Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF _o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr _arr_bwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr _a andr _b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr _o , Examples of Green's functions are given for the caser _a =0,r _b = and derived for the cases of finiter _a andr _b . The diffusion coefficient is assumed of the form = _o(p)r ^b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.     

Comparison between some Hα and X-ray flares

In the present paper, H-evolutive curves of chromospheric events are compared with flux evolutive curves of X-ray events observed at the same time in different spectral regions. A correspondence between the emissions E(I _H/I _chr)'s at higher and higher H-intensity levels, and the X-ray fluxes F()'s in harder and harder -ranges is shown. Further, the present observations seem to indicate the existence of a single triggering mechanism during the flash-phase of a flare. It is also shown that these results may be in agreement with Brown's model for chromospheric flares.     

Energetic properties of interplanetary plasma at the earth's orbit following the August 4, 1972 flare

Solar wind and interplanetary magnetic field data were obtained by the PROGNOZ 1 and PROGNOZ 2 satellites during the period following the August 4, 1972 (0621 UT) solar flare. A thermalized plasma was recorded one hour after the shock followed two hours later by the plasma piston with a bulk velocity higher than 1700 km s^-1. The comparison between the PROGNOZ and PIONEER 9 solar wind data shows an attenuation of the plasma properties with the deflection from the flare's meridian.     

The polarization of the inner solar corona at the eclipse of 10 July 1972

Photographs of the corona in the continuum spectrum (580–700 nm) have been obtained with a doublet camera (F=4m) through rotating sector polarizers with the vibrational directions oriented radially and tangentially to the solar limb. Isophotes of the total emission and its polarized component, as well as diagrams giving the degree of polarization for the (K+F)-corona and the electron corona proper (P _K), have been plotted up to the distance of 1R from the limb. In some inner regions the polarizationP _K exceeds the highest value possible for Thomson scattering under the given conditions. The reality of this anomally is dubious; systematic photometrical errors may account for it. Three-dimensional forms of 15 different coronal rays have been ascertained by comparing the course of polarization along the rays to the family of Baumach curves. The rays are found to deflect substantially from the radial directions out of the plane of the sky. Mean values of the coronal brightness and polarization versus the distance from the Sun have been determined. Contrary to well-known models (Van de Hulst) the mean polarization of the electron corona (P _K) decreases with distance after reaching the maximum (50%) at (1.4–1.6)R from the Sun's centre. This decrease can be explained by deflection of the streamers from radial directions.     

Analysis of the orbit of 1966-51C

The satellite 1966-51C was launched in June 1966 into a polar orbit with perigee height 180 km, apogee height 3600 km, and orbital period 125 min. The orbit contracted rapidly under the influence of air drag, and the satellite decayed in March 1967. The only available observations are from the NASA Minitrack system, and 825 of these have been used with PROP6 orbit refinement program, to determine orbital parameters at 20 epochs. For most of these orbits the standard deviations in inclination and right ascension of the node are less than 0.002° (corresponding to about 200 m cross-track) and the standard deviations in eccentricity are less than 0.00002 (150 m in height).The variation in inclination is analysed to determine upper-atmosphere zonal wind speeds, with excellent resolution in local time. The results, for heights near 210 km and a representative latitude near 30°, indicate west-to-east winds of 100 ± 40 m/s for local time 18–21 h, and east-to-west winds of 80 ± 25 m/s for 02–04 h and 09–12 h local time. The values of the right ascension of the node are also analysed, and provide independent confirmation of the wind speeds obtained from the inclination. Analysis of the decrease in perigree distance indicates values of density scale height within 5% of those predicted by the COSPAR International Reference Atmosphere 1972, for the conditions experienced by 1966-51C.     

Magnetic disturbance effects in the E region of the ionosphere

Detailed studies of the daytime E-region critical frequency at Aberystwyth (geomagnetic latitude +56°) show clear evidence for changes associated with both the axially-symmetric (Dst) and asymmetric (DS) components of the disturbance magnetic field. Comparison of the sensitivity of the E-region peak density to these two influences shows that the changes cannot entirely (if at all) be ascribed to the influence of electric currents in the region. It is suggested that a major role is played by dynamical influences associated with the neutral air “storm circulation” which distributes the energy fed into the auroral region to lower latitudes.     

Stochastic density fluctuations in the radiation era of the Universe

The linear stochastic hydrodynamical equations of the radiation-matter-one-component fluid in the Universe before the recombination era are solved. The stochastic forces in the heat flux and the viscous stress tensor are described according the procedure of Landau and Lifshitz. In the case of a low density universe, where the effects of the thermal conductivity can be neglected with respect to the shear viscosity, we find analytical solutions of the dispersion relation for the different modes and of the density correlation function . At the very Jeans length, this density correlation function exhibits a linear (for very large times) or a cubic (for small times) time dependence instead of a frozen-in character of this special mode.     

The system of old clusters in the magellanic clouds

IntegratedUBV colours have been computed for synthetic clusters older than one billion years and for two chemical composition: (a)Y=0.30;Z=10^–4 and (b)Y=0.30;Z=10^–2, taking into account the contribution to the integrated light of Main Sequence, subgiant, red giant and horizontal branch stars. It has been found that integrated colours depend onZ and allow an estimate of the metal content, however not generally. Horizontal branch stars contribute to the integrated colours of clusters not significantly and the contribution of stars in more advanced phases (e.g., asymptotic branch stars) is almost negligible.Old clusters in LMC and SMC have been studied in terms of colour calibrations and this analysis has been supplemented, when possible, by photometric and spectroscopic data of individual stars. It was found that in the LMC clusters withZ=10^–2 andt>5×10⁹ yr are lacking, clusters with relatively blue colours are similar, both in age and chemical composition, to the halo galactic globular clusters. Moreover, there is a group of clusters with 1×10⁹t5×10⁹. In the SMC clusters withZ=10^–2 andt>5×10⁹ yr are lacking and clusters with 1×10⁹t5×10⁹ are rare. Clusters with relatively blue colours are interpreted with the following parameters:t=5×10⁹ yr, 10^–4Z10^–3 andY=0.20.The implication of these results on the chemical history of the two galaxies is discussed.     

Unusual coronal activity following the flare of 6 November 1980

For almost 30 hr after the major (gamma-ray) two-ribbon flare on 6 November 1980, 03:30 UT, the Hard X-Ray Imaging Spectrometer (HXIS) aboard the SMM satellite imaged in > 3.5 keV X-rays a gigantic arch extending above the active region over the limb. Like a similar configuration on 22 May 1980, this arch formed the lowest part of a stationary post-flare radio noise storm recorded at metric wavelengths at Nançay and Culgoora. 6.5 hr after the flare a coronal region below the arch started quasi-periodic pulsations in X-ray brightness, observed by several SMM instruments. These brightness variations had no response in the chromosphere (H), very little in the transition layer (O v), but they clearly correlated with similar variations in brightness at 169 MHz. There were 13 pulses of this kind, with apparent periodicity of about 20 min, until another flare occurred in the active region at 15:00 UT. All the brightenings appeared within a localized area of about 30000 km² in the northern part of the active region, but they definitely did not occur all at the same place.The top of the X-ray arch, at an altitude of 155 000 km, was continuously and smoothly decaying, taking no part in the striking variations below it. Therefore, the area variable in brightness does not seem to be the footpoint of the arch, as we supposed for similar variations on 22 May. More likely, it is a separate region connected directly with the source of the radio storm; particles accelerated in the storm may be dumped into the low corona and cause the X-ray enhancements. The X-ray arch was enhanced by two orders of magnitude in 3.5–5.5 keV X-ray counts and the temperature increased from 7.3 × 10⁶ to 9 × 10⁶ K when the new two-ribbon flare occurred at 15:00 UT. Thus, it is possible that energy is brought into the arch via the upper parts of the reconnecting flare loops - a process that can continue for hours.