Nonlinear dynamics of Landau damped kinetic Alfvén waves

In the present paper we have studied the nonlinear dynamical equation of Landau damped kinetic Alfvén wave (KAW) to investigate the nonlinear evolution of KAW and the resulting turbulent spectra in solar wind plasmas. We have introduced a parameter g which governs the coupling between the amplitude of the pump KAW and the density perturbation. The numerical solution has been carried out to see the dependence on the parameter g in the nonlinear part of our equation. Our results reveal the formation of damped localized structures of KAW as well as steepening of the turbulent spectra by increasing g when damping is taken into account. The power spectra of magnetic field fluctuations indicate the redistribution of energy among the higher wave numbers. Each power spectrum with and without damping splits up into two different scaling ranges, Kolmogorov scaling followed by a steeper scaling. The steepening in the power spectra with Landau damping is more than without Landau damping case (for the same value of g). This type of steeper spectra has also been observed in the solar wind and is attributed to the Landau damping effects.     

Variation of the low-degree solar acoustic mode parameters over the solar cycle

VIRGO/SPM is a helioseismic sunphotometer on board SOHO that observes the disk-integrated sunlight irradiance at three different colors (red, green, and blue). The data obtained for SPM since the beginning of the SOHO mission, April 1996, to March 2001 have been used to study the differences of the p-mode parameters during the solar activity cycle. These time series have been divided in sub-series of 100 days, transformed to power spectra and averaged in sets of three to yield a total number of six averaged power spectra (around one per year). A new way of analyzing the power spectrum has been applied to the six power spectra of each color; it consists of fitting the whole p-mode spectrum at once with a unique background. The results for the frequencies, line widths, power, mode energy, energy rate fed in the mode and splittings along the activity cycle are found, compared and discussed.     

Cosmic ray fluctuations in compressible turbulent medium

The influence of compressibility of the medium on cosmic ray (CR) fluctuations has been investigated. The CR transport equation has been used to obtain an equation for the second moment of CR particle density (correlation function of the particle density). It is shown that the effects due to the compressibility of the medium has an essential influence on CR fluctuations. The relations between CR power spectra and random velocity field have been determined. For the turbulence which is created by an ensemble of weak sound waves we have obtained the connection between the spectral indices of CR power spectra and the velocity field. It is shown that the spectral indices of CR power spectra and the velocity field of random sound waves coincide.     

Combined and Comparative Analysis of Power Spectra

In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might have been, or one may wish to estimate the significance of a particular peak that shows up in two or more power spectra. One may also on occasion need to search for a complex of peaks in a single power spectrum, such as a fundamental and one or more harmonics, or a fundamental plus sidebands, etc. Visual inspection can be revealing, but it can also be misleading. This leads one to look for one or more ways of forming statistics, which readily lend themselves to significance estimation, from two or more power spectra. We derive formulas for statistics formed from the sum, the minimum, and the product of two or more power spectra. A distinguishing feature of our formulae is that, if each power spectrum has an exponential distribution, each statistic also has an exponential distribution. The statistic formed from the minimum power of two or more power spectra is well known and has an exponential distribution. The sum of two or more powers also has a well-known distribution that is not exponential, but a simple operation does lead to an exponential distribution. Concerning the product of two or more power spectra, we find an analytical expression for the case n = 2, and a procedure for computing the statistic for n > 2. We also show that some quite simple expressions give surprisingly good approximations.     

The role of the energy spectrum anisotropy in the variations of the cosmic-ray fluctuations power-spectrum before interplanetary medium disturbances

The variations in the form of the cosmic-ray fluctuation power spectrum as an interplanetary shock wave approaches the Earth have been calculated for different values of cosmic ray anisotropy. The relevant experimental estimates of the power spectra are inferred from the data of cosmic ray detection with the ground-based neutron monitors at cosmic-ray stations. A comparison between the theoretical and experimental estimates has demonstrated an important role of the cosmic ray anisotropy spectrum in the generation of the power spectrum as the latter is rearranged before the interplanetary medium disturbances.     

On the power in intermediate polars

I review some of the more interesting recent results on Intermediate Polars, with an emphasis on the information content of their periodic intensity variations, as provided by power spectra. The current definitions of the class are discussed, and new contenders listed with their properties. Results of the X-ray periodicities seen in IPs and developments in interpreting their light curves and power spectra are discussed. Studies of the morphology of IP X-ray light curves seem to show a bifurcation into single- or double-maxima spin profiles. An explanation for this behaviour, involving faster, weaker field, rotators accreting over a larger area, is discussed. Significant polarization has only been detected in three IPs, and the polarized flux distributions have been used to infer magnetic field strength. The failure to detect any IR cyclotron spectral features in IPs, even for polarized systems, limits our possibilities of direct magnetic field measurements. Recent tomographic results qualitatively support the accretion curtain models for IPs and some progress has been made in modelling the line emission using realistic physics.     

Time-Distance Helioseismology with f Modes as a Method for Measurement of Near-Surface Flows

Travel times measured for the f mode have been used to study flows near the solar surface in conjunction with simultaneous measurements of the magnetic field. Previous flow measurements of Doppler surface rotation, small magnetic feature rotation, supergranular pattern rotation, and surface meridional circulation have been confirmed. In addition, the flow in supergranules due to Coriolis forces has been measured. The spatial and temporal power spectra for a six-day observing sequence have been measured.     

Constraining the parameters of the LN model with reconstructed power spectrum of Ly-α forest

A sample of three quasar spectra observed by the Keck telescope is selected to reconstruct the perturbations of mass density using the Gaussianization method, with a calculation of the corresponding wavelet power spectra. The two parameters in the lognormal (LN) model, namely the shape factor Γ and the Jeans smoothing factor r, are set as free parameters. Their most probable values are determined by comparing the result of statistical analysis on the observed sample with that on a simulated sample, and they are: Γ0.50 and r0.09. Non-Gaussian features in the quasar spectra can not be excluded using the traditional Gaussianization method. However, on the scales larger than 100 kpc, these features have little or no influence on our results described above. This argument has been verified by comparing the observed sample with the simulated sample as regards their skewness and kurtosis spectra, as well as their scale-scale correlations.     

Asymmetries of Thomson scatter spectra from the terrestrial ionosphere

Asymmetries of Thomson scatter spectra occurring at different heights have been investigated through differential ion-flow technique using BGK form of Boltzmann equation. The result is useful to study the frequency broadening and bite-out centre of power spectra of incoherent scatter signals.     

Study of intensity fluctuations in cosmic rays during Forbush-decreases on the basis of the data obtained with the inzmiran scintillation supertelescope

The one-minute, five-minute, and hourly values of cosmic-ray intensity obtained with a scintillation telescope at Izmiran have been used to carry out the correlational and spectral analysis of large Forbush-decreases of cosmic rays in 1978. The spectra of power obtained for the periods of interplanetary disturbances are characterized by individual spectral lines whose amplitude exceeds at least a 95% interval of reliability.     

Linking jet emission and X-ray properties in the peculiar neutron star X-ray binary Circinus X-1

We present the results of simultaneous X-ray and radio observations of the peculiar Z-type neutron star X-ray binary Cir X-1, observed with the Rossi X-ray Timing Explorer satellite and the Australia Telescope Compact Array in 2000 October and 2002 December. We identify typical Z-source behaviour in the power density spectra as well as characteristic Z patterns drawn in an X-ray hardness–intensity diagram. Power spectra typical of bright atoll sources have also been identified at orbital phases after the periastron passage, while orbital phases before the periastron passage are characterized by power spectra that are typical neither of Z nor of atoll sources. We investigate the coupling between the X-ray and the radio properties, focusing on three orbital phases when an enhancement of the radio flux density has been detected, to test the link between the inflow (X-ray) and the outflow (radio jet) to/from the compact object. In two out of three cases, we associate the presence of the radio jet to a spectral transition in the X-rays, although the transition does not precede the radio flare, as detected in other Z sources. An analogous behaviour has recently been found in the black hole candidate GX 339-4. In the third case, the radio light curve shows a similar shape to the X-ray light curve. We discuss our results in the context of jet models, considering also black hole candidates.     

The spectra of radiation and relativistic electrons formed by Compton scattering at non-zero particle fluxes

The formation of steady-state spectra of radiation or particles by Compton scattering is discussed for the case when the flux from the source is present. Power-law distributions, or those characterized by a power-law asymptotic behaviour, can appear under these conditions.The power indices and normalizations have been found as well as the flux directions for the electron and photon distributions in two cases. The first case is that of differential energy transfer over the electron spectrum (interaction with soft radiation). For the case of integrated transfer, relations have been found between the indices.The possibility of a power-law electron spectrum (with an index =2) has been shown for scattering by equilibrium radiation (the black-body background included).     

Recent observations of high-degree solar p-mode oscillations at the Kitt Peak National Observatory

A brief summary is given of a program which is currently being carried out with the McMath telescope of the Kitt Peak National Observatory in order to study high-degree (l ≳ 150) solar p-mode oscillations. This program uses a 244 × 248 pixel CID camera and the main spectrograph of the McMath telescope to obtain velocity-time maps of the oscillations which can be converted into two-dimensional (k _h - ω) power spectra of the oscillations. Several different regions of the solar spectrum have been used in order to study the oscillations at different elevations in the solar atmosphere. The program concentrates on eastward- and westward-propagating sectoral harmonic waves so that measurements can be made of the absolute rotational velocities of the solar photospheric and shallow sub-photospheric layers. Some preliminary results from this program are now available. First, we have been unable to confirm the existence of a radial gradient in the equatorial rotational velocity as was previously suggested. Second, we have indeed been able to confirm the presence of p-mode waves in the solar chromosphere as was first suggested by Rhodes et al. (1977). Third, we have been able to demonstrate differences in photospheric and chromospheric power spectra.

     

Variation of the solar atmospheric rotation over the 11 year cycle

The synodic rotation period and power spectra of solar microwave sources are investigated using accurate data in the interval 1956 to 1970. The variation of the approximate 27 day period is obtained over a complete solar cycle and is thought to be a result of the latitude change over the solar cycle of the origins of the radio emissions. High resolution power spectra have also been obtained and revealed the existence of a double peaked line near 160 day period. This line is attributed to changes in either the Eartn's heliographic latitudes or the Earth's inclination to the Earth-Sun line.     

Comparison of low-harmonics spectra and maps according to the WMAP and Planck space missions

We present a comparison of the angular power spectra and maps represented by the WMAP and Planck mission teams. The spectra are compared in the the multi pole range (2 ≤ ? ≤ 50). The ? =5, 7, 13, 29, 37, 41–46 harmonics have a discrepancy in the angular power spectra. The maps of the microwave background and their phase characteristics are studied at these spatial frequencies. We show that the discrepancy of the spectra is due to a different account of the systematics linked with the Galaxy, the ecliptic, and possibly with the Earth. These effects, leading to a statistical anisotropy, may be responsible for the observed anomalies in both experiments at low harmonics.     

The power spectrum of rich clusters of galaxies on large spatial scales

We present an analysis of the redshift-space power spectrum, P ( k ), of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that P ( k ) can be approximated by a power law, P ( k )∝ kⁿ , with n ≈−1.6 over the wavenumber range 0.04< k <0.1 h Mpc⁻¹. Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution, but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale k ∼0.03 h Mpc⁻¹. We compare the power spectra estimated from simulated APM cluster catalogues with those estimated directly from cubical N -body simulation volumes, and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers k ≳0.02 h Mpc⁻¹. These results suggest that the observed turnover in the power spectrum may be a real feature of the cluster distribution, and that we have detected the transition to a near-scale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turnover in the cluster power spectrum is in good agreement with the scale of the turnover observed in the power spectrum of APM galaxies.     

Variability of Solar Five-Minute Oscillations in the Corona as Observed by the Extreme Ultraviolet Spectrophotometer (ESP) on the Solar Dynamics Observatory/Extreme Ultraviolet Variability Experiment (SDO/EVE)

Solar five-minute oscillations have been detected in the power spectra of two six-day time intervals from soft X-ray measurements of the Sun observed as a star using the Extreme Ultraviolet Spectrophotometer (ESP) onboard the Solar Dynamics Observatory (SDO)/Extreme Ultraviolet Variability Experiment (EVE). The frequencies of the largest amplitude peaks were found to match the known low-degree (?=0?–?3) modes of global acoustic oscillations within 3.7 μHz and can be explained by a leakage of the global modes into the corona. Due to the strong variability of the solar atmosphere between the photosphere and the corona, the frequencies and amplitudes of the coronal oscillations are likely to vary with time. We investigated the variations in the power spectra for individual days and their association with changes of solar activity, e.g. with the mean level of the EUV irradiance, and its short-term variations caused by evolving active regions. Our analysis of samples of one-day oscillation power spectra for a 49-day period of low and intermediate solar activity showed little correlation with the mean EUV irradiance and the short-term variability of the irradiance. We suggest that some other changes in the solar atmosphere, e.g., magnetic fields and/or inter-network configuration may affect the mode leakage to the corona.     

Cloud brightness distribution and turbulence in Venus using Galileo violet images

Venus cloud covered atmosphere offers a well-suited framework to study the coupling between the atmospheric dynamics and the structure of the cloud field. Violet images obtained during the Galileo flyby from 12 to 17 February 1990 have been analyzed to retrieve the zonal power spectra of the cloud brightness distribution field between latitudes 70° N and 50° S. The brightness distribution spectra serve as a diagnostic of the eddy kinetic energy spectrum providing indirect information about the distribution of energy along different spatial scales. We composed images covering a full rotation of the atmosphere at the level of the UV contrasted clouds obtaining maps of almost 360° that allowed us to obtain the brightness power spectra from wavenumbers k=1 to 50. A full analysis of the spectrum slope for different latitude bands and ranges of wave numbers is presented. The power spectra follow a classical law k−n with exponent n ranging from −1.7 to −2.9 depending on latitude and the wavenumber range. For the whole planet, the average of this parameter is −2.1 intermediate between those predicted by the classical turbulence theories for three- and two-dimensional motions (n=−5/3 and n=−3). A comparison with previous analysis of Mariner 10 (in 1974) and Pioneer Venus (in 1979) shows significant temporal changes in the cloud global structure and in the turbulence characteristics of the atmosphere.