Fractal turbulence and the origin of the galaxies and of the large-scale structure

Observations show that the geometry of the large-scale distribution of galaxies is like a self-similar sponge which can be regarded as a fractal in fractal geometry (the Sierpinski sponge) with the fractal dimensionD _f=3–, =1.7–1.8 is the index in the two-point correlation function.We suggest using a new scheme to explain the origin of galaxies and large-scale structure. In our model, we assume that the density perturbations in the early Universe are adiabatic, and once they come within the horizon, they might produce the vortices of the fractal turbulence because of the Thomson drag. A model of the fractal turbulence is also given in this paper. The results obtained show that the basic characteristics of the galaxies (massM _g, angular momentumJ _g) and the large-scale structure (fractal dimensionD _f) can be explained, if the spectrum of early perturbations is the scale-free Zeldovich spectrum.     

Fracton Excitations as a Driving Mechanism for the Self-Organized Dynamical Structuring in the Solar Wind

Structural properties of the interplanetary magnetic field (IMF) are discussed. Our main interest is concentrated on the dynamical structuring mechanisms associated with the dominant role of the wave processes in the solar wind. We argue that the IMF possibly reveals the self-organized clustering driven by the low-frequency magnetosonic waves. It is shown that the self-organized geometry of the IMF is a fractal, a specific object having a number of unusual topological features; this fractal geometry is self-consistently generated by the allowed magnetosonic modes. To give an accurate treatment of waves on fractals, we propose an unconventional approach based on the wave equation with the generalized, fractional time derivative. The allowed magnetosonic modes are then defined as the generalized "resonance" solutions to the fractional wave equation and termed "fractons", vibrational excitations of fractal objects. We found that the self-organized fractal geometry of the IMF as maintained by the fractons could be described by the value of the Hausdorff fractal dimension D≈ 4/3. Convection of the IMF fractal structures by a spacecraft observer is shown to result in the power-law behavior of the Fourier energy density spectrum of the in situobserved IMF turbulence, P(f) ∝ f ^−α, with the characteristic slope α ≈ 5/3. This revised version was published online in July 2006 with corrections to the Cover Date.     

Inhomogeneities in the spatial distribution of gamma-ray bursts

The distribution of pairwise distances f(l) for different dependences r(z) of the metric distance is used to reveal inhomogeneities in the spatial distribution of 201 long (T ₉₀>2^s) gamma-ray bursts with measured redshifts z. For a fractal set with dimensionality D, this function behaves asymptotically as f(l) ∼ l ^D−1 for small l. Signs of fractal behavior with dimensionality D = 2.2–2.5 show up in all the models considered for the spatial distribution of the gamma-ray bursts. Several spatially distinct groups of gamma-ray bursts are identified. The group with equatorial coordinates ranging from 23^h56^m to 0^h49^m and δ from +19° to +23° with redshifts of 0.81–0.94 is examined separately.     

Diffusion of magnetic flux elements on a fractal geometry

Recent observations have indicated that magnetic field elements are distributed on the Sun in fractal patterns with dimension D < 2. We suggest that the transport of magnetic field elements across the solar surface should be treated as diffusion on a fractal geometry. We review a semi-analytical, theoretical treatment of fractal diffusion. Comparison with observations of small-scale motions of solar magnetic flux concentrations indicates that fractal diffusion may be taking place with dimension in the range 1.3 to 1.8. It is shown that, compared to the predictions that would be made for two-dimensional diffusion, fractal diffusion in this range would lead to an increased level of in situ flux cancellation in decaying active regions by 7% to 35%. Other work in specialities outside of solar physics may be useful in explaining solar magnetic phenomena.     

Magnetic aggregation: II. Laboratory and microgravity experiments

In a previous publication (Dominik and Nübold, 2002, Icarus 157, 173-186), we presented analytical expressions and theoretical considerations concerning preplanetary dust aggregation with magnetized grains in the solar nebula. The present work is dedicated to the experimental study of magnetic aggregation in a ground-based laboratory as well as under microgravity conditions on parabolic flights. We conducted aggregation experiments with dust analogues in order to study the temporal evolution and the structural outcome of grain growth processes dominated by or comprising exclusively magnetic grains. Within aggregation times ranging from a couple of seconds to a few minutes only, formation of huge chain-like and/or web-like dust aggregates was observed. After aggregate retrieval we were able to study the sizes and structures of the aggregates in great detail. We established the fractal dimension of the aggregates as D_fs=1.20±0.05 for single chains and D_fc=1.50±0.21 for inter-connected web-like structures. This is considerably lower than for non-magnetic grain growth. The dynamic exponent z for the mass increase with time according to t^z was found to be z=2.7 from in-situ video images of the microgravity aggregation runs. The results are compared with the theoretical considerations presented earlier as well as with previous experimental work on the same and on related topics, respectively.     

An expanding circumstellar cloud of Zeta Aurigae

Strong absorption satellite lines of CaI 6572 were found on spectrograms taken on three successive days just after the fourth contact of the 1971–72 eclipse of Zeta Aurigae. The radial velocities of the satellite lines are –88 km s^–1, –74 km s^–1, and –180 km^–1, respectively, relative to the K-type primary star (K4 Ib). These absorptions should be due to a circumstellar cloud in which the column density of neutral calcium atoms is 1×10¹⁷ cm^–2 and the turbulent velocities come to 20–50 km s^–1. It is suggested that the cloud may be formed by the rocket-effect of the Lyman quanta of the B-type component (B6 V). We estimate the density in the cloud to be 2×10¹¹ atoms cm^–3 fors=10R _K and 2×10¹⁰ atoms cm^–3 fors=10² R _K, wheres denotes the distance of the cloud from the K star andR _K the K star's radius. The mass loss rate of the K-type component is also estimated to be about 10^–7 M yr^–1, assuming that the expansion of the K star occurs isotropically.     

The simulation of the initial mass function and star formation efficiency

The fragmentation of a molecular cloud is modelled as a random process by the Monte Carlo method. The probability of the fragmentation is a function of the cloud initial mass and decreases rapidly for mass lower than critical mass, which is a defined parameter. The modelled IMF is compared with the mean mass function in open clusters assumed here as the observed IMF. The best fit was found for initial mass 3×10³ M _s and for the critical mass range 0.4 to 0.6M _s . It also implies the star formation efficiency to be about 0.3.Paper presented at a Workshop on The Role of Dust in Dense Regions of Interstellar Matter, held at Georgenthal, G.D.R., in March 1986.     

Theoretical Ne v emission line ratios compared to solar observations

The recent level population calculations for Ne v by Aggarwal are used to determine the theoretical emission line ratios R ₁ = I(2s2p ^{3 1}D^o - 2s²2p^{2 1}D^e)/I(2s2p^{3 3}D ₂ ⁰ - 2s²2p^{2 3}P ₁ ^e ) and R ₂ = I(2s2p ^{3 1}D^o-2s²2p^{2 1}D^e)/I(2s2p ^{3 3}D ₃ ⁰ -2s²2p^{2 3}P ₂ ^e ). A comparison of these with observational data for a solar flare and erupting prominence obtained with the NRL XUV spectrograph on board Skylab reveals that R ₁ and R ₂ are in their predicted high density limits. Although the ratios cannot be used as density diagnostics for values of n _e typical of the solar transition region, it is shown that they are temperature sensitive and hence may be employed to determine the electron temperatures of Ne v line emitting regions.     

Temporal behaviour of pressure in solar coronal loops

The temporal evolution of pressure in solar coronal loops is studied using the ideal theory of magnetohydrodynamic turbulence in cylindrical geometry. The velocity and the magnetic fields are expanded in terms of the Chandrasekhar-Kendall (C-K) functions. The three-mode representation of the velocity and the magnetic fields submits to the investigation of chaos. When the initial values of the velocity and the magnetic field coefficients are very nearly equal, the system shows periodicities. For randomly chosen initial values of these parameters, the evolution of the velocity and the magnetic fields is nonlinear and chaotic. The consequent plasma pressure is determined in the linear and nonlinear regimes. The evidence for the existence of chaos is established by evaluating the invariant correlation dimension of the attractorD ₂, a fractal value of which indicates the existence of deterministic chaos.     

THEMIS-VIS observations of clouds in the martian mesosphere: Altitudes, wind speeds, and decameter-scale morphology

We present measurements of the altitude and eastward velocity component of mesospheric clouds in 35 imaging sequences acquired by the Mars Odyssey (ODY) spacecraft’s Thermal Emission Imaging System visible imaging subsystem (THEMIS-VIS). We measure altitude by using the parallax drift of high-altitude features, and the velocity by exploiting the time delay in the THEMIS-VIS imaging sequence.We observe two distinct classes of mesospheric clouds: equatorial mesospheric clouds observed between 0° and 180° L_s; and northern mid-latitude clouds observed only in twilight in the 200–300° L_s period. The equatorial mesospheric clouds are quite rare in the THEMIS-VIS data set. We have detected them in only five imaging sequences, out of a total of 2048 multi-band equatorial imaging sequences. All five fall between 20° south and 0° latitude, and between 260° and 295° east longitude. The mid-latitude mesospheric clouds are apparently much more common; for these we find 30 examples out of 210 northern winter mid-latitude twilight imaging sequences. The observed mid-latitude clouds are found, with only one exception, in the Acidalia region, but this is quite likely an artifact of the pattern of THEMIS-VIS image targeting. Comparing our THEMIS-VIS images with daily global maps generated from Mars Orbiter Camera Wide Angle (MOC-WA) images, we find some evidence that some mid-latitude mesospheric cloud features correspond to cloud features commonly observed by MOC-WA. Comparing the velocity of our mesospheric clouds with a GCM, we find good agreement for the northern mid-latitude class, but also find that the GCM fails to match the strong easterly winds measured for the equatorial clouds.Applying a simple radiative transfer model to some of the equatorial mesospheric clouds, we find good model fits in two different imaging sequences. By using the observed radiance contrast between cloud and cloud-free regions at multiple visible-band wavelengths, these fits simultaneously constrain the optical depths and particles sizes of the clouds. The particle sizes are constrained primarily by the relative contrasts at the available wavelengths, and are found to be quite different in the two imaging sequences: r_eff = 0.1 μm and r_eff = 1.5 μm. The optical depths (constrained by the absolute contrasts) are substantial: 0.22 and 0.5, respectively. These optical depths imply a mass density that greatly exceeds the saturated mass density of water vapor at mesospheric temperatures, and so the aerosol particles are probably composed mainly of CO₂ ice. Our simple radiative transfer model is not applicable to twilight, when the mid-latitude mesospheric clouds were observed, and so we leave the properties of these clouds as a question for further work.     

On separation of major meteoroid streams from the sporadic background

The paper deals with a search for chosen photographic meteoroid streams compiled from the IAU Meteor Data Center Lund catalogue from which less than 2% of the orbits had to be removed due to internal inconsistency among the orbit parameters. Additional 35 orbits were removed due to extremely high hyperbolic velocities. The final set consists of 3411 orbits. Members of the Quadrantids, Lyrids, Perseids and Geminids were searched for, firstly, by a stream-search procedure utilizing the Southworth-HawkinsD-criterion. This choice, as a rule, represents the most abundant filament of the stream. Secondly, rate distribution histograms ofD were divided into region of shower meteors and region of sporadic background meteors. The searched database with a relatively low abundance of sporadic meteors in the analyzed periods simplified this choice, and followingly, fitting the obtained values by means of power and exponential functions, the limitingD _s for particular showers were derived. The derivedD _s appears as the optimum value, as for higherD, the number of sporadic meteors included in the stream sample increases more rapidly than the number of additional shower meteors, and for smallerD, the number of shower meteors decreases quicker than the number of omitted sporadic meteors. The following counts of shower meteorsN and limitingD _s were found: Quadrantids (39, 0.22), Lyrids (11, 0.15), Perseids (595, 0.53) and Geminids (224, 0.32). Efficiency of the procedure was tested comparing the number of sporadic meteors in the region of radiant area and the neighbouring regions of the same size.     

The Behavior of Sunspot Contrast during Cycle 23

Results are presented from a study of various sunspot contrast parameters in broadband red (672.3 nm) Cartesian full-disk digital images taken at the San Fernando Observatory (SFO) over eight years, 1997 – 2004, of the twenty-third sunspot cycle. A subset of over 2700 red sunspots was analyzed and values of average and maximum sunspot contrast as well as maximum umbral contrast were compared to various sunspot parameters. Average and maximum sunspot contrasts were found to be significantly correlated with sunspot area (r _s=− 0.623 and r _s=− 0.714, respectively). Maximum umbral contrast was found to be significantly correlated with umbral area (r _s=− 0.535). These results are in agreement with the works of numerous other authors. No significant dependence was detected between average contrast, maximum contrast, or maximum umbral contrast during the rising phase of the solar cycle (r _s=0.024, r _s=0.033, and r _s=0.064, respectively). During the decay phase, no significant correlation was found between average contrast or maximum contrast and time (r _s=− 0.057 and r _s=0.009, respectively), with a weak dependence seen between maximum umbral contrast and cycle (r _s=0.102).     

Motion of Dust Structures in the Circumnuclear Region of Comet Hale–Bopp and Rotation of the Cometary Nucleus

The motion of dust structures in the circumnuclear region of comet Hale–Bopp is studied. About 270 envelope images were obtained with the AZT-8 reflector (D = 0.7 m, F = 28 m) and the Filin-3 image intensifier. We carried out our observations at the observational station of the Astronomical Observatory of Shevchenko Kiev State University in the village of Lesniki (near Kiev). The recording from the image-intensifier screen was made on Foto-100 film during 23 nights from March 24 to May 10, 1997. The circumnuclear region was imaged both in white light (without filters) and with IHW CO⁺ (_ef = 426 nm), C₃ (_ef = 496 nm), C₂ (_ef = 514 nm), and RC (red continuum, _ef = 684 nm) narrow-band interference filters. Based on our measurements of the radial expansion of dust structures, we determined the velocities, 0.61–1.99 km s^–1; accelerations, from –18.3 × 10^–3 to 4.0 × 10^–3 m s^–2; and rotation period of the cometary nucleus, 111.41^h ± 0.05^h.     

Numerical evaluation of statistical acceleration for energetic particles in the interplanetary medium at 2.5 and 5.0 AU

Numerical integration of particle trajectories is performed to evaluate the statistical acceleration coefficients D _TT for 1 to 100 MeV protons in a solar wind corotating interaction region (CIR) seen at 2.5 and 5.0 AU. Acceleration is followed in the solar wind reference frame and is due to random wave-particle interactions and to random drift motion in moderate scale field gradients. D _TT due to the first effect reaches a peak value of 4 × 10 ^–7 MeV² s^–1 post shock at 10 MeV at 2.5 AU consistent with estimates based both upon cyclotron resonance and transit time damping theory. D _TT from the second effect is less well established but is of the order of 10^–7 MeV² s^–1 at 10 MeV, 5 AU. A comparison is made between the time constant for statistical acceleration within this CIR and estimates for diffuse shock acceleration and adiabatic deceleration. All three time constants are of the same order, but deceleration is faster than shock acceleration which in turn is faster than statistical acceleration.     

Photon excitation of sodium emission in Comets

We consider the possibility of the excitation of sodium resonance emission in cometary matter under solar radiation at a heliocentric distance of 5 AU, as was observed when a fragment of Comet Shoemaker-Levy 9 plunged into Jupiter. When the sodium emission is calculated, the multiple scattering in the cometary cloud is taken into account. We use a non-LTE radiative transfer code for a two-level model sodium atom. A comparison of the computed and observed Na I D emission line profiles allows the column density of the sodium atoms for specific times of observations of Comet Shoemaker-Levy 9 to be determined. The observed Na I(D₁+D₂) line profile was found to agree well with the computed profile for an optically thick sodium cloud. We calculated the column density of the sodium atoms for three comets from the observed intensity of the D₂ line emission. We also calculated the D₂/D₁ intensity ratio for various optical depths of the sodium cloud and various phase angles.     

The seasonal behavior of water ice clouds in the Tharsis and Valles Marineris regions of Mars: Mars Orbiter Camera Observations

The Mars Global Surveyor Mars Orbiter Camera was used to obtain global maps of the martian surface with equatorial resolution of 7.5 km/pixel in two wavelength ranges: blue (400-450 nm) and red (575-625 nm). The maps used were acquired between March 15, 1999 (L_s=110°) and July 31, 2001 (L_s=205°), corresponding to approximately one and a quarter martian years. Using the global maps, cloud area (in km²) has been measured daily for water ice clouds topographically corresponding to Olympus Mons, Ascraeus Mons, Pavonis Mons, Arsia Mons, Alba Patera, the western Valles Marineris canyon system, and for other small surface features in the region. Seasonal trends in cloud activity have been established for the three Tharsis volcanoes, Olympus Mons, and Alba Patera. Olympus, Ascraeus, and Pavonis Mons show cloud activity from about L_s=0°-220° with a peak in cloud area near L_s=100°. One of our most interesting observational results is that Alba Patera shows a double peaked feature in the cloud area with peaks at L_s=60° and 140° and a minimum near L_s=100°. Arsia Mons shows nearly continuous cloud activity. The altitudes of several of these clouds have been determined from the locations of the visual cloud tops, and optical depths were measured for a number of them using the DISORT code of Stamnes et al. (1988, Appl. Opt. 27, 2502-2509). Several aspects of the observations (e.g., cloud heights, effects of increased dust on cloud activity) are similar to simulations in Richardson et al. (2002, J. Geophys. Res. 107, 5064). A search for short period variations in the cloud areas revealed only indirect evidence for the diurnal cloud variability in the afternoon hours; unambiguous evidence for other periodicities was not found.     

The Uppsala‐DLR Trojan Survey of L4, the preceding Lagrangian cloud of Jupiter

We have used the ESO Schmidt telescope during the apparitions 1996, 1997 and 1998 to study the preceding Lagrangian cloud of Jupiter, L₄. In our observed field of view, about 700 square degrees, during 1996 we found 399 moving objects that we classified as Trojans. From this we conclude that down to absolute magnitude H ≤ 13.0 there are ≈ 1100 Trojans in the L₄ cloud. Proper elements of 696 numbered and multiopposition Trojans were calculated and one of these in the L₅ cloud were found to be a non Trojan. A discussion of the Trojan proper elements is also presented.     

Detection of small scale structure in metal lines at the extreme solar limb

We describe a tangential limb spectrum at 5870 Å which geometrically probes the high photosphere through the low chromosphere. Velocity and brightness structures with sizes ranging from 500 to 1500 km are present in the stronger emission lines. Such structure is consistent between the Fe i and Ba ii lines, and emission knots in these lines coincide with continuum bright streaks. But no correlation is evident between structure in the He i D₃ line, emission in the Na i D₂ line, and emission in the Fe i and Ba ii lines as a group. Two classes of near-horizontal velocity structure are seen in the height range from 0 to 500 km above the limb: υ ? 1 km s^?1 for the weaker metals and υ ～ 7–10 km s^?1 for the Na i line. Differences in line opacity are suggested as the cause of the low correlation between the fine structure in the various lines.

     

Molecular cores of the high-latitude cloud MBM 40

Towards the high-latitude cloud MBM 40, we identify 3 dense molecular cores of M0.2–0.5 M, and sizes of 0.2 pc in diameter embedded in the H I cloud of 8 M which is observed to be extended along the northeast–southwest direction. The molecular cloud is located almost perpendicularly to the H I emission. We confirm the previous result of Magnani et al. that MBM 40 is not a site for new star formations. We found a very poor correlation between the H I and the IRAS 100 μm emissions, but the CO (1–0) and 100 μm emissions show a better correlation of W_CO/I₁₀₀=1±0.2 K km s⁻¹ (MJy sr⁻¹)⁻¹. This ratio is larger by a factor of ≥5 than in dense dark clouds, which may indicate that the CO is less depleted in MBM 40 than in dense dark clouds.     

Equilibrium Structures of Differentially Rotating and Tidally Distorted White Dwarf Models of Stars

In this paper we present a method for computing the equilibrium structures and various physical parameters of a primary component of the binary system assuming that the primary is more massive than the secondary and is rotating differentially according to the law of the w² = b₀ + b₁ × s² + b₂ × s⁴, w being the angular velocity of rotation of a fluid element distant s from the axis of rotation and b₀, b₁, b₂ suitably chosen numerical constants. This method utilizes the averaging approach of Kippenhahn and Thomas (1997) and the concept of Roche equipotentials in a manner earlier used by Mohan et al. (1997) to incorporate the effects of rotation and tidal distortions on the equilibrium structures of certain rotationally and tidally distorted stellar models. The use of the method has been illustrated by applying it to obtain the structures and some observable parameters of certain differentially rotating and tidally distorted binary systems whose primary component is assumed to be a white dwarf star.