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2 First Objects III

3 Introduction Big bang nucleosynthesis Recombination Primordial chemistry Chemical reaction network (First Objects) 2 4. Cooling diagram Time scale H 2 abundance H 2 dissociation formation Cooling H 2 abundance Free-fall time cooling time Primordial chemistry... 9

4 7.2 First objects APPENDIX 28 A 28 B 32 C H H + 2 H 2 32 D Fastest time scale 33

5 3 Abstract A < 8... H 2 HD first objects. first objects. (λ) scale factor λ λ first objects. H 2 HD LiD 85 z=0000. first objects free fall cooling time scale. λ first objects.

6 4. Introduction Big bang.. I a (Vishwakarma 2000). baryon dark matter K (CMB). Big bang 00 He D Li H D He Li CMB. (Lepp & Shull 984 Puy & Signore 997 Stancil et al. 998 Galli & Pall 998). H 2 Saslow & Zipoy (976) Peelbes & Dicke (968). H 2 abundance H + 2 H H 2 first objects ( ) progenitor cooling. cooling first objects. First objects progenitor free-fall H 2 cooling (Palla et al.983 Mac Low & Shull 986 Lahav 986 Puy & Signore 996 ). Tegmark et al. (997) cold dark matter model (CDM) first objects CDM z M. Abel et al. (997) H 2 cooling M. Nishi et al. (998) Tegmark time scale H 2 abundance CDM

7 5 0 7 M. first objects 5000m 64 ALMA (Atacama Large Millimeter/submillimeter Array) (Nakai 2002).. first objects Λ=Λ +Λ 2 a m ( Özer 999 Vishwakarma 2000 Kimura et al. 200) Λ first objects.

8 Robertson-Walker Einstein d da [(ρ + ȧ 2 = 8πG 3 ρa2 + Λ 3 a2 k () Λ 8πG )a3 ]= 3(p Λ 8πG )a2 (2). H =ȧ/a (ȧ = da/dt) ρ p k. c = scale factor a 0 =( 0 ). () (2). () Λ (ρ v = p v =Λ/(8πG)). () (2) Ω. Ω λ Ω 0 λ 0 k. (3) (4) z. ȧ 2 = H0(Ωa λa 2 + Ω 0 λ 0 ) (3) d da [(Ω + λ)a3 ]= 3( p λ)a 2 ρ crit (4) Ω ρ λ Λ ρ crit H0 2 ρ crit 3H 0 2 8πG (5) k = H 2 0(Ω 0 + λ 0 ) (6) dz dt = H 0( + z) Ω+λ +( Ω 0 λ 0 )( + z) 2 (7) d dz [(Ω + λ)( +z )3 ]=3( p λ)( ρ crit +z )4 (8) 2.2. Ω=Ω γ +Ω ν +Ω e ± +Ω M (9). Ω γ Ω ν Ω e ± Ω M. Ω M a 3. Ω M cold dark matter baryonic matter.

9 K. Ω=Ω γ +Ω ν +Ω M (0). ρ r = ρ γ + ρ ν = a r T 4 γ N νa r T 4 ν () a r T γ T ν ( ) T ν0 4 /3 = (2) T γ0. ( ( ) ) 4 4/3 7 ρ r = + 8 N ν a r Tγ 4 (3) N ν () (3) (0) ( ( ) ) 4 4/3 7 Ω= + 8 N ar ν Tγ 4 +Ω M0 ( + z) 3 (4) ρ crit Ω M0 scale factor (Wage 993 Özer 999). (4) T γ λ = λ 0 + λ 20 a m (5) T γ = ρ crit ( ) ) 4/3 (Ω Ω M0 ( + z) a r (+ 3) 4 78 N ν 4 (6). p = 3 [ + ( ) 4 ] N ν a r Tγ 4 (7)

10 8 (8) (5) (7) dω dz = (6). 4Ω +z ( + z)2 Ω M0 mλ 0 ( + z) m (8) Kimura et al. (200) λ. λ 20 m 0.00 (9) λ 20 = m =.5 (Kimura et al. 200) m=.5 λ 0 = T(K) 00 0 λ 20 = λ 20 = z Fig..

11 Big bang nucleosynthesis Big bang. 0 0 K.. decoupling K. 0 9 K 00 D He Li Recombination Big bang. (T 0 4 K) (recombination). recombination. Helium recombination He. He recombination 2. z He 2+ He + He 2+ +e He + + hν (20) z 2700 He + He He + +e He + hν (2) Hydrogen recombination H (3.6 ev) T < 3.6 ev ( 0 5 K). H recombination H + +e H+hν (22)

12 0 H recombination.. H recombination Peebles et al. (968) (Matsuda et al. 97 Jones & Wyse 985 Sasaki & Takahara 993). Recombination 2 continuum 3. Continuum nc 2S Rc2 R2c 2P n2 S Π Ly α n Ground Fig. 2. Continuum n e (Jones & Wyse 985) dn e dt +K( n + R c2 n e n p ) = R c2 n e n p +K( n + n R 2c + R c2 n e n p ) R 2c n c e hν α k T +K n B +K[( +R 2c )n + R c2 n e n p ] (23) n p n n 2 n c ν α Lyman α ( Hz) 2S (8.227 s ) R c2 continuum R 2c continuum K time scale ( c3 ȧ 3πνα 3 a ) k B Lithium recombination Li recombination He Li (6.9 ev) recombination Li Li 3+ +e Li 2+ + hν (24) Li 2+ +e Li + + hν (25) Li + +e Li + hν (26)

13 3.3. Primordial chemistry Recombination (z 000). CMB H 2 HD first objects. H 2 chemistry H 2 H H H. a)h H+e H + hν (27) H +H H 2 +e (28) b)h + 2 H + +H H hν (29) H + 2 +H H 2 +H + (30) (z > 500) H 2 CMB. H + hν H+e (3) H hν H+ + H (32) HD chemistry HD H + +D D + + H (33) D + +H 2 H + + HD (34) HD dipole moment H+D HD + hν (35).

14 Chemical reaction network e H H + H D D + He He + He 2+ Li Li + Li H 2 H + 2 HD HD+ HeH + LiH LiH + H + 3 H 2D + 2. z. 85 (Galli & Palla 998) Big bang.. 2 dy i dt = j k j (T γ )y j + n l k lm (T m )y l y m (36) m y i i abundance ( n i n N y i = n i /n N ) k j k lm l m n N T γ T m t z (7) dz dt = H 0( + z) Ω 0 ( + z) 3 + λ (37). H 0 =00h km s Mpc. n N n N (z) =Ω b n cr ( + z) 3 (38). n cr = h 2 cm 3 Ω b = ρ b /ρ cr. (Peebles 968) dt m dt ȧ = 2T m a + 8σ T a r Tγ 4 y e (T γ T m ) (39) 3m e c σ T a r m e c y e y e = n e /n N CMB Compton.

15 3 (39) (3). dt m dt = 2T m H 0 ( + z) Ω 0 ( + z) 3 + λ + 8σ T a r T 4 γ 3m e c y e (T γ T m ) (40) 4. (First Objects) CMB z 5. Intergalactic medium (IGM) z>5 first objects.. virialize cooling. cooling diagram. 4.. Cooling diagram progenitor free-fall time cooling time. t cool t dis t rec t form time scale H 2 (abundance) Time scale H 2 abundance T<0 4 K cooling rate H 2 abundance. H 2. T y e T<0 4 K. 4 time scale t dis t form t cool t rec H 2 dissociation time formation time cooling time recombination time) H 2 abundance (Nishi et al. 998).

16 4 time scale t dis n H 2 n ṅ dis = H2 H 2 i ki dis = n H2 n i t form n H 2 n ṅ form = H2 H 2 ij kform t cool T T = t rec n e ṅ e = i k dis i n i (4) y H2 = (42) ij n i n j ij kform ij n N n i n j 3k B T (43) n N m p Λ H2 y H2 n e k rec = n e n p k rec (44) n e n N n i i y i i abundance ki dis H 2 i H 2 k form ij i j H 2 k rec recombination Λ H2 H 2 cooling t dis t form. t dis (4) y H2 t form (42) y H2. 2 time scale t dis = t eq dis (45) t form = t eq y H2 formy eq (46) H 2 eq H 2 ((48) (49) ).. t eq dis = teq form (47) time scale t sys t dis t form. t sys t cool t rec. t sys y H2. ) y H2 >y eq H 2 dissociation formation. y H2 t dis. t dis y H2 t dis <t sys y H2 y eq H 2. 2) y H2 <y eq H 2 y H2 t form. y H2. t form. (42) t form y H2. t sys >t eq form (= t dis) t sys t form. ) 2) t dis t form t sys H 2.

17 H 2 dissociation formation H 2 Appendix C dn H2 = n 2 R 3 R 4 R 6 R 7 dt H[n e + n n H R 4 + n H +R 5 + R 2 /n H + ] N n H R 7 + n e R 8 + R 3 /n N R 9 R 8 n H2 [n H +n e + n n H R 7 + n e R 8 + R 3 /n H R 0 + n e R + R 4 /n N ] (48) N R n (Table 7). H 2 formation dissociation. dn H2 = 0(49) dt T y e n eq H Cooling H 2 H 2 H cooling. T<0000 K cooling H 2. cooling H H 2 H 2. H 2 abundance H 2 H 2. Martin et al. (996) Forrey et al. (997) (n 0.cm 3 ) cooling Λ H2 log 0 ( n H n H2 erg cm 3 s ) = log 0T m 48.05(log 0 T m ) (log 0 T m ) (log 0 T m ) 3 (50) H 2 abundance Time scale virial T vir y e H 2 abundance. T vir y e (4) (43) (44) y e T vir plane 3 (Fig 3). t rec = t dis t eq cool = t dis t eq cool t dis = t 2 rec (5) t eq cool yeq H 2 (43). (5) Appendix D.

18 6 0. t rec fastest t dis fastest 0.0 y e t cool fastest t rec =t dis t cool =t dis 0-5 t cool =t rec T(K) Fig. 3. y e T vir plane t dis t cool t rec Fig 3 3 y e T vir plane H 2 ) t dis <min(t cool t rec ) H 2. y H2 = y eq H 2 (52) 2) t rec <min(t cool t dis ) H 2. H 2 abundance recombination abundance t form = t rec. (4) (42) t form = y H2 /y eq H 2 t dis y H2 = y eq t rec H 2 (53) t dis 3) t cool <min(t rec t dis )

19 7 H 2. H 2 abundance t form = t cool. y H2. y H2 = y eq H 2 t eq cool /t dis (54) ) 2) 3) vilial Fig t cool =t rec t cool =t dis c c y H T vir (K) Fig. 4. virial H 2 abundance Free-fall time cooling time y e T vir H 2 abundance time scale. H 2 cooling time scale t cool

20 8 time scale t ff ( 0 ) time scale t H. time scale. t ff 3π ( ) /2 32Gρ vir (55) 3k B T vir n vir m p Λ H2 y H2 (56) t cool t H H (57) ρ vir 8π 2 Ωρ cr n vir Ω b ρ vir /m p ρ cr =3H 2 0/8πG ρ vir virial n vir virial m p 3 time scale ( + z vir ) T vir plane 3 (Fig ). ) t ff >t cool vilialize H 2 cooling. 2) t H >t cool >t ff cooling.. 3) t cool >t H vilialize. (baryon dark matter)m t ff t cool t H T vir (Blanchard et al. 992). T vir = 485h 2/3 ( M M ) 2/3 ( +z vir 00 ) (58) z vir virial

21 9 5. Table. 3. Table : Ω 0 λ 0 λ 20 m ( ) ( λ ) ( λ ) abundance H D Li He abundance Y e =0.24 ± (Peimbert et al. 2000) (D/H)=(3.0 ± 0.2) 0 5 (Burles et al. 200) (Li/H)= (Ryan et al. 2000) z=0000. H 0 ( ) 00h (km s Mpc ) h=0.67 T γ0 ( CMB ) (K) Ω b ( ) η 0 h 2 η 0 ( ) 5.5 N ν ( ) :3 Chemical network reaction Appendix A. First objects time scale Appendix B.

22 Primordial chemistry chemical reaction network. Fig z 000 He z 000 H D z<000 Li recombination. H H + D fractional abundance H 2 H + 2 H - fractional abundance D + HD + HD H H 2 D z +z He fractional abundance He + HeH + fractional abundance Li LiH Li + LiH 0-20 He Li z +z Fig. 5.. H( ) D ( ) He ( ) Li ( )

23 2 Fig 6 7 λ λ chemical reaction network. λ recombination. fractional abundance H H + H 2 H + 2 H - H z D fractional abundance D + HD H 2 D + HD z Fig. 6. λ ( ) λ ( ) H D

24 22 He fractional abundance He ++ He + HeH z fractional abundance Li Li + LiH LiH + Li z Fig. 7. λ ( ) λ ( ) He Li

25 23 Fig 8 λ λ 2 λ T r T(K) 0 λ 20 =0 0. λ 20 =0 0.0 λ 20 = λ 20 = T m z Fig. 8. λ ( ) λ ( ) Fig 9 H 2 HD abundance. H 2 HD H 2 H H. 2 H 2 HD abundance λ. H 2 HD cooling

26 24 first objects.. z = H 2 HD Table H 2 fractional abundance HD λ 20 = λ 20 = z Fig. 9. λ ( ) λ ( ) H 2 HD Table 2: z = H 2 HD abundance y e y H2 y HD ( ) ( λ ) ( λ )

27 First objects λ first objcets ( ). Fig 0 z = y H2. z =0 z =00 H 2 H H + 2 abundance z =200 H abundance. H 2. λ abundance z=0 00 abundance y H2 0-6 z=0 0-8 z=00 z= T vir (K) Fig. 0. z= H 2 abundance Fig z = 50 H 2 abundance 4..4 first objects. (t ff >t cool ) cooling time scale first objects. (t H >t cool >t ff ) cooling first objects. (t cool >t H )

28 26 time scale first objects t >t H >t >t cool ff t ff >t cool T vir (K) 3000 t cool >t >t H z vir Fig.. ( + z vir ) T vir plane first objects. Fig 2 λ first objects. λ. (58). first objects. 0 6 M λ cooling first objects.

29 t cool =t ff t cool =t =t H t =t cool-λ ff-λ t =t cool-λ H-λ t >t H >t cool >t ff t >t H-λ cool-λ >t ff-λ t >t ff-λ cool-λ T vir (K) 3000 t ff >t cool t cool >t >t H t >t cool-λ H-λ M 0 6 M 0 5 M z vir Fig. 2. ( + z vir ) T vir λ ( ) plane first objects. ( )

30 28 8. ) Kimura et al. (200) λ. 2) First objects H 2 λ. 3) Time scale first objects λ. ) 2) 3) λ. -Acknowledgement-.. ( ) ( ) ALMA.

31 29 9. APPENDIX A. Table 3: Reaction rates for Hydorgen species reaction rate (cm 3 s or s ) notes H + +e H+γ ( + z) 0.58 R 2c H + + γ H+e ( + z) T.5 γ exp( 39472/T γ) R c2 H+e H + γ Tm exp( T m /6200) H + γ H+e. 0 Tγ 2.3 exp( 8823/T γ ) H +H H 2 +e T m Tm 0.7 T m < 300 H +H + H + 2 +e Tm 0.35 T m Tm 0.9 T m < 8000 H +H + 2H Tm T 0.9 m T m H+H + H γ Tm.8exp( 20/T m) H γ H+H Tγ.59 exp( 82000/T γ ) T m exp( 32400/T γ ) H + 2 +H H 2 +H H + 2 +e 2H T 0.5 m H γ 2H+ +e T.48 γ exp( /T γ ) H + 2 +H 2 H + 3 +H H 2 +H + H + 2 +H exp( 2050/T m ) T m exp( 4000/T m ) T m > 0 4 H 2 +e H+H Tm.27 exp( 43000/T m ) H 2 +e 2H + e Tm 0.35exp( 02000/T m) H 2 + γ H + 2 +e Tγ 0.35 exp( 78500/T γ ) H + 3 +H H+ 2 +H exp( 7560/T m ) H + 3 +e H 2 +H Tm 0.65 H 2 +H + H γ.0 0 6

32 30 Table 4: Reaction rates for Deuterium species reaction rate (cm 3 s or s ) notes D + +e D+γ ( + z) 0.58 D+γ D + +e ( + z) Tγ.5 exp( 39472/T γ ) D+H + D + +H Tm 0.28exp( 43/T m) D + +H D+H Tm 0.28 D+H HD + γ D+H 2 H+HD exp( 3876/T m ) T m > 250 HD + +H H + +HD D + +H 2 H + +HD HD+H H 2 +D exp( 3624/T m ) T m > 200 HD+H + H 2 +D exp( 464/T m ) HD+H + 3 H 2 +H 2 D + (2. 0.4logT m ) 0 9 D+H + HD + + γ Tm.8 exp( 20/T m ) D + +H HD + + γ Tm.8exp( 20/T m) HD + + γ H+D exp( 32400/T γ ) HD + + γ H + +D exp( 32400/T γ ) HD + +e H+D Tm /2 HD + +H 2 H 2 D + +H HD + +H 2 H + 3 +D D+H + 3 H 2D + +H Tm H 2 D + +e H+H+D Tm / H 2 D + +e H 2 +D Tm / H 2 D + +e HD + H Tm / H 2 D + +H 2 H + 3 +HD exp( 25/T m ) T m 0 2 H 2 D + +H H + 3 +D T m > T m exp( 632/T m )

33 3 Table 5: Reaction rates for Helium species reaction rate (cm 3 s or s ) notes He ++ +e He + + γ.89 0 [ 0 Tm 9.37 ( + Tm 9.37 ) ( + Tm ).7524 ] He + + γ He ++ +e Tγ.63 exp( /T γ ) He + +e He + γ [ Tm 5.54 ( + Tm 5.54 )0.309 ( + Tm ).69 ] 7 He + γ He + +e Tγ.23 exp( /T γ ) He + H + He + +H Tm 4.74 He + +H He + H T 2.06 m He + H + HeH + + γ Tm [+9.9exp( 2570 )] He + H + He + + γ T 0.5 m T m T.06 m T m > 0 3 He + H + 2 HeH+ +H exp( 677/T m ) He + +H HeH + + γ Tm 0.33 T m T m > 4000 HeH + +H He + H HeH + +e He + H T 0.5 m HeH + +H 2 H + 3 +He HeH + + γ He + H T.5 γ exp( 22750/T γ ) He + γ He + +H T.2 γ exp( /T γ )

34 32 Table 6: Reaction rates for Lithium species reaction rate (cm 3 s or s ) notes Li + +e Li + γ [ T m /07.7 ( + T m /07.7) 0.62 ( + T m / ).388 ] Li + γ Li + +e Tγ.45 exp( 60500/T γ ) Li + +H Li + H Tm Tm T m Li + +H + Li+H Tm Tm 0.5 T m Li+e Li + γ Tm 0.58 exp( T m /7200) Li + γ Li + e Tγ.4 exp( 800/T γ ) Li+H + Li + +H Tm 7.9 exp( T m /20) Li+H + Li + +H+γ Tm 0.05 exp( T m /282000) Li+H LiH + γ ( Tm.5 Tm.2) LiH + γ Li + H Tγ 0.3 exp( 29000/T γ ) Li+H LiH + γ Tm 0.8 exp( T m /500) Li+H LiH + γ Tm 0.34 Li+H LiH+e Li +H LiH+e LiH + +H LiH + H exp( 67900/T m ) LiH+H + LiH + +H LiH+H Li+H LiH + +H LiH + + γ dex[ logT m 0.35(logT m ) 2 ] Li+H + LiH + + γ Tm 0.49 LiH+H + LiH + +H LiH+H + Li + +H LiH + +e Li+H Tm 0.47 LiH + +H Li + H exp( 66400/T m ) LiH + +H Li + +H LiH + + γ Li + +H exp( 900/T γ ) LiH + + γ Li+H T γ exp( 97000/T γ )

35 33 B. Table 7: H 2 abundance reaction R n rate (cm 3 s or s ) reference )H+e H + +2e Tm 0.5 ( + (T m /0 5 ) 0.5 ) exp( /T m ) HTL 2)H + +e H+γ Tm 0.7 (+(T m /0 6 ) 0.7 ) ) HTL 3)H+e H + γ Tm 0.93 exp( T m /6200) GP 4)H +H H 2 +e FC 5)H +H + 2H Tm 0.5 FC 6)H+H + H γ Tm.8 exp( 20/T m ) SLD 7)H + 2 +H H 2 +H GP 8)H + 2 +e 2H Tm 0.4 SLD 9)H 2 +H H H min( exp( 2050/T m ) GP exp( 4000/T m )) AAZN 0)H 2 +H 3H Tm 2.0 ( + (2.3T m /0 5 ) 3.5 ) AAZN exp( /T m ) GP )H 2 +e 2H + e Tm 0.35 exp( /T m ) GP 2)H + γ H+e. 0 Tγ 2.3 exp( 8823/T γ ) GP 3)H γ H+H exp( 32400/T γ ) GP 4)H 2 + γ H + 2 +e Tγ.56 exp( 78500/T γ ) GP AAZN: Abel et al. (997); FC: Fuller & Couchman (2000); GP: Galli & Pall (998); HTL: Haiman Thoul & Loeb (996); GP: Galli & Palla (998); SLD: Stancil Lepp & Dalgarno (998); C. H H + 2 H 2 H H H n H dn H dt dn H /dt 0 n H + 2 n H + 2 dt = n H n e R 3 n H [n H R 4 + n H +R 5 + R 2 /n N ] (C) n n H H n e R 3 n H R 4 + n H +R 5 + R 2 /n N (C2) = n H n H +R 6 + n H2 n H + n H + [n H R 7 + n e R 8 + R 3 /n N ] (C3) 2

36 34 n H + /dt 0 2 n H + 2 n H n H + R 6 + n H2 n H +R 9 n H R 7 + n e R 8 + R 3 /n N (C4) n H2 n H2 dt = n H n H R 4 + n H n H + R 7 2 n H2 [n H +R 9 + n H R 0 + n e R + R 4 /n N ] (C5) (C6) (60) (62) = n H2 n e R 3 R 4 n H R 4 + n H +R 5 + R 2 /n N R 6 R 7 R 9 R 7 +n H2 n H + + n n H R 7 + n e R 8 + R 3 /n H n H2 n H + N n H R 7 + n e R 8 + R 3 /n N n H2 [n H +R 9 + n H R 0 + n e R + R 4 /n N ] (C7). D. Fastest time scale (5) 3 timescale. t rec = t dis t cool = t dis t cool = t rec (D) (D2) (D3) (4) (44) t rec t dis y H2 t rec = t dis (D4). t cool = t dis t dis <min(t rec t cool ) t cool = t eq cool (65) t eq cool = t dis (D5). t cool = t rec t rec <min(t cool t dis ) t form = t rec. t form = y H2 /y eq H 2 t dis y H2 = y eq H 2 (t rec /t dis ) 3kT t cool = n N m p Λ H2 y H2 (D6)

37 35 (62). t cool = 3kT n N m p Λ H2 y eq ( t dis )=t eq cool H 2 t ( t dis ) rec t rec t eq cool t dis = t 2 rec (D7) (D8)

38 36 REFERENCES Abel, T., Anninos, P., Zhang, Y., Norman, M. L., 997, NewA, 2, 8 Abel, T., Anninos, P., Norman, M. L., Zang, Y., 998, ApJ, 508, 58 Blanchard, A., Valls-Gabaud, D., & Mamon, G. A., 992, A&A, 264, 365 Burles, S., Nollett, K., Truran, J. W. & Turner, M. S. 999, Phys. Rev.A Lett., 8, 476 Forrey, R. C., Balakrishnan, N., Dalgarno, A., Lepp S., 997, ApJ, 489, 00 Fuller, T. & Couchman, H. M. P., 2000, ApJ, 553,47 Galli, D., Palla, F., 998, A&A, 335, 403 Hmaiman, Z., Thoul, A. A., Loeb, A., 996, ApJ, 464, 523 Hutchings, R. M., Santoro, F., Thomas, P. A., Couchman, H. M. P, 2000, astro -ph/0027 Jones, B. J. T., & Wyse, R. F. G., 985, 49, 44 Kimura, K., Hashimoto, M., Sakoda, K., Arai, K., 200, ApJL, 56, L9 Lahav, O., 986, MNRAS., 220, 259 Lepp, S., Shull, M., 984, ApJ, 280, 465 MacLow, M. M., Shull, J. M., 986, ApJ, 302, 585 Martin, P. G., Schwarz, D. H., Mandy, M. E., 996, ApJ, 46, 265 Matsuda, T., Sato, H., and Takeda, H., 97, Prog. Theor. Phys., 46, 46 Nakai. N., 2002, private communication Nishi, R., Susa, H., 999, ApJL, 523, 03 Nishi, R., Susa, H., Uehara, H., Yamada, M., Omukai, K., 998, astro-ph/98236 Özer, M, 999, ApJ, 520, 45 Palla, F., Galli, D., 995, ApJ, 45, 44 Palla, F., Salpeter, E. E. & Stahler, S. W., 983 ApJ, 27, 632 Peebles, P. J. E., 968, ApJ, 53, Peebles, P. J. E., Dicke, R. H., 968, ApJ, 54, 89

39 37 Peimbert, M., Pembert, A., & Ruiz, M. T., 2000, ApJ, 54, 688 Puy, D., Alecian G., Le Bourlot, J., Le Bourlot, J., Leorat, J., Pineau des Forets, l., 993, A&A 267, 337 Puy, D., Signore, M., 996, A&A, 305, 37 Puy, D., Signore, M., 997, New Ast, 2, 299 Puy, D., 999, astro-ph/99267 Puy, D., Signore, M., 999, New Ast.43, 223 Puy, D., Signore, M., 200, astro-ph/0057 Ryan, S. G., Beers, T. C., Olive, K. A., Fields, B. D. & Norris, J. E., 2000, ApJ, 530, L57 Sasaki, S., Takahara, F., 993, PASJ, 45, 655 Saslaw, W., & Zipoy, D., 967, Nature, 26, 967. Stancil, P. C., Lepp, S., Dalgarno, A., 996, ApJ, 485, 40 Susa, H., Uehara, H., Nishi, R., Yamada, M., 998, astro-ph/ Tegmark, M., Silk, J., Rees, M.J., Blanchard, A., Abel, T., Palla, F., 997, ApJ, 474, Vishwakarma, 2000, astro-ph/002492

paper02v.dvi

paper02v.dvi Monte Carlo Λ First Objects III 1 Contents 1 Introduction 4 2 VCT 7 2.1 VCT......................................... 7 2.2............................................... 8 2.2.1 1.................... 8