Neutron Star Properties

Neutron stars are hard to model from first principles because they involve a regime where general relativity and Standard Model physics intersect with vast numbers of particles condensed in highly dense matter rather than in the small number of particles at time seen in particle colliders where high energy physics is usually done, even though they are, in principle, still rather simple systems. 

But astronomy observations can constrain their properties and provide us with insights about the underlying high energy physics in a domain that otherwise would be inaccessible to solar system bound physics experiments. This requires a mix of physics motivated models of neutron stars and carefully processed and analyzed astronomy data.

This data is homing in on a nearly universal neutron star to be pretty universally close to a 12 kilometer radius, and a maximum neutron star mass of modestly more than two solar masses. 

This maximum neutron star mass is low relative to other data that is more direct, but not by a lot. As I noted in a June 26, 2020 blog post (which later notes that two independent papers think that the 2.5-2.64 solar mass object observed with a gravitational wave detector is much more likely to be a black hole than a neutron star).

Gravitational wave detectors have observed what appears to be an intermediate sized black hole (26 times the mass of the Sun) collide with a "compact object" with a mass of 2.6 (2.5 to 2.64 at a 90% confidence interval) times the mass of the Sun.

Beyond a certain cutoff mass at a given radius, compact masses like neutron stars, collapse and form black holes. But, calculating the cutoff isn't a clean and simple calculation, because you have to model how tightly protons and neutrons can be squeezed together by gravity as nuclear forces push back against being squeezed too tightly, and those are complex systems involving vast numbers of protons and neutrons that can't be modeled exactly.

The most dense, large compact objects in the universe that are not black holes are neutron stars. Neutron stars are just massive, extremely dense, ordinary stars on the continuum of ordinary star behavior.

But black holes are qualitatively different. In classical General Relativity they are mathematical singularities. In theories of quantum gravity, black holes are "almost" singularities (from which nothing can escape) but leak slightly in a theoretically described phenomena called "Hawking Radiation" which is too slight to be observed over the noise of cosmic background radiation with current means.

This compact object is potentially more massive than any previously observed neutron star (it has a higher minimum mass within experimental uncertainties than any previously observed neutron star), but it is lighter than the lightest known black hole (see here), subject to outliers near the boundary with large error margins in their mass estimates.

The least massive black hole ever observed has a mass of 2.72-2.82 solar masses (in a 95% confidence range). The most massive previously observed neutron stars have masses of 2.32-3.15, 1.9-3.00, 2.15-2.70 and 2.16-2.64 solar masses (in a 95% confidence range). So, the cutoff has to be somewhere in the range of 2.32 solar masses to 2.82 solar masses. This object is squarely in the middle of that range.

Another recent study which I blogged on April 30, 2024, puts a 95% confidence interval maximum neutron star mass at 2.38 solar masses and a maximum radius of 12.0 km. 

A new study, whose abstract and citation appear below, puts the most massive possible neutron star at 2.43 solar masses at a 95% confidence interval by one method, and 2.64 solar masses at a 95% confidence interval by another, with best fit maximum neutron star masses of 2.15 solar masses by one method and 2.08 solar masses by another. 

A cutoff maximum neutron star mass of 2.32 to 2.38 solar masses would best harmonize the available information from the newest studies and observations.

The narrowing in of the maximum mass of a neutron star and its radius also fixes a quite narrow range for the highest observed mass per volume of any object at any scale observed in Nature. Maybe I'll calculate that as an exercise at some point in light of the updated data.

Pulse profile modeling of X-ray data from NICER is now enabling precision inference of neutron star mass and radius. Combined with nuclear physics constraints from chiral effective field theory (χEFT), and masses and tidal deformabilities inferred from gravitational wave detections of binary neutron star mergers, this has lead to a steady improvement in our understanding of the dense matter equation of state (EOS). 

Here we consider the impact of several new results: the radius measurement for the 1.42M⊙ pulsar PSR J0437−4715 presented by Choudhury et al. (2024), updates to the masses and radii of PSR J0740+6620 and PSR J0030+0451, and new χEFT results for neutron star matter up to 1.5 times nuclear saturation density. Using two different high-density EOS extensions -- a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS) -- 

we find the radius of a 1.4M⊙ (2.0M⊙) neutron star to be constrained to the 95% credible ranges 12.28+0.50−0.76 km (12.33+0.70−1.34 km) for the PP model and 12.01+0.56−0.75 km (11.55+0.94−1.09 km) for the CS model. The maximum neutron star mass is predicted to be 2.15+0.14−0.16 M⊙ and 2.08+0.28−0.16 M⊙ for the PP and CS model, respectively. 

We explore the sensitivity of our results to different orders and different densities up to which χEFT is used, and show how the astrophysical observations provide constraints for the pressure at intermediate densities. Moreover, we investigate the difference R2.0−R1.4 of the radius of 2M⊙ and 1.4M⊙ neutron stars within our EOS inference.

Nathan Rutherford, et al., "Constraining the dense matter equation of state with new NICER mass-radius measurements and new chiral effective field theory inputs" arXiv:2407.06790 (July 9, 2024).