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Register a new userEvolution of isolated neutron stars till accretion. The role of initial magnetic field
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We study evolution of isolated neutron stars on long time scale and calculate distribution of these sources in the main evolutionary stages: Ejector, Propeller, Accretor, and Georotator. We compare different initial magnetic field distributions taking into account a possibility of magnetic field decay, and include in our calculations the stage of subsonic Propeller. It is shown that though the subsonic propeller stage can be relatively long, initially highly magnetized neutron stars ($B_0ga 10^{13}$ G) reach the accretion regime within the Galactic lifetime if their kick velocities are not too large. The fact that in previous studies made $>$10 years ago, such objects were not considered results in a slight increase of the Accretor fraction in comparison with earlier conclusions. Most of the neutron stars similar to the Magnificent seven are expected to become accreting from the interstellar medium after few billion years of their evolution. They are the main predecestors of accreting isolated neutron stars.
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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.
Neutron star mergers are unique laboratories of accretion, ejection, and r-process nucleosynthesis. We used 3D general relativistic magnetohydrodynamic simulations to study the role of the post-merger magnetic geometry in the evolution of merger remnant discs around stationary Kerr black holes. Our simulations fully capture mass accretion, ejection, and jet production, owing to their exceptionally long duration exceeding $4$ s. Poloidal post-merger magnetic field configurations produce jets with energies $E_mathrm{jet} sim (4{-}30)times10^{50}$ erg, isotropic equivalent energies $E_mathrm{iso}sim(4{-}20)times10^{52}$ erg, opening angles $theta_mathrm{jet}sim6{-}13^circ$, and durations $t_jlesssim1$ s. Accompanying the production of jets is the ejection of $f_mathrm{ej}sim30{-}40%$ of the post-merger disc mass, continuing out to times $> 1$ s. We discover that a more natural, purely toroidal post-merger magnetic field geometry generates large-scale poloidal magnetic flux of alternating polarity and striped jets. The first stripe, of $E_mathrm{jet}simeq2times10^{48},mathrm{erg}$, $E_mathrm{iso}sim10^{51}$ erg, $theta_mathrm{jet}sim3.5{-}5^circ$, and $t_jsim0.1$ s, is followed by $gtrsim4$ s of striped jet activity with $f_mathrm{ej}simeq27%$. The dissipation of such stripes could power the short gamma-ray burst (sGRB) prompt emission. Our simulated jet energies and durations span the range of sGRBs. We find that although the blue kilonova component is initially hidden from view by the red component, it expands faster, outruns the red component, and becomes visible to off-axis observers. In comparison to GW 170817/GRB 170817A, our simulations under-predict the mass of the blue relative to red component by a factor of few. Including the dynamical ejecta and neutrino absorption may reduce this tension.
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.
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.
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