Acoustic-Power Maps of Solar Active Regions with Direction Filters and Phase-Velocity Filters

We study the properties of power maps of solar acoustic waves filtered with direction filters and phase-velocity filters. A direction filter is used to isolate acoustic waves propagating in a narrow range of directions. The acoustic-power map of the waves filtered with a direction filter shows extended reduced-power features behind magnetic regions with respect to the wave direction. A phase-velocity filter is further applied to isolate waves with similar wave paths. In the power maps of the waves filtered with both a direction filter and a phase-velocity filter, a reduced-power image of a sunspot appears behind the sunspot with respect to the wave direction. The distance between the sunspot and the secondary image is consistent with the one-skip travel distance of the wave packet associated with the phase-velocity filter. The waves filtered with direction and phase-velocity filters at the location of the secondary image could be used to probe the sunspot. In the quiet Sun, spatial fluctuations exist in any acoustic-power map. These fluctuations are mainly caused by interference among modes with the same frequency. The fluctuations are random with two properties: They change rapidly with time, and their magnitude decreases with the square root of the number of frames used in computing the acoustic-power map.     

Propagation of tropospheric gravity waves into the upper atmosphere of Mars

We study the propagation of gravity waves in the martian atmosphere using a linearized one-dimensional full-wave model. Calculations are carried out for atmospheric parameters characteristic of Mars Orbiter Laser Altimeter (on Mars Global Surveyor MGS) observations of apparent gravity waves in high latitude clouds and MGS radio occultation measurements of temperature variations with height suggestive of gravity wave activity. Waves that reach the thermosphere produce fluctuations in density comparable in amplitude with the density variations detected in Mars Odyssey aerobraking data. Gravity waves of modest amplitude are found to deposit momentum and generate significant heating and cooling in the martian atmosphere. The largest heating and cooling effects occur in the thermosphere, at altitudes between about 130 and 150 km, with heating occurring at the lower altitudes and cooling taking place above.     

A re-analysis of the 1971 Beta Scorpii occultation by Jupiter: study of temperature fluctuations and detection of wave activity

Data from the 13 May 1971 β Scorpii occultation by the southern polar region of Jupiter (Vapillon et al., 1973, Astron. Astrophys. 29, 135-149) are re-analyzed with current methods. We correct the previous results for an inacurrate background estimation and calculate new temperature profiles, that are now consistent with the results of other observers of this occultation, as well as with the current knowledge of the jovian atmosphere. The characteristics of the profiles of temperature gradient and the spectral behavior of the temperature fluctuations are found to be similar to the results of previous investigations of planetary atmospheres and in agreement with the presence of atmospheric propagating gravity waves in the jovian atmosphere. We use a wavelet analysis of the temperature profiles to identify the dominant modes of wave activity and compare the reconstructed temperature fluctuations to model-generated gravity waves.     

The energy scale of inflation: is the hunt for the primordial B-mode a waste of time?

Recent theoretical results indicate that the detection of primordial gravity waves from inflation may be a hopeless task. First, foregrounds from lensing put a strict lower limit on the detectability of the B-mode polarization signal in the cosmic microwave background, the “smoking gun” for tensor (gravity wave) fluctuations. Meanwhile, widely accepted theoretical arguments indicate that the amplitude of gravity waves produced in inflation will be below this limit. I argue that failure is not inevitable, and that the effort to detect the primordial signal in the B-mode, whether it succeeds or fails, will yield crucial information about the nature of inflation.     

Quenching of the beam-plasma instability by large-scale density fluctuations in 3 dimensions

A model is presented to explain the highly variable yet low level of Langmuir waves measured in situ by spacecraft when electron beams associated with type III solar bursts are passing by; the low level of excited waves allows the propagation of such streams from the Sun to well past 1 AU without catastrophic energy losses. The model is based, first, on the existence of large-scale density fluctuations that are able to efficiently diffuse small-k beam-unstable Langmuir waves in phase space, and, second, on the presence of a significant isotropic non-thermal tail in the distribution function of the background electron population, which is capable of stabilizing larger k modes. The strength of the model lies in its ability to predict various levels of Langmuir waves depending on the parameters. This feature is consistent with the high variability actually observed in the measurements. The calculations indicate that, for realistic parameters, the most unstable, small k modes are fully stabilized while some oblique mode with higher k and lower growth rate might remain unstable; thus a very broad range of levels of Langmuir waves is possible from levels of the order of enhanced spontaneous emission to the threshold level for nonlinear processes. On the other hand, from in situ measurements of the density fluctuations spectrum by ISEE-1 and 2 in the vicinity of the Earth, it is shown that measured 100 km scale fluctuations may be too effective in quenching the instability. If such strong density fluctuations are common in the solar wind, we show they must be highly anisotropic in order to allow the build-up of Langmuir waves to the observed mV m^–1 range. Moreover, the anisotropy must be such that the strongest variations of density occur in a plane perpendicular to the magnetic field.     

Inhomogeneities in the solar atmosphere from the CaII infra-red lines

From a time sequence of high dispersion spectra taken by Evans, the solar fine structures are studied in the Caii infra-red triplet. The Doppler shifts and the intensity fluctuations in different points of the profiles are converted into fluctuations of the model atmosphere. A weighting function method is worked out in that purpose. The theoretical line profiles are computed in non LTE from a program written by Dumont. The results are arranged in two parts:

1. Low temporal frequencies. A three-column model describes the steady field of temperature, microturbulence and radial velocities fluctuations in the photosphere-chromosphere transition zone.
2. Oscillations. The propagation of waves is considered in the three above-mentioned columns. The oscillation amplitudes seem statistically larger in the hot column. The vertical phase velocity is very large, even for frequencies higher than the cut-off frequency of acoustic waves. Velocity and temperature fluctuations are connected by different curves of phase-lags and amplitude ratios suggesting a short relaxation time of the temperature fluctuations in the low chromosphere.

     

Darkening and visibility functions for the global five-minute oscillations

A theory for the brightness fluctuations of the Sun as a star under the effect of its global oscillations has been developed. Formulas for the darkening and visibility of p-modes are derived and their calculations are performed in the local approximation for adiabatic oscillations. Observational data from the DIFOS multichannel photometer onboard the CORONAS-F satellite are used to solve the inverse problem of determining the amplitude of the five-minute temperature fluctuations in the solar photosphere as a function of the height. Analysis of the solution and comparison with the results of other authors suggest that the predicted temperature waves resulting from a linear transformation of p-modes in the photosphere exist in the photosphere. The wavelength and phase velocity of the temperature waves are considerably smaller than those of acoustic waves. It turns out that the solar brightness fluctuations should be produced mainly by the temperature waves in the photosphere, not by the p-modes themselves. The darkening function for the brightness fluctuations is oscillatory in behavior, while the visibility function can differ markedly from that for the Doppler shifts of spectral lines produced by p-modes. These properties are important for interpreting the observations of stellar oscillations based on stellar brightness fluctuations.     

Cassini imaging of Saturn's rings: II. A wavelet technique for analysis of density waves and other radial structure in the rings

We describe a powerful signal processing method, the continuous wavelet transform, and use it to analyze radial structure in Cassini ISS images of Saturn's rings. Wavelet analysis locally separates signal components in frequency space, causing many structures to become evident that are difficult to observe with the naked eye. Density waves, generated at resonances with saturnian satellites orbiting outside (or within) the rings, are particularly amenable to such analysis. We identify a number of previously unobserved weak waves, and demonstrate the wavelet transform's ability to isolate multiple waves superimposed on top of one another. We also present two wave-like structures that we are unable to conclusively identify. In a multi-step semi-automated process, we recover four parameters from clearly observed weak spiral density waves: the local ring surface density, the local ring viscosity, the precise resonance location (useful for pointing images, and potentially for refining saturnian astrometry), and the wave amplitude (potentially providing new constraints upon the masses of the perturbing moons). Our derived surface densities have less scatter than previous measurements that were derived from stronger non-linear waves, and suggest a gentle linear increase in surface density from the inner to the mid-A Ring. We show that ring viscosity consistently increases from the Cassini Division outward to the Encke Gap. Meaningful upper limits on ring thickness can be placed on the Cassini Division (3.0 m at r∼118,800 km, 4.5 m at r∼120,700 km) and the inner A Ring (10-15 m for r<127,000 km).     

The propagation of Alfvén waves and their directional anisotropy in the solar wind

The propagation of solar Alfvén waves in interplanetary space is studied in the approximation of geometrical optics. Ray paths and the change of wave vectors and amplitudes along the rays are determined assuming an Archimedean-spiral interplanetary magnetic field. In particular, the Alfvénic fluctuations in the 2 directions perpendicular to the magnetic field direction are calculated under the assumption that the Alfvén waves are produced at the Sun and emitted with an isotropic directional distribution from a reference level close to the Sun. It turns out that due to the combined effect of spherical expansion of the solar wind flow and the spiralling of the interplanetary field the magnetic fluctuations in the direction perpendicular both to the unperturbed field and the radial direction have much more power than in the other directions (directional anisotropy).Our results are compared with spacecraft observations made by Belcher and Davis (1971), that show an anisotropy of a similar character. It is argued that under average conditions the physical process leading to an anisotropy is not selective coupling of Alfvén waves into compressional waves, as suggested by Belcher and Davis, but rather the above mentioned dissipationfree effect of geometrical optics. Finally, arguments are presented to explain the discrepancy between the calculated high anisotropy and the measured low anisotropy in terms of finite amplitude effects and wavescattering.     

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.     

Traveling waves in the martian atmosphere from MGS TES Nadir data

We have characterized the annual behavior of martian atmospheric traveling waves in the MGS TES data set from the first two martian years of mapping. There is a high degree of repeatability between the two years. They are dominated by strong low zonal wavenumber waves with high amplitudes near the polar jets, strongest in late northern fall and early northern winter. The m=1 waves have amplitudes up to about 20 K, are vertically extended, and occasionally extend even into the tropics. Periods for m=1 range from 2.5 to 30 sols. Much weaker waves were identified in the south, with amplitudes less than about 3.5 K. Traveling waves with m=2 and m=3 are also seen, but their amplitudes are typically limited to less than 4 K, and are generally more confined near the surface. In the north, they are more evident in fall and spring rather than winter solstice, which is clearly dominated by m=1 waves. Some evidence of storm tracks has been identified in the data, with accentuated weather-related temperature perturbations near longitudes 200° to 320° E for both the southern and northern hemispheres near latitude ±65° at the surface. Some evidence was also found for a sharpening of longitudinal gradients into what may be frontal systems. EP flux divergences show the waves extracting energy from the zonal mean winds. When the m=1 waves were strongest, decelerations of the zonal jet of order 30 m/(s sol) were measured. Above 1 scale height, the waves extract energy from the jet predominately through barotropic processes, but their character is overall mixed barotropic/baroclinic. Inertial instabilities may exist at altitude on the equatorward flanks of the polar jets, and marginal stability extends through to the tropics. This may explain the coordination of the tropical behavior of the waves with that centered along the polar jet, consistent with the ideas expressed in Wilson et al. (2002, Geophys. Res. Lett. 29, #1684) and similar to those in Barnes et al. (1993, J. Geophys. Res. 98, 3125-3148). Throughout the year, there exist large regions with the meridional gradient of PV less than zero, but they are strongest near winter solstice. Poleward of the winter jet, the regions of instability reach the surface, equatorward they do not. These regions, satisfying a necessary criterion for instability, likely explain the genesis of the waves, and perhaps also their bimodal character between surface (faster waves) and altitude (slow m=1 waves).     

Wave localization in solar type III events

A suggested application of the theory of wave localization to type III solar radio events in the solar wind is discussed critically. A classical wave theory that enables one to relate wave localization to the observed spectrum of density fluctuations is summarized. Localization (in one dimension) is due to backscattering and depends on the density spectrum at a wavenumber equal to twice that of the scattered wave. The localization length is estimated for the Langmuir waves, for which the appropriate density fluctuations require ion sound waves, and for transverse waves, for which (at least for the fundamental) the spectrum of the appropriate density fluctuations has been measured in situ. In all cases the localization length is much shorter than the size of a type III event. For fundamental radiation the localization length can be even shorter than the observed sizes of clumps of Langmuir waves.It is concluded that although wave localization may be significant in type III events, most of its consequences have already been recognized in models that invoke multiple scattering. A notable exception is localization of fundamental transverse waves to the clumps of Langmuir waves, which provides a natural explanation for the observed brightness temperatures and for the initial predominance of fundamental over harmonic emission.     

Parametric coupling between electromagnetic ion-cyclotron and shear Alfvén waves

The nonlinear interaction between finite amplitude electromagnetic ion-cyclotron waves and shear-Alfvén waves is considered. It is shown that this process is governed by three coupled equations. They are here used to study modulational instabilities. The relevance of our investigation to low-frequency electromagnetic fluctuations in space plasmas is pointed out.     

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 detection and utilization of gravity waves in airglow studies

We develop here theoretical relations between fluctuations of airglow brightness, fluctuations of temperature as revealed by airglow, and the atmospheric gravity waves that are believed to cause these fluctuations. We note and account for differences between our relations and those obtained by Krassovsky (1972, Ann. Geophys. 28, 739) and Weinstock (1978, J. geophys. Res. 83, 5175), correcting both of the latter in the process. We explicitly repudiate the need for a nonlinear treatment of O₂(¹Σ_g) emissions as it was asserted by Weinstock, one aspect of the nonlinear treatment he gave, and the conclusions he drew from that treatment, including, inter alia, the conclusion that temperature fluctuations carry more meaning as a diagnostic than do brightness fluctuations. Instead, we note the dependence of both types of fluctuation on variable gravity-wave parameters, which dependence can be applied to the study of gravity waves via airglow or of airglow via gravity waves. As a first step, we note the ability of the present analysis to account for certain observations of OH and O₂(¹Σ_g) emissions that have been, until now, inadequately or incorrectly explained, and we stress the importance of the proper measurement of parameters such as wave frequency and propagation speed if our own tentative explanations are to be put to the test and further progress is to be made.     

Whistler wave cascades in solar wind plasma

Non-linear, three-dimensional, time-dependent fluid simulations of whistler wave turbulence are performed to investigate role of whistler waves in solar wind plasma turbulence in which characteristic turbulent fluctuations are characterized typically by the frequency and length-scales that are, respectively, bigger than ion gyrofrequency and smaller than ion gyroradius. The electron inertial length is an intrinsic length-scale in whistler wave turbulence that distinguishably divides the high-frequency solar wind turbulent spectra into scales smaller and bigger than the electron inertial length. Our simulations find that the dispersive whistler modes evolve entirely differently in the two regimes. While the dispersive whistler wave effects are stronger in the large-scale regime, they do not influence the spectral cascades which are describable by a Kolmogorov-like   k ^−7/3  spectrum. By contrast, the small-scale turbulent fluctuations exhibit a Navier–Stokes-like evolution where characteristic turbulent eddies exhibit a typical   k ^−5/3  hydrodynamic turbulent spectrum. By virtue of equipartition between the wave velocity and magnetic fields, we quantify the role of whistler waves in the solar wind plasma fluctuations.     

Clumpy Langmuir waves in type III radio sources

A model is developed for the clumpy Langmuir waves observed in type III source regions. In this model the waves are generated by instability of a beam which propagates outward from the Sun in a state close to marginal stability. Ambient density perturbations cause fluctuations about the marginally stable state, leading to nonuniformities in both beam and waves and, hence, to spatially inhomogeneous growth. High damping rates and high wave levels are strongly anti-correlated, leading to suppression of the net damping. Below saturation stochastic growth causes the waves to follow a random walk in the logarithm of their energy density and the resulting probability of observing a field of magnitude E is approximately proportional to E ^-1. Comparison with observations shows that this model can account for the levels and clumpiness of the Langmuir waves, the small net dissipation required for the beams to propagate to 1 AU, the characteristic decay time of type III electromagnetic emission, and the negative mean growth rate observed in situ in type III sources. At 1 AU only the very highest fields approach the threshold for nonlinear wave collapse, but this threshold may be more commonly exceeded closer to the Sun.     

A theory of the origin of the split pair burst emission from the solar corona

The radio emissions caused by electron streams in a non-isothermal plasma are studied quantitatively. It is proposed that conversion of the stream-excited plasma waves into electromagnetic waves by scattering on the thermal fluctuations at nonisothermal sonic oscillation frequency is the origin of the emission of the split-pair burst near the plasma frequency. The occurrence of the split-pair bursts near the second harmonic of the plasma frequency can be due to combination scattering of the stream-excited plasma waves by electron density fluctuations which are produced by the scattered plasma waves. With a streamer model in which the electron densities are two times those in Newkirk's model, both the observed frequency splitting and the rate of drift of the split pair can be explained as the result of plasma radiation caused by a stream of 10 keV electrons. A tentative model for the split-pair emission is suggested.     

Wave systems in the chromosphere

Observations are reported of two, possibly three, distinct wave systems in the Hα chromosphere.

1. Velocity films show waves propagating predominantly outwards along mottles and fibrils from as close as 2000 km to the network axis at velocities of the order of 70 km s^-1. The line-of-sight component of the velocity amplitude is estimated to be typically 5 km s^-1. The velocities are accompanied by propagating intensity fluctuations. The system is interpreted as one of basically Alfvén waves. Similar waves are observed propagating predominantly outwards along superpenumbral fibrils radiating from a small sunspot.
2. The velocities in the chromospheric granulation undergo fluctuations of an oscillatory character but without any observable horizontal propagation. The intensities show a close correlation with the velocities, maximum intensity occurring about T/4 after maximum downward velocity. The period is variable across the surface (2.5 min upwards). The intensity-velocity correlation is characteristic of a standing compressional wave.
3. Intensity cinefilms at Hα line centre show in places a horizontal drift of the chromospheric granulation pattern at about 12 km s^-1 without any accompanying vertical velocity fluctuations. It is not known whether this is due to a gas stream at sonic velocities, or to a horizontally propagating sound wave.

The Alfvén wave system is shown to make a significant contribution to coronal heating. Whether the velocity fluctuations in the chromospheric granulation also make an important contribution depends on whether there are upwardly propagating or standing waves; this is not yet established despite the intensity-velocity correlation.