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A neutron star is a sphere the size of a city but with the mass of the Sun. A single teaspoon of its material would weigh as much as a mountain. The star PSR J0030+0451 spins hundreds of times per second and emits narrow beams of X-rays. When a beam sweeps past Earth, we see a brief flash, like the light from a lighthouse.

Astronomers watched this "lighthouse" from 2017 to 2023 using the NICER space telescope. They collected 50% more X-ray photons than in previous studies and added older data from the XMM-Newton telescope. The main puzzle: where exactly on the star's surface are the hot spots that emit the X-rays? Earlier, different spot models gave different answers, and the results didn't line up with other measurements.

Now the picture is clearer. The new data showed that the spots are probably not uniformly hot: within each spot, the temperature changes from the center to the edge. Accounting for this "gradient" resolved the contradictions between different models. In the end, the star's mass came out to 1.43 solar masses (with an uncertainty from 1.26 to 1.63), and its radius to 12.68 kilometers (from 11.64 to 13.99). This agrees beautifully with data from other neutron stars and with the merger detected by gravitational-wave observatories.

The upshot: the same star, measured in different ways, now tells the same story. And that means we better understand how matter gets squeezed to unimaginable densities.

Original abstract

as written by the authors arXiv:2602.23743

Pulse-profile modeling of rotation-powered millisecond pulsars targeted by NICER has enabled mass--radius constraints of several neutron star sources, with implications for the dense-matter equation of state. For the bright isolated pulsar PSR J0030+0451, the inferred mass--radius was previously found to depend strongly on the assumed hot spot model. These hot-spot models yielded different mass--radius constraints, with the statistically preferred model exhibiting some mild tension with results inferred for PSR J0437$$-$$4715, PSR~J0614$$-$$3329, and GW170817. We present an updated pulse-profile analysis of PSR J0030+0451 using new NICER observations obtained between 2017 July to 2023 January, increasing the number of X-ray counts by about 50% compared to previous analyses. We jointly analyze the NICER data with archival XMM-Newton observations to better constrain the source spectrum and background. The new analysis significantly reduces the discrepancy between the hot spot models. The inferred mass and radius are $$M = 1.43^{+0.20}_{-0.17}\,M_\odot$$ and $$R_{\rm eq} = 12.68^{+1.31}_{-1.04}$$ km (68% credible intervals), reducing the tension with the results from other sources. In addition, the inferred hot spot configurations suggest the presence of intra-spot temperature gradients.