Revealing the internal magnetic field configuration of magnetars via their associated periodic signals

TL;DR

This study uses periodic signals from magnetars and FRBs to infer their internal magnetic field configurations, revealing strong poloidal and toroidal fields and constraining neutron superfluidity temperatures.

Contribution

It introduces a novel method to probe magnetar internal magnetic fields through their observed periodic signals, linking surface emissions with internal magnetic structures.

Findings

Internal poloidal fields are approximately 10^{14} to 10^{15} G.

Toroidal fields are roughly 10^{15} G, with a ratio to poloidal fields of 2 to 37.

Constraints on neutron superfluidity critical temperature are less than 6.4×10^8 K.

Abstract

The magnetic deformation of magnetars is affected by their internal magnetic fields, which are generally difficult to be measured directly through observations. In this work, the periodic pulse-phase modulations in the hard X-ray emissions of the magnetars 4U 0142+61, 1E 1547.0-5408, SGR 1900+14, and SGR 1806-20, and the periodicities of fast radio bursts (FRBs) 180916 and 121102 are interpreted as free precession of the (host) magnetars. Using these periodic signals, we investigate the magnetars' internal magnetic fields. In order to simultaneously account for the modulation periods and surface thermal emissions of the former four magnetars, and require that their internal poloidal fields smoothly connect with the surface dipole fields, the parameter that characterizes the distribution of toroidal field in the magnetar interior should satisfy $\beta\gtrsim1$. Moreover, their volume-averaged strengths of poloidal and toroidal fields are respectively $\bar{B}_{\rm p}\sim10^{14}$--$10^{15}$ G and $\bar{B}_{\rm t}\sim10^{15}$ G with the strength ratios $\bar{B}_{\rm t}/\bar{B}_{\rm p}$ generally distributing within $\sim2$--$37$. We could also constrain the critical temperature for neutron superfluidity in the neutron-star core considering that the former four magnetars are probably precessing, and the most stringent constraint is $T_{\rm c,core}<6.4\times10^8$ K. Adopting a possible critical temperature $T_{\rm c,core}=5\times10^8$ K, we could obtain $\bar{B}_{\rm p}\gtrsim10^{14}$--$10^{15}$ G and $\bar{B}_{\rm t}\gtrsim10^{14}$--$10^{15}$ G for the host magnetars of FRBs 180916 and 121102, which indicates that the magnetars of our interest possibly have similar poloidal and toroidal fields.