# What is the smallest neutron star radius possible?

According to the Chandrashekhar limit the minimum mass of a neutron star is about 1.44 solar masses, however I found some examples of neutron stars less massive than that.

Additionally, I thought that the minimum radius of a neutron star of a given mass would be more than the Schwarzchild radius of a blackhole with the same mass.

Still, wikipedia lists some small neutron stars like the CXOU J085201.4-461753 as having a radius of 1.2 km which I would not have thought was possible?

So my question is, what is the smallest radius a neutron star can be? And what is the smallest neutron star we have discovered?

Additionally, is the surface temperature of a neutron star in any way dependant on its radius and/or mass?

• Neutron stars get smaller with larger mass, so you should be looking at the top end of the mass range for neutron stars, not the bottom end. Sep 25 at 16:04
• Yeah I was aware the mass was inversely proportional to the radius, but even that makes it feel a bit more complicated since more mass means smaller radius which means even closer to the schwarzchild radius. Since the SR for 1.44 solar masses is 4.2 KM and the neutron stars mentioned on wiki there are smaller Sep 25 at 19:18

The minimum mass of a neutron star is actually about 0.2 solar masses and has nothing to do with the Chandrasekhar limit (see this Physics SE answer).

Several neutron stars have precisely measured masses that are smaller than 1.44 solar masses. The smallest is currently about 1.17 solar masses (Martinez et al. 2015). Note that more massive neutron stars may actually have smaller radii. It depends on the uncertain relationship between pressure and density.

Measuring the radii of neutron stars is incredibly difficult. The "measurements" that exist are rather indirect inferences and have large uncertainties.

There is a fundamental limit in General Relativity, that is larger than the Schwarzschild radius, for the minimum radius of an object at a given mass. This "Buchdahl limit" is 9/8 of the Schwarzschild radius. It does not matter what type of pressure support is provided, a spherically symmetric object will collapse to a black hole if smaller than that.

For realistic relationships between pressure and density, then the true limit is a bit bigger than the Buchdahl limit - perhaps 1.2 to 1.3 times the Schwarzschild radius. This is around 5 km, for neutron stars with the smallest measured masses, so presumably those neutron stars are bigger than that.

Rapid rotation could change some of these considerations, but the measured rotation rates of pulsars are too slow to have much effect.

I think the reason for the strange, small radius values you see (especially in Wikipedia, which does not have much quality control - always look at the original sources) is that it is a "fitting parameter" and represents the size of the emitting region and not necessarily the radius of the neutron star.

Finally, the surface temperature of a neutron star does not directly depend on its radius. Neutron stars start their lives very hot and cool down with time. To first order, the surface temperature of a neutron star would depend on its age. It could also depend on the rate at which it was accreting material from the interstellar medium (or a companion) or perhaps even its initial magnetic field strength.

• As usual, very informative answer! Are you aware of an analogous limit for Kerr black holes as the Buchdal limit? Sep 26 at 14:38