夏の学校恒星・太陽2022.8.23.

高分散分光で得られる恒星の化学組成
青木和光
国立天文台

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高分散分光で得られる恒星の化学組成• 恒星（表面）の化学組成の意味するもの• 恒星の化学組成にもとづく研究例• 恒星進化• 元素合成• 化学進化、銀河形成• 惑星系• 高分散分光にもとづく恒星の化学組成の測定
Gaiaによる太陽近傍星の色等級図2

恒星（表面）の化学組成の意味するもの
Surface abundances of stars
Composition in the cloud from which the star formed+ internal process/mixing+ interaction with companions/planets

Solar-type stars / red giants: composition is homogeneousin the surface convection zone
cf. Chemically peculiar stars: having very thin surface
convection zone (+ having strong magnetic field?)⚫

Red giants/supergiants: affected by mixing with products
of internal nucleosynthesis (ex. CNO cycle)⚫

Mass accretion from companion can be effective in binarysystems⚫

3Chemically peculiar stars
Ex. objects showing large excesses of heavy elements

Wahlgren et al. (1995)
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恒星の化学組成にもとづく研究例①

恒星進化：赤色巨星の内部構造進化

Li abundance in globular cluster red giants
NGC6397

Lind et al. (2009)

RGB bump
Red giants
First dredge-up
Main-sequence5

Lithium in very metal-poor stars
Main-sequence

Red giants

shallow convective layer
preserving initial Liabundance

Surface Li diluted by the internalmaterial due to 1st dredge-up

Initial LiLi
depleted

Li dilutedLi
depleted6恒星の化学組成にもとづく研究例②連星系の相互作用—
炭素や重元素(s-process元素）の増大
AGB star
C-rich envelope

Mass accretionfrom AGB

H shell burning
He shell flash
C-O core

Faint white dwarf
7CEMP=Carbon Enhanced Metal-Poor stars
Carbon-enhanced stars in the
Galactic halo are known as thespectral class CH stars (Keenan1942).

CNCH

A number of carbon-enhanced
stars were identified by the HK
survey (e.g. Beers et al. 1992)
The fraction of CEMP is
estimated to be 10-25% in[Fe/H]<-2.
Beers et al. (1992)
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Comparison with AGB nucleosynthesis models
Direct comparison of AGB models (e.g. Bisterzo et al. 2010)• Abundance pattern of neutron-capture elements (Sr-Ba-Pb)
are reproduced by models of s-process for low metallicity• Na and Mg abundances are useful to constrain AGB mass.
→1.4M◉ model AGB star

Zhang et al. (2019)

Ba

1.4M◉

PbSr

1.3M◉
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恒星の化学組成にもとづく研究例③

ビッグバン元素合成(BBN)⚫

“Li problem”⚫

Low-mass stars: ‘STARS’
including novae
Cosmic rays: ‘GCR’

Supernovae: ‘SN’⚫

Prantzos (2012)10

恒星の化学組成にもとづく研究例④

初代星の元素合成と質量First stars andsupernovae

Formation of
metal-poor stars

minihalos

External
enrichment

Formation ofdwarf galaxies

Formation of
Milky Way halo

Accretion andmerging

Big Bang

Lithium

Structureformation

Internal
enrichment

Chemical abundances of extremely metal-poor stars→ Nucleosynthesis of first stars/supernovae→ Masses of progenitor stars
Understanding of evolution of metal-poor (low-mass)
stars is needed.

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恒星の化学組成にもとづく研究例④

初代星の元素合成と質量初期世代星の生き残りの元素組成を測定→もとになった超新星の種類、親星としての初代星の質量を推定

重力崩壊型超新星の親星質量の推定
Aoki et al. 201813M⦿140太陽質量を超える星が起こす電子対生成型超新星の痕跡探査
Aoki et al. 2014

25M⦿

40M⦿
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恒星の化学組成にもとづく研究例⑤

爆発的な重元素合成（r-process）
初期世代星のなかには鉄より重い元素が相対的に多い星が存在→r-processの影響を強くうけた星間雲から誕生した星→r-processで作られる元素を検証できる
Sneden et al. 200813

Similar abundance patterns are also found forother r-process-enhanced stars“Universality” of the r-process

SrBa Eu

Th
Comparisons withsolar-system rprocess pattern

Sneden, Cowan, Gallino 2008
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恒星の化学組成にもとづく研究例⑥

化学進化と銀河形成
さまざまな年代・金属量の星の元素組成比を測定→星や超新星の元素合成の寄与の歴史を検証
銀河系の形成過程を探る

Reddy et al. 2006

α元素と鉄の組成比Thick disk
α元素：II型超新星
鉄：Ia型＋II型超新星

Thin disk15

恒星の化学組成にもとづく研究例⑦

惑星系形成と元素組成の関係
惑星をもつ星の頻度と金属量の相関※この図では大型の惑星をもつ太陽系型星の頻度

太陽と太陽類似星の組成比
太陽組成のわずかな異常は惑星の存在と関係しているか？

Melendez et al. 2009

Fischer et al. 2005

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星の化学組成の測定• 化学組成測定の実際– スペクトル線の測定– 恒星大気モデル• 化学組成測定の不定性、信頼性• 星の化学組成と元素の特性• 太陽の化学組成• 同位体組成

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星の化学組成の測定

Definition
Chemical abundance：abundance ratio with respect to H
log ε(X) = log(X/H)+12ex. Fe/H=10-4.5 → log ε(Fe)=7.5[X/Y] = log(X/Y)-log(X/Y)sun
例：[Fe/H]=-2.0 → 1/100 of the solar Fe/H ratio⚫

Metallicity： total abundance of heavy elements (elementsheavier than boron)
important for stellar structure and evolution
sometimes presented as mass ratio
ex. Solar metallicity = 0.02 (2%) or slightly lower⚫

usually represented by [Fe/H]18

星の化学組成の測定

Solar abundance table (example)

Asplund et al. (2009)19

星の化学組成の測定

Absorption in stellar spectra→ “equivalent widths” (等価幅）

Pagel 1997

Equivalent width dose not change by broadening ofstellar rotation and of instrument’s resolution.
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星の化学組成の測定Measurements of equivalent widths⚫
⚫
⚫

Gaussian fitting
Fitting of Vogt profile
Direct integration

Measurement errors
S/N, continuum estimate⚫Fitting error⚫contamination⚫

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星の化学組成の測定

Abundances and line strengths「成長曲線」
curve of growth

Gray 2005
The Observation and Analysis ofStellar Photospheres22

星の化学組成の測定

Absorption line strengths andabundance measurements
Measurements from weak lines○ line strength is in proportion to abundance→not severely model dependent× difficulty in line detection, sensitive to S/N of data
× sensitive to contamination of other lines⚫

Measurements from strong lines○ easy to detect lines, measurement of line can be accurate(though Gaussian fitting is not applicable.)× insensitive to abundances→low accuracy in abundance determination
dependent on treatment of line broadening
× line formation in upper photosphere, for which modeling is23
difficult in general⚫

星の化学組成の測定

Stellar atmosphere and its modelingSolar atmosphere with
Venus (Hinode)Temperature structureof the solar atmosphere

Gray 200524

星の化学組成の測定

Stellar atmosphere and spectra25

星の化学組成の測定

Modeling the solar photosphere

Gray 200526

星の化学組成の測定

3D hydrodynamical models

Asplund (2005)27

星の化学組成の測定

Observational evidence for the 3D
effects for the solar model
Asplund et al. (2009)
Wavelength dependence oflimb darkening

Line profile and wavelength
shiftwavelength28

星の化学組成の測定

3D models for metal-poor stars
Effect is large at the surface of metal-poor stars29

星の化学組成の測定

Abundance analysis using model photospheres
Input data
-model photosphere (←stellar parameters)-chemical composition assumed-line data
(wavelength λ, excitation potential χ,transition probability gf )⚫

Line opacity / radiative transfer
output → comparison with observational dataspectrum / equivalent widths⚫

Feedback to model parameters and chemicalcomposition given as input data if required30

星の化学組成の測定

Abundance determination

Analysis of equivalent widths

Aoki (2015)

Spectrum synthesis

Sneden et al. (2009)31

星の化学組成の測定：不定性と信頼性

Error sources in abundance analyses
Noise in observed spectrum (S/N), error in measurement ofequivalent widths (→ random error)→estimate from S/N, fitting error etc.
⚫Error in line transition probability (random error?)⚫

Incompleteness of model photosphere (→systematic?)⚫Incompleteness of spectrum calculation (NLTE effects etc.)(→systematic for each line, but depends on lines used)⚫Uncertainty of stellar parameters
estimates from spectral analysis →random + systematic
independent estimates (e.g. color index)→ random + systematic⚫

Uncertainty in solar abundances used to derive abundance ratios([X/Fe])32⚫

星の化学組成の測定：不定性と信頼性

Errors in abundance analyses
Uncertain case:-derived only from strong absorption features-derived from species in minor ionization stage⚫

ex. Fe abundances from neutral Fe in solar photosphere-derived from high excitation lines (minor population)
Robust case:-abundance ratios of two elements derived from the sameionization stage.
e.g. Mg/Fe from neutral Mg and Fe⚫

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星の化学組成の測定：不定性と信頼性

Avoiding errors by differential analysis
Differential analysis: deriving abundance ratio with respect
to a standard star (ex. the Sun)
Noise in observed spectrum (S/N)、error in measurementsof equivalent widths(→unavoidable)⚫Error in transition probability→avoidable by using the same line
⚫Incompleteness of model photospheres→(mostly) avoidable for the same type of stars⚫Incompleteness of spectrum calculations→(mostly) avoidable by using the same line for the sametype of stars⚫Uncertainty of stellar parameters→avoidable for the systematic components34⚫

星の化学組成の測定：不定性と信頼性

Differential analysis for “solar twin” stars

Melendez et al. (2009)

Observations and Analysis (1)• Targets:-11 solar twins (no planetinformation)-10 solar analogs (with andwithout giant planets)• Planets are not wellsearched for solar twins,while the solar analogs are
selected from planet survey.
• 6.5m Magellan telescopeand MIKE (E=65,000)+ Keck/HIRES for one object35

星の化学組成の測定：不定性と信頼性

Differential analysis for “solar twin” stars
Melendez et al. (2009)

Observations and Analysis (2)•A “model independent analysis”:
direct comparison of line EWs
between Sun and a star for different
excitation potential and elements.
•Analysis with models are also made.
•Parameters:-Effective temperatures (Teff) fromexcitation equilibrium-Surface gravity (log g): ionization
equilibrium of Fe I/Fe II
Solar twins have Teff within 75K, log g
within 0.10dex and [Fe/H] within
0.07dex.

0.1 dex36

Data driven approach for abundance measurements
Example: Ness et al. (2015) for SDSS/APOGEE data
• Generative models for different Teff, log g, [Fe/H] fromreference objects (~500 stars) in clusters• Determining Teff, log g, [Fe/H] of survey objects (~50,000stars) using the generative models
Spectrum of reference
objects with regions
sensitive to Teff, log g, [Fe/H]
Sensitivity of the spectra
to Teff, log g, [Fe/H]37

星の化学組成と元素の特性

Which elements can be measured?
②alkali elements⑤lead①noble gas③alkali earth elements④lantanides38

星の化学組成と元素の特性

Which elements can be measured?
①noble gas: Ar, Kr,...
No useful spectral features in the optical range measurable for coolstars. Emission lines are detectable in planetary nebulae.
②alkali elements: Na, K, Rb, Cs
Mostly ionized in stellar atmosphere. Remaining neutral Na and K have
however strong doublet features. Rb and Cs are detectable only in very
cool stars.
③alkali earth elements: Mg, Ca, Sr, Ba
Singly ionized species have strong doublet lines (ex. Ca K lines) andeasily detectable even in metal-poor stars.
④lantanides:La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, ....
Many lines of singly ionized stage exist in the optical. Relativeabundances are well determined.
⑤lead
Measurable lines exist in the optical range.
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星の化学組成と元素の特性

Cs absorption lines in brown dwarfs
Brown dwarf
GL229B

Oppenheimer et al. (1998)40

星の化学組成と元素の特性

Lantanides abundances determined for“r-process-enhanced” very metal-poor stars

Sneden et al. (2008) 41

Update of transition probability for rareearth elements
Experiments have been conducted from astronomicalinterests
La II: Lawler et al. (2000, ApJ, 556, 452)
Eu II: Lawler et al. (2001, ApJ, 563, 1075)
Tb II: Lawler et al. (2000, ApJS, 137, 341)
Nd II: Den Hartog et al. (2003, ApJS, 148, 543)
Ho II: Lawler et al. (2004, ApJ, 604, 850)
Pt I: Den Hartog et al. (2005, ApJ, 619, 639)
Sm II: Lawler et al. (2006, ApJS, 162, 227)
Gd II: Den Hartog et al. (2006, ApJS, 167, 292)
Hf II: Lawler et al. (2007, ApJS, 169, 120)
Er II: Lawler et al. (2008, ApJS, 178, 71)
Ce II: Lawler et al. (2009, ApJS, in press)
Pr II, Dy II, Tm II, Yb II, Lu II: Sneden et al. (2009, ApJS)
....

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太陽の化学組成

Solar abundances⚫Determination of abundances by spectral line analysis (asfor stars)
almost all elements including volatile elements C, N, O, …
advantage of solar spectral analysis
very high quality spectrum
accurate model parameters
spatially resolved spectra⚫Determination of abundances from meteorites analysis
metal abundancesadvantages
very accurate
isotope ratios⚫Solar wind, corona etc.
noble gases He, Ne, Ar, …
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太陽の化学組成

元素組成（対数スケール）

12●atmosphere○meteorites
Si: 106

1086420-2-40204060

原子番号8010045

太陽の化学組成

Analysis and compilation of solar abundances•Anders & Grevesse (1989)-analysis based on 1D model atmosphere-meteorite analysis•Asplund et al. (2009)-analysis based on 3D model atmosphere-updated atomic data-meteorite analysis
Cf. 理科年表「宇宙の組成」
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太陽の化学組成

Iron (Fe) abundance of the Sunlog ε = 7.50 or 7.67
Analysis of new Fe I and Fe II linesBlackwell et al. (1995a,b), Holweger et al. (1995)•Low excitation lines → high Fe abundance•New & more complete line data (Fe I and Fe II)→ low value
Cf. Fe II is dominant in solar atmosphere47太陽の化学組成
1.5

Hg

元素組成の比（新/旧）

1.4

Kr

1.3

I

1.2
1.1
1.0
0.9

C

0.8

Ne Ar
NO

0.7
0.6
0.50102030405060

原子番号70809010048

太陽の化学組成

CNO abundances
Re-estimate of blending[O I] spectrum
Allende-Prieto et al. (2001)

3D effect on molecular spectra49太陽の化学組成

Analysis of solar abundance:s-process v.s. r-process
Burris et al. (2000)
EuBaIr, Au Th, UPb50

同位体組成Isotope ratios
Isotopes: having same number of protons but different
number of neutrons→same(similar) chemical property, but different mass⚫

Spectral lines of isotopes are similar, but wavelengths
are slightly different-difference of nuclear mass-difference of nuclear spin⚫

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同位体組成Proton number→

Nuclear chart

Neutron number→52

同位体組成Li isotopes in interstellar matter

Kawanomoto et al. (2009)

同位体組成Measurement of isotopes: light elements
6Li measurements for a metal-poor star (1993)

Smith et al. (1993)
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同位体組成Measurement of isotopes: molecular lines
Large effect of mass difference on molecular spectra
CH molecules

13CH

12CH

Aoki et al. (2002)
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同位体組成Mg isotopes
MgH molecular lines
24Mg/25Mg/26Mg

Yong et al. (2003)
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同位体組成Measurement of isotopes: hyperfine splittingof spectral lines of heavy elements
Large effect of hyper fine splitting on spectral linesof heavy elements that depends on isotopes
Splitting of spectral lines due to differenceof nuclear spin⚫

⚫

Large effect on odd nuclei

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同位体組成Eu isotopes ～ easiest case?

Aoki et al. (2003)
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高分散分光で得られる恒星の化学組成• 恒星表面の化学組成は、銀河の化学進化、星の内部の構造進化、連星系での質量交換などの情報をもっている。
• 恒星の化学組成は、様々な天体や現象の研究に有用な情報となる。
恒星進化、元素合成、化学進化、銀河形成
惑星形成・惑星系進化• 高分散分光により、高い精度で恒星の化学組成を測定することが可能になる。信頼性の高い結果を得るには、恒星大気モデルの検証や比較解析の手法が重要である。

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超大型望遠鏡TMTTMT = Thirty Meter Telescope = 30m望遠鏡

望遠鏡サイズ比較

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©NAOJ

TMTの観測装置
第1期観測装置
第2期観測装置(予定)

MODHISNFIRAOS

HROS
WFOS
IRMOS

IRIS

MICHI

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