Two-Dimensional Simulation of the Dynamics of the Collapse of a Rotating Core with Formation of a Neutron Star on an Adaptive Triangular Grid in Lagrangian Coordinates

Results are presented from a two-dimensional numerical simulation of the collapse of a rotating core with formation of a neutron star that has strong differential rotation in its outer regions. A specially developed numerical method is used which is based on a fully conservative implicit operator difference scheme for gravitational gas dynamics problems in lagrangian coordinates on a variable-structure triangular grid. The recoil shock wave generated by the collapse causes ejection of a small amount of material. This cannot explain the explosion of type II supernovae. The strong differential rotation in the presence of even a weak initial magnetic field obtained in these calculations must lead to a rise in the magnetic pressure, formation of an MHD shock wave, and conversion of rotational energy into the energy of radial expansion (magnetorotational supernova explosion).     

Dynamo saturation in direct simulations of the multi‐phase turbulent interstellar medium

The ordered magnetic field observed via polarised synchrotron emission in nearby disc galaxies can be explained by a mean‐field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical‐flux initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the saturated state of the mean‐field dynamo. This is motivated by the observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three‐dimensional local boxes of the vertically stratified, turbulent interstellar medium, employing shearing‐periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth of the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coefficients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean‐field dynamo. The final magnetic field strength found in the direct simulation is in excellent agreement with a quenched α) dynamo. For supernova rates representative of the Milky Way, field losses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulent and regular magnetic fields in spiral galaxies may depend on the galaxy's star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub‐grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymmetric Supernovae: Yes, Rotation and Magnetic Fields are Important

Spectropolarimetry of core collapse supernovae has shown that they are asymmetric and often bi-polar. This raises the issue of whether some jet-like phenomena are at work involving rotation and magnetic fields. We summarize the importance of the magnetorotational instability for the core collapse problem and sketch some of the effects that large magnetic fields, ~10¹⁵ G, may have on the physics of the supernova explosion.     

Influence of a strong magnetic field on the neutrino heating of a supernova shock

Based on the magnetorotational model of a supernova explosion with core collapse, we investigate the significant processes of neutrino heating of the supernova shock. These processes should be taken into account in self-consistent modeling, since the neutrino heating mechanism is capable of increasing the explosion efficiency. We show that, even in the presence of a strong magnetic field (B ～ 10¹⁵ G) in the shock formation region, the heating rate is determined with good accuracy by the absorption and emission of neutrinos in direct URCA processes. Moreover, the influence on them of a magnetic field is reduced to insignificant corrections.     

Magnetorotational instabilities and pulsar kick velocities

At the end of their birth process, neutron stars can be subject to a magnetorotational instability in which a conversion of kinetic energy of differential rotation into radiation and kinetic energies is expected to occur at the Alfvén timescale of a few ms. This birth energy conversion predicts the observed large velocity of neutron stars if during the evolving of this instability the periods are of a few ms and the magnetic fields reach values of 10¹⁶ G.     

Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

The influence of gravitational acceleration on the supernova-driven Parker instability

Within a framework of 2D magnetohydrodynamic (MHD) simulations, we explore the dynamical regimes initiated by a supernova explosion in a magnetized stratified interstellar medium (ISM). We concentrate on the formation of large-scale magnetic structures and outflows connected with the Parker instability. For the sake of simplicity we only show models with a fixed explosion energy corresponding to a single supernova (SN) occurring in host galaxies with different fixed values of the gravitational acceleration g and different ratios of specific heats. We show that in general, depending on these two parameters, three different regimes are possible: a slowly growing Parker instability on time-scales much longer than the galactic rotation period for small g; the Parker instability growing at roughly the rotation period, which for ratios of specific heats larger than one is accompanied by an outflow resulting from the explosion for intermediate g; and a rapidly growing instability and a strong blow-out flow for large g . By means of numerical simulations and analytical estimates we show that the explosion energy and gravitational acceleration which separate the three regimes scale as Eg ²∼constant in the 2D case. We expect that in the 3D case this scaling law is Eg ³∼constant . Our simulations demonstrate furthermore that a single SN explosion can lead to the growth of multiple Parker loops in the disc and large-scale magnetic field loops in the halo, extending over 2–3 kpc horizontally and up to 3 kpc vertically above the mid-plane of the disc.     

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height.
We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.     

Envelope dynamics of iron-core supernova models

Wilson has found that the neutrino transport mechanisms is unable to generate a supernova explosion in stars with collapsing iron cores. We have utilized Wilson’s analysis to investigate the behavior of the overlying potentially explosive layers which Wilson omitted. The outer boundary of the core of Wilson’s models moves in such a, manner as to deliver a shock to the base of the envelope. We have numerically followed the progress of such shocks into the envelope of a realistic model obtained from evolutionary calculations. We find that only shocks so strong as to be inconsistent with our treatment are capable of ejecting material. For reasonable shocks the nuclear burning does not proceed rapidly at densities below ?～10⁶g cm^?3, and the nuclear energy released is less than the shock energy in all models that come near to ejecting matter. The initial model adopted here, which is based on a particular set of evolutionary calculations and which neglects rotation and magnetic fields, seems destined to generate a black hole. The creation of a black hole in such a way is probably not attended by a supernova explosion.     

A hydrodynamic model for asymmetric explosions of rapidly rotating collapsing supernovae with a toroidal atmosphere

We numerically solved the two-dimensional axisymmetric hydrodynamic problem of the explosion of a low-mass neutron star in a circular orbit. In the initial conditions, we assumed a nonuniform density distribution in the space surrounding the collapsed iron core in the form of a stationary toroidal atmosphere that was previously predicted analytically and computed numerically. The configuration of the exploded neutron star itself was modeled by a torus with a circular cross section whose central line almost coincided with its circular orbit. Using an equation of state for the stellar matter and the toroidal atmosphere in which the nuclear statistical equilibrium conditions were satisfied, we performed a series of numerical calculations that showed the propagation of a strong divergent shock wave with a total energy of ～0.2×10⁵¹ erg at initial explosion energy release of ～1.0×10⁵¹ erg. In our calculations, we rigorously took into account the gravitational interaction, including the attraction from a higher-mass (1.9M_⊙) neutron star located at the coordinate origin, in accordance with the rotational explosion mechanism for collapsing supernovae. We compared in detail our results with previous similar results of asymmetric supernova explosion simulations and concluded that we found a lower limit for the total explosion energy.     

Self-Regulating Supernova Heating in Interstellar Medium Simulations

Numerical simulations of the multi-phase interstellar medium have been carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box model, with random motions driven by supernova explosions. These calculations incorporate the effects of magnetic fields and rotation in 3D; these play important dynamical roles in the galaxy, but are neglected in many other simulations. The supernovae driving the motions are not arbitrarily imposed, but occur where gas accumulates into cold, dense clouds; their implementation uses a physically motivated model for the evolution of such clouds. The process is self-regulating, and produces mean supernova rates as part of the solution. Simulations with differing mean density show a power law relation between the supernova rate and density, with exponent 1.7; this value is within the range suggested from observations (taking star formation rate as a proxy for supernova rate). The global structure of the supernova driven medium is strongly affected by the presence of magnetic fields; e.g. for one solution the filling factor of hot gas is found to vary from 0.19 (with no field) to 0.12 (with initial mid-plane field B ₀ = 6 μG).     

Magnetorotational instability in a rotating liquid metal annulus

Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion discs, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid metal annulus (Couette flow) is explored by local and global stability analysis. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table-top apparatus, using easy-to-handle metals such as gallium. Practical issues of this proposed experiment are discussed.     

The Magnetic Field of the Solar Corona from Pulsar Observations

We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation resulting from propagation of the polarised emission from a number of pulsars through the magnetic field of the solar corona. This method yields independent measures of the integrated electron density, via dispersion of the pulsed signal and the magnetic field, via the amount of Faraday rotation. In principle this allows the determination of the integrated magnetic field through the solar corona along many lines of sight without any assumptions regarding the electron density distribution. We present a detection of an increase in the rotation measure of the pulsar J1801-2304 of approximately 170 rad m² at an elongation of 0.96° from the centre of the solar disc. This corresponds to a lower limit of the magnetic field strength along this line of sight of >41.8 nT. The lack of precision in the integrated electron density measurement restricts this result to a limit, but application of coronal plasma models can further constrain this to approximately 0.5 μT, along a path passing 2.7 solar radii from the solar limb, which is consistent with predictions obtained using extensions to the source surface models published by the Wilcox Solar Observatory.     

Dirac neutrino magnetic moment and possible time evolution of the neutrino signal from a supernova

We analyze the influence of neutrino helicity conversion, ν _L → ν _R, on the neutrino flux from a supernova attributable to the interaction of the Dirac neutrino magnetic moment with a magnetic field.We show that if the neutrino has a magnetic moment in the interval 10⁻¹³μ_B < μ_ν < 10⁻¹²μ_B and provided that a magnetic field of ∼10¹³–10¹⁴ G exists in the supernova envelope, a peculiar kind of time evolution of the neutrino signal from the supernova attributable to the resonance transition ν _L → ν _R in the magnetic field of the envelope can appear.     

New evidence for strong nonthermal effects in Tycho’s supernova remnant

For the case of Tycho’s supernova remnant (SNR) we present the relation between the blast wave and contact discontinuity radii calculated within the nonlinear kinetic theory of cosmic ray (CR) acceleration in SNRs. It is demonstrated that these radii are confirmed by recently published Chandra measurements which show that the observed contact discontinuity radius is so close to the shock radius that it can only be explained by efficient CR acceleration which in turn makes the medium more compressible. Together with the recently determined new value E _sn=1.2×10⁵¹ erg of the SN explosion energy this also confirms our previous conclusion that a TeV γ-ray flux of (2–5)×10⁻¹³ erg/(cm² s) is to be expected from Tycho’s SNR. Chandra measurements and the HEGRA upper limit of the TeV γ-ray flux together limit the source distance d to 3.3≤d≤4 kpc.     

Gamma-ray emission expected from Kepler’s SNR

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants (SNRs) is used to investigate the properties of Kepler’s SNR and, in particular, to predict the γ-eay spectrum expected from this SNR. Observations of the nonthermal radio and X-ray emission spectra as well as theoretical constraints for the total supernova (SN) explosion energy E _sn are used to constrain the astronomical and particle acceleration parameters of the system. Under the assumption that Kepler’s SN is a type Ia SN we determine for any given explosion energy E _sn and source distance d the mass density of the ambient interstellar medium (ISM) from a fit to the observed SNR size and expansion speed. This makes it possible to make predictions for the expected γ-eay flux. Exploring the expected distance range we find that for a typical explosion energy E _sn=10⁵¹ erg the expected energy flux of TeV γ-rays varies from 2×10⁻¹¹ to 10⁻¹³ erg/(cm² s) when the distance changes from d=3.4 kpc to 7 kpc. In all cases the γ-eay emission is dominated by π ⁰-decay γ-rays due to nuclear CRs. Therefore Kepler’s SNR represents a very promising target for instruments like H.E.S.S., CANGAROO and GLAST. A non-detection of γ-rays would mean that the actual source distance is larger than 7 kpc.     

Smoke rings around supernova 1987a

Detailed observations of the [Oiii]5007 Å emission from the elliptical rings around SN 1987A suggest a model wherein the two faint, outer rings are due to emission from two circular toroids moving outwards (at 25 km s^–1) along a bipolar cone centred on the site of the supernova. The brighter, central ring is expanding radially outward at 8.3 km s^–1. The rings must have been created 2-3 × 10⁴ years before the supernova explosion and are thought to be a consequence of the interaction of stellar winds emanating from the progenitor system during the final stages of its evolution to a supernova.     

Model of the Magnetic Field of HD 187474

A model is constructed for the magnetic field of the star HD 187474, which has a very long axial rotation period P = 2345^d. It turns out that the structure of the magnetic field is best described by a model of a displaced (Δα = 0.1) dipole inclined to the axis of rotation by an angle β = 24°. The star is inclined to the line of sight by an angle i = 86°. Because of the displaced dipole the magnitude of the magnetic field differs at the poles: Bp = +6300 and 11600 G. A Mercator map of the distribution of the magnetic field over the surface is obtained. The 7 slowly rotating CP stars studied thus far have an average angle β = 62°, which equals the average value for a random orientation of dipoles. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 575–583 (November 2005).     

Estimation of 56Ni Needed in the Explosion Process of the Super Luminous Supernova ASASSN-15lh

ASASSN-15lh is a super luminous supernova, whose light curve is similar to that of the type Ia supernova (SN Ia). Since the luminosity of SN Ia is directly related to the decay of ⁵⁶Ni, in this paper, we consider the de-excitation energy of the new nuclei, and calculate the energy generated by the decay of ⁵⁶Ni in the explosive environment of ASASSN-15lh. The calculated mass of ⁵⁶Ni needed by the ASASSN-15lh explosion is 31.32 M_⊙. This result agrees with the estimation of the mass of ⁵⁶Ni ≥ 30 M_⊙ derived from the observed light curve of ASASSN-15lh. No agreement has reached for the explosion mechanism of supernova ASASSN-15lh so far. The calculation in this paper provides a reference for the further study on the progenitor and explosion mechanism of the supernova ASASSN-15lh.     

Modelling the Global Solar Corona: III. Origin of the Hemispheric Pattern of Filaments

We consider the physical origin of the hemispheric pattern of filament chirality on the Sun. Our 3D simulations of the coronal field evolution over a period of six months, based on photospheric magnetic measurements, were previously shown to be highly successful at reproducing observed filament chiralities. In this paper we identify and describe the physical mechanisms responsible for this success. The key mechanisms are found to be (1) differential rotation of north – south polarity inversion lines, (2) the shape of bipolar active regions, and (3) evolution of skew over a period of many days. As on the real Sun, the hemispheric pattern in our simulations holds in a statistical sense. Exceptions arise naturally for filaments in certain locations relative to bipolar active regions or from interactions among a number of active regions.