Slowly varying component spectrum of the solar radio emission at millimetre wavelengths

This paper deals with the observed data on the solar S-component sources at millimetre wavelengths. The observations were made in 1968 and 1969 using the 22-m radio telescope of the Crimean Astrophysical Observatory at six wavelengths: 2, 4, 6, 8, 13 and 17 mm. The enhanced intensity of the solar active region in comparison with the quiet Sun level varies proportionally to ^–2 if the wavelength is within the range of 2 ÷ 6 mm. In the wavelength band of 6 ÷ 17 mm almost flat spectra of the solar S-component sources is observed. Assuming the bremsstrahlung mechanism of the radio emission for the quiet Sun and the solar active regions an attempt has been made to treat the above presented data. It appears that the most probable explanation of the 2 ÷ 6 mm spectrum is that the S-component sources are opaque. In the 6 ÷ 17 mm wavelength band there are two possibilities: the active region may be either transparent or opaque. But in the last case the source brightness temperature must be proportional to ². Some differences in the spectra of the sources, identified with flocculi and with bipolar sunspot groups, were mentioned. The cold regions (as compared with the quiet Sun) were observed up to = 2 mm and identified with the filaments. However, its visibility falls when the wavelength decreases.     

Facular structures derived from precise two-color contrast observations

A precise solar surface photometric observing system was developed and intensity observations of the whole Sun were carried out at a fairly quiet period from December 1987 to April 1988, attaining the photometric accuracy of 10^–3. Using 28 days observation of 4 hours duration each and 0.3 s time interval, we obtained the center-to-limb variation of the ratio of the facular intensity contrast (I _f÷I_o) between two colors of 545 nm (G) and 770 nm (R): (I _f÷I₀)_G÷(I_f÷I₀)_R = 2.20 – 1.16, where is the direction cosine between the line of sight and the surface normal. While this relationship was obtained mostly for active regions from the whole Sun data, we also found an almost identical relation for the quiet Sun network by excluding active regions. This suggests the similarity of faculae at both places.Using the above relation and the difference of optical depth, , in two colors, we found that the facular temperature gradient, dT/d _G, is smaller than that of the quiet photosphere if the gradient is measured more or less vertically (i.e., seen at > 0.7) in accord with Foukal and Duvall (1985), while it is larger than that of the quiet photosphere if the temperature gradient is measured more obliquely (i.e., seen at > 0.7). These findings are free from the low spatial resolution of the present observations because the contrast ratio was used, and also independent of a specific model of hot-wall or hillock. In particular, if the true contrast of facular bright points of 0'2 size is taken as 40% in the green from high-resolution observations, the facular point temperature may even be increasing towards higher geometrical levels ar _G 1. We found also that the area filling factor in active regions is on the order of a few percent or so in accordance with the previous studies.     

Stellar pulsation: (I) analysis of stability of envelope

The life-time of the star on AGB is approximately 6 × 10⁴ yr. We divide it into front half and back half of AGB (including to optical Mira variable and OH/IR star) according to their evolution character. The observations show that the star has non-pulsation, but constant mass loss rate ( 5 × 10^–7 M yr^–1) on front half of AGB. Its circumstellar envelope is formed. When the star has pulsation on back half of AGB, its mass loss rate is relative with time, and increases gradually. In this time the star is on the stage of optical Mira variable. When the mass loss rate reaches the value of 3 × 10^–6 M yr^–1, the star evoluted from the stage of optical variable into the stage of radio bright OH/IR star. On the end of AGB the mass loss rate reaches 10^–4 M yr^–1. (Band and Habing 1983, Hermen and Habing 1985).     

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.     

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.     

The effect of luminosity-redshift correlation on the analysis of the angular size-redshift relation for radio galaxies

The variation of radio luminosity with redshift and its effect on the analysis of the angular size-redshift ( –z) relation for a bright radio source sample (s ₁₇₈ 10Jy) has been investigated. By assuming a power law dependence of luminosity on redshift of the formP (1 +z), it was found that 4.4 (with correlation coefficientr 0.99) for at leastz 0.3. Correction for such a strongP – (1 +z) correlation when considering the –z data for the sample led to a steeper –z slope. This could be explained by assuming linear size evolution of the formD (1 +z)^–n withn = 2.8 – 3.3 consistent with both theoretical results and those obtained for more homogeneous source samples.     

Almost stable regions for an area-preserving mapping

The area preserving mapping x = x + a(y – y ³), y = y – a(x – x³), for 0.3 a 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).     

A correlation study between ozone and volcanic activity

A cross-correlation study for time-lags of ±5 yrs between eleven ground based ozone stations (1957–1985) for = 40°N–75° N and = 30° E-114° W and five volcanic emissivity indices has shown their close connection: significant correlations well above 90% were obtained. Intepretation of these positive/negative correlations () was based on the global wind circulation (aided also by a 2-D, 3-D representation between, , ), and the types of volcanic aerosols leading to heterogeneous chemical reactions with ozone.     

Lunar properties from transient and steady magnetic field measurements

The electrical conductivity of the lunar interior has been determined from magnetic field step transients measured on the lunar dark side. The simplest model which best fits the data is a spherically symmetric three layer model having a nonconducting outer crust of radial thickness 0.03R _moon; an intermediate layer of thicknessR0.37R _moon, with electrical conductivity ₁ 3.5 × 10^–4 mhos/m; and an inner core of radiusR ₂ 0.6R _m with conductivity ₂ 10^–2 mhos/m. Temperatures calculated from these conductivities in the three regions for an example of an olivine Moon are as follows: crust, < 440 K; intermediate layer, 890 K; and core, 1240 K. The whole-moon relative permeability has been calculated from the measurements to be/ ₀ = 1.03 ± 0.13. Remanent magnetic fields at the landing sites are 38 ± 3 at Apollo 12, 43 ± 6 and 103 ± 5 at two Apollo 14 sites separated by 1.1 km, and 6 ± 4 at the Apollo 15 site. Measurements show that the 38 remanent field at the Apollo 12 site is compressed to 54 by a solar wind pressure increase of 7 × 10^–8 dynes/cm².National Research Council Postdoctoral Associate.     

Solution of a transfer equation by a Modified Spherical Harmonic Method in a thin anisotropically scattering atmosphere

Wan, Wilson and Sen (1986) have examined the scope of Modified Spherical Harmonic Method in a plane medium scattering anisotropically. They have used the phase functionp(µ, µ) = 1 +aµµ. In this paper, the Transfer Equation has been solved by the Modified Spherical Harmonic Method using the phase functionp(µ, µ) = 1 + ₁ P ₁(µ)P ₁(µ) + ₂)P ₂(µ)P ₂(µ) and a few sets of numerical solution have been predicted for three different cases.     

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).     

Diffuse component of the cosmic far UV radiation and interstellar dust grains

The diffuse far UV radiation ( 1350–1480 Å) observed in the sky region ofl ^II180°, 0°b ^II40° is analyzed in connection with the distributions of stars and dust grains as well as with optical properties of grains. Its intensity (starlight+scattered light) is about 6×10^–7 erg cm^–2 sec^–1 sr^–1 Å^–1 in the direction ofb ^II0° andl ^II180°. The latitude dependence of the intensity is in approximate agreement with the plane parallel slab model of the galaxy with a reasonable set of parameters. The interstellar scattering gives an albedo close to unity and forward phase function of about 0.6, which are not inconsistent with the model of interstellar grains of Wickramasinghe. The upper limit of the extragalactic UV is 2×10^–8 erg cm^–2 sec^–1 sr^–1 Å^–1 in the same region of wave-length.     

Luminosity and colour distribution in the interacting system NGC 7770-71

Detailed surface photometry for the SB(s)a galaxy NGC 7771 has been carried out in the blue spectral band. Isophotes, luminosity profiles, and photometric parameters are obtained from photographs collected with the 74 inch telescope of Kottamia Observatory, Egypt. The total apparent magnitudem _T =13.08 with maximum dimensions 3.6±0.5×2.7±0.5 (at threshold µ _m = 27.38 mag s^–2). The absolute magnitude isM _T =–21.70 if the distance is =90.2 Mpc. The major axis is in position angle =69°.5±1° and the mean axis ratio of the outer regionsq=b/a=0.45 corresponds to an inclinationi=66°. The equivalent effective radiusr _e ^* =0.29 and the effective surface brightness µ _e = 22.30 mag s^–2.The equivalent luminosity distribution has been decomposed into two main components, anr ^1/4 spheroid and an exponential disk. The total apparent magnitudes of the spheroidal and disk components are 14.36 and 13.48, which correspond to contributions of 31 and 69% to the total blue luminosity, respectively.     

Steady mass-loss from supermassive stars

Structures of Newtonian super-massive stars are calculated with the opacity for Comptor effectK ₀/(1 + T), whereK ₀=0.21(1 +X and =2.2×10^–9K^–1. The track of the Main-Sequence is turned right in the upper part of the HR diagram. Mass loss will occur in a Main-Sequence stage for a star with mass larger than a critical mass. The cause of mass loss and the expansion of the radius is continuum radiation pressure. The critical mass for mass loss is 1.02×10⁶ M for a Population I star, and 1.23×10⁵ M for Population III star. Mass loss rates expected in these stars are 3.3×10^–3 and 4.0×10^–3 M yr^–1, respectively.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

The application of a non-static spherically-symmetric metric to clusters of galaxies

An approximate metric is found which represents a sphere of matter embedded in a background of dust. The use of this metric in conjunction with the Friedmann equations gives values of for the three possible values ofk as +6×10^–36 (k=+1), +3×10^–35 (k=0), +10^–36 (k=–1). These values depend on data regarding clusters of galaxies, and are probably accurate to within an order of magnitude given the correctness of the assumptions on which their derivation rests.     

On the Excitation Mechanism of Solar Five-minute Oscillations

The excitation mechanism of solar five-minute oscillations is studied in the present paper. We calculated the non-adiabatic oscillations of low- and intermediate-degree (l = 1 − 25) g4-p39 modes for the Sun. Both the thermodynamic and dynamic couplings are taken into account by using our non-local and time-dependent theory of convection. The results show that all the lowfrequencyf- and p-modes with periods P > 5.4 min are pulsationally unstable, while the coupling between convection and oscillations is neglected. However, when the convection coupling is taken into account, all the g- and low-frequency f- and p-modes with periods longer than 16 minutes (except the low-degree p1-modes) and the high frequency p-modes with periods shorter than 3 minutes become stable, and the intermediate-frequency p-modes with period from 3 to 16 minutes are pulsationally unstable. The pulsation amplitude growth rates depend only on the frequency and almost do not depend on l. They achieve the maximum at ν 3700 μHz (or P 270 sec). The coupling between convection and oscillations plays a key role for stabilization of low-frequency f- and p-modes and excitation of intermediate-frequency p-modes. We propose that the solar 5-minute oscillations are not caused by any single excitation mechanism, but they are resulted from the combined effect of “regular” coupling between convection and oscillations and turbulent stochastic excitation. For low- and intermediatefrequency p-modes, the coupling between convection and oscillations dominates; while for high-frequency modes, stochastic excitation dominates.     

Invariant properties of families of moon-to-earth trajectories

Analytical techniques are employed to demonstrate certain invariant properties of families of moon-to-earth trajectories. The analytical expressions which demonstrate these properties have been derived from an earlier analytical solution of the restricted three-body problem which was developed by the method of matched asymptotic expansions. These expressions are given explicitly to orderµ ^1/2 where is the dimensionless mass of the moon. It is also shown that the inclusion of higher order corrections does not affect the nature of the invariant properties but only increases the accuracy of the analytic expressions.The results are compared with the work of Hoelker, Braud, and Herring who first discovered invariant properties of earth-to-moon trajectories by exact numerical integration of the equations of motion. (Similar properties for moon-to-earth trajectories follow from the principle of reflection). In each instance the analytical expressions result in properties which are equivalent, to orderµ ^1/2, with those found by numerical integration. Some quantitative comparisons are presented which show the analytical expressions to be quite accurate for calculating particular geometrical characteristics.

Nomenclature

Orbital Elements near the Moon energy - angular momentum - semi-major axis - eccentricity - inclination - argument of node - argument of pericynthion Orbital Elements near the Earth h _e energy - l _e angular momentum - i inclination - argument of node - argument of perigee - t _f time of flight Other symbols parameters used in matehing - U a function of the energy near the earth - a function of the angular momentum near the earth - r _p perigee radius - perincynthion radius - radius at node near moon - true anomaly of node near moon - initial angle between node near moon and earth-moon line - a function ofU, , andi - earth phase angle - dimensionless mass of the moon - U ₀, U₁ U=U ₀+U ₁ - i ₀, i_1/2, i₁ i=i ₀+µ ^1/2 i _1/2+µ i ₁ - ₀, _1/2, ₁ = ₀+µ ^1/2 i _1/2+µ i ₁ - _p longitude of vertex line - _n latitude of vertex line - R _o ,S _o ,N _o functions ofU ₀ and - a function ofU ₀, and      

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).     

Annihilation radiation from a power-law distributed electron-positron plasma on the ground Landau level: the case of low magnetic fields

Intensity, polarization, and cooling rate of the two-photon annihilation radiation are studied in detail in the case of one-dimensional power-law distributions of electrons and positrons, assuming that they occupy the ground Landau level in a strong magnetic fieldB10¹⁰–10¹² G. Simple analytical expressions for limiting cases are obtained and results of numerical calculations of radiation characteristics are presented. Power-lawe ^± distributions _{± ±} ^–k are shown to generate power-law spectra of the annihilation radiation atEmc ² andEmc ², with indices depending on the direction of radiation. The annihilation spectra at =0 show the largest blue-shifts of their maxima and the hardest high-energy tailsI(Emc ², =0)E ^–(k–1). The blue-shifts reduce, and the hard tials steepen, with increasing . At >(2mc ²/E)^1/2 the slopes of the high-energy tails rapidly transform to that at =2,I(Emc ², =/2)E ^–(2k+3). The direction-integrated spectraS(E) also display the power-law tials at low and high energies,S(Emc ²)E ^–(k+1). The total annihilation rate and energy losses decrease with decreasingk, being higher than for the isotropice ^± power-law distributions at the samek. The radiation is linearly polarized in the plane formed by the magnetic field and wave-vector. The polarization degreeP is maximum atEmc ²:P _max0.6 for =/2. Annihilation features and power-law-like hard tails observed in many gamma-ray burst spectra may be associated with the annihilation radiation of the magnetized power-law distributed plasma near neutron stars. Comparison of the observed and theoretical spectra allows one to estimate the power-law index of thee ^– e ⁺-distribution and the gravitational redshift factor in the radiating region.