D. D. Sokoloff

Magnetic Field and Rotation in Lower Main-Sequence Stars: An Empirical Time-Dependent Magnetic Bode's Relation?

We find a significant correlation between the magnetic and rotational moments for a sample of 112 lower main-sequence stars. The rotational moment is calculated from measurements of the rotation period in most of the stars (not from the projected rotational velocity inferred from Doppler broadening). The magnetic moment is computed from a database of homogeneous measurements of the mean level of Ca II H and K emission fluxes sampled for most of the stars over an interval of 25 yr. The slope connecting the logarithm of the magnetic moment and the logarithm of the rotational moment is about +0.5-0.6, with a Pearson correlation coefficient of about +0.9. The scatter of points from the mean relation has a component that is natural and caused by decade-long surface variability.

Systematic bias in interstellar magnetic field estimates

Faraday rotation of the polarization plane in magnetized thermal plasma provides one of the most efficient methods to deduce regular magnetic fields from radio astronomical observations. Since the Faraday rotation measure RM is proportional to an integral, along the line of sight, of magnetic field weighted with thermal electron density, RM is believed to yield the regular magnetic field averaged over large volume. Here we show that this is not the case in a turbulent medium where fluctuations in magnetic field and electron density are not statistically independent, and so contribute to RM. For example, in the case of pressure equilibrium, magnetic field can be anticorrelated with plasma density to produce a negative contribution. As a result, the strength of the regular magnetic field obtained from RM can be underestimated if the fluctuations in electron density and magnetic field are neglected. The anticorrelation also reduces the standard deviation of RM. We further discuss the effect of the positive correlations where the standard treatment of RM leads to an overestimated magnetic field. Because of the anisotropy of the turbulent magnetic field, the regular magnetic fields strength, obtained from synchrotron emission using standard formulae, can be overestimated. A positive correlation between cosmic-ray number density and magnetic field leads to an overestimate of the strengths of the regular and total fields. These effects can explain the difference between the strengths of the regular Galactic magnetic field as indicated by RM and synchrotron emissivity data and reconcile the magnetic field strength in the Solar vicinity with typical strength of regular magnetic fields in external galaxies.

Time scales and trends in the central England temperature data (1659–1990): A wavelet analysis

We have applied the standard wavelet and the adaptive wavelet transform algorithms to the record of the Central England Temperature (CET) from 1659–1990. Peaks in the CET spectra include 7.5±1.0 yr, 14.4±1.0 yr, 23.5±2.0 yr, as well as a previously unreported variation at 102±15 yr. Our wavelet analysis of CET agrees with previous results from Singular Spectrum Analysis (SSA) by Plaut et al. [1995] and gives additional results of variability on longer timescales. The interdecadal and century-scale variability in CET is strongly dependent on the interval of analysis. Estimates of a data trend are also shown to be sensitive to the cutoff timescale of the filter. A cooling of ≈ 0.3°C during 1659–1720 is found relative to the temperatures during the 1800s. The complex time dependence of the actual data cautions against using model-derived representations of natural variability on such long timescales.

Galactic dynamo and helicity losses through fountain flow

Aims. Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. Methods. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic α-effect is explored. Results. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.

Kinematic dynamo problem in a linear velocity field

A magnetic field is shown to be asymptotically ( t → ∞) decaying in a flow of finite conductivity with v = Cr , where C = C ζ ( t ) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Evolution of magnetic fields in galaxies and future observational tests with the Square Kilometre Array

Aims. In the context of models of galaxy formation and evolution, we investigate the cosmological evolution of large- and small-scale magnetic fields inside galaxies. Methods. We use the dynamo theory to derive the timescales of amplification and ordering of magnetic fields in disk and puffy galaxies. Turbulence in protogalactic halos generated by thermal virialization can drive an efficient turbulent dynamo. Results from simulations of hierarchical structure formation cosmology provide a tool to develop an evolutionary model of regular magnetic fields coupled with galaxy formation and evolution. Results. The turbulent (small-scale) dynamo was able to amplify a weak seed magnetic field in halos of protogalaxies to a few μG strength within a few 10 8 yr. This turbulent field served as a seed to the mean-field (large-scale) dynamo. Galaxies similar to the Milky Way formed their disks at z ≈ 10 and regular fields of μG strength and a few kpc coherence length were generated within 2 Gyr (at z ≈ 3), but field-ordering on the coherence scale of the galaxy size required an additional 6 Gyr (at z ≈ 0.5). Giant galaxies formed their disks at z ≈ 10, allowing more efficient dynamo generation of strong regular fields (with kpc coherence length) already at z ≈ 4. However, the age of the Universe is short for fully coherent fields in giant galaxies larger than 15 kpc to have been achieved. Dwarf galaxies should have hosted fully coherent fields at z ≈ 1. After a major merger, the strength of the turbulent field is enhanced by a factor of a few. Conclusions. This evolutionary scenario can be tested by measurements of polarized synchrotron emission and Faraday rotation with the planned Square Kilometre Array (SKA). We predict an anticorrelation between galaxy size and ratio between ordering scale and galaxy size. Weak regular fields (small Faraday rotation) in galaxies at z < 3 are signatures of major mergers. Undisturbed dwarf galaxies should host fully coherent fields, giving rise to strong Faraday rotation signals. Radio observations may serve as a clock for measuring the time since the last major merger.

Current Status of Turbulent Dynamo Theory. From Large-Scale to Small-Scale Dynamos

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.

Magnetic helicity evolution during the solar activity cycle: Observations and dynamo theory

We study a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic α -quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstrate behaviour comparable with the observed phenomenology, provided that a suitable set of governing dynamo parameters is chosen. On the other hand, the observational data are shown to be rich enough to reject some other sets of governing parameters. We conclude that, in spite of the very preliminary state of the observations and the crude nature of the model, the idea of using observational data to constrain our ideas concerning magnetic field generation in the framework of the solar dynamo appears promising.

The Maunder minimum (1645–1715) was indeed a grand minimum: A reassessment of multiple datasets

Aims. Although the time of the Maunder minimum (1645–1715) is widely known as a period of extremely low solar activity, it is still being debated whether solar activity during that period might have been moderate or even higher than the current solar cycle #24. We have revisited all existing evidence and datasets, both direct and indirect, to assess the level of solar activity during the Maunder minimum. Methods. We discuss the East Asian naked-eye sunspot observations, the telescopic solar observations, the fraction of sunspot active days, the latitudinal extent of sunspot positions, auroral sightings at high latitudes, cosmogenic radionuclide data as well as solar eclipse observations for that period. We also consider peculiar features of the Sun (very strong hemispheric asymmetry of the sunspot location, unusual differential rotation and the lack of the K-corona) that imply a special mode of solar activity during the Maunder minimum. Results. The level of solar activity during the Maunder minimum is reassessed on the basis of all available datasets. Conclusions. We conclude that solar activity was indeed at an exceptionally low level during the Maunder minimum. Although the exact level is still unclear, it was definitely lower than during the Dalton minimum of around 1800 and significantly below that of the current solar cycle #24. Claims of a moderate-to-high level of solar activity during the Maunder minimum are rejected with a high confidence level.

Structures in the rotation measure sky

Coherent structures in the distribution of the Faraday rotation measure of extragalac-tic radio sources are isolated using wavelet transformation technique. A new algorithm of wavelet analysis for data points nonuniformly distributed on a sphere is developed and implemented. Signatures of the magnetic fields in the local (Orion) spiral arm, the Sagittarius and Carina arms, the synchrotron Loop I and, possibly, the Perseus arm have been revealed using the RM catalogues of Simard-Normandin et al. (1981, 551 source) and Broten et al. (1988, 663 sources). Unlike earlier analyses of the RM sky, our approach has allowed us to assess the stability of the results with respect to modifications of the data sample. Only the aforementioned features remain stable under mild sample modifications. We consider separately low-latitude sources at |b| < 10 • and, using the model of electron density distribution of Cordes et al. (1991), we estimate magnetic field strength by comparing the model wavelet transform with that of the real data. Independent estimates of the mean magnetic field strength in the Orion arm using low-and high-latitude sources converge to 1.4 ± 0.3 µG. Rotation measures of low-latitude sources provide a clear indication of a magnetic field reversal at a distance 0.6–1 kpc towards the Galactic centre. Our analysis has revealed for the first time the extension of the reversal in the Carina arm. Low-latitude sources from the catalogue of Broten et al. (1988) indicate a magneto-ionic structure in the direction of the Perseus arm with the magnetic field direction reversed with respect to that in the Orion arm. The average pitch angle of magnetic field in the nearby spiral arms is 15 • , and the mean field strength in the Sagittarius–Carina and Perseus arms is 1.7 ± 0.3 µG and 1.4 ± 1.2 µG, respectively. The line-of-sight magnetic field in Loop I is estimated as 0.9 ± 0.3 µG. We find firm evidence of a dominant even symmetry of the local mean magnetic field with respect to the galactic equator. Our results are compatible with a moderate large-scale north-south asymmetry, with magnetic field in the southern hemisphere being stronger in a region of at least 3 kpc in size. It cannot be excluded, however, that the asymmetry is local and results from vertical bending of magnetic lines in a region of about 400 pc in size, with the Sun being located close to the top of a magnetic loop …