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The Storyline of the Project:
How to turn this…
…into this!
1: Before and after
pictures of SN1987a.
E. MyraFigure
& D. Swesty
11/9/2004
Supercomputing 2004
Chapter 6
Core-collapse Supernovae
6.1 Infall phase
We begin with a massive star, in excess of 10 solar masses, burning the hydrogen in its core
under the conditions of hydrostatic equilibrium. When the hydrogen is exhausted, the core
contracts until the density and temperature are reached where 3α →12 C can take place. The
He is then burned to exhaustion. The pattern, fuel exhaustion, contraction, and ignition of
the ashes of the previous burning cycle repeats several time, leading finally to the explosive
burning of 28 Si to Fe. For a heavy star, the evolution is rapid: the star has to work harder
to maintain the hotter electron gas necessary to sustain itself against its own gravity, and
therefore consumes its fuel faster. Likewise, as the star contracts to higher density after each
burning stage, and because the energy liberated in late-stage burning cycles is modest (see
below), the evolution accelerates as the star progresses to later stages. A 25 solar mass star
would go through all of these cycles in about 7 My, with the final explosion Si burning stages
taking a few days. The resulting ”onion skin” structure of the precollapse star is shown in
Figure 2. Note that one can read off the nuclear history of the star by looking from the
surface inward.
1
apse
urning lighter
ear fusion,
nts
ce elements
hich then
e structure
ely heavier
H
He
He
C,O
C
Ne,Mg
O
S,Si
S,Si
Fe
Fe
ogresses
s becomes
es the core
elf against
collapses
Figure 2: Qualitative
depiction of the onionskin structure
to which a massive
star, above
a & D. Swesty
11/9/2004
Supercomputing
2004
about 8 solar masses, evolves. Core collapse is initiated when the inert iron core, augmented
by continuing silicon burning, reaches the Chandrasekar mass.
2
The source of energy for this evolution is nuclear binding energy. A plot of the nuclear
binding energy as a function of nuclear mass shows that the minimum is achieved at Fe. In
a scale where the 12 C mass is picked as zero:
12
C
δ/nucleon = 0.000 MeV
O
δ/nucleon = -0.296 MeV
28
Si δ/nucleon = -0.768 MeV
40
Ca δ/nucleon = -0.871 MeV
56
Fe δ/nucleon = -1.082 MeV
72
Ge δ/nucleon = -1.008 MeV
98
Mo δ/nucleon = -0.899 Mev
16
where δ is the nuclear binding energy relative to C. This defines the energy available from
burning carbon through iron, about 1 MeV. (Recall the energy liberated in burning protons
to He was about 6.5 MeV per nucleon.) Once the Si burns to produce Fe, there is no further
source of nuclear energy adequate to support the star. So as the last remnants of nuclear
burning take place, the core is largely supported by degeneracy pressure, with the energy
generation rate in the core being less than the stellar luminosity. The core density is about
2 ×109 g/cc and the temperature is kT ∼ 0.5 MeV.
As the Fe core, as it grows, cannot produce nuclear energy to sustain equilibrium, the
possibility for stable evolution is support by degeneracy pressure. We have encountered a
situation like this before: we previously discussed solar-mass-like red giants with degenerate
He cores, prior to He ignition. The current situation is different, in that we are envision a
massive star, perhaps 25M . We also have a core that is growing, as the ashes of Si burning
are added to the Fe core. Thus we need to determine whether anything interesting happens,
and if so, at what core mass? We can return to the Lane-Emden equation to try to answer
this. We started with an EoS
p(r) = kρ(r)γ
(1)
We introduced a function
Φ(r) =
ρ(r)
ρ0
!γ−1
=
p(r)
p0
! γ−1
γ
(2)
which was found to satisfy
1
d2 Φ(x) 2 dΦ(x)
+
+ Φ(x) γ−1 = 0.
2
dx
x dx
(3)
The boundary conditions were
Φ0 (0) = 0
Φ(0) = 1
(4)
and x ≡ r/rx where
"
p0 γ
rx =
4πGρ20 (γ − 1)
3
#1/2
(5)
The radius of the star is defined at the point where Φ(x) vanishes: that’s where the pressure
and density vanish. Previously we solved for this surface coordinate for γ = 4/3, which we
showed was an appropriate choice for the Sun. What is the appropriate γ for our present
situation? First the number density of electrons is
ne =
kF3
where ρ = ne mN µe
3π 2 h̄3
(6)
where the molecular weight µe = A/Z ∼ 2 and where we observe that all of the mass is in
nucleons (Fe). Solving this, we find the kF > me for ρ > 106 g/cm3 . But the density at
the mass of the Si zone in such a star is typically ∼ 2 · 107 . So we know the electron gas is
relativistic
Now in the present case, we are interested in the iron core, so we recognize that the gas
pressure will be dominated by electrons, as the electron/ion ratio is large. Since the gas is
relativistic p = /3, so
8π Z kF 3
k2
1 4
2(4π) Z kF
2
q
k dk →
k dk =
k
p=
3
3
3(2π) 0
3(2π) 0
12π 2 F
k 2 + m2e
But we also know
kF = (3π 2 ne )1/3 =
3π 2 ρ
mN µe
(7)
!1/3
(8)
Consequently
1
p=
12π 2
So we find
NA
p = 0.773
µe
3π 2 ρ
MN µe
!4/3
!4/3
ρ
g/cm3
(9)
!4/3
cm−4 h̄c
(10)
or equivalently
p = kρ4/3 where k = 0.776 · 1021 µe−4/3 cm MeV/g4/3
(11)
So a relativistic Fermi gas is also an n = 3 (γ = 4/3) polytrope. That is, we have already
solved this problem. Specifically we found
Φ(x) = 0 ⇒ x = 6.89685
(12)
which defines the surface as
"
p0 γ
Rs ≡ 6.89685rx = 6.89685
4πGρ20 (γ − 1)
#1/2
"
= 6.89685
kγ
2/3
4πGρ0 (γ − 1)
#1/2
(13)
Plugging in the numbers and doing the algebra gives
"
2
Rs = 3.35 · 10 km
µe
4
4
#2/3 "
106 g/cm3
ρ
#1/3
(14)
We also solved for the mass last time
M = 4πrx3 ρ0 (2.01824) ⇒ M = 1.46M
(15)
Now note that the mass is independent of ρ0 and Rs . Also note that the higher the density,
the smaller Rs . Now we have assume the ultra-relativistic limit. What this tells us is that
once the ultra-relativistic part of the iron core reaches a mass above the Chandrasekhar
limit, 1.46 M , there can be no stable solution.
Now this situation arises in a massive star. As Si burning proceeds to build a larger and
larger iron core, finally reaching the Chardrekhar limit, and as the last remnants of burning
within that mass turns off, forcing the iron core to support itself henceforth by degeneracy
pressure, then we see if that mass exceeds the Chadrasekhar mass, there is no stable solution.
The contraction will continue, a core collapse. This happens – core collapse of Ne – for stars
above over 11 solar masses. There are also core collapses of a somewhat different type for
ONeMg cores of 8-10 M .
The collapse alters many of the condition in the core, defining the conditions for the
following supernova explosion and neutron star (or black hole). As gravity does work on the
matter, the collapse leads to a rapid heating and compression of the matter. As the nucleons
in Fe are bound by about 8 MeV, sufficient heating can release αs and a few nucleons. At
the same time, the electron chemical potential is increasing. This makes electron capture on
nuclei and any free protons favorable
e− + p → νe + n
(16)
Note that the chemical equilibrium condition is
µe + µp = µn + hEν i
(17)
Thus the fact that neutrinos are not trapped plus the rise in the electron Fermi surface as
the density increases, lead to increased neutronization of the matter. The escaping neutrino
carry off energy and lepton number. Both the electron capture and the nuclear excitation
and disassociation takes energy out of the electron gas, which is the star’s only source of
support. This means that the collapse is very rapid. Numerical simulations find that the
iron core of the star (∼ 1.2-1.5 solar mases) collapses at about 0.6 of the free fall velocity.
In the early stages of the infall the νe s readily escape. But neutrinos are trapped when a
density of ∼ 1012 g/cm3 is reached. At this point the neutrinos begin to scatter off the matter
through both charged current and coherent neutral current processes. The neutral current
neutrino scattering off nuclei is particularly important, as the scattering cross section is off
the total nuclear weak charge, which is approximately N2 , where N is the neutron number.
This process transfers very little energy because the mass energy of the nucleus is so much
greater than the typical energy of the neutrinos. But momentum is exchanged. Thus the
neutrino “random walks” out of the star. When the neutrino mean free path becomes sufficiently short, the “trapping time” of the neutrino begins to exceed the time scale for the
5
collapse to be completed. This occurs at a density of about 1012 g/cm3 , or somewhat less
than 1% of nuclear density. After this point, the energy released by further gravitational
collapse and the star’s remaining lepton number are trapped within the star.
If we take a neutron star of 1.4 solar masses and a radius of 10 km, a rough estimate of its
binding energy is
GM 2
∼ 2.5 × 1053 erg
(18)
2R
Thus this is roughly the trapped energy that will later be radiated in neutrinos.
The trapped lepton fraction YL is a crucial parameter in the explosion physics: a higher
trapped YL leads to a larger homologous core, a stronger shock wave, and easier passage of
the shock wave through the outer core, as will be discussed below. Most of the lepton number
loss of an infalling mass element occurs as it passes through a narrow range of densities just
before trapping. The reasons for this are relatively simple: as we have seen in other plasmas,
electron capture (and other weak interactions) goes as T 5 . Thus the electron capture rapidly
turns on as matter falls toward the trapping radius. So the lepton loss is maximal just prior
to trapping. Inelastic neutrino reactions have an important effect on these losses (to be
described in detail in class).
6.2 The shock wave
The velocity of sound in matter rises with increasing density. The inner homologous core,
with a mass MHC ∼ 0.6 − 0.9 solar masses, is that part of the iron core where the sound
velocity exceeds the infall velocity. This allows any pressure variations that may develop in
the homologous core during infall to even out before the collapse is completed. As a result,
the homologous core collapses as a unit, retaining its density profile. That is, if nothing were
to happen to prevent it, the homologous core would collapse to a point.
A lot of interesting physics occurs as the matter approaches nuclear densities of about 1014
g/cm3 . Nuclear matter goes through a series of phase changes – bubbles, rods, pasta – as nuclei are forced together to form bulk nuclear matter. The physics is governed by the changing
minimum-energy state, which depends on Coulomb and nuclear forces and the competition
between nuclear volume and surface energies.
The collapse of the homologous core continues until nuclear densities are reached. Nuclear
matter is rather incompressible (∼ 200 MeV/f3 !) densities of 3-4 times nuclear density are
reached, e.g., perhaps 6 · 1014 g/cm3 . The innermost shell of matter reaches this supernuclear
density first, rebounds, sending a pressure wave out through the homologous core. This wave
travels faster than the infalling matter, as the homologous core is characterized by a sound
speed in excess of the infall speed. Subsequent shells follow. The resulting series of pressure
waves collect near the sonic point (the edge of the homologous core). As this point reaches
nuclear density and comes to rest, a shock wave breaks out and begins its traversal of the
outer core. That is, the shock wave forms at the boundary of the homologous core, the point
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where supersonic becomes subsonic.
Initially the shock wave may carry an order of magnitude more energy than is needed to
eject the mantle of the star (less than 1051 ergs). But as the shock wave travels through the
outer iron core, it heats and melts the iron that crosses the shock front, at a loss of ∼ 8
MeV/nucleon, reversing the effects of all prior stages of quiescent stellar burning. The net
drain of energy from the shock wave is about 1051 ergs for every 0.1 solar masses disassociated. So clearly the shock is in trouble if it has to transverse on the order of a solar mass
of material before ejecting the mantle. The enhanced electron capture that occurs off the
free protons left in the wake of the shock, coupled with the sudden reduction of the neutrino
opacity of the matter (recall σcoherent ∼ N 2 ), greatly accelerates neutrino emission. This is
another energy loss. [Many numerical models predict a strong “breakout” burst of νe s in
the few milliseconds required for the shock wave to travel from the edge of the homologous
core to the neutrinosphere at ρ ∼ 1012 g/cm3 and r ∼ 50 km. See Figure 4. The neutrinosphere is the term from the neutrino trapping radius, or surface of last scattering.] The
summed losses from shock wave heating and neutrino emission are comparable to the initial
energy carried by the shock wave. Thus most numerical models fail to produce a successful
“prompt” hydrodynamic explosion.
Consequently the shock wave stalls in the outer iron core, before it reaches the point just
outside the iron core where the shock can (in principle) deliver enough energy to the matter
to lift it off the star. Note that the supernova problem is entirely one of energy transfer: all
matter in the star was initially bound. Thus the energy released by the core in falling deep
into a gravitational potential must be transfered to the mantle to create an explosion. As we
see below, experts have not yet figured out how to make this transfer sufficiently efficient.
Dissipation by shock-wave heating of matter and by neutrino emission reduce the efficiency
of energy transfer by the shock wave.
Two explosion mechanisms were seriously considered in the last 20 years. In the prompt
mechanism described above, the shock wave is sufficiently strong to survive the passage of
the outer iron core with enough energy to blow off the mantle of the star. The most favorable results were achieved with smaller stars (less than 15 solar masses) where there is less
overlying iron, and with soft equations of state, which produce a more compact neutron star
and thus lead to more energy release. In part because of the lepton number loss problems
discussed earlier, now it is widely believed that this mechanism fails for all but unrealistically
soft nuclear equations of state.
The delayed mechanism begins with a failed hydrodynamic explosion; after about 0.01 seconds the shock wave stalls at a radius of 200-300 km. It exists in sort of equilibrium, gaining
energy from matter falling across the shock front, but loosing energy to the heating of that
material. However, after perhaps 0.5 sec, the shock wave is revived due to neutrino heating
of the nucleon “soup” left in the wake of the shock. This heating comes primarily from
7
charged current reactions off the nucleons in that nucleon gas; quasielastic scattering also
increases the energy transfer. This heated gas may reach 2 MeV in temperature; it has a
very high entropy. Thus the energy is in the radiation, not the matter. The pressure exerted
by this gas, perhaps augmented by convection, helps to push the shock outward. It is important to note that there are limits to how effective this neutrino energy transfer can be in
one-dimensional models: if matter is too far from the core, the coupling to neutrinos is too
weak to deposite significant energy. If too close, the matter may be at a temperature (or
soon reach a temperature) where neutrino emission cools the matter as fast or faster than
neutrino absorption heats it. It the parlance of the field, one hears the work “gain radius”
to describe the region where useful heating is done. Convection, however, can get around
such limits, as will be discussed in class in more detail.
This subject is still very controversial and unclear. The problem is extremely difficult numerical, challenging modelers to handle the difficult hydrodynamics of a shock wave; the
complications of the nuclear equation of state at densities not yet accessible to experiment;
modeling in two or three dimensions that is necessary for understanding convection; handling
the slow diffusion of neutrinos; etc. Not all of these aspects can be handled reasonably at
the same time, even with existing supercomputers. Thus there is considerable disagreement
about whether we have any supernova model that succeeds in ejecting the mantle.
There are some crude formulas that are often quite useful in working out factor-of-two
estimates for explosion properties. For example, as we have mentioned that the collapse
dynamics approaches (∼ 0.6) that of free-fall, we can make a rough dimensional estimate of
the collapse time
s
0.6
M 1/2 3/2
r3
1
(19)
∼ 102
r10 s,
τcoll ∼
α 2GM
α
M
where α ∼ 0.6 is the ratio of the infall velocity to the free-fall velocity, M ∼ 2.4–33 M is
the mass enclosed within r (the range represents what one gets by examining progenitors
from ∼ 10 M to ∼ 75 M ), and r10 is r in units of 1010 cm. So r10 ∼ 1 is quite far out in
most progenitors, perhaps the outer He shell, and for such shells the dynamic time scale for
collapse is much longer than, for example, the neutron star cooling time.
The shock wave heats the material. We can make a rough estimate of this, as a function of
the shock wave energy. The physical picture is that the shock wave energy declines relatively
steeply, so that at radius r most of its energy has been dissipated in the heating of the nucleon
or nuclear gas left in its wake. That energy goes primarily into radiation: if one works out
the energy in the photon gas at the temperatures produced in a supernova, the entropy per
baryon is typically on the order of 50-100 Boltzmann units. Thus we can equate the energy
of a radiation-dominated ball of radius r to the initial shock wave energy. One finds
1/4 −3/4
Tp,8 ∼ 2.37E50 r10 .
(20)
Here T8 denotes temperature in units of 108 K. A natural comparison is of this peak heating
temperature with the temperature of material before the shock wave passes. That material
8
Convection Occurs….
E. Myra & D. Swesty
11/9/2004
Supercomputing 2004
Figure 3: A two-D simulation by Myra and Swesty, involving both hydrodynamics and treatment of energy and lepton number transport by diffusing neutrinos, showing the development
of convection.
9
had a temperature consistent with hydrostatic equilibrium. One finds typically that the
shock wave increases the material by a factor of two or three. This is a big deal for exponentially suppressed nuclear rates, and means that significant additional nuclear burning is
triggered by shock wave passage.
The time of shock arrival can also be estimated,
M − MNS
τsh ∼ 21.8
M
!1/2
r10
1/2
E50
s,
(21)
This comes from the so-called Sedov solution of a spherical blast wave propagating through
a uniform medium. One notes that in the inner mantle – say the O and C zones of a supernova where the radius is on the order of 109 cm – the shock wave arrives on the order
of two seconds. So this is comparable to the neutrino e-folding time of roughly 3 seconds,
and means that if we are interested in neutrino physics (oscillations, or neutrino-induced nucleosynthesis) we might need to worry about two epochs, before and after shock wave arrival.
For example, the MSW potential depends on density. With the same 1) physical picture
of shock wave heating – a ball of heated gas that therefore exerts pressure; 2) an estimate
of the ambient pressure of the gas before shock wave arrival – this is given by hydrostatic
equilibrium, so can be easily derived from the gravitational constant and the radiusl and 3)
using some reasonable number for the compressibility of the matter at typical densities of,
say, 106 g/cm3 , one can estimate the degree to which the matter compresses due to shock
wave passages. A typical number is a factor of 7. So this is a big deal both in terms of
reaction rates (two-body reactions track linearly with density) and the MSW potential. The
compresses on a timescale comparable to τsh .
I should mention the term “mass cut”. This describes the bifurcation point of the star.
Below the mass cut, matter falls into the neutron star (or black hole). Outside the mass cut,
matter is ejected. Just above the mass cut, the matter is a very high entropy nucleon gas
that is blown off the star by neutrinos, or the “neutrino wind.” We will have a homework
problem on this wind.
6.3 Neutrinos
However the explosion proceeds, there is agreement that 99% of the 3 ·1053 ergs released in
the collapse is radiated in neutrinos of all flavors. The time scale over which the trapped
neutrinos leak out of the protoneutron star is about 3 seconds. (Fits to SN1987A give,
assuming an exponential cooling e−t/τ , τ ∼ 4.5 sec.) Through most of their migration out of
the protoneutron star, the neutrinos are in flavor equilibrium, e.g.,
νe + ν¯e ↔ νµ + ν¯µ
(22)
As a result, there is an approximate equipartition of energy among the neutrino flavors.
After weak decoupling, the νe s and ν¯e s remain in equilibrium with the matter for a brief
10
time due to scattering off electrons and, especially, the charged current reactions
νe + n ↔ p + e−
ν¯e + p ↔ n + e+
(23)
As a result, the heavy flavor neutrinos decouple from the matter first, at a somewhat higher
temperature. Typical calculations yield
Tνµ ∼ Tντ ∼ 6 − 8 MeV Tνe ∼ 3 − 3.5 MeV Tν¯e ∼ 3.5 − 4.5 MeV
(24)
The difference between the νe and ν¯e temperatures is a result of the neutron richness of the
matter, which enhances the reactions of the νe s, thereby keeping them coupled to the matter
to a larger, cooler radius.
This temperature hierarchy is crucially important to nucleosynthesis (we will see this when
we look at the r-process) and also to possible neutrino oscillation scenarios. The three-flavor
MSW level-crossing diagram is shown in Figure 6. One very popular scenario attributes the
solar neutrino problem to νµ − νe transmutation; this means that a second crossing with a ντ
could occur at higher density. It turns out plausible seasaw mass patterns suggest a ντ mass
on the order of a few eV, which would be interesting cosmologically. The second crossing
would then occur outside the neutrino sphere, that is, after the neutrinos have decoupled
and have fixed spectra with the temperatures given above. Thus a νe − ντ oscillation would
produce a distinctive T ∼ 8 MeV spectrum of νe s. This has dramatic consequences for
terrestrial detection and for nucleosynthesis in the supernova.
6.4 Convection
A current terascale computing grand challenge is 2D modeling to explore the possibility that
convection is might help achieve explosions. There is substantial evidence from SN1987A
and other supernovae that convection occurs during the explosion: explosion asymmetry,
early emission of x-rays and γ rays, and outward mixing of 56 Ni. Simulations, such as those
illustrated in Fig 3, show the development of convection as high-entropy material, heated
from below by neutrinos, rises and is replaced by cooler mater from above.
6.5 The light curve
Well after the explosion, observers can measure the light emitted by the supernova. At late
times mich of the observed power comes from radioactive species synthesized in the explosion.
Figure 7 shows isotopes that we believe contribute to the light curve. One exciting, very
recent result is the identification of a supernova remnant, about 300 years old, in our galaxy
due to observation of the gamma ray line from 44 Ti. This line was previously seen in a known
supernova remnant (Cass A). The second source has no optical counterpart in the historical
record.
11
34
Figure
4: A simulation of the very-early neutrino flux from a core-collapse supernova. The
F IG . 17.— Lν , Lν̄ , and Lν in units of 1053 erg s−1 at infinity for κ = 180 (dotted lines) and κ = 375 (solid lines).
spike in the deleptonization or breakout burst, dominantly νe s. Production of energetic
neutrinos of all flavors continues for several seconds: the flux declines with a time constant
of two or three seconds, models predict. From Burrows et al.
e
e
µ
12
Figure C.12: The IMB and Kamioka neutrino events from SN1987A.
Figure 5: The direct detection of supernova neutrinos is so far limited to a handful of
events F.2
recorded
by Neutrinos:
the IBM Current
and Kamioka
detectors
during
These detectors are
Supernova
and Future
Observatories.
TheSN1987A.
most important
overwhelmingly
sensitive
to anti-electron
neutrinos
because
of the charged-current
consideration
in preparing
for the next galactic
supernova
is to appreciate
that an opportunityabsorption
itself once
in a protons
lifetime: the
estimate of the galactic supernova frequency is 1/30y.
of thesepresents
neutrinos
on free
inbest
water.
There are two consequences. First, we need to be prepared at all times with detectors capable of
measuring the spectrum, including the flavor and time development, of the next supernova,
which could occur at any time. The minimum requirements are detectors operating in both
charge-current modes as well as some scheme for measuring neutral current interactions. Second,
most (though not all) supernova observatories are likely to be detectors with additional physics
goals, such as proton decay or solar neutrinos. Thus a theme of this field is the “supernova
watch” – the notion that we should try to coordinate the world’s program of underground
neutrino detectors to guarantee that the necessary supernova capability is always in place.
Directional sensitivity is also important, as this could help optical observers locate the supernova
quickly. Detectors exploiting elastic scattering off electrons provide some directional
information. Another possibility, if several detectors are able to measure enough events to
determine the turn-on time of the neutrino pulse to millisecond accuracy (or if the
deleptonization burst could be used as a clock), is to determine the direction by triangulation.
13
A-55
e
m
eff
e
e
12
3
10 g/cm
density
vacuum
Figure 14: Three-flavor neutrino level-crossing diagram. One popular scenario associates the
Figure 6:
depiction
of with
theνethree-flavor
oscillation
MSW
crossings.interested
The larger δ m2
solarAneutrino
problem
↔ νµ oscillations
and predicts
a cosmologically
massive νcrossing
ντ oscillations
near the supernova
neutrinosphere.
τ with νe ↔
atmospheric-neutrino
occurs
at a density
of about
104 g/cm3 . This places the
crossing, for typical supernova neutrino energies, near the base of the convective zone. This
is outside
where
interesting
explosion
However,
this estimate igarethe
notradius
produced
in sufficient
amounts
in thephysics
big bangoccurs.
or in any
of the stellar
nores a new
contribution
to discussed.
the MSW The
potential,
neutrino
scattering
thecosmic
trapped neutrino
mechanisms
we have
traditional
explanation
has off
been
sea. The
of this
new potential
onand
theNlocation
of the crossing
rayeffects
spallation
interactions
with C, O,
in the interstellar
medium. point
In thisis still being
picture, cosmic ray protons collide with C at relatively high energy, knocking
investigated.
the nucleus apart. So in the debris one can find nuclei like 10 B, 11 B, and 7 Li.
But there are some problems with this picture. First of all, this is an
example of a secondary mechanism: the interstellar medium must be enriched
in the C, O, and N to provide the targets for these reactions. Thus cosmic ray
spallation must become more effective as the galaxy ages. The abundance of
boron, for example, would tend to grow quadratically with metallicity, since
the rate of production goes linearly with metallicity. But observations, especially recent measurements with the HST, find a linear growth 49 in the boron
abundance.
A second problem is that the spectrum of cosmic ray protons peaks near
14
52
Figure 7: The nuclear decays thought to power the early light curve of a Type II supernova.
15
Explosive nucleosynthesis
Shell-Structured
Evolved Massive Star
Gravitational
Core Collapse
Supernova
Shock Wave
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
Shock Region
Explosive Nucleosynthesis
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
Proto-Neutron Star
Neutrino Heating
of Shock Region from Inside
XXXVIII Rencontres de Moriond: Radiactive Beams for Nuclear Physics and Neutrino Physics
ν
ν
Neutrino reactions in astrophysics – p. 10
Figure 8: A cartoon summary of the physics described in this chapter. The final frame, a
high-entropy neutron-rich nucleon gas expanded off the star, defines the initial conditions
for interesting nucleosynthesis – such as the r-process, which we will discuss soon. From
Martinez-Pinedo.
16