How a star ends: the Chandrasekhar and TOV limits
White dwarf, neutron star or black hole? Two mass limits decide, and neither one is about the mass the star was born with.
A star that starts with 9 times the mass of the Sun is more than four times heavier than the limit for a neutron star. So why does it make a neutron star, and not a black hole?
The path from nebula to remnant
Stellar Evolution Explorer
Set the mass of a star and watch its whole life in 3D, with its track on the H-R diagram. Open the “Core vs star mass” tab for the same idea as this lesson.
Open it full screenThe two limits
| Feature | Chandrasekhar limit | TOV limit |
|---|---|---|
| Mass of what? | a white dwarf | a neutron star |
| Supporting force | electron degeneracy pressure (Pauli exclusion principle for electrons) | neutron degeneracy pressure plus the short-range strong nuclear force |
| Approximate value | 1.44 M☉ | 2.1 to 2.3 M☉ |
| If the mass is exceeded | electron degeneracy pressure fails: core-collapse supernova, and a neutron star forms | neutron degeneracy pressure fails: the remnant collapses into a black hole |
- What happens when the core is squeezed past the Chandrasekhar limit
- electrons and protons combine into neutrons and a neutrino
Three masses, one limit each
Birth (initial) mass: The mass of the star when it forms. It decides how much mass is lost later and what the core becomes. It is never compared with either limit.
Core mass: The mass of the inner core when nuclear burning ends: a carbon–oxygen core for stars below about 8 M☉, an iron core above that. The Chandrasekhar limit is compared with this.
Remnant mass: The mass of the white dwarf, neutron star or black hole that is left. The TOV limit is compared with this.
Which mass is judged?
The idea: Drag the birth mass. Watch the core and remnant masses move along the ladder, and ignore the birth mass: it never lands on the ladder. The switch from white dwarf to neutron star is near 8 M☉ at birth, and from neutron star to black hole near 24 M☉ in this simplified model.
A star is born with 7 M☉. Before you move the slider: what does it leave behind?
Answer the prediction above to unlock the simulation. Then test it.
The Chandrasekhar limit is about 1.44 M☉. It is the maximum mass of…
What supports a neutron star against gravity?
A star is born with 4 M☉ and ends as a 0.8 M☉ white dwarf. The mass compared with the Chandrasekhar limit is…
A supernova leaves a remnant of 1.9 M☉. It is…
A supernova leaves a remnant of 3.1 M☉. It is…
Why is the TOV limit higher than the Chandrasekhar limit?
A student says: “A star of 12 M☉ is much heavier than the TOV limit, so it must collapse into a black hole.” Use the ideas of this lesson to explain what is wrong, and say what the star becomes.
Key points
- • Both limits are compared with the core or remnant, never with the mass the star is born with.
- • Chandrasekhar limit, about 1.44 M☉: the largest white dwarf, held up by electron degeneracy pressure.
- • TOV limit, about 2.1 to 2.3 M☉: the largest neutron star, held up by neutron degeneracy pressure and the strong force.
- • A core above 1.44 M☉ collapses: p + e⁻ → n + νₑ. A remnant above the TOV limit becomes a black hole.
Formulas
- p + e⁻ → n + νₑ
- L = 4πR²σT⁴
Key terms
- Electron degeneracy pressure :
- pressure that comes from the Pauli exclusion principle, not from temperature, because electrons cannot share a state
- TOV limit :
- Tolman–Oppenheimer–Volkoff limit: the maximum mass of a neutron star
- Remnant :
- the white dwarf, neutron star or black hole left when a star dies
Common errors
- • Comparing 1.44 or 2.2 M☉ with the star’s birth mass.
- • Thinking a star above 1.44 M☉ at birth must become a neutron star.
- • Giving the TOV limit as one exact number: it is a range of about 2.1 to 2.3 M☉.