A NICER View of PSR J0030+0451: Updated Constraints from Six Years of NICER Observations

Abstract

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.

Figures (8)

• Figure 1: NICER phase--channel--resolved counts for PSR J0030$+$0451. Counts are folded on the rotational phase and shown over two cycles for clarity; the second cycle repeats the first. The top panel shows the dataset analyzed by Vinciguerra:2024, while the bottom panel shows the new data used in this work. Both analyses use the PI channels subset $[30,300)$, corresponding nominally to the photon energy range $[0.3$--$3.0)$ keV. The rotational phase is divided into 32 equally spaced bins per cycle. The horizontal features present around PI channels 35 and 55 are due to fluorescence lines originating in the Earth’s atmosphere Mauviard:2025.
• Figure 2: Posterior distributions of the equatorial radius $R_{\rm eq}$, compactness $M/R_{\rm eq}$, and mass $M$. Solid curves show the results obtained in this work, while dashed curves correspond to the analysis of Vinciguerra:2024. Blue curves denote the PDT-U model and orange curves the ST+PDT model. The two-dimensional panels show the joint marginal posterior distributions, with contours enclosing the 68%, 95%, and 99% credible regions. The diagonal panels show the marginalized one-dimensional posterior distributions for each parameter and the black dotted curves indicate the corresponding one-dimensional priors. For each model and analysis, the median and 68% credible intervals are indicated in the corresponding color.
• Figure 3: Posterior distributions of hot spots parameters for PSR J0030$+$0451. Blue curves denote the PDT-U model and orange curves the ST+PDT model. The two-dimensional panels show the joint marginal posterior distributions, with contours enclosing the 68%, 95%, and 99% credible regions. The diagonal panels show the marginalized one-dimensional posterior distributions for each parameter. For each model and analysis, the median and 68% credible intervals are indicated in the corresponding color.
• Figure 4: Comparison of mass-radius constraints from NICER and XMM-Newton observations. The filled contours show the 68% and 95% credible regions for PSR J0030$+$0451 inferred in this work (PDT-U model), while dashed contours indicate the previous constraints from Vinciguerra:2024. Also shown are published constraints for PSR J0740$+$6620, PSR J0437$-$4715, and PSR J0614$-$3329. The updated PDT-U solution shifts toward lower mass and radius, reducing the previously noted tension with other $\sim 1.4$$M_{\odot}$ RMPs.
• Figure 5: Posterior distributions of mass $M$, equatorial radius $R_{\rm eq}$, and compactness $M/R_{\rm eq}$ for PSR J0030+0451 obtained using different sampler configurations to assess convergence. The left panel shows results for the ST+PDT model, while the right panel corresponds to the PDT-U model. Labels of the form ef:xx, LP:yk, MM:zz denote the sampling efficiency (xx), the number of live points (y in thousands), and whether multimodal sampling is enabled (zz = on or off), respectively.