arXiv subjects

A. Brandenburg

Publications and source records attributed to A. Brandenburg.

At least 19 recordsLinked to original sources

arXiv2024

Intergalactic magnetism in a gamma-ray beam as a model of Porphyrion

We estimate the magnetic field in the jets of the recently discovered 7 Mpc long Porphyrion system. We use non-detection of the system in gamma-rays to derive a lower bound on the co-moving magnetic field strength at the level of ~10 nG. This value is consistent with recent estimates of magnetic fields in the filaments of the Large Scale Structure. We discuss the possibility that, instead of being the extreme case of a radio jet formation scenario, Porphyrion actually traces a very-high-energy gamma-ray beam emitted by an active galactic nucleus. In such a model, jets do not need to spread into the voids of the Large Scale Structure to appear straight on a very large distance range, and several anomalies of the standard radio jet scenarios can be solved at once.

astro-ph.HE↗

arXiv2024

Resistively controlled primordial magnetic turbulence decay

Magnetic fields generated in the early Universe undergo turbulent decay during the radiation-dominated era. The decay is governed by a decay exponent and a decay time. It has been argued that the latter is prolonged by magnetic reconnection, which depends on the microphysical resistivity and viscosity. Turbulence, on the other hand, is not usually expected to be sensitive to microphysical dissipation, which affects only very small scales. We want to test and quantify the reconnection hypothesis in decaying hydromagnetic turbulence. We performed high-resolution numerical simulations with zero net magnetic helicity using the Pencil Code with up to $2048^3$ mesh points and relate the decay time to the Alfvén time for different resistivities and viscosities. The decay time is found to be longer than the Alfvén time by a factor that increases with increasing Lundquist number to the 1/4 power. The decay exponent is as expected from the conservation of the Hosking integral, but a timescale dependence on resistivity is unusual for developed turbulence and not found for hydrodynamic turbulence. In two dimensions, the Lundquist number dependence is shown to be leveling off above values of $\approx25,000$, independently of the value of the viscosity. Our numerical results suggest that resistivity effects have been overestimated in earlier work. Instead of reconnection, it may be the magnetic helicity density in smaller patches that is responsible for the resistively slow decay. The leveling off at large Lundquist number cannot currently be confirmed in three dimensions.

astro-ph.CO↗

arXiv2022

Dissipative magnetic structures and scales in small-scale dynamos

Small-scale dynamos play important roles in modern astrophysics, especially on Galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time scale of Galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that, during the kinematic phase of the small-scale dynamo, the cutoff wavenumber of the magnetic energy spectra scales as expected for large magnetic Prandtl numbers, but continues in the same way also for moderately small values - contrary to what is expected. For a critical magnetic Prandtl number of about 0.3, the dissipative and resistive cutoffs are found to occur at the same wavenumber. In the nonlinearly saturated regime, the critical magnetic Prandtl number becomes unity. The cutoff scale now has a shallower scaling with magnetic Prandtl number below a value of about three, and a steeper one otherwise compared to the kinematic regime.

astro-ph.GA↗

arXiv2021

Spectral characterisation of inertial particle clustering in turbulence

Clustering of inertial particles is important for many types of astrophysical and geophysical turbulence, but it has been studied predominately for incompressible flows. Here we study compressible flows and compare clustering in both compressively (irrotationally) and vortically (solenoidally) forced turbulence. Vortically and compressively forced flows are driven stochastically either by solenoidal waves or by circular expansion waves, respectively. For compressively forced flows, the power spectrum of the density of inertial particles is a useful tool for displaying particle clustering relative to the fluid density enhancement. Power spectra are shown to be particularly sensitive for studying large-scale particle clustering, while conventional tools such as radial distribution functions are more suitable for studying small-scale clustering. Our primary finding is that particle clustering through shock interaction is particularly prominent in turbulence driven by spherical expansion waves. It manifests itself through a double-peaked distribution of spectral power as a function of Stokes number. The two peaks are associated with two distinct clustering mechanisms; shock interaction for smaller Stokes numbers and the centrifugal sling effect for larger values. The clustering of inertial particles is associated with the formation of caustics. Such caustics can only be captured in the Lagrangian description, which allows us to assess the relative importance of caustics in vortically and compressively forced turbulence. We show that the statistical noise resulting from the limited number of particles in the Lagrangian description can be removed from the particle power spectra, allowing us a more detailed comparison of the residual spectra. We focus on the Epstein drag law relevant for rarefied gases, but show that our findings apply also to the usual Stokes drag.

physics.flu-dyn↗

arXiv2021

The timestep constraint in solving the gravitational wave equations sourced by hydromagnetic turbulence

Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the Reynolds and Maxwell stresses. We have implemented two different GW solvers into the {\sc Pencil Code} -- a code which uses a third order timestep and sixth order finite differences. Using direct numerical integration of the GW equations, we study the appearance of a numerical degradation of the GW amplitude at the highest wavenumbers, which depends on the length of the timestep -- even when the Courant--Friedrichs--Lewy condition is ten times below the stability limit. This degradation leads to a numerical error, which is found to scale with the third power of the timestep. A similar degradation is not seen in the magnetic and velocity fields. To mitigate numerical degradation effects, we alternatively use the exact solution of the GW equations under the assumption that the source is constant between subsequent timesteps. This allows us to use a much longer timestep, which cuts the computational cost by a factor of about ten.

physics.flu-dyn↗

arXiv2021

The effect of a dynamo-generated field on the Parker wind

Stellar winds are an integral part of the underlying dynamo, the motor of stellar activity. The wind controls the star's angular momentum loss, which depends on the magnetic field geometry which varies significantly in time and latitude. Here we study basic properties of a self-consistent model that includes simple representations of both the global stellar dynamo in a spherical shell and the exterior in which the wind accelerates and becomes supersonic. We numerically solve an axisymmetric mean-field model for the induction, momentum, and continuity equations using an isothermal equation of state. The model allows for the simultaneous generation of a mean magnetic field and the development of a Parker wind. The resulting flow is transonic at the critical point, which we arrange to be between the inner and outer radii of the model. The boundary conditions are assumed to be such that the magnetic field is antisymmetric about the equator, i.e., dipolar. At the solar rotation rate, the dynamo is oscillatory and of $α^2$ type. In most of the domain, the magnetic field corresponds to that of a split monopole. The magnetic energy flux is largest between the stellar surface and the critical point. The angular momentum flux is highly variable in time and can reach negative values, especially at midlatitudes. At rapid rotation of up to 50 times the solar value, most of the magnetic field is lost along the axis within the inner tangential cylinder of the model. The model reveals unexpected features that are not generally anticipated from models that are designed to reproduce the solar wind: highly variable angular momentum fluxes even from just an $α^2$ dynamo in the star. A major caveat of our isothermal models with a magnetic field produced by a dynamo is the difficulty to reach small enough plasma betas without the dynamo itself becoming unrealistically strong inside the star.

astro-ph.SR↗

arXiv2020

Helicity proxies from linear polarisation of solar active regions

The alpha effect is believed to play a key role in the generation of the solar magnetic field. A fundamental test for its significance in the solar dynamo is to look for magnetic helicity of opposite signs in the two hemispheres, and at small and large scales. However, measuring magnetic helicity is compromised by the inability to fully infer the magnetic field vector from observations of solar spectra, caused by what is known as the "pi ambiguity" of spectropolarimetric observations. We decompose linear polarisation into parity-even and parity-odd E and B polarisations, which are not affected by the "pi ambiguity". Furthermore, we study whether the correlations of spatial Fourier spectra of B and parity-even quantities such as E or temperature T are a robust proxy for magnetic helicity of solar magnetic fields. We analyse polarisation measurements of active regions observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics observatory. Theory predicts the magnetic helicity of active regions to have, statistically, opposite signs in the two hemispheres. We then compute the parity-odd E B and T B correlations, and test for systematic preference of their sign based on the hemisphere of the active regions. We find that: (i) E B and T B correlations are a reliable proxy for magnetic helicity, when computed from linear polarisation measurements away from spectral line cores, and (ii) E polarisation reverses its sign close to the line core. Our analysis reveals Faraday rotation to not have a significant influence on the computed parity-odd correlations. The EB decomposition of linear polarisation appears to be a good proxy for magnetic helicity independent of the "pi ambiguity". This allows us to routinely infer magnetic helicity directly from polarisation measurements.

astro-ph.SR↗

arXiv2020

The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) to meteorological cloud microphysics and engineering applications in combustion. Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to be used. The code can also evolve Lagrangian (inertial and noninertial) particles, their coagulation and condensation, as well as their interaction with the fluid.

astro-ph.IM↗

arXiv2019

Magnetic helicity and fluxes in an inhomogeneous alpha squared dynamo

Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur at large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains still unclear.

astro-ph.SR↗

arXiv2018

Compressibility in turbulent MHD and passive scalar transport: mean-field theory

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $τ$-approach. We find that compressibility decreases the $α$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Péclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large Péclet numbers. It can be interpreted as compressible turbophoresis of noninertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.

physics.flu-dyn↗

arXiv2018

Magnetic bipoles in rotating turbulence with coronal envelope

The formation of sunspots and starspots is not yet fully understood and is therefore one of the major open problems in solar and stellar physics. Magnetic flux concentrations can be produced by the negative effective magnetic pressure instability (NEMPI). This instability is strongly suppressed by rotation. However, the presence of an outer coronal envelope was previously found to strengthen the flux concentrations and make them more prominent. It also allows for the formation of bipolar regions (BRs). We want to know whether the presence of an outer coronal envelope also changes the excitation conditions and the rotational dependence of NEMPI. We use direct numerical simulations and mean-field simulations. We adopt a simple two-layer model of turbulence that mimics the jump between the convective turbulent and coronal layers below and above the surface of a star, respectively. The computational domain is Cartesian and located at a certain latitude of a rotating sphere. We investigate the effects of rotation on NEMPI by changing the Coriolis number, the latitude, and the box resolution. Rotation has a strong impact on the process of BR formation. Even rather slow rotation is found to suppress their formation. However, increasing the imposed magnetic field strength also makes the structures stronger and alleviates the rotational suppression somewhat. The presence of a coronal layer itself does not significantly alleviate the effects of rotational suppression.

astro-ph.SR↗

arXiv2018

Effect of turbulence on collisional growth of cloud droplets

We investigate the effect of turbulence on the collisional growth of um-sized droplets through high- resolution numerical simulations with well resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate, but only weakly on the Reynolds number. This can be explained through the energy dissipation rate dependence of the mean collision rate described by the Saffman-Turner collision model. Consistent with the Saffman-Turner collision model and its extensions, the collision rate increases as the square root of the energy dissipation rate even when coalescence is invoked. The size distribution exhibits power law behavior with a slope of -3.7 between a maximum at approximately 10 um up to about 40 um. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is due to the fact that turbulence enhances the collisional growth between similar sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth.

physics.ao-ph↗

arXiv2018

Varying the forcing scale in low Prandtl number dynamos

Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale-separation between the size of the simulation domain and the integral scale of the turbulence, i.e., the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.

physics.flu-dyn↗

arXiv2018

Strong nonlocality variations in a spherical mean-field dynamo

To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the convection zone where the size of the turbulent eddies is comparable to the depth of the convection zone itself. We approximate the underlying integro-differential equation by a partial differential equation corresponding to a reaction-diffusion type equation for the mean electromotive force, making an approach that is nonlocal in space and time feasible under conditions where spherical geometry and nonlinearity are included. In agreement with earlier findings, spatio-temporal nonlocality lowers the excitation conditions of the dynamo. Sharp structures are now found to be absent. However, in the surface layers the field remains similar to before.

astro-ph.SR↗

arXiv2018

Large-scale dynamos in rapidly rotating plane layer convection

Context: Convectively-driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component. Aims: Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability. Methods: The governing equations of three-dimensional nonlinear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes. Results: In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, it is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity ("grand minima"-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.

astro-ph.SR↗

arXiv2017

Laminar and turbulent dynamos in chiral magnetohydrodynamics-I: Theory

The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (\emph{chiral magnetic effect}). We present a self-consistent treatment of the \emph{chiral MHD equations}, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark--gluon plasma.

physics.plasm-ph↗

arXiv2017

The contribution of kinetic helicity to turbulent magnetic diffusivity

Using numerical simulations of forced turbulence, it is shown that for magnetic Reynolds numbers larger than unity, i.e., beyond the regime of quasilinear theory, the turbulent magnetic diffusivity attains an additional negative contribution that is quadratic in the kinetic helicity. In particular, for large magnetic Reynolds numbers, the turbulent magnetic diffusivity without helicity is about twice the value with helicity. Such a contribution was not previously anticipated, but, as we discuss, it turns out to be important when accurate estimates of the turbulent magnetic diffusivity are needed.

physics.flu-dyn↗

arXiv2017

Eulerian and modified Lagrangian approaches to multi-dimensional condensation and collection

Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here, an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or su- perdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow, or just gravitational acceleration without gas flow. Good agreement between the differ- ent schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. Higher moments of the size spectra are found to be a useful tool to characterize the growth of the largest drops through collection. Remarkably, the tails of the size spectra are reasonably well described by a gamma distribution in cases with gravity or turbulence. The Lagrangian schemes are generally found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results.

physics.flu-dyn↗