BB1,2H 3,4He 7Li

Intergalactic medium

Interstellar medium

Galaxy formation inflow Gal. winds, stripping, mergers

Cosmic rays

Small stars D, Li

Middling stars

Big stars

Star formation

Spallation 6Li, Be, B

WD NS BH

SN

Explosive r-process

Winds, PN, Novae He, 7Li, C, N

D, Li, Be, B

?

Nucleosynthesis Flowchart

Lecture 9: Supernova RatesStar-Formation Efficiency, Yield

How many supernovae per year for each galaxy type ?

Use power-law IMF, Salpeter slope -7/3 = -2.33

.

.Limits of validity, not well known

20 M0.1 M8 M

slope = -7/3 = -2.33

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

- 4/3 0.1 - 1 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-1. 7.2% have M > 8 M .

(8 M yr-1) x 0.072 ~ 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: Ellipticalst* = 1 Gyr e-folding time

t = 10 Gyr age= 0.95 efficiencyM0 = 1011 M total mass = initial gas massGas consumption:

Star formation:

SN rate:

3 SN per 105 yr. Negligible!

..

..

gas

stars

What Star Formation Efficiency and Yields of H, He and Metals ?

X = 0.75Y = 0.25Z = 0.00

X = ?Y = ?Z = ?

MG = M0

MS = 0

MG = 0MS = M0

MG = (1-) M0

MS = M0

= ?

KABOOM!

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 1987A23 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 1987A23 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 2003.

20032010

Use SN 1987A to calculate and yield.

SN 1987A: progenitor star mass = 20 M remnant neutron star mass = 1.6 Mmass returned to the ISM = 18.4 M

From IMF, 7.2% of MS is in stars with M > 8 M

= Fraction of MS returned to ISM:

Star Formation Efficiency = fraction of MS retained in stars:

Star Formation Efficiency

SN 1987A Lightcurve

56Ni => 56 Co 6d half-life 56Co => 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 H 9.0 M

He 7.0 M = 18.4 M

Z 2.4 M

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Q1: What changes to the particle content of the expanding Universe occur at the epochs of:

• Annihilation: – pair soup -> quark soup (109 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 Yp if mn = mp.

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-3 1 + z = R0 / R= crit ~ R0

whenz

• 1+z = ( / )1/3 = ( / )1/3 = 1.326• 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 109 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 2D, then 4He. Yp set by p/n ratio, as virtually all n go into 4He 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 Yp would emerge from Big Bang Nucleosynthesis?

• n(t) = n(0) exp(- t / )• p(t) = p(0)+(n(0)-n(t))• t~300s = 900s => 1s• Yp = 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.

• 10o Sachs-Wolf effect - photons last scattered from higher-density regions lose energy climbing out of the potential well.

• 1o Doppler effect - velocity of gas on last-scattering surface shifts photon wavelengths.

• 0.1o 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 M0 in gas

= fraction of M0 that has beenturned into stars

In dimensionless form

slope = -

OK, since some gas is recycled.