⚛️ nuclear theory

The Radius of the Neutron Star PSR J0614-3329 from NICER Data

This paper presents a NICER-based analysis of the neutron star PSR J0614-3329 that derives an equatorial circumferential radius of 9.88–12.77 km using a three-hot-spot model, while noting challenges in jointly fitting NICER and XMM-Newton data and discussing the resulting constraints on dense matter properties.

Original authors: M. C. Miller, A. J. Dittmann, I. M. Holt, F. K. Lamb, C. Chirenti, Z. Arzoumanian, J. Berteaud, S. Bogdanov, K. C. Gendreau, A. K. Harding, W. C. G. Ho, C. Kalapotharakos, S. M. Morsink, P. S. Ray, R.

Published 2026-09-02

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: M. C. Miller, A. J. Dittmann, I. M. Holt, F. K. Lamb, C. Chirenti, Z. Arzoumanian, J. Berteaud, S. Bogdanov, K. C. Gendreau, A. K. Harding, W. C. G. Ho, C. Kalapotharakos, S. M. Morsink, P. S. Ray, R. A. Remillard, Z. Wadiasingh, M. T. Wolff

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep in the cosmos, hidden within the remnants of exploded stars, lie objects so dense that a single teaspoon of their material would weigh as much as a mountain on Earth. These are neutron stars, the collapsed cores of massive stars that have run out of fuel. Inside them, matter is crushed to a state that cannot be recreated in any laboratory on Earth. The atoms are broken apart, and protons and electrons are forced together to form a sea of neutrons. Physicists have long wanted to know exactly how this exotic material behaves under such extreme pressure. Does it remain a simple fluid, or does it transform into something stranger, like a super-dense crystal or a soup of exotic particles? The answer lies in the size of these stars. If we can measure how big a neutron star is for a given weight, we can deduce the rules that govern the matter inside it.

For years, astronomers have struggled to get a precise measurement of these stellar sizes. The challenge is that neutron stars are small, distant, and often hidden behind clouds of dust or obscured by their own intense gravity. However, a new generation of space telescopes has changed the game. One such instrument, the Neutron star Interior Composition Explorer, or NICER, orbits Earth and watches these stars with incredible precision. It does not just take pictures; it counts individual X-ray particles arriving from the star's surface, timing their arrival to within a fraction of a billionth of a second. By watching how the light from hot spots on the star's surface changes as the star spins, scientists can use the warping of space and time caused by the star's gravity to calculate its size.

In a recent study, a team of researchers turned their attention to a specific spinning neutron star known as PSR J0614−3329. This star is located about 600 light-years away and spins 318 times every second. Previous radio observations had already determined its mass to be roughly 1.4 to 1.5 times that of our Sun, making it a perfect candidate for this kind of study. The researchers gathered years of data from NICER, filtering out interference from the Earth's atmosphere and the background noise of space to isolate the faint signal coming from the star. They then built detailed computer models to simulate what the X-ray light curve should look like if the star had different sizes and different patterns of hot spots on its surface.

The team tested several different scenarios. They considered models where the star had two circular hot spots, two oval spots, and three circular spots. After running millions of simulations to see which model matched the actual data best, they found that the model with three circular hot spots provided the most accurate fit. This model suggested that the star has a radius between 9.88 and 12.77 kilometers. To put this in perspective, if you were to take a sphere of matter with the mass of our Sun and squeeze it down until it was only about the size of a small city, it would become a neutron star. The researchers also tried to combine their NICER data with older observations from a different telescope, the XMM-Newton, but found that the standard way of handling background noise in the older data made the combined results unreliable. They decided to stick with the high-precision NICER data alone for their final conclusion.

The results of this study are significant because they add a new, precise data point to the growing map of neutron star sizes. When the researchers combined their findings for PSR J0614−3329 with data from other neutron stars, they found that the matter inside these stars is likely not as stiff as some theories had predicted. The new measurements suggest that the maximum weight a neutron star can hold before collapsing into a black hole is slightly lower than previously thought, and that a typical neutron star with the mass of our Sun is slightly smaller than earlier estimates. This helps narrow down the possible behaviors of matter at densities far beyond what we can create on Earth. While the study does not reveal the exact composition of the star's core, it rules out many of the more extreme possibilities and brings us closer to understanding the fundamental laws that govern the densest matter in the universe. The work stands as a testament to how carefully counting individual particles of light from a spinning star can reveal the secrets of the most extreme environments in existence.

Technical Summary: The Radius of the Neutron Star PSR J0614−3329 from NICER Data

Problem and Motivation
The internal composition of neutron stars, specifically the equation of state (EOS) of cold, catalyzed matter at densities exceeding nuclear saturation ( $n_0 \approx 0.16 \text{ fm}^{-3}$ ), cannot be replicated in terrestrial laboratories or derived from first principles. Consequently, astronomical observations constraining the mass and radius of these objects are essential. While the Neutron star Interior Composition Explorer (NICER) has previously provided radius estimates for several pulsars (e.g., PSR J0030+0451, PSR J0740+6620), this paper presents a new analysis of NICER data for the 318-Hz pulsar PSR J0614−3329. This object has a mass of $\sim 1.4\text{--}1.5 M_\odot$ determined from radio timing, making it a critical target for refining EOS constraints.

Methodology
The authors analyzed NICER X-ray Timing Instrument (XTI) data collected between March 2018 and May 2023, resulting in an effective exposure of 1.09 Ms. The analysis also incorporated archival XMM-Newton EPIC data from 2010, though joint fitting revealed systematic discrepancies in the background modeling for the XMM-Newton data.

The modeling approach follows established Bayesian inference frameworks used in previous NICER analyses:

Surface Emission Model: The authors model the neutron star surface as having heated regions ("hot spots") bombarded by relativistic particles from the magnetosphere. These spots are treated as uniform-temperature circular or oval regions. The local emission spectrum is modeled using a fully ionized non-magnetic hydrogen atmosphere (Ho & Lai 2001).
Ray Tracing: The "oblate Schwarzschild approximation" is employed to account for the star's rotation-induced oblateness while approximating the external spacetime as Schwarzschild.
Statistical Inference: The analysis uses the pocoMC sampler (and emcee for refinement) to explore the posterior probability distributions of model parameters. Key parameters include the gravitational mass ( $M$ ), equatorial circumferential radius ( $R_e$ ), spot geometry (location, size, temperature), observer inclination, and interstellar absorption ( $N_H$ ).
Model Comparison: Three classes of models were tested: two circular spots, two oval spots, and three circular spots.

Key Results

Preferred Model: The Bayesian evidence strongly favors the model with three uniform-temperature circular hot spots ( $\Delta \ln Z > 10$ compared to other configurations).
Radius and Mass Constraints: The best-fitting three-circle model yields a symmetric 68% credible range for the equatorial circumferential radius of 9.88–12.77 km. The mass posterior is dominated by the prior (derived from radio timing), remaining consistent with the $\sim 1.4\text{--}1.5 M_\odot$ range, while the radius posterior is strongly informed by the X-ray waveform data.
Geometry: The preferred geometry features non-antipodal emitting regions, suggesting a magnetic field configuration more complex than a simple centered dipole, potentially including multipolar components.
Goodness of Fit: The maximum-likelihood fit yields a phase-channel $\chi^2/\text{dof} = 5154.89/5252$ (probability 83%) and a bolometric $\chi^2/\text{dof} = 26.42/27$ (probability 50%), indicating an adequate fit with no significant residuals or outliers.
XMM-Newton Discrepancy: Joint fits of NICER and XMM-Newton data systematically underpredict the XMM-Newton counts when standard background assumptions (derived from surrounding fields) are applied, suggesting issues with background modeling for this specific target in XMM data.

Implications for the Equation of State (EOS)
The authors integrate the PSR J0614−3329 radius measurement with existing constraints, including:

Mass measurements of PSR J1614−2230 and PSR J0348+0432.
Tidal deformability from GW170817 and GW190425.
NICER-based mass/radius measurements of PSR J0030+0451, PSR J0740+6620, and PSR J0437−4715.
A constraint on the nuclear symmetry energy at saturation density ( $S = 32 \pm 2$ MeV).
The EOS below half-saturation density is modeled using the microscopically realistic QHC21 EOS (Kojo et al. 2022), extrapolated to higher densities using Gaussian processes.

Significance and Claims
The paper claims that the inclusion of the PSR J0614−3329 radius measurement (centered at a smaller radius than previous $\sim 1.4 M_\odot$ pulsar measurements) leads to a slight decrease in the estimated maximum stable mass of a non-rotating neutron star ( $M_{\text{TOV}}$ ) and the fiducial radius of a $1.4 M_\odot$ star.

Maximum Mass: The median $M_{\text{TOV}}$ decreases from 2.20 $M_\odot$ (previous work) to 2.15 $M_\odot$ (this work).
Fiducial Radius: The median radius for a $1.4 M_\odot$ star decreases from 12.56 km to 12.44 km.

The authors conclude that these results are broadly consistent with previous NICER analyses and continue to refine the understanding of the EOS of cold, equilibrated matter at high densities. They explicitly note that while the high mass estimate of PSR J0952−0607 ( $2.32 \pm 0.11 M_\odot$ ) could further constrain the EOS, systematic uncertainties in modeling "spider" pulsars warrant caution in its immediate inclusion. The study reinforces the utility of phase-resolved NICER data in constraining neutron star structure without relying on accretion physics.

More like this