Stellar Occultations by turbulent planetary atmospheres: A wave-optical theory including a finite scale height

A generalized wave-optical theory of stellar occultations by a turbulent planetary atmosphere is developed. The finite scale height of the atmosphere is retained for the first time. It is found that the finite scale height of the atmosphere affects the scintillations observed during the occultation in a number of ways which are most easily understood in terms of an effective Fresnel scale. We demonstrate the validity of a phase-changing screen approximation for occultation by a turbulent atmosphere in parameter ranges of general interest. Using this approximation various statistical properties of the fluctuating intensity are calculated explicitly. We present expressions for the total scintillation power, correlation function of the intensity, the cross-correlation at two frequencies, and its application to refractivity determinations. All of these expressions are given as a function of occultation depth and of parameters of the mean atmosphere and turbulence.     

Modeling the solar irradiance background via numerical simulation

Various small scale photospheric processes are responsible for spatial and temporal variations of solar emergent intensity. The contribution to total irradiance fluctuations of such small scale features is the solar irradiance background. Here we examine the statistical properties of irradiance background computed via a n-body numerical scheme mimicking photospheric space-time correlations and calibrated by means of IBIS/DST spectro-polarimetric data. Such computed properties are compared with experimental results derived from the analysis of a VIRGO/SPM data. A future application of the model here presented could be the interpretation of stellar irradiance power spectra observed by new missions such as Kepler.     

Plasmoid Dynamics in Flare Reconnection and the Frequency Drift of the Drifting Pulsating Structure

In the paper by Kliem, Karlický, and Benz (Astron. Astrophys. 360, 715, 2000) it was suggested, that plasmoids formed during the bursty regime of solar flare reconnection can be “visualised” in the radio spectra as drifting pulsating structures via accelerated particles trapped inside the plasmoid. In the present paper we investigate this idea in detail. First, simple statistical analysis supporting this hypothesis is presented. Then, by using the 2.5-D MHD (including gravity) model solar flare reconnection in the inhomogeneous, stratified atmosphere is simulated and the formation and subsequent ejection of the plasmoid is demonstrated. The ejected plasmoid, which is considered to be a trap for accelerated electrons, is traced and its plasma parameters are computed. To estimate the associated plasma radio emission we need to know locations of accelerated electrons and corresponding plasma frequencies. General considerations predict that these electrons should be distributed mainly along the magnetic separatrix surfaces and this was confirmed by using a particle-in-cell simulation. Finally, under some simplifying assumptions the model dynamic radio spectrum is constructed. The relation between the global frequency drift and the plasmoid motion in the inhomogeneous ambient atmosphere is studied. The results are discussed with respect to the observed drifting pulsation structures and their possible utilisation for flare magnetic field diagnostics.     

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model. II

We examine the effect produced by the variation of cosmological parameters on the power spectra of one-dimensional cross-sections of the cosmic microwave background maps in a narrow range of spatial frequencies. Variation of the Ω _b and Ω_Λ density parameters has little effect on the power spectrum deviation from the one expected within the ΛCDM model. At the same time, variations in the spectral index of primordial fluctuations significantly affect the amplitude of the power spectrum of one-dimensional cross-sections. We observe a lack of signal generated by the even harmonics in the ILC map as compared with model expectations.     

Galactic magnetic turbulence from radio data

Fluctuations in the Galactic synchrotron emission can be traced by the angular power spectrum of radio maps at low multipoles. At frequencies below few GHz, large-scale anisotropies are mainly induced by magnetic field turbulence, since non-thermal electrons radiating at these frequencies are uniformly distributed over the scales of magnetic field inhomogeneities. By performing an analysis of five radio maps, we extract constraints on turbulence spectral index and halo scale. Results favour a power spectrum significantly flatter than for 3D Kolmogorov-like turbulence, and a thin halo. This can be interpreted as an indication supporting non-conventional models of propagation of cosmic-ray particles in the Galaxy, or as a suggestion of a spectral-index break in the observed magnetic turbulence power spectrum.     

Mixing-length theory and the excitation of solar acoustic oscillations

The stability of radial solar acoustic oscillations is studied using a time-dependent formulation of mixing-length theory. Though the radiation field is treated somewhat simplistically with the Eddington approximation, and we appreciate that any coupling of the pulsation to the radiation field is important, for the lower frequency radial modes that have been computed this should not produce too serious an error. Instead, we have concentrated upon treating the coupling with convection as accurately as is currently possible with generalized mixing-length theory in order to learn something about its pertinence. Our principal conclusion is that, according to this theory, solar radial acoustic oscillations are expected to be stable and generated by turbulence. Moreover, the theory predicts changes in mode frequency that may, in part, explain the discrepancy between solar observations and the adiabatic pulsation frequencies of theoretical models. We also compute the amplitudes of the modes using a theory of stochastic excitation. These are in good agreement with observed power spectra.     

Turbulence in planetary occultations: I. A theoretical formulation

First- and second-order effects of turbulance on radio propagation through an atmosphere with uniformly varying average refractive index combined with a random component due to turbulence are calculated both from the Eikonal equation of geometrical optics and from a weak scattering wave-optical formulation. To second order in the strength of the turbulence, the average phase path is reduced relative to that in a nonturbulent atmosphere with the same average refractivity, implying a higher average phase velocity of the radiowave when turbulence is present. Also, the magnitude of the phase offset is controlled by the size of the principal Fresnel zone, implying that the medium becomes slightly dispersive by the addition of turbulence. Turbulence effects on the Doppler frequency separate into three distinct types involving: (1) zero-mean terms having the form of a coupling between the average and turbulent refractive field components; (2) terms of second order in the turbulence, modified by the average refractive field and consistent with an average bias in Doppler frequency when the rms turbulent intensity has a spatial variation normal to the raypath; and (3) additional second-order terms, again modified by the average refractive field, having a nozeroo average even for homogeneous turbulence. Under plausible conditions (1) produces the largest mean-square effects, while (2) represents the largest contribution to the average bias in Doppler frequency. For a turbulence power spectrum proportional to the (?p) power of the wave-number, the bias in Doppler frequency, like the average bias in phase path, depends on the radiation wavelength as $\text{λ}{}^{\mathrm{<mtext>p</mtext><mtext>2-2</mtext>}}$, or as $\text{λ}{}^{\mathrm{<mtext>?1</mtext><mtext>6</mtext>}}$ for Kolmogorov turbulence.     

Strong turbulence and atmospheric waves in stellar occultations

Many of the problems of stellar occultation observations stem from the difficulty of determining the effects of realistic atmospheric structure on the lightcurves. General techniques for producing model lightcurves for a variety of realistic atmospheric irregularities, including turbulence and inertia-gravity waves, are presented and applied. Using numerical simulations which model the propagation of a wave through a phase-changing screen, the limit of strong scintillations for one-dimensional, Kolmogorov-like turbulence, both for a point source and for extended sources, is investigated in some detail, and significant departures from the behavior in the weak scintillation regime are found. The results are compared with published analytical results and recent occultation data. The effects of large-scale atmospheric waves with realistic horizontal structure are examined, and the reliability of the numerical inversion method of retrieving the true atmospheric vertical structure under circumstances of strong ray crossing and horizontal inhomogeneities is assessed. The simulations confirm that large-scale layered features of the atmosphere are accurately recovered; horizontally inhomogeneous structures (including turbulence) with coherence scale $\text{L ? (2πRH)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ (where R = planetary radius and H = scale height) have little effect on the derived temperature profiles. It is concluded that analysis of occultations may eventually allow us to determine both the quasiglobal atmospheric structure and the statistical characteristics of small-scale refractivity variations.     

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.     

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.     

Turbulence in planetary occultations: III. Effects on atmospheric profiles derived from intensity measurements

The intensities of radio and optical signals observed during spacecraft and stellar occultations by planets scintillate due to atmospheric turbulence. The combined effect of turbulent fluctuations in refractivity and the average atmospheric gradient are found to produce slightly smaller signal intensity scintillations than the homogeneous case when there is no gradient, in contrast to a prediction that the scintillations would be markedly increased. Profiles of atmospheric temperature and pressure derived from intensity measurements are found to have much larger errors due to turbulence than do the corresponding profiles derived from radio Doppler frequency measurements. However, such errors are still small in the limit of weak scattering, which is assumed here. Radio and optical occultation experiments tend to be complementary since the generally shorter distances involved in the former mean that the radio experiments can probe relatively deeply into the atmosphere, while the optical experiments are limited to tenuous atmospheric regions. Because the radio experiments generally have a much greater dynamic measurement range, they are more likely to encounter conditions where strong scattering occurs than will the optical occultation experiments, provided the rms turbulent refractivity increases with depth approximately as the refractivity of the quiescent atmosphere.     

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.     

Quintessential Cosmology Novel Models of Cosmological Structure Formation

We examine the possibility that a substantial fraction of the total energy density in a spatially flat Universe is composed of a time-dependent and spatially inhomogeneous component whose equation-of-state differs from that of baryons, neutrinos, dark matter, or radiation. In this lecture, we report on our investigations of the case in which the additional energy component, dubbed "quintessence", is due to a dynamical scalar field evolving in a potential. We have computed the effects on the background cosmological evolution, the cosmic microwave background (CMB) and mass power spectrum, finding a broad range of cosmologically viable models. We stress three important features of the quintessence or Q-component: the time evolution of the equation-of-state; the length-scale dependence of the speed of propagation of the fluctuations in the Q-component; and, the contribution of quintessence fluctuations to the CMB anisotropy spectrum. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scintillations during occultations by planets I. An approximate theory

Fluctuations are observed during occultations of both stars and spacecraft by planetary atmospheres. Existing treatments of spacecraft scintillations ignore a major effect unique to occultations: the severe flattening of the Fresnel zone or source image by defocusing. Other large effects, due to “saturation” of the scintillation, have also been ignored. The deeper portions of atmospheric temperature and density profiles inferred from occultation data are seriously in error if other planets' atmospheres are as turbulent as our own. Thus, profiles obtained from entry probes (e.g., the Soviet Venera series) are probably more accurate than those from radio occultation (Mariner 5 and 10) data. Scintillation greatly reduces the information obtainable from occultation observations; much of the detail attributed to layering in published profiles is probably due to aliasing of turbulence. This paper gives an approximately correct theoretical treatment that is a substantial improvement over published theories, and shows how a more accurate theory could be constructed. Some methods for a more accurate determination of atmospheric structure are proposed.     

Measurements of the interplanetary magnetic field in relation to the modulation of cosmic rays

Field strength distributions and low frequency power spectra are derived from interplanetary field measurements made by the HEOS-1 and HEOS-2 satellites during the years 1969–1973. The spectral analysis involved the use of a technique which is shown to allow correctly for missing data. Comparison spectra, derived by the same technique, are presented for the years 1963–1968. The use of mear-field-aligned co-ordinates enabled the easy separation of the transverse and longitudinal fluctuation spectra. A power law function involving a ‘break point’-frequency was fitted to each spectrum by a least squares technique. The total power level, the power spectral density at zero frequency and the correlation length are found to vary significantly and in a similar way over the solar cycle. The magnitude and phase of these variations are compared with measurements of the cosmic ray neutron monitor rate and the coronal green line intensity and the influence of mid-latitude solar phenomena on the character of the interplanetary field in the ecliptic is demonstrated. The correlation length and zero frequency power density are found to be considerably larger than previously estimated and, contrary to the usual assumption in modulation theory, the rms amplitude of the perturbation field is comparable to the mean field experienced by the high rigidity particles. Although the mean interplanetary field strength is found to be independent of the level of solar activity, during higher activity the most probable vector average decreases by approximately 0.5 γ due to the enhanced directional fluctuation in the field. Power anisotropy measurements suggest that Alfvénic disturbances in the solar wind have fluctuation spectra confined mainly to frequencies larger than 10^?3 Hz. The data are interpreted as indicating that the cosmic ray intensity in the Galaxy is some 75% larger than the intensity recorded by neutron monitors on Earth. Previous failure to find a correlation between neutron monitor intensity and interplanetary field parameters is attributed to a lack of statistical accuracy in the field data. The measured power spectra are used to estimate the magnitude of the parallel diffusion coefficient using the relationships derived by Klimas and Sandri, Jokipii, and Quenby et al.     

Modeling of high-frequency variability in X-ray binaries with black holes

The properties of the aperiodic variability in X-ray binaries with black holes are considered. The power spectra of the luminosity variability for a flat accretion disk that is an emission source with a powerlaw energy spectrum have been modeled. At low frequencies the derived power spectrum has the form of a power law with a slope ? ≈ ?1 and a cutoff at a frequency corresponding to the characteristic frequency of fluctuations at the inner disk edge; at higher frequencies the power spectrum has a complex form. The high-frequency variability is suppressed due to the arrival time delays of photons emerged in different parts of the disk. The presence of azimuthal accretion rate fluctuations in the disk and the disk surface brightness nonuniformity in the observer’s imaginary plane caused by the relativistic effects give rise to an additional variability component at frequencies ～ 200 Hz.     

Power spectral analysis of Jupiter’s clouds and kinetic energy from Cassini

We present suggestive evidence for an inverse energy cascade within Jupiter’s atmosphere through a calculation of the power spectrum of its kinetic energy and its cloud patterns. Using Cassini observations, we composed full-longitudinal mosaics of Jupiter’s atmosphere at several wavelengths. We also utilized image pairs derived from these observations to generate full-longitudinal maps of wind vectors and atmospheric kinetic energy within Jupiter’s troposphere. We computed power spectra of the image mosaics and kinetic energy maps using spherical harmonic analysis. Power spectra of Jupiter’s cloud patterns imaged at certain wavelengths resemble theoretical spectra of two-dimensional turbulence, with power-law slopes near −5/3 and −3 at low and high wavenumbers, respectively. The slopes of the kinetic energy power spectrum are also near −5/3 at low wavenumbers. At high wavenumbers, however, the spectral slopes are relatively flatter than the theoretical prediction of −3. In addition, the image mosaic and kinetic energy power spectra differ with respect to the location of the transition in slopes. The transition in slope is near planetary wavenumber 70 for the kinetic energy spectra, but is typically above 200 for the image mosaic spectra. Our results also show the importance of calculating spectral slopes from full 2D velocity maps rather than 1D zonal mean velocity profiles, since at large wavenumbers the spectra differ significantly, though at low wavenumbers, the 1D zonal and full 2D kinetic energy spectra are practically indistinguishable. Furthermore, the difference between the image and kinetic energy spectra suggests some caution in the interpretation of power spectrum results solely from image mosaics and its significance for the underlying dynamics. Finally, we also report prominent variations in kinetic energy within the equatorial jet stream that appear to be associated with the 5 μm hotspots. Other eddies are present within the flow collar of the Great Red Spot, suggesting caution when interpreting snapshots of the flow inside these features as representative of a time-averaged state.     

Theory of radio occultation by Saturn's rings

The radio occultation technique is developed here as a new method for the study of the physical properties of planetary ring systems. Particular reference is made to geometrical and system characteristics of the Voyager dual-wavelength (13 and 3.6 cm) experiment at Saturn. The rings are studied based on the perturbations they introduce in the spectrum of coherent sinusoidal radio signals transmitted through the rings from a spacecraft in the vicinity of the planet to Earth. Two separate signal components are identified in a perturbed spectrum: a sinusoidal component that remains coherent with the incident signal but is reduced in intensity and possibly changed in phase, and a Doppler-broadened incoherent component whose spectral shape and strength are determined by the occultation geometry and the radial variation of the near-forward radar cross section of illuminated ringlets. Both components are derived in terms of the physical ring properties starting from a conventional radar formulation of the problem of single scattering on ensembles of discrete scatterers, which is then generalized to include near-forward multiple scattering. The latter is accomplished through special solutions of the equation of transfer for particles that are larger than the wavelength. When the occultation geometry is optimized, contributions of an individual ringlet to a perturbed spectrum can be identified with radial resolution on the order of a few kilometers for the coherent component and a few hundred kilometers for the incoherent one, thus permitting high-resolution reconstruction of the radial profile of the optical depth, as well as reconstruction of the radar cross section of resolved ringlets. Simultaneous estimates of the optical depth and radar cross section of a ringlet at 3.6 cm-gl allow separation of its aerial density and particle size, if the particles are of known material and form a narrow size distibution with radii greater than several tens of centimeters. This separation is also achieved for radii ?10 cm from differential effects on the coherent signal parameters at 3.6- and 13-cm wavelengths. For the more general case of a broad size distribution modeled by a power law, the absence of differential effects on the coherent signal binds the minimum size to be ?10 cm. In this case, the radius inferred from an estimate of the radar cross section represents an equivalent radius, which is strongly controlled by the maximum size of the distribution provided that the power index is in the range 3 to 4. On the other hand, detection of differential coherent signal extinction determines an upper bound on the maximum size and a lower bound on the power index, assuming water-ice particles. These bounds, together with an inferred equivalent size, constrain the size distribution at both its small and large ends.     

Stellar occultations by turbulent planetary atmospheres: A heuristic scattering model

A model of ray refraction by an isothermal atmosphere with a scattering screen at the center of bending is used to generate analytic results which simulate the effects of real atmospheric turbulence on occultations. Calculations are carried through for scattering which is constant with height and for exponential height dependence. The effect of the scattering is to bias the the mean intensity of the occulted source, and hence systematically to distort bending angles and height differences obtained from inversion of the intensity data. However, the effect is of order 〈δ?²〉/?² for either model, where 〈δ?²〉 is the mean square scattering angle and ? is the average bending angle. The effect turns out to be small for plausible turbulence, since 〈δ?²〉/gfe² is of approximately the same order as the relative mean square density fluctuation. Thus the random effects of turbulence are unlikely to be a source of large systematic error in occultations, provided that the data can be meaningfully averaged either temporally or over a number of occultation events.     

The continuous spectrum of MHD waves in 2D solar loops and arcades. First results on poloidal mode coupling for poloidal magnetic fields

A first attempt is made to study the continuous spectrum of linear ideal MHD for 2D solar loops and to understand how 2D effects change the continuum eigenfrequencies and continuum eigenfunctions. The continuous spectrum is computed for 2D solar loops with purely poloidal magnetic fields and it is investigated how non-circularity of the cross-sections of the poloidal magnetic surfaces and variations of density along the poloidal magnetic field lines change the continuous spectrum and induce poloidal wave number coupling in the eigenfunctions. Approximate analytical results and numerical results are obtained for the eigenfrequencies and the eigenfunctions and the poloidal wave number coupling is clearly illustrated. It is found that the continuum frequencies are substantially increased, that the ranges of the continuum frequencies are considerably enlarged and that the derivatives of the continuum frequencies normal to the magnetic surfaces are substantially increased. The eigenfunctions are strongly influenced by poloidal wave number coupling. Implications of these findings for the heating mechanisms of resonant absorption and phase mixing are briefly considered.Research Assistant of the Belgian National Fund for Scientific Research.