Modeling a Maunder minimum

We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3–3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the ¹⁰Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extragalactic jets on subpc and large scales

Jets can be probed in their innermost regions (d≲0.1 pc) through the study of the relativistically boosted emission of blazars. On the other extreme of spatial scales, the study of structure and dynamics of extragalactic relativistic jets received renewed impulse after the discovery, made by Chandra, of bright X-ray emission from regions at distances larger than hundreds of kpc from the central engine. At both scales it is thus possible to infer some of the basic parameters of the flow (speed, density, magnetic field intensity, power). After a brief review of the available observational evidence, I discuss how the comparison between the physical quantities independently derived at the two scales can be used to shed light on the global dynamics of the jet, from the innermost regions to the hundreds of kpc scale.     

General properties of magnetic CP stars

We present the review of our previous studies related to observational evidence of the fossil field hypothesis of formation and evolution of magnetic and non-magnetic chemically peculiar stars. Analysis of the observed data shows that these stars acquire their main properties in the process of gravitational collapse. In the non-stationary Hayashi phase, a magnetic field becomes weakened and its configuration complicated, but the fossil field global orientation remains. After a non-stationary phase, relaxation of young star’s tangled field takes place and by the time of joining ZAMS (Zero Age Main Sequence) it is generally restored to a dipole structure. Stability of dipole structures allows them to remain unchanged up to the end of their life on the Main Sequence which is 10⁹ years at most.     

Magnetic Field Diagnostics and Spatio-Temporal Variability of the Solar Transition Region

Magnetic field diagnostics of the transition region from the chromosphere to the corona faces us with the problem that one has to apply extreme-ultraviolet (EUV) spectro-polarimetry. While for the coronal diagnostics techniques already exist in the form of infrared coronagraphy above the limb and radio observations on the disk, one has to investigate EUV observations for the transition region. However, so far the success of such observations has been limited, but various current projects aim to obtain spectro-polarimetric data in the extreme UV in the near future. Therefore it is timely to study the polarimetric signals we can expect from these observations through realistic forward modeling. We employ a 3D magneto-hydrodynamic (MHD) forward model of the solar corona and synthesize the Stokes I and Stokes V profiles of C?iv (1548 Å). A signal well above 0.001 in Stokes V can be expected even if one integrates for several minutes to reach the required signal-to-noise ratio, and despite the rapidly changing intensity in the model (just as in observations). This variability of the intensity is often used as an argument against transition region magnetic diagnostics, which requires exposure times of minutes. However, the magnetic field is evolving much slower than the intensity, and therefore the degree of (circular) polarization remains rather constant when one integrates in time. Our study shows that it is possible to measure the transition region magnetic field if a polarimetric accuracy on the order of 0.001 can be reached, which we can expect from planned instrumentation.     

Hydrogen molecular ion in the magnetic field of a neutron star

A two-dimensional potential energy surface of an H ₂ ⁺ molecular ion is calculated for the case of the strong magnetic field of the neutron starB=10¹¹–10¹³ G. It is shown that the dependence of the potential energy from the angle between the magnetic field direction and the internuclear axis becomes very sharp as the magnetic field increases. The obtained potential energy surfaces can be used for studying the vibrational-rotational structure of the H ₂ ⁺ spectrum in a strong magnetic field and the development of the observational methods for the determination of the magnetic field of a neutron star.     

Magnetic helicity in stellar dynamos: new numerical experiments

The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios can give rise to different structures of the mean field which are obtained at early times, but the final saturation field strength is still decreasing with decreasing resistivity. In the presence of shear, cyclic magnetic fields are found whose period is increasing with decreasing resistivity, but the saturation energy of the mean field is in strong super‐equipartition with the turbulent energy. It is shown that artificially induced losses of small scale field of opposite sign of magnetic helicity as the large scale field can, at least in principle, accelerate the production of large scale (poloidal) field. Based on mean field models with an outer potential field boundary condition in spherical geometry, we verify that the sign of the magnetic helicity flux from the large scale field agrees with the sign of α. For solar parameters, typical magnetic helicity fluxes lie around 10⁴⁷ Mx² per cycle.     

Influence of accelerated particles on the large-scale magnetic field in young supernova remnants

We offer a possible explanation for the observational data on the magnetic-field structure in young supernova remnants (SN 1006, Tycho, Kepler, Cas A) that have been obtained by analyzing the polarizations of electromagnetic radiation in the radio, infrared, and other wavelength ranges. The authors of observational works interpret these data as evidence that the ordered magnetic-field component is predominantly radial, but it can be much smaller in amplitude than the stochastic field component that accounts for the bulk of the total magnetic energy. We calculate the magnetic field in supernova remnants by taking into account the shock compression of the primary field and the generation of a large-scale magnetic field by the particles accelerated at the shock front. The assumption that the field in the supernova remnant is the explosion-compressed primary field near the star is inconsistent with observational data, because the tangential (relative to the shock front) field component perpendicular to the radius must prevail in this case. However, allowing for the generation of an additional magnetic field by the electric current of the particles accelerated by a strong shock front leads us to conclude that the field components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. Such a field configuration for uniform injection does not lead to the generation of an additional magnetic field, and, in this sense, it is stable. This explains the data on the radial direction of the ordered field component. As regards the stochastic field component, we show that it is effectively generated by accelerated particles if their injection into acceleration at the shock front is nonuniform along the front. Injection nonuniformity can be caused by upstream density nonuniformities. A relative density nonuniformity of the order of several percent is enough for an observable magnetic field with scales on the order of the density nonuniformity scales to be generated.     

Flip-Flops as Observational Signatures of Different Dynamo Modes in Cool Stars

Cool, rapidly rotating stars exhibit enhanced magnetic activity with cyclic behavior on various time scales. In particular, the longitude of the dominant activity region switches quasi-periodically by 180^∘, which is known as the “flip-flop” phenomenon. In the present paper we introduce a new approach for the interpretation of stellar cycles based on light curve modeling with dipole and quadrupole dynamo modes. We discuss the observational signatures of different combinations of the dynamo modes. The proposed simple model is able to reproduce the basic properties of long-term photometric behavior of active stars and allows us to study different mechanisms resulting in flip-flops.     

High-Resolution Simulations of Nonhelical MHD Turbulence

According to the kinematic theory of nonhelical dynamo action, the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case, the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 1024³ meshpoints) with no large-scale imposed field, we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about five times larger than the forcing wavenumber. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of two to three. Both spectra are approximately parallel. The total energy spectrum seems to be close to k ^?3/2, but there is a strong bottleneck effect and we suggest that the asymptotic spectrum is instead k ^?5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ₂ = 0.70, suggesting a k ^?1.70 spectrum. The third-order structure function scaling exponent is very close to unity,—in agreement with Goldreich–Sridhar theory. Adding an imposed field tends to suppress the small-scale magnetic field. We find that at large scales the magnetic energy spectrum then follows a k ^?1 slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic energy spectra.     

Heating and cooling of the thermal X-ray plasma in solar flares

Characteristic times for heating and cooling of the thermal X-ray plasma in solar flares are estimated from the time profile of the thermal X-ray burst and from the temperature, emission measure and over-all length scale of the flare-heated plasma at thermal X-ray maximum. The heating is assumed to be due to magnetic field reconnection, and the cooling is assumed to be due to heat conduction and radiation. Temperatures and emission measures derived from UCSD OSO-7 X-ray flare observations are used, and length scales are obtained from Big Bear large-scale Hα filtergrams for 17 small (subflare to Class 1) flares. The empirical values obtained for the characteristic times imply (1) that flares are produced by magnetic field reconnection, (2) that conduction cooling of the thermal X-ray plasma dominates radiative cooling and (3) that reconnection heating and conduction cooling of the thermal X-ray plasma are approximately in balance at thermal X-ray maximum. This model in combination with the data gives estimates for the electron number density (10¹⁰–10¹¹ cm^?3) and the magnetic field strength (10–100 G) in the thermal X-ray plasma and for the total thermal energy generated in a subflare (≈ 10³⁰ erg for an Hα area ≈ 1 square degree) which agree with previous observational and theoretical estimates obtained by others.     

On the appearance of magnetic flux in the solar photosphere

Ideas and models for the appearance of photospheric magnetic structure are confronted with observational data. Some findings are: The magnetic flux emerging in an active region consists of a bundle of flux tubes which were already concentrated before penetrating into the photosphere. A model of a rising bunch of flux tubes joining into a few strands at larger depths describes the coalescence of spots near the leading and following edges of the active region while more flux may surface near the center of the region. There is no observational evidence for appreciable helical twists in the flux bundles.Throughout the region's lifetime the magnetic elements move coherently, the whole magnetic structure rotates faster than the quiet photosphere. In active regions the convective flow at scales larger than the granulation is arrested by the magnetic structure. The long-lived supergranular cells around spots and in the enhanced network in turn determine the decay properties of spots and facular clusters. The modulation of the convective flow by the magnetic structure explains the slow dispersal of faculae.The hierarchy of magnetic elements (sunspots-pores-knots-facular clusters-facular points) may be explained by a set of magnetostatic flux tube models in the top of the convection zone. The underlying assumptions are that the heat flow along the magnetic field is reduced and that there is no heat exchange across the field except by radiation.A tentative model is proposed to account for the amplification, ascent and emergence of intense flux bundles. The assumptions are: (i) the field is concentrated in toroidal bundles by differential rotation, (ii) in the deep convection zone flux bundles are contained by the external turbulent pressure, and (iii) for field strengths up to the equipartition value efficient lateral heat exchange is possible. After a loop has surfaced radiative cooling and subsequent convective downflow reduce the temperature in the top of the flux tubes which then contract to field strengths well above the local equipartition value. There the heat flow is channelled along the field, which creates the conditions for the magnetostatic flux tube models without requiring a blocking of the heat flow somewhere within the tubes.The paper contains a brief review on the evolution of the magnetic field from the emergence in active regions up to the enigmatic disappearance, and a list of topics for further observational investigation.     

Comment on ‘average photospheric poloidal and toroidal magnetic field components near solar minimum’ by Duvall et al.

We discuss the dynamical interpretation of evidence for an azimuthal tilt of the global magnetic field from the radial direction at the photosphere. We point out that the Reynolds stresses of supergranular convective motions might produce the required small tilt of intense flux tubes, without implying an unacceptably large momentum flux across the photospheric surface into the solar wind. Our calculations lead us to conclude that there is little reason, at present, to infer (Duvall et al., 1979) a separate low intensity constituent of the global magnetic field, from the observational evidence for an azimuthal tilt. More precise measurements of the vertical component of supergranular motions would be useful in determining the actual torque exerted by the Reynolds stresses on the magnetic field.     

The solar dynamo

The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.Received: 5 May 2003, Published online: 15 July 2003     

X-ray Radiation Mechanisms and the Beaming Effect of Hot Spots and Knots in AGN Jets

The observed broadband spectral energy distributions (SEDs) of 22 hot spots and 45 knots are modelled with single-zone lepton models. Considering the sources at rest, the X-rays of some hot spots can be explained by the SSC model with magnetic field being consistent with the equipartition magnetic field in magnitude of order 1, but at the same time an unreasonably low magnetic field is required to model the X-rays for all knots. When considering the relativistic bulk motion of the sources, the IC/CMB model well explains the X-ray emission for most of them under the equipartition condition. We show that the ratio of observational luminosity R _L is tentatively correlated with the co-moving equipartition magnetic field $B_{\rm eq}^{\prime}$ and the beaming factor ??. These facts suggest that the observational differences of the X-rays from the knots and hot spots may be mainly due to the differences in the Doppler boosting effect and the co-moving magnetic field of the two kinds of source.     

Small-scale magnetic structures on the Sun

Summary The Sun provides us with a unique astrophysics laboratory for exploring the fundamental processes of interaction between a turbulent, gravitationally stratified plasma and magnetic fields. Although the magnetic structures and their evolution can be observed in considerable detail through the use of the Zeeman effect in photospheric spectral lines, a major obstacle has been that all magnetic structures on the Sun, excluding sunspots, are smaller than what can be resolved by present-day instruments. This has led to the development of indirect, spectral techniques (combinations of two or more polarized spectral lines), which overcome the resolution obstacle and have revealed unexpected properties of the small-scale magnetic structures. Indirect empirical and theoretical estimates of the sizes of the flux elements indicate that they may be within reach of planned new telescopes, and that we are on the verge of a unified understanding of the diverse phenomena of solar and stellar activity.In the present review we describe the observational properties of the smallscale field structures (while indicating the diagnostic methods used), and relate these properties to the theoretical concepts of formation, equilibrium structure, and origin of the surface magnetic flux.On leave from Institute of Astronomy, ETH-Zentrum, CH-8092 Zürich, SwitzerlandThe National Center for Atmospheric Research is sponsored by the National Science Foundation     

A Fast Current-Field Iteration Method for Calculating Nonlinear Force-Free Fields

Existing methods for calculating nonlinear force-free magnetic fields are slow, and are likely to be inadequate for reconstructing coronal magnetic fields based on high-resolution vector magnetic field data from a new generation of spectro-polarimetric instruments. In this paper a new implementation of the current-field iteration method is presented, which is simple, fast, and accurate. The time taken by the method scales as N ⁴, for a three-dimensional grid with N ³ points. The method solves the field-updating part of the iteration by exploiting a three-dimensional Fast Fourier Transform solution of Ampere’s law with a current density field constructed to satisfy the required boundary conditions, and uses field line tracing to solve the current-updating part of the iteration. The method is demonstrated in application to a known nonlinear force-free field and to a bipolar test case.     

Remark on the Mean Energy of the Fluctuating Magnetic Field in Mean-field Magnetohydrodynamics

A relation between the mean square of the fluctuating magnetic field, B′ , and the square of the mean magnetic field, B̄ , is derived for the case of homogeneous isotropic turbulence. The second order correlations approximation is used under the assumption that the space and time scales L̄ and T̄ of the mean field are large compared with the scales L and T of the fluctuations. BOCHNER 's theorem manifests itself as a guarantee for the ratio B̄′²|B̄² to be non-negative.     

Strong magnetic field helical Čerenkov effect with some astrophysica implications

It is at very strong magnetic fields that the helical Čerenkov effect, originating from the electron guiding center for an electron in helical motion in a magnetic field which is superimposed on a dielectric medium, resembles most closely the ordinary Čerenkov effect. In the absence of extremely strong magnetic fields in the laboratory, we turn our attention to the neutron stars (pulsar) and supernovae which can have magnetic fields whose values can easily be in the range of 10⁵ — 10⁹ T. The medium in which these magnetic fields reside is likely to be an ionized medium; that is, a plasma, which, as usual, may be assumed to be dominated by electrons. Here we wish to argue that in such a strong magnetic field dominated medium, at least on a classical level, radiation process associated with the helical Čerenkov radiation could be rather important.     

Small-scale stochastic structure of the solar magnetic field

The small-scale (～10″) stochastic properties of the solar magnetic field B are analyzed in terms of the two-dimensional model of a fractal Brownian process (the mean square of the difference between the field strengths at two points separated by a distance D is proportional to D ^2H ). Digitized solar magnetograms with a 2″ resolution are used to determine the standard deviation s of the magnetic field and the exponents H at various levels of |B|. It has been established that the transition from the background magnetic field to the fields of an active region occurs near 25–50 G. A dependence of the exponent H on the magnetic field amplitude has been derived. The exponent H for the background magnetic field has been found to be much smaller than that for the fields of an active region. The relationship of the results obtained to certain fundamental properties of plasma in a magnetic field is discussed.     

Stellar polarization and the structure of the magnetic field of our galaxy

The stellar polarization data have been examined using a new catalogue containing accurate stellar distances. On the assumption of a magnetic alignment hypothesis, correlations on the larger distance scale indicate the existence of a dominant regular magnetic field, although its characteristics are difficult to determine. Within 500 pc its direction is towardsl45° and beyond this towardsl60°, though it is clear that such a longitudinal model is too simple. There is also some evidence for an inclination of this field to the galactic plane. The distribution of the polarization vectors away from the galactic plane has been examined and it is proposed that the two largest loop structures, previously identified as Supernova remnants, are linked by the regular field. Incremental polarization maps have been produced but they show little correlation with the spiral structure. The polarization appears to be saturated at about 1 kpc from the Sun, which is explained as the result of an observational selection effect. On the smaller distance scales an autocorrelation analysis in different directions has revealed no obvious coherence in the irregular component on scales greater than 50 pc.