A Study of the Peak Frequency of the Geosynchronous Spectrum in a Nonuniform Source

This paper investigates in detail the peak frequency of gyrosynchrotron radiation spectrum with self and gyroresonance absorption for a model of nonuniform magnetic field. It is found that the peak frequency shifts from lower frequency to higher frequency with increases in the low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength and viewing angle. When the number density and temperature of thermal electrons increase, the peak frequency also shifts to a slightly higher frequency. However, the peak frequency is independent of the energy spectral index, high-energy cutoff of energetic electrons and the height of the radio source’s upper boundary. It is also found for the first time that there is a good linear correlation between the logarithms of the peak frequency and the low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength, and viewing angle, respectively. Their correlation coefficients are higher than 0.95 and the standard errors are less than 0.06.     

Canonical Floquet theory

Classical Floquet theory is reviewed with careful attention to the case of repeated eigenvalues common in Hamiltonian systems. Floquet theory generates a canonical transformation to modal variables if the periodic matrix can be made symplectic at the initial time. It is shown that this symplectic normalization can always be carried out, again with careful attention to the degenerate case. The periodic modal vectors and canonical modal variables can always be chosen to be purely real. It is possible to introduce real valued action-angle variables for all modes. Physical interpretation of the canonical degenerate normal modal variables are offered. Finally, it is shown that this transformation enables canonical perturbation theory to be carried out using Floquet modal variables.     

Cosmology without Big Bang within the framework of the Projective Unified Field Theory and the influence on the motion of cosmic objects

The Projective Unified Field Theory having been developed by the author since 1957 is applied to a closed homogeneous isotropic cosmological model. By postulating a (new) conservation law for the scalaric substrate mass (derived from the balance equation of matter and leading to a basically new view on the concept of mass in context with the Mach principle) we obtained a coupled system of differential equations for the world radius and the scalaric world function, which could be treated numerically by Maple. Detailed calculations show that the big bang singularity of the Einstein theory can be avoided. Since the mass density and the temperature of the background radiation exhibit maxima at the same time after the cosmological “big start”, this fact could be of interest for cosmogonic activities. Within the framework of this theory there are hints for an antigravitational world era with repulsive forces after the big start. Furthermore, the balance equations for the energy and the angular momentum of a body as well as the equation of motion of a body (with a series of consequences) are derived. In this context we found a formula for the time dependence of the “effective Newtonian gravitational constant”. Further results refer to certain aspects for understanding the observed rotational curves of cosmic objects within galaxies as well as to the conservation of the number of photons and baryons and their mutual ratio etc.     

Energy Composition of the Universe: Time-Independent Internal Symmetry

The energy composition of the Universe, as emerged from the Type Ia supernova observations and the WMAP data, looks preposterously complex, – but only at the first glance. In fact, its structure proves to be simple and regular. An analysis in terms of the Friedmann integral enables to recognize a remarkably simple time-independent covariant robust recipe of the cosmic mix: the numerical values of the Friedmann integral for vacuum, dark matter, baryons and radiation are approximately identical. The identity may be treated as a symmetry relation that unifies cosmic energies into a regular set, a quartet, with the Friedmann integral as its common genuine time-independent physical parameter. Such cosmic internal (non-geometrical) symmetry exists whenever cosmic energies themselves exist in nature. It is most natural for a finite Universe suggested by the WMAP data. A link to fundamental theory may be found under the assumption about a special significance of the electroweak energy scale in both particle physics and cosmology. A freeze-out model developed on this basis demonstrates that the physical nature of new symmetry might be due to the interplay between electroweak physics and gravity at the cosmic age of a few picoseconds. The big ‘hierarchy number’ of particle physics represents the interplay in the model. This number quantifies the Friedmann integral and gives also a measure to some other basic cosmological figures and phenomena associated with new symmetry. In this way, cosmic internal symmetry provides a common ground for better understanding of old and recent problems that otherwise seem unrelated; the coincidence of the observed cosmic densities, the flatness of the co-moving space, the initial perturbations and their amplitude, the cosmic entropy are among them.     

用小波变换原理检测原子钟环境温度的变化

根据小演变换的奇异性检测原理，分析了环境温度变化对原子钟特性的影响；基于小坡变换的信号重建原理，将温度变化引起原子钟相位－时间起伏进行时域一频域分析；用小演变换理论分析了由于昼夜温度变化引起原子钟周期性波动的原因，结合传统的谱分析方法，认证了原子钟相位－时间起伏的周期性。结果表明：在有环境温度调节的环境中，氢原子钟的相位－时间起伏标准差为41ns左右；在一般环境中，铯原子钟的相位－时间起伏标准基为21ns左右，改善环境条件可以提高原子钟的频率稳定度。     

Heat expansion of star‐like cosmic objects induced by the cosmological expansion

The heat expansion of a star‐like cosmic object, induced by the cosmological bremsheat production within a moving body, that was predicted by the Projective Unified Field Theory of the author, is approximately treated. The difference to planet‐like bodies investigated previously arises from another material constitution. The exponential‐like expansion law is applied to a model with numerical values of the Sun. The results are not in contradiction to empirical facts.     

Non-circular beam correction to the CMB power spectrum

In the era of high precision CMB measurements, systematic effects are beginning to limit the ability to extract subtler cosmological information. The non-circularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. The effect of non-circular beam on the power spectrum is important at multipoles larger than the beam-width. For recent experiments with high angular resolution, optimal methods of power spectrum estimation are computationally prohibitive and sub-optimal approaches, such as the Pseudo-C_l method are used. We provide an analytic framework for correcting the power spectrum for the effect of beam non-circularity and non-uniform sky coverage (including incomplete/masked sky maps). The approach is perturbative in the distortion of the beam from non-circularity allowing for rapid computations when the beam is mildly non-circular. We advocate that when the non-circular beams are important, it is computationally advantageous to employ ‘soft’ azimuthally apodized masks whose spherical harmonic transforms die down fast with m.     

Further results for astrophysics from the cosmology within the framework of the Projective Unified Field Theory

Recently the 5‐dimensional Projective Unified Field Theory (PUFT) of the author (Schmutzer 1995a, Schmutzer 1995b) has been applied to a closed homogeneous isotropic cosmological model with the result of a cosmology without big bang (Schmutzer 1999a, Schmutzer 1999b). Continuing this approach, in this paper following subjects are treated: recalculation of numerical values of cosmological quantities, exact solution of the field equations to a point‐like body, motion of a test body in such a field, definition of the empirical effective gravitational factor (“constant”), Einstein effects compared to the empirical situation, adiabatic approximation of the motion of an orbiting testbody under the influence of the expanding cosmos (transition of the ellipses to circles, decrease of the radius of the orbiting bodies, decrease of the excentricity, increase of the frequency of orbiting objects etc.), heat production in a moving body induced by the cosmological expansion with application to various cosmic objects.     

Models, figures and gravitational moments of Jupiter’s satellite Io: Effects of the second order approximation

The effects of the equilibrium figure theory to within terms of the second order in a small parameter α on figure parameters and gravitational moments of the Galilean satellite Io have been considered. Integro-differential equations of the theory of figure to second order have been first solved numerically. Relations between the low-order coefficients of the gravitational field for satellites in hydrostatic equilibrium are generalized according to the second order theory. To show the effects of the second approximation, two three-layer trial models of Io are used. The considered models of the Io’s interiors differ by the size and density of the core, while having the same thickness and density of the crust, and the mantle density difference is only 20 kg/m³. The corrections of second order in smallness to the gravitational moments J₂ and C₂₂ decrease the third decimal digit of model gravitational moments by two units. As the effects of third and forth harmonics are determined mostly by outer layers of Io, to distinguish between model mantle density, the gravitational moments J₄, C₄₂ and C₄₄ should be determined to accuracy with three or four decimal digits. The second order corrections mostly effect the semi-axis a, and less the semi-axes b and c.     

Standing slow magnetosonic waves in a dipole-like plasmasphere

A problem of the structure and spectrum of standing slow magnetosonic waves in a dipole plasmasphere is solved. Both an analytical (in WKB approximation) and numerical solutions are found to the problem, for a distribution of the plasma parameters typical of the Earth's plasmasphere. The solutions allow us to treat the total electronic content oscillations registered above Japan as oscillations of one of the first harmonics of standing slow magnetosonic waves. Near the ionosphere the main components of the field of registered standing SMS waves are the plasma oscillations along magnetic field lines, plasma concentration oscillation and the related oscillations of the gas-kinetic pressure. The velocity of the plasma oscillations increases dramatically near the ionospheric conductive layer, which should result in precipitation of the background plasma particles. This may be accompanied by ionospheric F2 region airglows modulated with the periods of standing slow magnetosonic waves.     

地月系潮汐演化长期趋势的估计

根据角动量守恒原理,计算了地月系经潮汐演化到达平衡状态时的旋转周期和地月距离.并根据当前与平衡状态时地月系的总能量差,计算了到达平衡状态的时间.进而估计了地月距离变化和地球自转速率变化的长期趋势.     

Measuring statistical isotropy of CMB anisotropy

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson microwave anisotropy probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian and Souradeep [Hajian, A., Souradeep, T. (2003) Astrophys. J. Lett. 597, L5] for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian and Souradeep [Basak, S., Hajian, A., Souradeep, T. (2006) Phys. Rev. D74, 02130(R)]. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released first WMAP polarization maps, however, indicate significant violation of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.     

Angular power spectrum of CMB anisotropy from WMAP

The remarkable improvement in the estimates of different cosmological parameters in recent years has been largely spearheaded by accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum from multi-frequency observations has been proposed and implemented on the first year WMAP (WMAP-1) data by Saha et al. [Saha, R., Jain, P., Souradeep, T., 2006. ApJL, 645, L89]. We review the results from WMAP-1 and also present the new angular power spectrum based on three years of the WMAP data (WMAP-3). Previous estimates have depended on foreground templates built using extraneous observational input to remove foreground contamination. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. The primary product of WMAP are the observations of CMB in 10 independent difference assemblies (DA) distributed over five frequency bands that have uncorrelated noise. Our method utilizes maximum information available within WMAP data by linearly combining DA maps from different frequencies to remove foregrounds and estimating the power spectrum from the 24 cross-power spectra of clean maps that have independent noise. An important merit of the method is that the expected residual power from unresolved point sources is significantly tempered to a constant offset at large multipoles (in contrast to the l² contribution expected from a Poisson distribution) leading to a small correction at large multipoles. Hence, the power spectrum estimates are less susceptible to uncertainties in the model of point sources.     

Mysteries on universe’s largest observable scales

We review recent findings that the universe on its largest scales shows hints of violations of statistical isotropy, in particular alignment with the geometry and direction of motion of the solar system, and missing power at scales greater than 60°. We present the evidence, attempts to explain it using astrophysical, cosmological or instrumental mechanisms, and prospects for future understanding.     

Approximation of the observed motion of bolides by the analytical solution of the equations of meteor physics

A great volume of data has been accumulated thus far related to the photoregistration of the paths of meteor bodies in the terrestrial atmosphere. Most images have been obtained by four bolide networks, which operate in the USA, Canada, Europe, and Spain in different time periods. The approximation of the actual data using theoretical models makes it possible to achieve additional estimates, which do not directly follow from the observations. In the present study, we suggest an algorithm to find such parameters of the theoretical relationship between the height and the velocity of the bolide motion that help to fit observations along the luminous part of the trajectories in the best way. The main difference from previous studies is that the given observations are approximated using the analytical solution of the equations of meteor physics. The model presented in this study was applied to a number of bright meteors observed by the Canadian camera network and by the US Prairie network and to the Benésov bolide, which is one of the largest fireballs registered by the European network. The correct mathematical modeling of meteor events in the atmosphere is necessary for further estimates of the key parameters, including the extra-atmospheric mass, the ablation coefficient, and the effective enthalpy of evaporation of entering bodies. In turn, this information is needed by some applications, namely, those aimed at studying the problems of asteroid and comet security, to develop measures of planetary defense, and to determine the bodies that can reach Earth’s surface.     

New constraints on neutrino masses from cosmology

By combining data from cosmic microwave background (CMB) experiments (including the recent WMAP third year results), large scale structure (LSS) and Lyman-α forest observations, we derive upper limits on the sum of neutrino masses of Σm_ν < 0.17 eV at 95% c.l. We then constrain the hypothesis of a fourth, sterile, massive neutrino. For the third massless +1 massive neutrino case we bound the mass of the sterile neutrino to m_s < 0.26 eV at 95% c.l. These results exclude at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. We then generalize the analysis to account for active neutrino masses which tightens the limit to m_s < 0.23 eV and the possibility that the sterile abundance is not thermal. In the latter case, the constraints in the (mass, density) plane are non-trivial. For a mass of >1 eV or <0.05 eV the cosmological energy density in sterile neutrinos is always constrained to be ω_ν < 0.003 at 95% c.l. However, for a sterile neutrino mass of 0.25 eV, ω_ν can be as large as 0.01.     

Evidence of the complex structure of asteroid 21 Lutetia

We discuss the results of the analysis of three sets of observations of asteroid 21 Lutetia—spectrophotometry, simultaneous BVR photometry, and spectrometry—which show that the asteroid is not a monolithic body. The frequency analysis of the B-V and V-R color indices and the V values, which were obtained from simultaneous BVR measurements in 2004 and calculated from the spectrophotometric observations performed in 2000 (the synthetic values and the color indices), allowed us to demonstrate that the known rotation period of 8.^h172 of the asteroid does not exist at all. At a rather high confidence level, six new periods were found: 2.^h0, 2.^h93, 16.^h8, 1.^d25, 3.^d25, and 60^d. During spectral observations with a 1.25-m telescope at the southern laboratory of the Sternberg Astronomical Institute in Nauchnyi (Crimea) in 2004, the spectra of two components spaced 2.8″ apart were registered. In the short-wavelength spectral range, quick variations of the reflectance of the components were observed. They show the changes in their spectral types from S to C. The analysis of the synthetic values of the color indices determined from the spectrophotometric observations in 2000 confirmed the presence of quick spectral variations. We conclude that asteroid 21 Lutetia is a complex satellite system. This statement is confirmed by the analysis of data published in different sources.     

Photometric study of the major satellites of Uranus

In this paper, we analyze the results of ground-based and space-born photometric observations of the major satellites of Uranus—Miranda, Ariel, Umbriel, Titania, and Oberon. All sets of photometric observations of the satellites available in the literature were examined for uniformity and systematic differences and summarized to a unified set by wavelength ranging from 0.25 to 2.4 μm. This set covers the interval of phase angles from 0.034° to 35°. The compound phase curves of brightness of the satellites in the spectral bands at 0.25, 0.41, 0.48, 0.56, 0.75, 0.91, 1.4, and 1.8 μm, which include a pronounced opposition surge and linear part, were constructed. For each satellite, the geometric albedo was found in different spectral bands taking into account the brightness opposition effect, and its spectral dependence was studied. It has been shown that the reflectance of the satellites linearly depends on the wavelength at different phase angles, but has different spectral gradients. The parameters of the phase functions of brightness, including the amplitude and the angular width of the brightness opposition surge, the phase coefficient, and the phase angle at which the nonlinear increase in brightness starts, were determined and their dependences on wavelength and geometric albedo were analyzed. Our investigations show that, in their optical properties, the satellites Miranda and Ariel, Titania and Oberon, and Umbriel present three types of surfaces. The observed parameters of the brightness opposition effect for the Uranian satellites, some ice satellites of Jupiter and Saturn, and the E-and S-type asteroids are analyzed and compared within the framework of the coherent backscattering and mutual shadowing mechanisms.     

Refinement of the phase of a spherical planet located at a small distance from the Sun

Formulas for refining the phase of a spherical planet located a small distance from the Sun are derived. Finite heliocentric distance of the planet results in the formation on its visible disk of the geometric terminator, which is not coincident with the orthographic terminator. The visible disk is assumed to be observed from Earth in orthographic projection. We suggest introducing linear and surface phases for the geometric terminator in accordance with two existing definitions of the phase of a planet. Linear and surface phases of a planet are shown to be given by different sets of formulas. An example of the computation of the phase of Mercury is given.     

Pure pseudo-Cℓ estimators for CMB B-modes

Fast heuristically weighted, or pseudo-C_ℓ, estimators are a frequently used method for estimating power spectra in CMB surveys with large numbers of pixels. Recently, Challinor and Chon showed that the E–B mixing in these estimators can become a dominant contaminant at low noise levels, ultimately limiting the gravity wave signal which can be detected on a finite patch of sky. We define a modified version of the estimators which eliminates E–B mixing and is near-optimal at all noise levels.