Evolution of Massive Stars and the�Explosion Mechanism of Core-Collapse Supernovae
Luca Boccioli
IReNA Third Frontiers in Nuclear Astrophysics
Summer School
May 15th 2025
Massive stars, the progenitors of CCSNe:�
The early phases in the Main Sequence
Massive stars, a qualitative overview:�
The early phases in the Main Sequence
gravity
photons
Massive stars, a qualitative overview:�
The HR diagram
H
He
C
Ne
O
Si
Fe
Massive stars, a qualitative overview :�
The late phases as a supergiant
Mass number
Binding Energy
Fe
Fission
Fusion
Massive stars, a qualitative overview :�
The end is near
Fusion: light nuclei fuse into heavier nuclei and release photons
You cannot generate energy by fusing two Iron nuclei!
Gravity wins, the star collapses!
Massive stars, a qualitative overview :�
The end is near
gravity
photons
No more nuclear reactions,
no more radiation pressure
Fusion: light nuclei fuse into heavier nuclei and release photons
You cannot generate energy by fusing two Iron nuclei!
Massive stars, a quantitative overview :�
What is a star?
A star is a giant ball of gas.
Does it change much?
Not really, the Sun is always kind of the same
A star is a spherically symmetric plasma in hydrostatic equilibrium
Is mass conserved in a star? Yes
With this we have 2 equations for 3 unknowns:
P, M, ρ. But P and ρ are related!
Massive stars, a quantitative overview :�
Temperature
What is responsible for determining the temperature inside a star?
Heat transfer!
+ convection
radiation
Opacity. Can be very complicated but for most stellar evolution phases it has small uncertainties. But can be extremely important for mass loss!
Massive stars, a quantitative overview :�
Nuclear Burning
≈ 0 (until Carbon burning, then it becomes relevant, in particular for determining the Chandrasekhar Mass of the Iron Core and the compactness of the star). See Timmes et al. (1996), Sukhbold (2014)
Δm ≈ Mass of Reactants
Mass of Products
-
Massive stars, a quantitative overview :�
Composition
Reactants
Products
Reaction Rate
Except for convection, which we have not covered in detail, the equations we have derived are the skeleton of every stellar evolution code, which takes a timestep dt, calculates the new compositions, and then with those recalculates a new hydrostatic equilibrium for the star
Core-Collapse Supernova: a qualitative overview�
During collapse, temperature and density rapidly increase
ν
In this phase, electron capture on Fe occurs
The collapse phase
Core-Collapse Supernova: a qualitative overview�
ν
ν
The density keeps increasing. Now at high densities the neutrinos are trapped!
The collapse phase
Core-Collapse Supernova: a qualitative overview�
The density keeps increasing. Now at high densities the neutrinos are trapped!
Density is still increasing, until the strong force in the inner core becomes repulsive!
At what densities this happens and how hard (i.e. incompressible) the core is depends on the Nuclear Equation of State
Collapse is halted!
The collapse phase
Core-Collapse Supernova: a qualitative overview�
Infalling material suddenly finds an incompressible core.
This produces a bounce, and a shock wave forms
The bounce phase
Core-Collapse Supernova: a qualitative overview�
PNS
The shock wave initially expands and leaves behind a Proto Neutron Star (PNS)
Infalling material suddenly finds an incompressible core.
This produces a bounce, and a shock wave forms
The bounce phase
Core-Collapse Supernova:a qualitative overview�
PNS
After the initial expansion,
the shock stalls
The shock wave initially expands and leaves behind a Proto Neutron Star (PNS)
Infalling material suddenly finds an incompressible core.
This produces a bounce, and a shock wave forms
The early shock expansion phase
Core-Collapse Supernova: a qualitative overview�
PNS
The shock photodisintegrated the infalling Fe nuclei, and therefore loses energy
(~8.5 MeV/nucleon)
The stalled-shock phase
Core-Collapse Supernova: a qualitative overview�
PNS
The shock photodisintegrated the infalling Fe nuclei, and therefore loses energy
(~8.5 MeV/nucleon)
The shock loses too much energy to overcome the ram pressure of the infalling material
So how does the supernova explode?
Neutrinos!
The stalled-shock phase
Core-Collapse Supernova: a qualitative overview�
Radice et al. (2018)
The ram pressure of the infalling material is preventing the stalled shock from expanding
Snapshot at 200 ms after bounce
shock
Neutrino Heating and ν-driven convection
Core-Collapse Supernova: a qualitative overview�
ν
PNS
In the meantime, the PNS is emitting a huge flux of neutrinos
ν
PNS
shock
Radice et al. (2018)
Snapshot at 200 ms after bounce
Neutrino Heating and ν-driven convection
Core-Collapse Supernova: a qualitative overview�
ν
PNS
ν
PNS
Neutrinos can transfer energy to the matter via:
radiation
shock
Radice et al. (2018)
Snapshot at 200 ms after bounce
Neutrino Heating and ν-driven convection
Core-Collapse Supernova: a qualitative overview�
ν
PNS
ν
PNS
Neutrinos can transfer energy to the matter via:
convection
shock
Radice et al. (2018)
Snapshot at 200 ms after bounce
Neutrino Heating and ν-driven convection
Core-Collapse Supernova: a qualitative overview�
ν
PNS
ν
PNS
Neutrinos can transfer energy to the matter via:
convection
shock
Radice et al. (2018)
Snapshot at 200 ms after bounce
Neutrino Heating and ν-driven convection
Core-Collapse Supernova: a qualitative overview�
ν
PNS
ν
PNS
The combination of the two, in some cases is enough to launch the explosion!
shock
Snapshot at 200 ms after bounce
Radice et al. (2018)
Neutrino Heating and ν-driven convection
Couch et al (2020)
Boccioli et al (2021)
STIR
But also: Murphy et al. (2013), Mabanta & Murphy (2018), etc...
Radice et al. (2018)
Snapshot at 200 ms after bounce
Core-Collapse Supernova: a qualitative overview�
Numerical Simulations
Core-Collapse Supernova: a quantitative overview�
What is a CCSN?
A CCSN is a giant ball of gas exploding.
Does it change much?
Yes, that’s kind of the point of an explosion
Is mass conserved in an explosion? Yes, but also advected!
With this we have 3 equations for 4 unknowns:
P, M, v, ρ. In stars it was similar, except we did not have v, since stars are in hydrostatic equilibrium.
Again, P and ρ are related!
Core-Collapse Supernova: a quantitative overview�
Equation of State of Nuclear Matter
Instead of a simple polytropic EOS, one needs to rely on equation of state of nuclear matter, which are much more complicated (see Lectures from Day 1!)
T again changes because of heat transfer. However, now heat transfer happens in a hydrodynamic environment, so it is more convenient to write it in terms of the energy density e, i.e. sum of internal energy density (that we get from the EOS) and kinetic energy density
Core-Collapse Supernova: a quantitative overview�
Energy Equation
Nuclear Burning
(although small)
Neutrino Interactions
(extremely important!)
+ convection
Neutrinos are not in equilibrium with matter, while photons in stars are(*). So neutrinos are not a Fermi Gas, because their energy distribution is not equilibrated by interactions with matter.
(*) But not when they approach the photosphere, which makes atmospheric modeling of stars quite challenging!
We need to determine neutrino distributions!
Which BTW, is >90% of the computational cost of a SN simulation
Core-Collapse Supernova: a quantitative overview�
Solving the Boltzmann Equation
Scattering opacity
Absorption
opacity
Equilibrium
distribution
Isotropic
distribution
We then need to truncate at the nth moment, and specify a closure relation between the (n+1)th and nth moment.
Typically n=1 is enough! Which is what an M1-scheme is.
Core-Collapse Supernova: a quantitative overview�
Composition
In general the composition is advected with the fluid (we are ignoring any sort of nuclear burning now)
But for electron fraction we have to take into account neutrino interactions!
Core-Collapse Supernova: a quantitative overview�
Turbulent contributions
Turbulent Convection
In principle this also applies to stars!
Core-Collapse Supernova: a quantitative overview�
Some numbers
Energy released in the supernova:
final
initial
Neutron Star:
M = 1.4 M⨀
R = 10 km
Observed explosion energy:
99 % of the the energy is released in the form of neutrinos
Iron core:
M = 1.4 M⨀
R = 1000 km
If we can tap into that enormous reservoir of energy, and transfer some to the shock, we might overcome the ram pressure and launch an explosion!
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The life cycle of a massive star�
Supernova
engine
Nucleosynthesis
Stellar evolution
Microphysics
(EOS)
Microphysics
(ν interactions)
Light Curves
…
ν signal
Remnant Masses
Morphology
Explosion Energy
Output
ZAMS
mass
z
Input
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Incomplete List of Uncertainties in Stellar Evolution�
Implemented in current models
Subject of future research
37 of 30
Incomplete List of Uncertainties in Supernova Modeling�
Implemented in current models
Subject of future research
However, we are now able to run self consistent 3D explosion models from collapse all the way to shock breakout with
state-of-the-art physics!
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The life cycle of a massive star�
Supernova
engine
Nucleosynthesis
Stellar evolution
Microphysics
(EOS)
Microphysics
(ν interactions)
Light Curves
…
ν signal
Remnant Masses
Morphology
Explosion Energy
Output
ZAMS
mass
z
Input
binary
rotation
B
39 of 30
Supernova
engine
Nucleosynthesis
Stellar evolution
Microphysics
(EOS)
Microphysics
(ν interactions)
Light Curves
…
ν signal
Remnant Masses
Output
Morphology
Explosion Energy
Large uncertainties
Small(-ish) uncertainties
3D
ZAMS
mass
z
Input
(not to mention BSM, FC, etc…)
The life cycle of a massive star�
40 of 30
Nucleosynthesis
Stellar evolution
Microphysics
(EOS)
Microphysics
(ν interactions)
Light Curves
…
ν signal
Remnant Masses
Output
Morphology
Explosion Energy
Large uncertainties
Large(-ish) uncertainties
3D
ZAMS
mass
z
Input
Supernova
engine
1D
+
The life cycle of a massive star�
Open questions in CCSNe (my personal take)�
Some Useful References�