1

H

He

CONeO

PRE-SUPERNOVA STAGE

OSiS

H burning shell

He burning shell

T~4.0×109 K

C burning shell

Ne burning shell

O burning shell

Si burning shell

Fe

2PRE-SUPERNOVA STAGE

The Fe core is partially degenerate

The pressure due to degenerate electrons dominate

3CORE COLLAPSE SUPERNOVAE: ENERGETICS

Basic idea:

Fe core

NS

Energy liberated during collapse:

Energy required for the conversion

The minus sign means the energy content of the final state being lower than that of the initial one

AMU AMUerg 56Fe Nuclei/g

4CORE COLLAPSE SUPERNOVAE: ENERGETICS

Energy required for the electron capture

Energy lost by neutrino emission:

Energy required to unbind the stellar envelope:

Energy emitted through photons:

5CORE COLLAPSE SUPERNOVAE: ENERGETICS

Kinetic Energy of the ejecta:

derived from the observed spectra:

Combining all the energy required to explain the SN display with all the

energy lossess we get

There is still a lot of energy that must be liberated

Whichever is the process responsible for such an emission, getting a core collapse supernova to

explode seems easy!

6CORE COLLAPSE SUPERNOVAE: THE PATH TO INSTABILITY

Following Si burning the core is mainly composed by Iron Peak nuclei @ NSE.

Fe core

1. Photodisintegrations

2. Electron captures

- Contraction

- Increase the fraction of Fe core highly degenerate

Two physical processes rob the iron core of the energy it needs to maintain its pressure and avoid

collapse

- Loss of pressure support

- Decrease the limiting mass for a highly degenerate star

Highly degenerate zone

Limiting Mass

7

Following Si burning the core is mainly composed by Iron Peak nuclei @ NSE.

1. Photodisintegrations

2. Electron captures

- Contraction

- Increase the fraction of Fe core highly degenerate

Two physical processes rob the iron core of the energy it needs to maintain its pressure and avoid

collapse

- Loss of pressure support

- Decrease the limiting mass for a highly degenerate star

Highly degenerate zone

Fe core

Limiting MassWhen the highly degenerate mass

approaches the limiting mass the core becomes unstable and collapses

CORE COLLAPSE SUPERNOVAE: THE PATH TO INSTABILITY

CORE COLLAPSE SUPERNOVAE: COLLAPSE PHASEAnalytic description of core collapse: general

properties

Equation of motion

Mass conservation

By means of some algebra the equation of motion can be written as some algebra

If we assume an adiabatic collapse we have

some algebramass conservationadiabatic collapse

8

Using this last relation the equation of motion becomes

Which, by means of some algebra, can be rewritten as

Assuming which means

we finally get

CORE COLLAPSE SUPERNOVAE: COLLAPSE PHASE

9

Since

must be conserved

the homologous solution

Since the sound speed decreases with the radius, a radius must exist at which the infall velocity exceeds

the sound velocity

A fluid whose pressure is dominated by relativistic, degenerate electron pressure is expected to collapse

homologously

CORE COLLAPSE SUPERNOVAE: COLLAPSE PHASE

10

Inner Core

Outer Core

homologous subsonic

infall

supersonic infall

Sonic point

Maximum infall velocity

Sonic point: the radius at which the infall velocity exceeds the sound speed

Outside the sonic point a free fall solution is approximately valid

During collapse the core naturally splits into an Inner Core

and an Outer Core

CORE COLLAPSE SUPERNOVAE: COLLAPSE PHASE

11

depending on EOS

and

where

(Goldreich & Weber 1980)

During collapse, therefore, the Inner Core Mass decreases with decreasing the electron fraction due to electron captures down to about

CORE COLLAPSE SUPERNOVAE: COLLAPSE PHASE

12

Neutrinos are generated by electron capture on nuclei (dominate) and protons

13CORE COLLAPSE SUPERNOVAE: NEUTRINO TRAPPINGNeutrino opacities are dominated by neutral-current coherent

scattering off heavy nuclei for which the cross section is approximately given by:

(Freedman, 1974, PRD, 9, 1389)

the mean free path is given by:

being

Assuming we get

14CORE COLLAPSE SUPERNOVAE: NEUTRINO TRAPPING

This means that:

Neutrinos escape freely and carry away a bit of energyFrom this point on the neutrinos will not freely stream but must diffuse

At densities the weak interactions also approach an equilibrium (b-equilibirum)

15CORE COLLAPSE SUPERNOVAE: STIFFENNING OF THE EOS AND CORE

BOUNCEAfter neutrino trapping, the collapse proceeds until nuclear densities are reached

The pressure in the inner core increases dramatically

At this point the inner core undergoes a phase transition from a two-phase system of nucleons and nuclei to a one-phase system of bulk nuclear matter: a GIANT NUCLEUS

The EOS stiffens

Fermi effects and the repulsive nature of the nucleon-nucleon interaction potential at short distances

The inner core becomes incompressible, decelerates and rebounds

16CORE COLLAPSE SUPERNOVAE: FORMATION OF THE PROMPT SHOCK

AND SHOCK PROPAGATIONStarting from the center an increasing number of infalling mass shells are stoppedPressure waves travel outward and steepen

Waves accumulate @ sonic pointPrompt shock wave forms and propagates through the outer coreAs the shock propagates out, matter from the outer core continues to fall in supersonically

Numerical simulations show that the initial energy of the shock wave is:

17CORE COLLAPSE SUPERNOVAE: PROPAGATION AND STALLING OF THE

PROMPT SHOCKAs prompt shock propagates out: It dissociates Fe nuclei into free nucleons.

Severe energy losses

Neutrino burst at shock brackout

Limiting mass that can be photodisintegrated:

18CORE COLLAPSE SUPERNOVAE: PROPAGATION AND STALLING OF THE

PROMPT SHOCK

(Limongi & Chieffi 2006, ApJ, 647, 483)

The shock consumes entire kinetic energy still within iron core Shock turns into an accretion shock at a radius between 100 and 200 km, i.e., the matter downstream of the shock has negative velocities and continues falling inward

All state-of-art simulations of stellar core collapse show that:

Prompt explosion fails!

19CORE COLLAPSE SUPERNOVAE: DELAYED EXPLOSION MECHANISM

After the core bounce, a neutron star begins to form at the centerThe newly born neutron star is initially still proton-rich and contains a large number of degenerate electrons and neutrinos.The neutrinos are emitted from their respective neutrinospheres (surfaces of last scattering)

20CORE COLLAPSE SUPERNOVAE: DELAYED EXPLOSION MECHANISM

Between the neutrinosphere and the shock, the material both heats and cools by electron neutrino and antineutrino emission and absorption.

The neutrino heating and cooling have different radial profiles consequently, this region splits into a net cooling region and a net heating region, separated by a gain radius at which heating and cooling balance.

21CORE COLLAPSE SUPERNOVAE: DELAYED EXPLOSION MECHANISM

The persistent neutrino energy deposition behind the shock keeps the pressure high in this region and drives the shock outwards again, eventually leading to a supernova explosion.

22CORE COLLAPSE SUPERNOVAE: DELAYED EXPLOSION MECHANISM

This may take a few 100 ms and requires that during this time interval a few percent of the radiated neutrino energy (or 10–20% of the energy of electron neutrinos and antineutrinos) are converted to thermal energy of nucleons, leptons, and photons.Remember: The canonical explosion energy of a supernova is less than one percent of the total gravitational binding energy lost by the nascent neutron star in neutrinos.The success of the delayed supernova mechanism turned out to be sensitive to a complex interplay of neutrino heating, mass accretion through the shock, and mass accretion through the gain radius.After two decades of research the paradigm of the neutrino driven wind explosion mechanism is widely accepted

BUT

23

The most recent and detailed simulations of core collapse SN explosions show that:

the shock still stalls No explosion is obtained

the energy of the explosion is a factor of 3 to 10 lower than usually observed

Work is underway by all the theoretical groups to better understand the problem and we may expect progresses

in the next futureThe simulation of the explosion of the

envelope is needed to have information on:

the chemical yields (propagation of the shock wave compression and heating explosive nucleosynthesis)

the initial mass-remnant mass relation

THE SUPERNOVA PROBLEM

24

Propagation of the shock wave

through the envelope

Compression and

Heating

Explosive Nucleosynthe

sis

The explosive nucleosynthesis calculations for core collapse supernovae are still based on explosions induced by injecting an arbitrary amount of energy in a (also arbitrary) mass location of the presupernova model and then following the development of the blast wave by means of an hydro code.

• Piston

• Thermal Bomb

• Kinetic Bomb

EXPLOSIVE NUCLEOSYNTHESIS

25EXPLOSION AND FALLBACK

Matter Falling Back

Mass Cut

Initial Remna

nt

Final Remnant

Matter Ejected into the ISMEkin1051 erg

• Piston (Woosley & Weaver)

• Thermal Bomb (Nomoto & Umeda)

• Kinetic Bomb (Chieffi & Limongi)

Different ways of inducing the explosion

FB depends on the binding energy: the higher is the initial mass the higher is the

binding energy

Fe core

Shock WaveCompression and Heating

Induced Expansion

and Explosion

Initial Remna

nt

Injected Energy

26THE HYDRODYNAMICS

Sets the details of the physical conditions (temporal evolution of Temperature and Density) for each explosive burning the detailed products of each explosive burning

27

Since nuclear reactions are very temperature sensitive, this cause nucleosynthesis to occur within few seconds that might otherwise have taken days or years in the presupernova evolution.

CHARACTERISTIC EXPLOSIVE BURNING TEMPERATURES

Where in general:

The typical burning timescale for destruction of any given fuel is:

28CHARACTERISTIC EXPLOSIVE BURNING TEMPERATURES

These timescales for the fuels H, He, C, Ne, O, Si are determined by the major destruction reaction:

and in general are function of temperature and density:

He burning:C burning:

Ne burning:O burning:Si burning:

29CHARACTERISTIC EXPLOSIVE BURNING TEMPERATURES

If we take typical explosive burning timescales of the order of 1s

Explosive C burning

Explosive Ne burning

Explosive O burning

Explosive Si burning

30BASIC PROPERTIES OF THE

EXPLOSION• Behind the shock, the pressure is dominated by radiation• The shock propagates adiabatically

rT1

Fe core

r2

T2

r1

Shock

The peak temperature does not depend on the stellar structure

31

Complete Si

burning

3700

NSE

TiFeCoNi

5000

Incomplete Si burning

NSE

TiCrVMn

Explosive O burning

6400

QSE2 Clusters

SiSArKCa

Explosive Ne burning

11750

SiPClKSc

Explosive C burning

PSc

13400

RADIUS (Km)

No M

od

ificati

on

By combining the properties of the matter at high temperature and the basic properties of the explosion

32ROLE OF THE

PROGENITOR STAR• Mass-Radius relation @ Presupernova

Stage:determines the amount of mass contained in each volume determines the amount of mass processed by each explosive burning.

Complete Si

burning

NSE

ScTiFeCoNi

Incomplete Si burning

QSE2 Clusters

CrVMn

Explosive O burning

QSE1 Cluster

SiSArKCa

Explosive Ne burning

MgAlPCl

Explosive C burning

NeNa

No M

od

ificati

on

INTERIOR MASS

33

• The Ye profile at Presupernova Stage:it is one of the quantities that determine the chemical composition of the more internal zones that reach the NSE/QSE stage

Ye=0.50 56Ni=0.63 – 55Co=0.11 – 52Fe=0.07 – 57Ni=0.06 – 54Fe=0.05Ye=0.49 54Fe=0.28 – 56Ni=0.24 – 55Co=0.16 – 58Ni=0.11 – 57Ni=0.08

T=5∙109 K r=108 g/cm3

• The Chemical Composition at Presupernova Stage:it determines the final composition of all the more external regions undergoing explosive (in non NSE/QSE regine)/hydrostatic burnings

ROLE OF THE PROGENITOR STAR

34

Complete Si

burning

NSE

Sc,Ti,FeCo,Ni

Incomplete Si burning

QSE2 Clusters

Cr,V,Mn

Explosive O burning

QSE1 ClusterSi,S,ArK,Ca

Explosive Ne burning

Mg,Al,P,Cl

Explosive C burning

Ne,Na

No M

od

ificati

on

INTERIOR MASS

THE CHEMICAL COMPOSITION OF A MASSIVE STAR AFTER THE EXPLOSION

EXPLOSIVE BURNINGS

35

During the propagation of the shock wave through the mantle some amount of matter may fall back onto the compact remnantIt depends on the binding

energy of the star and on the final kinetic energy

FALLBACK AND FINAL REMNANT

36

The Iron Peak elements are those mostly affected by the properties of the explosion, in particular the amount of

Fallback.

COMPOSITION OF THE EJECTA

37

Sic

Sc,Ti,FeCo,Ni

56Ni

Sii

Cr,V,Mn

56Ni

Ox

Si,S,ArK,Ca

Fe Core

Initial Mass Cut

Sic

Sc,Ti,FeCo,Ni

56Ni

Sii

Cr,V,Mn

56Ni

Si,S,ArK,Ca

Fe Core

Ox

Initial Mass Cut

Sic

Sc,Ti,FeCo,Ni

56Ni

Sii

Si,S,ArK,Ca

56Ni

Cr,V,Mn

Ox

Sic

Sc,Ti,FeCo,Ni

56Ni

Sii

Cr,V,Mn

56Ni

Si,S,ArK,Ca

Ox

Final Mass Cut

THE EJECTION OF 56NI AND HEAVY ELEMENTS

The amount of 56Ni and heavy elements strongly depends on the Mass Cut

Remnant

38THE EJECTED 56NI

In absence of mixing a high kinetic energy is required to eject even a small amount of 56Ni

39MIXING BEFORE FALLBACK MODEL

56Ni and heavy elements can be ejected even with extended fallback

Sic

Sc,Ti,FeCo,Ni

56Ni

Sii

Cr,V,Mn

56Ni

Ox

Si,S,ArK,Ca

Fe Core

Initial Mass Cut

Sic

Sc,Ti,FeCo,Ni

Sii

Cr,V,Mn

56Ni

Ox

Si,S,ArK,Ca

Mixing Region

Fe Core

Initial Mass Cut

Sic

Sc,Ti,FeCo,Ni

Sii

Cr,V,Mn

56Ni

Ox

Si,S,ArK,Ca

Mixing Region

Final Mass Cut

Isotopes produced in

the innermost

zones

Remnant

56Ni 56Ni

56Ni

56Ni

56Ni

56Ni

56Ni

56Ni

40

No Mas

s Loss

Final Ma

ss

He-Cor

e Mass

He-CC Mass

CO-Core Mass

Fe-Core Mass

WNL

WNE WC/WO

Remnant Mass

Neutron Star

Black Hole

SNII SNIb/c

Fallback

RSG

Z=Z

E=1051 ergNL00 WIND

THE FINAL FATE OF A MASSIVE STAR

41THE YIELDS OF MASSIVE STARS

42THE YIELDS OF MASSIVE STARS

43CHEMICAL ENRICHMENT DUE TO A SINGLE MASSIVE STAR

The Production Factors (PFs) provide information on the global enrichment of the matter and its distribution

Solar MetallicityModels

44CHEMICAL ENRICHMENT DUE A GENERATION OF MASSIVE STARS

Yields averaged over a Salpeter

IMF

The integration of the yields provided by each star over an initial mass function provide the chemical

composition of the ejecta due to a generation of massive stars

Production Factors averaged over a Salpeter

IMF

45CHEMICAL ENRICHMENT DUE TO A GENERATION OF MASSIVE STARS

~2 < PF( C < Z < As ) < ~11 massive stars significantly contribute

to the production of these elements

46THE ROLE OF THE MORE MASSIVE

STARS

Large Fall Back

Mass Loss Prevents Destruction

Which is the contribution of stars with M ≥ 35 M?

They produce:

~60% of the total C and N (mass loss)~40% of the total Sc and s-process elements (mass loss)No intermediate and iron peak elements (fallback)

47CHEMICAL ENRICHMENT DUE TO

MASSIVE STARSThe average metallicity Z grows slowly and

continuously with respect to the evolutionary timescales of the stars that contribute to the

environment enrichment

Most of the solar system distribution is the result (as a first approximation) of the ejecta of ‘‘quasi ’’–solar-

metallicity stars.

The PFs of the chemical composition provided by a generation of solar metallicity stars should be

almost flat

48CHEMICAL ENRICHMENT DUE TO

MASSIVE STARSSecondary Isotopes?

No room for other sources (AGB)

Remnant Masses? Type IaAGB?

n process. Other sources

uncertainExplosion?

49

THE END

50

• For T>5 109 K all the forward and the reverse strong reactions (with few exceptions) come to an equilibrium and a NSE distribution is quickly established

COMPLETE EXPLOSIVE SI BURNING

In this condition the abundance of each nucleus is given by:

These equations have the properties of favouring the more bound nucleus corresponding to the actual neutrons excess.

51

jlik rr

i + k j + l

),max()(

jlik

jlik

rr

rrij

0)( ij

No equilibrium1)( ij

Full equilibrium

Since the matter exposed to the explosion has Ye>0.49

(h<0.02)

Most abundant isotope 56Ni

Elements also produced: Ti (48Cr) , Co (59Ni), Ni (58Ni)

COMPLETE EXPLOSIVE SI BURNING

52INCOMPLETE EXPLOSIVE SI BURNING• Temperatures between 4 109 K < T < 5 109 K are not high enough to

allow a complete exhaustion of 28Si, although the matter quickly reaches a NSE distribution

Main products: Ti (48Cr), V (51Cr), Cr (52Fe), Mn (55Co)

53EXPLOSIVE O BURNING• Temperatures between 3.3 109 K < T < 4 109 K are not high

enough to allow a full NSE

• Two equilibrium clusters form separted at the level of the bottleneck @ A=44

• Since the matter exposed to the explosion has A<44 and since there is a very small leackage through the bottleneck @ A=44, the path to the heavier elements is severely inhibited

54

• Temperatures between 3.3 109 K < T < 4 109 K are not high enough to allow a full NSE

• Two equilibrium clusters forms separted at the level of the bottleneck @ A=44

• Since the matter exposed to the explosion has A<44 and since there is a very small leackage through the bottleneck @ A=44, the path to the heavier elements is severely inhibited

Main products: Si (28Si), S (32S) , Ar (36Ar), Ca (40Ca)

EXPLOSIVE O BURNING

55EXPLOSIVE C/NE BURNING

• If T < 3.3 109 K the processes are far from the equilibrium and nuclear processing occur through a well defined sequence of nuclear reactions.

Elements preferrentially synthesized in these conditions over the typical eplosion timescales:

• If T < 1.9 109 K no nuclear processing occur over the typical explosion timescales.

Si (28Si), P (31P), Cl (35Cl), K (39K), Sc (45Sc)

56HIGH TEMPERATURE NSE COMPOSITION

As the temperature is rised, an increasing fraction of the composition resides in lighther particles

At core Si exhaustion the matter is at the Nuclear Statistical Equilibrium

All the strong and electromagnetic interactions are balanced by their reverses and all the nuclei are in

equilibrium with exchange of p,n

The gas is described by the Maxwell-Boltzmann distribution for fixed T, r, Ye (p/n) ratio the abundance of

each nucleus is given by:

57HIGH TEMPERATURE NSE COMPOSITION

NSE 1 NSE 2

An increasing fraction of gravitational energy is

used to melt down heavy isotopes to a,p,n

(photodisintegration)10,10,0.4248Ca(0.48)

5,1,0.556Ni(.9)

10,1,0.5a(0.9)

2.4

1015 e

rg/g

r

10,10,0.5a(0.2)

54Fe(0.18)

7.4 1014 erg

/gr

3.7 1014 erg/gr

En

erg

y a

bs

orb

ed

by

th

e

ch

an

gin

g

of

the

NS

E a

bu

nd

an

ce

s

time

T,r,Ye

Comp.

T1 > T2Dt

B.E.=(Zmp+Nmn-Mnuc)c2

B.E

./n

ucle

on

partially undoing in less than an hour the last million years or so of nuclear evolution!!!

58

(Chandrasekhar, S., 1935, MNRAS, 95, 207)

Pure non relativistic solution

Fraction of the star in relativistic regime

Real solution

taking into

account

relativistic effects

THE LIMITING CHANDRASEKHAR MASS

The maximum mass that can be supported by the

degenerate electrons is:

When the star is fully relativistic

For a fully degenerate star the EOS is Non relativistic

Relativistic

As the total mass increases the relativistic effects become progressively important, the equation of state progressively change from P=k1r5/3 to P=k2r4/3 and the total radius of the star decreases