scholarly journals General Relativistic Mean-Field Dynamo Model for Proto-Neutron Stars

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 83 ◽  
Author(s):  
Kevin Franceschetti ◽  
Luca Del Zanna
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Growth Rates ◽  
Exponential Growth ◽  
Mean Field ◽  
Dynamo Model ◽  
Time Interval ◽  
General Relativistic ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Neutron stars, and magnetars in particular, are known to host the strongest magnetic fields in the Universe. The origin of these strong fields is a matter of controversy. In this preliminary work, via numerical simulations, we study, for the first time in non-ideal general relativistic magnetohydrodynamic (GRMHD) regime, the growth of the magnetic field due to the action of the mean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process, combined with the differential rotation of the (proto-)star, is able to produce an exponential growth of any initial magnetic seed field up to the values required to explain the observations. By varying the dynamo coefficient we obtain different growth rates. We find a quasi-linear dependence of the growth rates on the intensity of the dynamo. Furthermore, the time interval in which exponential growth occurs and the growth rates also seems to depend on the initial configuration of the magnetic field.

Existence and Energy Balance of the Solar Dynamo

1993 ◽  
Vol 157 ◽  
pp. 19-23
Author(s):  
J.H.G.M. van Geffen
Keyword(s):  
Magnetic Field ◽  
Energy Balance ◽  
Energy Method ◽  
Magnetic Energy ◽  
Mean Field ◽  
Solar Dynamo ◽  
Ensemble Averaging ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Mean Field Dynamo

The idea behind the use of ensemble averaging and the finite magnetic energy method of van Geffen and Hoyng (1992) is briefly discussed. Applying this method to the solar dynamo shows that the turbulence — an essential ingredient of traditional mean field dynamo theory — poses grave problems: the turbulence makes the magnetic field so unstable that it becomes impossible to recognize any period.

scholarly journals Application of a helicity proxy to edge-on galaxies

2020 ◽  
Vol 496 (4) ◽  
pp. 4749-4759
Author(s):  
Axel Brandenburg ◽  
Ray S Furuya
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Numerical Results ◽  
Magnetic Helicity ◽  
The Galaxy ◽  
Rotationally Invariant ◽  
The Magnetic Field ◽  
Mean Field Dynamo

ABSTRACT We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the centre of the galaxy and are not a signature of magnetic helicity.

MAGNETIZED ROTATING NEUTRON STARS SIMULATED BY GENERAL-RELATIVISTIC POLYTROPIC MODELS: THE NUMERICAL TREATMENT

2011 ◽  
Vol 22 (10) ◽  
pp. 1107-1137
Author(s):  
V. S. GEROYANNIS ◽  
A. G. KATELOUZOS ◽  
F. N. VALVI
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Liouville Problem ◽  
Spherical Shape ◽  
Rotation Periods ◽  
Prolate Shape ◽  
Shafranov Equation ◽  
General Relativistic ◽  
Sturm Liouville ◽  
The Magnetic Field

We compute general-relativistic polytropic models of magnetized rotating neutron stars, assuming that magnetic field and rotation can be treated as decoupled perturbations acting on the nondistorted configuration. Concerning the magnetic field, we develop and apply a numerical method for solving the relativistic Grad–Shafranov equation as a nonhomogeneous Sturm–Liouville problem with nonstandard boundary conditions. We present significant geometrical and physical characteristics of six models, four of which are models of maximum mass. We find negative ellipticities owing to a magnetic field with both toroidal and poloidal components; thus the corresponding configurations have prolate shape. We also compute models of magnetized rotating neutron stars with almost spherical shape due to the counterbalancing of the rotational effect (tending to yield oblate configurations) and the magnetic effect (tending in turn to derive prolate configurations). In this work such models are simply called "equalizers." We emphasize on numerical results related to magnetars, i.e. ultramagnetized neutron stars with relatively long rotation periods.

scholarly journals Asymptotic Methods in the Nonlinear Mean-field Dynamo

1991 ◽  
Vol 130 ◽  
pp. 135-139
Author(s):  
D.D. Sokoloff ◽  
A. Shukurov ◽  
A.A. Ruzmaikin
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Steady State ◽  
Main Part ◽  
Asymptotic Methods ◽  
Mean Field ◽  
Coriolis Forces ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

AbstractWe discuss the methods and results of analysis of nonlinear mean-field dynamo models based on α-quenching in two asymptotic regimes, namely for weakly and highly supercritical excitation. In the former case the spatial distribution of the steady-state magnetic field is close to that given by the neutrally stable eigenfunction of the corresponding kinematic dynamo. In the latter case the magnetic field distribution within the main part of the dynamo volume is presumably determined by the balance between the Lorentz and Coriolis forces while near the boundaries boundary layers arise in which the field adjusts itself to the boundary conditions. The asymptotic behaviour of the highly supercritical αω-dynamos is sensitive to the particular form of dependence of the mean helicity on magnetic field while α2-dynamos are less sensitive to this dependence.

scholarly journals A dynamo amplifying the magnetic field of a Milky-Way-like galaxy

2020 ◽  
Vol 641 ◽  
pp. A165
Author(s):  
Evangelia Ntormousi ◽  
Konstantinos Tassis ◽  
Fabio Del Sordo ◽  
Francesca Fragkoudi ◽  
Rüdiger Pakmor
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Spiral Galaxies ◽  
Mean Field ◽  
Dark Matter Halo ◽  
Random Component ◽  
Galactic Magnetic Field ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Context. The magnetic fields of spiral galaxies are so strong that they cannot qualify as primordial. Their typical values are over one billion times higher than any value predicted for the early Universe. Explaining this immense growth and incorporating it in galaxy evolution theories is one of the long-standing challenges in astrophysics. Aims. So far, the most successful theory for the sustained growth of the galactic magnetic field is the alpha-omega dynamo. This theory predicts a characteristic dipolar or quadrupolar morphology for the galactic magnetic field, which has been observed in external galaxies. So far, however, there has been no direct demonstration of a mean-field dynamo operating in direct, multi-physics simulations of spiral galaxies. We carry out such a demonstration in this work. Methods. We employed numerical models of isolated, star-forming spiral galaxies that include a magnetized gaseous disk, a dark matter halo, stars, and stellar feedback. Naturally, the resulting magnetic field has a complex morphology that includes a strong random component. Using a smoothing of the magnetic field on small scales, we were able to separate the mean from the turbulent component and analyze them individually. Results. We find that a mean-field dynamo naturally occurs as a result of the dynamical evolution of the galaxy and amplifies the magnetic field by an order of magnitude over half a Gyr. Despite the highly dynamical nature of these models, the morphology of the mean component of the field is identical to analytical predictions. Conclusions. This result underlines the importance of the mean-field dynamo in galactic evolution. Moreover, by demonstrating the natural growth of the magnetic field in a complex galactic environment, it brings us a step closer to understanding the cosmic origin of magnetic fields.

scholarly journals The nature of mean-field generation in three classes of optimal dynamos

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
Axel Brandenburg ◽  
Long Chen
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Boundary Conditions ◽  
Magnetic Energy ◽  
Mean Field ◽  
Dynamo Action ◽  
Magnetic Diffusivity ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an $\unicode[STIX]{x1D6FC}^{2}$ dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23–45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.

scholarly journals Periodic and Aperiodic Behaviour in Stellar Dynamos

1983 ◽  
Vol 102 ◽  
pp. 307-310
Author(s):  
F. Cattaneo ◽  
C.A. Jones ◽  
N.O. Weiss
Keyword(s):  
Mean Field ◽  
Finite Amplitude ◽  
Velocity Shear ◽  
Dynamo Model ◽  
Oscillatory Solutions ◽  
Dynamical Interaction ◽  
Stable Periodic ◽  
The Magnetic Field ◽  
Mean Field Dynamo ◽  
Dynamo Waves

We have constructed a simple parametrized mean field dynamo model that includes the dynamical interaction between the magnetic field and differential rotation. This system of seven coupled nonlinear ordinary differential equations has finite amplitude oscillatory solutions (corresponding to Parker's dynamo waves) when the dynamo number D>1. We have studied two regimes. In the first, the velocity shear is reduced by the Lorentz force and there are stable periodic solutions for all D>1. In the second there is a transition from strictly periodic oscillations to aperiodic (chaotic) behaviour as D is increased. This simple example shows that nonlinear hydromagnetic dynamos can produce aperiodic cycles, with Maunder minima, as observed in the sun and other late-type stars.

scholarly journals Turbulent transport coefficients in galactic dynamo simulations using singular value decomposition

2019 ◽  
Vol 491 (3) ◽  
pp. 3870-3883 ◽  
Author(s):  
Abhijit B Bendre ◽  
Kandaswamy Subramanian ◽  
Detlef Elstner ◽  
Oliver Gressel
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Turbulent Transport ◽  
Transport Coefficients ◽  
Mean Field ◽  
Dynamo Model ◽  
The Mean ◽  
Value Decomposition ◽  
Svd Method ◽  
Mean Field Dynamo

ABSTRACT Coherent magnetic fields in disc galaxies are thought to be generated by a large-scale (or mean-field) dynamo operating in their interstellar medium. A key driver of mean magnetic field growth is the turbulent electromotive force (EMF), which represents the influence of correlated small-scale (or fluctuating) velocity and magnetic fields on the mean field. The EMF is usually expressed as a linear expansion in the mean magnetic field and its derivatives, with the dynamo tensors as expansion coefficients. Here, we adopt the singular value decomposition (SVD) method to directly measure these turbulent transport coefficients in a simulation of the turbulent interstellar medium that realizes a large-scale dynamo. Specifically, the SVD is used to least-square fit the time series data of the EMF with that of the mean field and its derivatives, to determine these coefficients. We demonstrate that the spatial profiles of the EMF reconstructed from the SVD coefficients match well with that taken directly from the simulation. Also, as a direct test, we use the coefficients to simulate a 1D mean-field dynamo model and find an overall similarity in the evolution of the mean magnetic field between the dynamo model and the direct simulation. We also compare the results with those which arise using simple regression and the ones obtained previously using the test-field method, to find reasonable qualitative agreement. Overall, the SVD method provides an effective post-processing tool to determine turbulent transport coefficients from simulations.

scholarly journals On the problem of large-scale magnetic field generation in rotating compressible convection

2013 ◽  
Vol 723 ◽  
pp. 529-555 ◽  
Author(s):  
B. Favier ◽  
P. J. Bushby
Keyword(s):  
Magnetic Field ◽  
Compressible Flows ◽  
Large Scale ◽  
Mean Field ◽  
Dynamo Model ◽  
Small Scale ◽  
Test Field ◽  
Computational Domain ◽  
Magnetic Field Generation ◽  
Mean Field Dynamo

AbstractMean-field dynamo theory suggests that turbulent convection in a rotating layer of electrically conducting fluid produces a significant $\alpha $-effect, which is one of the key ingredients in any mean-field dynamo model. Provided that this $\alpha $-effect operates more efficiently than (turbulent) magnetic diffusion, such a system should be capable of sustaining a large-scale dynamo. However, in the Boussinesq model that was considered by Cattaneo & Hughes (J. Fluid Mech., vol. 553, 2006, pp. 401–418) the dynamo produced small-scale, intermittent magnetic fields with no significant large-scale component. In this paper, we consider the compressible analogue of the rotating convective layer that was considered by Cattaneo & Hughes (2006). Varying the horizontal scale of the computational domain, we investigate the dependence of the dynamo upon the rotation rate. Our simulations indicate that these turbulent compressible flows can drive a small-scale dynamo but, even when the layer is rotating very rapidly (with a mid-layer Taylor number of $Ta= 1{0}^{8} $), we find no evidence for the generation of a significant large-scale component of the magnetic field on a dynamical time scale. Like Cattaneo & Hughes (2006), we measure a negligible (time-averaged) $\alpha $-effect when a uniform horizontal magnetic field is imposed across the computational domain. Although the total horizontal magnetic flux is a conserved quantity in these simulations, the (depth-dependent) horizontally averaged magnetic field always exhibits strong fluctuations. If these fluctuations are artificially suppressed within the code, we measure a significant mean electromotive force that is comparable to that found in related calculations in which the $\alpha $-effect is measured using the test-field method, even though we observe no large-scale dynamo action.

scholarly journals Simulations of astrophysical dynamos

2010 ◽  
Vol 6 (S274) ◽  
pp. 402-409
Author(s):  
Axel Brandenburg
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Mean Field ◽  
Integral Kernel ◽  
Turnover Time ◽  
Dynamo Theory ◽  
Magnetic Prandtl Number ◽  
Artificial Diffusion ◽  
The Magnetic Field ◽  
Mean Field Dynamo

AbstractNumerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing the magnetic field in its Euler potential representation. The importance of using integral kernel formulations in mean-field dynamo theory is emphasized in cases where the dynamo growth rate becomes comparable with the inverse turnover time. Finally, the significance of microscopic magnetic Prandtl number in controlling the conversion from kinetic to magnetic energy is highlighted.

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