Similarity law in spectral estimation of a time series. V

A continuation of [V. Yu. Terebizh, Astrofizika,40, 139, 273, 413 (1997);41, 113 (1998)]. When following recommendations based on a similarity law, a least-squares estimate is justified. Ockham’s approach is free of assumptions, but more complicated; it leads to results close to those for the least-squares method in conjunction with a similarity law and the condition of nonnegativity of the solution. The theoretical conclusions are illustrated by calculations for an AR-1 process. Translated from Astrofizika, Vol. 41, No. 2, pp. 303–309, April-June. 1998.     

Similarity law in spectral estimation of a time series. III

A continuation of [V. Yu. Terebizh, Astrofizika, 40, 139 (1997); 40, 273 (1997)]. An exact representation is found for the main quantity characterizing the inverse problem: the Fisher matrix for the covariation coefficients. Application of the (Rao-Cramer) information inequality enabled us to find the lower limit of the dispersion of an arbitrary unbiased estimate of the covariation coefficients. The conclusions are illustrated by an example of a first-order autoregression process. Translated from Astrofizika, Vol. 40, No. 3, pp. 413–423, August, 1997.     

Spectrophotometric investigation of five galaxies with A UV excess

The results of a spectroscopic investigation of galaxies Nos. 22, 35, 133, 317, and 321 from the lists of [M. A. Kazarian, Astrofizika,15, 5 (1979); M. A. Kazarian and é. S. Kazarian, Astrofizika,16, 17 (1980)] are given. The equivalent widths of lines, the relative intensities of emission lines, and their half-widths are determined. Translated from Astrofizika, Vol. 40, No. 4, pp. 619–626, October-December, 1997.     

Similarity law in spectral estimation of a time series. IV

A continuation of V. Yu. Terebizh, Astrofizika,40, 139, 273, 413 (1997). An explicit representation is found for the Fisher matrix for spectral density, enabling one to calculate the lower limit of the variance of an arbitrary unbiased density estimate. Basic equations describing smoothed density estimates are given for comparison with exact results. By numerical modeling based on the example of an AR-1 process, it is shown that the relative accuracy q of estimation of density is some universal function of the parameter w = (F -1)/N, where F is the number of parameters underlying the estimate and N is the length of the time series. The relationship q = θ(w), a similarity law, explains why a number of density estimates proposed earlier (Schuster’s periodogram, in particular) proved to be statistically inconsistent. It is just these estimates that presume an extremely detailed model of spectral density. The need for the complexity of the model to be consistent with the observational data follows from the limitation of information about the spectrum of the random process included in a sample of readings from a series of fixed volume. Translated from Astrofizika, Vol. 41, No. 1. pp. 113–122, January-March, 1998.     

Similarity law in the spectral estimation of a time series. I

The inverse problem of finding a consistent natural estimate of spectral density is studied using the example of a stationary Gaussian process. The initial equations are given and the main results are briefly described in the first part of the paper. Translated from Astrofizika, Vol. 40, No. 1, pp. 139–148, January–March, 1997.     

Spectrophotometric and morphological investigation of galaxies with a uv excess that comprise physical systems

The results of a spectroscopic and morphological investigation of galaxies with a UV excess, Nos. 205,206, 208, and 209 from the list of [M. A. Kazarian, Astrofizìka,15, 5 (1979);15, 193 (1979)], are presented. The equivalent widths, relative intensities, and half-widths of lines were determined. The mass of galaxy No. 205 was also determined. Translated from Astrofizika, Vol. 40, No. 2, pp. 179–185, April–June, 1997.     

Main stages of evolution of matter in the universe. I

The problem of the equation of state of cosmic matter is discussed and the constants of integration in the Friedmann solutions are determined. Translated from Astrofizika, Vol. 40, No. 1, pp. 117–124, January–March, 1997.     

Distribution of B stars in the directions of some southern cepheids

The distribution of B stars in the vicinity of nine southern, long-period (P > 11 days) Cepheids is studied on the basis of U, B, V data. The parameters Q, the normal color indices (B — V)₀ and (U — B)₀, the color excesses E(B — V), the spectral types, and the distance moduli of these stars are determined. Translated from Astrofizika, Vol. 40. No. 4, pp. 573–580, October-December, 1997.     

Continuity and stability of families of figure eight orbits with finite angular momentum

Numerical solutions are presented for a family of three dimensional periodic orbits with three equal masses which connects the classical circular orbit of Lagrange with the figure eight orbit discovered by C. Moore [Moore, C.: Phys. Rev. Lett. 70, 3675–3679 (1993); Chenciner, A., Montgomery, R.: Ann. Math. 152, 881–901 (2000)]. Each member of this family is an orbit with finite angular momentum that is periodic in a frame which rotates with frequency Ω around the horizontal symmetry axis of the figure eight orbit. Numerical solutions for figure eight shaped orbits with finite angular momentum were first reported in [Nauenberg, M.: Phys. Lett. 292, 93–99 (2001)], and mathematical proofs for the existence of such orbits were given in [Marchal, C.: Celest. Mech. Dyn. Astron. 78, 279–298 (2001)], and more recently in [Chenciner, A. et al.: Nonlinearity 18, 1407–1424 (2005)] where also some numerical solutions have been presented. Numerical evidence is given here that the family of such orbits is a continuous function of the rotation frequency Ω which varies between Ω = 0, for the planar figure eight orbit with intrinsic frequency ω, and Ω = ω for the circular Lagrange orbit. Similar numerical solutions are also found for n > 3 equal masses, where n is an odd integer, and an illustration is given for n = 21. Finite angular momentum orbits were also obtained numerically for rotations along the two other symmetry axis of the figure eight orbit [Nauenberg, M.: Phys. Lett. 292, 93–99 (2001)], and some new results are given here. A preliminary non-linear stability analysis of these orbits is given numerically, and some examples are given of nearby stable orbits which bifurcate from these families.     

Rotation of a two-component model neutron star in the GTR

Equations are obtained for the dynamics of the rotation of a two-component model neutron star within the framework of the generai theory of relativity. It is shown that for steady rotation of the star’s normal component, Ω_c = const, the angular velocity Ω_s of the superfluid component depends on the coordinates and is Ω_c + ω, where ω is the nondiagonal component of the metric tensor. Translated from Astrofizika, Vol. 40, No. 3, pp. 403–412, August, 1997.     

Stochastic data in astronomy. II. Search for harmonic components of time series with very large gaps

This is an analysis of certain aspects of using the CLEAN algorithm for Fourier analysis of short segments of time series and of time series consisting of short segments of length ΔT separated by very long irregular gaps. It is assumed that the time series contain a harmonic component of amplitude A with a period longer than the length of the longest of the segments of the time series plus white noise with dispersion N². Reliability plots are constructed for determining the ranges of the parameters (ν, ϕ) for which the CLEAN procedure can be used to determine the values of ν, the frequency, and ϕ, the phase of the harmonic component, with a given accuracy. The results of this analysis are used to search for harmonic components in the variation of the Hβ line profile in spectra of the triple star δ Ori A obtained in 2004 with the BTA telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 281–297 (May 2007).     

Long-term evolution of orbits about a precessing oblate planet. 2. The case of variable precession

We continue the study undertaken in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] where we explored the influence of spin-axis variations of an oblate planet on satellite orbits. Near-equatorial satellites had long been believed to keep up with the oblate primary’s equator in the cause of its spin-axis variations. As demonstrated by Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)], this opinion had stemmed from an inexact interpretation of a correct result by Goldreich [Astron. J. 70, 5–9 (1965)]. Although Goldreich [Astron. J. 70, 5–9 (1965)] mentioned that his result (preservation of the initial inclination, up to small oscillations about the moving equatorial plane) was obtained for non-osculating inclination, his admonition had been persistently ignored for forty years. It was explained in Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)] that the equator precession influences the osculating inclination of a satellite orbit already in the first order over the perturbation caused by a transition from an inertial to an equatorial coordinate system. It was later shown in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] that the secular part of the inclination is affected only in the second order. This fact, anticipated by Goldreich [Astron. J. 70, 5–9 (1965)], remains valid for a constant rate of the precession. It turns out that non-uniform variations of the planetary spin state generate changes in the osculating elements, that are linear in , where is the planetary equator’s total precession rate that includes the equinoctial precession, nutation, the Chandler wobble, and the polar wander. We work out a formalism which will help us to determine if these factors cause a drift of a satellite orbit away from the evolving planetary equator.By “precession,” in its most general sense, we mean any change of the direction of the spin axis of the planet—from its long-term variations down to nutations down to the Chandler wobble and polar wander.     

On some exceptional cases in the integrability of the three-body problem

We consider the Newtonian planar three-body problem with positive masses m ₁, m ₂, m ₃. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian orbit besides three exceptional cases ∑m _i m _j /(∑m _k )² = 1/3, 2³/3³, 2/3² where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis of the three-body problem started in papers [Tsygvintsev, A.: Journal für die reine und angewandte Mathematik N 537, 127–149 (2001a); Celest. Mech. Dyn. Astron. 86(3), 237–247 (2003)] and based on the Morales–Ramis–Ziglin approach.     

Do Quasi-Regular Structures Really Exist in the Solar Photosphere? I. Observational Evidence

Two series of solar-granulation images – the La Palma series of 5 June 1993 and the SOHO MDI series of 17 – 18 January 1997 – are analysed both qualitatively and quantitatively. New evidence is presented for the existence of long-lived, quasi-regular structures (first reported by Getling and Brandt, Astron. Astrophys. 382, L5 (paper I), 2002), which no longer appear unusual in images averaged over 1 – 2-hour time intervals. Such structures appear as families of light and dark concentric rings or families of light and dark parallel strips (“ridges” and “trenches” in the brightness distributions). In some cases, rings are combined with radial “spokes” and can thus form “web” patterns. The characteristic width of a ridge or trench is somewhat larger than the typical size of granules. Running-average movies constructed from the series of images are used to seek such structures. An algorithm is developed to obtain, for automatically selected centres, the radial distributions of the azimuthally averaged intensity, which highlight the concentric-ring patterns. We also present a time-averaged granulation image processed with a software package intended for the detection of geological structures in aerospace images. A technique of running-average-based correlations between the brightness variations at various points of the granular field is developed and indications are found for a dynamical link between the emergence and sinking of hot and cool parcels of the solar plasma. In particular, such a correlation analysis confirms our suggestion that granules – overheated blobs – may repeatedly emerge on the solar surface. Based on our study, the critical remarks by Rast (Astron. Astrophys. 392, L13, 2002) on the original paper by Getling and Brandt (paper I) can be dismissed.     

The morphological and spectral investigation of the galaxies Kaz 5, Kaz 92, and Kaz 390

The results of morphological and spectral study of the galaxies Kaz 5, Kaz 92, and Kaz 390 are presented. The observations were made on the 2.6-m telescope at the Byurakan Observatory with the VAGR microlenses spectrograph. Isophotes of the images of the galaxies are constructed in the Hα, [NII] λλ6584 , 6548, and [SII] λλ6731, 6717 emission lines and in the continuum. The masses of Kaz 5 and Kaz 92 are determined to be 8.6 × 10⁸ M_⊙ and 6.1 × 10⁹ M_⊙ , respectively. The mass of the gaseous component in the centers of regions I and IV of Kaz 390, which encompass a 1 pixel area, are also determined. The morphological structure of the central region of Kaz 5 in the observed spectral range, λλ6400–6800?, differs completely from the structure of the same part of the galaxy observed with the 6-m and 2.5-m telescopes. It is shown that these differences in the structure in images of Kaz 5 are mostly explained by the comparatively low resolution of the telescope in combination with the VAGR spectrograph. Absorbing matter also contributes to this effect. It is also shown that a “deficit” of nitrogen has been observed in the region of Kaz 390 studied here (a circle of diameter 40″). Translated from Astrofizika, Vol. 52, No. 1, pp. 63–74 (February 2009).     

Gnevyshev Peaks and Gaps for Coronal Mass Ejections of Different Widths Originating in Different Solar Position Angles

The sunspot number series at the peak of sunspot activity often has two or three peaks (Gnevyshev peaks; Gnevyshev, Solar Phys. 1, 107, 1967; Solar Phys. 51, 175, 1977). The sunspot group number (SGN) data were examined for 1997 – 2003 (part of cycle 23) and compared with data for coronal mass ejection (CME) events. It was noticed that they exhibited mostly two Gnevyshev peaks in each of the four latitude belts 0° – 10°, 10° – 20°, 20 ° – 30°, and > 30°, in both N (northern) and S (southern) solar hemispheres. The SGN were confined to within latitudes ± 50° around the Equator, mostly around ± 35°, and seemed to occur later in lower latitudes, indicating possible latitudinal migration as in the Maunder butterfly diagrams. In CMEs, less energetic CMEs (of widths < 71°) showed prominent Gnevyshev peaks during sunspot maximum years in almost all latitude belts, including near the poles. The CME activity lasted longer than the SGN activity. However, the CME peaks did not match the SGN peaks and were almost simultaneous at different latitudes, indicating no latitudinal migration. In energetic CMEs including halo CMEs, the Gnevyshev peaks were obscure and ill-defined. The solar polar magnetic fields show polarity reversal during sunspot maximum years, first at the North Pole and, a few months later, at the South Pole. However, the CME peaks and gaps did not match with the magnetic field reversal times, preceding them by several months, rendering any cause – effect relationship doubtful.     

Green’s function for the linear Kompaneets equation

Green’s function for the linear Kompaneets equation is calculated; it is expressed in terms of a Whittaker function W_2,iμ(Z) or a MacDonald function K_iμ(z) with a purely imaginary index. A method is proposed for calculating these functions. Langer’s asymptotic solution for large μ is refined in Cherry’s second approximation. With a series expansion for small values of the argument and the asymptotic form for large values, this approximation enables one to calculate Green’s function to five significant figures. Solutions of the Kompaneets equation will be used to estimate the accuracy of numerical methods and to calculate the evolution of the spectrum of a photon gas during Compton scattering, as well as the average frequencies and the dispersion of photon frequencies for different initial spectra. Translated from Astrofizika, Vol. 40, No. 1, pp. 97–116, January–March, 1997.     

Moment of inertia of a neutron star. I. Relativistic equation for the accumulated moment of inertia

A relativistic, first-order differential equation is derived for the accumulated moment of inertia of a spherically symmetric celestial body. An approximate equation is proposed to describe the contribution of relativistic effects to the moment of inertia of a superdense star. For configurations of an incompressible fluid, this approximation describes the results of the numerical calculations of Chandrasekhar and Miller to within 5% in the entire range of central pressures from 0 to ∞. Translated from Astrofizika, Vol. 40, No. 1, pp. 87–96, January–March, 1997.     

Radial Evolution of Well-Observed Slow CMEs in the Distance Range 2 – 30 <Emphasis Type="Italic">R</Emphasis><Subscript>⊙</Subscript>

We performed a detailed analysis of 27 slow coronal mass ejections (CMEs) whose heights were measured in at least 30 coronagraphic images and were characterized by a high quality index (≥4). Our primary aim was to study the radial evolution of these CMEs and their properties in the range 2 – 30 solar radii. The instantaneous speeds of CMEs were calculated by using successive height – time data pairs. The obtained speed – distance profiles [v(R)] are fitted by a power law v = a(R−b) ^c . The power-law indices are found to be in the ranges a=30 – 386, b=1.95 – 3.92, and c=0.03 – 0.79. The power-law exponent c is found to be larger for slower and narrower CMEs. With the exception of two events that had approximately constant velocity, all events were accelerating. The majority of accelerating events shows a v(R) profile very similar to the solar-wind profile deduced by Sheeley et al. (Astrophys. J. 484, 472, 1997). This indicates that the dynamics of most slow CMEs are dominated by the solar wind drag.     

X-RAY and Radio Monitoring of GX 339-4 and CYG X-1

Previous work by Motch et al. [1985, Space Sci. Rev. 40, 219] suggested that in the low/hard state of GX, the soft X-ray power-law extrapolated backward in energy agrees with the IR flux level. Corbel and Fender [2002, ApJ 573, L35–L39] later showed that the typical hard state radio power-law extrapolated forward in energy meets the backward extrapolated X-ray power-law at an IR spectral break, which was explicitly observed twice in GX. This has been cited as further evidence that jet synchrotron radiation might make a significant contribution to the observed X-rays in the hard state. We explore this hypothesis with a series of simultaneous radio/X-ray hard state observations of GX. We fit these spectra with a simple, but remarkably successful, doubly broken power-law model that indeed requires a spectral break in the IR. For most of these observations, the break position as a function of X-ray flux agrees with the jet model predictions. We then examine the radio flux/X-ray flux correlation in CYG through the use of 15 GHz radio data, obtained with the Ryle radio telescope, and Rossi X-ray Timing Explorer data, from the All Sky Monitor and pointed observations. We find evidence of ‘parallel tracks’ in the radio/X-ray correlation which are associated with ‘failed transitions’ to, or the beginning of a transition to, the soft state. We also find that for CYG the radio flux is more fundamentally correlated with the hard, rather than the soft, X-ray flux.