Probing neutron star interiors and the properties of cold ultra-dense matter with the SKAO

TL;DR

This work surveys how the SKAO can illuminate the neutron-star dense-matter equation of state by converting high-precision radio pulsar timing into constraints on global quantities like $M$, $R$, and $I$, as well as internal physics through glitches and potential free precession. It reviews the current understanding of dense matter physics and superfluidity, and explains how SKAO measurements—especially when combined with X-ray and gravitational-wave data—can break degeneracies with dark matter and modified gravity effects to reveal the NS interior composition and phases. The paper details SKAO-era expectations for ToA precision, large-scale surveys, and dedicated glitch/precession programs, and emphasizes the importance of flexible observing, subarraying, and multi-messenger synergies to maximize the dense-matter science return.

Abstract

Matter inside neutron stars is compressed to densities several times greater than nuclear saturation density, while maintaining low temperatures and large asymmetries between neutrons and protons. Neutron stars, therefore, provide a unique laboratory for testing physics in environments that cannot be recreated on Earth. To uncover the highly uncertain nature of cold, ultra-dense matter, discovering and monitoring pulsars is essential, and the SKA will play a crucial role in this endeavour. In this paper, we will present the current state-of-the-art in dense matter physics and dense matter superfluidity, and discuss recent advances in measuring global neutron star properties (masses, moments of inertia, and maximum rotation frequencies) as well as non-global observables (pulsar glitches and free precession). We will specifically highlight how radio observations of isolated neutron stars and those in binaries -- such as those performed with the SKA in the near future -- inform our understanding of ultra-dense physics and address in detail how SKAO's telescopes unprecedented sensitivity, large-scale survey and sub-arraying capabilities will enable novel dense matter constraints. We will also address the potential impact of dark matter and modified gravity models on these constraints and emphasise the role of synergies between the SKA and other facilities, specifically X-ray telescopes and next-generation gravitational wave observatories.

Figures (15)

• Figure 1: The parameter space and states of matter present in NS, as compared to terrestrial experiments. The figure shows temperature against baryon number density against asymmetry, $\alpha = 1 - 2 Y_q$, where $Y_q$ is the hadronic charge fraction (generally equal to the ratio of the proton number to the total number of baryons). $\alpha = 0$ for matter with equal numbers of neutrons and protons, and $\alpha = 1$ for pure neutron matter. The orange regions show the parameters space occupied by NS projected onto the temperature-baryon density and asymmetry-baryon density planes, respectively. The grey regions show projections onto the same planes for isolated nuclei, which exist up to $\alpha \approx 0.3$. Above this value, one would find a mix of nuclei and light particles.
• Figure 2: Schematic structure of a NS: The outer layer---a solid crust of fully ionised nuclei---is supported mainly by electron degeneracy pressure. The inner crust starts around the neutron drip density, $4 \times 10^{11} \, \text{g/cm}^3$, where neutrons begin to leak out of the nuclei. From this point on, neutron degeneracy pressure starts to contribute. At densities of approximately $2 \times 10^{14} \, \text{g/cm}^3$, at the crust-core boundary, nuclei dissolve entirely. In the core, densities can reach up to ten times the nuclear saturation density---the typical density of atomic nuclei---and the pressure due to the repulsive channels of the nuclear interaction is essential to counterbalance gravity.
• Figure 3: The observed NS mass spectrum with 68% confidence intervals sourced from Extended Data Tables 1 and 2 of You2025 plus updated radio timing measurements (see https://www3.mpifr-bonn.mpg.de/staff/pfreire/NS_masses.html). The latter are shown in black. Other data points are redback and black widow systems (spider pulsars; dark purple), observations of pulsars with main-sequence companions (PSR/MS binaries; purple), gravitational wave events (GWs; light purple), low-mass X-ray binaries (LMXBs; magenta), high-mass X-ray binaries (HMXBs; pink) and NICER X-ray pulse profile modelling results (light pink). NS indexed with a '(c)' indicate the companion to an observed pulsar. Note that those with names in blue could be either a NS or a white dwarf based on current constraints. For NS detected via GW merger events, '(p)' indicates the primary or heavier object and '(s)' the secondary or less massive object.
• Figure 4: NS mass-radius relations (left panel) and mass-moment of inertia relations (right panel) for different nuclear EoS. The solid lines correspond to the $M$-$R$ and $M$-$I$ sequences for specific EoS models described in LattimerPrakash2001 that satisfy the condition of having a maximum mass exceeding 2.08(7) $M_\odot$, as measured for PSR J0740$+$6620 Fonseca:2021wxt and shown by the orange shaded regions on both plots. The dashed lines represent the $M$-$R$ and $M$-$I$ sequences of EoS models that do not meet this maximum mass requirement. The brown and blue shaded regions represent the $M$-$R$ and $M$-$I$ ranges corresponding to the 68% and 95% quantiles of the posterior distribution from a Bayesian inference based on a relativistic meta-model representation of the EoS Char:2023fue. For comparison, the dash-dotted black and blue contour lines represent the same quantiles obtained from an equivalent analysis with casual and chemically stable instances for a non-relativistic meta-model montefusco_2025. On the left plot, the grey shaded region, bounded by solid black lines, represents the 95% confidence bounds on the mass and radius of J0740+6620 from NICER measurements, while the inner dashed black line denotes the 68% confidence interval Salmi24a. The green downward arrow in the left panel shows the 90% upper limit for $I$ of PSR J0737$-$3039A using the data from Kramer:2021jcw.
• Figure 5: Maximum spin frequency for a NS as a function of its mass for different EoS. The calculations were made with the Rotating Neutron Star (RNS) code (https://github.com/cgca/rns). EoS names are as listed by LattimerPrakash2001 and in the repository for the RNS code, see also Stergioulas1996. The solid curves represent families of maximally rotating NSs from EoS that can produce slowly rotating NS configurations with masses consistent with that of PSR J0740+6620 Fonseca:2021wxt and other multi-messenger constraints as discussed in Dietrich2020. Dashed lines represent those EoS that do not meet the constraints. The red horizontal line shows the spin period of the fastest-spinning pulsar known, PSR J1748$-$2446ad Hessels2006. For this system no mass has been measured. Higher spin frequencies, especially for systems with well-measured masses, have the potential to constrain the EoS in the near future. Calculations and figure by Norbert Wex.