Correlations, spectra, and instability of phase-space density fluctuations in open-cluster models

The dynamical evolution of six open star cluster models is analyzed using the correlation and spectral analysis of phase-space density fluctuations. The two-time and mutual correlation functions are computed for the fluctuations of the phase-space density of cluster models. The data for two-time and two-particle correlations are used to determine the correlation time for phase-space density fluctuations ((0.1–1) τ _v.r., where τ _v.r. is the violent relaxation time of the model) and the average phase velocities of the propagation of such fluctuations in cluster models. These velocities are 2–20 times smaller than the root mean square velocities of the stars in the cluster core. The power spectra and dispersion curves of phase-space density fluctuations are computed using the Fourier transform of mutual correlation functions. The results confirm the presence of known unstable phase-space density fluctuations due to homologous fluctuations of the cluster cores. The models are found to exhibit a number of new unstable phase-space density fluctuations (up to 32–41 pairs of fluctuations with different complex conjugate frequencies in each model; the e-folding time of the amplitude growth of such fluctuations is (0.4–10) τ _v.r. and their phases are distributed rather uniformly). Astrophysical applications of the obtained results (irregular structure of open star clusters, formation and decay of quasi-stationary states in such clusters) are discussed.     

Parameters of oscillation generation regions in open star cluster models

We determine the masses and radii of central regions of open star cluster (OCL) models with small or zero entropy production and estimate the masses of oscillation generation regions in clustermodels based on the data of the phase-space coordinates of stars. The radii of such regions are close to the core radii of the OCL models. We develop a new method for estimating the total OCL masses based on the cluster core mass, the cluster and cluster core radii, and radial distribution of stars. This method yields estimates of dynamical masses of Pleiades, Praesepe, and M67, which agree well with the estimates of the total masses of the corresponding clusters based on proper motions and spectroscopic data for cluster stars.We construct the spectra and dispersion curves of the oscillations of the field of azimuthal velocities v _φ in OCL models. Weak, low-amplitude unstable oscillations of v _φ develop in cluster models near the cluster core boundary, and weak damped oscillations of v _φ often develop at frequencies close to the frequencies of more powerful oscillations, which may reduce the non-stationarity degree in OCL models. We determine the number and parameters of such oscillations near the cores boundaries of cluster models. Such oscillations points to the possible role that gradient instability near the core of cluster models plays in the decrease of the mass of the oscillation generation regions and production of entropy in the cores of OCL models with massive extended cores.     

Rigidity Dependence of the Long-Term Variations of Galactic Cosmic-Ray Intensity in Relation to the Interplanetary Magnetic-Field Turbulence: 1968 – 2002

We studied the relationship between the power-law exponent γ on the rigidity R of the spectrum of galactic cosmic-ray (GCR) intensity variation (δD(R)/D(R)∝R ^?γ ) and the exponents ν _y and ν _z of the power spectral density (PSD) of the B _y and B _z components of the interplanetary magnetic field (IMF) turbulence (PSD～f ^?ν , where f is the frequency). We used the data from neutron monitors and IMF for the period of 1968?–?2002. The exponents ν _y and ν _z were calculated in the frequency interval Δf=f ₂?f ₁=3×10^?6 Hz of the resonant frequencies (f ₁=1×10^?6 Hz, f ₂=4×10^?6 Hz) that are responsible for the scattering of GCR particles with the rigidity range detected by neutron monitors. We found clear inverse correlations between γ and ν _y or ν _z when the time variations of the resonant frequencies were derived from in situ measurements of the solar wind velocity U _sw and IMF strength B during 1968?–?2002. We argue that these inverse relations are a fundamental feature in the GCR modulation that is not restricted to the analyzed years of 1968?–?2002.     

Mixing ratios of methane,ethane, and acetylene in Neptune's stratosphere

Matching computed spectra for the ν₄ band of methane, the ν₉ band of ethane, and the R branch of the ν₅ band of acetylene to observed spectra for Neptune suggests mixing ratios of CH₄/H₂ ～ 10^?3?10^?2, C₂H₆/H₂ ～ 10^?6, and C₂H₂/H₂ ～ 10^?8 in the stratosphere.     

Sub-terahertz emission from solar flares: The plasma mechanism of chromospheric emission

We consider the plasma mechanism of sub-terahertz emission from solar flares and determine the conditions for its realization in the solar atmosphere. The source is assumed to be localized at the chromospheric footpoints of coronal magnetic loops, where the electron density should reach n ≈ 10¹⁵ cm^?3. This requires chromospheric heating at heights h ? 500 km to coronal temperatures, which provides a high degree of ionization needed for Langmuir frequencies ν _p ≈ 200–400 GHz and reduces the bremsstrahlung absorption of the sub-THz emission as it escapes from the source. The plasma wave excitation threshold for electron-ion collisions imposes a constraint on the lower density limit for energetic electrons in the source, n ₁ > 4 × 10⁹ cm^?3. The generation of emission at the plasma frequency harmonic ν ≈ 2ν _p rather than the fundamental tone turns out to be preferred. We show that the electron acceleration and plasma heating in the sub-THz emission source can be realized when the ballooning mode of the flute instability develops at the chromospheric footpoints of a flare loop. The flute instability leads to the penetration of external chromospheric plasma into the loop and causes the generation of an inductive electric field that efficiently accelerates the electrons and heats the chromosphere in situ. We show that the ultraviolet radiation from the heated chromosphere emerging in this case does not exceed the level observed during flares.     

Fluctuations in mid-latitude 6300 Å airglow and their relationship to F-region irregularities

Observations of fluctuations in the 6300 Å airglow emission at night have been studied using a tilting filter photometer. Spectral analysis of the fluctuations shows that at times the fluctuations are primarily due to wavelike disturbances with relatively well defined periods. At other times the spectrum of the fluctuations contains significant power only at long periods and there is a relatively sharp cut-off at the short period end. Most spectra are of these two types and are probably indicative of gravity waves. A third category is observed in which the spectra are of the form $\text{P∽?}{}^{\mathrm{?1.3}}$ Fewer spectra of this type are observed when the magnetic activity increases and the periods of spectral peaks observed changes with magnetic activity. The total power in the airglow fluctuations increases with K_p and the occurrence of spread F.     

Quasi-harmonic faraday-rotation fluctuations of radio waves when sounding the outer solar corona

A statistical analysis of the Faraday-rotation fluctuations (FRFs) of linearly polarized radio signals from the Helios 1 and Helios 2 spacecraft shows that the FRF time power spectra can be of three types. Spectra of the first type are well fitted by a single power law in the range of fluctuation frequencies 1–10 mHz. Spectra of the second type are a superposition of a power law and two quasi-harmonic components with fluctuation frequencies of about v₁=4 mHz (fundamental frequency) and v₂=8 mHz (second harmonic). Spectra of the third type exhibit only one of the two quasi-harmonic components against the background of a power law. The spectral density of the quasi-harmonic components can be represented by a resonance curve with a fairly broad [Δυ ≈ (0.5–1.3)υ_1,2] distribution relative to the v=v_{1, 2} peak. The intensity of the quasi-harmonic FRF has a radial dependence that roughly matches the radial dependence for the background FRF, while their period at the fundamental frequency is approximately equal to the period of the wellknown 5-min oscillations observed in the lower solar atmosphere. The fluctuations with 5-min periods in FRF records can be explained by the presence in the outer corona of isolated trains of Alfvén waves generated at the base of the chromosphere-corona transition layer and by acoustic waves coming from deeper layers.     

Delay of emission from extragalactic gamma-ray burst sources as a test for selecting a model of the universe

We obtained an order-of-magnitude estimate for the dispersion of light caused by the effect of quantum fluctuations on the propagation of electromagnetic waves in four-dimensional spacetime. We calculated the delay of the photons from cosmological gamma-ray bursts (GRBs) for the flat, open, and closed cosmological models. This delay is attributable to the effect of expansion of the Universe on the propagation of a dispersive light wave in space. Analysis shows that the delay of GRB photons contains a regular component related to the expansion of the Universe. We conclude that cosmological models of the Universe can be selected by the delay of emission of various energies from GRBs; the accuracy of measuring the parameter Δt/ΔE _γ must be no lower than 10^?6 s MeV^?1.     

Disparity between Hα and Hβ in SN 2008 in: Inhomogeneous external layers of type IIP supernovae?

We study disparity between Hα and Hβ in early spectra of the type IIP supernova SN 2008in. The point is that these lines cannot be described simultaneously in a spherically-symmetric model with the smooth density distribution. It is shown that an assumption of a clumpy structure of external layers of the envelope resolves the problem. We obtain estimates of the velocity at the inner border of the inhomogeneous zone (≈6100 km s^?1), the filing factor of inhomogeneities (≤0.5), and the mass of the inhomogeneous layers (～0.03 M _⊙). The amplitude of flux fluctuations in the early spectrum of Hα (ΔF/F ～ 10^?2) imposes a constraint on the size of inhomogeneities (≤200 km s^?1). A detection of fluctuations in the early Hα of type IIP supernovae might become an observational test of the inhomogeneous structure of their envelopes. We propose also the indirect test of the clumpy structure of external layers: the study of properties of the initial radiation outburst due to the shock breakout. The inhomogeneous structure of external layers of type IIP supernovae could be an outcome of density perturbations and density inversion in outer convective layers of presupernova red supergiant.     

The Effect of Twisted Magnetic Field on the Resonant Absorption of MHD Waves in Coronal Loops

The standing quasi-modes in a cylindrical incompressible flux tube with magnetic twist that undergoes a radial density structuring is considered in ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae, the dispersion relation for the MHD waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was found that a magnetic twist will increase the frequencies, damping rates and the ratio of the oscillation frequency to the damping rate of these modes. The period ratio P ₁/P ₂ of the fundamental and its first-overtone surface waves for kink (m=1) and fluting (m=2,3) modes is lower than two (the value for an untwisted loop) in the presence of twisted magnetic field. For the kink modes, particularly, the magnetic twists B _φ /B _z =0.0065 and 0.0255 can achieve deviations from two of the same order of magnitude as in the observations. Furthermore, for the fundamental kink body waves, the frequency band width increases with increasing magnetic twist.     

How do binaries affect the derived dynamical mass of a star cluster?

The dynamical mass of a star cluster can be derived from the virial theorem, using the measured half-mass radius and line-of-sight velocity dispersion of the cluster. However, this dynamical mass may be a significant overestimation of the cluster mass if the contribution of the binary orbital motion is not taken into account. Here, we describe the mass overestimation as a function of cluster properties and binary population properties, and briefly touch on the issue of selection effects. We find that for clusters with a measured velocity dispersion of σ _los?10 km?s^?1 the presence of binaries does not affect the dynamical mass significantly. For clusters with σ _los?1 km?s^?1 (i.e., low-density clusters), the contribution of binaries to σ _los is significant, and may result in a major dynamical mass overestimation. The presence of binaries may introduce a downward shift of Δlog?(L _V /M _dyn)=0.05–0.4 (in solar units) in the log?(L _V /M _dyn) versus age diagram.     

The Sun and the transcendental world of binaries

The theory of gravity says that a binary with orbital frequency ν should be a source of gravitational waves at the double frequency and higher harmonics. This implies that long-term exposure of an ensemble of binaries to gravity waves with frequency ν _G can result in (a) a lack of binaries with frequencies near frequency ν _G /2 and its higher harmonics (the effect of unstable orbits) and/or (b) an excess of binaries whose orbital frequencies are “absolutely” incommensurable with ν _G /2 and its higher harmonics (the effect of stable orbits). It is assumed that the stable-orbit frequencies are almost equal to multiples of πν _G /2 and ν _G /2π, where π plays the role of a “perfect” factor ensuring the best antiresonance of binaries. The statistical analysis of frequencies of 5774 Galactic close binary systems (CBSs) with periods P less than 10 days is based on calculating the resonance spectrum that indicates the best common multiple for a given set of frequencies with allowance for the factor π. The CBS distribution turns out to be modulated by the frequency ν _G = 104.4(5) μHz, and this effect is the most pronounced for superfast and compact rotators, such as cataclysmic variables (CVs) and related objects. The frequency ν _G is, within the error, equal to the “enigmatic” frequency ν₀ = 104.160(1) μHz com discovered earlier in the power spectra of the Sun and brightness variations of some extragalactic sources. This confirms the existence of a “coherent cosmic oscillation” of the Universe with frequency ν₀(ν _G ). The new astrophysical phenomenon naturally explains an “CV period gap” at frequencies ≈πν _G /3 (P ≈ 153 min) and maxima at the neighboring frequencies ≈πν _G /2 and ≈πν _G /4 (P ≈ 102 and ≈204 min, respectively). The remarkable and “mysterious” role of the transcendental number π for the world of binaries is emphasized, and the mystery of physical nature of the “universal” oscillation ν₀(ν _G ) is highlighted.     

Towards a theory for type III solar radio bursts

The mechanisms for the transformation of plasma waves into radiation near the fundamental and second harmonic of the plasma frequency are reviewed and equations are given for both the emission and absorption coefficients for these mechanisms. Near the fundamental the process is the scattering of plasma waves on the polarization clouds of ions and the absorption coefficient can be negative, i.e. the radiation can be amplified. Near the second harmonic the process is the combination of two excited plasma waves for which the absorption coefficient can only be positive. These results are applied to construct models of the radiation source for type III solar radio bursts both at high frequencies where the fundamental is dominant and at low frequencies where the second harmonic is dominant using two model plasma wave spectra, one being one-dimensional, the other isotropic. At high frequencies second harmonic radiation is used to determine the source area for a given energy density in plasma waves W _p . The source size and W _p are detrmined uniquely for a given plasma wave spectrum by tracing rays in a model source taking into account amplification of the fundamental. The results for a strong source at the 80 MHz plasma level with a ratio of emissivities of the fundamental to second harmonic P(ω _p )/P(2ω _p ) ≈ 10 are that the source with a one-dimensional plasma wave spectrum is about 14000 km in diameter and W _p = 10^?6.52 erg cm^?3, and the source with an isotropic distribution of plasma waves is about 200 km in diameter and W _p = 10^?6.3 erg cm^?3. It is shown that at low frequencies, where amplification of the fundamental is no longer possible, second harmonic radiation must be dominant and thus very little information about the source can obtained from the radiation.     

Pressure-induced absorption by H2 in the atmosphere of Jupiter and Saturn

The S(1) line of the pressure-induced fundamental band of H₂ was identified and measured in the spectra of Saturn and Jupiter. This broad line at 4750 cm^?1 lies in a region free from telluric and planetary absorptions. It is about 99% absorbing in the core; the high-frequency wing extends to at least 5100 cm^?1. We compare the obseved line shape to the predictions of both a reflecting-layer model (RLM) and a homogeneous scattering model (HSM). The RLM provides a good fit to the Saturn line profile for temperatures near 150K; the derived base-level density is 0.52 (+0.26, ?0.17) amagat and the H₂ abundance is 25 (+10, ?9) km-amagat, assuming a scale height of 48 km. The Jupiter line profile is fit by both the RLM and HSM, but for widely differing temperatures, neither of which seems probable. The precise fitting of the observed S(1) line profile to computed models depends critically on the determination of the true continuum level; difficulties encountered in finding the continuum, especially for Jupiter, are discussed. Derived RLM densities and abundances for both planets are substantially lower than those derived from RLM analyses of the H₂ quadrupole lines, the 3ν₃ band of CH₄, and from other sources.     

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.     

On the discovery of new behaviour in the oscillation of HD 101065

A 9 h of observation through high-speed B photometry was carried out on HD 101065 using the 0.5-m telescope of the South African Astronomical Observatory (SAAO). These photometric data were obtained between 2013 April 21 and June 19, in search of temporal variations in the oscillation of HD 101065. The frequency analysis of our data sets shows that the known principal frequency of oscillation (${\nu }_1=1.37287$ mHz) is still much intact. On nightly basis, we detected the presence of secondary frequencies (ν₂) that are well resolved from the principal frequency (ν₁) in the region of 1.0 mHz (P ∼ 17 min). These frequencies with very good signal-to-noise ratio have no harmonic period ratio with the principal frequency (ν₁). Furthermore, the amplitude spectra of individual nights reveal that the newly detected frequency (ν₂) is undergoing amplitude modulation on a short time-scale of few hours.     

The power-law behaviours of angular spectra of polarized Galactic synchrotron

We study the angular power spectra of polarized Galactic synchrotron in the range 10≲l≤800, at several frequencies between 0.4 and 2.7 GHz and at several Galactic latitudes up to near the North Galactic Pole. Electric- and magnetic-parity polarization spectra are found to have slopes around α_E,B=1.4–1.5 in the Parkes and Effelsberg Galactic-Plane surveys, but strong local fluctuations of α_E,B are found at |b|≃10° from the 1.4 GHz Effelsberg survey. The C_PIl spectrum, which is insensitive to the polarization direction, is somewhat steeper, being α_PI=1.6–1.8 for the same surveys. The low-resolution multifrequency survey of Brouw and Spoelstra [A&AS 26 (1976) 129] shows some flattening of the spectra below 1 GHz, more intense for C_E,Bl than for C_PIl. In no case we find evidence for really steep spectra. The extrapolation to the cosmological window shows that at 90 GHz the detection of E-mode harmonics in the cosmic background radiation should not be disturbed by synchrotron, even around l≃10 for a reionization optical depth τ_ri≳0.05.     

Particle acceleration and Alfvén wave generation by an interplanetary shock

Based on the event observed by ISEE 3 near the Earth’s orbit at 01:21 UT on April 5, 1979, we investigate the diffusive shock acceleration of ions and the generation of Alfvén waves by accelerated particles near the quasi-parallel parts of interplanetary shock fronts within a quasi-linear approach. The theory is shown to give an excessively high level of Alfvén wave generation by accelerated particles at significant deflection angles of the interplanetary magnetic field from the normal to the shock front. At the Earth’s orbit, the Alfve´ n waves produced by accelerated ions are confined within the frequency range 5 × 10^?2?0.5 Hz, and their spectral peak with a wave amplitude δB ≤ B corresponds to a frequency ν = (1?2)×10^?2 Hz. The high-frequency part of the wave spectrum (ν ≥ 0.5 Hz) is subjected to damping on thermal protons. The calculated spectra of the accelerated ions and Alfvén waves generated by them reproduce the main features observed in experiments.     

Effect of linear waves on kinetic Alfvén wave localization and turbulent spectrum

We have presented the localization of kinetic Alfvén wave (KAW) in intermediate β plasma (m _e /m _i ?β?1) by developing a model based on pump kinetic Alfvén wave and finite amplitude magnetosonic fluctuations. When KAW is perturbed by these background magnetosonic fluctuations, filamentary structures of KAW magnetic field are formed. First, a semi analytical model based on paraxial approximation has been developed to understand this evolution process. Localized structures and magnetic fluctuation spectrum of KAW has also been studied numerically for finite frequency of KAW. The calculated magnetic fluctuation spectrum follows two types of scalings. Above the proton gyroradius scale lengths (in inertial range), spectrum follows Kolmogorovian scaling. Below this scale dispersion starts and the spectrum steepens to about \(k_{x}^{-2.5}\) . The result shows the steepening of power spectra which can be responsible for particle acceleration in solar wind due to the energy transfer from larger to smaller lengthscales. Obtained magnetic turbulent spectra are consistent with observations of Cluster spacecraft in solar wind.     

A study of the 3ν3CH4 region in a high-resolution spectrum of Jupiter recorded by Fourier transform spectroscopy

A spectrum of Jupiter between 6000 and 12 000 cm^? at high resolution (0.05 cm^?) was recorded with a Michelson interferometer at Palomar Mountain in October 1974. An analysis of the R branch of the 3ν₃CH₄ band with the reflecting-layer model, taking into account the H₂ absorption which occurs in the same spectral range, leads to a Lorentzian half-width of 0.09 ± 0.02 cm^?1, a rotational temperature of 175 ± 10° K, and a CH₄ abundance of order 52m atm. Five lines of the ¹³CH₄3ν₃ band have been identified; a comparison with new laboratory spectra indicates that the ¹³CH₄/¹²CH₄ ratio in the Jupiter atmosphere is close to the terrestrial ratio.