GALAXIES 626. The Milky Way II. Chemical evolution:

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1 GALAXIES 626 The Milky Way II. Chemical evolution:

2 Chemical evolution Observation of spiral and irregular galaxies show that the fraction of heavy elements varies with the fraction of the total mass which is in the form of gas: heavy element abundance gas fraction

3 What we need to model galactic chemical evolution Initial conditions (open or closed box; chemical composition of the gas) Birthrate versus mass SFRxIMF Stellar yields (how elements are produced and inserted into the ISM) Gas flows (infall, outflow, radial flow)

4 Gas Infall at the present time

5 Summary of Nucleosynthesis During the Big Bang light elements are formed, Spallation process in the ISM produces 6Li, Be and B Supernovae II produce alpha elements (O, Ne, Mg, Si, S, Ca), some Fe

6 Summary of Nucleosynthesis Type Ia SNe produce mainly Fe and Fe peak elements plus some traces of elements from C to S

7 Type Ia SN nucleosynthesis A Chandrasekhar mass (1.44 Msun) explodes by C deflagration C deflagration produces 0.6 Msun of Fe plus traces of other elements from C to Si

8 Type II SNe Type II SNe arise from the core collapse of massive stars (M=8 40 Msun) and produce mainly alpha elements (O, Mg, Si, Ca...) and some Fe

9 Stellar Yields We call stellar yield the newly produced and ejected mass of a given chemical element by a star of mass m Stellar yields depend upon the mass and the chemical composition of the parent star

10 Stellar Yields Low and intermediate mass stars (0.8 8 Msun): produce He, N, C They die as C O white dwarfs, when single, and can die as Type Ia SNe when binaries Massive stars (M>8 10 Msun): produce mainly alpha elements, some Fe, light and explode as core collapse SNe

11 Primary and Secondary elements We define a primary element as an element produced directly from H and He A typical primary element is carbon or oxygen which originate from the 3 alpha reaction We define a secondary element an element produced starting from metals already present in the star at birth (e.g. Nitrogen produced in the CNO cycle)

12 Simple Model and Secondary Elements The solution of the Simple model of chemical evolution for a secondary element Xs formed from a seed element Z Xs is proportional to Z^(2) Xs/Z goes like Z

13 Primary versus secondary Figure from Pettini et al. (2002) Small dots are extragalactic HII regions Red triangles are Damped Lyman alpha systems (DLA) Dashed lines mark the solution of the simple model for a primary and a secondary element

14 Stellar Yields Oxygen yields from massive stars Different studies agree on O yields Oxygen increases continuously with stellar mass from 10 to 40 Msun Not clear what happens for M>40 Msun

15 Stellar Yields Yields for Fe in massive stars

16 Stellar Yields Mg yields from massive stars Big differences among different studies Mg yields are too low to reproduce the Mg abundances in stars

17 The returned fraction We define returned fraction the amount of mass ejected into the ISM by an entire stellar generation Instantaneous recycling approximation (IRA) is assumed, namely stellar lifetimes of stars with M> 1 Msun are neglected and all more massive stars evolve instantaneously

18 The Yield per stellar generation The yield per stellar generation of a single chemical element, can be defined as Where p_im is the stellar yield and the instantaneous recycling approximation has been assumed

19 Instantaneous Recycling Approximation The I.R.A. states that all the stars with masses < 1 Msun live forever but also that the stars with masses > 1 Msun die instantaneously (poor approximation) I.R.A. affects mainly the chemical elements produced on long timescales (e.g. N and Fe)

20 POSSIBLE MODELS a) Start from a gas cloud already present at t=0 (monolithic model). No flows allowed (closed box) OR b) Assume that the gas accumulates either quickly or slowly and the system undergoes inflows and outflows (open model) c) We assume that the gas at t=o is primordial (no metals) OR d) We assume that the gas at t=o is pre enriched by Pop III stars

21 Simplest model is the one-zone model. Consider the history of an annulus of a spiral galaxy at some radius R. Make several simplifying assumptions: No material (gas, stars) enters or leaves the annulus Initially the annulus contains only gas, with no heavy elements (i.e. just hydrogen, helium) As stars are formed, massive stars explode `instantaneously as supernovae, returning enriched gas to the ISM Turbulent motions keep the gas well mixed, so it has a single well-defined composition How does the metal fraction of the gas evolve with time?

22 Let mass of interstellar gas in annulus be Mg Mass of heavy elements in gas Mh Define metallicity: Zº Mh Mg Suppose the mass of stars at this time is Ms Imagine forming new stars, with mass Ms Of these: Stars with mass M > 8 Solar masses explode rapidly as supernovae, returning metals to the ISM Lower mass stars, with mass Ms, remain The mass of heavy elements produced by this episode of star formation is p Ms, defining the yield p.

23 Total change in the mass of heavy elements due to star formation is then: DM h = pdm s ZDM s = p Z DM s existing metals locked up in low mass stars Corresponding change in metallicity is: DZ =D Mh Mg = DM h Mg Mh M 2g DM g = By conservation of mass: DM s = DM g 1 Mg DM h ZDM g

24 Combining the two previous equations get: DZ = p DM g Mg Can write this as a differential equation: dm g dz = Mg p If p is a constant (ie does not vary between subsequent generations of stars), then this integrates immediately to give: Z t = p ln [ ] Mg t Mg 0 Gas mass over total mass (using assumption that Z(t=0) was zero). Relation of this form is very roughly what is observed in some galaxies.

25 Simple Model by Element If we assume that Xi is the abundance by mass of an element i, we have: where

26 Abundance ratios Under the assumption of the instantaneous recycling approximation the ratio of two abundances is equal to the ratio of the corresponding yields:

27 When the I.R.A. is relaxed it is no longer true that the ratio between the abundances of two different elements is equal to the ratio of the corresponding yield because of the time dependent effects

28 The G-dwarf problem A basic requiremenf for a model is that it predict the relative numbers of low mass stars with different metallicities. Does the simple model work? All stars with metallicity < Z must have been formed at time t < t1. Mass of such stars is: [ ] M s Z t 1 = M s t 1 = M g 0 M g t 1 Mg 0 [ 1 e / p ] Z t 1 Apply this analysis to the Solar neighborhood. Ratio Mg(t) / Mg(0) is the ratio of the surface density of gas to the total surface density of stars + gas near the Sun. Approximately 0.1. Metallicity of this gas is Z ~ Derive p = using previous equation.

29 Using this estimate of p, what mass of stars should have metallicity Z < 0.25 Solar value (ie Z < 0.005)? [ M s [ Z ] =M g 0 1 e / ] Find that roughly half of the stars should be this metal poor. Observations suggest that only 2% of F and G stars near the Sun have this low a metallicity! G-dwarf problem. What s wrong with the model? p is not a constant (required trend seems unlikely) Region near the Sun is not a closed box - gas enters and / or leaves Initial metallicity was non-zero

30 G dwarf distribution

31 Could radial flows in the disk do this?

32 Stars near the Sun Stars have random velocities w.r.t. LSR Spiral structure increases random velocities over time Hipparcos data

33 Spiral structure Local Standard of Rest (LSR) on circular(?) orbit around GC Shifts stars radially Sun has probably moved out ~2kpc N body simulation

34 Pollution Older stars have fewer heavy elements Radial migration leads to big spread in [Fe/H] at given age

35 Sun more metal rich than local gas even now Sun probably formed ~2 kpc nearer centre not nearly large enough effect however

36 Change the overall assumptions? The Simple Model of galactic chemical evolution assumes... One zone, closed box model (no infall or outflow) IMF constant in time Instantaneous recycling approximation Instantaneous mixing approximation

37 The outflow law The rate of gas loss from a galaxy through a galactic wind can be expressed as:

38 Simple model with outflow

39 The Infall law The infall rate can simply be constant in space and time Or described by an exponential law:

40 Simple model with infall

41 Complete Equations (including time dependence)

42 Definitions of variables dgi/dt is the rate of time variation of the gas fraction in the form of an element i Xi(t) is the abundance by mass of a given element i Qmi is a term containing all the information about stellar evolution and nucleosynthesis

43 Definition of variables A = is the fraction in the IMF of binary systems of that particular type to give rise to Type Ia SNe. B=1 A Tau_m is the lifetime of a star of mass m f(mu) is the distribution function of the mass ratio in binary systems A(t) and W(t) are the accretion and outflow rate, respectively

44 The formation of the Milky Way Eggen, Lynden Bell & Sandage (1962) suggested a rapid collapse lasting 300 Myr for the formation of the Galaxy Searle & Zinn (1978) proposed a central collapse but also that the outer halo formed by merging of large fragments taking place over a timescale > 1Gyr

45 Different approaches in modelling the MW Serial approach: halo, thick and thin disk form as a continuous process Parallel approach: the different galactic component evolve at different rates but they are inter connected

46 Different approaches in modelling the MW Two infall approach: halo, thick and thin disk form out of different infall episodes Focus on this...

47 A scenario for the formation of the Galaxy One two infall model assumes two main episodes of gas accretion During the first one the halo and bulge formed, the second gave rise to the disk

48 Recipe for this two infall model SFR Kennicutt s law with a dependence on the surface gas density (exponent k=1.5) plus a dependence on the total surface mass density (feedback). Threshold of 7 solar masses per pc squared IMF, Scalo (1986) normalized over a mass range of solar masses Exponential infall law with different timescales for inner halo (1 2 Gyr) and disk (inside out formation with 7 Gyr at the S.N.)

49 Solar Vicinity We study first the solar vicinity, namely the local ring at 8 kpc from the galactic center Then we study the properties of the entire disk from 4 to 22 Kpc

50 Stellar Lifetimes

51 The star formation rate (threshold effects)

52 Stellar abundances [X/Fe]= log(x/fe)_star log(x/fe)_sun is the abundance of an element X relative to iron and to the Sun The most recent accurate solar abundances are from Asplund et al. (2005) Previous abundances from Anders & Grevesse (1989) and Grevesse & Sauval (1998) The main difference is in the O abundance, now lower

53 Predicted SN rates Type II SN rate (blue) follows the SFR Type Ia SN rate (red) increases smoothly (small peak at 1 Gyr)

54 Time delay model Blue line= only Type II SNe to produce Fe Red line= only Type Ia SNe to produce Fe Black line: Type II SNe produce 1/3 of Fe and Type Ia SNe produce 2/3 of Fe

55 Detailed predictions of the two infall model

56 Different timescales for disk formation

57 G dwarf distribution Ok for this SFR history

58 Many constraints...

59 Abundance Gradients The abundances of heavy elements decrease with galactocentric distance in the disk Gradients of different elements are slightly different (depend on their nucleosynthesis and timescales of production)

60 How does the gradient form? If one assumes the disk to form inside out, namely that first collapses the gas which forms the inner parts and then the gas which forms the outer parts Namely, if one assumes a timescale for the formation of the disk increasing with galactocentric distance, the gradients are well reproduced

61 Abundance gradients Predicted and observed abundance gradients Data from HII regions, PNe and B stars, red dot is the Sun The gradients steepen with time (from blue to red)

62 The Galactic Bulge A model for the Bulge (green line, Ballero et al. 2006) Yields from Francois et al. (04), SF efficiency of 20 Gyr^( 1), timescale of accretion 0.1 Gyr Data from Zoccali et al. 06, Fulbright et al. 06, Origlia &Rich (04, 05)

63 The Galactic Bulge Metallicity Distribution of Bulge stars, data from Zoccali et al. (2003) and Fulbright et al. (2006) (dot dashed) Models from Ballero et al. 06, with different SF eff.

64 The Galactic Bulge Models with different IMF The best IMF for the Bulge is flatter than in the S.N: and flatter than Salpeter Best IMF: x=0.95 for M> 1 solar mass and x=0.33 below

65 Conclusions on the Bulge The best model for the Bulge suggests that it formed by means of a strong starburst The efficiency of SF was 20 times higher than in the rest of the Galaxy The IMF was very flat, as it is suggested for starbursts The timescale for the Bulge formation was 0.1 Gyr and not longer than 0.5 Gyr

66 Conclusions on the Milky Way The Disk at the solar ring formed on a time scale not shorter than 7 Gyr The whole Disk formed inside out with timescales of the order of 2 Gyr in the inner regions and 10 Gyr in the outer regions The inner halo formed on a timescale not longer than 2 Gyr Gradients from Cepheids are flatter at large Rg than gradients from other indicators

67 GALAXIES 626 End