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Lecture 10 Metalicity Evolution
•
Simple models for Z( m( t ) )
(Closed Box, Accreting Box, Leaky Box)
mass of new metals added to ISM by SNe ( ZSN -Z ) (1- a )
Yield = y º
=
mass of ISM converted to long-lived stars
a
•
•
•
•
•
•
Z = - y ln( m ) = y ln( 1 / m )
“G dwarf problem” Closed Box model fails, predicts too many
low-Z stars.
No Pop III (Z=0) stars seen (were they all high mass?).
Infall of Z = 0 material causes Z => y.
Z » min [ y, y ln(1/ m )]
Observed Yields:
y
Yeff = Zobs / ln(1/m) ~ 0.01
~0.001 in small Galaxies
(SN ejecta escape)
1
m
Lecture 11:
Ages and Metalicities
from Observations
A Quick Review
Ages from main-sequence turn-off stars
Main sequence lifetime:
HR diagram
lifetime = fuel / burning rate
t MS
MV
-1
é M ùé L ù
= 7 ´10 ê úê ú
ë M . ûë L . û
9
yr
MV(TO)
.
B-V
Luminosity at the top of the main sequence
(turn-off stars) gives the age t.
Ages from main-sequence turn-off stars
MV(TO) = 2.70 log ( t / Gyr ) + 0.30 [Fe/H] + 1.41
Globular Cluster in Halo
47 Tuc: 12.5 Gyr
Open Clusters in Disk
M67: 4 Gyr
NGC188: 6 Gyr
Multiple Ages of stars in Omega Cen
Star Formation Rates
Cosmic Star Formation History
Abundance Measurements
•
•
•
•
Star spectra: absorption lines
Gas spectra: emission lines
Galaxy spectra: both
Metal-rich/poor stars: stronger/weaker metal lines
relative to H.
HII region spectra
Stellar spectra
• Lab measurements: Unique signature (pattern of
wavelengths and strengths of lines) for each element.
High-Resolution Spectra
Measure line strengths (equivalent widths) for individual elements.
Equivalent
Width
measures the
strength
(not the width)
of a line.
EW is width of
a 100% deep
line with same
area.
Abundance Measurements
Þ
Spectra
Line strengths (equivalent widths)
+
Astrophysics
Physics
Þ
Þ
Abundances:
Stellar atmosphere models
+
Laboratory calibrations
ß
é Fe ù
êë H úû, etc.
(Temperature, surface gravity, and metal abundances in the stellar
atmosphere models are adjusted until they fit the observed equivalent
widths of lines in the observed spectrum. Full details of this are part of
other courses)
Bracket Notation
Bracket notation for Fe abundance of a star relative to the Sun:
æ n(Fe) ö
æ n(Fe) ö
é Fe ù
êë H úû º log10 ç n(H) ÷ - log10 ç n(H) ÷
è
ø*
è
ø.
atoms of Fe
atoms of H
æ ( n(Fe) n(H)) ö
* ÷
= log10 çç
÷
è ( n(Fe) n(H)) . ø
And similarly for other metals, e.g. relative to Fe:
é O ù é C
êë Fe úû, êë Fe
ù
úû, ...
é
ù
Star with solar Fe abundance: ê Fe ú = 0.0
ë H û
é Fe ù
Twice solar abundance: êë H úû = log10 (2) = +0.3
é Fe ù
Half solar abundance:
êë H úû = log10 (1/2) = -0.3
Metallicity
vs Abundance
Metalicity (by mass):
åA
i
Z=
Abundance (by number):
ni
metals
n(H) + 4 n(He) +
åA
ni
i
æ n(Mg) ö
æ n(Mg) ö
é Mg ù
êë H úû º log10 çè n(H) ÷ø - log10 çè n(H) ÷ø .
*
æ Z ö
æ Z ö
= log10 ç
÷ - log10 ç
÷
è f X ø*
è f Xø .
æZ f . X. ö
÷÷
= log10 çç *
è Z . f* X* ø
metals
X=
n(H)
n(H) + 4 n(He) +
åA n
i
i
metals
To infer Z from a single line:
Z
n(Mg)
= f
X
n(H)
Primordial:
Solar:
åA n
i
f º
metals
n(Mg)
i
Z*
X* f* [ Mg
=
10
Z. X.f.
H
]
» 10[ Mg
Xp = 0.75,
Yp = 0.25,
Zp = 0.00
X = 0.70,
Y = 0.28,
Z = 0.02
H
]
Solar Abundances
Solar Abundances
Primordial He/H measurement
• Emission lines from
H II regions in low-metalicity
galaxies.
• Measure abundance ratios:
He/H, O/H, N/H, …
• Stellar nucleosynthesis
increases He along with metal
abundances.
• Find Yp by extrapolating to
zero metal abundance.
[Xi/Fe] vs [Fe/H]
Most metals enrich at
approx same rate as Fe
(e.g. to a factor of 2-3
over a factor of 30
enrichment).
Some elements
(Mg,O,Si,Ca,Ti,Al)
formed early, reaching
2-3 x Fe abundance in
metal-poor stars
Lowest metal
abundance seen in
stars: [Fe/H] ~ -4
O
Na
Mg
Al
Si
Y
Ca
Zr
Ti
Ba
Ni
Nd
Stars with high a elements
must have formed early, e.g.
before a less a-enhanced mix
added to ISM by Type Ia SNe
(WD collapse due to accretion
from binary companion).
Most MW bulge stars are aenhanced => Bulge must
have formed early.
[O/Fe]
a-elements = multiples of He,
more stable, produced by
Type II Supernovae
(high-mass stars, M > 8M)
[O/Fe]
Enhancement of a- Elements
[Fe/H]
Some Key Observational Results
Z
y
•
Gas consumption: Z = -ylog(m ) for Z < y
More gas used --> higher metallicity.
•
Radius: more metals near galaxy centre
•
Galaxy Mass : Low-mass galaxies have lower metallicity.
1 m
Near centre of galaxy: Shorter orbit period--> More passes thru
spiral shocks --> More star generations --> m lower --> Z
higher. (Also, more infall of IGM on outskirts.)
•
Dwarf irregulars: form late (young galaxies),
have low Z because m is still high.
•
Dwarf ellipticals: SN ejecta expel gas from the galaxy,
making m low without increasing Z.
M31: Andromeda in Ultraviolet Light
UV light traces
hot young stars,
current star
formation.
Gas depleted,
hence no current
star formation in
the inner disk.
More metals near Galaxy Centres
Ellipticals
(NGC 3115)
Spirals
(M100)
Mass-Metalicity relation
Why are low-mass galaxies
•
are metal poor?
Some are young
(not much
gas used yet, -so ISM not yet
enriched).
Supernovae eject the
enriched gas from small
galaxies.
Less Metals in Small Galaxies
faint
---->
bright
SFR
Stellar Mass
• Two fundamental parameters seem to
determine observed metallicity:
mass and SFR.
• This forms a fundamental
metallicity relation (FMR).
• Despite extremely complex
underlying physics, the relation seems
to hold out to z = 2.5 and in a huge
range of galaxies / environments.
Stellar Mass
More Metals => More Planets
Doppler wobble
surveys find Jupiters
orbiting 5% of stars
with solar metalicity.
This rises to 25%
for stars with 3x
solar abundance
[Fe/H]=+0.5
Fischer & Valenti 2005
A Quick Review
• Main events in the evolution of the Universe:
–
–
–
–
–
–
The Big Bang (inflation of a bubble of false vacuum)
Symmetry breaking  matter/anti-matter ratio
Quark + antiquark annihilation  photon/baryon ratio
The quark soup  heavy quark decay
Quark-Hadron phase transition and neutron decay  n/p ratio
Big Bang nucleosynthesis  primordial abundances
Xp = 0.75
Yp = 0.25
Zp = 0.0
– Matter-Radiation equality R ~ t1/2  R ~ t2/3
– Recombination/decoupling  the Cosmic Microwave
Background
– CMB ripples (T/T~10-5 at z=1100) seed galaxy formation
– Galaxy formation and chemical evolution of galaxies
• Main events in the chemical evolution of galaxies:
– Galaxy formation  Jeans Mass ( ~106M )
• Ellipticals
• Spirals
• Irregulars
Initial mass and angular momentum, plus mergers.
 Star formation history S( t ), gas fraction m( t )
– Star formation  a = efficiency of star formation
• The IMF ( e.g., Salpeter IMF power-law with slope -7/3 )
• First stars (Population III) from gas with no metals (none seen)
– Stellar nucleosynthesis  metals up to Fe
– Supernovae (e.g. SN 1987A)  metals beyond Fe
• p, s, and r processes
• white dwarfs (M < 8 M) or black holes, neutron stars (M > 8 M).
– Galaxy enrichment models: (e.g. Z = - y ln(m  yield y )
• Metal abundances rise 
X = 0.70 Y = 0.28 Z = 0.02
(solar abundances)
– Gas with metals  Stars with Planets  Life!
fini
Lecture 11:
Age and Metalicity from Observations
“Closed Box” model with constant Yield:
Z(t) = - y ln ( m (t))
Metalicity
Yield
Z » min [ y, y ln(1/ m )]
y
Gas
fraction
Z(t) ® y as m ® 0
1 m
mass of new metals added to ISM by SNe ( ZSN -Z ) (1- a )
Yield = y º
=
But (with infall):
mass of ISM converted to long-lived stars
a
Closed Box model ignores:
1.
IGM--ISM exchanges: IGM falls in, ISM blown out of galaxy
2.
SN Ia, stellar winds, PNe, novae, etc.
3.
Initial enrichment by e.g. Pop.III stars prior to galaxy formation?
4.
Faster enrichment (more SNe) in denser regions of galaxy.