Stellar Evolution in General and in Special Effects:

Core Collapse, C-Deflagration, Dredge-up Episodes

Cesare Chiosi

Department of Astronomy

University of Padova, Italy

Part B: Massive stars and core collapse supernovae

History of Pre-Supernova Evolution of Massive Stars

(Type II SN)

• Semiconvection • Semiconvection & Mass Loss• Convective Overshoot• Convective Overshoot & Mass

Loss• Rotation & Mixing• Rotation, Mixing & Mass Loss

SemiconvectionElectron scattering and radiation pressure cause physical inconsistency at the border of the formal convective core fixed by the Schwarzschild condition.

Cured by introducing partial mixing in the border layers so that neutrality condition is achieved. Two possible criteria: Schwarzschild or Ledoux

R A R A

Inner structure & Loops in HRD: Schwarzschild or Ledoux?

Schwarzschild: no loops

Ledoux: loops

Debate still with us !!!

Mass Loss by Stellar Wind: in the blue

In the blue Radiation Pressure on ions

Massive, blue stars lose lots of mass at the observed rates!!

Mass Loss by Stellar Wind: in the red

• RSG lose mass at rates as high as those of O, BSG.

• Two components: gas + dust interacting thermally and dynamically.

• Radiation pressure on dust (atoms and/or molecules). However other mechanisms are also proposed.

In massive stars, mass loss cannot be ignored !!!

An old interpretation of the HRD…

The blue-red connection

Mass loss and semiconvection

……….The Family Tree

• M > 60 Mo Always Blue O OF BSG (+LBV) WN WC (WO) SN

• 25 Mo < M< 60 Mo Blue-Red-Blue• O BSG YSG RSG WN (WC) SN High Ms |-------------- SN Low Ms

• M < 25 Mo• O (BSG) RSG YSG + Cepheids RSG SN BSG SN (Z)

Overshoot: Generalities

• Convective elements must cross the Schwarzchild border to dissipation their Kinetic Energy

• How far can they go ? Controversial, likely l=LHp with L = 0.5

• Is mixing complete & instantaneous (as in MLT) or partial & slow?

• How does energy transport occur?• What is the temperature profile in

the overshoot region? Adiabatic or radiative?

OVERSHOOT ……..

Two current models for overshoot

• The ballistic description

• The diffusive description

The ballistic model

1

1

*'

' '

*'

' '

3

1

2

1 1

3 2

R C

rr

r

r

r

C P r

r

Cr Tr

P

F F F

MLT

vv g

r

drr r

T TF c v dr

r r

Fv g gv

r T c

1r r l

Pl H

Integrate to get vr and vMax( r )

The diffusive model

• Split the problem in three parts:• A) size of the unstable region (fully

unstable + overshooting) Lov= lo/(1-f) with lo = Hp and f breaking exponent in turbulent cascade (0.5).

• B) Energy transport: in overshoot region both radiative and adiabatic thermal structures yield akin results (Xiong 90).

• C) Mixing mechanism.

Looking for better overshoot models diffusion

Artistic view of overshoot

The Diffusion Coefficient

Velocity Cascade, Intermittence & Stirring

• Velocity cascade (energy conservation)

• Intermittence (volume filling)

• Stirring (spoons & cups)

3 30

0

d

d

v v

l l

3 30

0

d

d

v v

l l 3 / 2( )d

io

lF

l1/ 2( )d

o

l

l

1

22

3 3

0 0

( ) ( 1)os

L l LF

l l

Results for Massive Stars: HRD & Lifetimes

Diffusive Overshoot & WR Stars

But WR…. &BSG Gap…

Diffusion & New Mass Loss Rates

from RSG

WR and Blue Gap perhapssimultaneously explained!!

Overshoot in Intermediate Mass Stars

Brigther and longer lived on the MS.

Brighter and shorter lived on PMS.

Changes the ratio NPMS/NMS.

The HRD of intermediate mass stars

Shorter Loops

Central Conditions

Mup goes down to about6.5 Mo (in these models).

Fate of Intermediate Mass Stars

Overhoot increases both MHe and Mco and therefore shifts to lower initial masses the regime for Type II SN and for those stars they may end up as SN or WDs .

Overshoot and Late Evolutionary Stages

• Most important consequence of convective overshoot are the larger He and C-O cores built up during the H- and He-burning phases.

• In intermediate mass stars, it will lower the mass Mup (to about 5-6 Mo) so-called Type I+1/2 SN are ruled out, will decrease the minimum mass for Type II SN.

• In massive stars it will decrease the transition mass for them to end up as a Neutron Star or a Black Hole.

Rotation

• Among the most important achievements of the past ten years are the stellar models with rotation (and mass loss)

From Maeder & Meynet

A bit of formalism

• Replace spherical eulerian (lagrangian) coordinates with a new system characterized by equipotentials

gravitational potential

If constant on isobars “shellular” rotation (it results from turbulence being highly anisotropic, much stronger transport horizontally than vertically).

2 2 21sin

2r

von Zeipel Theorem & Transport of Angular Momentum (AM)

For shellular rotation, the transport of AM along the vertical direction is

1

4( )eff effT g ( )

4 ( ) eff

L PF g

GM P

::::::::::::::::::::::::::::

2

( ) (1 )2

M P MG

L(P) is the luminosity of

isobars

2 4 42 2

1 1( ) ( ( )) ( )

5r

dr M r U r Dr

dt r r rr r

Continued 1 (r) angular velocity, U(r) vertical

component of the meridional circulation velocity, D diffusion coefficient.

Rotation law allowed to evolve with time as a result of transport of AM by convection, diffusion, meridional circulation. Differential rotation caused by these processes further turbulence & meridional circulation coupling & feed-back solution for (r).

Timescales

Transport of Chemical Elements

U( r) vertical component of velocity;

Dh coefficient of horizontal turbulence (vertical advection is inhibited by strong horizontal turbulence);

Deff combined effect of advection and horizontal turbulence.

Meridional Circulation

• Velocity of meridional circulation

• Important effects of horizontal turbulence and

• At increasing the circulation velocity slows down.

• E and E suitable quantities functions of and

• Eddington-Sweet time scale tES.

Convective Instability

• Schwarzschild or Ledoux stability criteria no longer apply and are replaced by Solberg-Hoiland condition above (it accounts for differences in centrifugal forces on adiabatically displaced elements)

• is named the Brunt-Vaisala frequency

• s is the distance from rotation axis.

Shear Instabilities: dynamical & secular

• In radiative zones differential rotation efficient mixing on tdyn = trot & which is maintained if Richardson number obeys above condition (V horizontal velocity, z vertical coordinate).

• In presence of thermal dissipation, the restoring force of buoyancy is reduced and instability can easily occur but on a longer timescale (secular).

• Secular on MS phase and dynamical on advanced stages.

Evolution of Internal Rotation

• Passing from nearly rigid body on ZAMS to highly differential.

• The core spins up and the outer layers slow down as the star expands.

Rotation & Mass Loss

Mass loss rate increased by rotation!

[ ] [ 0]

1( ) ( )

1rot rotV V

rot

cri

dM dMVdt dtV

Evolution of Vrot & /crit

HRD of Rotating Mass-losing Stars

Consequences in Relation to SNs

• Masses of He cores are larger and less C is left over, shorter lifetimes of C-burning phase, less neutrino cooling, formation of BH favoured.

• Masses of CO cores are larger, e.g. a 20 Mo Vrot =300 km/s has 5.7 Mo instead of 3.8 Mo for the nonrotating case.

Nuclear Reaction Rates

This reaction is perhaps the most important one as far as the fate of a massive star is concerned.

It controls the amount of Carbon left over at the end of the core He-burning phase and hence the duration (together with neutrinos) of the core C-burning phase and the entropy profile throughout a star.

12 16( , )C O

Neutrinos in early stages

• Neutrinos are the starring actors of a star’s evolutionary history.

• It was not so in the past. In the sixties there was a vivid debate among stellar evolutionists looking for astrophysical tests of neutrino emission. The lifetime of the C-burning phase in massive stars, the third long-lived phase before the end (blue to red supergiant number ratio NB/NR).

• Coupled with much of the final history depends on these two physical ingredients.

12 16( , )C O

Final Structure of a Massive Star

What does determine the size of the various regions?

MHe, MCO, ….. Convective Cores & Shells……

The various processes we have discussed above.

Fortunately the evolution of the core

is decoupled from that of the envelope.

Characteristics of a massive star

Burning Temperature Density Lifetime

Million K g/cm3

Hydrogen 37 3.8 7.3x10^6 years

Helium 180 620 720 000 years

Carbon 720 6.4 x 10^5 320 years

Neon 1200 > 10^6 < 10 years

Oxygen 1800 1.3 x 10^7 ~ 0.5 year

Silicon 3400 1.1 x 10^8 < 1 day

Collapse 8300 > 3.4 x 10^9 0.45 sec

Neutron Star < 8000 > 1.4 x 10^14 –

Structure of a massive star

Up to the end of C-burning

The chemical structure at the end of C-Burning

The inner stratification

The inner chemical structure at theonset of collapse

Chemical and energy profiles at the onset of collapse

Mass cut

A 25 Mo

Plane of central conditions

Core collapse in a snapshot: 1

ee

A

nY

N

2 2 22

25.83 1Ch e

F

k TM Y

• Iron core in excess of MCh collapses on a thermal timescale as neutrino emission carries away binding energy.

• Collapse accelerated by two instabilities:

1. e-captures on Fe-group increase n-rich composition, decrease of ne & Pe, reduce MCh;

2. Photodisintegration increase number a-particles without

leading to total disintegration;

Core collapse in a snapshot: 2

• Bounce relatively cold with heavy nuclei persisting until they merge just below nuclear density stellar mass nucleus which would bounce acting like a spring which stores energy at compression and rebound at the end.

• Portions of neutronized hard core (v r) and infalling region

(v 1/r^2 ) nearly equal.

• Bounce shock forms and moves outward and could explode the star. It does not because energy is consumed to disintegrate the infall staff (some 10e51 ergs per 0.1Mo) and to emit neutrinos behind the shock. The shock wave stalls and dies.

• A succesful shock requires an additional source of energy: neutrino deposit.

• The situation is however unclear and controversial.

Closer look at the physics of core collapse: rules

• If contraction heats up matter and N is activated, particle kinetic energy increases P and contraction is opposed (stellar boiler).

• If energy absorbing processes are present the opposite occurs (stellar refrigerators).

• Two possible refrigerators drive the Fe core into an uncontrolled collapse.

• Photo disintegration of nuclei (Fe -particles)• Captures of electrons via inverse -decay.

Rules: continue

• In the former, kinetic energy is used to unbind nuclei

• In the latter, kinetic energy of degenerate electrons is converted to kinetic energy of e which escape from the core

• P failure Collapse 0 53 32 1fft G ms .( / )

Nuclear photo-dissociation: Iron

• Thermal photons are energetic enough to disintegrate Fe nuclei into less tightly bound nuclei and energy is absorbed. The process is schematically indicated as

• The fraction of Fe dissociated is derived in analogy to ionization

• Implies treshold T and (10^9 g/cm^3 and 10^10 K, respectively)

56 4

4 1 56

13 4

13 4 124 4

Fe He n

Q m m m Mev

( ) .

13 413 4 13 44 14 1 4 1

56 56 56

3 2

2

2

Q Q

Q

AQA

A

n nn n g g Q

n g n KT

where

m KTn

hg

/

4 1 56

( ) ( )exp( )

( ) quantum concentration

statistical factor (depends on angular momentum),

g =1, g =2, g =1

Photo-dissociation: Helium

Θ

51

51

Total amount of energy absorbed by these photo - dissociation

processes for a Fe core of about 1.4 M

4x10 erg for Fe 13 He + 4 n

10x10 erg for He 2 p + 2n

or in a more practical form52

Θ1.5 x 10 erg per 0.1 M of Fe

This energy nearly parallels the total energy radiated by the SUN

over 10 Gyr

• At higher temperatures helium is broken

• Similar consideration apply as above4 γ + He 2p + 2n Q = -28.3 Mev

Neutronization 1• In normal circumstances n p + e + e on a time scale of

15 min• Electrons and neutrinos have a combined energy of 1.3 Mev

(the mass-energy difference between n and p)• When neutrons decay, electrons with energies up to 1.3 Mev

are produced it follows that neutrons cannot decay if the electrons cannot be accepted by the medium. This is case when neutrons are in a dense degenerate gas of electrons where all energy states up to 1.3 Mev are filled. The density for this to occur can be estimated from the Fermi momentum – energy

• Furthermore, if the gas is denser, electrons with energies > 1.3 Mev exist and they may be captured by protons to form neutrons

e + p n + e . The new formed neutrons cannot decay: the nuclei becomes richer in neutrons.

NEUTRONIZATION

42e

22FF

1/3eF cmcpε and ]

8π

3nh[P

Neutronization: continue

FeMn 5656

• Neutronization begins when

• Normally a nucleus of Mn Fe with a half-life of 2.4 h, but in the dense stellar cores it captures an electron to form Cr which in turn captures another electron. Many other captures are possible with many other nuclei. Very soon e-captures get very fast. The neutrinos carry away the energy originally stored in the electrons.

• THE NUMBER DENSITY OF ELECTRONS and Pe IN TURN FALL DOWN THE COLLAPSE IS STARTED.

• How much energy is subtracted by e-captures?

Mev 3.7cm)(eε

g/cm10 x 1.1ρat νMneFe2

eF

39e

5656

Energy removed by e-captures

• A core of about 1.4 Mo has about 10^57 electrons and can produce an equal

number of neutrinos. Assume that the typical energy of a captured electron is

about 10 Mev (roughly the mean energy of a degenerate electron at densities

of 2x10^10 g/cm^3 ) we have

erg 106.1)106.11010(10E 5213657cap

Number of electrons Energy per electron Conversion factor

Energy budget in the collapse

3-143N

nNuc g/cm 102.3

4ππ

3Amρ

• Pressure removal by e-captures & photo-dissociations induce collapse: very

rapid and almost unopposed until the matter reaches nearly nuclear densities

• At these densities neutron degeneracy and nuclear forces oppose to compression

and bring collapse to a halt when = 2-3 nuc. Furthermore at these densities the

mininum energy configuration requires the neutrons to drip out of nuclei, free

neutrons appears and the final configuration is that all nuclei dissolve into a gas

of free neutrons new EOS.

• The mass and the radius of the newly formed object ( a neutron star) are about

MNS = 1 Mo (or more) and RNS =10 km.

• How much energy has been liberated by gravitational contraction?

3143 1032

4

3 -

N

nNuc g/cm.

R

Amρ

Energy budget in the collapse: continue

253 2

ΩNS Θ

Ω photo capt kin opt

53 52 52 51 49

-

GM M 10kmE 3 10 [ ] [ ] erg

R M R

Balance

E E E E E ?

3 10 1.5 10 1.6 10 1.0 10 1.0 10 ? erg

There is a factor of 10 missing! NEUTRINOS

Neutrinos from e e annihilation, plas

ma, photo, bremsstrahlung.

The real event of a SN explosion is the burst of neutrinos!!!

Collapse: basic questions

• Can the collapse of the inner core induce the ejection of the remaining mass (core plus mantle)?

• The key problem is how to transfer even a small amount of the energy liberated by the collapsing nucleus to the rest of the star.

Simple description of collapse

• Onset of collapse with • Electrons degenerate and relativistic

• The collapse can be described as a politrope of index 3.• The collapsing core can be split in two regions whose

velocity profile is

• The homologous region is in sound communication. The peak position shifts outward with time v(r)max = 70000 km/s

10 1010 / and T 10 Kg cm

3/43/4 )(

e

KP

Elastic vs anelastic bounce • When the central part gets it becomes rigid and almost

incompressible.

• If the whole process were completely elastic, the kinetic energy of the collapsing matter would be sufficient to bring it back to the original state (bounce). The energy is simply

The energy required to expell the remaining part of the star would be

For a 10 Mo star. Only a small fraction of E.

• What happens next depends on understanding what fraction of the collapse energy goes into kinetic energy of the outward motion

ergR

GME

NS

NS 532

103

ergR

MMGE

WD

NSesc

522

103)(

314 /105 cmg

Schock Wave• Suppose that by inertia the central sphere is compressed beyond its equilibrium

state and like a spring it expands, pushing back the infalling material above.

• This creates a pressure wave that steepens while travelling into regions of lower

density. A rough estimate of the kinetic energy of the SW is

comparable to the potential energy of the nucleus and thus fully sufficient

to expell the mantle (rest of the star).

• However the SW must find its way out through layers of still undissociated Fe

• and dissipate (or may) the whole energy in doing this. The SW dies inside the

collapsing Fe core.

• This depends on where the SW is formed: if too inside very little hope, if very

external it may be succesful (this depends in turn on the original size of the

Fe core).

ΩSW E 0.1E

Neutrino Cavalry• The typical energy of neutrinos emitted during collapse is of the order of that of

relativistic electrons

• If heavy nuclei are present neutrino interact via cherent scattering rather than

scattering by free nucleons

• Neutrinos may be trapped and release their energy to the SW, to the star. Even

0.01 of their energy is enough. SW does not die and SN explosion may occur.

NS3-9

2493/5

e

22/3

e

24522

e

R km 10 ,g/cm 10 100,A 2,for

cm 10)(1

n

1

path freemean

section cross cm )(A10m

E

process ),(),(

l

Al

Ac

AZAZ

e

3/1222

)(10ee

F

e

F

e cm

p

cmcm

Schematic view

1410 1110

Neutrino sphereShock Front

Border Fe nucleus

Radius

Static dense core Slow infalling matter Rapidly infalling

cool matter

810

U

N

B

U

R

N

E

D

S

T

A

F

F

Seven years to explosion

Oxygen and Magnesium Nucleus

One year to explosion

Hydrogen/ HeliumCarbonNeon / MagnesiumMagnesium /

OxygenIron

Ten seconds to explosion

High density Iron Nucleus

Millisecs after collapse

A few seconds after collapse

Neutron Star

Hours after collapse

Ejection of outer layers

Neutron Star

• One is left 10ms after the core has bounced with a hot, dense proto-neutron star accreting matter at the high rate of 1-10 Mo /s

Collapse & Bounce of the Iron Core of a 13 Mo SN

Shock Waves

• SW revived for 0.1s, long compared to tdyn (ms) bur short compared to the 3-10 s of the tKH time scale for NS to emit the binding energy

• Convective flows of neutrinos (increase neutrino absorption)

• Problems: Too much n-rich nucleosynthesis because

neutrinos interact with nucleons in the convective bubble decrease Ye; Remnant masses too small

Neutrino-driven convection after core bounce in a 13 Mo

Mixing in the explosion of a 15 Mo

Failure of Supernova Explosion

• NS will have masses comprised between the Fe-core and the O-shell: for 1-20 Mo stars 1.3-1.6 Mo.

• At higher initial masses either larger NS or eventually BH.

Remnants: NS & BH

Final vs initial mass

SN Types: metallicity & mass

METALLICITY

INITIAL MASS

SN Types : metallicity & mass

SN and Remnants of Massive Stars with Solar

Metallicity

Summary 1

Summary 2

25 Mo

25 Mo

Summary 3

Summary 4

Radiactive decay in ejecta

Light Curves

SN 1987A in LMC

SN1087A in the LMC: main facts

• Sn1987a brightened very rapidly compact progenitor: SK69202, B3I, logL/Lo=5.1, logTeff=4.2

• Core mass 6 1 Mo, total mass 16-22 Mo.• With distance to LMC of kpc

cm event took place 160,000 years ago.• Detected Neutrinos (20) estimate of gravitational energy ergs or from their temperature ergs Baryon mass inside neutron star Mo.

50 5 23(1.5 0.15) 10x

53(2.5 1) 10GE x 53 (3.7 2) 10GE x

(1.6 0.4)

Main facts: continued

• Prominent H lines (Type II)

• Chemical Abundances: [O] & [N] much larger than solar CNO-cycle material exposed; expansion velocities of about 30 km/s progenitor was in the past a RSG, lost part of the envelope, and subsequently contracted to the size of a BSG

• Relatively small mass in the original envelope

• Observational evidence of mixing and mass loss in progenitor: both stronger than expected

• Evidence of mixing in the ejecta

Possible evolutionary history of progenitor

New Family Tree after SN1987A