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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 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 formation and evolution of magnetic field of neutron stars, paying special attention to field decay processes. Then we present important observational results related to field properties of different types of compact objects: magnetars, cooling neutron stars, radio pulsars, sources in binary systems. After that, we discuss which observations can shed light on obscure characteristics of neutron star magnetic fields and their behaviour. We end the review with a subjective list of open problems.
In this study, we examine the magnetic field evolution occurring in a neutron star crust. Beyond the elastic limit, the lattice ions are assumed to act as a plastic flow. The Ohmic dissipation, Hall drift, and bulk fluid velocity driven by the Lorent
Young neutron stars (NSs) have magnetic fields $B$ in the range $10^{12}-10^{15}$ G, believed to be generated by dynamo action at birth. We argue that such a dynamo is actually too inefficient to explain the strongest of these fields. Dynamo action i
Isolated neutron stars show a diversity in timing and spectral properties, which has historically led to a classification in different sub-classes. The magnetic field plays a key role in many aspects of the neutron star phenomenology: it regulates th
We propose the mean field dynamo model for the generation of strongest magnetic fields, $Bsim 10^{15},{rm G}$, in a neutron star (NS) accounting for the chiral magnetic effect (CME) driven by the shock in a supernova (SN) progenitor of that NS. The t
The flow of a matter, accreting onto a magnetized neutron star, is accompanied by an electric current. The closing of the electric current occurs in the crust of a neutron stars in the polar region across the magnetic field. But the conductivity of t