# Evaluating the Evidence of Multipolar Surface Magnetic Field in PSR J0108$-$1431

## TL;DR

This study investigates the surface magnetic field structure of pulsar PSR J0108-1431, finding evidence for a multipolar magnetic field based on phase offset analysis of thermal X-ray and radio emissions.

## Contribution

The paper provides the first evidence for multipolar surface magnetic fields in PSR J0108-1431 through phase offset analysis of X-ray and radio emission peaks.

## Key findings

- Bayesian analysis suggests thermal emission models are ambiguous.
- Phase offset > 0.1 indicates multipolar magnetic field presence.
- Thermal emission models cannot reliably estimate polar cap area.

## Abstract

PSR J0108$-$1431 is an old pulsar where the X-ray emission is expected to have a thermal component from the polar cap and a non-thermal component from the magnetosphere. Although the phase-integrated spectra are fit best with a single non-thermal component modeled with a power-law (PL) of photon index $\Gamma=2.9$, the X-ray pulse profiles do show the presence of phase-separated thermal and non-thermal components. The spectrum extracted from half the rotational phase away from the X-ray peak fits well with either a single blackbody (BB) or a neutron star atmosphere (NA) model, whereas, the spectrum from the rest of the phase range is dominated by a PL. From Bayesian analysis, the estimated BB area is smaller than the expected polar cap area for a dipolar magnetic field with a probability of 86% whereas the area estimate from the NA model is larger with a probability of 80%. Due to the ambiguity in the thermal emission model, the polar cap area cannot be reliably estimated and hence cannot be used to understand the nature of the surface magnetic field. Instead, we can infer the presence of multipolar magnetic field from the misalignment between the pulsar's thermal X-ray peak and the radio emission peak. For J0108$-$1431, we estimated a phase-offset $\Delta\phi > 0.1$ between the thermal polar cap emission peak and the radio emission peak and argue that this is best explained by the presence of a multipolar surface magnetic field.