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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

2

3

4

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.

CDE VI WS 2019/20 SF

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

CDE VI 4

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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CDE VI

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

CDE VI

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

6

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.

21

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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WS 2019/20 CDE VI 51

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

53 CDE VI

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,

CDE VI

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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

WS 2019/20 CDE VI 62

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.