Multipolar Magnetic-Field Inference for PSR J0740+6620 with Neural-Network-Accelerated NICER Pulse-Profile Modeling

We investigate the multipolar surface magnetic-field structure of the high-mass millisecond pulsar PSR J0740+6620 using the 32-bin bolometric NICER pulse profile of Dittmann et al.

(2024).

Building on the neural-network surrogate framework of Olmschenk et al.

(2025), we model the emitting regions as open-field-line footpoints of an offset dipole plus axisymmetric quadrupole static vacuum field, rather than as prescribed geometric hotspots.

We fix the stellar mass, radius, observer inclination, and hotspot temperature ratio to the Dittmann et al.

(2024) maximum-likelihood values and explore the resulting 11-dimensional magnetic-field space.

To make this feasible, we train convolutional neural-network surrogates on $5.12\times10^7$ synthetic bolometric light curves and use them in a parallel ensemble Markov Chain Monte Carlo calculation on 4000 CPU cores, accelerating likelihood evaluations by a factor of $\gtrsim 400$.

We perform independent inferences for two calibrated temperature-weight prescriptions, Tw=1.31 and Tw=1.41, encoding the relative bolometric weight associated with the hotspot temperature difference.

The posteriors, posterior-predictive light curves, and maximum-likelihood values are very similar, indicating weak sensitivity to this choice.

The offset model reproduces the observed double-peaked profile and yields broad, multimodal posteriors, reflecting both the background-dominated data and degeneracies of the multipolar parameterization.

The hotspot-density map shows that pulse phases constrain the approximate azimuthal placement of the emission, while latitude, surface extent, and morphology remain weakly constrained.

A restricted zero offset run is disfavored within the adopted field basis.

This work extends neural-network-accelerated magnetic-field inference to PSR J0740+6620 and motivates future energy-dependent, force-free, and joint X-ray/$\gamma$-ray extensions.