An Investigation of Systematic Effects from Background Priors on PSR J0740$+$6620 Radius Estimates using Synthetic NICER and XMM-Newton Data

TL;DR

This study tests how misparameterization of unmodulated background in joint NICER+XMM-Newton analyses affects neutron-star radius inferences, using PSR J0740+6620 as a prototypical case. By generating synthetic NICER and XMM-Newton data under two background regimes and applying two background treatments, the authors show that radius estimates are robust to substantial background misestimation, with median shifts around $1\sigma$ at most; Bayesian evidence consistently prefers the correct background model. The work employs a two-spot hydrogen-atmosphere waveform model, a hybrid MN+PT-emcee sampling strategy, and rigorous model-evidence comparisons to demonstrate that NICER-like analyses yield accurate radii when the data are thoroughly sampled and models fit the data well. The results reinforce the reliability of NICER-based constraints on the neutron-star equation of state and highlight Bayesian model selection as a practical tool for validating background assumptions in joint X-ray analyses.

Abstract

Accurate and precise measurements of neutron star radii provide invaluable information about the cold, dense matter in neutron star cores. Analyses of synthetic X-ray pulse waveform data similar to the data obtained from non-accreting neutron stars using the Neutron star Interior Composition Explorer (NICER) have indicated that mass and radius estimates made using such data are robust against some systematic errors that may be made when modeling these data, such as errors in the assumed pattern of the thermal X-ray emission from the surface of these stars. A potentially important but so far unexplored source of systematic error is misparameterization of unmodulated background components, which can bias the inferred radius, particularly when data from different telescopes are used in the analysis. In this study, we investigate the effects of the background model on radius estimates by jointly analyzing synthetic NICER and XMM-Newton data, using the $\sim 2.1~M_\odot$ pulsar PSR~J0740$+$6620 as a prototypical example. Our analysis shows that even if the background assumed in the model underestimates the actual background by a factor of more than five, the resulting shift of the radius posterior from the true value of the radius corresponds to only $\sim1σ$. In all the cases we examined, the Bayesian evidence for the correct background model is greater than for the incorrect background model. These results add to the evidence that analyses of NICER-like data provide accurate measurements of neutron star radii when the statistical sampling is thorough and the model fits the data well.

Figures (8)

• Figure 1: The data we used to define the priors on the backgrounds when fitting synthetic Data Set 1 and synthetic Data Set 2. In panel (a) the purple histograms show the counts that were generated by Poisson sampling the sum of the modeled spot emission and the XMM-Newton blank-sky background, while the orange curves show the same data smoothed using a Savitzky-Golay filter. When we analyzed synthetic Data Set 1, which includes only the XMM-Newton blank-sky background, using a model that allows for an additional unmodulated background, we used the smoothed data to define the prior for that additional background. In panel (b) the purple histograms show the counts generated by Poisson sampling the sum of the modeled spot emission, the XMM-Newton blank-sky background, and the additional unmodulated background we considered. Again, the orange curves show the smoothed data. In this case we used the smoothed data to define the priors on the additional backgrounds when we analyzed synthetic Data Set 2 using a model that includes the XMM-Newton blank-sky background and an additional unmodulated background.
• Figure 2: The mass and radius posterior probability distributions from our combined MultiNest and PT-emcee analysis for Case 1 (a) and Case 2 (b). In each case, the orange diamond in the 2D plot and the orange dashed lines in the 1D plots mark the mass and radius values assumed in generating the synthetic data. Solid blue and dot–dashed purple curves show the PT-emcee and MultiNest posteriors, respectively. As discussed in the text, the radius distribution broadens from the initial MultiNest result to the converged PT-emcee distribution, while the mass posterior remains dominated by the prior.
• Figure 3: Quality of Fits to the Synthetic Data
• Figure 4: The mass and radius posterior probability distributions from our combined MultiNest and PT-emcee analysis for Case 3 (a) and Case 4 (b). In each case, the orange diamond in the 2D plot and the orange dashed lines in the 1D plots mark the mass and radius values assumed in generating the synthetic data.
• Figure 5: The full set of 1D and 2D posterior distributions from our MultiNest and PT-emcee analysis of Case 1. The synthetic data were constructed assuming that the background is the XMM-Newton blank-sky background plus an additional background (see text). The analysis model also assumes that the background is the XMM-Newton blank-sky background plus an additional background.