# What determines the outcome of a supernova?

Question: What determines the outcome of a supernova? When a sun collapses into itself creating a supernova what decides if it will be a white dwarf star, neutron star or black hole? I’ve pondered over the question myself but alas I feel as if I need help from my peers.

• – Kyle Kanos May 24 '18 at 11:25

Supernovae do not produce white dwarfs. This is a distinct evolutionary pathway followed by stars with mass below about 8 times the Sun ($8M_{\odot}$) - their cores are destined to become electron-degenerate white dwarfs with masses less than about $1.25 M_{\odot}$.

Neutron stars and perhaps black holes are produced in supernovae, involving the collapse of the core of a star that is more massive than $\simeq 8M_{\odot}$.

If the collapsing core is not particularly massive (resulting from a progenitor say of $<15M_{\odot}$, though the boundary is not certain, and also probably depends on the initial composition of the star), then it is likely that the collapse will be halted by the strong nuclear repulsion felt between neutrons (produced by electron capture onto protons) and to a lesser extent by neutron degeneracy pressure. This results in "core bounce", and subsequently a transfer of a tiny fraction of the collapse energy into the stellar envelope, causing a supernova.

If the proto-neutron star is too massive ($>2-3M_{\odot}$), or it accretes more mass, then it may further collapse into a black hole. Alternatively, the collapse may never be halted in the first place if the initial core was too massive ($>3M_{\odot}$) and there may be direct collapse to a black hole without a supernova at all.

The key parameters determining the fate of a massive star are the initial progenitor mass - the more massive, the more likely to form a black hole. Metallicity is also important. If a star is born from gas that has a higher concentration of heavier elements, its envelope is more opaque and the progenitor is likely to lose more of its initial mass through a radiatively driven wind. Low metallicity progenitors probably have more massive cores at the time of core-collapse and are therefore more likely to form black holes.

The plot below (from work by Heger et al. 2003) illustrates the argument above and shows the likely remnant as a function of initial mass and metallicity.

• This may have to be turned into a question. I am interested in your comment “collapse will be halted by the strong nuclear repulsion felt between neutrons ..... and to a lesser extent by neutron degeneracy pressure” because a lot of sources state that neutron degeneracy pressure is the mechanism. – Farcher May 24 '18 at 7:14
• @Farcher Yes, and they have all read it on the internet. Oppenheimer & Volkhoff showed in 1939 that ideal neutron degeneracy could not support a ball of neutrons more massive than 0.75 solar masses. Equations of state that support real neutron stars rely on the strong repulsion felt by nucleons when you try and compress them to higher than nuclear densities. – Rob Jeffries May 24 '18 at 7:19
• Thank you and I have found an amplification from you here physics.stackexchange.com/a/105445/104696 – Farcher May 24 '18 at 7:42
• @RobJeffries - I recall seeing this plot in grad school but do not recall (or perhaps never understood) the white/blank region in the lower right-hand corner. I assume that region still results in a black hole, but why is it blank or different from the surrounding "direct black hole" regions? – honeste_vivere Jun 15 '18 at 16:26

See the second half of this answer: https://physics.stackexchange.com/a/407833/170832.

Theoretical studies indicate that most supernovae are triggered by one of two basic mechanisms: the sudden re-ignition of nuclear fusion in a degenerate star (white dwarfs, neutron stars, and black holes) or the sudden gravitational collapse of a massive star's core.

In the first instance, a degenerate white dwarf may accumulate sufficient material from a binary companion, either through accretion or via a merger, to raise its core temperature enough to trigger runaway nuclear fusion, completely disrupting the star. In the second case, the core of a massive star may undergo sudden gravitational collapse, releasing gravitational potential energy as a supernova.

While some observed supernovae are more complex than these two simplified theories, the astrophysical collapse mechanics have been established and accepted by most astronomers for some time. Source: Wikipedia "Supernova".

The Chandrasekhar limit is the maximum mass of a stable white dwarf star. The currently accepted value of the Chandrasekhar limit is about 1.4 M$_{\odot}$ ($2.765×10^{30}$ kg).

White dwarfs resist gravitational collapse primarily through electron degeneracy pressure (compare main sequence stars, which resist collapse through thermal pressure). The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction.

Consequently, a white dwarf with a mass greater than the limit is subject to further gravitational collapse, evolving into a different type of stellar remnant, such as a neutron star or black hole. Those with masses under the limit remain stable as white dwarfs. Collapse is not inevitable: most white dwarfs explode rather than undergo collapse.

To first order, just the mass. If the mass is less than the Chandrasekhar limit (about 1.4 solar masses), the electron degeneracy pressure is sufficient to stop the collapse and you end up with a white dwarf. If the mass of the star remnant is greater than the Tolman-Oppenheimer-Volkoff limit (somewhere around 2 to 3 solar masses) it collapses into a black hole.

Note that these masses are both the mass of whatever is left as it is collapsing, which is much less than the original mass of the star. The limit for a black hole corresponds to something more like 15 to 20 times the mass of our sun for the original star, and to form a neutron star is more like 10 solar masses.

• Note taken thank you. Question: The atoms that a star consist of no matter the mass are the same? – Austin Tucker May 24 '18 at 1:16
• @AustinTucker Originally, more or less. The more massive stars burn longer, though, and so end up with heavier elements than lighter stars by the end. – Chris May 24 '18 at 3:23

Most stars on the Hertzsprung-Russell diagram are on the main-sequence. When main-sequence stars like the sun exhaust their hydrogen fusion, their cores collapse and they begin to fuse helium. Likewise, when they exhaust their helium, they can begin to fuse carbon and oxygen. Whether or not they can continue to burn depends on their mass.

When the fusion finally stops, there is no thermal or radiative pressure to hold up the star against its own gravitational force. In in the case of low-mass stars ($M < 1.4M_\odot$), electron degeneracy pressure can stop their imminent collapse. This pressure is a product of the Pauli exclusion principle - a quantum mechanics principle which states that two Fermions cannot occupy the same state simultaneously. Most white dwarfs are about $0.6M_\odot$ and have radii comparable to Earth, about $6000$ km.

If the stellar mass exceeds $1.4M_\odot$ (the Chandrasekhar limit), electron degeneracy will crumble in the force in the gravity. Electrons will be captured by nuclei, producing neutrons. The star is then held up by neutron degeneracy pressure, also a result of Pauli exclusion principle. These stars are called neutron stars, and they have radii on the order of 10-20 kilometers, and maximum masses around $2M_\odot$.

Any more massive than this, and even neutron degeneracy cannot withstand the overpowering force of gravity. In this case, nothing can stop the gravitational collapse, and the stellar core becomes a black hole. These stars represent a singularity with infinite density, where all stellar density has been compressed into a single point.

Type 1a supernovae are generated by the binary mergers with white dwarfs with the total mass exceeds the Chandrasekhar limit. Type II supernovae are generated when a massive star, on the order of $10M_\odot$, collapses. It ejects a supernovae and the core becomes a neutron star or black hole.

• "Most stars on the Hertzsprung-Russell diagram will follow the main-sequence." The main sequence isn't something you follow, it's something you're on. – NeutronStar May 24 '18 at 1:20
• @Joshua That was poor wording on my end. Thanks, I have edited my response. – zhutchens1 May 24 '18 at 1:28
• Neutron stars are not principally supported by neutron degeneracy pressure. – Rob Jeffries May 24 '18 at 6:18
• "Type 1a supernovae are generated by the binary mergers with white dwarfs with the total mass exceeds the Chandrasekhar limit." Not exactly. A type 1a SN resulting from the merger of two white dwarves is possible but rare. It's more typically the result of a white dwarf accreting matter from a giant binary partner. Also, the Chandrasekhar limit for electron degeneracy is never reached: at about 99% of the limit, the white dwarf's core reaches the ignition temperature for carbon fusion and a runaway reaction completely disrupts the star. – Chappo Hasn't Forgotten Monica Jun 1 '18 at 13:19
• @RobJeffries: I was going to ask why, but I found your answer from 2014 explains it. If neutron repulsion is the principle factor, is PEP negligible or what proportion would it be? – Chappo Hasn't Forgotten Monica Jun 1 '18 at 14:07