A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.     

Magnetic properties of x-ray bright points

Using high resolution KPNO magnetograms and sequences of simultaneous S-054 soft X-ray solar images we have compared the properties of X-ray bright points (XBP) and ephemeral active regions (ER). All XBP appear on the magnetograms as bipolar features, except for very newly emerged or old and decayed XBP. We find that the separation of the magnetic bipoles increases with the age of the XBP, with an average emergence growth rate of 2.2 ± 0.4 km s^–1. The total magnetic flux in a typical XBP living about 8 hr is found to be 2 x 10¹⁹ Mx. A proportionality is found between XBP lifetime and total magnetic flux, equivalent to 10²⁰ Mx per day of lifetime.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

The north-south distribution of major solar flare events,sunspot magnetic classes and sunspot areas (1955–1974)

The north-south incidence has been studied of 31 white-light flares observed since 1859 and of 1669 events meeting the criteria for major flares of Dodson and Hedeman (1971) for the period 1955–1974. The asymmetry in favor of the northern hemisphere increases strikingly with the importance of the events. Similarly, magnetically complex sunspot groups (Mt. Wilson classes, and) display a more pronounced asymmetry in favor of the north than non-complex groups for 1962–1970. Contrary to the flare asymmetry, the spottedness asymmetry is independent of the size of sunspots.     

The absorption of energetic electrons by argon gas

The processes by which energetic electrons lose energy in a weakly ionized gas of argon are analysed and calculations are carried out taking into account the discrete nature of the excitation processes. The excitation, ionization and heating efficiences are computed for energies up to 200 eV absorbed in a gas with fractional ionizations varying up to 10^?2.     

Thermal response properties of the Earth's ionospheric plasma

The thermal response of the Earth's ionospheric plasma is calculated for various suddenly applied electron and ion heat sources. The time-dependent coupled electron and ion energy equations are solved by a semi-automatic computational scheme that employs Newton's method for coupled vector systems of non-linear parabolic (second order) partial differential equations in one spatial dimension. First, the electron and composite ion energy equations along a geomagnetic field line are solved with respect to a variety of ionospheric heat sources that include: thermal conduction in the daytime ionosphere; heating by electric fields acting perpendicular to the geomagnetic field line; and heating within a stable auroral red are (SAR-arc). The energy equations are then extended to resolve differential temperature profiles, first for two separate ion species (H⁺, O⁺) and then for four separate ion species (H⁺, He⁺, N⁺, O⁺) in addition to the electron temperature. The electron and individual ion temperatures are calculated for conditions within a night-time SAR-arc excited by heat flowing from the magnetosphere into the ionosphere, and also for typical midlatitude daytime ionospheric conditions. It is shown that in the lower ionosphere all ion species have the same temperature; however, in the topside ionosphere above about 400 km, ion species can display differential temperatures depending upon the balance between thermal conduction, heating by collision with electrons, cooling by collisions with the neutrals, and energy transfer by inter-ion collisions. Both the time evolution and steady-state distribution of such ion temperature differentials are discussed.The results show that below 300km both the electrons and ions respond rapidly (<30s) to variations in direct thermal forcing. Above 600 km the electrons and ions display quite different times to reach steady state, depending on the electron density: when the electron density is low the electrons reach steady state temperatures in 30 s, but typically require 700 s when the density is high; the ions, on the other hand, reach steady state in 700 s when the density is high, and 1500–2500 s when the density is low. Between 300 and 600 km, a variety of thermal structures can exist, depending upon the electron density and the type of thermal forcing; however steady state is generally reached in 200–1000 s.     

Fitting of hydrodynamic and kinetic solar wind models

In isothermal models of the expanding solar corona there exists in general an exobase level where the collision mean free path becomes equal to the density scale height. At this level the hydrodynamic approximations of the transport equations fail to be justified and a kinetic approach is more appropriate. This exobase is located below the altitude of the critical point proper to the hydrodynamic solutions. The bulk velocity at the exobase is subsonic and smaller than the expansion velocity at the critical point. Therefore the transition to a supersonic solar wind velocity occurs in the collisionless ion-exosphere.     

Relative flow of H+ and O+ ions in the topside ionosphere at mid-latitudes

Theoretical results on the daily variation of O⁺ and H⁺ field-aligned velocities in the topside ionosphere are presented. The results are for an L = 3 magnetic field tube under sunspot minimum conditions at equinox. They come from calculations of time-dependent O⁺ and H⁺ continuity and momentum balance in a magnetic field tube which extends from the lower F2 region to the equatorial plane (Murphy et al., 1976).There are occasions when ion counterstreaming occurs, with the O⁺ velocity upward and H⁺ velocity downward. The conditions causing this counterstreaming are described: the H⁺ layer is descending whilst O⁺ is supplied from below either to increase the O⁺ concentration at fixed heights or to replace O⁺ ions lost by charge exchange with neutral H. It is suggested that the results of observations at Arecibo by Vickrey et al. (1976) of O⁺ and H⁺ concentrations and counterstreaming velocities are significantly affected by $\text{E}\text{×}\text{B}$ drift.     

Mars surface properties observed by earth-based radar at 70-, 12.5-, and 3.8-cm wavelengths

A review of Mars radar data obtained through the 1973 opposition confirms that the surface of the planet has many diverse characteristics. Analysis of the quasi-specular echo component shows changes in apparent reflectivity of at least 5 to 1. If attributed entirely to variations in surface material, these correspond to dielectric constants between 1.6 and 4.0. Values of rms surface slope on 1- to 100-m scales range from as low as 0.5° in tablelands near Vlles Marineris to more than 3.0° (the upper limit for which these analysis techniques are appropriate) in certain other areas such as inside Coprates Chasma itself. There is weak correlation between the small-scale surface characteristics inferred from radar and those inferred from Mariner 9 images, geologic maps derived from those images, and other remote sensing data sets. Topography, a large-scale surface characteristic for which good correlation exists between radar and other data sets, was not considered in this study. A search for guidelines which would allow extrapolation of radar properties to new areas on the basis of those studied has been singularly unsuccessful. Data obtained during the 1973 opposition at Arecibo, Goldstone, and Haystack Observatories indicate that the scattering behavior of Mars varies little over the 70- to 3.8-cm wavelength range. Comparison of 1971 and 1973 Goldstone results shows no detectable variation with time.     

High spectral resolution ground-based observations of Venus in the 450- to 1250-cm−1 region

Ground-based observations of Venus were made with a 5-cm drive Michelson interferometer during December 1970 and December 1973. The thermal emission spectrum of the central portion of the apparent disk was recorded from 450–1250 cm^?1 with an apodized spectral resolution of 0.25 cm^?1. All statistically significant sharp line absorption features in the spectrum have been identified with gaseous CO₂. Comparison between the observed spectrum and a synthetic spectrum computed from a model atmosphere, assuming gaseous CO₂ and a sulfuric acid haze as opacity sources, indicates good agreement. A broad diffuse absorption feature associated with the sulfuric acid haze is evident in the 870- to 930 cm^?1 region. With the exception of the rotational lines of the 927-cm^?1 CO₂ band, the above feature appears as a continuum down to 0.25 cm^?1 resolution. In the 750- to 1250-cm^?1 range, the spectrum exhibits moderate thermal contrast with maximum brightness temperatures of 234–238°K occurring near 825 cm^?1. These temperatures are in general agreement with previous measurements.     

Interpretation of spatial and temporal variations of hydrogen quadropole absorptions in the Jovian atmosphere observed during the 1972 apparition

During the 1972 apparition of Jupiter, we carried out a patrol of the (3,0) S(1) and (4,0) S(1) quadrupole lines of molecular hydrogen in the equatorial region and in bands bounded by ±15 and ±49° zenographic latitude from the McDonald and Table Mountain Observatories. At the center of the Jovian disk, we found evidence of temporal variability of both lines over the duration of our observing period. We employ a technique which takes into account all radiative transfer processes in an inhomogeneous model of Jupiter's atmosphere, and use it to derive the effective level of formation of the spectral lines and the relative abundance of hydrogen. In this way, we are able to correlate measured changes in the equivalent widths of the hydrogen lines with variations in cloud structure. The effective pressure level at which the (4,0) S(1) line is formed varies in the range 2 ± 0.5 to 1.3 ± 0.2 atm, while for the (3,0) S(1) line, the pressure varies between 1.6 ± 0.5 and 1 ± 0.4 atm. If these variations are interpreted in terms of changes in elevation of the top of a dense lower cloud deck, the elevation apparently varied with an amplitude of 25 km during the observational period.Spatial variations in the strengths of both lines were also found. Both lines are weaker at the east limb than at the center of the disk (15–19%) while the variations toward the west limb are less pronounced (5%). Similar center-to-limb variations were found in the latitude bands bounded by ±15 and ±49°, although the lines were stronger in the northern component at the time of the observations.