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Register a new userA new code for the Hall-driven magnetic evolution of neutron stars
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Over the past decade, the numerical modeling of the magnetic field evolution in astrophysical scenarios has become an increasingly important field. In the crystallized crust of neutron stars the evolution of the magnetic field is governed by the Hall induction equation. In this equation the relative contribution of the two terms (Hall term and Ohmic dissipation) varies depending on the local conditions of temperature and magnetic field strength. This results in the transition from the purely parabolic character of the equations to the hyperbolic regime as the magnetic Reynolds number increases, which presents severe numerical problems. Up to now, most attempts to study this problem were based on spectral methods, but they failed in representing the transition to large magnetic Reynolds numbers. We present a new code based on upwind finite differences techniques that can handle situations with arbitrary low magnetic diffusivity and it is suitable for studying the formation of sharp current sheets during the evolution. The code is thoroughly tested in different limits and used to illustrate the evolution of the crustal magnetic field in a neutron star in some representative cases. Our code, coupled to cooling codes, can be used to perform long-term simulations of the magneto-thermal evolution of neutron stars.
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We propose a general method to self-consistently study the quasistationary evolution of the magnetic field in the cores of neutron stars. The traditional approach to this problem is critically revised. Our results are illustrated by calculation of the typical timescales for the magnetic field dissipation as functions of temperature and the magnetic field strength.
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.
Observational and theoretical work has now established that the fossil fields of magnetic massive stars are surviving remnants from an earlier event, or an earlier evolutionary phase. However, many important questions remain regarding the effects of these fields on the late stages of stellar evolution, as well as their impact on the core-collapse mechanism and the formation of exotic compact objects such as magnetars and gravitational wave progenitors. There is currently a critical need to incorporate the impact of fossil fields in models of the structure and evolution of magnetic stars, and to determine the evolutionary history of magnetic massive stars. We present a preliminary population study of a cluster of co-evolving stars based on MESA evolutionary tracks that account for the effect of magnetic mass-loss quenching.
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.
Atomic diffusion has been recognized as an important process that has to be considered in any computations of stellar models. In solar-type and cooler stars, this process is dominated by gravitational settling, which is now included in most stellar evolution codes. In hotter stars, radiative accelerations compete with gravity and become the dominant ingredient in the diffusion flux for most heavy elements. Introducing radiative accelerations into the computations of stellar models modifies the internal element distribution and may have major consequences on the stellar structure. Coupling these processes with hydrodynamical stellar motions has important consequences that need to be investigated in detail. We aim to include the computations of radiative accelerations in a stellar evolution code (here the TGEC code) using a simplified method (SVP) so that it may be coupled with sophisticated macroscopic motions. We also compare the results with those of the Montreal code in specific cases for validation and study the consequences of these coupled processes on accurate models of A- and early-type stars. We implemented radiative accelerations computations into the Toulouse-Geneva stellar evolution code following the semi-analytical prescription proposed by Alecian and LeBlanc. This allows more rapid computations than the full description used in the Montreal code. We present results for A-type stellar models computed with this updated version of TGEC and compare them with similar published models obtained with the Montreal evolution code. We discuss the consequences for the coupling with macroscopic motions, including thermohaline convection.
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