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Register a new userLong-term GRHMD simulation of magnetic field in isolated neutron stars
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Strong magnetic fields play an important role in powering the emission of neutron stars. Nevertheless a full understanding of the interior configuration of the field remains elusive. In this work, we present General Relativistic MagnetoHydroDynamics simulations of the magnetic field evolution in neutron stars lasting 500 ms (5 Alfven crossing times) and up to resolutions of 0.231 km using Athena++. We explore two different initial conditions, one with purely poloidal magnetic field and the other with a dominant toroidal component, and study the poloidal and toroidal field energies, the growth times of the various instability-driven oscillation modes and turbulence. We find that the purely poloidal setup generates a toroidal field which later decays exponentially reaching 1% of the total magnetic energy, showing no evidence of reaching equilibrium. The initially stronger toroidal field setup, on the other hand, loses up to 20% of toroidal energy and maintains this state till the end of our simulation. We also explore the hypothesis, drawn from previous MHD simulations, that turbulence plays an important role in the quasi equilibrium state. An analysis of the spectra in our higher resolution setups reveal, however, that in most cases we are not observing turbulence at small scales, but rather a noisy velocity field inside the star. We also observe that the majority of the magnetic energy gets dissipated as heat increasing the internal energy of the star, while a small fraction gets radiated away as electromagnetic radiation.
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The strong magnetic field of neutron stars is intimately coupled to the observed temperature and spectral properties, as well as to the observed timing properties (distribution of spin periods and period derivatives). Thus, a proper theoretical and numerical study of the magnetic field evolution equations, supplemented with detailed calculations of microphysical properties (heat and electrical conductivity, neutrino emission rates) is crucial to understand how the strength and topology of the magnetic field vary as a function of age, which in turn is the key to decipher the physical processes behind the varied neutron star phenomenology. In this review, we go through the basic theory describing the magneto-thermal evolution models of neutron stars, focusing on numerical techniques, and providing a battery of benchmark tests to be used as a reference for present and future code developments. We summarize well-known results from axisymmetric cases, give a new look at the latest 3D advances, and present an overview of the expectations for the field in the coming years.
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 the crust along the magnetic field greatly exceeds the conductivity across the field, so the current penetrates deep into the crust down up to the super conducting core. The magnetic field, generated by the accretion current, increases greatly with the depth of penetration due to the Hall conductivity of the crust is also much larger than the transverse conductivity. As a result, the current begins to flow mainly in the toroidal direction, creating a strong longitudinal magnetic field, far exceeding an initial dipole field. This field exists only in the narrow polar tube of $r$ width, narrowing with the depth, i.e. with increasing of the crust density $rho$, $rpropto rho^{-1/4}$. Accordingly, the magnetic field $B$ in the tube increases with the depth, $Bpropto rho^{1/2}$, and reaches the value of about $10^{17}$ Gauss in the core. It destroys super conducting vortices in the core of a star in the narrow region of the size of the order of ten centimeters. Because of generated density gradient of vortices they constantly flow into this dead zone and the number of vortices decreases, the magnetic field of a star decreases as well. The attenuation of the magnetic field is exponential, $B=B_0(1+t/tau)^{-1}$. The characteristic time of decreasing of the magnetic field $tau$ is equal to $tausimeq 10^3$ years. Thus, the magnetic field of accreted neutron stars decreases to values of $10^8 - 10^9$ Gauss during $10^7-10^6$ years.
We perform population synthesis studies of different types of neutron stars (thermally emitting isolated neutron stars, normal radio pulsars, magnetars) taking into account the magnetic field decay and using results from the most recent advances in neutron star cooling theory. For the first time, we confront our results with observations using {it simultaneously} the Log N -- Log S distribution for nearby isolated neutron stars, the Log N -- Log L distribution for magnetars, and the distribution of radio pulsars in the $P$ -- $dot P$ diagram. For this purpose, we fix a baseline neutron star model (all microphysics input), and other relevant parameters to standard values (velocity distribution, mass spectrum, birth rates ...), allowing to vary the initial magnetic field strength. We find that our theoretical model is consistent with all sets of data if the initial magnetic field distribution function follows a log-normal law with $<log (B_0/[G])>sim 13.25$ and $sigma_{log B_0}sim 0.6$. The typical scenario includes about 10% of neutron stars born as magnetars, significant magnetic field decay during the first million years of a NS life (only about a factor of 2 for low field neutron stars but more than an order of magnitude for magnetars), and a mass distribution function dominated by low mass objects. This model explains satisfactorily all known populations. Evolutionary links between different subclasses may exist, although robust conclusions are not yet possible.
With the first detections of binary neutron star mergers by gravitational-wave detectors, it proves timely to consider how the internal structure of neutron stars affects the way in which they can be asymmetrically deformed. Such deformations may leave measurable imprints on gravitational-wave signals and can be sourced through tidal interactions or the formation of mountains. We detail the formalism that describes fully-relativistic neutron star models with elastic crusts undergoing static perturbations. This formalism primes the problem for studies into a variety of mechanisms that can deform a neutron star. We present results for a barotropic equation of state and a realistic model for the elastic crust, which enables us to compute relevant quantities such as the tidal deformability parameter. We find that the inclusion of an elastic crust provides a very small correction to the tidal deformability. The results allow us to demonstrate when and where the crust starts to fail during a binary inspiral and we find that the majority of the crust will remain intact up until merger.
The fastest-spinning neutron stars in low-mass X-ray binaries, despite having undergone millions of years of accretion, have been observed to spin well below the Keplerian break-up frequency. We simulate the spin evolution of synthetic populations of accreting neutron stars in order to assess whether gravitational waves can explain this behaviour and provide the distribution of spins that is observed. We model both persistent and transient accretion and consider two gravitational-wave-production mechanisms that could be present in these systems: thermal mountains and unstable $r$-modes. We consider the case of no gravitational-wave emission and observe that this does not match well with observation. We find evidence for gravitational waves being able to provide the observed spin distribution; the most promising mechanisms being a permanent quadrupole, thermal mountains and unstable $r$-modes. However, based on the resultant distributions alone it is difficult to distinguish between the competing mechanisms.
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