Big Bang - PowerPoint PPT Presentation

東京大学宇宙線研究所 川崎雅裕 元素合成の現状 研究会「宇宙初期における時空と物質の進化」 Big Bang Nucleosynthesis (BBN)

1. Introduction BBN: Theory vs. Observation

1. Introduction BBN: Theory vs. Observation

今日の予定 • Introduction • He4 • Li7 • Li6 • D

2. He4

NGC 6611 Measurement of He in HII region • HII region • OB stars ionize H and He • E(HI)= 13.6eV, E(HeI)= 24.6eV,E(HeII)= 56.4eV • Recombination lines H II HeII • measure HeII/HII UV Fluxes HII HII Recombination Lines O,B Stars HeII T ~ 30000-50000K HeII

Energy Level Diagram of HeI Benjamin, Skillman, Smits 1999, ApJ 514,307

MRK 193 Izotov, Thuan, Lipovetsky (1994) Spectrum 3889Å 5876Å 7065Å 6678Å 4471Å

Abundance of singly ionized Helium y + = n (HeII) /n (HII) � � � W ( λ ) + a HeI � F ( λ ) E ( H β ) W ( H β ) 10 f ( λ ) C ( H β ) 1 y + = F ( H β ) E ( λ ) W ( H β ) + a HI W ( λ ) f λ E ( Hβ ) • : Theoretical emissivity scaled to H β E ( λ ) • : observed line intensity F ( λ ) • : underlying stellar absorption a HI , a HeI • : equivalent width L H β = W ( H β ) L λ ( λ 4861) W ( λ ) • : extinction relative to H β f ( λ ) C ( H β ) • : optical depth function with collisional correction f λ ( τ )

Abundance of singly ionized Helium y + = n (HeII) /n (HII) � � � W ( λ ) + a HeI � F ( λ ) E ( H β ) W ( H β ) 10 f ( λ ) C ( H β ) 1 y + = F ( H β ) E ( λ ) W ( H β ) + a HI W ( λ ) f λ E ( Hβ ) • : Theoretical emissivity scaled to H β E ( λ ) • : observed line intensity F ( λ ) • : underlying stellar absorption a HI , a HeI HI balmer lines • : equivalent width L H β = W ( H β ) L λ ( λ 4861) W ( λ ) • : extinction relative to H β f ( λ ) C ( H β ) • : optical depth function with collisional correction f λ ( τ )

Reddening and Stellar absorption • Reddening (extinction) scattering and absorption by interstellar dust I λ = I λ 0 e − τ λ extinction law τ λ = Cf ( λ ) � I ( λ ) � F ( λ ) � � log = log + C ( Hβ ) f ( λ ) I ( Hβ ) F ( Hβ ) intrinsic line observed line intensity intensity • Underlying stellar absorption Solving for reddening and underlying absorption

Hα/Hβ, Hγ/Hβ, Hδ/Hβ ⇒ C ( Hβ ) , a HI • correction for stellar absorption � W ( λ ) + a HI � W: EW (equivalent width) F A ( λ ) = F ( λ ) W ( λ ) L H β = W ( H β ) L λ ( λ 4861) • reddening correction I ( λ ) F A ( λ ) F A ( H β )10 f ( λ ) C ( H β ) X R ( λ ) = I ( H β ) = • theoretical value X T (6563) = 0 . 3862(log T 4 ) 2 − 0 . 4817 log T 4 + 2 . 86 . . . T 4 ≡ T/ 10 4 K • take minimum χ 2 ( X R ( λ ) − X T ( λ )) 2 χ 2 = � σ 2 X R ( λ ) λ

Abundance of singly ionized Helium y + = n (HeII) /n (HII) � � � W ( λ ) + a HeI � F ( λ ) E ( H β ) W ( H β ) 10 f ( λ ) C ( H β ) 1 y + = F ( H β ) E ( λ ) W ( H β ) + a HI W ( λ ) f λ E ( Hβ ) • : Theoretical emissivity scaled to H β E ( λ ) theory • : observed line intensity F ( λ ) obs. • : underlying stellar absorption a HI , a HeI HI balmer lines • : equivalent width W ( λ ) • : extinction relative to H β f ( λ ) C ( H β ) • : optical depth function with collisional correction f λ ( τ )

Theoretical emissivities Benjamin, Skillman, Smits 1999, ApJ 514,307 [BSS] 0 . 904 T − 0 . 173 − 0 . 00054 n e E ( H β ) /E (3889) = 4 . 297 T 0 . 090 − 0 . 0000063 n e E ( H β ) /E (4026) = 2 . 010 T 0 . 127 − 0 . 00041 n e E ( H β ) /E (4471) = 0 . 735 T 0 . 230 − 0 . 00063 n e E ( H β ) /E (5876) = 2 . 580 T 0 . 249 − 0 . 00020 n e E ( H β ) /E (6678) = 12 . 45 T − 0 . 917 E ( H β ) /E (3889) = [3 . 494 − (0 . 793 − 0 . 0015 n e + 0 . 000000696 n 2 / e ) T ]

Helium Abundance � � � W ( λ ) + a HeI � F ( λ ) E ( H β ) W ( H β ) 10 f ( λ ) C ( H β ) 1 y + = F ( H β ) E ( λ ) W ( H β ) + a HI W ( λ ) f λ determine y + ( λ ) 1 � � y = ¯ σ ( λ ) 2 / minimize χ 2 parameters σ ( λ ) 2 λ λ ( T ) , n e , a HeI , τ [ T = T(OIII) ] uncetainties in ( y + ( λ ) − ¯ y ) 2 χ 2 = � ∆ χ 2 = 1 parameters σ ( λ ) 2 λ

λ2321 λ4363 λ4959 λ5007 Osterbrock’s text book §5.2 Temp. measurement from [OIII] lines OIII 1 S 0 = 7 . 73 exp[(3 . 29 × 10 4 ) /T ] j λ 4959 + j λ 5007 1 + 4 . 5 × 10 − 4 ( n e /T 1 / 2 ) j λ 4363 collisional de-excitation 1 D 2 T 3 P

MRK 193 Izotov, Thuan, Lipovetsky (1994) Spectrum 3889Å 5876Å 7065Å 6678Å 4471Å

Recent Works • Izotov & Thuan 1998, 2004 • 45 (89) low metallicity HII regions • use [OIII] emission lines to determine T T (HeII) = T (OIII) Y p = 0 . 244 ± 0 . 002 • Peimbert,Peimbert & Ruitz 2000 • HII region NGC 346 in SMC • use HeI emission line to determine T T (HeII) < T (OIII) Y p = 0 . 2345 ± 0 . 0026 • Luridiana et al 2003 • 5 metal poor HII regions Y p = 0 . 239 ± 0 . 002

Izotov, Thuan 2004 Fig. 2.— Linear regressions of the helium mass fraction Y vs. oxygen and nitrogen abun- dances for a total of 82 H ii regions in 76 blue compact galaxies. In panels a) and b), Y was derived using the 3 λ 4471, λ 5876 and λ 6678 He i lines, and in panels c) and d), Y was derived using the 5 λ 3889, λ 4471, λ 5876, λ 6678 and λ 7065 He i lines.

Number of Oxygen Nitrogen Method H ii Regions Regression Regression σ σ 3 He i lines a ,b 45 0.2451 ± 0.0018 + 21 ± 21(O/H) 0.0048 0.2452 ± 0.0012 + 603 ± 372(N/H) 0.0044 3 He i lines b 89 0.2429 ± 0.0009 + 51 ± 9(O/H) 0.0040 0.2439 ± 0.0008 + 1063 ± 183(N/H) 0.0037 5 He i lines c ,d 7 0.2421 ± 0.0021 + 68 ± 22(O/H) 0.0035 0.2446 ± 0.0016 + 1084 ± 442(N/H) 0.0040 5 He i lines c ,e 7 0.2444 ± 0.0020 + 61 ± 21(O/H) 0.0040 0.2466 ± 0.0016 + 954 ± 411(N/H) 0.0044 a Data are from IT98. b Only collisional and fluorescent enhancements are taken into account. We have adopted T e (He ii ) = T e (O iii ) and ICF (He) = 1. c Collisional and fluorescent enhancements of the He i lines, collisional excitation of hydrogen lines, underlying He i stellar absorption and di ff erences between T e (He ii ) and T e (O iii ) are taken into account. ICF (He) is set to 1. d Calculated with EW a (H8 + He i 3889) = 3.0˚ A, EW a (He i 4471) = 0.4˚ A, EW a (He i 5876) = 0.3 EW a (He i 4471), EW a (He i 6678) = EW a (He i 7065) = 0.1 EW a (He i 4471). e Calculated with EW a (H8 + He i 3889) = 3.0˚ A, EW a (He i 4471) = 0.5˚ A, EW a (He i 5876) = 0.3 EW a (He i 4471), EW a (He i 6678) = EW a (He i 7065) = 0.1 EW a (He i 4471). Y p = 0 . 244 ± 0 . 002

Peimbert, Peinbert, Luridiana (2002) T(HeII)/T(OIII) average temp � Tn e n p dV T 0 = � n e n p dV mean square temp variation � ( T − T 0 ) 2 n e n p dV t 2 = T 2 � n e n p dV 0 pure OIII nebula F IG . 1.ÈThe ratio T e (He II )/ T e (O III ) as a function of T e (O III ) and � 90800 � t 2 temperature Ñuctuations for the case in which all the O is O `` . When O ` � � is present, higher t 2 values are expected, particularly for those objects with T (HeII) = T (OIII) 1 − T (OIII) − 0 . 2 III ) values (see Fig. 2). Typical t 2 values in H II regions are the highest T e (O 2 in the 0.01 È 0.04 range.

Recent Works (cont.) • Olive & Skillman 2004 • 7 HII regions of IT98 • use HeI emission lines to determine T • underlying stellar absorption Y p = 0 . 249 ± 0 . 009 • Fukugita, MK 2006 • 33 HII regions of IT04 • use OIII emission line to determine T • underlying stellar absorption Y p = 0 . 250 ± 0 . 004

Olive, Skillman 2004 η 10 = 6 . 64 +11 . 1 Y p = 0 . 2491 ± 0 . 0091 − 3 . 82 .27 Y p .26 .25 Y .24 .23 IT 98 Our Re � analysis .22 0 .2 .4 .6 .8 1 4 O/H x 10

Helium Abundance in HII region Fukugita,Kawasaki (2006)

Without stellar absorption Fukugita,Kawasaki (2006) Y p = 0 . 234 ± 0 . 004

95%CL 95%CL 68%CL 68%CL 95%CL 95%CL 68%CL 68%CL w/abs. w/o abs. IT04 w/o abs. w/abs. IT04

New Determination of Y p Use of new computation of HeI emissivity Porter, Bauman, Ferland, MacAdam 2006 • Peimbert, Luridiana & Peimbert 2007 PBFM • 5 HII regions of IT98 • use HeI emission lines to determine T Y p = 0 . 249 ± 0 . 009 • Izotov, Thuan & Stasinska 2007 • 93 HII regions (HeBCD) + 271 HII regions in SDSS DR5 • T(HeII) = (0.95 - 1.0)T(OIII) • underlying stellar absorption Y p = 0 . 2516 ± 0 . 0011

New Emissivity

Izotov, Thuan, Stasinska 2007 BBS PBFM Y p = 0 . 2472 ± 0 . 0012 Y p = 0 . 2516 ± 0 . 0011

Systematic errors • He I emissivity • T(OIII) may be different from T(HeII) • Underlying HeI stellar absorption • Collisional excitation of hydrogen emission lines • HeII and HII regions may not coincident correction factor ICF (He + + He 2+ )

Error Budget IT (2007) Property ∆ Y p He i emissivity � +1.7% T e (He + ) = (0.95 – 1.0) × T e (O iii ) � − 1.0% Underlying He i stellar absorption � +3.0% Collisional excitation of hydrogen emission lines � +1.0% ICF (He + + He 2+ ) � − 1.0%

Yp History WMAP3 prediction

3. Li7

Li7 • Spite plateau [Spite & Spite (1987)] constant Li7 abundance in warmest metal-poor stars Primordial abundance of Li 7 T <5700K T >5700K Bonifacio, Molaro 1997

6708Å line LP815-43