Towards Calibration of the Mean Magnetic Field of the sun

The 1968–2000 data on the mean magnetic field (MMF, longitudinal component) of the Sun are analysed to study long-time trends of the Sun's magnetic field and to check MMF calibration. It is found that, within the error limits, the mean intensity of photospheric magnetic field (the MMF strength, |H|), did not change over the last 33 years. It clearly shows, however, the presence of an 11-year periodicity caused by the solar activity cycle. Time variations of |H| correlate well with those of the radial component, |B _r|, of the interplanetary magnetic field (IMF). This correlation (r=0.69) appears to be significantly higher than that between |B _r| and the results of a potential source-surface extrapolation, to the Earth's orbit, of synoptic magnetic charts of the photosphere (using the so-called `saturation' factor <sup>–1</sup> for magnetograph measurements performed in the line Fei 525.0 nm; Wang and Sheeley, 1995). It seems therefore that the true source surface of IMF is the `quiet' photosphere – background fields and coronal holes, like those for MMF. The average `effective' magnetic strength of the photospheric field is determined to be about 1.9 G. It is also shown that there is an approximate linear relation between |B <sub>r</sub>| and MMF intensity |H| (in gauss)|B <sub>r</sub>|(H <sub>0</sub>)<sub>min</sub>×(1+C|H|)where =1.5×10<sup>–5</sup> normalizes the photospheric field strength to 1 AU distance from the Sun, (H <sub>0</sub>)<sub>min</sub>=1.2 G is some minimal `effective' intensity of photospheric background fields and C=1.3 G^–1 an empirical constant. It is noted that good correlation between time variations of |H| and |B _r| makes suspicious a correction of the photospheric magnetic fields with the use of saturation factor ^–1.     

Evolution of binaries with ultra-short periods: Systematic study

A detailed investigation of the evolution of low-mass binaries is performed for the case when the secondary fills its Roche lobe at the stage of core hydrogen exhaustion. The obtained results are compared with observational data for ultra-short periodic X-ray systems MXB 1820-30 and MXB 1916-05. In the frame of the proposed evolutionary scenario it is possible to obtain for MXB 1820-30 its periodP=11.4 min twice (see Figure 2). In the first case the parameters of the system are:M ₂ 0.13–0.15M ,X0.05–0.13, |P/P| (3.6–6.2) } 10^–7 yr^–1, M₂ (4.1–9.6) } 10^–9 M yr^–1, for the second:M ₂ 0.08–0.09M ,X= 0, |P/P| (1.3–1.5) } 10^–7 yr^–1, M₂ (1.4–1.8) } 10^–8 M yr^–1. It is suggested that MXB 1916-05 is the progenitor of the system MXB 1820-30 (M ₂ = 0.1M,X 0.221,M ₂ 1.8 × 10^–10 M yr^–1).     

A new approach to the theory with variable gravitational constant

A theory with variable gravitational constant, based on the bimetric formulation of general relativity, is suggested. It is in agreement with the Newtonian and post-Newtonian approximations of the theory of gravitation when the theory parameter ||4×10^–6. The statical spherical-symmetric distribution of gravitating masses is investigated. It is shown that the total action (including the own gravitational field of the system)S=–M, where is the time in the remote system of reference, relative to which the celestial body is in rest. In the Brans-Dicke theory ||1 andS–M. The Tolman formula for the massM in the Einstein theory is also valid in the suggestedGeneralized Bimetric Theory of Gravitation. External analytical and internal numerical solutions of the field equations are found for the case of incompressible matter. It is shown that static and supermassive configurations may exist if –0.13<0.     

Cyclotron waves in the solar wind

Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for _p < 0, where _p 1 –T _p/T _p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range _r | _p | _p for _p < 0, where _p is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range | _p | _p > _r > | _p | _p /(1– _r ) for _p < 0. The marginal state is at _r =| _p | _p .Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974     

The clustering of Lα absorption lines in the QSO spectra

For nine published high-resolution QSO spectra a correlation analysis of their L forest lines has been performed. The two-point correlation functions show some quasi-periodic structure of magnitude ||0.3. Their characteristic separation along the line-of-sight amounts to s ₀=3×10^–3 or to s ₀=5×10^–3 for =1 and 0.2, respectively. Especially the distribution of nearest neighbouring line positions in two close QSO pairs allows for the interpretation that the absorption clouds lie in sheet-like structures as predicted by the pancake theory. The correlation data contain some hints on metal absorbers within the forest of unidentified lines.     

A prominence model based on spectral observations

Intensities and profiles of the H, H, H, K, and D₃ lines are measured in a solar prominence. From the profiles of these lines we estimate T = 6400 K and _t = 5.7 km s^–1. We construct a simple isothermal model which explains the H intensity and profile for an assumed total particle density n _T = 3 × 10¹¹ cm^–3, and a filling factor, = 1/6.From this model we find that the source function in the H line is nearly constant through the prominence. We estimate from the model that the radiative energy loss at the center of the prominence is of the order of 10⁷ erg s^–1 g^–1.     

Observational study of the ‘post’-flare loops on June 4, 1991

A limb, two-ribbon H flare on June 4, 1991, associated with a white-light flare and followed by an emission spray and post-flare loops, is studied. A region of rapidly enhanced brightness at the bottom of the H ribbon above the white-light flare is revealed. The energy released by the white-light flare at _eff = 4100 is estimated to be about 1.5 × 10²⁸ erg s^–1.     

Lyman continuum observations of solar flares

A study is made of Lyman continuum observations of solar flares, using data obtained by the Harvard College Observatory EUV spectroheliometer on the Apollo Telescope Mount. We find that there are two main types of flare regions: an overall mean flare coincident with the H flare region, and transient Lyman continuum kernels which can be identified with the H and X-ray kernels observed by other authors. It is found that the ground level hydrogen population in flares is closer to LTE than in the quiet Sun and active regions, and that the level of Lyman continuum formation is lowered in the atmosphere from a mass column density m 5/sx 10^–6 g cm^–2 in the quiet Sun to m 3/sx 10^–4 g cm^–2 in the mean flare, and to m 10^–3g cm^–2 in kernels. From these results we derive the amount of chromospheric material evaporated into the high temperature region, which is found to be - 10¹⁵g, in agreement with observations of X-ray emission measures. A comparison is made between kernel observations and the theoretical predictions made by model heating calculations, available in the literature; significant discrepancies are found between observation and current particle-heating models.     

Linearly expanding universes in JBD-theory

The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.     

Astrophysical constraints on the gravitational constant

We study the astrophysical bounds on the change of the gravitational constant with time. We found that |/G|<10^–12yr^–1 is the condition that has to be satisfied in order not to cause a conflict with the observations. We find the condition to be in accord with the lower limits, the superstring theory predicts.     

Electron acceleration and heating in solar flares: Interpretation of Hα signatures

Vector magnetogram, H, and hard X-ray observations of flares are reviewed which show that nonthermal electron signatures in H are never cospatial with regions of maximum current density for the small number of flares analyzed, but lie to the sides of these regions. By considering electron acceleration and transport requirements, four conditions are found that must be fulfilled to observe nonthermal electron signatures in H: (1) The plasma beta 0.3 in the acceleration region. (2) The energy flux of electrons above 20 keV is greater than 10¹⁰ erg cm^–2 s^–1. (3) The column densityN 10²⁰ cm^–2 between the electron source and the chromosphere. (4) The coronal pressure in the flux tube connecting to the H layerp 100 dyne cm^–2. Condition 2 can be most easily met in the initial stages of flares. In contrast, the only condition for a high-pressure H signature isp 1000 dyne cm^–2, which is most easily met in a region of maximum current density or heating and far enough into the flare for significant heating to have occurred. Thus, high-pressure signatures should be expected to occur more frequently than nonthermal electron signatures and to occur generally later in time.Also Guest Worker at NOAA Space Environment Laboratory Boulder Colorado U.S.A.     

Search for the matter clumps in scalesZ ~ 1

The diagramV - log(1 +z _e ) as function of (, ) is considered for the quasars. HereV is the apparent visual magnitude,z _e is the emission line redshift, and are the equatorial coordinates. Two opposite extreme spots NE and SE are observed on the sky, where the inclination of the straight line fitting the dependenceV - log(1 +z _e ) is maximum and minimum. The coordinates of the centres of these extreme spots are ( _NE, _NE) = (282°, +42°) and ( _SE, _SE) = (70°, -38°) with errors 5°. A hypothesis of the Superattractor (SA) is proposed to explain such an effect. Two independent tests of this hypothesis are realized. First, the dependence or the frequency a of the absorbers in QSO spectra on (, ) is investigated. A region of the larger a is found. The coordinates of its centre are (, ) = (82°, - 10°) with error 5°. Second, the cases ofz _a >z _e are plotted in the Mercatorial projection (, ). The most of the casesz -z _e > 0.02 are concentrated within the circle with radiusR = 34° and centre (, ) = (50°, - 15°). The both anomalous regions overlap the Southern extreme spot around SE. The SA direction is (, ) = (67°, -21°) with errors about 12°. The redshift of SA isz _SA = 1.7 ± 0.3 that corresponds to the distancer _SA = (3100 ± 300)h ^–1 Mpc for the Hubble constantH ₀ = 75h kms^–1 Mpc^–1. The SA mass isM _SA ~ 10¹⁸-10²⁰ M . The orientation of the normal to the quasiperiodical large-scale sheet structure on the sky occurs near SA.     

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times t between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail (t) for large waiting times (t>10hours). It is shown that the power-law index varies with the solar cycle. For the minimum phase of the cycle the index is =–1.4±0.1, and for the maximum phase of the cycle the index is –3.2±0.2. For all years 1975–2001, the index is –2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate (t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(), the time distribution of the rate . If f() has a power-law form for low rates, the waiting time-distribution is predicted to have a power-law tail (t)^–(3+) (>–3). Distributions f() are constructed from the GOES data. For the entire catalog a power-law index =–0.9±0.1 is found in the time distribution of rates for low rates (<0.1hours ^–1). For the maximum and minimum phases power-law indices =–0.1±0.5 and =–1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices –2.2±0.1 (1975–2001), –2.9±0.5 (maximum phase) and –1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.     

Theory of the Trojan asteroids,IV

In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies ₁ and ₂. In terms of thecritical masses m_j(₂), or the associatedcritical energies _j ² (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |₂– _j ² |<_j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 0²1, lying in: and (2) despite the clustering of _j ² (m) atj=, the family () includes, for ²=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL ₃.In a similar manner, the family () can be extended to the horseshoe branch 1<_{2 2} ² .     

Statistical survey of planetary nebulae: Distances,masses, and distribution in the galaxy

On the basis of empirical (D)-dependency at the frequency of 5 GHz constructed using 15 planetary nebulae with the independently measured distances (10^–171×10^–20 W m^–2 Hz^–1 ster^–1), we evaluated distances of 335 objects. Independent evidence of the correctness of the accepted scale are given. Then(D)-dependency is constructed and it is shown that atD<0.08 pc the mean electron density is higher than the one determined by the Seaton method. We showed that the filling factor diminishes with the increase of the PN diameter (1 atD0.08 pc and 0.2 atD0.4 pc). the ionized mass of 33 PNs is determined. With the diameter increase the ionized mass grows and atD0.4 pc reaches the valueM0.07M . We used the new distance scale when investigating the space distribution of PNs. The mean scale height =130±15 pc and the mean gradient of the change of surface densitym=0.37, which allowed us to estimate the total number of nebulae in the GalaxyN4×10⁴. We divided the PNs according to their velocities (withV _LSR>35 km s^–1 andV _LSR<35 km s^–1) and permitted us to confirm that the PN belong to different sub-systems of the Galaxy. The estimated local formation rate of PNs [=(4.6±2.2)×10^–12 pc^–3 yr^–1] is a little higher than the one of the white dwarfs. That can be explained by a large number of PNs having binary cores, which used in our sample. The statistical estimation of PN expansion velocity showed thatV _ex increases from 5–7 km s^–1 (atD0.03 pc) to 40–50 km s^–1 (atD0.8 pc).     

On solving Kepler's equation for nearly parabolic orbits

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0.001 in 0–2 iterations. This accuracy holds for the true anomaly || 135° and |e – 1| 0.01. We explain the reason for this effect also.Dedicated to the memory of Professor G.N. Duboshin (1903–1986).     

Compton scattering of relativistic electrons in compact X-ray sources

The problem of single Compton scattering is considered and the resulting spectrum, angular distribution and polarization of scattered photons in a general case are obtained. The inverse Compton scattering (ICS) for arbitrary energies of electronsE and photons ₀ is investigated in detail. In the case of isotropically-distributed initial photons and relativistic electrons, a strong rise of the scattered spectrum near the upper edge takes place, starting from the values of the characteristic parameterb4E ₀10 (in units of mc²=1). The energy-loss rate of relativistic electrons due to ICS is calculated. It is shown that the relativistic electrons of the energiesE100 MeV, when scattering on the X-rays with ₀~10KeV, transmit the dominant part of their energy to the photons which fall after scattering into the energy range of the electrons (100 MeV).The radiation spectrum of ICS, as well as the energy-losses of relativistic electrons distributed by power-lawE ^–, are calculated. The radiation spectrum reveals the power-law behaviour with the different indices in two limits: the dependence ^–(1)/2 at ₀1 gradually changes to ^–(+1) ln (₀) law for ₀1.     

Nonsemisimple 1∶1 resonance at an equilibrium

Consider a Hamiltonian system of two degrees of freedom at an equilibrium. Suppose that the linearized vectorfield has eigenvaluesi,i,–i,–i ( , >0) and is not semisimple. In this paper we discuss the real normalization of the Hamiltonian function of such a system. We normalize the Hamiltonian up to 4th order and show how to compute its coefficients. For the planar restricted three body problem atL ₄ the coefficient that plays an important role in the investigation of the qualitative behaviour of periodic solutions near the equilibrium is explicitly calculated.     

Acoustic oscillations in the K2III star arcturus

Simultaneous spectrometric and photometric observations have been performed, on the red giant star Arcturus ( Boo), in a search for radial velocity or luminosity variations related to global oscillations of the stellar structure. From a preliminary analysis of the spectrometric data, several frequencies have been discovered in the range from 1 to 50 Hz, the highest amplitude being of 60 ms^–1 at 4.3 Hz. From the analysis of the photometric data, slight evidence of this variation has been found, yielding a value of V/m=48 km s^–1 mag^–1.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.     

Analysis of spectra of α CMi and α Cen A observed with the orbiting stellar ultraviolet spectrophotometer S59 in ESRO's TD1A satellite

Ultraviolet spectra of CMi and Cen A taken with moderate spectral resolution (approx. 1.8 Å) are used to analyse whether a determination of stellar chemical abundances of Fe and Cr and of the photospheric parameters is possible. For CMi, for which good spectral data are available, we findT _eff=7660±110 K; logg _eff=3.05±0.1. Further, log(Fe)=–0.06±0.09; log (Cr)=–0.01±0.09 with regard to standard (solar) abundances. For Cen A the resulting data — particularly the photospheric ones — are less certain, but it seems that the Fe abundance may be smaller than the standard value.