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VI. Models of Chemical Evolution Planetary Nebulae Supernovae
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Stars
Gas
Stars are formed from interstellar gas; Stars “live“ only a finite time; During their “lifes“ stars release stellar material (mostly unprocessed) by
means of winds; Their ultimate evolutionary phase is determined by mass ejecta (with
processed matter) Gas has to cool again and forms mol.clouds
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1. simple model
0
1
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5
0 1 2 3 4 5
m
g
s
Z
With the knowledge of stellar
mass function IMF, stellar
lifetimes, and stellar nucleo-
synthesis the stellar element
production rate can be calculated.
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r
SF
ej
SF
g
SF
SF
r
s
g
rsgtot
M
MR
M
ME
MαM
RMdt
d
)RE1(Mdt
d
)1E(Mdt
d
.constMMMM
:fraction mass up-lock
:fraction mass ejected
timescale SF folding-e the is
; :Formation Star
:Remnants
:Stars
:Gas
:box closeda of model ryevolutiona simple A
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1. simple chemical evolutionary model
)ln(0
ln :ymetallicit total
)()1()()1()]([
:yield total
abundance with ielement ofmatrix production as and
)()M-(mRfraction gasreturn as R
function, mass initial as )(with
)())()1(
1: :jelement of yield""
1
00
m
m
rem
u
l
yZ)(M
(t)MyZ
(t)M
(t)M Z(t)
tRytXRtd
tMXd
yy
dmm
m
dmm(tXmQR
y
g
g
g
z
ii
gi
i
i
m
m
iijj
u
l
(t)X (m)Q iij
:ndescriptio enrichment chemical
With • IMF, • stellar lifetimes, and • stellar nucleosynthesis
the yields are calculated.
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Assumptions:
closed box
constant Yields yi (m)
Effect:
Zi(t) = Zi(0) – yi · ln[Mg(t)/Mg(0)]
= Zi(0) – yi · ln[1/μ]
i.e. y determines the slope in the
Z-1/μ diagram.
y
Z
- ln (μ)
6
2. Yields
From stellar evolutionary
models the abundances
released can be derived for a
single stellar population:
Yields
BUT!! Yields depend on
metallicity,
stellar rotation
explosive nucleosynthesis CDE VI WS 2019/20
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Trials with different yields Cescutti et al. (2009)
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Prantzos 2006
Comparison of stellar element abundences with non-dynamical chemical models shows our incomplete understanding of stellar yields and the weakness of evolutionary models.
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Prantzos (2008) EAS publ.
3. Element release by stars - Instantaneous Recycling Approx.………
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4. The solar neighbourhood and the G-dwarf problem
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The solar vicinity
lacks of metal-
poor G dwarfs:
G-dwarf Problem
Consequences:
The gas in the disk
was already metal-
enriched when the
first disk stars
were born.
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P = y represents the yield.
The actual yield for a Z
stellar population with a Salpeter IMF amounts to
y 2 Z
.
This slope is only fullfilled in the Bulge, but smaller in the solar neighbourhood
effective yield yeff < y.
Conclusions: gas infall or outflow.
Pagel 1987
ln μ =
- ln *
- y
f = Z/Z
G dwarf Problem
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Chiappini et al. (1997) ApJ, 472
5. GCE Formalism:
Infall
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Chiappini et al. (1997) ApJ, 472
Conclusion: 2-Infall model WS 2019/20 14 CDE VI
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extreme inflow model
0
1
2
3
4
5
0 1 2 3 4 5
m
g
s
Z
Modell mit abnehmender inflow-Rate
0
1
2
3
4
5
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7
8
9
10
0 1 2 3 4 5
m
g
s
Z
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t
g
r
s
gg
rsg
eMMdt
d
RMdt
d
REMdt
d
MEMdt
d
OMMMdt
d
g
inf,inf,
inf,
.
)(
)(
:infall with
model ryevolutionasimple A 6.
:rate Infall
:Remnants
:Stars
:Gas
.
Assumptions:
closed box,
constant Yields yi
O+Fe from SNeII
of massive stars,
Fe by SN Ia from
WD-WD or
WD-RG
slow evolution fast gas consumption
Effects:
The ratio of element abundances from particular precursor stars
allow the age dating of their lifetimes and the derivation of the
gas consumption.
7. SF timescale from element abundances
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[Fe/H]
[/F
e]
The [/Fe] ratio indicates the star
formation timescale.
Type II Type Ia
Types II+Ia
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SNeII of massive stars produce a constant ratio [O/Fe]0.5, while Fe increases
continuously. After the typical formation timescale of SN Ia Fe is further enhanced
independently of the O enrichment. Thus, O/Fe decreases. From the age of the disk, the
SN Ia timescale must be of the same order.
Tolstoy & Venn, 2003
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Tolstoy & Venn, 2004 Koch (2009) Rev. Mod. Astron.
Conclusion: dSph stars do not match the MW halo stars!!
Tolstoy et al. (2009) ARAA
At low Z dSphs
coincide with halo
star abundance ratios
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8. The N/O Problem
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N/O production:
• O is produced in massive stars and
released by supernovae II (hot gas);
• N is mainly produced in intermediate-
mass stars (warm gas);
• Massive stars live shorter than IMS;
• (N also produced and released by
massive stars as primary and secondary
element)
N/O signatures:
• HII regions in gSs along second.-N
production track;
• outer HII regions resemble dIrrs scatter;
• dIrrs show low N/O (~ -1.6) at low O!
• radial abundance homogeneity in dIrrs
global homogenisation
Pagel (1985)
ESO Workshop
“ ... C,N,O El.s”
Henry & Worthey (1999)
the N/O problem
solutions:
• dIrrs are very young like DLAs: no!
• O loss by galactic winds: O/H-N/O
• Starbursts produce fresh O: O/H-N/O
• Infall of pristine gas: O/H-N/O CDE VI WS 2019/20
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N/O evolution models
Garnett
(1990)
Pilyugin
(1992) Henry, Edmunds, Köppen, (1999)
early evolution: track through DLA
regime
at later epochs: models settle at
secondary N-line,
But: no return to dIrr regime !
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Extremely fast rotating
massive stars pass the
low-O regime.
But: no return to dIrr
regime !
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• early evolution: SF timescale determines the early O enrichment;
• model A: longest SF timescale DLAs: more rapid
• at later epochs: models settle at secondary N-line (CNELGs)
But: no return to dIrr regime !
Henry, Edmunds, Köppen, (1999)
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Gas Infall: its Effect on Abundances
Model assumptions:
Yields same as in Henry,
Edmunds, Köppen (2000):
van der Hoek &
Groenewegen (1997),
Maeder (1992)
Galaxy models evolve for
13 Gyrs with different yeff of 0.1 ... 1
different locations in
(N/O)-(O/H) diagram
Infall of clouds with
primordial abund. and
masses of 106... 108 M
.
Köppen & G.H. (2005) A&A, 434 27 CDE VI WS 2019/20
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Results:
Extension of
tracks depends
on yeff
(N/O) scatter
reproducible by
age differences
of start models
Köppen & G.H. (2005) A&A, 493
S
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8. Star-formation relations
Facts: SF in galactic disks,Global relations
Schmidt (1959, 1963): n 1.5 … 2.5
see Rana & Wilkinson (1986) for discussion:
k 1 … 4
k
g SF r r
.
n
g SF S S
.
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Why is Star-formation self-regulation required on small scales?
Timescales:
SF time = free-fall time:
for n 100 cm-3 τff 1014 s 3·106 yrs
and for clouds of Mgas 109 … 1010 M
SF rate 102 … 103 M
/yr
not observed!
Energetics:
Energy release by stars/stellar explosions:
massive stars: ion. rad. + winds 1049 … 1051 ergs supernovae : 1051 ergs
heating of the ISM by various other processes!
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152
1
2
)(1063.132
3
2
3
)1(
r
nG
n
kT
n
Tkne
ff
oo
cool
Plausibility reasons
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Kennicutt (1998) ApJ, 498
ggdyn
gSF S
S
S 0170.
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15041
2
4
1107052
kpcyrM
pcMs
s
g
SF
..
)..(S
S
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Can we understand the SF – gas surface density relation?
short very be could :but
H) const. (for
:area large a over dynamics scale-small by
produced is SF scale-large if
.
SF
g
g
g
SF
gSF
G
r
.
)(S
S
SS
1.5
1/2
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9. Problem of star-formation efficiency
tff 3
32Gr
3.4 107
nyear
tff 8 106 year
Gas in the galaxy should be wildly gravitationally unstable. It
should convert all its mass into stars on a free-fall time scale:
For interstellar medium (ISM):
Total amount of molecular gas in the Galaxy:
Expected star formation rate:
Observed star formation rate:
Something slows star formation down...
~ 3Msun /year
~ 250 Msun /year
~ 2 109Msun
n 17 cm-3
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SF efficiency depending on gas pressure
Plausibility reasons:
The average ISM pressure determines the density of the cool phase.
At high pressure no warm phase exists in equil.
Elmegreen & Efremov (1997, ApJ, 480))
found that the SF efficiency increases
with PISM.
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The molecular
gas fraction
depends on the ISM
pressure:
H2/HI ∝ P0.92
after: Blitz & Rosolowsky, 2006, ApJ, 650 WS 2019/20 35 CDE VI
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Stellar IMF:
Meyer et al. PP IV
Similarity of stellar IMF
Salpeter (1955) IMF:
dN
d lnMM1.35
10. The Initial Mass Function
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10.1. IMF
log M/M
Kroupa (2002)
Salpeter (1955): γ = –2.35
Kroupa IMF:
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One can derive the
Initial Mass Function
dN(M) Mγ dM
Definition:
(M) = dN(M)/dM Mγ = M-α
normalized to
mu
(M) dM =1 ml
dN/d(logM) = dN/dM · M MΓ
Γ=1+γ
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10.2. Cloud mass spectrum vs. IMF
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determination of the
cluster mass function
Lupus, Taurus and Chamaeleon are
low-mass(!) star-forming regions.
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HBL DBL
Com
ple
teness
lim
it
Initial Mass Function (Trapezium cluster, Muench et al. 2001)
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An excess of massive stars in the local 30 Doradus starburst
Schneider et al. 2018, Science, 359
Spectroscopy of 247 stars with
>15 M
in 30 Dor (upto 200 M
).
32±12% more stars above 30 M
Numerical simulations with
different Z yield insights into the
fragmentation and collapse
scenario of proto-stellar clumps.
10.3. Metal-dependent IMF?
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For a small range of metallicity the
IMF at low- and intermediate-mass
protostellar clumps seems to be
almost Z independent.
10.4. Derivations of star-formation rates from spectroscopic SF indicators
without dust:
SFRH(M/yr) = 7.9 × 10−42 LHα(ergs/s)
= LH(ergs/s)/1.26 x 1041 (Kennicutt, 1998)
= 5.5 × 10−42 LHα(ergs/s) (Calzetti et al., 2007)
The variation of the calibration constant is ~ 15% for variations in Te = 5000-20000 K ,
and < 1% for variations in ne = 100-106 cm-3 (Osterbrock & Ferland 2006).
SFRFUV(M
/yr) = 1.4 × 10-28 L FUV(erg s-1 Hz-1)
with dust:
SFR24μm(M
/yr) = 1.31×10−38 (L24)0.885 (local, 1·1040 < L24μm/ergs/s < 3·1044)
uncertainty of 0.02 in the exponent, 15% in the calibration constant
= 2.04 × 10−43 L24 (global, 4·1042 < L24μm/ergs/s < 5·1043)
(Calzetti et al., 2007)
SFR(M
/yr) = 5.3 × 10−42 [LH + 0.031 L24μm]
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Facts
The total energy of ionizing photons from massive stars over
their lifetimes are comparable to the supernova type II energy.
Star formation is visible as HII regions.
Star formation visible as HII regions.
HII regions visible in Hα Lyc flux from massive stars: with
IMF SFR
Massive stars in UV: with IMF SFR
Calibration of IR emission by dust SFR
Star formation is self-regulated.
Massive stars clear-up their birthplaces.
How to disentangle low SFRs
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SFRs derived from indicators (massive
stars normalized to IMF) H and UV begin
to deviate below ~ 10-2 M
yr-1.
Explanation: H preferably from higher-
mass stars than UV IMF not complete in
uppermost mass range.
10.5. Star formation at low rates
Lee et al., 2009, ApJ, 706 WS 2019/20 50 CDE VI
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Boselli et al. (G.H.)
H is only a necessary, but not a sufficient condition for SF!
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Can the IMF be global?
What are the consequences of low star-formation rates
for the evolution of dwarf galaxies?
How is it treatable in numerical models of galaxy evolution?
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10.6. Possibilities to fill the IMF according to the SFR/cloud mass
star fractions!!
filled IMF reduced to star fraction IMF truncated at
upper mass interval with N*=1
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Consequences of low SFR:
Filled IMF: star fractions lead to SNII fractions heating
Truncated IMF: longer lifetimes of heaviest stars; w/o SNeII? WS 2019/20
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1
1
)(
)(
)()()(
~)(
)(
*
u
m
m
m
mm
mN
dmmAmM
dmmAdmmAmN
mdm
mdNm
u
l
u
l
:condition
:SFR
:IMF
At low SFR 3 possibilities emerge:
• a filled IMF can lead to N(m)
becoming fractions of 1 only!
i.e. for massive stars
also NSNII(m)
• The IMF is truncated
• A stochatic IMF allows for individual massive stars
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MV of brightest star cluster vs. column SFR in various galaxies
Larsen, 2002, AJ, 124
Maximum star-
cluster V brightness
is correlated with
the K-S SFR.
Exceptions are
galaxies with
starbursts, forming
super star clusters.
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11.. Chemical feedback by the IMFs
What do we expect?
In the case of lacking massive stars α-element yields should be reduced.
filled IMF truncated IMF
For the truncated IMF [O/Fe] becomes < 0; observed e.g. in dSphs.
The same should be studied for Ba vs. Mg! Steyrleithner , G.H.,et al. (2017)
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http://sagadatabase.jp/
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Various explanations of the huge
Ba scatter are proposed; the
scatter is much larger than the
obserational uncertainty.
Normally, Ba has a s-process
origin. Moreover,
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Interestingly, Ba should originate from
IMS, while Eu should be produced by
massive-star mergers.
Therefore, Ba vs. Eu represents the IMF
yields.
Halo EMP stars (upper panel),
Ultra-faint dSph stars (right)
Sextans
Segue I, II
With courtesy by Tsujimoto
09.01.2020
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ti & Ciappini, 2014, A&A, 565
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Aoki et al., 2013, ApJ, 766
Various models
Left: r-process
based on el-capture in SNeII
and magnetorot.-driven SNe.
Middle right: with r-process +
turbulence in SNeII of M>20
M (blue), without in red.
Lower right: chemodynamical
DG model with truncated IMF.
Halo stars from disrupted star
clusters (no GCs) of different,
but also low masses with
various lack of massive stars.