GALACTIC CHEMICAL EVOLUTION - Max Planck Society€¦ · Sun: X⊙=0.71 Y⊙=0.275 Z ⊙=0.015 2)...

I) INTRODUCTION TO GALACTIC CHEMICAL EVOLUTION

II) A CASE STUDY: THE SOLAR NEIGHBORHOOD

III) THE MILKY WAY HALO: FROM C TO Zn

IV) THE LIGHT ELEMENTS (Li,Be, B)

AND THE HEAVIER THAN Fe ELEMENTS (s- AND r-)

V) THE MILKY WAY DISK

GALACTIC CHEMICAL EVOLUTION N. Prantzos

(Institut d’Astrophysique de Paris)


I.1) Historical context, abundances, solar composition

I.2) Basics of stellar nucleosynthesis

I.3) Formalism, ingredients, yields

I.4) Analytical solutions (IRA) : closed box, outflow, infall

I.5) SSP: tool for chemo-dynamical models



Chart of the nuclides

~300

Solar

Photosphere, (absorption

line spectrum)

unmodified

by nucleosynthesis

in Sun’s core,

it reflects

the composition

of the gas

from which

the Sun formed

4.5 Gyr ago

Elemental

composition

determined

C1 Carbonaceous chondrites

formed in early Solar system

and unaffected by fractionation

Isotopic composition

determined

Solar (Cosmic) Abundances

Symbol By number By mass

Hydrogen X 90 70

Helium Y 9 28

Metals Z <1 ~ 2

Abundance scales

1) By mass (Mass fraction): X i Σ Xi = 1 Theoreticians

X: H Y: He Z: Metals (A>4) X+Y+Z=1

Sun: X⊙=0.71 Y⊙=0.275 Z⊙=0.015

2) By number : (Ni = Xi / Ai ) Observers with respect to a reference (=abundant) element : Ni / NR

Astronomy : NH = 1012 AH = log(NH) = 12

Meteoritics : NSi = 106 ASi = log(NSi) = 6

3) Relative to solar ratio (Xi / Xj)⊙ Practical

[Xi/Xj ] = log(Xi/Xj) – log(Xi/Xj)⊙ [Xi/Xj]⊙ = 0

e.g. [Fe/H]⊙ = 0

Cosmic abundances

of nuclides are locally correlated with

nuclear stability

(alpha-nuclei, Fe peak nuclei or

nuclei with even nucleon number

are more abundant

than their neighbors)

alpha-nuclei : mass number = multiple of 4

(C-12, O-16, Ne-20, Mg-24,

Si-28, S-32, Ar-36, Ca-40)

Nuclear processes have shaped the

cosmic abundances

of the chemical elements

Solar ( = Cosmic) abundances : related to nuclear properties (nuclear binding energies)

➔ a hot (many MK) site is required : which one ?

G. Gamow (mid-40ies): all elements produced in the

hot primordial Universe (Big Bang) by successive neutron captures

F. Hoyle (mid-40ies): all elements produced inside

stars during their evolution, by thermonuclear reactions

Old stars of galactic halo (Population II) contain less heavy elements (metals)

than the younger stellar population (Population I) of the galactic disk

The chemical composition of the Milky Way was substantially different in the past

Early 50ies: metal (heavier than He) abundances are not always the same ;

Galactic halo stars have low metallicities

F. Hoyle: almost all elements produced inside

stars during their evolution, by thermonuclear reactions

…except H and He, which

do come from the Big Bang

BURBIDGE

Margaret Geoff

FOWLER

William HOYLE

Fred

1957: Origin of the elements in stars

AGB

Red Super giant

SN

Evolution and nucleosynthesis in intermediate mass stars

Karakas and Lattanzio (2014)

Massive star evolution and nucleosynthesis

months

Role of winds

NEUTRON

STAR

BLACK HOLE

Silicium

Oxygène

Néon

Carbon

Hélium

Enveloppe

Hydrogène

4.5 3.0

2.5 1.5

0.5 0.1

0.001

In case of successful explosion

the shock wave propagates in the

envelope and heats the stellar layers

to high temperatures, inducing

explosive nucleosynthesis

Explosive nucleosynthesis in supernovae

Products of hydrostatic and

explosive nucleosynthesis

are ejected

in the interstellar medium

Supernovae are

the chief-alchemists

of the Universe

Stable Fe-56 is made in the

unstable (radioactive) form of Ni-56 :

Ni-56 ➔ Co-56 ➔ Fe-56

Ni56

THE WAY TOWARDS NSE (Nuclear Statistical Equilibrium)

Ca40 is the last stable

nucleus with N=Z

on the way of Si-melting

towards NSE

Note : in explosive nucleosynthesis, weak interactions have no time to

operate and remains close to 0. Ni56 dominates the NSE composition

In the stellar core

weak interactions shift

the neutron excess

towards ∼0.05 – 0.10

and Fe56 dominates

the NSE composition

The mass of the white dwarf

(carbon-oxygen) increases

by matter accretion

from the companion

The nuclear flame propagates rapidly outwards, burning in a second

about half of the white dwarf to radioactive Ni-56

and disrupting the whole star

Thermonuclear supernovae

(SNIa)

White dwarves exploding

in binary systems

SNIa produce 2/3 of Fe (stable product of Ni-56) in the Milky Way

When it becomes greater than the mass-limit

of Chandrasekhar (1.4 M⊙)

the white dwarf collapses,

its temperature increases and

thermonuclear reactions

ignite explosively in

a degenerate medium

THE PRODUCTION OF HEAVIER THAN Fe NUCLEI

Neutron captures, on timescales:

long w.r.t. the β-decay lifetimes (few neutrons available): S-process short w.r.t. the β-decay lifetimes (many neutrons available): R-process

S-nuclei: in the valley of nuclear stability

Most nuclei have mixed (S- and R-) origin, but there exist pure S- or R- nuclei

Nuclei unreachable by n-captures: P-nuclei

R-nuclei: neutron rich

Primordial Nucleosynthesis

Galactic Cosmic Rays

Helium burning

Carbon-Neon burning

Oxygen burning

Nuclear Statistical Equilibrium

Neutron captures

(s- and r- processes)

Hydrogen burning

Processes occuring in diferent sites and on different timescales

Nucleosynthesis

Woosley 2002

Big Bang H, D, He-3, He-4, Li-7

Small

Stars

(Gyr)

Massive

Stars

(Myr)

Red

Giants

Red

Supergiants

He→C,O…

Si→ Fe

He→C,O

Planetary

nebulae Supernova

White

dwarf Neutron

star Black

hole

Companion

star

Fe

White

dwarf SNIa

Cosmic rays

CNO ⇒ Li Be B

(1954)

SN CO

Metals Gas

Galactic chemical evolution: sketch

Εnriched gas

Gas Stars

Μetals

Time

New stars

Old stars

dtdm = [f à o] (1)

dt

dmG = àÑ+ ï+ [f à o] (2)

ï(t) =R

Mt

MU (Mà C(M)) Ñ(t à ü(M)) Ð(M) dM (3)

m = mS + mG (4)

GALAXY: Box of gas and stars,

exchanging matter between them

(via star formation from gas

and mass ejection from stars) Infall Outflow

m : total mass of the system

mG : mass of gas in the system

mS : mass of stars in the system

The box may be

closed or open

(i.e. via infall or

outflow of gas)

Galactic Chemical Evolution Basics (1)

Ψ : star formation rate (SFR)

ε : stellar mass ejection rate

f,o : infall and ouflow rates

τ(M) : lifetime of star of mass M

C(M) : mass of compact residue

(M) : Initial Mass Function (IMF)

Variation of total mass of the system :

Variation of the mass of gas :

Mass ejection rate :

Mass of stars = Total - Gas :

Eqs. (1)-(4) allow to calculate m(t), mG(t), mS(t), if Ψ(t) and (t) [as wel as f(t) and o(t)] are given

MU : Upper mass limit of IMF Mt : Mass of star with lifetime τ(M) < t

c(t) =R

Mt

MU C(M) Ñ(t à ü(M)) Ð(M) dM (6)

mS = mL + mC (5)

dt

d(mGXi) =àÑXi + ïi + [fXi;f à oXi;o] (8)

ïi(t) =R

Mt

MU Yi(M)Ñ(t à ü(M))Ð(M)dM (9)


Mass of stars = Mass(Live) + Mass(Dead) :

Creation rate

of Compact

Objects :

Mass of dead stars (compact objects) :

Eqs. (5)-(7) allow to calculate the mass of luminous stars mL

Variation of mass

of element i :

(Xi : mass fraction of i)

Eqs. (8)-(9) allow to calculate the evolution of the chemical composition of the gas

Ejection rate

of element i :

(Yi : stellar yield of i)

mC =

8;

t

0c(t0) dt0 (7)

Lifetime (Gyr)

Main ingredients of Galactic Chemical Evolution

(GCE) models


Stellar properties (function of mass M and metallicity Z)

- Lifetimes

- Yields (quantities of elements ejected)

- Masses of residues (WD, NS, BH)

Collective Stellar Properties

- Star Formation Rate (SFR)

- Initial Mass Function (IMF)

Gas Flows - Infall

-Outflow

- ( Feedback from Supernovae )

Stellar lifetimes depend very slightly

on metallicity

No star of mass M<0.8 Mʘ has ever died

Stellar Residues (Compact Objects)

Mass (Mʘ) of

Compact Object

Mass fraction of Compact Object

Ejected Fraction

0.7 < M / Mʘ < 9 White Dwarf (WD) C(M) = 0.446 + 0.1

9 < M / Mʘ < 30[?] Neutron Star (NS) C(M) = 1.5

M>30 Mʘ [?] Black Hole (BH) [?] C(M)=0.25*(M-30)+1.5

Initial Mass Residue Mass (Mʘ)

More massive stars expel a larger fraction of their mass

(either through stellar winds or supernova explosions)

The mass limits for formation

of neutron stars and black holes

are only theoretically motivated

NOT Salpeter ( x= 1.35) in the whole mass range

Certainly less steep than x=1.35 in low masses

Perhaps steeper for M>1 Mʘ (Scalo: x=1.70)

Salpeter (x=1.35)

M<1 Mʘ : Kroupa M>1 Mʘ: Scalo (x=1.70)

M<1 Mʘ : Chabrier M>1 Mʘ: Salpeter (x=1.35)

The fraction of stars with M>10 Mʘ determines the amount of metals

produced (metallicity)

while the fraction of stars with M>1 Mʘ determines the amount of astration

(material recycled through stars, depleted in fragile elements)

IMF

IMF / Salpeter

The Stellar Initial Mass Function – IMF

R

ML

MUÐ(M) M dM = 1

Because of the normalization

The true IMF has less low M stars

than Salpeter’s IMF…

…and may have more or less stars

of high mass than Salpeter’s

fMAS(M) = R

M1

M2Ð(M`)M`dM`

R

M

M2Ð(M`)M`dM`

fNUM(M) = R

M1

M2Ð(M`)dM`

R

M

M2Ð(M`)dM`

Fraction by number

Fraction by mass By number

By mass

M<1 Mʘ : Chabrier M>1 Mʘ: Salpeter (x=1.35)

M<1 Mʘ : Kroupa M>1 Mʘ: Scalo (x=1.70)

Salpeter (x=1.35) Massive stars (>10 M⊙)

represent a few 0.1% by

number, but ~10% by mass

Low mass stars (<1 M⊙)

represent ~90% by

number, but ~50% by mass

The Stellar Initial Mass Function – IMF between M1=0.1 M⊙ and M2=100 M⊙

LOW MASS

MASSIVE INTERMEDIATE

MASS

Mass distribution of stars

(Initial Mass Function)

Lifetimes of stars

(in millions of years)

SN PN

Contributions of stars to Galactic Chemical Evolution

Massive stars (M > 10 Mʘ) contribute

almost all of the nuclei between C and Kr

and neutron-rich (r-) nuclei

Intermediate mass stars (1<M/Mʘ<10)

produce s-nuclei and part of

He3, He4, N14, C12, C13, O17, F19

and are more efficient (because of IMF)

in astrating fragile elements (e.g. D)

Low mass stars (M < 1 Mʘ)

are “eternal”

and just block gas,

removing it from circulation

Most metals (O-Fe, r-nuclei, light s-nuclei) are ejected in first part

About 1/2 of He-4, C-12, N-14, as well as heavy s-nuclei are in second part

Third part contains mostly heavy s-nuclei

Fe from SNIa is released from 50-100 Myr to >10 Gyr

First 1/3 of the mass is returned by M>10 M⊙ stars within 20 Myr

Second 1/3 of the mass is returned by 3<M/M⊙<10 stars within 500 Myr

Last 1/3 of the mass is returned by 1<M/M⊙<3 stars within 10 Gyr

Yields of low and intermediate mass stars

Karakas and Lattanzio (2014)

They depend a lot on assumptions about AGB mass loss and mixing processes

(+ nuclear uncertainties)

Just from first principles, neither the absolute yields (i.e. whether a star of

given mass is important producer of an isotope)

nor the nature of the process (i.e. primary or secondary)

for key isotopes (N14, C13) can be known with certainty

Most abundant

nuclei ejected

by a star

of 25 M⊙

(WW95)

Thickness of layers depends on assumptions about convection and mixing processes

Abundances in each layer depend on adopted nuclear reaction rates

Abundances in inner layers depend also on explosion mechanism

Overall structure/evolution also depends on rotation, mass loss etc.

Large uncertainties still affecting the supernova yields (amounts of elements ejected)

Yields of massive stars (1)


Yield (mass ejected) : Yi(M)

Net Yield : yi(M) = Yi(M) – M0,i(M)

fi(M) =M0;i(M)

Yi(M)

Mass initially present

in the ejected part of the star

M0,i(M) = X0,i ( M - C(M) )

Overproduction factor

Y y f

>M0 >0 >1

=M0 =0 =1

<M0 <0 <1

Created

Destroyed

Carbon

Oxygen

Iron

Re-ejected

Yields in Mʘ

Woosley and Weaver 1995: Yields (overproduction factors) for various initial metallicities


How to test theoretical stellar yields ?

Ideally: measure ejected amounts

of various elements in supernovae

or supernova remnants

of known progenitor mass

(and metallicity!)…

Crab nebula

SN1987A in LMC

From light curve:

0.07 Mʘ of Ni56 ( Fe56)

produced in the explosion

of a 18-20 Mʘ star

Yields of massive stars

STELLAR YIELDS M(M⊙)

Yields of intermediate

and low mass stars

STELLAR YIELDS M(M⊙)

Yields of intermediate

and low mass stars:

much fewer sets available

Yields of massive stars :

several sets available

(but incomplete)

Current yields are incomplete,

in coverage of mass, metallicity,

or physical properties (e.g. rotation)

Calculations require

sometimes hazardous

interpolations/extrapolations

IMF S

N19

87A

Folding

massive star yields

with an IMF

leads to

a mean

stellar value

of 25 M⊙

(“typical star

enriching the ISM”)

W7: a very successful parameterized SNIa model

Ideally: the flame should start slowly and pre-expand the star,

to avoid too much e- captures and production of Fe54, Ni58 (for nucleosynthesis)

Then move at densities 107-108 g/cm3, to produce ≈0.6 Mʘ of Ni56

in intermediate layers (for the optical lightcurve)

and ≈0.2 Mʘ of Si, S, Ar, Ca (for the early spectra)

Thielemann, Nomoto, Yokoi 1986

Thermonuclear SN (SNIa) : explosions of WDs in binaries

Producers of Fe-peak elements

Fe – peak isotopes produced

plus ~30% of major isotopes of solar Si, S, Ar, Ca

Problem with overproduction of Fe54, Ni58 (minor isotopes of Fe and Ni)

Ove

rpro

du

ctio

n f

acto

rs (

Fe=

1)

SNIa are ~5 times less frequent

than Core collapse SN (SNII+SNIbc)

in a Sbc galaxy, like the MW

but each SNIa produces

~10 times more Fe than a CCSN

SNIa produce ~50 - 65 % of solar Fe

Mannucci et al. 2005

The role of SNIa in GCE

Calculation of SNIa rate involves

assumptions about progenitors

and IMF of binary systems

Results are constrained

from observations of SNIa rates

in galaxies of different ages

Simple, phenomenological prescription

R (SNIa) = a t -1

Howell 2011

Delay Time Distribution

from observations

SFR ∑GAS N

N = 1.4

An equally good fit is obtained for

SFR ∑GAS /DYN with DYN = R/ V(R) at optical radius Ropt

The Star Formation Rate – SFR

Kennicutt (1998): in normal spirals and circumnuclear starbursts,

fair correlation of average SFR density with average total surface density of gas

A threshold in the SFR

around a few Mʘ/pc2 ?

WHICH PRESCRIPTION FOR

STAR FORMATION ?

SFR vs Gas (HI+H2)

SFR vs Molecular Gas

Krumholz 2014

pi =1àR1

R

M(T)

MU yi(M) Ð(M) dM

Net Yield : yi(M) = Yi(M) – M0,i(M)

dt

dmG = àÑ+ ï+ [f à o] (2)

ï(t) =R

Mt

MU (Mà C(M)) Ñ(t à ü(M)) Ð(M) dM (3)

The chemical evolution equations are coupled through the stellar lifetimes (M)

They are simplified by assuming that stars in the system (of age T) are

Eternal (Small Mass) (M)>>T

Dying at birth (Massive) (M) = 0

Instantaneous

Recycling

Approximation

(IRA)

Return Mass Fraction

Yield

(of a stellar generation)

IRA: replace t - (M) by t in equations of GCE, allowing to separate variables

R =R

M(T)

MU(MàC(M))Ð(M)dM

mG = m eà÷(1àR)t

Xi àXi;0 = pi ÷ (1 àR) t

XiàXi;0 = pi ln mG

mð ñ

= pi ln (1=û)

Ñ = ÷ mG

Instantaneous Recycling Approximation

Assuming that :

û =m

mGGas fraction

IRA is

an excellent

approximation

for massive star

products

and values of

gas fraction

not too small

(>0.3)

Independent

of SFR Analytical

solution

Analytical

solutions

IRA

Non-IRA

IRA

Non-IRA

X/Xʘ

σ

X/Xʘ

Closed box

or Outflow with ROUT = k SFR

and SFR = ν mG

Infall with mG = constant

and SFR = ν mG

Initial

conditions mG = mT = 1 mT = mG = mG,0

Gas Mass

mG

Total mass

mT

H,He,Metals

X - X0

Deuterium

X / X0

eà÷(1àR+k)t mG;0

1+k1+keà÷(1+k)t mG;0+ (÷mG;0àR)t

pi 1àR+k1àR ln

mG

1ð ñ

pi 1àe(1àû1)

ð ñ

mG1àR+k

R

1àR(1à e 1àR

1à1=û

)

Analytical solutions with IRA, as a function of Return fraction R and yield p

In all cases: Gas fraction σ = mG / mT and stars mS = mT - mG

Closed Box

Analytical (IRA)

Numerical (τ(M)=0)

Closed Box

Analytical (IRA)

Numerical (τ(M)≠0)

Outflow Rate = 8 SFR

Analytical (IRA)

Numerical (τ(M)=0)

Outflow Rate = 8 SFR

Analytical (IRA)


Infall Rate : Gas=const

Analytical (IRA)

Numerical (τ(M)=0)

Infall Rate : Gas=const

Analytical (IRA)


In order to reach a given metallicity Z,

a certain amount of stars

has to be created : mS=m-mG or n=1-σ

(Gas fraction σ = mG/m and Star fraction n = mS/m)

Z = p ln

ð

û1á

=) û= expàà

pZñ

For a system of final metallicity Z1 and n1=1-σ1 the cumulative metallicity distribution (CMD) is :

n1

n(<Z)=

1àû1

1àû

and the differential metallicity distribution (DMD) is

d(logZ)

d(n=n1) =1àexp(àZ1=p)

ln(10)

pZ eàZ=p

DMD = max for Z = p Allows to determine p from observations !

Independent of system’s history

The metallicity distribution

of long-lived stars

For comparison to observations ,

the DMD is folded with a Gaussian error

distribution, of width determined by

observational uncertainties

Outflow models with Outflow Rate = k SFR

have a reduced effective yield

pEFF =1àR+k1àR pTRUE

which displaces the MD to lower metallicities

(interesting for Galactic HALO)

Infall models reduce slightly

the effective yield, but

they produce much narrower Diferential Metallicity Distributions

(interesting for local disk)

ïi(t) =R

Mt

MUYi(M)Ñ(tà ü(M))Ð(M)dM (9)

dïi(t;M) =Yi(M)Ñ(tà ü(M))dt

Ð(M)dMdt (10)

For SPH and Chemodynamical models: Single Stellar Population (SSP) method

Burst of star formation

τ(M) years ago Ejecta of star M,

released after time τ

after the burst

t-τ(M) years

ïi(t) =R

t0

tYi(M)Ñ(tàü(M))

dtdN dt (10a)

=R

t0

tÑ(tà ü(M))dt

dt

Yi(M)dN(10b)

Mass of stars formed at time t-τ(M) during dt

Mass of element ι released at time t per unit mass of stars

formed and per unit time

Mass distribution of stars

(Initial Mass Function)

Lifetimes of stars

(in millions of years)

Stellar death rate dN/dt = dN/dM x dM/dt =

IMF x slope (Mass vs lifetime)

Z=Z⊙

10-1 Z⊙

10-2 Z⊙

10-4 Z⊙

Z=0

SNIa

per unit mass of stars formed For a SSP:

Recipes for chemical evolution

in Chemodynamical calculations

1) Take lifetimes of stars τ(M) from theory

2) Take tables of yields Yi(M) from theory

3) Adopt an IMF Φ(M) normalised to ∫ΜΦ(M)dM=1

4) Calculate tables of rates Ri of release of element I

(including SNIa, which requires a prescription for their rate…)

5) Distribute the mass released (mi = Rdt)

in neighbouring gas particles

6) Check that Σ Xi = 1 in each star and gas particle

Tinsley, B. M. (1980)

Evolution of the Stars and Gas in Galaxies

Fundamentals of Cosmic Physics, Volume 5, pp. 287-388

Asplund, M., Grevesse, N., Sauval, A. J., Scott, P. (2009)

The Chemical Composition of the Sun

Annual Review of Astronomy & Astrophysics, vol. 47,

pp.481-522

Karakas, Amanda I.; Lattanzio, John (2014)

Nucleosynthesis and stellar yields

of low and intermediate-mass single stars

eprint arXiv:1405.0062

Nomoto, K, Kobayashi, C., Tominaga, N., (2013)

Nucleosynthesis in Stars and

the Chemical Enrichment of Galaxies

Annual Review of Astronomy and Astrophysics,

vol. 51, pp. 457-509

Krumholz, M (2014)

The Big Problems in Star Formation: the Star Formation

Rate, Stellar Clustering, and the Initial Mass Function

eprint arXiv:1402.0867

Some references

http://adsabs.harvard.edu/cgi-bin/author_form?author=Karakas,+A&fullauthor=Karakas,%20Amanda%20I.&charset=UTF-8&db_key=PRE

http://adsabs.harvard.edu/cgi-bin/author_form?author=Lattanzio,+J&fullauthor=Lattanzio,%20John%20C.&charset=UTF-8&db_key=PRE

GALACTIC CHEMICAL EVOLUTION - Max Planck Society€¦ · Sun: X⊙=0.71 Y⊙=0.275 Z ⊙=0.015 2)...

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Transcript of GALACTIC CHEMICAL EVOLUTION - Max Planck Society€¦ · Sun: X⊙=0.71 Y⊙=0.275 Z ⊙=0.015 2)...