Transcript and mass loss

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
Semiconvection
Electron 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 R   A or Ledoux  R   A   
Inner structure & Loops in HRD:
Schwarzschild or Ledoux?
Schwarzschild: no loops
Debate still with us !!!
Ledoux: loops
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…
Mass loss and semiconvection
The blue-red connection
……….The Family Tree
• M > 60 Mo
Always Blue
O OF BSG (+LBV)
WN
• 25 Mo < M< 60 Mo
• O BSG YSG
RSG
• M < 25 Mo
• O (BSG)
RSG
WC
(WO)

SN
Blue-Red-Blue
WN (WC)
 SN High Ms
|-------------- SN Low Ms
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
F  FR  FC
MLT
vr

g
vr

r
r  r1  l
l  H P
  *   '
    '  ' dr
r 
r1  r
r
 T * T  '
FC  2cP vr   '  ' dr
r 
r1  r
r
g 
1 vr 3 1 g T FC


   1  vr
2 T   cP    
3 r
Integrate to get vr and vMax( r )
The diffusive model
Looking for better overshoot models  diffusion
• 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.
Artistic view of overshoot
The Diffusion Coefficient
Velocity Cascade, Intermittence & Stirring
• Velocity cascade (energy conservation)
v 30 v 3 d

l0
ld
• Intermittence (volume filling)
 2

1
2
l
  ( d )1/ 2
lo
v 30
v3d

l0
ld
• Stirring (spoons & cups)
Fs  (
L  lo 3
L
)  (  1)3
l0
l0
ld 3 / 2
Fi  ( )
lo
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 perhaps
simultaneously 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 about
6.5 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
1 2 2 2
    W r sin 
2
gravitational potential

If W constant on isobars  “shellular” rotation (it results
from turbulence being highly anisotropic, much stronger
transport horizontally than vertically).
von Zeipel Theorem & Transport of
Angular Momentum (AM)
L( P )
F 
g eff
4 GM  ( P)
W2
M  ( P)  M (1 
)
2 G 
Teff  geff ( )
1
4
L(P) is the luminosity of isobars
For shellular rotation, the transport of AM
along the vertical direction is
d 2
1 
1 
4
4 W
 ( r W) M r  2
(  r WU (r ))  2
(  Dr
)
dt
r
5r r
r r
Continued 1
W(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 W(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.
• EW and E suitable quantities functions of W 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 W
• 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
dM
(
)[Vrot ]
dt

 1
dM
(
)[Vrot 0] 
dt
 Vrot
1 V
cri








Mass loss rate increased by rotation!
Evolution of Vrot & W/Wcrit
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
C ( ,  ) O
12
16
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.
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).
C ( ,  ) O
12
16
• Coupled with
much of the final history
depends on these two physical ingredients.
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
Hydrogen
Helium
Carbon
Neon
Oxygen
Silicon
Collapse
Neutron Star
Temperature
Million K
37
180
720
1200
1800
3400
8300
< 8000
Density
g/cm3
3.8
620
6.4 x 10^5
> 10^6
1.3 x 10^7
1.1 x 10^8
> 3.4 x 10^9
> 1.4 x 10^14
Lifetime
7.3x10^6
720 000
320
< 10
~ 0.5
<1
0.45
–
years
years
years
years
year
day
sec
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 the
onset of collapse
Chemical and energy profiles at the
onset of collapse
A 25 Mo
Mass cut
Plane of central conditions
Core collapse in a snapshot: 1
ne
Ye 
 NA
2 2 2


kT 
2
M Ch  5.83Ye 1 
2 
F 

• 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
leading to total disintegration;
without
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 ne
which escape from the core
0.5
• P failure  Collapse t ff  ( 3 / 32G  )  1ms
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
  56 Fe  13 4 He  4n
Q  ( 13m4  4m1  m56 )  124.4Mev
• The fraction of Fe dissociated is derived in analogy to ionization
13
4
( n4 )13 ( n1 )4
g 413 g14 nQ 4 nQ1
Q

exp( 
)
n56
g 56
nQ 56
KT
where
2 m A KT 3 / 2
)
quantum concentration
2
h
statistical factor (depends on angular momentum),
nQA  (
gA
g4 =1, g1 =2, g56 =1
• Implies treshold T and  (10^9 g/cm^3 and 10^10 K, respectively)
Photo-dissociation: Helium
• At higher temperatures helium is broken
γ + 4 He  2p + 2n
Q = -28.3 Mev
• Similar consideration apply as above
Total amount of energy absorbed by these photo - dissociation
processes for a Fe core of about 1.4 M Θ
4x1051 erg
for Fe  13 He + 4 n
10x1051 erg
for He  2 p + 2n
or in a more practical form
1.5 x 1052 erg per 0.1 M Θ of Fe
This energy nearly parallels the total energy radiated by the SUN
over 10 Gyr
Neutronization 1
• In normal circumstances n  p + e + ne 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
3n e 1/3
PF  h[
]
8π
and
ε F  p F c2  me c4
2
2
• 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 + ne . The new formed neutrons cannot decay: the nuclei
becomes richer in neutrons.
NEUTRONIZATION
Neutronization: continue
• Neutronization begins when
56
Fe  e  56 Mn  ν e at ρ  1.1 x 109 g/cm 3
ε F (e  )  me c 2  3.7 Mev
• 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.
Mn  by
Fee-captures?
• How much energy is subtracted
56
56
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
13
Ecap  10 (10 10 1.6 10 )  1.6 10
57
Number of electrons
6
Energy per electron
52
erg
Conversion factor
Energy budget in the collapse
• Pressure removal by e-captures & photo-dissociations induce collapse: very
rapid and almost unopposed until the matter reaches nearly nuclear densities
ρNuc
3 Amn
14
-3


2
.
3

10
g/cm
3
4RN
• At these densities neutron degeneracy and nuclear forces oppose to compression
3Am
ρ 
 2.3 10 g/cm
4ππ
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.
Nuc
n
3
N
14
-3
• How much energy has been liberated by gravitational contraction?
Energy budget in the collapse: continue
GM 2
M 2 10km
53
EΩ 
 3  10 [
] [
] erg
RNS
MΘ
R
Balance
EΩ  E photo  Ecapt  Ekin  Eopt  ?
3  10 53  1.5  10 52  1.6  10 52  1.0  10 51  1.0  10 49  ? erg
There is a factor of 10 missing! NEUTRINOS
Neutrinos from e  e - annihilation, plasma, 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   1010 g / cm and T  1010 K
• Electrons degenerate and relativistic
 4/3
P  K4/3 ( )
e
• 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
Elastic vs anelastic bounce
• When the central part gets 5 1014 g / cm3 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
2
GM NS
EW 
 31053 erg
RNS
The energy required to expell the remaining part of the star would be
Eesc
G ( M  M NS ) 2

 3 1052 erg
RW D
For a 10 Mo star. Only a small fraction of EW.
• What happens next depends on understanding what fraction of the
collapse energy goes into kinetic energy of the outward motion
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
ESW  0.1  E Ω
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).
Neutrino Cavalry
• The typical energy of neutrinos emitted during collapse is of the order of that of
relativistic electrons
n
me c 2

F
me c 2

pF

 10  2 ( )1/ 3
me c
e
• If heavy nuclei are present neutrino interact via cherent scattering rather than
scattering by free nucleons
n  ( Z , A)  n  ( Z , A)
n 
process
En

A2  10  45  A 2 ( ) 2/3 cm 2 cross section
2
mec
e
mean free path
1
1  5 / 3
ln 

( )
 10  49 cm 2
n n  e A  e
for   2, A  100,   109 g/cm -3 , ln  10 km  R NS
• 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.
Schematic view
Radius
  10
14
Static dense core
Neutrino sphere
  1011
  108
Slow infalling matter
Rapidly infalling
cool matter
Shock Front
U
N
B
U
R
N
E
D
S
T
A
F
F
Border Fe nucleus
Seven years to explosion
Oxygen and Magnesium Nucleus
One year to explosion
Hydrogen/ Helium
Carbon
Neon / Magnesium
Magnesium / Oxygen
Iron
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
Collapse & Bounce of the
Iron Core of a 13 Mo SN
• One is left 10ms after
the core has bounced with
a hot, dense protoneutron star accreting
matter at the high rate
of 1-10 Mo /s
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
Remnants: NS & BH
• 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.
Final vs initial mass
SN Types: metallicity & mass
M
E
T
A
L
L
I
C
I
T
Y
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 50  5 kpc (1.5  0.15) x1023
cm  event took place 160,000 years ago.
• Detected Neutrinos (20) 
53
E

(2.5

1)
x
10
estimate of gravitational energy G
ergs
53
or from their temperature
EG  (3.7  2) x 10 ergs

Baryon mass inside neutron star (1.6  0.4) Mo.
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