Core-Collapse and Thermonuclear Supernovae

Ch. 13 of Notes by Onno Pols.

Day 18 - October, 28, 2025

Agenda:

• Reminders - HW3 - Due: Nov. 4, before class (2m)
• Lecture (25m)
• ICA 16 - 3/4 Groups - Due: EoD Today (25m)
• ICA 16 Report out (10m)

• Massive stars reach temperatures of K

  • allowing them to ignite Carbon under non-degenerate conditions.
  • a critical core mass () is required to reach these ignition conditions, this critical mass is usually reached for stars with initial mass greater than but this is subject to uncertainties in mixing etc.

• Stars with initial mass greater than will go on to burn elements heavier than Carbon up to the formation of an iron core.

Core-Collapse and explosion of massive stars

Collapse of the Iron Core: Stars massive enough to form an iron core () can end their lives as core-collapse supernovae.

We can highlight two processes that contribute to the dynamical collapse of an iron core:

• (1) - Electron captures
  • at high density, free electrons can be captured via inverse -decay - core becomes more neutron rich - Neutronization.

Core-Collapse and explosion of massive stars

The Chandrasekhar mass for a predominantly core is given by:

• Recall is the ratio of the total nucleons (protons plus neutrons) in all nuclei to the total number of free electrons.
• Electron captures reduce the number of free electrons, thus increasing , and decreasing the Chandrasekhar mass limit.

This alone can push the core over the critical mass for collapse.

Core-Collapse and explosion of massive stars

• Electron captures can also facilitate the collapse of stars with that degenerate O-Ne cores,
  • if this core exceeds the it can produce an electron-capture supernova (ECSN) - recent Nature article on SN2018zd.

Core-Collapse and explosion of massive stars

• (2) - Photo-disintegration
  • the pre-collapse contracting core can reach K and cause photons to break up heavy nuclei into lighter ones:

• This process takes about 2 MeV per nucleon and is eventually absorbed by the radiation field from the internal energy.
• The net result is a drastic decrease in pressure, potentially triggering the free-fall collapse of the core.

Steps of Core-Collapse in a Massive Star

• The collapse is extremely rapid, ms (recall our dynamical timescale and typical core density g cm).

• Photo-disintegration/electron captures continue due to increases photon energies/density and lead to further neutronization.

• The temperature and pressures rise, but not enough to halt collapse until nuclear densities are reached ( g cm).

• The composition becomes predominantly neutrons, modifying the equation of state, the gas becomes nearly incompressible and the proto-neutron star halts collapse at a radius of about 20 km.

Energetics of Core-Collapse in a Massive Star

We can estimate the gravitational energy released during collapse:

for homologous collapse of a 1.4 core from 3000 km to 20 km.

We can compare this to the energy needed to unbind the stellar envelope (aka blow up the star):

Energetics of Core-Collapse in a Massive Star

The upper limit for this is about 10 erg but for a realistic mass distribution more like 10 erg,

• suggesting only a small fraction of the energy in the collapse of the core is needed to unbind the star.

Some of the explosion energy goes into kinetic energy with ejecta velocities on the order of 10 km / s, giving erg and into radiation with erg.

Energetics of Core-Collapse in a Massive Star

To summarize:

• only a small fraction of the energy released in the collapse is used in the actual explosion
• The question is how this fraction of about 1% of the can be converted into of the envelope, which turns out to be a very difficult problem.

Core-Collapse Supernovae - Explosion Mechanism

At densities of g cm), the neutrons become degenerate, leading to an increase in pressure, and the strong nuclear force between nucleons becomes repulsive halting further collapse.

Core Bounce: When the inner core is compressed to about a few times nuclear density it recoils like a spring causing the core bounce.

• The velocity of the inner core is reversed due to the bounce and travels towards still infalling material of the outer core.

• These material impact each other, the supersonic material creates a shock wave that steepens as it moves outward into lower density.

Core-Collapse Supernovae - Explosion Mechanism

• The kinetic energy stored in this shock was once thought to be enough to unbind the envelope and lead to a prompt explosion.

We now know that two things limit the prompt explosion scenario:

• Energy is removed via photo-disintegration of the infalling iron group nuclei.
• Electron captures onto free protons behind the shock produce energetic neutrinos which carry away about 90% of the energy released in the collapse.

The shock wave in this scenario fizzles out and no explosion occurs.

The Delayed-Neutrino Driven Mechanism

During collapse the core becomes opaque for neutrinos, they're trapped.

Can only diffuse out via many scattering events, similar to photons.

Neutrinosphere - outer layers of the core where the density is low enough for neutrinos to escape. Within this radius is a neutrino trapping surface. The trapped neutrinos provide an energy source to revive the shock and lead to explosion.

The Delayed-Neutrino Driven Mechanism

Neutrino heating - neutrinos able to diffuse out of the core heat the region where the shock has already passed (the post shock region) - from about 30 km to 100-300 km.

• Region becomes convective.
• Provides a way to convert thermal energy deposited by neutrinos into kinetic energy potentially leading to revival of stalled shock overcoming ram pressure to lead to explosion. Example 3D CCSN explosion - O’Connor et al. 2018.

Type Ia Supernovae - how to ignite a white dwarf?

These explosions are not associated with the core-collapse of a massive star.

• Instead, they are caused by the thermonuclear explosion of a CO white dwarf reaching a critical mass for carbon ignition.

Ignition

• Carbon-burning can occur at low temperatures, such as white dwarfs, if the central density is sufficiently high. This is often reach for a near Chandrasekhar mass white dwarf of 1.4.

Type Ia Supernovae - how to ignite a white dwarf?

Ignition

• Because the gas is strongly degenrate the carbon-burning is unstable and leads to a large increase in temperature at constant density and pressure.

Burning

• The ignition of carbon causes all of the core to be transformed into Fe-peak elements in nuclear statistical equilibrium.

• An explosive burning flame front propagates outward, behind which material undergoes explosive nuclear burning.

Type Ia Supernovae - how to ignite a white dwarf?

Ashes

• The composition of the resulting ash depends on the temperature behind the flame front, in the central part it is primarily and leads to progressively light elements (Ca, S, Si, and others).
• The total energy released by the burning is about erg, sufficient to unbind the entire star and no remnant is left behind.

Type Ia Supernovae - how to ignite a white dwarf?

Single degenerate scenario (SD)

• white dwarf accretes H-/He-rich material from a non-degenerate companion star - a main sequence star, red giant, or helium star.

Problems with this scenario:

• The mass transfer rate of H/He that can facilitate steady burning and growth of the mass of the WD is very narrow.

Type Ia Supernovae - how to ignite a white dwarf?

Single degenerate scenario (SD)

• The mass transfer rate of H/He that can facilitate steady burning and growth of the mass of the WD is very narrow. Example Video.

  • too fast: a H-rich envelope would form on the WD and be seen observationally - its not.
  • too slow: the matter burns in an unstable manner and leads to a nova outburst, that limits mass growth.

Type Ia Supernovae - how to ignite a white dwarf?

Double degenerate scenario (DD)

Merger of two WDs, merger product exceeds the and ignites the WD. Example 3D WD Merger Simulation.

• These systems would be formed in close binary systems underoing common envelope evolution followed by orbital decay due to gravitational radiation.

Main challenges is the nature of the burning of the merger product: is it enough to unbind the the WD or does it lead to core-collapse?

In-Class Assignment 16

In class: Work on ICA here with groups per usual. Discuss conceptual questions together and prepare answers to share at the end of class.

• Choose someone that will report out the groups responses ahead of time!

After Class: Due: Submitted to D2L by EoD

Note: The goal of ICAs are to use plots produced in the notebook for discussion and interpretation of results presented in lecture in groups and as a class.