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In the primordial plasma, at temperatures above the scale of electroweak symmetry breaking, the presence of chiral asymmetries is expected to induce the development of helical hypermagnetic fields through the phenomenon of chiral plasma instability. It results in magnetohydrodynamic turbulence due to the high conductivity and low viscosity and sources gravitational waves that survive in the universe today as a stochastic polarized gravitational wave background. In this article, we show that this scenario only relies on Standard Model physics, and therefore the observable signatures, namely the relic magnetic field and gravitational background, are linked to a single parameter controlling the initial chiral asymmetry. We estimate the magnetic field and gravitational wave spectra, and validate these estimates with 3D numerical simulations., 8 pages, 4 figures, 1 table

In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic field, the spectral magnetic energy density increases with time at small wavenumbers $k$, provided the spectrum at low $k$ is sufficiently steep. This is inverse cascading and occurs for an initial Batchelor spectrum, where the magnetic energy per linear wavenumber interval increases like $k^4$. For an initial Saffman spectrum that is proportional to $k^2$, however, inverse cascading is known not to occur. We study here the case of an intermediate $k^3$ spectrum, which may be relevant for magnetogenesis in the early Universe during the electroweak epoch. This case is not well understood in view of the standard Taylor expansion of the magnetic energy spectrum for small $k$. Using high resolution MHD simulations, we show that also in this case there is inverse cascading with a strength just as expected from the conservation of the Hosking integral, which governs the decay of an initial Batchelor spectrum., 15 pages, 6 figures, 3 tables, submitted to J. Plasma Physics

The origin and evolution of magnetic fields of neutron stars from birth has long been a source of debate. Here, motivated by recent simulations of the Hall cascade with magnetic helicity, we invoke a model where the large-scale magnetic field of neutron stars grows as a product of small-scale turbulence through an inverse cascade. We apply this model to a simulated population of neutron stars at birth and show how this model can account for the evolution of such objects across the $P\dot{P}$ diagram, explaining both pulsar and magnetar observations. Under the assumption that small-scale turbulence is responsible for large-scale magnetic fields, we place a lower limit on the spherical harmonic degree of the energy-carrying magnetic eddies of $\approx 40$. Our results favor the presence of a highly resistive pasta layer at the base of the neutron star crust. We further discuss the implications of this paradigm on direct observables, such as the nominal age and braking index of pulsars., Comment: Submitted. 6 pages, 3 figures

Mean-field dynamo theory has important applications in solar physics and galactic magnetism. We discuss some of the many turbulence effects relevant to the generation of large-scale magnetic fields in the solar convection zone. The mean-field description is then used to illustrate the physics of the $\alpha$ effect, turbulent pumping, turbulent magnetic diffusivity, and other effects on a modern solar dynamo model. We also discuss how turbulence transport coefficients are derived from local simulations of convection and then used in mean-field models., Comment: 64 pages, 20 figures, 2 tables, submitted to Space Science Reviews, special issue "Solar and stellar dynamos: a new era"

We study the propagation of cosmological gravitational wave (GW) backgrounds from the early radiation era until the present day in modified theories of gravity. Comparing to general relativity (GR), we study the effects that modified gravity parameters, such as the GW friction $\alpha_{\rm M}$ and the tensor speed excess $\alpha_{\rm T}$, have on the present-day GW spectrum. We use both the WKB estimate, which provides an analytical description but fails at superhorizon scales, and numerical simulations that allow us to go beyond the WKB approximation. We show that a constant $\alpha_{\rm T}$ makes relatively insignificant changes to the GR solution, especially taking into account the constraints on its value from GW observations by the LIGO--Virgo collaboration, while $\alpha_{\rm M}$ can introduce modifications to the spectral slopes of the GW energy spectrum in the low-frequency regime depending on the considered time evolution of $\alpha_{\rm M}$. The latter effect is additional to the damping or growth occurring equally at all scales that can be predicted by the WKB approximation. In light of the recent observations by pulsar timing array (PTA) collaborations, and the potential observations by future detectors such as SKA, LISA, DECIGO, BBO, or ET, we show that, in most of the cases, constraints cannot be placed on the effects of $\alpha_{\rm M}$ and the initial GW energy density $\mathcal{E}_{\rm GW}^*$ separately, but only on the combined effects of the two, unless the signal is observed at different frequency ranges. In particular, we provide some constraints on the combined effects from the reported PTA observations., Comment: 36 pages, 11 figures, 2 tables

Turbulence is typically not in equilibrium, i.e. mean quantities such as the mean energy and helicity are typically time-dependent. The effect of non-stationarity on the turbulent hydromagnetic dynamo process is studied here with the use of the two-scale direct-interaction approximation (TSDIA), which allows to explicitly relate the mean turbulent Reynolds and Maxwell stresses and the mean electromotive force (EMF) to the spectral characteristics of turbulence, such as e.g. the mean energy, as well as kinetic and cross-helicity. It is demonstrated, that the non-equilibrium effects can enhance the dynamo process when the magnetohydrodynamic (MHD) turbulence is both helical and cross-helical. This effect is based on the turbulent infinitesimal-impulse cross-response functions, which do not affect turbulent flows in equilibrium. The evolution and sources of the cross-helicity in MHD turbulence is also discussed., 23 pages, 3 figures

We study the evolution of magnetic fields coupled with chiral fermion asymmetry in the framework of chiral magnetohydrodynamics with zero initial total chirality. The initial magnetic field has a turbulent spectrum peaking at a certain characteristic scale and is fully helical with positive helicity. The initial chiral chemical potential is spatially uniform and negative. We consider two opposite cases where the ratio of the length scale of the chiral plasma instability (CPI) to the characteristic scale of the turbulence is smaller and larger than unity. These initial conditions might be realized in cosmological models such as certain types of axion inflation. The magnetic field and chiral chemical potential evolve with inverse cascading in such a way that the magnetic helicity and chirality cancel each other at all times. The CPI time scale is found to determine mainly the time when the magnetic helicity spectrum attains negative values at high wave numbers. The turnover time of the energy-carrying eddies, on the other hand, determines the time when the peak of the spectrum starts to shift to smaller wave numbers via an inverse cascade. The onset of helicity decay is determined by the time when the chiral magnetic effect becomes efficient at the peak of the initial magnetic energy spectrum. When spin flipping is important, the chiral chemical potential vanishes and the magnetic helicity becomes constant, which leads to a faster increase of the correlation length, as expected from magnetic helicity conservation. This also happens when the initial total chirality is imbalanced. Our findings have important implications for baryogenesis after axion inflation., Comment: 21 pages, 20 figures, 4 tables

The conversion of axionlike particles (ALPs) and photons in magnetised astrophysical environments provides a promising route to search for ALPs. The strongest limits to date on light ALPs use galaxy clusters as ALP--photon converters. However, such studies traditionally rely on simple models of the cluster magnetic fields, with the state-of-the-art being Gaussian random fields (GRFs). We present the first systematic study of ALP-photon conversion in more realistic, turbulent fields from dedicated magnetohydrodynamic (MHD) simulations, which we compare with GRF models. For GRFs, we analytically derive the distribution of conversion ratios at fixed energy and find that it follows an exponential law. We find that the MHD models agree with the exponential law for typical, small amplitude mixings but exhibit distinctly heavy tails for rare and large mixings. We explain how non-Gaussian, local spikes in the MHD magnetic field are mainly responsible for the heavy tail. Our results indicate that limits placed on ALPs using GRFs are conservative but that MHD models are necessary to reach the full potential of these searches., Comment: 8 pages, 3 figures

Chirality, or handedness, enters astrophysics in three distinct ways. Magnetic field and vortex lines tend to be helical and have a systematic twist in the northern and southern hemispheres of a star or a galaxy. Helicity is here driven by external factors. Chirality can also enter at the microphysical level and can then be traced back to the parity-breaking weak force. Finally, chirality can arise spontaneously, but this requires not only the presence of an instability, but also the action of nonlinearity. Examples can be found both in magnetohydrodynamics and in astrobiology, where homochirality among biomolecules probably got established at the origin of life. In this review, all three types of chirality production will be explored and compared., 20 pages, 6 figures, 1 table, to appear in the proceedings to Nobel Symposium 167: Chiral Matter, eds. E. Babaev, D. Kharzeev, M. Larsson, A. Molochkov, & V. Zhaunerchyk, World Scientific, in press

In this study we present a compressible test-field method (CTFM) for computing $\alpha$ effect and turbulent magnetic diffusivity tensors, as well as those relevant for mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method, and compare it to the quasi-kinematic test-field method, and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry, and also compare with the imposed-field method. We show that, for moderate imposed field strengths, the nonlinear CTFM (nCTFM) gives results in agreement with the imposed-field method. Comparison of different flavors of the nCTFM in the shear dynamo case also agree up to equipartition field strengths. Some deviations between the CTFM and SMHD variants exist. As a relevant physical application, we study non-helically forced shear flows, which exhibit large-scale dynamo action, and present a re-analysis of low Reynolds number, moderate shear systems, where we previously neglected the pressure gradient in the momentum equation, and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo action, while here it is self-consistently driven by purely kinetic forcing. The kinematic CTFM with general validity forms the core of our analysis. We still find no coherent shear-current effect, but do recover strong large-scale dynamo action that, according to our analysis, is driven through the incoherent effects., Comment: 23 pages, 11 figures, submitted to the Astrophysical Journal

We study the leading-order nonlinear gravitational waves (GWs) produced by an electromagnetic (EM) stress in reheating magnetogenesis scenarios. Both nonhelical and helical magnetic fields are considered. By numerically solving the linear and leading-order nonlinear GW equations, we find that the GW energy from the latter is usually larger. We compare their differences in terms of the GW spectrum and parameterize the GW energy difference due to the nonlinear term, $\Delta\mathcal{E}_{\rm GW}$, in terms of EM energy $\mathcal{E}_{\rm EM}$ as $\Delta\mathcal{E}_{\rm GW}=(\tilde p\mathcal{E}_{\rm EM}/k_*)^3$, where $k_*$ is the characteristic wave number, $\tilde p=0.84$ and $0.88$ are found in the nonhelical and helical cases, respectively, with reheating around the QCD energy scale, while $\tilde p=0.45$ is found at the electroweak energy scale. We also compare the polarization spectrum of the linear and nonlinear cases and find that adding the nonlinear term usually yields a decrease in the polarization that is proportional to the EM energy density. We parameterize the fractional polarization suppression as $|\Delta \mathcal{P}_{\rm GW}/\mathcal{P}_{\rm GW}|=\tilde r \mathcal{E}_{\rm EM}/k_*$ and find $\tilde r = 1.2 \times 10^{-1}$, $7.2 \times 10^{-4}$, and $3.2 \times 10^{-2}$ for the helical cases with reheating temperatures $T_{\rm r} = 300 {\rm TeV}$, $8 {\rm GeV}$, and $120 {\rm MeV}$, respectively. Prospects of observation by pulsar timing arrays, space-based interferometers, and other novel detection proposals are also discussed., Comment: 17 pages, 7 figures, 3 tables, to be submitted to PRD

If the alpha effect plays a role in the generation of the Sun's magnetic field, the field should show evidence of magnetic helicity of opposite signs at large and small length scales. Measuring this faces two challenges: (i) in weak-field regions, horizontal field measurements are unreliable because of the pi ambiguity, and (ii) one needs a truly global approach to computing helicity spectra in the case where one expects a sign reversal across the equator at all wavenumbers. Here we develop such a method using spin-2 spherical harmonics to decompose the linear polarization in terms of the parity-even and parity-odd E and B polarizations, respectively. Using simple one- and two-dimensional models, we show that the product of the spectral decompositions of E and B, taken at spherical harmonic degrees that are shifted by one, can act as a proxy of the global magnetic helicity with a sign that represents that in the northern hemisphere. We then apply this method to the analysis of solar synoptic vector magnetograms, from which we extract a pseudo-polarization corresponding to a "pi-ambiguated" magnetic field, i.e., a magnetic field vector that has no arrow. We find a negative sign of the global EB helicity proxy at spherical harmonic degrees of around 6. This could indicate a positive magnetic helicity at large length scales, but the spectrum fails to capture clear evidence of the well-known negative magnetic helicity at smaller scales. This method might also be applicable to stellar and Galactic polarization data., 11 pages, 7 figures, 5 tables, ApJ, in press

We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water-vapor mixing ratio, and the resulting supersaturation fields together with the Navier-Stokes equation. We find that the droplet-size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation fluctuation-induced broadening of droplet-size distributions enhances the collisional growth. This is contrary to classical (non-turbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet-size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation., Comment: revised version, 17 pages, 1 table, 13 figures

Simulations show for the first time how the magnetic fields that produce solar flares can extend out of the Sun by acquiring a twist., Comment: 2 pages, 2 figures, "Viewpoint" article on arXiv:1601.00749 by Chatterjee et al., to be published in Physics. Edited by Jessica Thomas

In the presence of strong density stratification, hydromagnetic turbulence attains qualitatively new properties: the formation of magnetic flux concentrations. We review here the theoretical foundations of this mechanism in terms of what is now called the negative effective magnetic pressure instability. We also present direct numerical simulations of forced turbulence in strongly stratified layers and discuss the qualitative and quantitative similarities with corresponding mean-field simulations. Finally, the relevance to sunspot formation is discussed., Comment: 23 pages, 13 figures, special issue "Focus on Turbulence in Astrophysical and Laboratory Plasmas" of New Journal of Physics, published

We show that in the presence of a harmonically varying magnetic field the fundamental or $f$-mode in a stratified layer is altered in such a way that it fans out in the diagnostic $k\omega$ diagram, but with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014) where a uniform magnetic field was considered, we employ here a nonuniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic fields. The expansion of the $f$-mode is stronger for fields confined to the layer below the surface. In some of those cases, the $k\omega$ diagram also reveals a new class of low frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the $f$-mode expansion might be a new and sensitive tool to determining subsurface magnetic fields with longitudinal periodicity., Comment: 6 pages, 4 figures, submitted to Astrophysical Journal Letters

We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field evolution for a turbulent flow. We emphasize the theoretical difficulties in explaining non-axisymmetric magnetic fields in galaxies and discuss the observational basis for such results in terms of rotation measure analysis. Next, we discuss nonlinear theory, the role of magnetic helicity conservation and magnetic helicity fluxes. This leads to the possibility that galactic magnetic fields may be bi-helical, with opposite signs of helicity and large and small length scales. We discuss their observational signatures and close by discussing the possibilities of explaining the origin of primordial magnetic fields., Comment: 28 pages, 15 figure, to appear in Lecture Notes in Physics "Magnetic fields in diffuse media", Eds. E. de Gouveia Dal Pino and A. Lazarian

In the presence of strong density stratification, turbulence can lead to a large-scale instability of a horizontal magnetic field if its strength is in a suitable range (within a few percent of the turbulent equipartition value). This instability is related to a suppression of the turbulent pressure so that the turbulence contribution to the mean magnetic pressure becomes negative. This results in the excitation of a negative effective magnetic pressure instability (NEMPI). This instability has so far only been studied for an imposed magnetic field. We want to know how NEMPI works when the mean magnetic field is generated self-consistently by an $\alpha^2$ dynamo, whether it is affected by global spherical geometry, and whether it can influence the properties of the dynamo itself. We adopt the mean-field approach which has previously been shown to provide a realistic description of NEMPI in direct numerical simulations. We assume axisymmetry and solve the mean-field equations with the Pencil-Code for an adiabatic stratification at a total density contrast in the radial direction of approximately 4 orders of magnitude. NEMPI is found to work when the dynamo-generated field is about 4% of the equipartition value, which is achieved through strong $\alpha$ quenching. This instability is excited in the top 5% of the outer radius provided the density contrast across this top layer is at least 10. NEMPI is found to occur at lower latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI can make the dynamo oscillatory with poleward migration. NEMPI is a viable mechanism for producing magnetic flux concentrations in a strongly stratified spherical shell in which a magnetic field is generated by a strongly quenched $\alpha$ effect dynamo., Comment: published in A&A

Studies of solar and stellar convection often employ simple polytropic setups using the diffusion approximation instead of solving the proper radiative transfer equation. This allows one to control separately the polytropic index of the hydrostatic reference solution, the temperature contrast between top and bottom, and the Rayleigh and Peclet numbers. We extend such studies by including radiative transfer in the gray approximation using a Kramers-like opacity with freely adjustable coefficients. We study the properties of such models and compare them with results from the diffusion approximation. We use the Pencil Code, which is a high-order finite difference code where radiation is treated using the method of long characteristics. The source function is given by the Planck function. The opacity is written as kappa=kappa_0 rho^a T^b, where b is varied from -3.5 to +5, and kappa_0 is varied by four orders of magnitude. We consider sets of one dimensional models and perform a comparison with the diffusion approximation. Except for the case where b=5, we find one-dimensional hydrostatic equilibria with a nearly polytropic stratification and a polytropic index close to n=(3-b)/(1+a), covering both convectively stable (n>3/2) and unstable (n, 16 pages, 17 figures, submitted to A&A

We report on turbulent dynamo simulations in a spherical wedge with an outer coronal layer. We apply a two-layer model where the lower layer represents the convection zone and the upper layer the solar corona. This setup is used to study the coronal influence on the dynamo action beneath the surface. Increasing the radial coronal extent gradually to three times the solar radius and changing the magnetic Reynolds number, we find that dynamo action benefits from the additional coronal extent in terms of higher magnetic energy in the saturated stage. The flux of magnetic helicity can play an important role in this context., 4 pages, 1 figure, To appear in proceedings of IAUS 302: Magnetic fields throughout stellar evolution (August 2013, Biarritz, France)

We consider mean-field dynamo models with fluctuating ��effect, both with and without shear. The ��effect is chosen to be Gaussian white noise with zero mean and given covariance. We show analytically that the mean magnetic field does not grow, but, in an infinitely large domain, the mean-squared magnetic field shows exponential growth of the fastest growing mode at a rate proportional to the shear rate, which agrees with earlier numerical results of Yousef et al (2008) and recent analytical treatment by Heinemann et al (2011) who use a method different from ours. In the absence of shear, an incoherent ��^2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third and fourth order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian., Mysteriously missing a line in introduction, ("Heinemann et al. (2011) have recently proposed a simple analytically tractable model ..") which has now been added

The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNS) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in formation of large-scale inhomogeneous magnetic structures from initial uniform magnetic field. Earlier investigations of this instability in DNS of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L^2/eta_t, where eta_t is the turbulent diffusivity and L is the scale of the domain. DNS are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number., Comment: 14 pages, 8 figures, submitted to special issue "Advances of European Solar Physics" in Solar Physics

At large magnetic Reynolds numbers, magnetic helicity evolution plays an important role in astrophysical large-scale dynamos. The recognition of this fact led to the development of the dynamical alpha quenching formalism, which predicts catastrophically low mean fields in open systems. Here we show that in oscillatory alpha-Omega dynamos this formalism predicts an unphysical magnetic helicity transfer between scales. An alternative technique is proposed where this artifact is removed by using the evolution equation for the magnetic helicity of the total field in the shearing--advective gauge. In the traditional dynamical alpha quenching formalism, this can be described as an additional magnetic helicity flux of small-scale fields that does not appear in homogeneous alpha-squared dynamos. In alpha-Omega dynamos, the alternative formalism is shown to lead to larger saturation fields than previously obtained with the traditional formalism., Comment: 9 pages, 7 figures, Published, ApJ

The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability, which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that a new instability develops as long as the Hall effect is present, which we therefore term as the Hall magneto-shear instability. As a particular case, we recover the so-called magneto-rotational instability and quantitatively assess the role of the Hall effect on its development and evolution., 25 pages, 12 figures, version accepted for publication in ApJ

In turbulent dynamos the production of large-scale magnetic fields is accompanied by a separation of magnetic helicity in scale. The large- and small-scale parts increase in magnitude. The small-scale part can eventually work against the dynamo and quench it, especially at high magnetic Reynolds numbers. A one-dimensional mean-field model of a dynamo is presented where diffusive magnetic helicity fluxes within the domain are important. It turns out that this effect helps to alleviate the quenching. Here we show that internal magnetic helicity fluxes, even within one hemisphere, can be important for alleviating catastrophic quenching., 3 pages, 6 figures, proceedings of IAU Symp. 274, Advances in Plasma Astrophysics, ed. A. Bonanno, E. de Gouveia dal Pino and A. Kosovichev

We study the ability of magnetic helicity expulsion to alleviate catastrophic $\alpha$-quenching in mean field dynamos in two--dimensional spherical wedge domains. Motivated by the physical state of the outer regions of the Sun, we consider $\alpha^2\Omega$ mean field models with a dynamical $\alpha$ quenching. We include two mechanisms which have the potential to facilitate helicity expulsion, namely advection by a mean flow ("solar wind") and meridional circulation. We find that a wind alone can prevent catastrophic quenching, with the field saturating at finite amplitude. In certain parameter ranges, the presence of a large-scale meridional circulation can reinforce this alleviation. However, the saturated field strengths are typically below the equipartition field strength. We discuss possible mechanisms that might increase the saturated field., Comment: consistent with the published version

The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is found to decay on a turbulent time scale regardless of the nature of the forcing and the value of the Reynolds number., Comment: 7 pages, 8 figures, Astron. Nachr. (accepted)

Autocatalysis is a fundamental concept, used in a wide range of domains. From the most general definition of autocatalysis, that is a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. The notion of autocatalysis covering a large variety of mechanistic realisations with very similar behaviors, it is proposed that the key signature of autocatalysis is its kinetic pattern expressed in a mathematical form., 10 pages, 5 figures, Submitted to J Phys Chem A

We investigate the emergence of a large-scale magnetic field. This field is dynamo-generated by turbulence driven with a helical forcing function. Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Time series of the magnetic field structure show recurrent plasmoid ejections., 2 pages, 2 figures, conference proceeding

Magnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress--and--relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space--time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results., 4 pages, 8 figures, To appear in the proceedings of the IAU273 "Physics of Sun and Star Spots"

The degree of intermittency of the magnetic field of a large-scale dynamo is considered. Based on simulations it is argued that there is a tendency for the field to become more diffuse and non-intermittent as the dynamo saturates. The simulations are idealized in that the turbulence is strongly helical and shear is strong, so the tendency for the field to become more diffuse is somewhat exaggerated. Earlier results concerning the effects of magnetic buoyancy are discussed. It is emphasized that the resulting magnetic buoyancy is weak compared with the stronger effects of simultaneous downward pumping. These findings are used to support the notion that the solar dynamo might operate in a distributed fashion where the near-surface shear layer could play an important role., Comment: 10 pages, 7 figures, to be published in Solar-stellar dynamos as revealed by helio- and asteroseismology, ed. M. Dikpati et al

Several aspects of mathematical astrobiology are discussed. It is argued that around the time of the origin of life the handedness of biomolecules must have established itself through an instability. Possible pathways of producing a certain handedness include mechanisms involving either autocatalysis or, alternatively, epimerization as governing effects. Concepts for establishing hereditary information are discussed in terms of the theory of hypercycles. Instabilities toward parasites and possible remedies by invoking spatial extent are reviewed. Finally, some effects of early life are discussed that contributed to modifying and regulating atmosphere and climate of the Earth, and that could have contributed to the highly oxidized state of its crust., Comment: 32 pages, 16 figures, to appear in Encyclopedia of Complexity and System Science

Some basic properties of the solar convection zone are considered and the use of helioseismology as an observational tool to determine its depth and internal angular velocity is discussed. Aspects of solar magnetism are described and explained in the framework of dynamo theory. The main focus is on mean field theories for the Sun's magnetic field and its differential rotation., 45 pages, 17 figures, to appear in Handbook of Solar-Terrestrial Environment, eds. Y. Kamide & A. C.-L. Chian, Springer

The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, . When $\bra{\rho}$ is in the range 1-5 x 10^{-24} g cm^{-3} the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 10^4 K, respectively. However, in all cases the resulting average pressure is independent of and just a little above the minimum value. For a constant heating rate of 0.015 erg g^{-1} s^{-1}, the mean pressure is around 24 x 10^{-14} dyn (corresponding to p/k_B ~ K cm^{-3}). Cool patches tend to coalesce into bigger ones. In all cases investigated there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km/s are obtained, the resulting dissipation rates rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10^{-14} dyn, corresponding to p/k_B ~ 2170 K cm^{-3}. This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability., Comment: 10 pages, 13 figures

Arguments are presented in favor of the idea that the solar dynamo may operate not just at the bottom of the convection zone, i.e. in the tachocline, but it may operate in a more distributed fashion in the entire convection zone. The near-surface shear layer is likely to play an important role in this scenario., 4 pages, 2 figures, in Solar activity: exploration, understanding and prediction, ed: H. Lundstedt, ESA, ESTEC Noordwijk

Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic., Comment: 19 pages, 15 figures, some errors corrected, Astron. Nach. (submitted). For higher quality images, see http://www.nordita.dk/~brandenb/papers/stellardyn/

The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location and that the solar dynamo may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo disposing of its excess small scale magnetic helicity., Comment: 6 pages, 3 figures, in Solar MHD: Theory and Observations, eds: J. W. Leibacher, H. Uitenbroek, & R. F. Stein, Astron. Soc. Pac. Conf. Ser

The effect of compressibility on the onset of nonhelical turbulent dynamo action is investigated using both direct simulations as well as simulations with shock-capturing viscosities, keeping however the regular magnetic diffusivity. It is found that the critical magnetic Reynolds number increases from about 35 in the subsonic regime to about 70 in the supersonic regime. In the high resolution direct simulations the shock structures are much sharper than in the low resolution shock-capturing simulations. Nevertheless, the magnetic field looks roughly similar in both cases and does not show shock structures. Similarly, the onset of dynamo action is not significantly affected by the shock-capturing viscosity., 6 pages

Three-dimensional turbulence simulations are used to show that the turbulent root mean square velocity is an upper bound of the speed of turbulent diffusion. There is a close analogy to magnetic diffusion where the maximum diffusion speed is the speed of light. Mathematically, this is caused by the inclusion of the Faraday displacement current which ensures that causality is obeyed. In turbulent diffusion, a term similar to the displacement current emerges quite naturally when the minimal tau approximation is used. Simulations confirm the presence of such a term and give a quantitative measure of its relative importance., 4 pages, 3 figures, to appear in Progress in Turbulence, Eds. M. Oberlack, J. Peinke, A. Kittel, S. Barth. Springer-Verlag, 2004

The excitation of gravity waves by penetrative convective plumes is investigated using 2D direct simulations of compressible convection. The oscillation field is measured by a new technique based on the projection of our simulation data onto the theoretical g-modes solutions of the associated linear eigenvalue problem. This allows us to determine both the excited modes and their corresponding amplitudes accurately., Comment: 4 pages, 2 figures, proceeding of the Porto conference "Asteroseismology Across the HR Diagram", edited by M.J. Thompson, M.S Cunha & M.J.P.G. Monteiro, Kluwer Academic Publishers (also in Ap&SS, 284, 237)

The dimensionless kinetic energy dissipation rate C_epsilon is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number Re_lambda range is 20 < Re_lambda < 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re_lambda dependence of C_epsilon abates when Re_lambda approx. 100 after which C_epsilon slowly approaches approx 0.5 a value slightly different to previously reported simulations but in good agreement with experimental results. If C_epsilon is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +-30%. This may explain the spread in results from previously published estimates of C_epsilon., 7 pages, 7 figures. Submitted to Phys. Rev. E

Considerable progress has been made in understanding the hydrodynamics, but only to a certain extent the magnetohydrodynamics, of shaping bipolar outflows forming protoplanetary nebulae (PPNs) and planetary nebulae (PNs). In particular, Blackman et al. (2001b,2001a) point out two problems related to the formation of PNs and PPNs, regarding the formation of multipolar structures and the origin of the nebulae. They propose a solution by giving a semi-quantitative physical model which should be investigated by numerical simulations., 4 pages, 6 figures, APN3 conference proceedings

The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable forms of the nonlinearity. The crucial discriminant is the magnetic helicity, which is known to evolve only on a slow resistive time scale in the limit of large magnetic Reynolds number. Particular emphasis is put on the possibility of memory effects, which means that an additional explicitly time-dependent equation for the nonlinearity is solved simultaneously with the mean-field equations. This approach leads to better agreement with the simulations, while it would also produce more favorable agreement between models and stellar dynamos., 30 pages, 16 figures, to appear in "Simulations of magnetohydrodynamic turbulence in astrophysics" eds. T. Passot & E. Falgarone, Springer Lecture Notes in Physics

The advantages of high-order finite difference scheme for astrophysical MHD and turbulence simulations are highlighted. A number of one-dimensional test cases are presented ranging from various shock tests to Parker-type wind solutions. Applications to magnetized accretion discs and their associated outflows are discussed. Particular emphasis is placed on the possibility of dynamo action in three-dimensional turbulent convection and shear flows, which is relevant to stars and astrophysical discs. The generation of large scale fields is discussed in terms of an inverse magnetic cascade and the consequences imposed by magnetic helicity conservation are reviewed with particular emphasis on the issue of alpha-quenching., Comment: 68 pages, 36 figures, to be published in "The Fluid Mechanics of Astrophysics and Geophysics", Vol. 8, ed. Antonio Ferriz-Mas

Helicity, a measure of the linkage of flux lines, has subtle and largely unknown effects upon dynamics. Both magnetic and hydrodynamic helicity are conserved for ideal systems and could suppress nonlinear dynamics. What actually happens is not clear because in a fully three-dimensional system there are additional channels whereby intense, small-scale dynamics can occur. This contribution shows one magnetic and one hydrodynamic case where for each the presence of helicity does not suppress small-scale intense dynamics of the type that might lead to reconnection., 8 pages, 5 figs, (Quantized Vortex Dynamics and Superfluid Turbulence, Eds. C.F. Barenghi, R.J. Donnelly, W.F. Vinen

We perform direct numerical simulations of three-dimensional freely decaying magnetohydrodynamic (MHD) turbulence. For helical magnetic fields an inverse cascade effect is observed in which power is transfered from smaller scales to larger scales. The magnetic field reaches a scaling regime with self-similar evolution, and power law behavior at high wavenumbers. We also find power law decay in the magnetic and kinematic energies, and power law growth in the characteristic length scale of the magnetic field., 6 pages, 5 figures, minor changes to match published version

Analysis using new calculations with 3 times the resolution of the earlier linked magnetic flux tubes confirms the transition from singular to saturated growth rate reported by Grauer and Marliani \cite{GrauerMar99} for the incompressible cases is confirmed. However, all of the secondary tests point to a transition back to stronger growth rate at a different location at late times. Similar problems in ideal hydrodynamics are discussed, pointing out that initial negative results eventually led to better initial conditions that did show evidence for a singularity of Euler. Whether singular or near-singular growth in ideal MHD is eventually shown, this study could have bearing on fast magnetic reconnection, high energy particle production and coronal heating., 5 pages, 5 figures

The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field strength exceeds the equipartition field strength for large scale separation. However, helicity conservation controls the speed at which this final state is reached. In the presence of open boundaries magnetic helicity fluxes out of the domain are possible. This reduces the timescales of the field growth, but it also tends to reduce the maximum attainable field strength., Comment: 8 pages, 4 figs, to be published in "Dynamo and dynamics, a mathematical challenge", Ed: P. Chossat, Nato ASI Series

In a recent work (Covas et al. 1997), the behaviour and the robustness of truncated $\alpha\Omega$ dynamos with a dynamic $\alpha$ were studied with respect to a number of changes in the driving term of the dynamic $\alpha$ equation, which was considered previously by Schmalz and Stix (1991) to be of the form $\sim A_{\phi}B_{\phi}$. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form $\alpha|B|^2$. We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the sun., Comment: Figures included. Also in http://www.maths.qmw.ac.uk/~eoc

We investigate the behaviour of $\alpha\Omega$ dynamos with a dynamic $\alpha$, whose evolution is governed by the imbalance between a driving and a damping term. We focus on truncated versions of such dynamo models which are often studied in connection with solar and stellar variability. Given the approximate nature of such models, it is important to study how robust they are with respect to reasonable changes in the formulation of the driving and damping terms. For each case, we also study the effects of changes of the dynamo number and its sign, the truncation order and initial conditions. Our results show that changes in the formulation of the driving term have important consequences for the dynamical behaviour of such systems, with the detailed nature of these effects depending crucially on the form of the driving term assumed, the value and the sign of the dynamo number and the initial conditions. On the other hand, the change in the damping term considered here seems to produce little qualitative effect., Comment: Figures included. Also in http://www.maths.qmw.ac.uk/~eoc