Powering Central Compact Objects with a Tangled Crustal Magnetic Field

Central Compact Objects (CCOs) are X-ray sources with luminosity ranging between 1032-1034 erg s−1, located at the centres of supernova remnants. Some of them have been confirmed to be neutron stars. Timing observations have allowed the estimation of their dipole magnetic field, placing them in the range ∼1010-1011 G. The decay of their weak dipole fields, mediated by the Hall effect and Ohmic dissipation, cannot provide sufficient thermal energy to power their X-ray luminosity, as opposed to magnetars whose X-ray luminosities are comparable. Motivated by the question of producing high X-ray power through magnetic field decay while maintaining a weak dipole field, we explore the evolution of a crustal magnetic field that does not consist of an ordered axisymmetric structure, but rather comprises a tangled configuration. This can be the outcome of a non-self-excited dynamo, buried inside the crust by fallback material following the supernova explosion. We find that such initial conditions lead to the emergence of the magnetic field from the surface of the star and the formation of a dipolar magnetic field component. An internal tangled magnetic field of the order of 1014 G can provide sufficient Ohmic heating to the crust and power CCOs, while the dipole field it forms is approximately 1010 G, as observed in CCOs

Three-dimensional Modeling of the Magnetothermal Evolution of Neutron Stars: Method and Test Cases

Neutron stars harbor extremely strong magnetic fields within their solid outer crust. The topology of this field strongly influences the surface temperature distribution and, hence, the star's observational properties. In this work, we present the first realistic simulations of the coupled crustal magnetothermal evolution of isolated neutron stars in three dimensions accounting for neutrino emission, obtained with the pseudo-spectral code parody. We investigate both the secular evolution, especially in connection with the onset of instabilities during the Hall phase, and the short-term evolution following episodes of localized energy injection. Simulations show that a resistive tearing instability develops in about a Hall time if the initial toroidal field exceeds $\approx {10}^{15}$ G. This leads to crustal failures because of the huge magnetic stresses coupled with the local temperature enhancement produced by dissipation. Localized heat deposition in the crust results in the appearance of hot spots on the star surface, which can exhibit a variety of patterns. Because the transport properties are strongly influenced by the magnetic field, the hot regions tend to drift away and get deformed following the magnetic field lines while cooling. The shapes obtained with our simulations are reminiscent of those recently derived from NICER X-ray observations of the millisecond pulsar PSR J0030+0451

3D Magnetothermal Simulations of Tangled Crustal Magnetic Field in Central Compact Objects

Central compact objects (CCOs) are young neutron stars emitting thermal X-rays with bolometric luminosities LX in the range of 1032–1034 erg s−1. Gourgouliatos, Hollerbach, and Igoshev recently suggested that peculiar emission properties of CCOs can be explained by tangled magnetic field configurations formed in a stochastic dynamo during the proto–neutron star stage. In this case the magnetic field consists of multiple small-scale components with negligible contribution of global dipolar field. We study numerically three-dimensional magnetothermal evolution of tangled crustal magnetic fields in neutron stars. We find that all configurations produce complicated surface thermal patterns that consist of multiple small hot regions located at significant separations from each other. The configurations with initial magnetic energy of (2.5–10) × 1047 erg have temperatures of hot regions that reach ≈ 0.2 keV, to be compared with the bulk temperature of ≈ 0.1 keV in our simulations with no cooling. A factor of two in temperature is also seen in observations of CCOs. The hot spots produce periodic modulations in light curve with typical amplitudes of ≤9%–11%. Therefore, the tangled magnetic field configuration can explain thermal emission properties of some CCOs

Strong toroidal magnetic fields required by quiescent X-ray emission of magnetars

Magnetars are neutron stars (NSs) with extreme magnetic fields1 of strength 5 × 1013−1015 G. These fields are generated by dynamo action during the proto-NS phase, and are expected to have both poloidal and toroidal components2,3,4,5,6, although the energy of the toroidal component could be ten times larger7. Only the poloidal dipolar field can be measured directly, via NS spin-down8. The magnetic field provides heating and governs how this heat flows through the crust9. Magnetar thermal X-ray emission in quiescence is modulated with the rotational period of the NS, with a typical pulsed fraction 10–58%, implying that the surface temperature is substantially non-uniform despite the high thermal conductivity of the star’s crust. Poloidal dipolar fields cannot explain this large pulsed fraction10,11. Previous two-dimensional simulations12,13 have shown that a strong, large-scale toroidal magnetic field pushes a hot region into one hemisphere and increases the pulsed fraction. Here, we report three-dimensional magneto-thermal simulations of magnetars with strong, large-scale toroidal magnetic fields. These models, combined with ray propagation in curved spacetime, accurately describe the observed light curves of 10 out of 19 magnetars in quiescence and allow us to further constrain their rotational orientation. We find that the presence of a strong toroidal magnetic field is enough to explain the strong modulation of thermal X-ray emission in quiescence

Strongly magnetized pulsars: explosive events and evolution

Well before the radio discovery of pulsars offered the first observational confirmation for their existence (Hewish et al., 1968), it had been suggested that neutron stars might be endowed with very strong magnetic fields of $10^{10}$-$10^{14}$G (Hoyle et al., 1964; Pacini, 1967). It is because of their magnetic fields that these otherwise small ed inert, cooling dead stars emit radio pulses and shine in various part of the electromagnetic spectrum. But the presence of a strong magnetic field has more subtle and sometimes dramatic consequences: In the last decades of observations indeed, evidence mounted that it is likely the magnetic field that makes of an isolated neutron star what it is among the different observational manifestations in which they come. The contribution of the magnetic field to the energy budget of the neutron star can be comparable or even exceed the available kinetic energy. The most magnetised neutron stars in particular, the magnetars, exhibit an amazing assortment of explosive events, underlining the importance of their magnetic field in their lives. In this chapter we review the recent observational and theoretical achievements, which not only confirmed the importance of the magnetic field in the evolution of neutron stars, but also provide a promising unification scheme for the different observational manifestations in which they appear. We focus on the role of their magnetic field as an energy source behind their persistent emission, but also its critical role in explosive events.Comment: Review commissioned for publication in the White Book of "NewCompStar" European COST Action MP1304, 43 pages, 8 figure

Magnetic-field evolution in a plastically failing neutron-star crust

Under normal conditions in a neutron-star (NS) crust, ions are locked in place in the crustal lattice and only electrons are mobile, and magnetic-field evolution is thus directly related to the electron velocity. The evolution, however, builds magnetic stresses that can become sufficiently large for the crust to exceed its elastic limit, and to flow plastically. We consider the nature of this plastic flow and the back-reaction on the crustal magnetic-field evolution. We formulate a plane-parallel model for the local failure, showing that surface motions are inevitable once the crust yields, in the absence of extra dissipative mechanisms. We perform numerical evolutions of the crustal magnetic field under the joint effect of Hall drift and Ohmic decay, tracking the build-up of magnetic stresses, and diagnosing crustal failure with the von Mises criterion. Beyond this point we solve for the coupled evolution of the plastic velocity and magnetic field. Our results suggest that to have a coexistence of a magnetar corona with small-scale magnetic features, the viscosity of the plastic flow must be roughly 1036–1037 g cm−1s−1. We find significant motion at the surface at a rate of 10–100 cm yr−1, and that the localized magnetic field is weaker than in evolutions without plastic flow. We discuss astrophysical implications, and how our local simulations could be used to build a global model of field evolution in the NS crust

Current closure through the neutron star crust

Force-free pulsar magnetospheres develop a large-scale poloidal electric current circuit that flows along open magnetic field lines from the neutron star to the termination shock. The electric current closes through the interior of the neutron star where it provides the torque that spins-down the star. In the present work, we study the internal electric current in an axisymmetric rotator. We evaluate the path of the electric current by requiring the minimization of internal Ohmic losses. We find that, in millisecond pulsars, the current reaches the base of the crust, while in pulsars with periods of a few seconds, the bulk of the electric current does not penetrate deeper than about 100 m. The region of maximum spin-down torque in millisecond pulsars is the base of the crust, while in slowly spinning ones it is the outer crust. We evaluate the corresponding Maxwell stresses and find that, in typical rotation-powered radio pulsars, they are well below the critical stress that can be sustained by the crust. For magnetar-level fields, the Maxwell stresses near the surface are comparable to the critical stress and may lead to the decoupling of the crust from the rest of the stellar rotation