Neutron stars are natural physical laboratories allowing us to study a plethora of phenomena in extreme conditions. In particular, these compact objects can have very strong magnetic fields with non-trivial origin and evolution. In many respects, its magnetic field determines the appearance of a neutron star. Thus, understanding the field properties is important for the interpretation of observational data. Complementing this, observations of diverse kinds of neutron stars enable us to probe parameters of electro-dynamical processes at scales unavailable in terrestrial laboratories. In this review, we first briefly describe theoretical models of the formation and evolution of the magnetic field of neutron stars, paying special attention to field decay processes. Then, we present important observational results related to the field properties of different types of compact objects: magnetars, cooling neutron stars, radio pulsars, and sources in binary systems. After that, we discuss which observations can shed light on the obscure characteristics of neutron star magnetic fields and their behaviour. We end the review with a subjective list of open problems.

Evolution of Neutron Star Magnetic Fields

Fast Radio Bursts and Their High-energy Counterparts from Magnetar Magnetospheres

The frequency-dependent periodic active window of the fast radio burst FRB 180916.J0158+65 (FRB 180916B) was observed recently. In this Letter, we propose that a Be/X-ray binary (BeXRB) system, which is composed of a neutron star (NS) and a Be star with a circumstellar disk, might be the source of a repeating FRB with periodic activities, and apply this model to explain the activity window of FRB 180916B. The interaction between the NS magnetosphere and the accreted material results in evolution of the spin period and the centrifugal force of the NS, leading to the change of the stress in the NS crust. When the stress of the crust reaches the critical value, a starquake occurs and further produces FRBs. The interval between starquakes is estimated to be a few days that is smaller than the active window of FRB 180916B. When the NS moves out of the disk of the Be star, the interval between starquakes becomes much longer than the orbital period, which corresponds to the non-active phase. In this model, due to the absorption of the disk of the Be star, a frequency-dependent active window would appear for the FRBs, which is consistent with the observed properties of FRB 180916B. And the contribution of dispersion measure (DM) from the disk of the Be star is small. In addition, the location of FRB 180916B in the host galaxy is consistent with a BeXRB system.

Periodic Activities of Repeating Fast Radio Bursts from Be/X-ray Binary Systems

Fast radio bursts (FRBs) are cosmic sources emitting millisecond-duration radio bursts. Although several hundreds FRBs have been discovered, their physical nature and central engine remain unclear. The variations of Faraday rotation measure and dispersion measure, due to local environment, are crucial clues to understanding their physical nature. The recent observations on the rotation measure of FRB 20201124A show a significant variation on a day time scale. Intriguingly, the oscillation of rotation measure supports that the local contribution can change sign, which indicates the magnetic field reversal along the line of sight. Here we present a physical model that explains observed characteristics of FRB 20201124A and proposes that repeating signal comes from a binary system containing a magnetar and a Be star with a decretion disk. When the magnetar approaches the periastron, the propagation of radio waves through the disk of the Be star naturally leads to the observed varying rotation measure, depolarization, large scattering timescale, and Faraday conversion. This study will prompt to search for FRB signals from Be/X-ray binaries. 

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Repeating fast radio burst 20201124A originates from a magnetar/Be star binary

FRB 20121102A is the first known fast radio burst (FRB) from which repeat bursts were detected, and one of the best-studied FRB sources in the literature. Here we report on the analysis of 478 bursts (333 previously unreported) from FRB 20121102A using the 305-m Arecibo telescope - detected during approximately 59 hours of observations between December 2015 and October 2016. The majority of bursts are from a burst storm around September 2016. This is the earliest available sample of a large number of FRB 20121102A bursts, and it thus provides an anchor point for long-term studies of the source's evolving properties. We observe that the bursts separate into two groups in the width-bandwidth-energy parameter space, which we refer to as the low-energy bursts (LEBs) and high-energy bursts (HEBs). The LEBs are typically longer duration and narrower bandwidth than the HEBs, reminiscent of the spectro-temporal differences observed between the bursts of repeating and non-repeating FRBs. We fit the cumulative burst rate-energy distribution with a broken power-law and find that it flattens out toward higher energies. The sample shows a diverse zoo of burst morphologies. Notably, burst emission seems to be more common at the top than the bottom of our 1150 - 1730 MHz observing band. We also observe that bursts from the same day appear to be more similar to each other than to those of other days, but this observation requires confirmation. The wait times and burst rates that we measure are consistent with previous studies. We discuss these results, primarily in the context of magnetar models. 

Arecibo observations of a burst storm from FRB 20121102A in 2016

Fast radio bursts (FRBs) are mysterious radio transients with millisecond durations. Recently, a periodic activity of $\sim$16 day and a possible periodicity of $\sim$159 day were detected to arise from FRB 180916.J0158+65 and FRB 121102, respectively, and the spin period of a slow-rotation magnetar was further considered to be one of possibilities to explain the periodic activities of repeating FRBs. For isolated neutron stars, the spin evolution suggests that it's difficult to reach several hours. In this work, we mainly focus on the possible maximum spin period of isolated NSs / magnetars dominated by an interaction between star's magnetic field and the disk. We find that the disk wind plays an important role in spin evolution, whose influence varies the power law index in the evolution equation of mass flow rate. For a magnetar without disk wind, the longest spin period is tens of hours. When the disk wind with a classical parameter is involved, the maximum spin period can reach hundreds of hours. But for a much extremely large index of mass flow rate due to disk wind or other angular momentum extraction processes, a spin period of $\sim$(16-160) days is still possible.

Kun Xu

Papers

Periodic Activities of Repeating Fast Radio Bursts from Be/X-ray Binary Systems

Do the periodic activities of repeating fast radio bursts represent the spins of neutron stars

Periodic Activities of Repeating Fast Radio Bursts from Be/X-ray Binary Systems

Do the periodic activities of repeating fast radio bursts represent the spins of neutron stars