe The H 2 and HD are effective coolant at low temperature The H 2 and HD are effective coolant at low temperature The H 2 and HD increase if the shock heating ( or re-ionization) occurs The H 2 and HD increase if the shock heating ( or re-ionization) occurs Shock heating is caused by the Supernova Remnant (SNR) Shock heating is caused by the Supernova Remnant (SNR) First star is massive ⇒ short life time ⇒ Supernova explosion occurs in short period First star is massive ⇒ short life time ⇒ Supernova explosion occurs in short period Gas can cool to low temperature by first generation SNR (shock heating) ⇒ low mass star formation Gas can cool to low temperature by first generation SNR (shock heating) ⇒ low mass star formation

4. DM+baryon First Collapsed Objects radiative cooling first star formation Supernova explosion SNR SNR shell Fragmentation in the SNR shell cylindrical fragmentation Star formation in the fragments Scenario Our Study 10 6 ~10 7 M sun Next generation low mass stars 1.First collapsed object is formed (M= 10 6 ~10 7 M sun, z=10~50) 2.Baryon component cools for radiative cooling 3.First star is formed (massive star) 4.Supernova explosion occurs 5.SNR evolves in the host cloud 6.Fragmentation occurs in the shell of the SNR 7.Low mass star forms in the fragments

5. Recent Studies Bromm, Yoshida & Hernquist (2003) Bromm, Yoshida & Hernquist (2003) SPH simulation of an SNR by a pair-instability supernova (PISN) SPH simulation of an SNR by a pair-instability supernova (PISN) High energy SN (10 53 erg) High energy SN (10 53 erg) Low-mass star formation does not occurs Low-mass star formation does not occurs host cloud (~10 6 M sun ) is completely disrupted host cloud (~10 6 M sun ) is completely disrupted gas with Z > 10 -2 Z sun is ejected into IGM gas with Z > 10 -2 Z sun is ejected into IGM No including HD, only two models No including HD, only two models Salvaterra, Ferrara & Schneider (2004) Salvaterra, Ferrara & Schneider (2004) Calculation of the SNR triggered by the PISN: analytical SNR evolution, many models Calculation of the SNR triggered by the PISN: analytical SNR evolution, many models Fragmentation (low mass star formation) occurs only when the following condition is fulfilled: Fragmentation (low mass star formation) occurs only when the following condition is fulfilled: high explosion energy (  0 > 3x10 52 erg) high explosion energy (  0 > 3x10 52 erg) high ambient density (14< n 0 < 790 cm -3 ) high ambient density (14< n 0 < 790 cm -3 ) They does not calculate the chemical reaction (approximation form of chemical composition) They does not calculate the chemical reaction (approximation form of chemical composition) HD cooling effect is not considered, only H 2 HD cooling effect is not considered, only H 2 They assume the high constant ambient gas pressure (~10 4 K) ⇒ suppress the SNR evolution, promote fragmentation They assume the high constant ambient gas pressure (~10 4 K) ⇒ suppress the SNR evolution, promote fragmentation ⇒ They does not calculate the ambient gas evolution ⇒ They does not calculate the ambient gas evolution Our study (Machida, Tomisaka, Nakamura & Fujimoto ApJ 2005 in press) Our study (Machida, Tomisaka, Nakamura & Fujimoto ApJ 2005 in press) SNR evolution (analytical), chemical reaction (1-zone approximation) for the SNR shell and the ambient gas SNR evolution (analytical), chemical reaction (1-zone approximation) for the SNR shell and the ambient gas Including HD, effect of ambient gas pressure; we calculate 20 models Including HD, effect of ambient gas pressure; we calculate 20 models Low mass star formation occurs, trigged by low energetic SN (10 51 erg) in minihalo (10 6-7 M sun ) Low mass star formation occurs, trigged by low energetic SN (10 51 erg) in minihalo (10 6-7 M sun ) Bromm, Yoshida & Hernquist 2004

6. We solve the followings at the same time We solve the followings at the same time 1.SNR radius (R SNR ), velocity (V SNR ), inner pressure (P in ), radius (R SNR ), velocity (V SNR ), inner pressure (P in ), outer pressure (P out ) outer pressure (P out ) 2.Shocked Shell density (n SH ), temperature (T sh ), chemical composition (X i ), shell pressure (P sh ) density (n SH ), temperature (T sh ), chemical composition (X i ), shell pressure (P sh ) 3.Ambient gas temperature (T hc ), ambient pressure (P hc ), chemical composition (Y i ), (constant density) temperature (T hc ), ambient pressure (P hc ), chemical composition (Y i ), (constant density) Numerical Model(1) SNR ambient gas R SNR V SNR P in P out Shell ambient gas Inside of SNR n SH T sh XiXiXiXi T hc P hc YiYiYiYi P sh Shell Parameters ・  0 : explosion energy =1, 3, 5, 10 x 10 51 erg ・ z: redshift (or ambient density) =10, 20, 30, 40, 50 Chemical composition: primordial composition (Galli & Palla 1998) ◆ 20 models ◆ Chemical composition: primordial composition (Galli & Palla 1998) 00  0 ∝ (1+z) 3 Parameters, Initial Conditions and Calculation results

7. Numerical Model (2) Evolution of the SNR Evolution of the SNR Sedov-Taylor phase (  cool >  exp ) Sedov-Taylor phase (  cool >  exp ) Pressure-driven phase (  cool <  exp ) Pressure-driven phase (  cool <  exp ) (, ) (, ) Fragmentation (  ff   dyn ) Fragmentation (  ff   dyn ) Post fragmentation phase (  ff <  dyn ) Post fragmentation phase (  ff <  dyn ) Evolution of gas in the shell and ambient gas Evolution of gas in the shell and ambient gas Temperature Temperature Density Density Chemical Composition Chemical Composition H 、 H + 、 H - 、 H 2 、 He 、 He + 、 He ++ 、 D 、 D + 、 HD 、 HD + 、 e H 、 H + 、 H - 、 H 2 、 He 、 He + 、 He ++ 、 D 、 D + 、 HD 、 HD + 、 e ・ Four typical timescales (Λ ： He 、 H 、 H2 、 HD 、 IC) After fragmentation (Ostreiker 1964) (), where Before fragmentation

8. ・ SNR radius evolve to about 100 pc in 10 6 ～ 10 7 yr ・ The SNR radius increases with lower ambient density ・ The temperature of gas shell and ambient temperature falls more quickly in the model with high-z because radiative cooling is more effective ・ Ambient gas temperature cools enough ⇒ ambient gas hardly affects the SNR evolution Results ST phase PD phase r (pc) v (km/s) time (yr) SNR radius SNR velocity Evolution of SNR Evolution of Shell Evolution of ambient gas ★ Evolution of the SNR, shell temperature and ambient gas temperature with different initial density (redshift: z) shell temperature ambient gas temperature time (yr)

9. t ff t cool t exp t dyn ★ Four typical timescales ・  ff : free fall timescale ・  dyn : dynamical timescale ・  exp : expansion timescale ・  cool : cooling timescale Sedov-Taylor (  exp <  cool ) Pressure-Driven (  exp >  cool ) Post-Fragmentation (  dyn >  ff ) t (yr) ◆ After fragmentation, the time scale shortens very much because the density may increase in the fragments ◆ The feature of the timescale does not depend on the parameter so much Fragmentation (  dyn =  ff )  0 =1x10 51, z=20

10. ◆ Fractional abundances The time variation of the fractional abundances for 10 species temperature Number density Before Fragmentation After Fragmentation ◆ H 2 :1.1×10 -6 ⇒ 1.7×10 -3 ⇒ 0.85 ◆ HD:1.2×10 -11 ⇒ 7.5×10 -6 ⇒ 1.7×10 -4 Model: (z,   )=(20, 10 51 erg) initial Fragmentation epoch optically thick

11. ◆ Cooling rates due to contribution from various molecules ◆ Because H 2 and HD is increased for shock heating, H 2 and HD become effective coolant at low temperature (H 2 : 5000<T<200k HD: T<200K) in the ante-fragmentation phase ◆ In the post-fragmentation phase, H 2 and HD are effective coolant ◆ n>10 8 cm -3, H 2 increase for 3-body reaction Before Fragmentation After Fragmentation He H H2H2 HD H2H2 H2H2 Total Model: (z,   )=(20,10 51 erg)

12. ◆ Fragmentation condition Fragmentation region is plotted on the  0 - z parameter space ◆ Solid lines: the relation that swept mass is equal to the baryonic mass in the host cloud ◆ Dotted line: the relation that the shell expansion speed at the fragmentation is equal to the sound speed in the host cloud of c s,0 =2,3,5 km/s V SNR = C s,hc (T)

13. Post Fragmentation Phase Temperature and Jeans mass when the gas becomes optically thick, Jeans mass becomes ・ M J = 0.16 M sun for cylindrical geometry ・ M J = 0.89 M sun for spherical geometry Low mass star formation is possible ! Metallicity of the low mass star ・ [Fe/H] is estimated by the ratio of the swept mass and the ejected iron mass ・ Ejected iron mass is assumed to be M Fe,ej = 0.1, 0.05 and 0.5 M sun [Fe/H]=log (x [Fe] / x [H] ) – log (x [Fe] / x [H] ) sun ≈ -3.5 +log [ (M ej,Fe / 0.1M o )/ (M sw /5x10 4 M o )] -4.5< [Fe/H] < -2.5 metal deficient !

14. Summary Before Fragmentation Phase Before Fragmentation Phase H 2 and HD increase by about 10 3 times compared with primordial composition because of re-ionization caused by SNR shock H 2 and HD increase by about 10 3 times compared with primordial composition because of re-ionization caused by SNR shock Fragmentation (or low mass star formation) condition: Fragmentation (or low mass star formation) condition: M hc = 1x10 6 Msun : fragmentation impossible M hc = 1x10 6 Msun : fragmentation impossible M hc = 3x10 6 Msun : z>20  0 >3x10 51 M hc = 3x10 6 Msun : z>20  0 >3x10 51 Fragments (formed low mass star) have the metal abundance of -2.5~-4.5 ([Fe/H]) Fragments (formed low mass star) have the metal abundance of -2.5~-4.5 ([Fe/H]) After Fragmentation Phase After Fragmentation Phase In both of cylindrical and spherical collapse, Only H 2 and HD are effective coolant In both of cylindrical and spherical collapse, Only H 2 and HD are effective coolant In both of cylindrical and spherical geometry, the low mass star that survives up to now forms In both of cylindrical and spherical geometry, the low mass star that survives up to now forms