GALACTIC CHEMICAL EVOLUTION N. Prantzos (Institut d Astrophysique de Paris)

GALACTIC CHEMICAL EVOLUTION N. Prantzos (Institut d Astrophysique de Paris) I) INTRODUCTION TO GALACTIC CHEMICAL EVOLUTION II) III) A CASE STUDY: THE SOLAR NEIGHBORHOOD 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) INTRODUCTION TO GALACTIC CHEMICAL EVOLUTION 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 X i = 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 : (N i = X i / A i ) Observers with respect to a reference (=abundant) element : N i / N R Astronomy : N H = 10 12 A H = log(n H ) = 12 Meteoritics : N Si = 10 6 A Si = log(n Si ) = 6 3) Relative to solar ratio (X i / X j ) Practical [X i /X j ] = log(x i /X j ) log(x i /X j ) [X i /X j ] = 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? F. Hoyle (mid-40ies): all elements produced inside stars during their evolution, by thermonuclear reactions G. Gamow (mid-40ies): all elements produced in the hot primordial Universe (Big Bang) by successive neutron captures

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

1957: Origin of the elements in stars BURBIDGE Margaret Geoff FOWLER William HOYLE Fred

Red Super SN giant AGB

Evolution and nucleosynthesis in intermediate mass stars Karakas and Lattanzio (2014)

Massive star evolution and nucleosynthesis months Role of winds

Explosive nucleosynthesis in supernovae In case of successful explosion the shock wave propagates in the envelope and heats the stellar layers to high temperatures, inducing explosive nucleosynthesis Enveloppe Hydrogène Hélium Carbon Products of hydrostatic and explosive nucleosynthesis are ejected in the interstellar medium Néon Oxygène Silicium NEUTRON STAR BLACK HOLE 4.5 Ni56 3.0 2.5 1.5 0.5 0.1 0.001 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

THE WAY TOWARDS NSE (Nuclear Statistical Equilibrium) Ca40 is the last stable nucleus with N=Z on the way of Si-melting towards NSE In the stellar core weak interactions shift the neutron excess towards 0.05 0.10 and Fe56 dominates the NSE composition Note : in explosive nucleosynthesis, weak interactions have no time to operate and remains close to 0. Ni56 dominates the NSE composition

Thermonuclear supernovae (SNIa) White dwarves exploding in binary systems The mass of the white dwarf (carbon-oxygen) increases by matter accretion from the companion 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 nuclear flame propagates rapidly outwards, burning in a second about half of the white dwarf to radioactive Ni-56 and disrupting the whole star SNIa produce 2/3 of Fe (stable product of Ni-56) in the Milky Way

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 R-nuclei: neutron rich Most nuclei have mixed (S- and R-) origin, but there exist pure S- or R- nuclei Nuclei unreachable by n-captures: P-nuclei

Processes occuring in diferent sites and on different timescales Nucleosynthesis Primordial Nucleosynthesis Galactic Cosmic Rays Hydrogen burning Helium burning Carbon-Neon burning Oxygen burning Nuclear Statistical Equilibrium Neutron captures (s- and r- processes)

Woosley 2002

Big Bang H, D, He-3, He-4, Li-7 Small Stars (Gyr) Massive Stars (Myr) Red Giants He C,O Cosmic rays CNO Li Be B Red Supergiants He C,O Si Fe Planetary nebulae Fe Supernova White dwarf Companion star White dwarf SNIa Neutron star Black hole

(1954)

Galactic chemical evolution: sketch Old stars SN CO Gas Metals Εnriched gas New stars Gas Stars Μetals Time

GALAXY: Box of gas and stars, exchanging matter between them (via star formation from gas and mass ejection from stars) Galactic Chemical Evolution Basics (1) Infall Outflow The box may be closed or open (i.e. via infall or outflow of gas) m : total mass of the system m G : mass of gas in the system m S : mass of stars in the system 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 : dm dt = [f à o] (1) dm G dt = à Ñ + ï + [f à o] (2) Mass ejection rate : ï(t) = M U : Upper mass limit of IMF M t : Mass of star with lifetime τ(m) < t Mass of stars = Total - Gas : R M U (M à C(M)) Ñ(t à ü(m)) Ð(M) dm (3) M t m = m S + m G (4) Eqs. (1)-(4) allow to calculate m(t), m G (t), m S (t), if Ψ(t) and (t) [as wel as f(t) and o(t)] are given

Galactic Chemical Evolution Basics (2) Mass of stars = Mass(Live) + Mass(Dead) : m S = m L + m C (5) Creation rate of Compact Objects : c(t) = Mass of dead stars (compact objects) : R M U C(M) Ñ(t à ü(m)) Ð(M) dm (6) M t 8 m C = ; t c(t 0 ) dt 0 (7) 0 Eqs. (5)-(7) allow to calculate the mass of luminous stars m L Variation of mass of element i : (X i : mass fraction of i) d(m G X i ) dt = à ÑXi + ï i + [fx i;f à ox i;o ] (8) Ejection rate of element i : (Y i : stellar yield of i) ï i (t) = R M t M U Y i (M)Ñ(t à ü(m))ð(m)dm (9) Eqs. (8)-(9) allow to calculate the evolution of the chemical composition of the gas

Galactic Chemical Evolution Basics (3) 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) Lifetime (Gyr) 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) Initial Mass Residue Mass (Mʘ) 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 Mass (Mʘ) of Compact Object M>30 Mʘ [?] Black Hole (BH) [?] C(M)=0.25*(M-30)+1.5 The mass limits for formation of neutron stars and black holes are only theoretically motivated Mass fraction of Compact Object Ejected Fraction More massive stars expel a larger fraction of their mass (either through stellar winds or supernova explosions)

The Stellar Initial Mass Function IMF Salpeter (x=1.35) IMF 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) R Because of the normalization M U Ð(M) M dm = 1 M<1 Mʘ : Kroupa M>1 Mʘ: Scalo (x=1.70) M<1 Mʘ : Chabrier M>1 Mʘ: Salpeter (x=1.35) IMF / Salpeter M L 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 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)

Fraction by number R M 2 Ð(M`)dM` M f NUM (M) = R M1 The Stellar Initial Mass Function IMF between M 1 =0.1 M and M 2 =100 M M 2 Ð(M`)dM` By mass Fraction by mass R M 2 Ð(M`)M`dM` M MAS(M) = R M 1 M 2 Ð(M`)M`dM` By number Massive stars (>10 M ) represent a few 0.1% by number, but ~10% by mass 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) Low mass stars (<1 M ) represent ~90% by number, but ~50% by mass

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 Lifetimes of stars (in millions of years) 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) Mass distribution of stars (Initial Mass Function) Low mass stars (M < 1 Mʘ) are eternal and just block gas, removing it from circulation LOW MASS INTERMEDIATE MASS PN MASSIVE SN

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 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

Yields of low and intermediate mass stars 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 Karakas and Lattanzio (2014)

Yields of massive stars (1) 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 (2) Carbon Yield (mass ejected) : Y i (M) Oxygen Yields in Mʘ Net Yield : y i (M) = Y i (M) M 0,i (M) Mass initially present in the ejected part of the star M 0,i (M) = X 0,i ( M - C(M) ) Overproduction factor Y i (M) f i (M) = M0;i (M) Iron Y y f >M 0 >0 >1 =M 0 =0 =1 <M 0 <0 <1 Created Re-ejected Destroyed

Yields of massive stars (3) 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!) SN1987A in LMC From light curve: 0.07 M ʘ of Ni56 ( Fe56) produced in the explosion of a 18-20 M ʘ star Crab nebula

STELLAR YIELDS M(M ) Yields of massive stars Yields of intermediate and low mass stars

STELLAR YIELDS M(M ) Yields of massive stars : several sets available (but incomplete) Yields of intermediate and low mass stars: much fewer sets available Current yields are incomplete, in coverage of mass, metallicity, or physical properties (e.g. rotation) Calculations require sometimes hazardous interpolations/extrapolations

SN1987A IMF 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 Thielemann, Nomoto, Yokoi 1986 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 10 7-10 8 g/cm 3, 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)

Overproduction factors (Fe=1) 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)

The role of SNIa in GCE 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 Mannucci et al. 2005 Delay Time Distribution from observations Howell 2011 SNIa produce ~50-65 % of solar Fe 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

SFR GAS N N = 1.4 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 An equally good fit is obtained for SFR GAS / DYN with DYN = R/ V(R) at optical radius R opt A threshold in the SFR around a few M ʘ /pc 2?

WHICH PRESCRIPTION FOR STAR FORMATION? SFR vs Gas (HI+H2) Krumholz 2014 SFR vs Molecular Gas

The chemical evolution equations are coupled through the stellar lifetimes (M) ï(t) = R M t dm G dt = à Ñ + ï + [f à o] (2) M U (M à C(M)) Ñ(t à ü(m)) Ð(M) dm (3) 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 R = R M U (M à C(M))Ð(M)dM M(T) Yield (of a stellar generation) p i Net Yield : y i (M) = Y i (M) M 0,i (M) R 1 M = U 1àR M ( T) y i (M) Ð(M) dm IRA: replace t - (M) by t in equations of GCE, allowing to separate variables

Analytical solution Instantaneous Recycling Approximation ð m X i àx i;0 = p i ln mg ñ = p i ln (1=û) Independent of SFR Gas fraction û = m m G Analytical solutions Assuming that : m G = m e à (1àR)t X i à X i;0 Ñ = m G = p i (1 à R) t X/Xʘ σ Non-IRA IRA X/Xʘ IRA Non-IRA IRA is an excellent approximation for massive star products and values of gas fraction not too small (>0.3)

Analytical solutions with IRA, as a function of Return fraction R and yield p Initial conditions Closed box or Outflow with R OUT = k SFR and SFR = ν m G Infall with m G = constant and SFR = ν m G m G = m T = 1 m T = m G = m G,0 Gas Mass m G e à (1àR+k)t m G;0 Total mass m T H,He,Metals X - X 0 1+ke à (1+k)t 1+k p 1àR i 1àR+k ð 1 ln mg ñ m G;0 + ( m G;0 à R)t p i ð 1 à e (1à û 1 ) ñ Deuterium X / X 0 m G R 1àR+k 1à1=û 1 à R(1 à e 1àR ) In all cases: Gas fraction σ = m G / m T and stars m S = m T - m G

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) Numerical (τ(m) 0)

Infall Rate : Gas=const Analytical (IRA) Numerical (τ(m)=0)

Infall Rate : Gas=const Analytical (IRA) Numerical (τ(m) 0)

The metallicity distribution of long-lived stars In order to reach a given metallicity Z, a certain amount of stars has to be created : m S =m-m G or n=1-σ (Gas fraction σ = m G /m and Star fraction n = m S /m) ð 1 Z = p ln á =) û = exp à ñ Z à p û For a system of final metallicity Z 1 and n 1 =1-σ 1 the cumulative metallicity distribution (CMD) is : n(<z) n 1 1àû = 1àû1 and the differential metallicity distribution (DMD) is d(n=n 1 ) ln(10) Z d(logz) = 1àexp(àZ1 =p) p e àz=p DMD = max for Z = p Allows to determine p from observations! Independent of system s history 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 p EFF = 1àR 1àR+k p TRUE 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)

For SPH and Chemodynamical models: Single Stellar Population (SSP) method ï i (t) = R M t M U Y i (M)Ñ(t à ü(m))ð(m)dm (9) Burst of star formation τ(m) years ago Ejecta of star M, released after time τ after the burst t-τ(m) years dï i (t; M) = Y i (M)Ñ(t à ü(m)) Ð(M)dM dt (10) dt ï i (t) = R t t 0 Y i (M)Ñ(t àü(m)) dn dt dt (10a) = R t Y t 0 Ñ(t à ü(m))dt i (M)dN dt (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

Stellar death rate dn/dt = dn/dm x dm/dt = IMF x slope (Mass vs lifetime) Lifetimes of stars (in millions of years) Mass distribution of stars (Initial Mass Function)

For a SSP: per unit mass of stars formed Z=Z 10-1 Z 10-2 Z 10-4 Z Z=0 SNIa

Recipes for chemical evolution in Chemodynamical calculations 1) Take lifetimes of stars τ(m) from theory 2) Take tables of yields Y i (M) from theory 3) Adopt an IMF Φ(M) normalised to ΜΦ(M)dM=1 4) Calculate tables of rates R i of release of element I (including SNIa, which requires a prescription for their rate ) 5) Distribute the mass released (m i = Rdt) in neighbouring gas particles 6) Check that Σ X i = 1 in each star and gas particle

Some references 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