Chap.2 Stellar populations and chemical
evolution• Stars in a color-magnitude diagram– nearby stars, globular clusters• Stellar evolution and population synthesis– evolutionary tracks, metallicity vs. age– star formation, single starburst model• Origin of elements and yields– Supernovae and hypernovae• Extremely metal-poor stars– Neutron capture elements, CEMP stars• Galactic chemical evolution– IMF, SFR, Simple model, G-dwarf problem

11. Stars in a color-magnitude diagram (CMD)
CMD for nearby stars with Hipparcos satellite (1989~1993)
Hertzsprung gap

Red-Giant Branch

Red Clump
Subgiant Branch

Mv from trigonometricdistances = 1/π(where relative error
in parallax Δπ<10%)
Many young stars+ some old stars2

Astrometry Satellites
1989~1993

2013~

Hipparcos

Gaia

Magnitude limit
CompletenessBright limit
Number of objects

12 mag
7.3 – 9.0 mag
0 mag
120,000

Effective distancelimit
Quasars
Galaxies
Accuracy

1 kpc
1 (3C 273)
None
1 milliarcsec

20 mag
20 mag
6 mag
26 million to V = 15
250 million to V = 18
1000 million to V = 20
50 kpc500,000
1,000,000
7 µarcsec at V = 10
10 – 25 µarcsec at V = 15300 µarcsec at V = 20
Low-res. spectra to V = 20
15 km s-1 to V = 17
Complete and unbiased

Photometry
photometry
Radialvelocity
Observing
programme

2-colour (B and V)
None
Pre-selected~10μas3

Gaia:
10as = 10% error @distance 10kpc, 10as/yr = 1km/s @20kpc
Hipparcos: 1mas = 10% error @distance 100pc, 1mas/yr = 5km/s @ 1kpc

4

The Map of the Milky Way with Gaia

Magellanic Clouds5CMD for nearby stars with Gaia

6

Photometric Systems

M. Bessel 2005 ARAA, 43, 293

7

Photometric Systems

M. Bessel 2005 ARAA, 43, 2938Prime focus

HSC broad-band filters

9CMD for a Galactic globular cluster
M68[Fe/H]= -1.99

Horizontal Branchmv

11 Gyr
13 GyrTurn Off10

CM diagrams for Galactic globular clusters
M3[Fe/H]= -1.57

47 Tuc[Fe/H]= -0.76

Asymptotic Giant Branch
Horizontal Branch

112. Stellar evolution and population synthesis
Evolutionary tracks

M ≥ 0.08 Msun
≥ 1.1 Msun
≤2
Msun
≥8
Msun

Iben 1967, ARAA, 5, 571: nuclear reaction: convective core, CNO: helium flash (Tc~108K): C core burning12dP
GM ( r )
 
dr
r2

Equation for hydrostatic equilibriumr

M ( r )   4r 2  (r )dr 0dP
GM ( r )dM ( r )4r 4
Pc, Tc at the centerdM ( r )
 4r 2 
dr

M
Pc
Tc R

Equation of state

Tc is higher for larger M / smaller R

Low-mass stars(M < 1.1 Msun)
Nuclear energy generation

H

High-mass stars(M > 1.1 Msun)

H⇒He

H⇒He

radiation

convection

log ε (erg/g/s)

convection

log Tc (K)Hradiation

H fraction for 1 Msun
H fraction for 5 Msun
14

Evolutionary tracks for low/high mass stars

・ Low mass, long-lived stars:
dominate stellar photometry・ High mass, short-lived stars:
dominate stellar spectroscopy
Evolutionary track for low mass stars(Iben 1985, QJRAS, 26, 1)

15

Evolutionary tracks for low/high mass stars

・ Low mass, long-lived stars:
dominate stellar photometryof old stellar systems
・ High mass, short-lived stars:
dominate stellar spectroscopyof old stellar systems(Iben 1985, QJRAS, 26, 1)

16

HHe⇒C,O

C,O

Shell Hburning

Shell He
burning
AGB

H

RGB

HB

⇒photometric propertiesof old stellar systems

H
He

He⇒C,O

Evolutionary track
for low-mass, longlived stars

Core He:e degeneracy
⇒Tc↑

H⇒He

Shell Hburning

H
H⇒He

17

Isochrones

mV

Salaris et al 1997, ApJ, 479, 665

18

M3[Fe/H]= -1.57

M15[Fe/H]= -2.22

47 Tuc[Fe/H]= -0.76

19

Worthey 1994, ApJS, 95, 107

Age-metallicity degeneracy
20Population synthesis of E galaxies
Worthey 1994, ApJS, 95, 107

Age-metallicity degeneracy

21Horizontal Branch (HB) morphology
Redder for more metal-rich stars

Mc=0.477Msun

He-core mass
Z=0.01
Mmax before
He flash~ 0.8 Msun
⇒ ~ 0.2 Msun
must be lost
until reaching
HB

Number:= total mass(incl. H envelopeof ~ 0.1Msun)

Mc=0.498Msun

Z=0.0001

Moe massive total mass
⇒ younger population

Sweigart 1987, ApJS, 65, 95

Lee et al. 1990, ApJ, 350, 155

tHB ~ 0.1 Gyr22

HB type (color) vs. metallicity in Galactic globular clusters
More red HBs
for higher [Fe/H]
B: # of blue HBs
R: # of red HBs
V: # of RR Lyrae
B V R
dispersion

Color distribution23

3. Origin of elements and yields
Type II SNe
M > 8 Msun
α-elements (O, Mg, Si)

Type Ia SNe(white dwarf + companion)
M < 8 Msun
iron-peak elements

24Origin of elements and yields• M<8Msun (Type Ia SNe) white dwarf, mass accretion from a companion– Iron peak elements (Cr, Mn, Fe, Co, Ni)• M>8Msun (Type II SNe) Core-collapse supernovae– -elements (16O,20Ne,24Mg,28Si,32S,36Ar,40Ca, 44Ti)
hydrostatic burning– 8<M<10Msun• C-burning、O+Ne+Mg-core、AGB star
• O+Ne+Mg WD after losing H-He envelope or collapse due to e- capture– 10<M<140Msun• Fe-core、gravitational collapse、neutron star or black hole

– 140<M<300Msun Pair-Instability SNe• Electron-positron pair creation & core collapse、high Tc & explosive O
burning、disrupt out completely due to explosion, release a lot of Fe & Ca

– M > 300Msun• Photo-disintegration、core collapse, BH formation• Hypernovae (M>20Msun, E>1052erg) gamma-ray burst– Large [Zn/Fe] & [Co/Fe] ratios

25Supernova and Hypernova Yields(Nomoto et al. 2009)26

Elements from Type II SN
α elements: 16O,20Ne,
24Mg,28Si,32S,36Ar,40Ca
Created at C- & O-burning phase
12C+12C→20Ne+4He, …
20Ne+4He→24Mg+γ, …
16O+16O→28Si+4He, …

α elements

Tsujimoto et al. 1995,
MN, 277, 945

Mass Number

Elements from Type Ia SN
Iron peak nuclides
Cr,Mn,Fe,Co,Ni

27

Solar System Abundances

Solar System Abundances

r-process

Mass Number

s-process28

Big Bang Nucleosynthesis• p & n creation•n+p→D+
(D creation)• D+D→3H+p, 3H+D→4He+n• After Big Bang
H, D, 3He, 4He, 7Li remained（7Be, 3H are unstable）

29

Big Bang Nucleosynthesis
1st 3min: 4He creation
H
4He
D
3He

n
7Be→7Liへ

3H→3He7Li

6Li

After big bang
H, D,
3He, 4He,
7Li
are remained30

Stellar evolution & nuclear reaction
Neutron Star
Brown Dwarf

White Dwarf

Type II SN

Slow mass loss

M<0.08Msun 0.46Msun

HCore collapse

8Msun

He

C+O

H

He
H

8~10MsunO, Ne,
Mg

C+O
He
H
10^9

Tc（K）
3x10^8
10^7
10^8
Star
H-burning
He-burning
C・O-burning
formation （Main Sequence）

ISM

Black Hole

10Msun<M

Si Fe Mg

C+O
He
H
5x10^9Si-burning

31

Origin of elements heavier than Fe~ neutron capture process ~Atomic Number ⇒After neutron capture, atomic number isincreased through beta decay
134Ba

56

135Ba

136Ba

 decay

133Cs

55

134Cs

131Xe

132Xe

(τ > τ (β decay))
Sr, Ba, Pb
AGB stars

133Xe

Neutron capture

77

78

79

Neutron number ⇒(τ < τ (β decay))
Eu, Pt, Au, Th, U
core-collapse SNeor merging of
neutron stars

s-process decay54

r-process80
32

Neutron star mergers and r-process

1.Neutron starbinary2.GW released,close encounter3.merging,
GW propagation

GW170817
Optically identified object

キロノバ
Kilonova
4. Heavy-element production via r-process33

Solar System Abundances
Solar System Abundances

Nuclearreaction Neutron capture process（AGB・neutron star merger）
r-processs-process

Big Bang

Mass Number

34

Where elements came from35

Families of elements
1) Light odd-Z elements (Na and Al):
Mainly made in the hydrostatic burning shells of massive stars. Their yields are
related to the mass of the shell, which is related to the initial mass of the star
2) Magnesium: Made in the hydrostatic burning shells of massive stars (specificallythe C-burning shell), and the yield is related to the initial mass of the star.
3) The other alpha elements (O, Si, Ca, and Ti):
O is formed in a hydrostatic burning shell (the He-burning shell). The heavier
alpha-elements Si, Ca and Ti are formed deep within massive stars during
the explosive burning phase of a supernova (SN).
4) Fe-peak elements (Sc, V, Cr, Mn, Fe, Co, Ni, Cu and Zn):
With the exception of Cu and maybe Zn, these elements are made in bothType Ia and Type II SNe during the explosive phases. Co and possibly Zn are
made almost exclusively in Type II SNe. Hypernovae is required for Zn.
5) Light s-process elements (Sr, Y, and Zr):
(Nearly all the elements heavier than Zn are made by neutron-capture processes.)
Made in metal-rich AGB stars. The peak of the s-process production moves tolighter elements as metallicity increases because there are more Fe-group“seed” nuclei at higher metallicity,6) Heavy s-process elements (Ba and La):
Made in metal-poor AGB stars, although some of the inventory of both elementsin the Sun came form the r-process.
7) r-process element (Eu):By the explosive phase of Type II SNe or most probably merging of neutron stars.

36

List of elements and their production sites•Lithium (Z=3): Produced in Big Bang nucleosynthesis and cosmic ray spallation.
•Carbon (Z=6): Results from the triple-alpha He-burning process. Isotope ratios
between 12C and 13C are affected by hydrogen burning on the CNO cycle.
•Oxygen (Z=8): Results from hydrostatic He-burning burning in massive stars, yield
related to the mass of the He-burning shell, which is a function of the star’s initial mass.
•Sodium (Z=11): Results mostly from carbon-burning. Production depends on the
n/p ratio, so there is a predicted metallicity dependence of the yield from SN II.
Can also be affected by H-burning in intermediate-mass stars, as seen in the so-called“Na-O anti-correlation” often seen in globular cluster stars.
•Magnesium (Z=12): Results from carbon-burning. Effectively 12C → 24Mg
via 20Ne + 4He. Released from SN II.
•Aluminum (Z=13): Carbon-burning; closely tied to the production of the minor Mg
Correlated
isotopes 25,26Mg. Production depends on the n/p ratio, so there is a predicted
strongly to C+N
metallicity dependence of the yield from SN II. Can also be affected by H-burning in initial abundanceintermediate-mass stars, as seen in “Na-O anti-correlation” in globular cluster stars.
•Silicon (Z=14): Explosive oxygen burning via 2O→Si + He, with Mg + He→Si.
SN II+SN Ia.
•Calcium (Z=20): Oxygen and silicon burning, both hydrostatic and explosive. SN II.
•Scandium (Z=21): SN II from oxygen burning + the alpha-rich freezeout.
•Titanium (Z=22): Explosive Si burning, + alpha-rich freezeout, including white dwarfs
37(SN Ia). Appears to be mostly SN II.

•Vanadium (Z=23): Explosive oxygen burning + silicon burning. SN Ia probably
dominate production. The [V/Fe] value is very sensitive to the value of Teff.
•Chromium (Z=24): Equilibrium process in explosive Si burning. SN II + SN Ia, but
dominated by SN II.
•Manganese (Z=25): Explosive Si burning + alpha-rich freezeout. SN II. Metallicity dep.
•Iron (Z=26): Equilibrium process. SN II + SN Ia, with a large yield from SN Ia.
•Cobalt (Z=27): Explosive Si burning + alpha-rich freezeout (which produces
a large Co/Fe yield). Possibly metallicity-dependent yields in Type II SN.
•Nickel (Z=28):. Explosive Si burning + alpha-rich freezeout. SN II + SN Ia•Copper (Z=29): Possibly from SN II “only” with metallicity-dependent yields. Minor
contributions from the s-process and SN Ia.
•Zinc (Z=30): Explosive Si burning + alpha-rich freezeout + s-process. Zn does notform on dust grains, so it is used in the study of damped Lyman-alpha systems
as metallicity indicator.
•Strontium (Z=38), Yttrium (Z=39), Zirconium (Z=40), Molybdenum (Z=42), andPalladium (Z=46): Light s-process. AGB stars and maybe massive stars(“weak s-process”).
•Barium (Z=56): Heavy s-process. AGB stars. [heavy s/light s]= f(Z).
•Lanthanum (Z=57): Heavy s-process. AGB stars. [heavy s/light s]= f(Z).
•Europium (Z=63): Bypassed by s-process (mostly), best r-process “only” element in
the optical. The r-processes were believed to occur in a sub-class of SN II, the lowermass SN II, but now the merging of neutron stars is thought to be most likely.

38

4. Extremely metal-poor stars[Fe/H] ≤ -2.5
These stars were enrichedby just one supernova.

Their abundance patterns
reflect the mass ofa progenitor star (first star).

39

Dispersion due to differencein progenitor’s mass+ inhomogeneous
chemical evolution[Mg/Fe]Abundance ratios

Aoki et al. (2002)[Fe/H][Eu/Fe]Honda et al. (2004)40[Fe/H]

r-process elements
for a star with [Fe/H]=-3.1

s-process elements
for a star with [Fe/H]=-2.7

Atomic Number
Carbon-enhanced extremely metal-poor star
(CEMP stars)

Universal mechanism (by SNe II
or merging of neutron stars)
is at work for r-process.

41

Nucleosynthesis from Hypernovae(Tominaga et al. 2007)
M=25Msun, E=1052 erg[X/Fe]

Mixing-fallback model

(obs)

Z
Observed large [Zn/Fe] & [Co/Fe] ratios are reproduced.

42

5. Galactic chemical evolution• Simple model– Key parameters: SFR: (t), IMF: (m)φ(m)  m- (mφ(m)dm = 1 Msun)– star: Ms, gas: Mg, metal: Mz, metallicity: Z=Mz/Mg– closed box: Mtot = Ms+Mg = const.
– instantaneous recycling: Massive stars die immediately andleave enriched gas (age: ≪1).
The rate of gas ejection is:(𝑚 − 𝑤 ) 𝜑(𝑚)𝜓(𝑡 − 𝜏(𝑚))𝑑𝑚 →(𝑚 − 𝑤 )𝜑(𝑚)𝜓(𝑡)𝑑𝑚 ≡ 𝑅𝜓(𝑡)wm: remnant mass, R: return fraction– y: yield
metallicity when a unit gas mass is locked into stars

43

dM g



dt
d ZM g dt

dM s   R  (1  R)
dt  Z (1  R)  y (1  R)

 Z  y ln
S (Z ) M tot
 y ln f g1
Mg

Ms
M s ,current



1 fg
1  f g ,current

fg: gas fraction <1→ Z increases with decreasing fg

/ Z0
1  f gZ,current

1  f g ,current

S(Z): cumulative metallicity
distribution of stars

Obs: G-dwarf stars near the Sun

simple modelobs
pre-enrichment

Simple model: too many metal-poor stars⇒ G-dwarf problem
Tinsley 1980, FCPs, 5, 287

extreme infall

44

Gaseous Oxygen abundance in M81
Garnett & Shields 1987, ApJ, 317, 82

Gaseous Oxygen in various galaxies

Simple modelGas fraction (HI)Gas fraction (HI)45

SFR law for 61 disk galaxies and 36 starburst galaxies
Kennicutt 1998,
ApJ, 498, 541

log  SFR

SFR   Ngas

N=1.4

log  gas

46

Initial Mass Function
Kroupa (2002)

logφφ(m)  m- (mφ(m)dm=1Msun)

m/Msun• Salpeter (1955)
 = 2.35 for 1Msun < m• Miller and Scalo (1979), Scalo (1986)
 → 0 for m < 1Msun• Kroupa (2002)
 = 0.3 for m < 0.08Msun
1.3 for 0.08 < m < 0.5Msun
2.3 for 0.5Msun < m47

MDF of G-dwarfs in the solar neighborhood(model: Sommer-Larsen & Yoshii 1990, MN, 243, 468)

dΣgas/dt∝exp(-t / tinfall)
tinfall~4-5 Gyr is required

no infall

The Galactic (thin) disk
formed slowly over 4-5 Gyr.
gas flow

tinfall=4.6Gyrbulge

Galactic disk
The Sun& nearby stars

48

Chemical clock
Yoshii et al. 1996, ApJ,
426, 266[α element/Fe]

Time scale forType Ia SN :~ 1 Gyr(at [Fe/H] ~ -1
near the Sun )break[Fe/H]
Pace of chemical enrichment (or SFR)

49

Comparison with metallicity distribution (MD) of
young stars (B-type stars)
Feltzing & Chiba (2013)using Nieva and Przybilla (2012) data

B stars

MD of B-type stars
reflects that of ISM
near the Sun
Very meal-rich stars
with [Fe/H] > + 0.2
cannot be formednear the Sun
These very metal-rich stars(possibly having exo-planets)
are migrated from inner radii
50Radial migration of stars
Sellwood & Binney 2002, Schoenrich & Binney 2009

・Epicycle motion
・Angular-momentum
transfer by transientspiral arms
Radial migration of stars

Metal-rich star

Metal-poor star

R
Solar neighborhood
Lz=VφR～const.
Star moving from inner R： Vφ is slower
Star moving from outer R： Vφ is faster

51

[/Fe] ratios in several MW dSphs(Tolstoy+ 2009)52