# Pushing the Limit

18 September 2019

When an old star dies, its core runs out of nuclear fuel to produce heat and pressure. It’s the pressure that keeps the core from collapsing under its own weight. The gravity of large stars is so strong that the atoms of the core can’t fight against it. For stars like our Sun, the core collapses so tightly that electrons of the atoms reach a peak pressure. The star reaches a stable state known as a white dwarf, where the pressure of the electrons balances the gravitational pressure of the star’s mass.

But a white dwarf is only stable up to a mass of 1.4 Suns, known as the Chandrasekhar Limit. If an old star’s core is more massive than that, the electron pressure isn’t strong enough to counter gravity. The electrons are squeezed into the protons of the atoms, turning them into neutrons. The star collapses to the point that the pressure of neutrons counters gravity. This is known as a neutron star.

Of course, there is a limit to the mass of a neutron star. If the core is more massive than that limit, the neutron pressure will be overwhelmed by gravity, and the star will collapse into a black hole. But we aren’t exactly sure what that limit is.

The mass limit of a star depends upon the how the pressure of a material is determined by its temperature and density. The relation is typically described by an equation known as the equation of state. The equation of state for electrons was calculated by Subrahmanyan Chandrasekhar in 1930, from which he determined the mass limit for a stable white dwarf.

But electrons are simple elementary particles. Neutrons are complex particles comprised of quarks and their interactions. As a result, the equation of state for neutrons is much more complex. In 1939 Robert Oppenheimer and George Volkoff devised an equation of state for neutrons building the work of Richard Tolman. Together this yielded a mass limit for neutron stars known as the Tolman–Oppenheimer–Volkoff (TOV) limit.

The calculations for the TOV limit are so complex that it is difficult to get a precise value. Original estimates put the neutron mass limit at somewhere between 1.5 and 3.0 solar masses. Later estimates put the limit closer to 2 solar masses, and gravitational wave observations of merging neutron stars suggested a limit of 2.17 solar masses.

Recently astronomers have found a neutron star that’s right on the edge of that limit.1 PSR J0740+6620 is a pulsar 4,600 light years from Earth. Pulsars are neutron stars that flash radio pulses in our direction due to powerful radio beams streaming from their magnetic poles. PSR J0740+6620 pulses about 350 times a second, which means it’s rotating about 350 times a second. Because the radio pulses of a pulsar are due to the neutron star’s rotation, they are very stable.

This pulsar has a white dwarf partner. The two orbit each other, and their orbits happen to be oriented in such a way that the white dwarf passes between us and the pulsar with each orbit. This is really fortunate for us, because it allows us to measure two things about them. The first is the orbital period of the stars, how long it takes for the white dwarf to make one orbit. The second is the mass of the white dwarf. Because the white dwarf passes in front of the pulsar, the gravity of the white dwarf distorts the timing of the radio pulses we see from the pulsar. It’s an effect known as the Shapiro Time Delay. The amount of delay depends upon the mass of the white dwarf, so by measuring it we have the mass.

This is important, because the orbital period depends on the mass of both stars. Since we know the mass of the white dwarf, we can calculate the mass of the neutron star. When the team did this calculation, they got a mass of between 2.05 and 2.24 solar masses. It’s the most massive neutron star yet obsevered, and it could be the most massive neutron star possible.

This discovery is important because it helps narrow down our estimates for the TOV limit. For example, some astronomers argued that the neutron star mass limit couldn’t be larger than 2 solar masses. PSR J0740+6620 clearly breaks that limit. If we find similar neutron stars, we should be able to determine a more precise TOV limit.

1. H. T. Cromartie, et al. “Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar” Nature Astronomy (2019) DOI: 10.1038/s41550-019-0880-2 ↩︎