BB 1,2 H 3,4 He 7 Li Intergalactic medium Interstellar medium Galaxy formation inflowGal. winds, stripping, mergers Cosmic rays Small stars D, Li Middling stars Big stars Star formation Spallation 6 Li, Be, B WD NS BH SN Explosive r-process Winds, PN, Novae He, 7 Li, C, N D, Li, Be, B ? Nucleosynthesis Flowchart

Lecture 9: Supernova Rates Star-Formation Efficiency, Yield How many supernovae per year for each galaxy type ? Use power-law IMF, Salpeter slope -7/3 = Limits of validity, not well known 20 M  0.1 M  8 M  slope = -7/3 = Supernova limit

“Universal” IMF (Kroupa 2002) log( M / M  )  MW MC GC local log( M / M  ) M42 M35 Pleiades local  ~ - 7/3 M > 1 M  - 4/ M  - 1/3 M < 0.1 M 

Number of stars : Fraction of stars with M > 8 M  ( for B = -7/3 ) 500 stars --> 1 supernova! Most stars at low-mass end! Integrating a Power-Law IMF

Supernovae are rare, but each is very massive. What fraction of the mass goes into SNe? Most of mass is in low-mass stars. SN Mass Fraction

Median mass: Mean mass:. “Typical” SN Mass.

Spiral Galaxy: SFR: ~ 8 M  yr % have M > 8 M . (8 M  yr -1 ) x ~ 0.6 M  yr -1 go into SNe SN rate: (fewer seen due to dust) Irregular Galaxy: ~10x this rate during bursts (1 SN per 2 yr)! No SNe between bursts... SN Rates vs Galaxy Type

SN Rates: Ellipticals t * = 1 Gyr e-folding time t = 10 Gyr age  = 0.95 efficiency M 0 = M  total mass = initial gas mass Gas consumption: Star formation: SN rate: 3 SN per 10 5 yr. Negligible!.... gas stars

What Star Formation Efficiency  and Yields of H, He and Metals ? X = 0.75 Y = 0.25 Z = 0.00 X = ? Y = ? Z = ? M G = M 0 M S = 0 M G = 0 M S = M 0 M G = (1-  ) M 0 M S =  M 0  = ? KABOOM!

Estimates for efficiency , yield in X, Y, Z Assume: 1.Type-II SNe enrich the ISM. (Neglect: Type-I SNe, stellar winds, PNe,....) 2.Closed Box Model: (Neglect: Infall from the IGM, outflow to the IGM) 3.SN 1987A is typical Type-II SN. Better models include these effects. What do we know about SN 1987A?

SN 1987A 23 Feb 1987 in LMC Brightest SN since 1604! First SN detected in neutrinos. Visible (14 --> 4.2 mag) to naked eye, in southern sky. Progenitor star visible: ~20 Msun blue supergiant. 3- ring structure (pre-SN wind) UV flash reached inner ring in 80 d. Fastest ejecta reached inner ring in ~6 yr. Fast ejection velocity v~c/30~11,000 km/s. Slower (metal-enriched) ejecta asymmetric.

SN 1987A 23 Feb 1987 in LMC Brightest SN since 1604! First SN detected in neutrinos. Visible (14 --> 4.2 mag) to naked eye, in southern sky. Progenitor star visible: ~20 Msun blue supergiant. 3- ring structure (pre-SN wind) Shockwave reaches inner ring

Use SN 1987A to calculate  and yield. SN 1987A: progenitor star mass = 20 M  remnant neutron star mass = 1.6 M  mass returned to the ISM = 18.4 M  From IMF, 7.2% of M S is in stars with M > 8 M   = Fraction of M S returned to ISM: Star Formation Efficiency  = fraction of M S retained in stars: Star Formation Efficiency

SN 1987A Lightcurve 56 Ni => 56 Co 6d half-life 56 Co => 56 Fe 78d half-life Powered by radioactive decay of r-process nuclei. Use to measure metal abundances in ejected gas.

X, Y, Z of ejecta from SN1987A Initial mass~ 20 M  NS mass~ 1.6 M  Mass ejected~ 18.4 M  in H9.0 M  He7.0 M  = 18.4 M  Z2.4 M  }

Q1: What changes to the particle content of the expanding Universe occur at the epochs of: Annihilation: – pair soup -> quark soup (10 9 photons/quark) Baryogenesis: – quarks bound (by strong force) into baryons. – UUD = proton DDU = neutron Nucleosynthesis: –Atomic nuclei: 75% H, 25% He, traces of Li, Be Recombination: –Neutral atoms form as free electrons recombine – photons fly free

Q2: Given present-day density parameters  M = 0.3 for matter and  R = 5x10 -5 for radiation, at what redshift z were the energy densities equal ?

Q3 a) Evaluate the neutron/proton ratio in thermodynamic equilibrium at high and low T. b) Evaluate the n/p ratio and Y p if m n = m p.

Q4 Alien’s CMB-meter reads 5.1K and 4.9K in the fore and aft directions. Evaluate the velocity. Are humans present on Earth at this time?

Assume a Universe filled with uniform density fluid. [ OK on large scales > 100 Mpc ] Density: Energy density: Critical density: 3 components: 1. Radiation 2. Matter “Dark Matter” baryons 3. “Dark Energy” Total Cosmological Models Only ~4% is matter as we know it!

Cold Matter: ( m > 0, p << mc ) Radiation: ( m = 0 ) Hot Matter: ( m > 0, p >> mc ) Energy Density of expanding box

3 Eras: radiation…matter…vacuum

Q1: Given the density parameters   =0.3 for matter and   =0.7 for Dark Energy, evaluate the redshift z at which the energy densities of matter and Dark Energy are equal.   =    crit ~ R z = R 0 / R   =    crit ~ R 0     when     z       1+z = (   /   ) 1/3 = (  /  ) 1/3 = z = 0.326

Q2: What changes to the particle content of the expanding Universe occur at the following epochs: Annihilation: particles and anti-particles annihilate, producing photons. Small excess of particles (~1 per 10 9 photons) Baryogenesis: free quarks confined by strong force in (colourless) groups of 3 producing neutrons (ddu) and protons (uud). Nucleosynthesis: protons and neutrons bind to form 2 D, then 4 He. Y p set by p/n ratio, as virtually all n go into 4 He leaving residual p as H. Recombination: H and He nuclei capture free electrons. Universe now transparent to photons.

Q3: If the neutron decay time were 1 s, rather than 900s, what primordial helium abundance Y p would emerge from Big Bang Nucleosynthesis? n(t) = n(0) exp(- t /  ) p(t) = p(0)+(n(0)-n(t)) t~300s  = 900s => 1s Y p = 2n/(p+n) => 0 since virtually all neutrons decay.

Q4: Name and describe three effects that give rise to anisotropy in the Cosmic Microwave Background, indicating which are most important on angular scales of 10, 1 and 0.1 degrees. 10 o Sachs-Wolf effect - photons last scattered from higher-density regions lose energy climbing out of the potential well. 1 o Doppler effect - velocity of gas on last-scattering surface shifts photon wavelengths. 0.1 o Sunyaev-Zeldovich effect - re-ionised gas (e.g. X-ray gas in galaxy clusters) scatters CMB photons passing thru, changing photon direction and energy.

= fraction of M 0 in gas = fraction of M 0 that has been turned into stars In dimensionless form slope = -  OK, since some gas is recycled.