Peter Frick

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.

Wavelet Analysis of Stellar Chromospheric Activity Variations

Observations of chromospheric activity variations for some lower main-sequence stars from the Mount Wilson Observatorys HK project reveal a cyclic behavior comparable to the sunspot cycle. Even in the relatively short interval that they have been observed, those stars show stellar cycles and other features, like grand minima. The quasi-periodic nature of such variations is not completely compatible with the standard Fourier analysis, so we applied a wavelet analysis to study the nature of regularities in the data. We computed wavelet transforms and energy spectra for the 25 yr records of surface magnetic activity in four stars: HD 3651, HD 10700, HD 10476, and HD 201091. We present a modified wavelet technique that is suitable for analysis of data with gaps and find that the common aliasing problems due to the finite length of the observations and irregularly spaced gaps between data can be reduced on both large and small scales by applying this algorithm.

Analysis of spiral arms using anisotropic wavelets: gas, dust and magnetic fields in M51

Context. The origin of the spiral pattern of magnetic fields in disc galaxies is an open question. Aims. Comparison of the regular magnetic field orientation with the gaseous spiral arm pitch angles can tell us whether spiral shock compression is responsible for the magnetic spirals. We also wish to see whether the ridges of different components of the ISM show the large-scale, systematic shifts expected from density wave theory. Methods. We have developed a technique of isolating elongated structures in galactic images, such as spiral arms, using anisotropic wavelets and apply this to maps of the CO, infrared and radio continuum emission of the grand-design spiral galaxy M 51. Results. Systematic shifts between the ridges of CO, infrared and radio continuum emission that are several kpc long are identified, as well as large variations in pitch angle along spiral arms, of a few tens of degrees. We find two types of arms of polarized radio emission: one has a ridge close to the ridge of CO, with similar pitch angles for the CO and polarization spirals and the regular magnetic field; the other does not always coincide with the CO arm and its pitch angle differs from the orientation of its regular magnetic field. Conclusions. The offsets between ridges of regular magnetic field, dense gas and warm dust are compatible with the sequence expected from spiral density wave triggered star formation, with a delay of a few tens of millions of years between gas entering the shock and the formation of giant molecular clouds and a similar interval between the formation of the clouds and the emergence of young star clusters. At the position of the CO arms the orientation of the regular magnetic field is the same as the pitch angle of the spiral arm, but away from the gaseous arms the orientation of the regular field varies significantly. Spiral shock compression can explain the generation of one type of arm of strong polarized radio emission but a different mechanism is probably responsible for a second type of polarization arm.

Multi-scale radio-infrared correlations in M 31 and M 33: The role of magnetic fields and star formation

Interstellar magnetic fields and the propagation of cosmic ray electrons have an important impact on the radio-infrared (IR) correlation in galaxies. This becomes evident when studying different spatial scales within galaxies. We investigate the correlation between the IR and free-free/synchrotron radio continuum emission at 20 cm from the two local group galaxies M 31 and M 33 on spatial scales between 0.4 and 10 kpc. The multi-scale radio-IR correlations have been carried out using a wavelet analysis. The free-free and IR emission are correlated on all scales, but on some scales the synchrotron emission is only marginally correlated with the IR emission. The synchrotron-IR correlation is stronger in M 33 than in M 31 on small scales (<1 kpc), but it is weaker than in M 31 on larger scales. Taking the smallest scale on which the synchrotron-IR correlation exists as the propagation length of cosmic ray electrons, we show that the difference on small scales can be explained by the smaller propagation length in M 33 than in M 31. On large scales, the difference is due to the thick disk/halo in M 33, which is absent in M 31. A comparison of our data with data on NGC 6946, the LMC and M 51 suggests that the propagation length is determined by the ratio of ordered-to-turbulent magnetic field strength, which is consistent with diffusion of CR electrons in the ISM. As the diffusion length of CR electrons influences the radio-IR correlation, this dependence is a direct observational evidence of the importance of magnetic fields for the radio-IR correlation within galaxies. The star-formation rate per surface area only indirectly influences the diffusion length as it increases the strength of the turbulent magnetic field.

Wavelet-based Faraday rotation measure synthesis

The Faraday rotation measure synthesis, as a method for analysing multichannel observations of polarized radio emission to investigate galactic magnetic field structures requires the definition of complex polarized intensity in the wavelength range −∞ <λ 2 < ∞. The problem is that the measurements at negative λ 2 are not possible. We introduce a simple method for continuation of the observed complex polarized intensity P (λ 2 ) into the domain λ 2 < 0u sing symmetry arguments. The method is suggested in context of magnetic field recognition in galactic discs where the magnetic field is supposed to have a maximum in the equatorial plane. The method is quite simple when applied to a single Faraday rotating structure on the line of sight. Recognition of several structures on the same line of sight requires a more sophisticated technique. We also introduce a wavelet-based algorithm which allows us to consider a set of isolated structures in the (φ, λ 2 ) plane (where φ is the Faraday depth). The method essentially improves the possibilities for reconstruction of complicated Faraday structures using the capabilities of modern radio telescopes.

Faraday rotation measure synthesis for magnetic fields of galaxies

Rotation measure (RM) Synthesis was recently developed as a new tool for the interpretation of polarized emission data in order to separate the contributions of different sources lying on the same line of sight. Until now, the method was mainly applied to discrete sources in Faraday space (Faraday screens). Here we consider how to apply RM Synthesis to reconstruct the Faraday dispersion function, aiming at the further extraction of information concerning the magnetic fields of extended sources, for example galaxies. We pay attention mainly to two related novelties in the method, i.e. the symmetry argument in Faraday space and the wavelet technique. We give a relation between our method and the previous applications of RM Synthesis to point-like sources. We demonstrate that the traditional RM Synthesis for a point-like source indirectly implies a symmetry argument and, in this sense, can be considered as a particular case of the method presented here. Investigating the applications of RM Synthesis to polarization details associated with small-scale magnetic fields, we isolate an option which was not covered by the ideas of the Burn theory, i.e. using quantities averaged over small-scale fluctuations of the magnetic field and electron density. We describe the contribution of small-scale fields in terms of Faraday dispersion and beam depolarization. We consider the complex polarization for RM Synthesis without any averaging over small-scale fluctuations of the magnetic field and electron density and demonstrate that it allows us to isolate the contribution from a small-scale field. A general conclusion concerning the applicability of RM Synthesis to the interpretation of the radio polarization data for extended sources, such as galaxies, is that quite severe requirements (in particular to the wavelength range covered by observations) are needed to recognize at least the principal structure of the Faraday dispersion function. If the wavelength range of observations is not adequate, we describe which features of this function can be reconstructed.

Shell models of magnetohydrodynamic turbulence

Abstract 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.

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

The first direct measurements of effective magnetic diffusivity in turbulent flow of electroconductive fluids (the so-called β effect) under the 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≈3×10(6), which corresponds to the magnetic Reynolds number Rm≈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 laminar value reaches about 50%.

Lifetime of Surface Features and Stellar Rotation: A Wavelet Time-Frequency Approach

We explore subtle variations in disk-integrated measurements spanning 18 yr of stellar surface magnetism by using a newly developed time-frequency gapped wavelet algorithm. We present results based on analysis of the Mount Wilson Ca II H and K emission fluxes in four, magnetically active stars (HD 1835 [G2 V], HD 82885 [G8 IV-V], HD 149661 [K0 V], and HD 190007 [K4 V]) and sensitivity tests using artificial data. When the wavelet basis is appropriately modified (i.e., when the time-frequency resolution is optimized), the results are consistent with the existence of spatially localized and long-lived Ca II features (assumed here as activity regions that tend to recur in narrowly confined latitude bands), especially in HD 1835 and HD 82885. This interpretation is based on the observed persistence of relatively localized Ca II wavelet power at a narrow range of rotational timescales, enduring as long as 10 yr.

Turbulent convective heat transfer in a long cylinder with liquid sodium

Turbulent convective heat transfer in a closed cylinder with aspect ratio L = 5D (D is the diameter and L is the cylinder length) filled with liquid sodium, heated at one end face and cooled at the other, is studied experimentally for three different positions: vertical, inclined at 45 degrees to the vertical and horizontal. The Rayleigh number, which is determined by the superimposed temperature difference and the cylinder diameter, varies within the range . It is shown that the convective heat transfer along the cylinder is most effective in the inclined cylinder, where an intense large-scale circulation exists on a background of developed small-scale turbulence. In the horizontal cylinder, the turbulence is weak, but the large-scale circulation provides moderate heat transfer. In the vertical cylinder, the large-scale circulation is absent, the turbulent fluctuations are most active, but the heat transfer is the weakest. The dependence of the Nusselt number on the Rayleigh and the Prandtl numbers, and the dependence of the Reynolds number on the Grashof number are shown and discussed.