Cosmic-ray fluctuations in interplanetary space

Cosmic-ray (CR) fluctuations in both the drift and diffusion approximations are investigated and the results compared with experimental data. Kinetic equation is used to obtain equations for the second moment of the CR distribution function (the correlation function of the distribution function fluctuations) in both approximations. An application of these approximations to the correlation function equation gives the relations between the CR power spectra and random magnetic fields in interplanetary space. Different magneto-turbulence models are taken in consideration and the relations between the spectral indices are obtained in various frequency intervals.The theoretical results are compared with experimental data obtained by the network of neutron monitors. The CR power spectra observed at the ground level during the years 1978–1981 has been calculated. The investigated frequency range of 3×10^–8 to 10^–4 Hz consists of two parts, with a transient region of 10^–6 to 10^–5 Hz. Together with the background CR fluctuations the contribution of both the periodic and aperiodic phenomena is observed.     

Directivity of non-thermal X-ray emission from solar flares

An attempt has been made in the present work to reveal the directivity of solar non-thermal X-ray emission using the data obtained from the Prognoz and Explorer satellites. The frequency of occurrence of X-ray bursts and the mean intensities of the emission are studied as a function of distance from the central meridian. The most complete statistics have been obtained for the 4–24 keV X-ray bursts for the period 1970–1973. The X-ray burst frequency of occurrence normalized to the corresponding H flare frequency increases towards the solar limb. During the studied period this trend is more pronounced to the east than to the west. Distributions of the mean intensities of X-ray bursts are very similar to those of the frequency of occurrence of X-ray bursts; the effect is more noticeable for the low intensity bursts. The effect of the east-west asymmetry for H flares has been found to vary in magnitude and direction during the 20th solar activity cycle.     

Spontaneous and induced Čerenkov emission in a turbulent medium

It is shown that the presence of spatially random fluctuations in refractive index, about a mean exceeding unity, influences the power output of erenkov waves emitted by a charged particle in several ways.(1) The frequency spectrum of the spontaneous emission is altered by the fluctuations. (2) There is an induced erenkov emission, due to the interaction of the spontaneous field with the random refractive index variations. This induced field can, in certain frequency bands, be as large as the spontaneous field. And it also contains a backscattered component which propagates in theopposite direction to the particle. (3) The conditions for emission of the erenkov waves, be they spontaneous or induced, depend critically on both the mean refractive index, the particle velocity, the intensity and correlation length of the fluctuations. And the dependence is sensitive to the precise functional form of the two-point correlation function.Instruments detect the optical erenkov emission produced by cosmic ray particles penetrating the Earth's atmosphere (below about 5 km). Also gas erenkov counters are triggered by the passage of highly energetic particles through the gas. Since both the Earth's lower atmosphere and the gas counters contain turbulent fluctuations, the present calculation is of some interest in connection with particle energy loss mechanisms in turbulent media and the basic structure of such media.     

Observational study of the five-minute oscillations in the solar atmosphere

The 5-min oscillations in the photospheric velocity fields have been studied in detail from measurements on 14 absorption lines from three time sequences of spectrograms of high quality. The lines cover a range of heights in the solar atmosphere from log = + 0.2 to -1.2. Regions oscillating coherently are seen to have an average dimension of 8000 km and the oscillations in general last for 2 to 3 periods. The power spectrum analysis of high resolution enabled to determine the period of oscillation at each level very precisely. The period decreases with increase in height, being 304 s at the level log = + 0.2 and 295 s at the level log = -1.2. The low level lines possess considerable power in the low frequency range representing the convective overshoot from below. The oscillatory power increases with height, while the low frequency power decreases and the high frequency component remains substantially constant in the heights studied.The intensity fluctuations in the continuum, the line wing and core of Fe i 6358.695 have also been studied. The continuum power spectrum has practically all the power near the zero frequency range, with a very weak oscillatory component. The line wing intensity fluctuations resemble those in the continuum, whereas the line core clearly shows an oscillatory component similar to the velocity oscillations.     

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.     

p Modes in and Away from a Sunspot

A time series of GONG Dopplergrams for the period 10–14 May 1997 from Udaipur and Big Bear sites has been used to measure the velocity fluctuations in a sunspot (NOAA active region 8038) and quiet photosphere simultaneously. We observe that the power of pre-dominant p mode is reduced in the sunspot as compared to quiet photosphere by 39–52% depending on the location of the sunspot region on the solar disk. We also observe a relative peak frequency deviation of p modes in the sunspot, of the order of 80–310 Hz, which shows a linear dependence on the magnetic field gradient in the active region. The maximum frequency deviation of 310 Hz on 12 May appears to be an influence of a long-duration solar flare that occurred in this active region. We interpret this relative peak frequency deviation as either due to power re-distribution of p modes in the sunspot or a consequence of frequency modulation of these modes along the magnetic flux tubes due to rapidly varying magnetic field structure.     

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.     

Studies of granular velocities

Continuum brightness and Doppler velocity fluctuations in the lines 6301.5 and 6302.5 Å of Fei, measured in two selected spectrograms, are analysed by standard statistical (power- and coherence spectrum) methods. It is shown qualitatively that the oscillatory component of the velocity fluctuations (at spatial wavelengths > 4) decreases, while the supposedly granular component (at spatial wavelengths < 4) as well as the coherence between brightness and velocity fluctuations increases with optical depth.The spatial resolution of the spectrograms is estimated by comparing the observed power spectrum of brightness fluctuations with spectra found in the literature, assuming the combined instrumental and seeing spread function to be Gaussian. The resolution thus determined is = 1.24 ± 0.07. If the measured values are corrected accordingly, we obtain a true brightness rms of 10 to 14%, depending upon the shape of the power spectrum chosen for comparison, and a velocity rms at continuum optical depth of 1.3 km/sec. It is shown, however, that using the same correction function for the velocity power spectrum as for the brightness possibly gives rise to misestimating the velocity rms.Mitteilungen aus dem Fraunhofer Institut Nr. 100.     

The interplanetary magnetic field environment at Mercury's orbit

Mercury is exposed to the most dynamic heliospheric space environment of any planet in the solar system. The magnetosphere is particularly sensitive to variations in the interplanetary magnetic field (IMF), which control the intensity and geometry of the magnetospheric current systems that are the dominant source of uncertainty in determinations of the internal planetary magnetic field structure. The Magnetometer on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft has made extensive magnetic field observations in the inner heliosphere over the heliocentric distances of Mercury's orbit, between 0.31 and 0.47 AU. In this paper, Magnetometer data from MESSENGER, obtained at rates of 2 and 20 vector samples per second, are used together with previous observations in the inner heliosphere by Helios and at Earth by the Advanced Composition Explorer, to study the characteristics of IMF variability at Mercury's orbit. Although the average IMF geometry and magnitude depend on heliocentric distance as predicted by Parker, the variability is large, comparable to the total field magnitude. Using models for the external current systems we evaluate the impact of the variability on the field near the planet and find that the large IMF fluctuations should produce variations of the magnetospheric field of up to 30% of the dipole field at 200 km altitude, corresponding to the planned periapsis of MESSENGER's orbit at Mercury. The IMF fluctuations in the frequency range are consistent with turbulence, whereas evidence for dissipation was observed for . The transition between the turbulent and dissipative regimes is indicated by a break in the power spectrum, and the frequency of this break point is proportional to the IMF magnitude.     

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.     

Galaxy clustering in the nonlinear regime

We calculate the r.m.s. density fluctuations using the ID Zel'dovich approximation implemented with a virialization scheme for the very dense fluctuations. The results are quite different from those found in the linear regime with strong implications for the normalization of the power spectrum of the initial density fluctuations. We also calculate the nonlinear two-point correlation function for matter with an initial spectrum (equivalent to white noise in 3D) of fluctuations; differences from the linear approximation appear at scales much larger than those considered previously of 10h ^–1 Mpc.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Spectral analyses of solar photospheric fluctuations

Residual intensity fluctuation measurements within the wings of the 5183.6 Mgi b₁ line, obtained from two, high-resolution, high-dispersion, Sacramento Peak Observatory spectrograms, have been subtracted from intensity fluctuations in the adjacent continuum in order to isolate fluctuations associated exclusively with line formation. The useable spectral range for studying these lineformation fluctuations is restricted to wavelengths between 1040 and 7170 km because the subtraction increases the relative importance of noise and large-scale photographic variations across the spectrograms could not be completely removed. Power and cross-power (coherence and phase) spectra proved to be valuable diagnostic tools in isolating line-formation fluctuations.Over this spectral range, the line-formation fluctuations are characterized by flat power spectra as compared to those for continuum fluctuations, appreciable fluctuation rms relative to that for continuum fluctuations, and the necessity to multiply the wing fluctuations by a factor 0.95 _min 1.00 to most effectively isolate these fluctuations (Figures 3 and 4). That continuum fluctuations are modified in shape but otherwise not drastically changed in the line wings explains the flat spectrum. The relative rms's vary from 0.34 in the inner wing to 0.22 in the outer. The range of possible values for _min results from uncertainties in the photographic density-residual intensity calibration.     

Hydromagnetic waves associated with possible flux transfer events

Magnetic fluctuations in the hydromagnetic frequency band 0 to 0.05 Hz are examined at magnetospheric cusp latitudes during two times when ionospheric signatures of possible flux-transfer events were evident in the data. Ultralow frequency power is found to be very broad band in the range 0.02–0.05 Hz and to be more narrowly confined at a frequency 0.0025 Hz. At lower latitudes, the higher frequency (broad-band) power excites narrower-band field line resonances at the fundamental frequency of the respective field line — a standing Alfvén wave. The narrow-band power in the lower frequency band (period around 400 s) is approximately that expected for a field line resonance on a closed field line near the magnetopause; it also corresponds approximately to the width of the convected field-aligned current filament as observed on the ground. The reconnection process at the dayside magnetopause evidently plays an important role in the generation of low-frequency (0.008 Hz) hydromagnetic energy in the dayside magnetosphere, energy which can produce Alfvén waves deeper in the magnetosphere.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Modelling of temperatures of selected points in lunar maria

The purpose of this paper is to propose a numerical model representing the brightness temperature of ten selected sites of the Moon as measured in CERGA. A theoretical approach is proposed in which the temperature is expressed as a function of the local zenith distance of the Sun and a quantity depending upon the local zenith distance of the observer and the difference of their azimuths. The coefficients of this expression depend upon various integrals involving frequency function of the slopes of the lunar surface. The shadows are being qualitatively taken care of by introducing the phase angle .Using the observations, the most important coefficients of the formulae have been determined. The individual measurements are represented to about 2°.2. In the mean, the model seems to have an accuracy of about 1°, this number being confirmed by observations by the satellite METEOSAT.Finally, we give a tentative frequency function of the lunar slopes that is consitent with the temperature model.     

Spectral density of the burst component of solar noise storms

A spectral analysis of the radio noise storm (NS) fluctuations has shown that the power spectrum of any NS is not flat but hyperbolic and is satisfactorily described by the expression G(F) ～ c/F. The spectrum is monotonic and contains no components exceeding the level of statistical fluctuations, i.e., the observations reveal no steady periodic or resonant properties of the emission source. Therefore, the universally accepted assumption about the NS formation from short type I bursts is in conflict with the observations, because the spectrum of the sum of short pulses is flat, while the total energy of all short bursts with durations of the order of one second in actual NSs accounts for only 3–5% of the total energy of the burst component. The remainining 95% of the energy is emitted as long-lived bursts with durations from 1–2 to 300 s. The listed NS properties are inconsistent with the hypothesis of their emission through the action of nanoflares, because the time it takes for the bulk of the energy to be released as pulses with durations >10 s exceeds considerably the lifetime of the events called nanoflares.     

Fine structure in the inner corona observed at the 1970 eclipse

On the slit spectrogram obtained at the 1970 eclipse in Mexico, the intensities of four coronal lines (Nixiii 5116, Fexiv 5303, Fex 6374, and Nixv 6702) and the continuum were measured as a function of distance along the slit. It is found that there exist a lot of fine fluctuations both in the lines and in the continuum intensities superposed on a large scale formation. The correspondence of such fluctuations between the continuum and the lines is good, with the exception of the line 6374 which shows a peculiar fluctuation. It is shown that the intensities of the three lines 5116, 5303, and 6702 seem to be proportional to the square of the continuum intensity while the 6374 line intensity may be proportional to the fourth power or more.     

Infrared array measurements of sunspot magnetic fields

We have used a 128 × 128 format HgCdTl infrared array with the Sacramento Peak Observatory Vacuum Telescope (VTT) and Echelle spectrograph to obtain two-dimensional observations of the true magnetic field strength in a sunspot. The system we describe retains all of the spectral information contained in the unpolarized IR Fraunhofer line profile with time resolution of about a minute (depending on the scan area and spatial resolution). Unlike previous optical observations (cf. Adam, 1990), infrared observations readily allow direct field strength measurements out to the outer edge of the penumbra. Our data suggest that the magnetic flux density in the outer penumbra is not well described by an extrapolation of the quadratic polynomial, in normalized central distance, that describes the umbral field. We measure a relatively high field strength of 800 G at the penumbra-quiet-Sun boundary, which is consistent with the return-flux model of Osherovich and Garcia (1989).     

Small-Scale Angular Fluctuations of Cosmic Background Radiation. Basic relations

A statistical treatment is given of small-scale angular fluctuations of cosmic background radiation propagating in FRIEDMANN models with Λ= o. It is assumed that the fluctuations arise from

• i the discrete nature of radiation sources;
• ii density inhomogeneities in continuously distributed radiating matter or from
• iii variable absorption along different light paths towards the observer.

The observable angular correlation function of the intensity fluctuations is expressed in terms of statistical measures of the sources of fluctuations. The rather general formulae are reduced as far as possible without specifying the frequency region.     

Statistical Analysis of Periodic Oscillations in LASCO Coronal Mass Ejection Speeds

A large set of coronal mass ejections (CMEs, 3463) has been selected to study their periodic oscillations in speed in the Solar and Heliospheric Observatory (SOHO) mission’s Large Angle and Spectrometric Coronagraph (LASCO) field of view. These events, reported in the SOHO/LASCO catalog in the period of time 1996?–?2004, were selected based on having at least 11 height–time measurements. This selection criterion allows us to construct at least ten-point speed–distance profiles and evaluate kinematic properties of CMEs with a reasonable accuracy. To identify quasi-periodic oscillations in the speed of the CMEs a sinusoidal function was fitted to speed–distance profiles and the speed–time profiles. Of the considered events 22 % revealed periodic velocity fluctuations. These speed oscillations have on average amplitude equal to \(87~\mbox{km}\,\mbox{s}^{-1}\) and period \(7.8 R _{\odot}/241~\mbox{min}\) (in distance/time). The study shows that speed oscillations are a common phenomenon associated with CME propagation implying that all the CMEs have a similar magnetic flux-rope structure. The nature of oscillations can be explained in terms of magnetohydrodynamic (MHD) waves excited during the eruption process. More accurate detection of these modes could, in the future, enable us to characterize magnetic structures in space (space seismology).