Galaxies Astro 530 Prof. Jeff Kenney. CLASS 22 April 11, 2018 Chemical EvoluFon in Galaxies PART 1

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1 Galaxies Astro 530 Prof. Jeff Kenney CLASS 22 April 11, 2018 Chemical EvoluFon in Galaxies PART 1 1

2 Gas is the raw material for star formafon, but where does the gas in galaxies come from? 1. primordial (from Big Bang) 2. reprocessed & recycled, through stars Figuring out how much the raw material in stars has been recycled through previous generafons of stars offers powerful evidence on galaxy evolufon!

3 Elemental abundances Heavy elements are produced in stars, and elemental ( chemical ) abundances offer a record through which we can trace star formafon histories & galaxy evolufon Abundances of elements heavier than helium ( metals ) vary among stars and galaxies; abundances vary strongly with galaxy mass In most small systems (star clusters and dwarf galaxies), abundances are relafvely uniform, but in larger galaxies there are systemafc variafons with radius and large dispersions at any locafon

4 Q: Why does the amount of elements heavier than Helium indicate the amount of processing thru stars?

5 Q: Why does the amount of elements heavier than Helium indicate the amount of processing thru stars? Why elements heavier than Helium rather than heavier than Boron?

6 Solar system elemental abundances made mostly in Big Bang (A=1-5) made mostly in stars & supernovae A= Solar abundances: Hydrogen: M H /M gas = 0.74 Helium: M He /M gas = 0.24 heavies (Everything else): M h /M gas = 0.02 = Z sun ( metals )

7 Astronomy definifon of abundance rafo: [Fe/H] is logarithmic rafo of Fe/H in star relafve to sun Fe is pre6y good indicator of overall heavy element abundance. Some=mes [Fe/H] represents average heavy- element abundance not just Iron. [Fe/H] = 0 solar abundance [Fe/H] = - 1 1/10 th solar abundance [Fe/H] = - 2 1/100 th solar abundance [Fe/H] = - 3 1/1000 th solar abundance 7

8 Q: What is special about iron? Iron is the most =ghtly bound nucleus Iron 56 Fe 26 protons 30 neutrons Nuclear reacfons involving Fe require energy rather than release energy once core makes iron it can t generate any more fusion energy to support star

9 Range of heavy element abundances in Milky Way stars: Z = > 3 Z sun [Fe/H] = > 0.5 9

10 Stars with different elemental abundances SDSS SEGUE website [Fe/H]=- 0.9 [Fe/H]=- 0.9 (confnuum removed) [Fe/H]=- 3.4 [Fe/H]=- 3.4 (ConFnuum removed) Hγ Hβ Hα All H lines Stars with fewer heavy elements have: Weaker absorpfon lines of heavy elements Bluer confnuum (fewer absorpfon lines in UV- blue part of spectrum) 10

11 Spectrum of extremely metal- poor halo star with [Fe/H]=- 5.5 (heavy element content 1/300,000 x solar) [Fe/H]=0.0 [Fe/H]=- 5.5

12 Range of heavy element abundances in Milky Way: Z = > 3 Z sun SUN: 1 Z sun = 0.02 = M h /M gas [Fe/H] = > 0.5 SUN: [Fe/H] = 0.0 There are no stars in Milky Way with primordial = Big Bang abundances, i.e. Z 0, i.e. PopulaFon III stars. All stars in Milky Way formed from gas that was polluted at least a bit by previous generafon(s) of stars! 12

13 Q: Stars make new elements but not all the new elements get out of the stars. What stellar material has not been returned to space?

14 not all mass in stars get returned to ISM Cores of stars Low mass stars

15 not all mass in stars get returned to ISM Cores of stars Low mass stars Q: Why haven t low mass stars returned much gas to ISM?

16 Some ma-er does not get returned to ISM: Low mass stars MS lifefme for 0.7 M sun star = τ MS = 14 Gyr* > age of universe = 13.8 Gyr *MS lifefme depends on metallicity for 0.7M sun : t MS = 13 Gyr [Fe/H]=- 2.5 ; t MS = 15 Gyr [Fe/H]=- 1.5

17 Some ma-er does not get returned to ISM: Low mass stars MS lifefme for 0.7 M sun star = τ MS = 14 Gyr* > age of universe = 13.8 Gyr - > so no low mass stars have ever evolved off the MS or returned much mass to the ISM anywhere in the universe! *MS lifefme depends on metallicity for 0.7M sun : t MS = 13 Gyr [Fe/H]=- 2.5 ; t MS = 15 Gyr [Fe/H]=- 1.5

18 Some marer does not get returned to ISM Cores of stars White dwarf made by stars with M<1.4M sun Neutron star made by stars with ~1.4<M<~8M sun Black Hole made by stars with M<~8M sun

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20 This stuff gets out into ISM This stuff doesn t

21 One- Zone / Closed Box Model of chemical evolufon Simplest possible chemical evolufon model Nothing enters or leaves box

22 Simplest possible chemical evolufon model: One- Zone / Closed Box Nothing enters or leaves box, gas well mixed t = 0 no stars 100% H+He gas no heavy el. gas gas metallicity=0 t = later some stars lots H+He gas some heavy el. gas gas metallicity=low t = much later mostly stars lirle H+He gas lirle heavy el. gas gas metallicity=high

23 One- Zone / Closed Box Model Simplest possible chemical evolufon model Nothing enters or leaves box IniFally mass in box is 100% gas, no heavy elements, no stars As Fme goes on, stars form from gas, massive stars explode and return H, He, and heavies to ISM; gas in ISM is gradually consumed and remaining gas becomes increasingly polluted by heavy elements Gas is always well- mixed within box Some stellar systems are roughly consistent with CBM, but many are not, and are instead more consistent with a leaky or accre=ng box

24 M g = mass of interstellar gas M h = mass of heavy elements in interstellar gas Z = M h / M g = metallicity (Z sun = 0.02) M s total mass in stars

25 M g = mass of interstellar gas M h = mass of heavy elements in interstellar gas Z = M h / M g = metallicity (Z sun = 0.02) M s total mass in stars Consider a suitably short Fme interval Δ. What are net changes in this short Fme? Δ M s mass of new stars formed in Fme interval Δ ΔM s mass of new stars locked up in compact remnants & long- lived stars (in Δ) Δ M s - ΔM s mass of new stars returned to ISM (in Δ)

26 This stuff gets out into ISM Part of ΔM s - ΔM s This stuff doesn t Part of ΔM s

27 This stuff gets out into ISM Part of ΔM s - ΔM s This stuff doesn t Part of ΔM s what contributes to other parts of ΔM s and ΔM s - ΔM s?

28 Consider a suitably short Fme interval Δ What is net change in heavy element content (mass) of ISM in a short Fme interval? Net change = GAIN LOSS This is complex in general, but becomes much simpler with assumpfon of instantaneous recycling

29 Instantaneous recycling! approximafon Neglect delay between formafon of generafon of stars and the ejecfon of elements by those stars as they evolve (ignore the change in ISM metallicity that happens between star formafon & later stages of stellar evolufon that return gas to ISM)

30 Instantaneous recycling! approximafon Neglect delay between formafon of generafon of stars and the ejecfon of elements by those stars as they evolve (ignore the change in ISM metallicity that happens between star formafon & later stages of stellar evolufon that return gas to ISM) OK for elements produced by core collapse SN (Type II, Ib) since these happen in massive stars which explode <100 Myr << T H (=14 Gyr) azer formafon less OK for elements produced by less massive stars (Type Ia SN, PN, binary NS) since these occur >1 Gyr azer formafon (so more correct models take this Fme delay into account)

31 LOSS =?? LOSS write an expression for the mass of heavy elements locked up in newly- formed low mass stars and compact remnants, in a short Fme interval

32 LOSS LOSS = ZΔM s (in IR appx) Mass of heavy elements locked up in newly- formed low mass stars and compact remnants Massive stars blow up so fast that we ignore their temporary capture of heavy elements ΔM s mass of new stars locked up in compact remnants & long- lived stars (in Δ)

33 GAIN =?? GAIN write an expression for the Mass of heavy elements produced by newly- formed high- mass stars and returned to ISM in a short Fme interval

34 GAIN GAIN = p (Δ M s - ΔM s ) (in IR appx) Mass of heavy elements produced by newly- formed high- mass stars and returned to ISM p = fracfon of mass returned to ISM by massive stars which are metals produced by those stars Δ M s - ΔM s mass of new stars returned to ISM (in Δ)

35 GAIN GAIN = p (Δ M s - ΔM s ) (in IR appx) Mass of heavy elements produced by newly- formed high- mass stars and returned to ISM p = fracfon of mass returned to ISM by massive stars which are metals produced by those stars We can also express: Δ M s - ΔM s mass of new stars returned to ISM (in Δ) ΔM s mass of new stars locked up in compact remnants & long- lived stars (in Δ) GAIN = pδm s Even though the low mass stars & compact remnants aren t creafng the metals which pollute the ISM, we can write it this way because it s mathemafcally convenient & easier to measure ΔM s than Δ M s ΔM s

36 follow the fate of gas which forms a bunch of stars for example, start with 100 M sun which forms stars.

37 follow the fate of gas which forms a bunch of stars for example, start with 100 M sun which forms stars. some fracfon (typically ~60%) is mass locked up in long- lived stars and compact remnants ( ~60 M sun ).

38 follow the fate of gas which forms a bunch of stars for example, start with 100 M sun which forms stars. some fracfon (typically ~60%) is mass locked up in long- lived stars and compact remnants ( ~60 M sun ). some fracfon (typically ~40%) is returned to ISM (~40 M sun ).

39 follow the fate of gas which forms a bunch of stars for example, start with 100 M sun which forms stars. some fracfon (typically ~60%) is mass locked up in long- lived stars and compact remnants ( ~60 M sun ). some fracfon (typically ~40%) is returned to ISM (~40 M sun ). some fracfon of the mass returned to ISM are metals made by stars (~1.2 M sun ).

40 follow the fate of gas which forms a bunch of stars for example, start with 100 M sun which forms stars. some fracfon (typically ~60%) is mass locked up in long- lived stars and compact remnants ( ~60 M sun ). some fracfon (typically ~40%) is returned to ISM (~40 M sun ). some fracfon of the mass returned to ISM are metals made by stars (~1.2 M sun ). à new- metal fracfon of mass returned to ISM is p = 1.2M sun /40M sun = 0.03 à but yield p = 1.2M sun /60M sun = 0.02

41 Meaning of yield p Yield of heavy elements by parfcular stellar generafon Yield p = rafo of mass in metals produced by stars and returned to ISM to mass locked up in long- lived stars and compact remnants Dimensionless number, rafo of masses, like metallicity Normal yield p ~ solar metallicity ~ 0.02 If stars are made from gas that is inifally free of metals, so that Z(0) = 0, the closed box model predicts that, when all the gas is gone, the mean metal abundance of stars is exactly p.

42 LOSS = ZΔM s GAIN = pδm s Loss & gain (with IR appx)

43 on board: derive Z(t)

44 Metallicity of ISM gas in One- Zone / Closed Box Model: Z(t) = - p ln [ M g (t)/m g (0) ] +Z(0) at t=0 start M g (t)/m g (0) =1, Z(t) = Z(0) [ = 0 if no pre- enrichment]

45 evolufon in closed box model 1 1 M gas M stars Z gas 0.37 t 1 t 1 t 1 t t p t

46 Metallicity of ISM gas in One- Zone / Closed Box Model: Z(t) = - p ln [ M g (t)/m g (0) ] +Z(0) at t=0 start M g (t)/m g (0) =1, Z(t) = Z(0) [ = 0 if no pre- enrichment] at t = later (=t 1 ) e.g. M g (t) = 0.37 M g (0) and assume Z(0) =0 so ln [ M g (t)/m g (0) ] ~= ln [0.37] = - 1 so Z(t) = p

47 Metallicity of ISM gas in One- Zone / Closed Box Model: Z(t) = - p ln [ M g (t)/m g (0) ] +Z(0) at t=0 start M g (t)/m g (0) =1, Z(t) = Z(0) [ = 0 if no pre- enrichment] at t = later (=t 1 ) e.g. M g (t) = 0.37 M g (0) and assume Z(0) =0 so ln [ M g (t)/m g (0) ] ~= ln [0.37] = - 1 so Z(t) = p at t = much later, M g (t) << M g (0) e.g. M g (t) = 0.05 M g (0) and assume Z(0) =0 so ln [ M g (t)/m g (0) ] ~= ln [0.05] = - 3 so Z(t) = 3p so can get very metal rich stars but not many (since available gas mass is really low for such stars)

48 evolufon in closed box model 1 1 M gas 0.37 M stars Z gas p t t t when gas supply is 37% of original, gas metallicity = p gas metallicity can get to high values but only once most of gas is gone!

49 we can predict number of stars with different metallicifes in closed box model

50 we can write M s (t)= M s [<Z(t)] since all the stars which exist at any =me t have metallicity of Z(t) or less than Z(t) in CBM, gas metallicity increases smoothly with Fme at Fme t, gas has metallicity Z(t), and a star formed at this Fme has metallicity Z(t) but stars formed at earlier =mes have metallicity <Z(t) so all the stars which exist at any Fme t have metallicity of Z(t) or less than Z(t).

51 derive M s [<Z(t)] expression on board

52 One- Zone / Closed Box Model with Instantaneous Recycling (IR) approximafon (best for elements produced by massive stars, e.g. O, Mg, Si) metallicity of ISM gas Z(t) = - p ln [ M g (t)/m g (0) ] + Z(0) mass in stars as funcfon of metallicity M s [<Z(t)] = M g (0) [1 - exp - {(Z(t)- Z(0))/p} ] mean metallicity of stars azer gas gone Z S = p ~ Z sun Yield p = RaFo of: mass in metals made by stars & returned to ISM to mass locked up in long- lived stars and compact remnants (normal yield ~ solar metallicity ~ 0.02)

53 [Fe/H] in bulge of MW ~fits closed box model closed box model Fe/H distr. roughly matches closed box model with p eff =Z sun =0.02 [although the bulge has fewer very low mass stars than this model predicts! and detailed abundances rafos don t match this model! So CBM gives decent 1 st - order fit to bulge abundances, but not to 2 nd order]

54 Where does the Closed Box Model work? Bulge of Milky Way OK fit (to 1st order) with Closed Box model with IR and reasonable yield p=2x10-2

55 Where does the Closed Box Model work? Bulge of Milky Way OK fit (to 1st order) with Closed Box model with IR and reasonable yield p=2x10-2 BUT Disk of Milky Way is NOT well fit by CBM (not enough low Z stars - - G- dwarf problem )

56 Fe/H of nearby (disk) MW F & G stars vs. age 0.25Z sun very few disk stars with Z<0.25Z sun à G dwarf problem closed box model predicts ~50% of stars should have Z < 0.25 Z sun so CBM is wrong for disk! [Fe/H] < - 0.4