1. Supernova Neutrinos Christian Y. Cardall Oak Ridge National Laboratory
Physics Division
University of Tennessee, Knoxville
Department of Physics and Astronomy
It’s a pleasure to speak to you today about Supernova Neutrinos---especially in this wonderful location.
In addition to my affiliations with Oak Ridge and the University of Tennessee, I am a member of the Terascale Supernova Initiative (or TSI), led by Tony Mezzacappa. This is a large collaboration involving about 20 Pis and some 100 people altogether. Its purpose is to elucidate the core-collapse supernova mechanism through large-scale computer simulations. Working with me on this particular prong of TSI’s efforts are Alex Razoumov, Eirik Endeve, and Eric Lentz.
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Before getting into my talk, by way of advertisement I’d like to mention that in addition to my affiliations with Oak Ridge National Laboratory and the University of Tennessee, Knoxville, I am a member of the Terascale Supernova Initiative. This is a large collaboration involving about 20 Pis and some 100 people altogether. Its purpose is to elucidate the core-collapse supernova mechanism through large-scale computer simulations.

2. Core-collapse supernovae Survey of collapse simulations Supernova neutrino signals New effects at small ∆m2?
There are four things I’d like to do in my talk today. First I will sketch the physics of core-collapse supernovae. Then I will describe the outcome of simulations being performed by several groups around the world. I will spend some time on supernova neutrino signals, and very briefly mention some effects of flavor mixing that may even occur at small delta m^2.

3. Core-collapse supernovae
So first then, an introduction to core-collapse supernovae.

4. SN 1998aq
(in NGC 3982)
A supernova is an awe-inspiring phenomenon. In their optical emission, supernovae at their peak are up to a billion times as luminous as the sun. To get an idea of what that means, consider this image, which shows a face-on spiral galaxy with a supernova (the blue object here; the other point sources are foreground stars). The peak optical luminosity of a supernova, a billion times the solar luminosity, can be of the same order of magnitude as the combined optical output of the billion or so other stars in its host galaxy!
..consider this image, which shows the spiral galaxy NGC 3982, which happens to be face-on to us. The blue object is SN 1998aq. The peak optical luminosity of a supernova, a billion times the solar luminosity, can be of the same order of magnitude as the combined optical output of all the other stars in the galaxy!

5. Spectral classification of supernovae:
Type Ia
(no H, strong Si)
Type I
(no H)
Type II
(obvious H)
Type Ic
(no H, He, Si)
Type Ib
(no H, obvious He)
Supernovae are classified by astronomers into two broad classes, imaginatively called "Type I” and "Type II,” based on their spectra. Type II supernovae are distinguished by obvious hydrogen lines. These result from the core collapse of a star with a massive hydrogen envelope as its outermost layer. Type I supernovae have no hydrogen lines, and there are three subtypes. Type Ia have strong silicon lines. These result not from the core collapse of a massive star, but a totally different mechanism: the thermonuclear disruption of a white dwarf that has exceeded the Chandrasekhar mass limit due to the accretion of mass from a companion star. With Types Ib and Ic, however, we return to core collapse events, typically of the most massive stars. Stars giving rise to Type Ib have lost their hydrogen layer to stellar winds (or perhaps mass loss to a companion), revealing the helium layer underneath in their spectra; while those of Type Ic have lost their helium layer as well.
Supernovae are classified by astronomers into two broad classes based on their spectra, imaginitavely called "Type I" (which have no hydrogen features) and "Type II" (which have obvious hydrogen features). These types have further subcategories, depending on the presence or absence of silicon and helium features in Type I, and the presence or absence of narrow hydrogen features in the case of Type II.
In these representative spectra one can see the silicon line characteristic of Type Ia, obvious hydrogen features associated with Type II, the helium feature in Type Ib, and the absence of all of these in Type Ic.
In these representative spectra one can see the silicon line characteristic of Type Ia, obvious hydrogen features associated with Type II, the helium feature in Type Ib, and the absence of all of these in Type Ic.
Filippenko (1997)

6. For most of their existence stars burn hydrogen into helium
For most of their existence stars burn hydrogen into helium. Stars with masses greater than about 8 times that of the Sun can subsequently burn to carbon and oxygen, and then a growing core of oxygen, neon, and magnesium ash. Those greater than about 10 solar masses, such as this representative 15 solar mass star, burn further to silicon and iron group elements. The iron group nuclei are the most tightly bound, and here burning in the core ceases.
The oxygen/neon/magnesium or iron core, supported by electron degeneracy pressure, becomes unstable when it reaches the Chandrasekhar mass. Its inner portion, denoted by the purple region, collapses subsonically (velocities are indicated by the black arrows). Electron capture on nuclei is one instability leading to collapse, and this process continues, releasing neutrinos (represented by the red arrows) until densities become so high that even neutrinos are trapped. Collapse is halted when the matter reaches a few times nuclear density; a shock wave forms when supersonically infalling matter from the outer core (indicated in light blue) hits the inner core, whose collapse has halted. The shock wave begins to move out (black arrows), but stalls as energy is lost to neutrino emission and dissociation of infalling heavy nuclei falling through the shock.
As I mentioned, electron capture resulting in energy loss to neutrinos is a major source of instability leading to collapse (the other being endoergic nuclear photodissociation). For later discussion, it’s convenient at this point to highlight the connection between charged-current neutrino reactions (such as electron capture) and the electron fraction Ye. Ye is defined as the ratio of net electron number to baryon number. By charge conservation, this can be written in terms of proton and neutron numbers, and therefore becomes an important parameter in nucleosynthesis, as I will mention later. Ye < 0.5 corresponds to neutron rich material, and Ye > 0.5 is proton rich.
Here is the familiar composition layering in the pre-supernova star, with the iron core, resulting from its sequence of burning stages. Here is the collapsing iron core, with the region in purple in sonic contact; the region in blue infalling supersonically; black arrows representing velocity, both infall and then some outflow immediately after bounce; red arrows indicating neutrino emission; an orange ring denoting the shock generated by supersonic infall on the halted inner core; and the shocked region in yellow.
Electron capture resulting in energy loss to neutrinos is a major source of instability leading to collapse. For later discussion, it’s convenient at this point to highlight the connection between charged-current neutrino reactions (such as electron capture) and the electron fraction Ye. Ye is defined as the ratio of net electron number to baryon number. By charge conservation, this can be written in terms of proton and neutron numbers, and therefore becomes an important parameter in nucleosynthesis, as I will mention later. Ye < 0.5 corresponds to neutron rich material, and Ye > 0.5 is proton rich.
For most of their existence stars burn hydrogen into helium. In massive stars temperatures and densities are sufficient to burn to carbon, oxygen, neon, magnesium, and silicon and iron group elements. The iron group nuclei are the most tightly bound, and here burning in the core ceases.
The iron core, supported by electron degeneracy pressure, becomes unstable when it reaches the Chandrasekhar mass. Its inner portion, denoted by the purple region, collapses subsonically (velocities are indicated by the black arrows). Electron capture on nuclei is one instability leading to collapse, and this process continues, releasing neutrinos (represented by the red arrows) until densities become so high that even neutrinos are trapped. Collapse is halted when the matter reaches nuclear density; a shock wave forms when supersonically infalling matter from the outer core (indicated in light blue) hits the inner core, whose collapse has halted. The shock wave begins to move out (black arrows), but stalls as energy is lost to neutrino emission and dissociation of infalling heavy nuclei falling through the shock.
This is the usual basic story of stellar collapse, but all the spheres in this depiction may leave this particular audience rather unhappy.
If spherical symmetry brings tears to your eyes, then let me say that realistic progenitors may wipe those tears away, for their rotation and magnetic fields will give rise to aspherical collapse. This asphericity, together with the fact that you have a lot of mass ending up at high densities via high infall velocity, gives rise to gravitational wave signal from core collapse and bounce that may well be detectable by first-generation LIGO for a supernova occurring in our galaxy. After core bounce there are other phenomena that could generate gravitational radiation, but at weaker levels, perhaps detectable by advanced LIGO.
In the last section of the talk I’ll discuss [two of these phenomena: Core bounce, because it gives the most promising signal for first-generation LIGO, and] the accretion shock instability, which will give me a chance to show a movie. It’s relatively new work done by TSI collaborators, probably unfamiliar to most here, so shameless advertising on behalf of my collaboration provides another motivation for selecting this topic.
[The depiction here is spherically symmetric, and unfortunately this is how most supernova simulations begin. This is in part because of the unavailability of multidimensional progenitors, but also because of the computational difficulty of performing Eulerian collapse in multiple spatial dimensions. (Lagrangian collapse in spherical symmetry is much more practical.)]

7. Rotation Magnetic Fields
Focusing on the region interior to the shock—which has stalled due to cooling by neutrino emission and photodisintegration of iron falling through the shock—we have a region of net cooling region just outside the so-called neutrinosphere, and heating further out just behind the shock. The need for neutrino transport—as opposed to the inclusion of the neutrinos in the hydrodynamic fluid—arises from the fact that the neutrino distributions go from nearly isotropic diffusion inside the protoneutron star to strongly forward peaked free streaming outside. The region behind the shock sits in this transition region; hence the fact that the net heating rate depends on the neutrino angular distributions motivates angle-dependent neutrino transport. Moreover, this transition has a different spatial dependence for different energies, motivating the retention of energy dependence as well.
Complicating the spherical appearance of these figures is the fact that negative electron fraction and entropy gradients may cause convection in the protoneutron star and heating region respectively.
Beyond convection is the instability of the spherical accretion shock, as well as rotation and magnetic fields (here I have given up using images, and resort to big fancy word art). Altogether, this means we have a time-dependent problem in three space dimensions plus three momentum space dimensions. That is, we wish to track the energy and angle dependence of the neutrino distributions at every point in space.
Moreover, we wish to do this carefully. The energy scale of a phenomenon we wish to study—the explosion—is 10^51 erg. If during our simulation we lose 10^51 erg while sloshing and streaming 10^53 erg in neutrinos, it raises questions about our ability to accurately resolve one of our target phenomenona.
The nascent neutron star is a hot thermal bath of dense nuclear matter, electron/positron pairs, photons, and neutrinos, containing most of the gravitational potential energy released in the collapse. Neutrinos, having the weakest interactions, are the most efficient means of cooling; they diffuse outward on a time scale of seconds towards a semi-transparent region near the surface of the neutron star, and eventually escape with about 99% of the released gravitational energy (pink arrows).
In the reigning paradigm, the neutrino-driven explosion mechanism, neutrinos from the nascent neutron star heat the material behind the stalled shock, reviving it and propelling it through the outward layers in a successful explosion.
As the neutrinos are transported from inside the neutron star, they go from a nearly isotropic diffusive regime to a strongly forward-peaked free-streaming region. The region behind the shock sits in this transition region; hence the fact that the net heating rate depends on the neutrino angular distributions motivates angle-dependent neutrino transport. This transition has a different spatial dependence for different energies, which together with the inherent energy dependence of neutrino interactions requires the retention of energy dependence as well.
Complicating the spherical appearance of these cartoons is the presence of convection in two regions. First, loss of electron neutrinos from the outer layers of the neutron star causes a composition gradient that drives convection in this inner region. Second, heating from below gives rise to a negative entropy gradient. The resulting convection increases the efficiency of neutrino heating by delivering heated material to the region just behind the shock and allowing cooler material to flow down into regions of higher neutrino flux.
Beyond convection is the instability of the spherical accretion shock, which, as has only been discovered in the past few years, can both create bipolar outflows and spin up the neutron star even in the absence of initial rotation. And here I give up using images, resorting to fancy word art to indicate that strong rotation and magnetic fields may also play important roles, perhaps especially in the more extreme supernova events associated with GRB.
Altogether, this means we have a time-dependent problem in three space dimensions plus three momentum space dimensions. That is, we wish to track the energy and angle dependence of the neutrino distributions at every point in space.
This process may be aided by convection in two regions. First, loss of electron neutrinos from the outer layers of the neutron star causes a composition gradient that drives convection, which boosts neutrino luminosities by bringing hotter material to the surface. Second, heating decreases further from the neutron star surface, giving rise to a negative entropy gradient. The resulting convection increases the efficiency of neutrino heating by delivering heated material to the region just behind the shock.

8. Some key ingredients are
Neutrino transport/interactions,
Spatial dimensionality;
Dependence on energy and angles;
Relativity;
Comprehensiveness of interactions;
(Magneto)Hydrodynamics/gravitation,
Dimensionality;
Equation of state/composition,
Dense matter treatments;
Number and evolution of nuclear species;
Diagnostics,
Accounting of lepton number;
Accounting of energy;
Accounting of momentum.
From our discussion of the supernova process we can identify several key pieces of physics.
Because neutrinos dominate the system, their treatment is very important, including the number of spatial dimensions treated; dependence on both energy and angle in order to properly model the transition from isotropic diffusion to forward-peaked free streaming; relativistic effects; and comprehensiveness of interactions.
[Let me mention that in these large-scale simulations of the collapse phenomenon, neutrinos are assumed to be massless. The standard view is that the mass differences known from atmospheric and solar neutrino observations only give rise to flavor-changing resonances too far out in the envelope to affect the explosion mechanism or r-process nucleosynthesis. It may turn out that LSND, sterile neutrinos, or nonlinear effects of an oscillating neutrino background overturn this standard wisdom; but in the meantime we assume massless neutrinos, and studies of the effects of flavor mixing in outer envelope are done separately in kind of post-processing mode.]
We saw that convection can play an important role, so allowance for flows in multiple spatial dimensions is important in the hydrodynamics. Ultimately relativity should be included, but most studies addressing gravitational wave phenomena simply use the quadrupole formalism in post-processing mode.
The equation of state and composition involve a lot of cutting-edge nuclear physics, and arguably even condensed matter physics.
Very important to making convincing explosions is fastidious accounting of total lepton number and energy. Because the explosion energy is only 1% of the basic energy scale in the problem, it turns out that energy needs to be conserved at a level of about 1 part in 10^9 per time step.
From our discussion of the supernova process we can identify several key aspects of physics that a simulation must address.
Because neutrinos dominate the system, their treatment is very important, including the number of spatial dimensions treated; dependence on both energy and angle in order to properly model the transition from isotropic diffusion to forward-peaked free streaming; relativistic effects; and comprehensiveness of interactions. Let me mention that in these large-scale simulations of the collapse phenomenon, neutrinos are assumed to be massless. The standard view is that the mass differences known from atmospheric and solar neutrino observations only give rise to flavor-changing resonances too far out in the envelope to affect the explosion mechanism or r-process nucleosynthesis. It may turn out that LSND, sterile neutrinos, or nonlinear effects of an oscillating neutrino background overturn this standard wisdom; but in the meantime we assume massless neutrinos, and studies of the effects of flavor mixing in outer envelope are done separately in kind of post-processing mode.
We saw that convection can play an important role, so allowance for flows in multiple spatial dimensions is important in the hydrodynamics. Ultimately relativity should be included.

9. The observables to understand include
Explosion (and energy thereof);
Neutrinos;
Remnant properties,
Mass, spin, kick velocity, magnetic fields;
Gravitational waves;
Element abundances;
Measurements across the EM spectrum,
IR, optical, UV, X-ray, gamma-ray; images, light curves, spectra, polarimetry...
Supernovae have a rich phenomenology---observations of many types that simulations would like to reproduce and explain.
Chief among the observables is the explosion itself, which is not produced robustly in simulations. I mentioned that 99% of the gravitational potential energy released during collapse escapes as neutrinos; the kinetic energy of expelled matter accounts for about 1%, and the optical display just a tiny fraction of this. Energetically supernovae really are neutrino events; the explosion is just a minor sideshow, the optical display a trivial detail, in spite of the fact that this optical display is equal to the optical output of its host galaxy. That the explosion is such a minor part of the system is what makes it so challenging to model convincingly. But the optical data are what we perceive with our unaided inborn detectors---our eyes---and in our anthropic chauvinism, explaining the explosion seems most interesting.
While the explosion is sexy, neutrino signatures are of great importance. The handful of neutrinos detected from supernova 1987A confirmed the theoretical prediction of neutrinos releasing the gravitational energy on a time scale of seconds. This was a remarkable success of supernova theory and modeling.
There are many other interesting observables. Core-collapse simulations, which I emphasize in my talk today, typically address the first few. Another class of simulation assumes a successful explosion---puts it in artificially---and studies its interaction with the surrounding layers of the star and beyond in order to study things like nucleosynthesis and measurements across the electromagnetic spectrum.
Supernovae have a rich phenomenology---observations of many types that simulations would like to reproduce and explain.
Chief among the observables is the explosion itself, which is not produced robustly in simulations. I mentioned that 99% of the gravitational potential energy released during collapse escapes as neutrinos; the kinetic energy of expelled matter accounts for about 1%, and the optical display just a tiny fraction of this. Energetically supernovae really are neutrino events; the explosion is just a minor sideshow, the optical display a trivial detail, in spite of the fact that this optical display is equal to the optical output of its host galaxy. That the explosion is such a minor part of the system is what makes it so challenging to model convincingly. But the optical data are what we perceive with our unaided inborn detectors---our eyes---and in our anthropic chauvinism, explaining the explosion seems most interesting.
While the explosion is sexy, neutrino signatures are of great importance. The handful of neutrinos detected from supernova 1987A confirmed the theoretical prediction of neutrinos releasing the gravitational energy on a time scale of seconds. This was a remarkable success of supernova theory and modeling.
There are many other interesting observables. Core-collapse simulations, which I emphasize in my talk today, typically address the first few. Another class of simulation assumes a successful explosion and studies its interaction with the surrounding layers of the star and beyond in order to study things like nucleosynthesis and measurements across the electromagnetic spectrum.

10. Survey of collapse simulations

11. Neutrino radiation transport
2S 0M
1S 1M
3S 0M
1S 2M
2S 1M
1.5 2M S
3S 1M
2S 3M N GR 1S 2S B 3S
Magnetohydrodynamics
“Hydro” axis:
1 1D N
2 1D GR
3 2D N
4 2D N MHD
5 2D GR
6 2D GR MHD
7 3D N
8 3D MHD
9 3D GR
10 3D GR MHD
“Neutrino transport” axis:
1 1SD+2MD N + v/c
2 1SD+2MD GR
5 2SD+0MD N + v/c
6 2SD+0MD GR
11 3SD+0MD N + v/c
12 3SD+0MD GR
7 2SD+1MD N + v/c
8 2SD+1MD GR
3 1.5SD+2MD N + v/c
4 1.5SD+2MD GR
13 3SD+1MD N + v/c
14 3SD+1MD GR
9 2SD+3MD N + v/c
10 2SD+3MD GR
15 3SD+3MD N + v/c
16 3SD+3MD N + v/c

12. Two observables beyond explosion…
Accretion continues until the stalled shock is reinvigorated: relation between neutron star mass and delay to explosion
The abundance of nuclei with a closed shell of 50 neutrons
The electron fraction… is set by neutrino interactions:

13. Neutrino transport: 1D + 1D Fluid dynamics: 2D, 3D
Neutrino transport: 2D + 0D, 3D + 0D
Mezzacappa et al. (1998)
Fryer & Warren (2002)
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.

14. Neutron star mass too small; heating drives explosion too soon.
Neutrino radiation transport
2S 0M
1S 1M
3S 0M
1S 2M
2S 1M
1.5 2M S
3S 1M
2S 3M N GR 1S 2S B 3S
Neutron star mass too small; heating
drives explosion too soon.
N=50 overproduction; Ye too low.
Magnetohydrodynamics
“Hydro” axis:
1 1D N
2 1D GR
3 2D N
4 2D N MHD
5 2D GR
6 2D GR MHD
7 3D N
8 3D MHD
9 3D GR
10 3D GR MHD
“Neutrino transport” axis:
1 1SD+2MD N + v/c
2 1SD+2MD GR
5 2SD+0MD N + v/c
6 2SD+0MD GR
11 3SD+0MD N + v/c
12 3SD+0MD GR
7 2SD+1MD N + v/c
8 2SD+1MD GR
3 1.5SD+2MD N + v/c
4 1.5SD+2MD GR
13 3SD+1MD N + v/c
14 3SD+1MD GR
9 2SD+3MD N + v/c
10 2SD+3MD GR
15 3SD+3MD N + v/c
16 3SD+3MD N + v/c

15. Neutrino transport: 1D + 2D
Fluid dynamics: 1D
Neutrino transport: 1D + 2D
Liebendörfer et al. (2001, 2004)
Rampp & Janka (2000, 2002)
Thompson, Burrows, & Pinto (2002)
Kitaura, Janka, & Hillebrandt (2006)
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.

16. Explosion only for 8-10 M stars with O-Ne-Mg cores.
Neutrino radiation transport
2S 0M
1S 1M
3S 0M
1S 2M
2S 1M
1.5 2M S
3S 1M
2S 3M N GR 1S 2S B 3S
Explosion only for 8-10 M stars with
O-Ne-Mg cores.
Reasonable neutron star mass; accretion continues during delay.
Reasonable N=50 element production
expected; ejected matter has Ye > 0.46.
May explain some subluminous Type II-P.
Magnetohydrodynamics
“Hydro” axis:
1 1D N
2 1D GR
3 2D N
4 2D N MHD
5 2D GR
6 2D GR MHD
7 3D N
8 3D MHD
9 3D GR
10 3D GR MHD
“Neutrino transport” axis:
1 1SD+2MD N + v/c
2 1SD+2MD GR
5 2SD+0MD N + v/c
6 2SD+0MD GR
11 3SD+0MD N + v/c
12 3SD+0MD GR
7 2SD+1MD N + v/c
8 2SD+1MD GR
3 1.5SD+2MD N + v/c
4 1.5SD+2MD GR
13 3SD+1MD N + v/c
14 3SD+1MD GR
9 2SD+3MD N + v/c
10 2SD+3MD GR
15 3SD+3MD N + v/c
16 3SD+3MD N + v/c

17. Neutrino transport: 2D + 1D
Fluid dynamics: 2D
Neutrino transport: 2D + 1D
Swesty & Myra (2005)
Burrows et al. (2006)
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.

18. Explosion for 11, 15, 25 M progenitors.
Neutrino radiation transport
2S 0M
1S 1M
3S 0M
1S 2M
2S 1M
1.5 2M S
3S 1M
2S 3M N GR 1S 2S B 3S
Explosion for 11, 15, 25 M progenitors.
Some neutrino transport details left out;
is the acoustic mechanism physical?
Reasonable neutron star mass; accretion continues during delay.
Not yet clear if Ye gives reasonable
nucleosynthesis or if the model is resolved.
Magnetohydrodynamics
“Hydro” axis:
1 1D N
2 1D GR
3 2D N
4 2D N MHD
5 2D GR
6 2D GR MHD
7 3D N
8 3D MHD
9 3D GR
10 3D GR MHD
“Neutrino transport” axis:
1 1SD+2MD N + v/c
2 1SD+2MD GR
5 2SD+0MD N + v/c
6 2SD+0MD GR
11 3SD+0MD N + v/c
12 3SD+0MD GR
7 2SD+1MD N + v/c
8 2SD+1MD GR
3 1.5SD+2MD N + v/c
4 1.5SD+2MD GR
13 3SD+1MD N + v/c
14 3SD+1MD GR
9 2SD+3MD N + v/c
10 2SD+3MD GR
15 3SD+3MD N + v/c
16 3SD+3MD N + v/c

19. Neutrino transport: 1.5D + 2D
Fluid dynamics: 2D
Neutrino transport: 1.5D + 2D
Buras et al. (2006)
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.
Many groups published two-dimensional simulations in the early 90s, and a group centered at Los Alamos was one of the first. Descended from those efforts is a recent simulation in 3D by Fryer & Warren. Pictured is the isosurface of matter having outward radial velocities of 1000 km/s. One sees the outward flowing plumes; the open spaces are downflows.
Another group that did 2D simulations in the mid-90's was centered at the University of Arizona.
Explosions are seen in both these models.
Limits on computational resources required an important liability: a simplified treatment of neutrino transport in which dependence on both energy and angle are integrated out, and some important interactions are left out. They are (at least mostly) nonrelativistic.

20. Full 180º allows an 11 M star to explode;
Neutrino radiation transport
2S 0M
1S 1M
3S 0M
1S 2M
2S 1M
1.5 2M S
3S 1M
2S 3M N GR 1S 2S B 3S
Full 180º allows an 11 M star to explode;
what about higher mass progenitors?
Reasonable neutron star mass; accretion continues during delay.
Reasonable N=50 element production
expected; some of ejecta has Ye > 0.5.
Acoustic mechanism not yet probed.
Magnetohydrodynamics
“Hydro” axis:
1 1D N
2 1D GR
3 2D N
4 2D N MHD
5 2D GR
6 2D GR MHD
7 3D N
8 3D MHD
9 3D GR
10 3D GR MHD
“Neutrino transport” axis:
1 1SD+2MD N + v/c
2 1SD+2MD GR
5 2SD+0MD N + v/c
6 2SD+0MD GR
11 3SD+0MD N + v/c
12 3SD+0MD GR
7 2SD+1MD N + v/c
8 2SD+1MD GR
3 1.5SD+2MD N + v/c
4 1.5SD+2MD GR
13 3SD+1MD N + v/c
14 3SD+1MD GR
9 2SD+3MD N + v/c
10 2SD+3MD GR
15 3SD+3MD N + v/c
16 3SD+3MD N + v/c

21. Neutrino radiation transport
2S 0M
1S 1M
3S 0M
1S 2M
2S 1M
1.5 2M S
3S 1M
2S 3M N GR 1S 2S B 3S
Magnetohydrodynamics
“Hydro” axis:
1 1D N
2 1D GR
3 2D N
4 2D N MHD
5 2D GR
6 2D GR MHD
7 3D N
8 3D MHD
9 3D GR
10 3D GR MHD
“Neutrino transport” axis:
1 1SD+2MD N + v/c
2 1SD+2MD GR
5 2SD+0MD N + v/c
6 2SD+0MD GR
11 3SD+0MD N + v/c
12 3SD+0MD GR
7 2SD+1MD N + v/c
8 2SD+1MD GR
3 1.5SD+2MD N + v/c
4 1.5SD+2MD GR
13 3SD+1MD N + v/c
14 3SD+1MD GR
9 2SD+3MD N + v/c
10 2SD+3MD GR
15 3SD+3MD N + v/c
16 3SD+3MD N + v/c

22. Supernova neutrino signals
Next, we’ll discuss supernova neutrino detection, and what we might learn about neutrino properties and about supernovae.

23. Neutrino predictions ca. 1987
Did anyone do gravitational collapse as a Fermi problem?
Assume the stellar core is basically a white dwarf: a Chandrasekhar mass of 1.4 M and about 104 km.
Assume that the neutron star it collapses to is essentially a giant nucleus, and hence has density n = 0.16 fm-3.
From the mass and final density,

24. Neutrino predictions ca. 1987
How long will it take to collapse? The free-fall time scale is
The iron core is roughly half protons before collapse. Electron capture converts each proton to a neutron with the emission of an antineutrino.
Assume the neutrinos are trapped (check the consistency of this later). Then the number density of antineutrinos is half the final nucleon density.

25. Neutrino predictions ca. 1987
From the number density of antineutrinos, find their typical energy from the inter-particle spacing:
On what timescale will the neutrinos diffuse out?
This ‘validates’ the assumption of neutrino trapping.

26. Neutrino predictions ca. 1987
Almost forgot: the gravitational binding energy released during collapse will be released in neutrinos.
If neutrinos are trapped we expect all flavors to be produced. They will be emitted with a hierarchy of energies because differences in their interactions cause them to decouple at different radii:

27. Neutrino predictions ca. 1987
~ 1s hydrodynamic simulations with decent neutrino transport (Wilson 1984)

28. Neutrino predictions ca. 1987
~ 20s ‘stellar evolution’ with crude transport
Burrows and Lattimer 1986

29. This is the Tarantula Nebula in the Large Magellanic Cloud
This is the Tarantula Nebula in the Large Magellanic Cloud. The left image shows the region before SN 1987A. The right shows SN 1987A in its optical glory. Truly a remarkable change in the heavens!It isn't possible to discern by eyeballing an image like this, but it turns out that at their peak supernovae are about a billion times as luminous as the sun. To give a further idea of what that means...
This is the Tarantula Nebula in the Large Magellanic Cloud. The left image shows the region before SN 1987A. The right shows SN 1987A in its optical glory. Truly a remarkable change in the heavens!It isn't possible to discern by eyeballing an image like this, but it turns out that at their peak supernovae are about times as luminous as the sun. To give a further idea of what that means...
Tarantula Nebula
SN 1987A

30. The lucky messengers…
SN1987A sent ~1058 “messengers,” with ~two dozen detected
Raffelt (1999)
Each “event” involves ~109 “messengers,” with at most 1 “detected”
SN rate only 1 every 100 years…
Collimation…
Active veto

31. Prediction vs. observation
Burrows and Lattimer (1987)

32. A neutrino window into the supernova…
Liebendörfer et al. (2004)
Buras et al. (2005)

33. …could provide information about, for instance, rotation and the nuclear equation of state.
Thompson et al. (2005)
Sumiyoshi et al. (2006)
Pons et al. (2001)

34. Neutrino mixing unknowns: 13 and hierarchy
Raffelt (2005)

35. New effects at small ∆m2?

36. Duan et al. (2006)

37. Duan et al. (2006)

38. Core-collapse supernovae Survey of collapse simulations Supernova neutrino signals New effects at small ∆m2?