Download Lecture 13 Presupernova Models, Core Collapse and Bounce

Baade and Zwicky, Proceedings of the National Academy
of Sciences, (1934)
Lecture 13
With all reserve we advance the view that a supernova
represents the transition of an ordinary star into a neutron star
consisting mainly of neutrons. Such a star may possess a very
small radius and an extremely high density. As neutrons can be
packed much more closely than ordinary nuclei and electrons, the
gravitational packing energy in a cold neutron star may become
very large, and under certain conditions, may far exceed the ordinary
nuclear packing fractions ...
Presupernova Models, Core
Collapse and Bounce
Chadwick discovered the neutron
in 1932 though the idea of a neutral
massive particle had been around
since Rutherford, 1920.
When Massive Stars Die,
How Do They Explode?
Neutron Star
+
Neutrinos
Colgate and White (1966)
Arnett
Wilson
Bethe
Janka
Burrows
Fryer
Mezzacappa
etc.
Neutron Star
+
Rotation
Hoyle (1946)
Fowler and Hoyle (1964)
LeBlanc and Wilson (1970)
Ostriker and Gunn (1971)
Bisnovatyi-Kogan (1971)
Meier
Wheeler
Usov
Thompson
Burrows
How the star dies is determined by its properties at
birth – its mass, composition, rotation rate, and binary
membership.
Mass affects the “central engine” by
determining the density structure in the inner few
solar masses of the presupernova star.
Pc ~
GM ρ Tc3
⇒
∝ µ 3 M 2 (for an ideal gas)
R
ρc
S = const + ln
N A k T 3/2 4a T 3
+
(heavier stars have higher entropy)
µ ρ
3 ρ
15 Solar masses
Nordhaus et al. (2010)
Using CASTRO
Density Profiles of Supernova Progenitor Cores
These will be hard
to explode. High binding energy.
High prompt accretion rate.
These should be
easy to explode
2D SASI-aided,
Neutrino-Driven
Explosion?!
Ansatz:
•  Most groups have or shortly will be able to
successfully model the explosion of a 15 solar mass
star using unboosted neutrino energy transport
(Colgate and White 1966)
•  The success or failure of this standard mechanism
depends chiefly upon the compactness of the oxygensilicon-iron core. Therefore other cores with similar
or greater central concentration of matter
will also explode.
nb. For a Salpeter IMF integrated from 8 to 120 solar masses, 15 solar
masses is the typical supernova by number (Schramn and Arnett 1973)
O’Connor and Ott, ApJ, 730, 70, (2011)
Characterize possibility of a neutrino powered explosion based
upon the compactness parameter, ,"
ξM =
2.5
R(M bary = 2.5M  ) / 1000 km
t−bounce
If  is big, R is small and the 2.5 solar mass point lies
close in. The star is hard to explode. Based upon a series
of 1D models they find stars with  over 0.45 are particularly
difficult to explode.
ξ (explosion) < 0.45
Gravitational Binding Energy
of the Presupernova Star Outside
the Iron Core.
Density Profiles of Supernova Progenitor Cores
Large 
-1051 erg
Small 
2D SASI-aided,
Neutrino-Driven
Explosion?!
solar
low Z
-2 x 1051 erg
O’Connor and Ott (2011)
Presupernova stars – Type IIp and II-L
(low metallicity,
i.e., low mass loss)
(solar metallicity)
Black holes
Supernovae
Smartt, 2009
ARAA
Black holes
Type Ic supernovae
Results up here sensitive to
poorly known mass loss rates
Progenitors
heavier than 20
solar masses
excluded at the
95% condidence
level.
The solid line is for a Salpeter IMF with a maximum mass of 16.5
solar masses. The dashed line is a Salpeter IMF with a maximum of 35
solar masses
What About Type Ib and Ic Supernovae?
ς crit = 0.20 - 0.25 may be more appropriate
Type Ib
Lots of mixing
Type Ic
It is popular (mis)conception
that the production of Type Ic
supernovae requires the removal
of the hydrogen envelope and
helium shell of a very massive
star in order to have a weak
helium line at 5876 A.
(no mass loss)
(solar metallicity)
The two models on the left are
both derived from a 5.1 helium
star that originated from a binary
pair in which each star was lighter
than 20 solar masses (Yoon,
Langer and Woosley 2010)
?
Some mixing
Dessart, Hillier, & Woosley, in prep.
O’Connor and Ott (2011)
Summary – Reasonable Expectations
For Most Core-Collapse Supernovae
• 
Typical supernovae (SN IIp) are the result of neutrino energy
transport in stars with main sequence masses 8 to ~22 solar masses.
• 
Rotation may boost the explosion and mixing of supernovae
coming from (rapidly rotating) stars above 25 solar masses, but
most stars above ~22 solar masses become black holes.
• 
SN Ib and SN Ic are the product of binary evolution
for stars less than 22 solar masses. The distinction between
SN Ib and SN Ic is one of mixing but that may involve the stellar
mass. More massive stars in this range might make SN Ic.
• 
There is an island of “compact” pre-supernova stars at around
30 solar masses that might be exploded by unboosted neutrino
transport
Comment
•  Supernovae with explosion energies over 3 x 1051 probably
do not come from unboosted neutrino transport.
Explosion E ~ BEn* ×(fraction in ν eν e ) × (
τ exp
) × (Deposition efficiency)
τ KH
⎛ 1⎞ ⎛ 1 ⎞
~ 3×1053 erg ⎜ ⎟ ⎜ ⎟ ( 0.1) ~1051 erg
⎝ 3 ⎠ ⎝ 10 ⎠
Kasen and Woosley (2009)
Observationally
The typical SN IIp has
kinetic energy at infinity
of 6 x 1050 erg, but with
a wide spread.
7 − 12 M  Stars
Mα = 2.2 M i.e., main sequence mass ≈ 9 M (Nomoto et al)
Poelarends, Herwig, Langer and Heger (2008)
Ignite carbon burning
Specific Cases in
Greater Detail
> 7.25 M 
Heaviest to lose envelope
by winds and thermal pulses
9.0 M 
Ignite Ne and O burning
9.25 M 
O, Ne, Mg core develops - residual of carbon burning, but not
hot enough to ignite Ne or O burning. Degenerate core (may) grow by
thin helium shell burning. M → 1.375 M if envelope not lost
24
Mg(e − , ν e )24 Na,
20
Ne(e − , ν e )20 Na
reduce Ye hence ρ ↑
runaway collapse
Range of e-capture NeO SNe
9.0 - 9.25 M 
Expected number 4%; Maximum number 20%
Larger percentage at lower metallicity
12 M  Model has binding 1 x 10
50
erg
49
erg
external to 1.7 M  baryon; 1 x 10
external to 2.6 M 
At about 2 × 1010 g cm -3, ignite oxygen burning, but matter is
already falling in rapidly. Very degenerate runaway. Burn to
iron group but kT < ε Fermi . No appreciable overpressure.
Instead capture electrons on Fe group nuclei. Collapse accelerates.
Oxygen burning continues, but in a thin shell through which matter
is falling supersonically. Collapse continues to nuclear density without
ever having formed a large iron core.
Original model due to Miyaji et al (1980). Studied many times since.
A similar evolution may occur for accreting Ne-O white dwarfs (or
very rapidly accreting CO-white dwarfs) in binary systems - an
alternate outcome to Type Ia supernovae. This phenomena in a binary
is generally referred to as Accretion Induced Collapse (AIC) .
Once the collapse is well underway, the outcome does not
vary appreciably from what one would expect for a collapsing
iron core of the same (zero temperature Chandrasekhar)
mass.
M MS ≈ 9 M 
M He ≈ 2.2 M 
Nomoto, ApJ, 322, 206, (1987)
The energy release from oxygen burning and silicon burning is
small compared with the gravitational potential at which the
burning occurs
Miyaji et al, PASJ, 32, 303 (1980)
Nomoto, ApJ, 277, 791(1984)
Nomoto, ApJ, 322, 206 (1987)
Mayle and Wilson, ApJ, 334, 909 (1988)
Baron et al, ApJ, 320, 304, (1987)
Qian and Woosley (1996) – Neutrino powered winds
Kitaura, Janka, and Hillebrandt
(2006) using 2.2 solar mass He
core from Nomoto (1984, 1987)
Explosion ~1050 erg,
basically the neutrino wind.
Very little Ni or heavy
elements ejected.
Faint supernova(?)
Star of ~ 10 solar masses suggested as progenitor of the
Crab nebula by Nomoto et al. (1982, Nature, 299, 803)
Observed for Crab: KE = 0.6 to 1.5 x 1050 erg in 4.6+- 1.8 solar masses
of ejecta (Davidson and Fesen 1985)
O
"
T
As the convective flame
moves deeper into the star
it gets hotter. Oxygen is
burning to completion
now and silicon is starting
to burn. The shell burning
temperature now is 2.6
billion K and the central
density is 1.7 x 108 g cm-3
The peculiar – 9 – 10.5
solar mass stars. Here is
an example
O
Ne
O
Mg
Interior of 9.5 solar mass model
as oxygen ignites off center
and burns inwards in a
convectively bounded
conductive flame.
The “inside out” formation of
an iron core. The convective
front nears the center of a star
where neon has still not burned.
Central density is now
1.0 x 108 g cm-3. After the
silicon burning reaches the
center, shell Si burning occurs
outside of 0.9 Msun and
the iron core collapses to a
neutron star.
Density structure, 9.5 Msun
(Woosley unpublished)
Largest known neutron star
mass is now 2.0 solar masses
(plus neutrino losses ~ 2.5
solar masses of baryons)
The gravitational binding energy
outside the helium core is only
2 x 1047 erg
Energy of explosion given by (unavoidable) neutrino wind
~1050 erg. 8 M ejected so v ~ 1000 km s −1
But what about the Crab?
Light curve from
Shock
breakout
9.2 M model
Typical SN IIp
KE∞ = 1.0 × 1050 erg
(parameter)
In a calculation that included current approximations
to all known mechanisms of angular momentum transport
in the study, the final angular momentum in the iron core
of a 10 solar mass star when it collapses was
7 x 1047 erg s
This corresponds to a pulsar period of 11 ms, about half
of what the Crab is believed to have been born with.
Teff ≈ 6000 K
2 - 3 × 1041 erg s-1
Spruit (2006) suggests modifications to original model
that may result in still slower spins.
Therefore--The explosion of the Crab
SN was probably not (initially)
powered by rotation and the
explosion was therefore weak.
But historical accounts suggest
that it was very bright…
Could be shortentened
by mass loss, e.g., in a binary.
Stellar evolution including approximate magnetic torques gives
slow rotation for common supernova progenitors.
10 M  Woosley
and Heger (2009)
Fine zoning and careful
treatment of nuclear physics
(250 isotope network)
times 2 ?
Si - ignition at 5 x 108 g
cm-3 in a core of almost
pure 30Si (Ye = 0.46).
Very degenerate but not
so degenerate as a Ia.
T ~ 2.5 x 109 at runaway.
Peak T = 6 x 109 K.
Heger, Woosley, & Spruit (2004)
using magnetic torques as derived in
Spruit (2002)
Total nuclear energy
liberated 3 x 1050 erg
Thermonuclear
supernova!
Final kinetic energy
3.7 x 1049 erg
Other results for stars near 10 solar masses at death
L ~ 3 - 10 x 1040 erg/s
for ~ 1 year.
Mass
He
core
CO
core
Typical ejection speeds
few x 107 cm s-1.
9.2
10 
10.5
1.69
2.2
2.47
1.43
1.58
1.68
Fe
core
1.22
1.29
1.29
comment
envelope intact
envelope ejected
envelope ejected
Leaves 1.63 solar masses
One year later, SN of
about 1050 erg inside 8
solar masses of ejecta
already at 1015 cm.
Caveat: Multi-D effects not explored!
11 Solar Masses – PreSN (Woosley and Weaver 1995)
Moving up in mass to 11 solar masses …
(note thin shells of heavy elements outside Fe core)
11 Solar Mass Presupernova (Woosley and Heger 2007)
He core
2.83 M
Fe core
1.32 M
Only the
inner 3
solar masses
of the 11
solar mass
star are
shown
Temperature
Density
For masses heavier than 12 solar masses all
burning stages ignite in the center
Fe
edge of helium core
He shell burning
C,O shell burning
C
O
Si
C
core C-burning
does not power
convecction
O
Si
He
Si
O
H
Fe
Si
O
He
H
Ye
vcollapse
Stars of larger mass have thicker, more massive shells of heavy elements
surrounding the iron core when it collapses.
Distribution of collapse velocity and Ye (solid line) in the inner
2.5 solar masses of a 15 solar mass presupernova star. A collapse
speed of 1000 km/s anywhere in the iron core is a working
definition of presupernova . The cusp at about 1.0 solar masses is the
extent of convective core silicon burning.
Note that the final masses of the 15 and 25 solar mass main sequence stars
are nearly the same – owing to mass loss.
Neutrino Trapping
Core Collapse
Once the collapse is fully underway, the time scale becomes
very short. The velocity starts at 108 cm s-1 (definition of the
presupernova link) and will build up to at least c/10 = 30,000 km s-1 before
we are through. Since the iron core only has a radius of 5,000 to
10,000 km, the next 0.2 seconds are going to be very interesting.
Trapping is chiefly by way of elastic neutral current scattering
on heavy nuclei. Freedman, PRD, 9, 1389 (1974) gives the cross
section
2
⎛ ε ⎞
σ coh ≈ a02 A2 ⎜ ν ⎟ i1.5 ×10−44 cm 2
⎝ MeV ⎠
hence
2
a0 = sin 2 (θW ) where
θ W is the "Weinberg
angle", a measure of the
importance of weak
neutral currents
⎛ ε ⎞
κ coh ≈ ao2 A N A ⎜ ν ⎟ i1.5 ×10−44 cm 2 gm -1
⎝ MeV ⎠
2
⎛ A ⎞⎛ ε ⎞
= 5.0 ×10−19 a02 ⎜ ⎟ ⎜ ν ⎟ cm 2 gm -1
⎝ 56 ⎠ ⎝ MeV ⎠
2
⎛ A ⎞⎛ ε ⎞
κ coh = 2.6 ×10−20 ⎜ ⎟ ⎜ ν ⎟ cm 2 gm -1
⎝ 56 ⎠ ⎝ MeV ⎠
2
4
if one takes a0 = sin (θW ) = (0.229) 2 = 0.0524
ε F =1.11( ρ7Ye )1/3 MeV
Bounce
~ 20 MeV at
Therefore neutrino trapping will occur when
κ ν ρ R ~1
ρ =1011 g cm -3
R ~ 10 cm
(3 × 10 )( 2) (100) ρ (10 ) ~1 ⇒ ρ ~ 10
−20
(εν ~ 10 MeV is better)
6
6
11
gcm -3
(for A ~ 100)
From this point on the neutrinos will not freely stream but must
diffuse. Neutrino producing reactions will be inhibited by the
filling of neutrino phase space. The total lepton number
YL = Ye +Y"
!
will be conserved, not necessarily the individual terms. At the point
where trapping occurs YL = Ye ~ 0.37. At bounce Ye~ 0.29; Y~ 0.08.
Up until approximately nuclear density the structural adiabatic
index of the collapsing star is governed by the leptons – the
electrons and neutrinos, both of which are highly relativistic,
hence nearly =4/3.
As nuclear density is approached however, the star first experiences
the attactive nuclear force and  goes briefly but dramatically
below 4/3.
At still higher densities, above nuc, the repulsive hard core
nuclear force is encountered and abruptly  >> 4/3.!
R 2κρ
to the collapse
c
time, ~10 ms. Get ρ ~1012 (crude)
Alternatively set τ diff =
Throughout the collapse,
nuclei stay, for the most
part, bound, but above
nuclear density it makes
sense to talk of individual
nucleons again.
As the density reaches and
surpasses nuclear )(2.7 x 1014 gm
cm-3), the effects of the strong
force become important. One first
experiences attraction and an
acceleration of the collapse, then a
very strong repulsion leading to
 >> 4/3 and a sudden halt to the
collapse.
1 MeV = 11.6 billion K
ρ =1.66 ×1015 n(fm -3 ) g cm -3
In general, favor the curves K = 220. For densities significantly
below nuclear,  is due to relativistic positrons and electrons.
= ( N A 10−39 ) −1 "
The portion of the core that collapses together is
called the homologous core . It collapses subsonically
(e.g., Goldreich & Weber, ApJ, 238, 991 (1980); Yahil ApJ, 265,
1047 (1983)). This is also approximately equivalent to the sonic core .
This part of the core is called homologous because it can be shown
that within it, vcollapse is proportional to radius. Thus the homologous
core collapses in a sef similar fashion. Were  = 4/3 for the entire iron
core, the entire core would contract homologously, but because  becomes
significantly less than 4/3, part of the inner core pulls away from the
outer core.
As the center of this inner core approaches and exceeds nuc the resistance
of the nuclear force is communicated throughout its volume by sound waves,
but not beyond its edge. Thus the outer edge of the homologous core is
where the shock is first born. Typically, MHC = 0.6 – 0.8 solar masses.
The larger MHC and the smaller the mass of the iron core, the less
dissipation the shock will experience on its way out.
Factors affecting the mass of the homologous core:
at about point b) on
previous slide
•  YL – the
lepton number , the sum of neutrino and electron
mole numbers after trapping. Larger YL gives larger
MHC and is more conducive to explosion. Less
electron capture, less neutrino escape, larger initial
Ye could raise YL.
•  GR – General relativistic effects decrease MHC, presumably by
strengthening gravity. In one calulation 0.80 solar masses
without GR became 0.67 with GR. This may be harmful
for explosion but overall GR produces more energetic
bounces and this is helpful.
•  Neutrino transport – how neutrinos diffuse out of the core
and how many flavors are carried in the calculation.
Relevant Physics To Shock Survival
The Equation of State and General Relativity
Photodisintegration:
As the shock moves through the outer core, the temperature
rises to the point where nuclear statistical equilibrium favors
neutrons and protons over bound nuclei or even -particles
⎛ 492.26 MeV ⎞
qnuc (56 Fe → 26 p,30n) = 9.65 ×1017 ⎜
⎟
56
⎝
⎠
18
-1
= 8.5 ×10 erg gm
A softer nuclear equation of state is springier and gives a
larger amplitude bounce and larger energy to the initial shock.
General relativity can also help by making the bounce go deeper .
Stellar Structure and the Mass of the Homologous Core
A larger homologous core means that the shock is born farther
out with less matter to photodisintegrate and less neutrino losses
on its way out.
=1.7 ×1051 erg/0.1 M 
The Mass of the Presupernova Iron Core
Neutrino losses
Especially as the shock passes to densities below 1012 g cm-3, neutrino
losses from behind the shock can rob it of energy. Since neutrinos of
low energy have long mean free paths and escape more easily, reactions
that degrade the mean neutrino energy, especially neutrino-electron scattering
are quite important. So too is the inclusion of µ and  flavored neutrinos
Collapse and bounce in a
13 solar mass supernova.
Radial velocity vs. enclosed
mass at 0.5 ms, +0.2 ms,
and 2.0 ms with respect to
bounce. The blip at 1.5
solar masses is due to
explosive nuclear burning
of oxygen in the infall
(Herant and Woosley
1996).
Unless the mass of the iron core is unrealistically small
(less than about 1.1 solar masses) the prompt shock dies
It is now generally agreed (despite what you may read in
old astronomy text books), that the so called prompt
shock mechanism – worked on extensively by Bethe,
Brown, Baron, Cooperstein, and colleagues in the 1980 s –
does not work. The shock fails and becomes in a short time
(< 10 ms) an accretion shock.
It will turn to neutrinos and other physics to actually blow up
the star. But the success of the neutrino model will depend, in part,
upon the conditions set up in the star by the failure
of the first shock. How far out did it form? What is the
neutrino luminosity? Does convection occur beneath the
neutrinosphere? So all the factors listed on the previous
pages are still important.