# The illusion of neutron star magnetic field estimates

## TL;DR

This paper challenges traditional estimates of neutron star magnetic fields, emphasizing the importance of multipolar components, particle loading, and relativistic effects, which significantly alter the inferred physical parameters and their evolution.

## Contribution

It introduces revised methods for estimating neutron star magnetic fields by incorporating multipolar fields, winds, and relativistic corrections, highlighting inaccuracies in previous simple dipole models.

## Key findings

- Magnetic field estimates are significantly affected by multipolar components and particle winds.
- Standard dipole models underestimate or misestimate neutron star magnetic fields.
- All studied neutron stars have magnetic fields below the quantum critical value.

## Abstract

Neutron stars radiate in a broad band spectrum from radio wavelengths up to very high energies. They have been sorted into several classes depending on their respective place in the $P-\dot{P}$ diagram and depending on spectral/temporal properties. Fundamental physical parameters such as their characteristic age and magnetic field strength are deduced from these primary observables. However this deduction relies mostly on interpretations based on simple vacuum or force-free rotating dipole models that are unrealistic. In this paper, we show that the computation of the stellar surface magnetic field is poorly estimated or even erroneous if multipolar components and particle loading are neglected. We show how quadrupolar magnetic field and monopolar winds alter field estimates and characteristic ages in the $P-\dot{P}$ diagram. Corrections brought by general relativity are also discussed. We derive some important parameters of pulsar physics such as the wind Lorentz factor~($\gamma$) times the pair multiplicity~($\kappa$) to be around $\gamma\,\kappa \approx 10^8-10^{10}$. Therefore, the standard magnetodipole radiation losses formula must be used with caution to reckon neutron star surface magnetic fields and related secular evolution parameters. Depending on models we found that all field strengths, both for magnetars and for pulsars lie below the quantum critical value of $B_{\rm c} \approx 4.4\cdot 10^9$~T.