Magnetorotational Research Articles

Nucleosynthesis in outflows of compact objects and detection prospects of associated kilonovae

ABSTRACT We perform a comparative analysis of nucleosynthesis yields from binary neutron star (BNS) mergers, black hole-neutron star (BHNS) mergers, and core-collapse supernovae (CCSNe) with the goal of determining which are the most dominant sources of r-process enrichment observed in stars. We find that BNS and BHNS binaries may eject similar mass distributions of robust r-process nuclei post-merger (up to third peak and actinides, A ∼ 200−240), after accounting for the volumetric event rates. Magnetorotational (MR) CCSNe likely undergo a weak r-process (up to A ∼ 140) and contribute to the production of light element primary process (LEPP) nuclei, whereas typical thermal, neutrino-driven CCSNe only synthesize up to first r-process peak nuclei (A ∼ 80−90). We also find that the upper limit to the rate of MR CCSNe is $\lesssim 1~{{\ \rm per\ cent}}$ the rate of typical thermal CCSNe; if the rate was higher, then weak r-process nuclei would be overproduced. Although the largest uncertainty is from the volumetric event rate, the prospects are encouraging for confirming these rates in the next few years with upcoming surveys. Using a simple model to estimate the resulting kilonova light curve from mergers and our set of fiducial merger parameters, we predict that ∼7 BNS and ∼2 BHNS events will be detectable per year by the Vera C. Rubin Observatory (LSST), with prior gravitational wave (GW) triggers.

Assessment of a new sub-grid model for magnetohydrodynamical turbulence. I. Magnetorotational instability

ABSTRACT Insufficient numerical resolution of grid-based, direct numerical simulations (DNS) hampers the development of instability-driven turbulence at small (unresolved) scales. As an alternative to DNS, sub-grid models can potentially reproduce the effects of turbulence at small scales in terms of the resolved scales, and hence can capture physical effects with less computational resources. We present a new sub-grid model, the MHD-instability-induced-turbulence (MInIT) mean-field model. MInIT is a physically motivated model based on the evolution of the turbulent (Maxwell, Reynolds, and Faraday) stress tensors and their relation with the turbulent energy densities of the magnetorotational (MRI) and parasitic instabilities, modelled with two partial differential evolution equations with stiff source terms. Their solution allows obtaining the turbulent stress tensors through the constant coefficients that link them to the energy densities. The model is assessed using data from MRI in-box DNS and applying a filtering operation to compare the filtered data with that from the model. Using the L2-norm as the metric for the comparison, we find less than one order-of-magnitude difference between the two sets of data. No dependence on filter size or length scale of unresolved scales is found, as opposed to results using the gradient model (which we also use to contrast our model) in which the L2-norm of some of the stresses increases with filter size. We conclude that MInIT can help DNS by properly capturing small-scale turbulent stresses which has potential implications on the dynamics of highly magnetized rotating compact objects, such as those formed during binary neutron star mergers.

Magnetorotational Explosion of a Massive Star Supported by Neutrino Heating in General Relativistic Three-dimensional Simulations

Abstract We present results of three-dimensional (3D), radiation-magnetohydrodynamics (MHD) simulations of core-collapse supernovae in full general relativity (GR) with spectral neutrino transport. In order to study the effects of the progenitor’s rotation and magnetic fields, we compute three models, where the precollapse rotation rate and magnetic fields are included parametrically to a 20 M ⊙ star. While we find no shock revival in our two nonmagnetized models during our simulation times (∼500 ms after bounce), the magnetorotational (MR) driven shock expansion immediately initiates after bounce in our rapidly rotating and strongly magnetized model. We show that the expansion of the MR-driven flows toward the polar directions is predominantly driven by the magnetic pressure, whereas the shock expansion toward the equatorial direction is supported by neutrino heating. Our detailed analysis indicates that the growth of the so-called kink instability may hinder the collimation of jets, resulting in the formation of broader outflows. Furthermore, we find a dipole emission of lepton number, only in the MR explosion model, whose asymmetry is consistent with the explosion morphology. Although it is similar to the lepton number emission self-sustained asymmetry (LESA), our analysis shows that the dipole emission occurs not from the proto–neutron star convection zone but from above the neutrino sphere, indicating that it is not associated with the LESA. We also report several unique neutrino signatures, which are significantly dependent on both the time and the viewing angle, if observed, possibly providing rich information regarding the onset of the MR-driven explosion.

Simulation of magnetorotational astrophysical processes by implicit operator-difference scheme

The application of the Lagrangian completely conservative implicit operator-difference scheme for the simulation of magnetorotational (MR) processes in astrophysics is described. Results of 2D simulations of MR core-collapsed supernova explosion are represented.

Dwarf nova outbursts with magnetorotational turbulence

The phenomenological Disc Instability Model has been successful in reproducing the observed light curves of dwarf nova outbursts by invoking an enhanced Shakura-Sunyaev $\alpha$ parameter $\sim0.1-0.2$ in outburst compared to a low value $\sim0.01$ in quiescence. Recent thermodynamically consistent simulations of magnetorotational (MRI) turbulence with appropriate opacities and equation of state for dwarf nova accretion discs have found that thermal convection enhances $\alpha$ in discs in outburst, but only near the hydrogen ionization transition. At higher temperatures, convection no longer exists and $\alpha$ returns to the low value comparable to that in quiescence. In order to check whether this enhancement near the hydrogen ionization transition is sufficient to reproduce observed light curves, we incorporate this MRI-based variation in $\alpha$ into the Disc Instability Model, as well as simulation-based models of turbulent dissipation and convective transport. These MRI-based models can successfully reproduce observed outburst and quiescence durations, as well as outburst amplitudes, albeit with different parameters from the standard Disc Instability Models. The MRI-based model lightcurves exhibit reflares in the decay from outburst, which are not generally observed in dwarf novae. However, we highlight the problematic aspects of the quiescence physics in the Disc Instability Model and MRI simulations that are responsible for this behavior.

Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow

The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes.

Nondissipative Saturation of the Magnetorotational Instability in Thin Disks

A new nondissipative mechanism is proposed for the saturation of the axisymmetric magnetorotational (MRI) instability in thin Keplerian disks that are subject to an axial magnetic field. That mechanism relies on the energy transfer from the MRI to stable magnetosonic waves. Such mode interaction is enabled due to the vertical stratification of the disk that results in the discretization of its MRI spectrum, as well as by applying the appropriate boundary conditions. A second order Duffing-like amplitude equation for the initially unstable MRI modes is derived. The solutions of that equation exhibit bursty nonlinear oscillations with a constant amplitude that signifies the saturation level of the MRI. Those results are verified by a direct numerical solution of the full nonlinear reduced set of thin disk magnetohydrodynamics equations.

VERTICAL STRUCTURE OF STATIONARY ACCRETION DISKS WITH A LARGE-SCALE MAGNETIC FIELD

In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because the hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. Here, we calculate the vertical profiles of the {\it stationary} accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the surface of the disk. Also, here we require that the radial accretion speed be zero at the disk's surface and we assume that the ratio of the turbulent viscosity to the turbulent magnetic diffusivity is of order unity. Thus at the disk's surface there are three boundary conditions. As a result, for a fixed dimensionless viscosity $\alpha$-value, we find that there is a definite relation between the ratio ${\cal R}$ of the accretion power going into magnetic disk winds to the viscous power dissipation and the midplane plasma-$\beta$, which is the ratio of the plasma to magnetic pressure in the disk. For a specific disk model with ${\cal R}$ of order unity we find that the critical value required for a stationary solution is $\beta_c \approx 2.4r/(\alpha h)$, where $h$ the disk's half thickness. For weaker magnetic fields, $\beta > \beta_c$, we argue that the poloidal field will advect outward while for $\beta< \beta_c$ it will advect inward. Alternatively, if the disk wind is negligible (${\cal R} \ll 1$), there are stationary solutions with $\beta \gg \beta_c$.

LARGE-SCALE MAGNETIC FIELD IN ACCRETION DISKS AND RELATIVISTIC POYNTING-FLUX JETS

In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because of hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. We have derived equations for the vertical profiles of stationary accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the surface of the disk. Our recent analysis in Ref. 1 shows that the inward or outward advection of the large-scale magnetic field depends on the ratio [Formula: see text] of the accretion power going into magnetic disk winds to the viscous power dissipation and the plasma-β which is the ratio of the midplane plasma pressure to the magnetic pressure. Recent radio emission, polarization, and Faraday rotation maps of the radio jet of the galaxy 3C303 have been obtained in Ref. 2 and show that one component of this jet has a galactic-scale electric current of ~ 3 × 1018 A flowing along the jet axis. We show that this current can be used to calculate the electromagnetic energy flow in this magnetically dominated jet.

Spectral and algebraic instabilities in thin Keplerian discs under poloidal and toroidal magnetic fields

Linear instability of two equilibrium configurations with either poloidal (I) or toroidal (II) dominant magnetic field components are studied in thin vertically-isothermal Keplerian discs. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio of the disc. In both equilibrium configurations the perturbations are decoupled into in-plane and vertical modes. For equilibria of type I those two modes are the Alfv\'en-Coriolis and sound waves, while for equilibria of type II they are the inertia-Coriolis and magnetosonic waves. Exact expressions for the growth rates as well as the number of unstable modes for type I equilibria are derived. Those are the discrete counterpart of the continuous infinite homogeneous cylinder magnetorotational (MRI) spectrum. It is further shown that the axisymmetric MRI is completely suppressed by dominant toroidal magnetic fields (i.e. equilibria of type II). This renders the system prone to either non-axisymmetric MRI or non-modal algebraic growth mechanisms. The algebraic growth mechanism investigated in the present study occurs exclusively due to the rotation shear, generates the inertia-Coriolis driven magnetosonic modes due to non-resonant or resonant coupling that induces, respectively, linear or quadratic temporal growth of the perturbations.

Planetesimal dynamics in hydromagnetic turbulence

AbstractPlanet formation theory is founded on the concept of dust coagulation and subsequent growth into planetesimals. This process is by no means an isolated one, but possibly happens in a turbulent nebula. It is therefore crucial to understand how particles of different sizes are affected by their gaseous environment via stochastic forcing and aerodynamic damping. We here report on the effects of magneto-rotational (MRI) turbulence in the presence of non-uniform ionisation leading to the formation of a magnetically inactive dead-zone. While we find that collisional growth is impeded by fully-active MRI, it may be possible within a dead-zone.

ON THE SATURATION OF THE MAGNETOROTATIONAL INSTABILITY VIA PARASITIC MODES

We investigate the stability of incompressible, exact, non-ideal magnetorotational (MRI) modes against parasitic instabilities. Both Kelvin-Helmholtz and tearing-mode parasitic instabilities may occur in the dissipative regimes accessible to current numerical simulations. We suppose that a primary MRI mode saturates at an amplitude such that its fastest parasite has a growth rate comparable to its own. The predicted alpha parameter then depends critically on whether the fastest primary and parasitic modes fit within the computational domain and whether non-axisymmetric parasitic modes are allowed. Hence even simulations that resolve viscous and resistive scales may not saturate properly unless the numerical domain is large enough to allow the free evolution of both MRI and parasitic modes. To minimally satisfy these requirements in simulations with vertical background fields, the vertical extent of the domain should accommodate the fastest growing MRI mode while the radial and azimuthal extents must be twice as large. The fastest parasites have horizontal wavelengths roughly twice as long as the vertical wavelength of the primary.

Different magneto-rotational supernovae

We present the results of two-dimensional calculations of a magneto-rotational (MR) supernova explosion with a collapsing core for various core masses, rotational angular momenta, and magnetic-field configurations. It is shown that the MR mechanism produces an explosion energy that corresponds to observed values. The form of the explosion depends substantially on the initial configuration of the magnetic field. MR instability develops during the evolution of the magnetic field in an MR supernova explosion, resulting in an exponential increase of all components of the magnetic field, thereby substantially decreasing the time scale of the MR explosion. The energy of the supernova increases with the core’s mass and initial rotational energy.

OUTFLOWS FROM MAGNETOROTATIONAL SUPERNOVAE

We discuss results of 2D simulations of magnetorotational (MR) mechanism of core collapse supernova explosions. Due to the nonuniform collapse, the collapsed core rotates differentially. In the presence of an initial poloidal magnetic field its toroidal component appears and grows with time. Increased magnetic pressure leads to the formation of a compression wave which moves outwards. It transforms into the fast MHD shock wave (supernova shock wave). The shape of the MR supernova explosion qualitatively depends on the configuration of the initial magnetic field. For a dipole-like initial magnetic field, the supernova explosion develops mainly along the rotational axis, forming a mildly collimated jet. A quadrupole-like initial magnetic field leads to the explosion developing mainly along the equatorial plane. The magnetorotational instability was found in our simulations. The supernova explosion energy grows with an increase of the initial core mass and rotational energy of the core, and corresponds to the observational data.

Magnetorotational supernovae. Magnetorotational instability. Jet formation

2D numerical simulations of magnetorotational (MR) supernova mechanism are described. It is shown that magnetic field is amplified due to the differential rotation after core collapse. When magnetic pressure reaches some level, a compression wave starts to move outwards. Moving along steeply decreasing density profile the compression wave transforms quickly into fast MHD shock. The magnetorotational instability (MRI) was found in our simulations. MRI leads to the exponential growth of the components of the magnetic field. The MRI significantly reduces MR supernova explosion time. Configuration of the initial magnetic field qualitatively defines the shape of MR supernova explosion. For the quadrupole-like initial poloidal field the MR supernova explosion develops mainly along equatorial plane, the dipole-like initial field results in MR supernova developing as mildly collimated jet along axis of rotation. The explosion energy of MR supernova found in our simulations is ∼0.5–0.6×1051 erg.

Core-collapse supernovae: magnetorotational mechanism

The results of two-dimensional numerical simulations of the magnetorotational (MR) supernova mechanism are presented. The shape of the explosion qualitatively depends on the symmetry type of the initial magnetic field. For the initial quadrupole-type magnetic field, the MR supernova explosion develops mainly near the equatorial plane while, for the initial dipole magnetic field, the MR supernova explosion has the shape of a mildly collimated proto-jet. The ejected energy in the MR supernova explosion in our simulations was about (0.5–0.6) × 1051 erg. MR instability was found during simulations of the MR supernova explosion and leads to the exponential growth of both the toroidal and the poloidal magnetic fields.

A magnetorotational core-collapse model with jets

We present the results of the 2D simulation of a magnetorotational (MR) core-collapse model accompanied by jet formation in the core-collapse model explosion. The initial magnetic field used in the simulations has a dipole-like symmetry. Contrary to the simulations of the MR core-collapse model with an initial quadrupole-like magnetic field, where the matter was ejected mainly near the equatorial plane, in the presence of the dipole-like initial magnetic field the core-collapse model explosion is developing preferably along a rotational axis and leads to the formation of a protojet. We expect that protojet propagation through the envelope of the star will be accompanied by its collimation. The magnetorotational instability (MRI) was found in the simulations, similar to the earlier considered case of the quadrupole-like initial magnetic field. Our estimations show that the characteristic time for the reconnection of the magnetic field is much larger than the MRI development time. The supernova explosion energy for the dipole-like field is about 0.61 x 10 51 erg, and about 0.13 M ⊙ of mass was ejected during the explosion.