arXiv subjects

Rodion Stepanov

Publications and source records attributed to Rodion Stepanov.

At least 37 records · Page 2Linked to original sources

arXiv2015

The formation of regular interarm magnetic fields in spiral galaxies

Observations of regular magnetic fields in several nearby galaxies reveal magnetic arms situated between the material arms. The nature of these magnetic arms is a topic of active debate. Previously we found a hint that taking into account the effects of injections of small-scale magnetic fields generated, e.g., by turbulent dynamo action, into the large-scale galactic dynamo can result in magnetic arm formation. We now investigate the joint roles of an arm/interarm turbulent diffusivity contrast and injections of small-scale magnetic field on the formation of large-scale magnetic field ("magnetic arms") in the interarm region. We use the relatively simple "no-$z$" model for the galactic dynamo. This involves projection on to the galactic equatorial plane of the azimuthal and radial magnetic field components; the field component orthogonal to the galactic plane is estimated from the solenoidality condition. We find that addition of diffusivity gradients to the effect of magnetic field injections makes the magnetic arms much more pronounced. In particular, the regular magnetic field component becomes larger in the interarm space compared to that within the material arms.The joint action of the turbulent diffusivity contrast and small-scale magnetic field injections (with the possible participation of other effects previously suggested) appears to be a plausible explanation for the phenomenon of magnetic arms.

astro-ph.GA↗

arXiv2015

Measuring magnetism in the Milky Way with the Square Kilometre Array

Magnetic fields in the Milky Way are present on a wide variety of sizes and strengths, influencing many processes in the Galactic ecosystem such as star formation, gas dynamics, jets, and evolution of supernova remnants or pulsar wind nebulae. Observation methods are complex and indirect; the most used of these are a grid of rotation measures of unresolved polarized extragalactic sources, and broadband polarimetry of diffuse emission. Current studies of magnetic fields in the Milky Way reveal a global spiral magnetic field with a significant turbulent component; the limited sample of magnetic field measurements in discrete objects such as supernova remnants and HII regions shows a wide variety in field configurations; a few detections of magnetic fields in Young Stellar Object jets have been published; and the magnetic field structure in the Galactic Center is still under debate. The SKA will unravel the 3D structure and configurations of magnetic fields in the Milky Way on sub-parsec to galaxy scales, including field structure in the Galactic Center. The global configuration of the Milky Way disk magnetic field, probed through pulsar RMs, will resolve controversy about reversals in the Galactic plane. Characteristics of interstellar turbulence can be determined from the grid of background RMs. We expect to learn to understand magnetic field structures in protostellar jets, supernova remnants, and other discrete sources, due to the vast increase in sample sizes possible with the SKA. This knowledge of magnetic fields in the Milky Way will not only be crucial in understanding of the evolution and interaction of Galactic structures, but will also help to define and remove Galactic foregrounds for a multitude of extragalactic and cosmological studies.

astro-ph.GA↗

arXiv2014

Joint inverse cascade of magnetic energy and magnetic helicity in MHD turbulence

We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic turbulence for helicity injection at a scale that is much smaller than the scale of energy injection. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in a domain with a high level of relative magnetic helicity, which determines that part of the magnetic energy related to the helical modes at a given scale. If the relative helicity approaches unity, the spectral slope tends to $-3/2$. We show that this energy pileup is caused by an inverse cascade of magnetic energy associated with the magnetic helicity. This negative energy flux is the contribution of the pure magnetic-to-magnetic energy transfer, which vanishes in the non-helical limit. In the context of astrophysical dynamos, our results indicate that a large-scale dynamo can be affected by the magnetic helicity generated at small scales. The kinetic helicity, in particular, is not involved in the process at all. An interesting finding is that an inverse cascade of magnetic energy can be provided by a small-scale source of magnetic helicity fluctuations without a mean injection of magnetic helicity.

physics.plasm-ph↗

arXiv2014

A systematic bias in the calculation of spectral density from a 3D spatial grid

The energy spectral density $E(k)$, where $k$ is the spatial wave number, is a well-known diagnostic of homogeneous turbulence and magnetohydrodynamic turbulence. However in most of the curves plotted by different authors, some systematic kinks can be observed at $k=9$, $k=15$ and $k=19$. We claim that these kinks have no physical meaning, and are in fact the signature of the method which is used to estimate $E(k)$ from a 3D spatial grid. In this paper we give another method, in order to get rid of the spurious kinks and to estimate $E(k)$ much more accurately.

physics.comp-ph↗

arXiv2014

Faraday signature of magnetic helicity from reduced depolarization

Using one-dimensional models, we show that a helical magnetic field with an appropriate sign of helicity can compensate the Faraday depolarization resulting from the superposition of Faraday-rotated polarization planes from a spatially extended source. For radio emission from a helical magnetic field, the polarization as a function of the square of the wavelength becomes asymmetric with respect to zero. Mathematically speaking, the resulting emission occurs then either at observable or at unobservable (imaginary) wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the reconstruction of the underlying Faraday dispersion function in the former case, but not in the latter. The presence of positive magnetic helicity can thus be detected by observing positive RM in highly polarized regions in the sky and negative RM in weakly polarized regions. Conversely, negative magnetic helicity can be detected by observing negative RM in highly polarized regions and positive RM in weakly polarized regions. The simultaneous presence of two magnetic constituents with opposite signs of helicity is shown to possess signatures that can be quantified through polarization peaks at specific wavelengths and the gradient of the phase of the Faraday dispersion function. Similar polarization peaks can tentatively also be identified for the bi-helical magnetic fields that are generated self-consistently by a dynamo from helically forced turbulence, even though the magnetic energy spectrum is then continuous. Finally, we discuss the possibility of detecting magnetic fields with helical and non-helical properties in external galaxies using the Square Kilometre Array.

astro-ph.CO↗

arXiv2013

An observational test for correlations between cosmic rays and magnetic fields

We derive the magnitude of fluctuations in total synchrotron intensity in the Milky Way and M33, from both observations and theory under various assumption about the relation between cosmic rays and interstellar magnetic fields. Given the relative magnitude of the fluctuations in the Galactic magnetic field (the ratio of the rms fluctuations to the mean magnetic field strength) suggested by Faraday rotation and synchrotron polarization, the observations are inconsistent with local energy equipartition between cosmic rays and magnetic fields. Our analysis of relative synchrotron intensity fluctuations indicates that the distribution of cosmic rays is nearly uniform at the scales of the order of and exceeding $100\p$, in contrast to strong fluctuations in the interstellar magnetic field at those scales. A conservative upper limit on the ratio of the the fluctuation magnitude in the cosmic ray number density to its mean value is 0.2--0.4 at scales of order 100\,pc. Our results are consistent with a mild anticorrelation between cosmic-ray and magnetic energy densities at these scales, in both the Milky Way and M33. Energy equipartition between cosmic rays and magnetic fields may still hold, but at scales exceeding 1\,kpc. Therefore, we suggest that equipartition estimates be applied to the observed synchrotron intensity smoothed to a linear scale of kiloparsec order (in spiral galaxies) to obtain the cosmic ray distribution and a large-scale magnetic field. Then the resulting cosmic ray distribution can be used to derive the fluctuating magnetic field strength from the data at the original resolution. The resulting random magnetic field is likely to be significantly stronger than existing estimates.

astro-ph.GA↗

arXiv2013

Shell Models of Magnetohydrodynamic Turbulence

Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models. In this review we set up a general mathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decaying MHD turbulence, dynamo action, Alfven waves and the Hall effect.

physics.flu-dyn↗

arXiv2011

Multiscale magnetic fields in spiral galaxies: evolution and reversals

Magnetic fields in nearby, star-forming galaxies reveal both large-scale patterns and small-scale structures. A large-scale field reversal may exist in the Milky Way but no such reversals have been observed so far in external galaxies. The effects of star-forming regions of galaxies need to be included when modelling the evolution of their magnetic fields, which can then be compared to future radio polarization observations. The causes of large-scale field reversals also need clarification. Our model of field evolution in isolated disc galaxies includes a standard mean-field dynamo and continuous injection of turbulent fields (the effect of supernova explosions) in discrete star forming regions by implicit small-scale dynamo action. Synthetic maps of radio synchrotronemission and Faraday rotation measures are computed. A large-scale dynamo is essential to obtain regular large-scale spiral magnetic fields, observed in many galaxies. These appear, on kpc scales in near energy equilibrium with the turbulence, after 1-2 Gyr (redshift 4-3). Turbulent field injection generates small-scale field structures. Depending on model parameters, large-scale field reversals may persist over many Gyrs and can survive until the present epoch. Significant polarized radio synchrotron emission from young galaxies is expected at redshifts less than 4. Faraday rotation measures (RM) are crucial to detect field reversals. Large-scale patterns ofrotation measures can be observed at redshifts less than 3. Our model can explain the general form of axisymmetric spiral fields with many local distortions, as observed in nearby galaxies. For a slightly different choice of parameters, large-scale field reversals can persist over the lifetime of a galaxy. Comparison of our synthetic maps with future observations of distant galaxies with the planned Square Kilometre Array (SKA) will allow refinement of models.

astro-ph.GA↗

arXiv2010

Cascades and dissipation ratio in rotating MHD turbulence at low magnetic Prandtl number

A phenomenology of isotropic magnetohydrodynamic turbulence subject to both rotation and applied magnetic field is presented. It is assumed that the triple correlations decay-time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and Alfvén wave period. For $Pm=1$ it leads to four kinds of piecewise spectra, depending on the four parameters, injection rate of energy, magnetic diffusivity, rotation rate and applied field. With a shell model of MHD turbulence (including rotation and applied magnetic field), spectra for $Pm \le 1$ are presented, together with the ratio between magnetic and viscous dissipation.

physics.flu-dyn↗

arXiv2010

Long-term decaying evolution of MHD turbulence

The free decay of MHD turbulence at large Reynolds numbers is studied numerically using a shell model. We study the statistical properties based on representative sample of realisations (128 realisations for each type of initial conditions) over the period of $10^5$ large-scale turnover times. The performed simulations show that the force-free non-helical MHD turbulence can demonstrate two different scenarios of evolution in spite of similar initial conditions. Within the first scenario, the cross-helicity accumulation is so fast that the energy cascade vanishes before significant magnetic energy dissipates. Then the system approaches the state of maximal cross-helicity. Within the second scenario, the cascade process continues to remain active until time $10^4$ in units of large-scale turnover time. Then the magnetic field becomes vastly helical due to magnetic helicity conservation. Thus the magnetic energy does not dissipate with kinetic energy.

physics.flu-dyn↗

arXiv2010

Direct Measurement of Effective Magnetic Diffusivity in Turbulent Flow of Liquid Sodium

The first direct measurements of effective magnetic diffusivity in turbulent flow of electro-conductive fluids (the so-called beta-effect) under magnetic Reynolds number Rm >> 1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re \approx 3 10^6, which corresponds to the magnetic Reynolds number Rm \approx 30. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal deviation of magnetic diffusivity from its basic (laminar) value reaches about 50% .

physics.flu-dyn↗

arXiv2009

Deciphering solar turbulence from sunspots records

It is generally believed that sunspots are the emergent part of magnetic flux tubes in the solar interior. These tubes are created at the base of the convection zone and rise to the surface due to their magnetic buoyancy. The motion of plasma in the convection zone being highly turbulent, the surface manifestation of sunspots may retain the signature of this turbulence, including its intermittency. From direct observations of sunspots, and indirect observations of the concentration of cosmogenic isotopes $^{14}$C in tree rings or $^{10}$Be in polar ice, power spectral densities in frequency are plotted. Two different frequency scalings emerge, depending on whether the Sun is quiescent or active. %magnetic activity is maximum or minimum. From direct observations we can also calculate scaling exponents. These testify to a strong intermittency, comparable with that observed in the solar wind.

astro-ph.SR↗

arXiv2009

Evolution of magnetic fields in galaxies in the frame of hierarchical structure formation cosmology: future tests with the SKA

Results from simulations of hierarchical structure formation cosmology provide a tool to develop an evolutionary model of regular magnetic fields coupled to galaxy formation and evolution. We use the dynamo theory to derive the timescales of amplification and ordering of magnetic fields in disk and puffy galaxies. Galaxies similar to the Milky Way formed their disks at $z\approx10$ and regular fields of $μ$G strength and a few kpc coherence length were generated within 2 Gyr (at $z\approx3$), but field ordering up to the coherence scale of the galaxy size took another 6 Gyr (at $z\approx0.5$). Giant galaxies formed their disk already at $z\approx10$, allowing more efficient dynamo generation of strong regular fields (with kpc coherence length) already at $z\approx4$. Dwarf galaxies should have hosted fully coherent fields at $z\approx1$. This evolutionary scenario and number of predictions of the model can be tested by measurements of polarized synchrotron emission and Faraday rotation with the planned Square Kilometre Array. This model is used to simulate the evolution of regular fields in disk galaxies and the polarized radio sky as part of the Square Kilometer Array Design Studies (SKADS).

astro-ph.CO↗

arXiv2009

Role of Cross Helicity in Cascade Processes of MHD turbulence

The purpose of this work is to investigate the spectral properties of the developed isotropic (non-Alfven) MHD turbulence stationary excited by an external force, which injects the cross helicity into the flow simultaneously with the energy. It is shown that the cross helicity blocks the spectral energy transfer in MHD turbulence and results in energy accumulation in the system. This accumulation proceeds until the vortex intensification compensates the decreasing efficiency of nonlinear interactions. The formula for estimating the average turbulence energy is obtained for the set ratio between the injected helicity and energy. It is remarkable that the turbulence accumulates the injected cross helicity at its low rate injection -- the integral correlation coefficient significantly exceeds the ratio between the injected helicity and the energy. It is shown that the spectrum slope gradually increases from "5/3" to "2" with the cross helicity level.

physics.plasm-ph↗

arXiv2008

Magnetic field structures of galaxies derived from analysis of Faraday rotation measures, and perspectives for the SKA

The forthcoming new-generation radio telescope SKA (Square Kilometre Array) and its precursors will provide a rapidly growing number of polarized radio sources. Our analysis aims on what can be learned from these sources concerning the structure and evolution of magnetic fields of external galaxies. Recognition of magnetic structures is possible from Faraday rotation measures (${\rm RM}$) towards background sources behind galaxies. We construct models for the ionized gas and magnetic field patterns of different azimuthal symmetry (axisymmetric, bisymmetric and quadrisymmetric spiral, and superpositions) plus a halo magnetic field. $\RM$ fluctuations with a Kolmogorov spectrum due to turbulent fields and/or fluctuations in ionized gas density are superimposed. Assuming extrapolated number density counts of polarized sources, we generate a sample of $\RM$ values within the solid angle of the galaxy. Applying various templates, we derive the minimum number of background sources and the minimum quality of the observations. For a large number of sources, reconstruction of the field structure without precognition becomes possible. Any large-scale regular component of the magnetic field can be clearly recognized from $\RM$ data with help of the $χ^2$ criterium. Under favourite conditions, about a few dozens of polarized sources are sufficient for a reliable result.

astro-ph↗

arXiv2007

Phenomenology of turbulent dynamo growth and saturation

With a non local shell model of magnetohydrodynamic turbulence we investigate numerically the turbulent dynamo action for low and high magnetic Prandtl numbers ($Pm$). The results obtained in the kinematic regime and along the way to dynamo saturation are understood in terms of a phenomenological approach based on the local ($Pm\ll 1$) or non local ($Pm\gg 1$) nature of the energy transfers. In both cases the magnetic energy grows at small scale and saturates as an inverse `` cascade ''.

astro-ph↗

arXiv2007

Fully developed turbulent dynamo at low magnetic Prandtl numbers

We investigate the dynamo problem in the limit of small magnetic Prandtl number ($\Pm$) using a shell model of magnetohydrodynamic turbulence. The model is designed to satisfy conservation laws of total energy, cross helicity and magnetic helicity in the limit of inviscid fluid and null magnetic diffusivity. The forcing is chosen to have a constant injection rate of energy and no injection of kinetic helicity nor cross helicity. We find that the value of the critical magnetic Reynolds number ($\Rm$) saturates in the limit of small $\Pm$. Above the dynamo threshold we study the saturated regime versus $\Rm$ and $\Pm$. In the case of equipartition, we find Kolmogorov spectra for both kinetic and magnetic energy except for wave numbers just below the resistive scale. Finally the ratio of both dissipation scales (viscous to resistive) evolves as $\Pm^{-3/4}$ for $\Pm < 1$

physics.flu-dyn↗

arXiv2006

The mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean--field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-like dynamo. In view of this application the second--order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $α$--effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.

physics.flu-dyn↗