Characteristics of Coronal Alfvén Waves Deduced from Helios Faraday Rotation Measurements

A statistical study of Faraday rotation fluctuations (FRF) has been performed using polarization angle data of S-band (f = 2.3 GHz) radio spacecraft signals. The measurements were recorded during the recurring superior conjunctions of the Helios probes, during which the solar proximate point of the radio ray path reached heliocentric distances between 3 and 34 R. The most commonly found temporal FRF spectra are power laws with an average spectral index 1.5 over the frequency range from 1 mHz < v < 10 mHz. The FRF variance decreases with heliocentric distance, the falloff exponent being 8 for R < 6 R and 3 for distances 8 < R < 6 R < 16 R. The results are interpreted under the assumption that the FRF are produced by Alfvén waves propagating in the coronal plasma. For the applicable range of heliocentric distances it is shown that Alfvén waves are in a regime of free propagation and probably transfer much of their energy to the kinetic energy of the solar wind. The spatial power spectrum of magnetic field fluctuations is inferred to be strongly anisotropic, the irregularities extending along the background magnetic field with axial ratios of the order of 10.     

Five-minute magnetic field fluctuations in the solar wind acceleration region

A spectral analysis of coronal Faraday rotation (FR) data obtained with the linearly polarized signals of the two Heliosspacecraft reveals that about one-third of the temporal FR spectra contain a distinct spectral line superposed onto the background power-law spectrum. The most prevalent frequency of this quasi-harmonic component (QHC) is about 4 mHz, corresponding to a 4–5 min periodic oscillation of the coronal magnetic field. Physical reasons for the existence of QHC Alfvén fluctuations in the inner solar wind are discussed. FR fluctuations (FRF) are considered to arise from both a turbulent background as well as an isolated Alfvén wave train of finite extent and duration. An estimate can be made for the conditions under which the isolated wave train is observed above the ever present background. It is shown that the wave train must have a sufficiently long duration and transverse wavelength. It is suggested that the QHC at periods near 4–5 min in the FRF spectra are most probably produced by outward-propagating Alfvén waves excited initially in the anisotropic structures of the chromospheric network.     

A solar wind model with the power spectrum of Alfvénic fluctuations

A new solar wind model has been developed by including in the model the Alfvénic fluctuation power spectrum equation proposed by Tu et al. (1984). The basic assumptions of the model are as follows: (1) for heliocentric distances r > 10 R _⊙, the radial variation of the power spectrum of Alfvénic fluctuations is controlled by the spectrum equation (1), (2) for heliocentric distances r < 10 R _⊙, the radial variation of the fluctuation amplitude is determined by the Alfvén wave WKB solution, (3) no energy cascades from the low-frequency boundary of the Alfvénic fluctuation power spectrum into the fluctuation frequency range, and the energy which cascades from the high-energy boundary of the spectrum into the higher frequency range is transported to heat of the solar wind flow. Some solutions of this model which, on one hand, describe the major properties of the Alfvénic fluctuations and the high-speed flow observed by Helios in the space range between 0.3–1 AU and, on the other hand, are consistent with the observational constraints at the coronal base have been obtained under the following conditions: (1) the spectrum index of the fluctuations is near to -1 for almost the whole frequency range at 10 R _⊙, (2) the particle flux density at 1 AU is not greater than 3 × 10⁸ cm^?2 s^?1, (3) the solution is for spherically-symmetric flow geometry or the solution passes through the outermost of the three critical points of the rapidly diverging flow geometry with f _max = 7. Some solutions passing through the innermost critical point of the rapidly diverging flow geometry with f _max = 7 have been found, however, with too low pressure at the coronal base to compare with the observational constraints. Heat addition or other kind of momentum addition for r < 10 R _⊙ is required to modify this model to yield better agreement with observations. A cascade energy flux function which leads to Kolmogorov power law in the high-frequency range of Alfvénic fluctuations is presented in Appendix A. More detailed discussions about the characteristics, the boundary conditions and the solution of the spectrum equation (1) are given in Appendix B.     

MESSENGER Observations of Magnetohydrodynamic Waves in the Solar Corona from Faraday Rotation

During the declining phase of the longest solar minimum in a century, the arrival of the MESSENGER spacecraft at superior conjunction allowed the measurement of magnetohydrodynamic (MHD) waves in the solar corona with its 8 GHz radio frequency signal. MHD waves crossing the line of sight were measured via Faraday rotation fluctuations (FRFs) in the plane of polarization (PP) of MESSENGER’s signal. FRFs in previous observations of the solar corona (at greater offset distances) consisted of a turbulent spectrum that decreased in power with increasing frequency and distance from the Sun. Occasionally a spectral line, a distinct peak in the power spectral density spectrum around 4 to 8 mHz, was also observed in these early data sets at offset distances of about 5 to 10 solar radii. The MESSENGER FRF data set shows a spectral line at an offset distance between 1.55 to 1.85 solar radii with a frequency of 0.6±0.2 mHz. Other possible spectral lines may be at 1.2, 1.7, and 4.5 mHz; MHD waves with these same frequencies have been observed in X-ray data traveling along closed coronal loops at lower offset distances. An initial analysis of the MESSENGER spectral line(s) shows behavior similar to turbulent spectra: decreasing power with increasing frequency and distance from the Sun. Here we detail the steps taken to process the MESSENGER change in PP data set for the MHD wave investigation.     

On the possibility of heating of local solar chromospheric regions by magnetoacoustic-gravity waves in a thin flux tube

The response of an isothermal atmosphere of a thin vertical magnetic flux tube to the presence of an acoustic-gravity wave field in the external medium is considered. The Laplace transform method is used to solve a problem with initial conditions. The structure of the solution for disturbances in the tube is a superposition of forced oscillations at the source frequency and oscillations decaying as ～ t ^?3/2 (the so-called wave wake). Both components are analogues of the corresponding disturbances in an external medium with a modified amplitude. The excitation under consideration is shown to be effective in the ranges of external oscillation frequencies 0 mHz ≤ v ≤ 3.3 mHz and v ≥ 6.5 mHz. The time-averaged energy flux density for high-frequency magnetoacoustic-gravity waves in the tube is estimated to be ∝ 3.0 × 10⁷ erg cm^?2 s^?1, a value of the same order of magnitude as that required for heating local regions in the solar chromosphere, ∝ 10⁷ erg cm^?2 s^?1.     

Spectral properties of hydromagnetic fluctuations near 4 and 5 a.u.

Power spectra of vector components of interplanetary magnetic field fluctuations near 4–5 a.u. during quiet intervals show a frequency dependence very close to f^s over the frequency range 4 × 10^?5 to 9 × 10^?3 Hz (corresponding to periods of 7 h-2 min). While the spectra are generally very close to power law in frequency, variations in slope among the spectra exceed those expected from random errors and may represent true temporal variations. Mean slopes corrected for systematic error are s = ? 1.50±0.02 (Pioneer 10, mean heliocentric distance 5.3 a.u.) and s = ? 1.52±0.02 (Pioneer 11, mean heliocentric distance 3.9 a.u.) and are consistent with several determinations of spectral slope for magnetic fluctuations near 1 a.u. Radial evolution of the perturbations is investigated by choosing data samples in which Pioneer 10 and 11 and the sun are nearly colinear. The dependence on heliocentric distance of σ_c², the composite vector variance, and of σ_c/B_mag, where B_mag is the mean magnitude of the magnetic field, show that the radial variation of fluctuation amplitude is highly variable in time with a dependence on heliocentric distance typically in the range R^?1 to R^?1.5. These observations are compared with theoretical models of outward propagating Alfven waves of solar origin and of MHD turbulence. The mean slopes agree well with that expected for turbulence. The significant variability observed in spectral slopes and in the radial dependence of fluctuation amplitude in data selected specifically for conditions of relative magnetic quiet is noteworthy and urges caution in modeling heliospheric magnetic microstructure in studies of galactic cosmic ray modulation.     

Power spectrum analysis of limb and disk spicule using Hinode Ca H-line broadband filter

We present observations of a solar quiet region obtained using the Hinode Solar Optical telescope (SOT) in the Ca II H-line with broadband filter taken on November 2006. We study off-limb and on-disk spicules to find a counterpart of the limb spicule on the disk. This investigation shows a strong correspondence between the limb and near limb spicules (on-disk spicules that historically were called dark or bright mottles, especially when observed in Hα, being a rather cool line) from the dynamical behavior (e.g., periodicity). An excellent time sequence of images obtained near the equatorial region with a cadence of 8 s was selected for analysis. 1D Fourier power spectra made at different positions on the disk and above the limb are shown. We take advantage of the so-called mad-max operator to reduce the effects of overlapping and improve the visibility of these hair-like features. A definite signature with strong power in the 3-min (5.5 mHz) and 5-min (3.5 mHz) oscillations for both places exists. A full range of oscillations was found and the high frequency intensity fluctuation (greater than 10 mHz or less than 100 s) corresponding to the occurrence of the so-called type II spicules and, even more impressively, dominant peaks of Fourier power spectra are seen in a wide range of frequencies and for all places of “on” and “off” disk spicules, in rough agreement with what historical works report regarding disk mottles and limb spicules. Also, some statistically significant behavior, based on the power spectrum computed for different positions, is discussed. The power for all kinds of power spectra is decreasing with increasing distance from the limb, except for photospheric oscillations (5 min or p-mode), which show a dominant peak for on-disk power spectra.     

The Effect of Twisted Magnetic Field on the Resonant Absorption of MHD Waves in Coronal Loops

The standing quasi-modes in a cylindrical incompressible flux tube with magnetic twist that undergoes a radial density structuring is considered in ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae, the dispersion relation for the MHD waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was found that a magnetic twist will increase the frequencies, damping rates and the ratio of the oscillation frequency to the damping rate of these modes. The period ratio P ₁/P ₂ of the fundamental and its first-overtone surface waves for kink (m=1) and fluting (m=2,3) modes is lower than two (the value for an untwisted loop) in the presence of twisted magnetic field. For the kink modes, particularly, the magnetic twists B _φ /B _z =0.0065 and 0.0255 can achieve deviations from two of the same order of magnitude as in the observations. Furthermore, for the fundamental kink body waves, the frequency band width increases with increasing magnetic twist.     

On the isotropization of electrons in synchrotron sources

Electrons radiating synchrotron radiation develop a pitch angle anisotropy, and so become unstable to the coherent emission of hydromagnetic waves. The evolution of the coupled system of anisotropic electrons and waves is studied in the absence of any dissipation of the waves in the ambient medium. The anisotropy of the electrons approaches a steady state in which the anisotropy is energy independent and of orderv _A/c (v _A=Alfvén speed). The conditions for this small degree of anisotropy to be maintained are examined.Due to this scattering the bend in the synchrotron spectrum, from an inverse power law with index to one with index 4/3+1, due to an initial or recurrent injection of electrons, could only occur at infrared or higher frequencies.     

Small-Amplitude Disturbances In A Radiating And Scattering Grey Medium Ii. Solutions Of Given Real Wave Number <Emphasis Type="BoldItalic">k</Emphasis>

We study the fundamental modes of radiation hydrodynamic waves arising from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium using the Eddington approximation. The dispersion relation analyzed is the same as that of Paper I (Kaneko et al., 2000), but is solved as a quintic in angular frequency ω while a quadratic in k ² in Paper I. Numerical results reveal that wave patterns of five solutions are distinguished into three types of the radiation-dominated and type 1 and type 2 matter-dominated cases. The following wave modes appear in our problem: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusion modes, adiabatic sound wave, cooling-damped and drag–force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. The radiation-dominated case is characterized by the gap between the isothermal sound and isentropic radiation-acoustic speeds within which there is not any acoustic wave propagating with real phase speed. One of the differences between type 1 and type 2 matter-dominated cases is the connectivity of the constant-volume diffusion mode, which originates from the radiative mode in the former case, while from the Newtonian-cooling wave in the latter case. Analytic solutions are derived for all wave modes to discuss their physical significance. The criterion, which distinguishes between radiation-dominated and type 1 matter-dominated cases, is given by Γ₀ = 9, where Γ₀ = C _p ^(tot)/C _V ^(tot) is the ratio of total specific heats at constant pressure and constant volume. Waves in a scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.     

On viscous attenuation of Alfvenic fluctuations in the solar wind

It is shown that the viscous attenuation of Alfvenic fluctuations is anisotropic and is proportional to the fluctuation component parallel to the mean magnetic field. If the ratio between the parallel and perpendicular components is a constant, then the viscous attenuation experienced by waves with wavelengths larger than the collisional free-path will be concentrated within 20 $\text{R?}$. Between 0.3 AU and l AU, no Alfvenic fluctuations of any frequency is appreciably damped by viscosity determined by Coulomb collision. The mechanism of viscous attenuation caonot explain the observed radial development of the spectrum. If, near the Sun, the Alfvenic fluctuations do have a parallel component, then the viscous damping will have an important accelerating effect on the solar wind in fast diverging stream tubes. If the parallel component is negligible, then the Alfvenic fluctuation will not be attenuated by any classical viscosity.     

Time variability of viscosity parameter in differentially rotating discs

We propose a mechanism to produce fluctuations in the viscosity parameter (α) in differentially rotating discs. We carried out a nonlinear analysis of a general accretion flow, where any perturbation on the background α was treated as a passive/slave variable in the sense of dynamical system theory. We demonstrate a complete physical picture of growth, saturation and final degradation of the perturbation as a result of the nonlinear nature of coupled system of equations. The strong dependence of this fluctuation on the radial location in the accretion disc and the base angular momentum distribution is demonstrated. The growth of fluctuations is shown to have a time scale comparable to the radial drift time and hence the physical significance is discussed. The fluctuation is found to be a power law in time in the growing phase and we briefly discuss its statistical significance.     

The Energy of High-Frequency Waves in the Low Solar Chromosphere

High-frequency acoustic waves have been suggested as a source of mechanical heating in the chromosphere. In this work the radial component of waves in the frequency interval 22 to 1 mHz are investigated. Observations were performed using 2D spectroscopy in the spectral lines of Fe i 543.45 nm and Fe i 543.29 nm at the Vacuum Tower Telescope, Tenerife, Spain. Speckle reconstruction has been applied to the observations. We have used Fourier and wavelet techniques to identify oscillatory power. The energy flux is estimated by assuming that all observed oscillations are acoustic running waves. We find that the estimated energy flux is not sufficient to cover the chromospheric radiative losses.     

On the Possible Connection between Photospheric 5-Min Oscillation and Solar Flare Microwave Emission

Dynamic spectra of low-frequency modulation of microwave emission from solar flares are obtained. Data of 15 bursts observed in 1989–2000 with Metsähovi radio telescope at 37 GHz have been used. During 13 bursts a 5-min modulation of the microwave emission intensity was detected with the frequency of ν _I = 3.2± 0.24 (1σ) mHz. Five bursts revealed a 5-min wave superimposed on a ～1 Hz, linear frequency modulated signal generated, presumably, by coronal magnetic loop, this wave frequency is ν_fm = 3.38± 0.37 (1σ) mHz. Both intensity and frequency modulations detected are in good agreement with the data on 5-min global oscillations of photosphere and with the data on the umbral velocity oscillations observed in the vicinity of sunspots. Possible role of p-mode photospheric oscillations in modulation of microwave burst emission is discussed.     

Fundamental emission for type III bursts in the interplanetary medium: The role of ion-sound turbulence

It is argued (a) that the onset times of type III radio emission and of the streaming electrons implies that type III bursts in the interplanetary medium are generated predominantly at the fundamental, (b) that in view of recent observations of ion-sound waves in the interplanetary medium the theory of the generation of the bursts should be revised to take account of these waves, and (c) the revised theory favours fundamental emission. A detailed discussion of the effect of ion-sound waves on type III bursts is given. The most important results are: (1) Ion-sound waves cause enhanced (over scattering off thermal ions) fundamental emission. (2) Second harmonic emission is also enhanced for T _e> 5 × 10⁵ K, e.g., low in the corona, but is suppressed for T _e< 5 × 10⁵ K, e.g., in the interplanetary medium. (3) The bump-in-the-tail instability for Langmuir waves can be suppressed by the presence of ion-sound waves; it may be replaced by an analogous instability in which fundamental transverse waves are generated directly, with no associated second harmonic, but there are unresolved problems with theory for this process. (4) Very low frequency ion-sound waves can scatter type III radiation. (5) Although the ion-sound waves which have been observed are at too high a frequency to be relevant for these processes, it seems likely that ion-sound waves of the required frequencies are present and do play important roles in the generation of type III bursts.     

New light on solar infrared intensity oscillations

The detection of large-amplitude infrared solar intensity oscillations in the 5-min region is reported. Using a broad-band multichannel photometer, the peak-to-peak intensity variation at 2.23 m is found to be as high as 2.4% for a circular aperture of 1 arc min and 0.8% in the full disk observations, i.e., remarkably higher than at the other four observed wavelength regions.The spatially-integrated power spectrum shows the 5-min oscillation plus a strong feature near 4 mHz. This feature coincides in frequency with the fundamental p-mode resonance of the chromosphere. However, a power-spectrum autocorrelation as well as a second-order Fourier transform of the data suggest that a high-frequency tail of the 5-min power spectrum is a more likely interpretation of this feature.     

Smoothing of force functions and the fluctuation spectra of an open star cluster model

We perform the correlation and spectral analysis of phase-space density and potential fluctuations in a model of an open star cluster for various values of the smoothing parameter ? of the force functions in the equations of motion of cluster stars, and compute the mutual correlation functions for the fluctuations of potential U and phase-space density f of the cluster model at different clustercentric distances. We use the Fourier transform of the mutual correlation functions to compute the power spectra and dispersion curves of the potential and phase-space density fluctuations. The spectrum of potential fluctuations proves to be less complex than that of phase-space density fluctuations. The most powerful potential fluctuations are associated with phase-space density fluctuations, and their spectrum lies in the domain of low frequencies ν < 3/τ _v.r.; at intermediate and high frequencies (ν > 3/τ _v.r.), the contribution of potential fluctuations to those of the phase-space density is small or equal to zero (here τ _v.r. is the violent relaxation time scale of the cluster). We find a number of unstable potential fluctuations in the core of the cluster model (up to 30 pairs of fluctuations with different complex conjugate frequencies). We also find and analyze the dependences of the spectra and dispersion curves of phase-space density and potential fluctuations on ?. We find a “repeatability” (significant correlation) of the spectra at some values of parameter ?. The form of the dispersion curve is unstable against small variations of ?. We discuss the astrophysical applications of our results: the break-up in the cluster core of the phase-space density wave running from the cluster periphery toward its center into several waves with frequencies commensurable to that of the external (tidal) influence; emission and reflection of phase-space and potential waves near the cluster core boundary; possible wavelength and phase discretization of the phase-space and potential waves in the cluster model.     

The luminosity functions of the 1969 Perseid and Orionid meteor showers

Visual counts of the 1969 Perseid and Orionid meteor showers are presented, comprising 288 Perseids and 56 Orionids. On the basis of the maximum-likelihood method of determining the power law luminosity function index, we derive s ≡ 1 + 2.5 log(r) = 1.56 ± 0.06 for the Perseids with m_v = +1 to ?5, and s ≈ 1.85 ± 0.1 for the Orionids with m_v = +2 to ?3. These values are somewhat lower than those found by other observers, but we confirm the approximate power law nature of the luminosity functions. Under the assumption that the masses of visual meteors are proportional to a power law function of the luminosities, this implies power law mass functions. If mass is directly proportional to luminosity, we have power law mass functions with the indices s given above.     

Simple Pi burst micropulsation events and associated aurora at two sites in Alaska

Type Pi magnetic-field pulsation bursts were selected for which the associated aurorae were relatively simple and stable and occurred in the ionosphere between College and Fort Yukon in alaska. Power spectral-density traces for College and Fort Yukon HandD were computed and were studied relative to the aurora and to more complex events presented in earlier studies. The power spectral-density traces associated to simpler aurora were found to be consistent with the assumption of simpler 3-dimensional current systems as generators of the Pi waves. The spectra of associated precipitation pulsations had a peak near 10mHz in common with the magnetic field spectra in all events, and also near 3 mHz in one event. The precipitation pulsations at 3 and 10mHz may have enhanced the magnetic field spectra at those frequencies through modulation of the ionospheric resistance to the current.