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Maurizio Paolillo » 10.Core-collapse Supernovae


Contents

  • Latest stages of stellar evolution.
  • Internal structure of massive stars.
  • Core collapse.
  • Nucleosynthesis.
  • Radioactive decay and Supernovae lightcurves.

Solar mass stars

Evolutionary path of solar mass stars:

  • Leave the main sequence when core hydrogen is exhausted.
  • Red giants: burn H in a shell, around an inert He core.
  • Horizontal branch: core He burning, with H burning in a shell.
  • Asymptotic giants: He and H burning shells, around an inert C,O core
  • Envelope is expelled, leaving a hot, degenerate C,O white dwarf behind.
The Herzprung-Russel diagram of the Globular Cluster M55, showing the different regions occupied by stars in different phases of their evolution, depending on their initial mass.

The Herzprung-Russel diagram of the Globular Cluster M55, showing the different regions occupied by stars in different phases of their evolution, depending on their initial mass.


Massive stars

Massive stars continue their evolution:

  • Helium burning continues to add ash to the C-O core, which continues to contract and heat up.
  • Carbon is ignited, forming: _8 ^{16}O, _{10}^{20}Ne, _{11} ^{23}Na, _{12} ^{23}Mg, _{12} ^{24}Mg
The internal structure of a massive star with a carbon core.

The internal structure of a massive star with a carbon core.


Internal structure

  • If each reaction has time to reach equilibrium, the stellar interior will consist of shells of different composition and reactions.
  • Oxygen is ignited next producing a Silicon core.
Internal structure of a massive star with a Si core.

Internal structure of a massive star with a Si core.


Silicon burning

  • Silicon burning produces numerous elements near the iron peak of stability
  • The most abundant:

_{26} ^{54}Fe

_{26} ^{56}Fe

_{28} ^{56}Ni

  • Further reactions are endothermic and thus do not provide stellar luminosity.
The shell structure of a massive star with a Fe core.

The shell structure of a massive star with a Fe core.

The binding energy per nucleon as a function of mass number, A.

The binding energy per nucleon as a function of mass number, A.


Element burning timescales

As the iron peak is approached, the energy released per unit mass of reactant decreases. Thus the timescale becomes shorter and shorter.

Timescales of nuclear reactions for different elements.

Timescales of nuclear reactions for different elements.


Photodisintegration

  • During Silicon burning the core has reached extremely high temperatures and densities
  • The photons produced are so energetic they can destroy heavy nuclei, reversing the process of fusion.

In particular:

_{26} ^{56}Fe+\gamma=>13_{2} ^{4}He+4n

_{2} ^{4}He+\gamma=>2p^+ + 2n

The photodisintegration process.

The photodisintegration process.


Photodisintegration (cont.ed)

This process removes thermal energy that would otherwise be supporting the core

Furthermore, free electrons (which were providing support through degeneracy pressure) get captured by the protons produced by photodisintegration:

p^+ + e^- => n+\nu_e

An enormous amount of energy is carried away by the neutrinos; about 10 million times more energy than carried by the photons (the luminosity)!

Excercise

Most of the (heavy) core’s pressure support has disappeared very quickly and it starts to rapidly collapse.

The typical central core density for a 15 MSun star is 1013 kg/m3. What is the free-fall time for core collapse?

(work out the answer before checking the result on next slide)

Free fall timescale

Solution:

t_{ff}=\left( \frac{3\pi}{32G\rho_0}\right)^{1/2} = 0.021s

Core collapse

The inner core collapses, leaving the surrounding material suspended above it, and in supersonic free-fall at velocities of ~100,000 km/s.

The core density increases to 3x the density of an atomic nucleus and becomes supported by neutron degeneracy pressure.

The core rebounds somewhat, sending pressure waves into the infalling material.

Schematic view of the Core Collapse process.

Schematic view of the Core Collapse process.


Stalled shocks

As the shock wave propagates outward and encounters the infalling core, the high temperatures result in further photodisintegration.

  • This removes a lot of energy from the shock: it loses 1.7×1051 erg of energy for every 0.1M of iron it breaks down.
  • If the iron core is too large, the shock becomes a stationary accretion shock, with matter accreting onto it.
  • A buildup of neutrino energy behind the shock (which is so dense it hinders neutrino penetration) causes it to slowly resume its advance.
  • Once it penetrates the iron core, explosion occurs.

Acoustic explosion & Instability growth

  • Acoustic power generated in the inner core drives explosion.
  • Sound pulses radiated from the core steepen into shock waves that merge as they propagate into the outer mantle and deposit their energy and momentum with high efficiency.
  • The rapid, unsaturated, nonlinear growth of long-wavelength mode instabilities may play a role in the explosion mechanism.
The growth of instabilities after core collapse, which are believed to play a fundamental role in allowing the shock to emerge from the stellar interior.

The growth of instabilities after core collapse, which are believed to play a fundamental role in allowing the shock to emerge from the stellar interior.


Explosion

  • As the shock moves toward the surface, it drives the hydrogen-rich envelope in front of it.
  • When the expanding shell becomes optically thin, the radiation can escape, in a burst of luminosity that peaks at about 1043 erg/s.
SN1987A before (left) and after (right) the Supernova explosion.

SN1987A before (left) and after (right) the Supernova explosion.

An example of a supernova explosion in a Spiral Galaxy.

An example of a supernova explosion in a Spiral Galaxy.


Light curves

  • After the initial burst of luminosity, the supernova slowly fades away over a period of several hundred days. This fading is due to the radioactive decay of elements (typically nickel and cobalt) produced during the explosion.
  • As the shock wave propagates through the star, it creates a large amount of heavy, radioactive elements.
  • Each species decays exponentially with a unique timescale
  • The shape of the light curve is due to the superposition of the decay of each species.
An example of a Supernova lightcurve. The different colors show the intervals dominated by the radioactive decay of a specific element (see next slides).

An example of a Supernova lightcurve. The different colors show the intervals dominated by the radioactive decay of a specific element (see next slides).


Radioactive decay

For example, the following beta-decay reaction occurs:

$^{56}_{27}Co\rightarrow Fe+e^++\nu_e+\gamma$

This decay is a statistical process: the rate of decay must be proportional to the number of atoms in the gas:

\frac{dN}{dt}=-\lambda N

or

N(t)=N_0e^{-\lambda t}

The half-life is the time to reduce the number of atoms to N0/2

N(\tau)=N_0e^{-\lambda \tau}=N_0/2

\tau=\frac{\ln 2}{\lambda}

The energy production rate is proportional to dN/dt: thus we can measure the half-life of decay from the light curve and deduce what species are present.

Example: radioactive decay

The energy released by the decay of one cobalt-56 atom is 3.72 MeV.
Given 0.075 M of this isotope (this is how much was estimated to have been produced in SN1987A) how much energy does the decay release?

L=9.8\times10^{34} e^{-3.26 t}

where t is measured in years.

The initial luminosity is 2.5×108 L.
After one year it has decreased to 9.9×106 L.

SN1987A

  • Occurred in the Large Magellanic cloud, a small galaxy near the Milky Way.
  • Progenitor was a much smaller star than usually responsible for Type II explosions.
  • Smaller stars are denser, so more energy was required to lift the atmosphere, and this resulted in a slower brightening and fainter peak luminosity.
The Large Magellanic Cloud.

The Large Magellanic Cloud.

SN1987A before and after the explosion.

SN1987A before and after the explosion.


SN1987A light curve

  • The decay of Ni-56 occurred when the timescale for the energy to be radiated away was still quite long: thus it just produced a bump near maximum light.
  • The initial decay mostly tracks Co-56, followed by Co-57

_{27} ^{56}Co=>_{26} ^{56}Fe+e^+ + \nu_e + \gamma

  • This reaction produces high energy gamma rays which were detected for the first time, confirming the presence of this isotope.
  • Neutrinos were also detected: this was the first time neutrinos were detected from an astronomical source other than the Sun.
The lightcurve of SN1987A. The contributions of the different decaying radioactive elements, add up to form the total luminosity at any given timescale.

The lightcurve of SN1987A. The contributions of the different decaying radioactive elements, add up to form the total luminosity at any given timescale.


Nucleosynthesis

  • Stellar evolution theory can also predict the abundances of the elements.
  • Big Bang theory accounts for the hydrogen and most of the helium and lithium.
  • Boron, lithium and beryllium are very underabundant relative to hydrogen. This has to do with the cross-section of the different nucleosynthesis stages in stellar interiors.
Cosmic elements abundance.

Cosmic elements abundance.


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