Effect of drift-resonance broadening on radial diffusion in the magnetosphere

In the quasilinear theory of magnetospheric radial diffusion caused by fluctuating electrostatic (E) or magnetic (B) fields, the diffusion coefficientD _LLis proportional to the spectral density of E or B at the particle drift frequency ₃/2. Since ₃ varies withL at fixedM andJ (adiabatic invariants), the drift resonance =₃ can be maintained only transiently, and therefore is not perfectly sharp. Its bandwidth ^* is approximately (16D _LL /L ²₃)^1/3₃. In magnetospheric radial diffusion caused mainly by electrostatic fluctuations, the value of ^*₃ typically exceeds 0.4 for particle energiesE40 keV. However, the numerical value ofD _LLis correctly given (within 1% in all cases) by quasilinear theory because the spectrum of E is rather flat at resonance frequencies for which the bandwidth is an appreciable fraction of ₃. (Numerical conclusions are based on a quasilinear model forD _LLused successfully by Cornwall in 1972.)     

Confirmation of radio absorption by the intergalactic medium

The conventional interpretation of the cosmic background radiation (CBR) as a relic of the Big Bang assumes that the intergalactic medium is highly transparent to radio frequency radiation. Previous work (Lerner, 1990) used the well-known correlation of IR and radio luminosities of spiral galaxies to test this assumption. That analysis, using 237 Shapley-Ames galaxies showed that radio luminosity (L _R ) for a given IR-luminosity, declines with distance, implying that the IGM strongly absorbs radio frequency radiation. That absorption has now been confirmed using a sample of 301 IR-bright galaxies. Using two independent methods of determining the correlation of IR and radio luminosities of spiral and interacting galaxies, the sample shows that for a givenL _IR ,L _R D ^{–0.32±0.04} over a range of distances from 0.7-300 Mpc. (H ₀ = 75 km s^–1 Mpc^–1). The correlation is significant at the 8 or 10^–14 level. Absorption by the IGM is the only reasonable explanation for this correlation. The existence of such absorption implies that neither the isotropy nor the spectrum of the CBR are primordial and that neither is evidence for a Big Bang.     

Convergence of Liapunov Series for Maclaurin Ellipsoids

According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q : above mentioned series converge for all bodies if q < q . Using Liapunov's algorithm and symbolic calculus tools we have calculated q = 0.000370916. Evidently, convergence radius q ₀ may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q ₀ for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q ₀ = 0.337 for Maclaurin ellipsoids.     

The Restricted Three -Body Problem. Comments on the `Spatial' Equilibrium Points

In the photogravitational restricted three-body problem, the role of theradiation-pressure is reviewed. By the analytical considerations, the existence of the `spatial' equilibrium points is analysed. In order to avoid the unknown parameters of the infinitesimal body, for the two component stars an analytical function ₂ =f(₁ ) is established.In contrast to results given by other authors, here only one pair of suchpoints is found. A numerical simulation for RW Monocerotis is undertakenand it is found L ₆(–0.055; 0; +1.07) and L ₇(–0.055; 0; –1.07).     

An Improved Optical Model for the Non-LTE Problem for the CO2 Molecule in the Atmosphere of Mars: Nighttime Populations of Vibrational States and the Rate of Radiative Cooling of the Atmosphere

The estimates of the population of excited vibrational states of the CO₂ molecule and of the rate of radiative cooling of the atmosphere in the 15-m CO₂ band are given for the nighttime mesosphere and thermosphere of Mars. For the first time, these estimates are made (1) with allowance for the overlap of lines in the 15-m band; (2) for a wide set of vibrational states of seven isotopes of the CO₂ molecule, which was used earlier in the solution of a similar terrestrial problem; and (3) using the rate constant for quenching of the CO₂(01¹0) state in collisions with oxygen atoms, which has been recently measured for low temperatures by Khvorostovskaya et al. (2002). The main results are as follows. 1. The approximation of isolated lines provides a satisfactory accuracy of determining the radiative cooling rate and overestimates vibrational temperatures of the states of the ₂ mode by no more than 3 K for the ¹²C¹⁶O₂ molecule and by no more than 2 K for low-abundant isotopes of the CO₂ molecule. 2. A reasonably high accuracy of estimating the cooling rate can be achieved by taking into account only fundamental vibrational transitions in ¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O, and ¹⁶O¹²C¹⁷O molecules and the hot transitions 2_{2 2} and 3₂ 2₂ in the ¹²C¹⁶O₂ molecule. 3. The vertical profile of the total rate of radiative cooling displays two peaks. The maximum near a height of 130 km is very sensitive to temperature and to the ratio of the mixture for oxygen in the atmosphere.     

Structure of close binaries

Internal models have been obtained for uniformly rotating synchronous close binary systems using a modified double approximation scheme. We have considered primaries of 10M , 5M , and 2M with mass ratios of 0.0 to 1.0 in steps of 0.1, and some results are given for a 1M primary with a mass ratio of 1.0. A maximum luminosity reduction of 2.3% was found for a 10M primary with a mass ratio of 1.0 and 7.7% for a mass ratio of 0.0. The corresponding values for 5M are 2.0% and 7.0%, and for 2M they are 1.6% and 5.3%, respectively. These values were not found to be sensitive to small changes in composition. The maximum equatorial velocity varies from 399 km s^–1 for 2M to 567 km s^–1 for 10M when the mass ratio is zero, but these velocities decrease by 200–300 km s^–1 if the mass ratio is unity. The effect of gravity darkening on the apparent position of the primary in the theoretical H-R diagram was investigated. It was determined that an unresolved close binary of unit mass ratio can lie up to 0.9 magnitudes (depending on inclination) above the main sequence, whereas if the effects of distortion are ignored this number is at most 0.75 magnitudes. There seems to be some observational support for the larger value. Two models of the secondaries are given and their dimensions are compared with their critical Roche lobes.     

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).     

Non-thermal solar wind heating by supra-thermal ions

The effect of a new energy source due to energies transferred from supra-thermal secondary ions on the temperature profile of the solar wind has been considered. For this purpose a solution of a tri-fluid model of the solar wind including solar electrons, protons, and -particles, and starting with the boundary conditions of Hartle and Barnes at 0.5 AU is given. On the base of the assumption that suprathermal He⁺-ions which have four times the temperature of suprathermal protons are predominantly coupled to solar -particles by Alfvén waves, it is shown that the temperature T of solar -particles should be appreciably higher than those T _p of solar protons beyond the orbit of the Earth. For 1 AU a temperature excess T over T _p according to that which has been found in some solar wind ion spectrograms can only be explained for a small part of the orbit of the earth which is inside the cone of enhanced helium densities. Around 1 AU the temperatures T and T _p are found to decrease much slighter with solar distance than given in the two-fluid model of Hartle and Barnes. Beyond 1.7 and 2.2 AU the temperatures T and T _p even start increasing with solar distance and come up to about 10⁵ at about 10 AU. These predictions should lend some support to future temperature measurements with deep-space probes reaching Solar distances of some AU.Forschungsberichte des Astronomischen Institutes, Bonn, 72-10.     

Third and fourth order resonances in Hamiltonian systems

The stability of the origin of an autonomous Hamiltonian system is investigated when the system possesses a third or fourth-order resonance.H ₂, the quadratic part ofH isH ₂=ⁿ _{i=1 i} J _i and the resonance condition is ⁿ _i=1 k _{i i} where thek 0,i = 1, 2, ...,n are the natural or fundamental frequencies. It is shown that the only case in which the origin can be unstable is ifk _i0,i=1,2,...,n. The condition for instability is then given in terms of the coefficients of the higher order terms in the Hamiltonian. The transfer of energy between modes is also investigated when a near-resonant condition exists.     

Dependence of the meridional motions of sunspot groups on life spans and age of the groups,and on the phase of the solar cycle

We have analyzed data on sunspot groups compiled during 1874–1981 and investigated the following: (i) dependence of the `initial' meridional motion (v <sub>ini</sub>()) of sunspot groups on the life span () of the groups in the range 2–12 days, (ii) dependence of the meridional motion (v(t)) of sunspot groups of life spans 10–12 days on the age (t) of the spot groups, and (iii) variations in the mean meridional motion of spot groups of life span 2–12 days during the solar cycle. In each of the latitude intervals 0°–10°, 10°–20° and 20°–30°, the values of both v <sub>ini</sub>() and v(t) often differ significantly from zero. In the latitude interval 20°–30°, the forms of v <sub>ini</sub>() and v(t) are largely systematic and mutually similar in both the north and south hemispheres. The form of v(t) suggests existence of periodic variation in the solar meridional motion with period of 4 days and amplitude 10–20 m s<sup>–1</sup>. Using the anchoring depths of magnetic structures for spot groups of different and testimated earlier, (Javaraiah and Gokhale, 1997), we suggest that the forms of v <sub>ini</sub>() and v(t) may represent radial variation of meridional flow in the Sun's convection zone, rather than temporal variation of the flow. The meridional flows (v <sub>e</sub>(t)) determined from the data during the last few days (i.e., age t: 10–12 days) of spot groups of life spans of 10–12 days are found to have magnitudes (10–20 m s<sup>–1</sup>) and directions (poleward) similar to the those of the surface meridional plasma flows determined from the Dopplergrams and magnetograms. The mean meridional velocity of sunspot groups living 2–12 days seems to vary during the solar cycle. The velocity is not significantly different from zero during the rising phase of the cycle and there is a suggestion of equatorward motion (a few m s<sup>–1</sup>at lower latitudes and 10 m s<sup>–1</sup>at higher latitudes) during the declining phase (last few years) of the cycle. The variation during the odd numbered cycles seems to anticorrelate with the variation during the even numbered cycles, suggesting existence of 22-year periodicity in the solar meridional flow. The amplitude of the anticorrelation seems to be depending on latitude and the cycle phase. In the latitude interval 20°–30° the `surface plasma meridional motion', v _e(t), is found to be poleward during maximum years (v _e(t) 20 m s^–1at 4th year) and equatorward during ending years of the cycle (v _e(t) –17 m s^–1at 10th year).     

On the evolution of low mas binary systems

The evolution of parameters of close binary systems containing a red dwarf (with mass loss) and a condensed star is investigated. The mass loss from the system and asynchronism of the red dwarf rotation are taken into consideration. The calculations show that if the initial mass ratioq ₀2 then during 10⁷ yr the instability of mass loss process arises, and a bright X-ray source forms with luminosity close to the Eddington one. Ifq ₀>2 then during the mass loss phase the bright X-ray source arises twice. The models explain the existence of the forbidden interval of orbital periods and the absence of systems with periods less than 80 min.     

Asymptotic properties of disk dynamo

The asymptotic properties of a turbulent disk dynamo at large dimensionless numbersR andR characterizing the helicity and the differential rotation are analysed. Three types of generations in the dependence of the relations betweenR andR are found: ²-dynamo and two types of -dynamo. For each of these types the rates of growth are obtained and the forms of solution are pointed out. Boundaries of the disk dynamo approximation are given.     

Pulsars: Observational parameters and a discussion on dispersion measures

The relevant data for the known 147 pulsars are presented in graphical and tabular forms. Various data correlations are discussed, and a detailed analysis of pulsar dispersion measures and distances is given. The range of the electron densities in the diffuse interstellar medium is found to be 0.01 cm^–3n _e0.1 cm^–3, and n _e0.03 cm^–3. The dispersion scale height for pulsars is found to be 5.9±0.7 pc cm^–3 implying a linear scale height of 200 pc, which is much smaller than the electron scale height of our Galaxy.Astrophysics and Space Science Review Paper.     

Comparison between stability limits for satellite motion

Numerical and analytical comparisons are made between three methods of obtaining stability information on satellite motion using the model of the restricted problem of three bodies. Kuiper's (1961) and Szebehely's (1978) approximate results are compared with computer solutions obtained by successive iterations. The three methods show close agreement regarding the maximum values of the orbital radii for stability. The lowest result and therefore the most conservative estimate is obtained by the simplest formula, _max=(/81)^1/3 where is the ratio of the satellite's orbital radius to the distance between the primaries with massesm ₁>m ₂ and is the mass-ratio given bym ₂/(m ₁+m ₂).     

Spatial dependence of the pitch-angle and associated spatial diffusion coefficients for cosmic rays in interplanetary space

The spatial dependence of the pitch-angle and associated spatial diffusion coefficients for cosmic ray particles in interplanetary space is calculated in the WKB approximation. The model considers only Alfven waves of solar origin to be responsible for scattering of moderate energy particles. After developing the general theory results are presented for the asymptotic case corresponding to radial distancesr greater than about 1 to 2 AU. The radial diffusion coefficient _r increases with energyE like _r E , wherev2/3. The radial mean free path turns out to increase proportional tor ³ at medium and low heliographic latitudes. This behaviour is consistent with a very small radial cosmic ray gradient and the existence of a free boundary for particle diffusion. At equal radial distances the high latitude mean free path is not only much smaller than the one calculated at the lower latitudes but in addition increases only weakly with distance. Some conceivable dynamical implications for the outer solar system are indicated.     

Linear current instability in loop prominences

By use of the dispersion equation given by Song, Wu, and Dryer (1987) for a cylinder plasma with mass motion and gravity included, we investigate the linear current instabilities developed in loop prominences. The results indicate that the mode of linear instability depends mainly on whetherv _s ² > or not, wherev _s is the sonic velocity at heightz, =GM/(R +z) is the gravity potential,G the gravitational constant,M andR the mass and the radius of the Sun respectively. Ifv _s ² > , then the sausage instability will be dominant. Otherwise, the kink instability will be more important. A possible explanation of knot structure, which appears sometimes in solar loop prominences has been given.     

Numerical Study of the First Compression of a Two-Dimensional Pinch

For studying the first compression phase of a Plasma Focus machine, we developed a 2-fluid, time-dependent, 2-D code. The code includes two species (ions and electrons), two temperatures, radiation, thermal conductivity, electrical conductivity, magnetic diffusion, and viscosity and is coupled to an external circuit. In order to get reasonable initial conditions for the pinch phase, a simple 1-D model is used for the run-down phase. Under this somewhat ideal Plasma Focus discharge condition, relatively simple scaling laws are obtained. In particular, for a given machine, the pressure (p_o) of maximum thermonuclear production scales with the charging voltage (V_o) as p_o V_{o 2}; the thermonuclear production (Y_n) at these pressures increases with the current (I_o) as Y_n I_o ⁴ and the mean energy per particle is almost independent of all parameters (note that this means that the converging speed should be almost the same regardless of the machine at the optimum conditions). These laws show a reasonable agreement with experimental data and can be explained with a dimensional analysis.     

Additional results for unstable stratified toroidal magnetic fields in stars

General conditions for adiabatic instability of weak axisymmetric toroidal magnetic fields are obtained. In particular all fields which haveH =0 and H ² />0 simultaneously are unstable. This includes all fields which exist near to the axis of symmetry and, indeed, any without an infinite current density anywhere. A detailed discussion is given of fields with an angular dependenceH ² |P (cos )|. These fields are dynamically unstable with respect to both axisymmetric and non-axisymmetric perturbations for all values of the azimuthal wave number |m|. The maximum growth rates are independent ofm and they are largest for the fields that are defined in the regions closest to the polar axis.     

Macro-and micro-turbulent filter functions for weak lines in stellar atmospheres

Following a similar discussion given earlier for the solar case (De Jager, 1972) we compute in this paper spectral line profiles for the spatial wavelengths in which a stellar motion field can be decomposed, and thereafter the macro-and micro-turbulent filter functionsf _M(k) andf (k), where is the optical scale height andf ²(k) dk the fraction of the energy of the turbulent motions between wavenumbersk andk+dk of the spectrum of turbulence that contributes to either kind of turbulence. If micro-and macro-turbulent velocity components are known for a certain star, and if the spectrum of turbulence is sharp enough, the ratiof _M/f would enable one to derive the average size of the turbulent elements in the star's atmosphere. The computations apply to weak lines in idealized stellar atmospheres, and refer to two cases: isotropic turbulence, and radial pulsations. These filters can be suitably used in a diagnostic method for the analysis of the motion field in the solar and stellar atmospheres. Some examples of applications to stars of very different kinds are given.