Planetary accretions in jet streams

The problem of planetary accretion in a jet stream is studied using the model developed by Alfvén and Arrhenius. We find that there are basically three types of planetary accretion: namely, fast process _c < _i , slow process _c ~ _i and delayed process _c > _i where _c is the characteristic time of the occurrence of catastrophic accretion and _i the time-scale of mass injection to the planetary system (3×10⁸ yr). These different time scales of accretion are found to be closely related to the primordial thermal profiles and equatorial inclinations of the planets. Finally, Venus' retrograde rotational spin is shown to be a possible result of accretion process in a jet stream.     

On Geovenelli's approximate form of j(τ)

The accuracy of the approximate replacement of the frequency meanj() of the total intensityJ () byJ _c+a{J ₀()–J _c} by Geovenelli, whereJ _c is the total intensity at the continuum,J ₀() is that at the line center anda is independent of depth, is studied. Numerical calculations for strong solar lines show very high values of the residual intensities. A slight change in the approximation is then suggested to get a result quite consistent with observational and existing calculated data.     

Linear hydrodynamical equations coupled with radiative transfer in a non-isothermal atmosphere

A method coupling the hydrodynamical equations and radiative transfer in a realistic solar model atmosphere is described. The influence of the temperature gradient of the model and the radiative dissipation is pointed out.The effect of the large temperature gradient is important in the layers where the optical depth ₅₀₀₀ is greater than 0.5; the ratio between the amplitude of the temperature and the velocity fluctuations decreases with the altitude by a factor 2 between = 1 and = 0.5 and in the case of the acoustic waves, the phase shift between these fluctuations is small.The radiative energy loss in the thick layers ( ₅₀₀₀ = 1) leads to a decrease of the vertical phase velocity of the waves and to a damping of their amplitudes in the layers of intermediate optical depth (10^-2 < ₅₀₀₀ < 0.5). The effect of the dissipation is negligible in the thin layers (₅₀₀₀ < 10^-2).     

On intensity ratios of helium and hydrogen lines in quiescent prominences

Observations of the lines He i 3888 and H8 in 80 quiescent prominences by the author, and in other prominences by Kubota et al. (1972) and Morozhenko (1971), have been used to derive the dependences of I(3888)/I(H8) on I(H8), N ₂ ³ _s on ₀ (H), and N ⁺ n _e on ₀(H) (Figures 1, 2, 3 and 4). The equations of ionization equilibrium and triplet system steady state for a helium atom (27 levels and continuum were considered) were solved together with the radiation transfer equation in the helium Lyman continuum. As given n _e () distribution with depth and T _e =7500 K were assumed. The 2³ S level population N₂ ³ s, helium emission measure N ⁺ n _e and the intensity ratios of the He i 3888 and H8 lines were calculated and compared with observation (Figures 2, 3 and 4, solid lines). The figures show that in bright prominences the observed values of N ₂ ³ s and N ⁺ n _e are systematically higher than the calculated ones. These deviations cannot be eliminated by decreasing n _e . One can make the calculations and observations agree for bright prominences by increasing the UV radiation which penetrates into the prominence.     

On the A-transform of the exponential integrals

In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE _n which is denoted as _n (). The main result of this analysis enables us to establish a two-term recurrence formula for _n (0) and a three-term recurrence formula for _n (); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.     

A novel methodology for radiative transfer in a planetary atmosphere

A novel methodology for evaluating the field of anisotropically scattered radiation within a homogeneous slab atmosphere of arbitrary optical thickness is provided. It departs from the traditional radiative transfer approach in first considering that the atmosphere is illuminated by an isotropic light source. From the solution of this problem, it subsequently proceeds to that for the more conventional case of monodirectional illumination. The azimuthal dependence of the field is separated in the usual manner by an harmonic expansion, leaving a problem in four dimensions (=optical depth, ₀=thickness, , =directions of incidence and scattering) which, as is well known, is numerically extremely inconvenient. Two auxiliary radiative transfer formulations of increasing dimensionality are considered: (i) a transfer equation for the newly introduced functionb ^m(,,₀) with Sobolev's function ^m(,₀) playing the role of a source-function. Because the incident direction does not intervene, ^m is simply expressed as a single integral term involvingb ^m. For bottom illumination, an analogous equation holds for the other new functionh ^m(,,₀). However, simple reciprocity relations link the two functions so that it is only necessary to considerb ^m; (ii) a transfer equation for the other new functiona ^m(,,,₀) with a source-function provided by Sobolev's functionD ^m(,,₀). For bottom illumination, another functionf ^m(,,,₀) is introduced; by a similar argument using reciprocity relations,f ^m is reduced toa ^m rendering necessary only the consideration ofa ^m. However, a fundamental decomposition formula is obtained which shows thata ^m is expressible algebraically in terms of functions of a single angular variable. The functions ^m andD ^m are shown to be the values in the horizontal plane ofb ^m anda ^m, respectively. The other auxiliary functionsX ^m andY ^m are also expressed algebraically in terms ofb ^m. These results enable one to proceed to the final step of evaluating the radiation field for monodirectional illumination. The above reductions toalgebraic relations involving only the functionb ^m appear to be more advantageous than Sobolev's (1972) recent approach; they also circumvent some basic numerical difficulties in it. We believe the present approach may likewise prove to be superior to most (if not all) other methods of solution known heretofore.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory under Contract No. NAS-7-100 sponsored by the National Aeronautics and Space Administration.     

Les raies du triplet de l'helium de la Nova Delphini 1967

The aim of this paper has been to study the neutral helium triplet emission lines identified in the spectrum of the envelope of Nova Delphini. By comparing the observed flux of the neutral helium lines with that calculated theoretically by Robbins, we find that the optical thickness in the center of the line 3889 is of the order of 21.50 for summer 1969. The optical thickness obtained by this method is here denoted _tran(3889).On the other hand, we obtain the number of neutral helium atoms in the 2³S state [N(2³S)] by considering the equilibrium between the mechanisms that populate and depopulate this state. We then find that the depopulation by photoionization due to the radiation of Ly (Hi), transitions to the 2¹S, 2¹p and 2³p states by electron collision, photoionization due to the continuum radiation of the central star, are 82.70%, 13.20%, 2.40%, 0.90% and 0.80% respectively. We find that the mechanism of the photoionization by Ly is the dominant mechanism of depopulation of 2³S state. We calculated ( 3889) of the order of 82.37, fromN(2³S), obtained in the preceding paragraph. The optical thickness obtained by this method is here denoted _bal(3889).The difference between _tran(3889) and _bal(3889) is very large and it cannot be attributed to calculation errors. We have considered all the mechanisms that can depopulate the 2³S state, so we then conclude that the difference between _tran(3889) and _bal(3889) is due to the heterogeneity of the envelope of the Nova, already found by us in our previous study of the profiles of the permitted and forbidden lines. Finally, we find from this study a filling factor of the order of 0.30.     

A systematic method for the analysis of high-resolution fraunhofer line profiles

A fraunhofer line profile depends on various parameters, partly related to the photospheric structure (T, P _g, P _e, v _conv, v _turb), partly to the atom or ion involved (such as oscillator strength, energy levels), partly also resulting from the interaction of the relevant kind of particles with the photosphere, and the photospheric radiation field. In this paper we shall mainly pay attention to the determination of: the macroturbulent (convective) velocities, v _conv (); the damping constant (); the abundance, A _el; the distribution function (v _conv, ) of the convective velocities at each depth ; the source function, S (); the microturbulent velocities, v _turb ().The particular difficulty with these unknowns is that they are, as a rule, coupled in the resulting line profiles, that is: the shapes and intensities in these profiles are determined by the combined influence of these unknowns (together with the other above-given parameters).In this paper we describe a method to determine these six unknowns empirically by separating them, in analysing accurate high-resolution observations of line profiles of a multiplet. The unknown functions and quantities are consecutively determined in the above given succession. For each determination another, appropriate part of the line profile is used. In some cases the influence of the mutual coupling of the various parameters cannot be completely eliminated, and an iterative method has to be used.The method is summarized in Table II and section 2, and is further explained in sections 3 to 8. It is applied to an infrared Ci multiplet. The main results are the following:     

Analysis of extreme-ultraviolet spectroheliograms of solar prominences

The optical depth at the head of the Lyman continuum, _H, is determined at a number of positions in three hedgerow prominences using spectroheliograms (5 × 5 resolution) of C III 977, LC 896, and O IV 554 observed with the Harvard experiment on Skylab. At heights greater than 10 above the limb the maximum value of _H is 30 to 50, which occurs at the central part of the prominences. For one of the prominences the determination of _H is found to be consistent with data from spectroheliograms of Mg X 625. The degree of ionization of hydrogen is estimated from the intensity of LC 896 at _H 1. In the central part of a model prominence N _P/N _HI1.9 for a reasonable range of the electron densities, where N _P and N _HI are the proton density and the neutral hydrogen density, respectively.     

Analysis of the time profile of type III bursts at meter wavelengths

The time profile of two sets of isolated type III bursts, observed in the meter wavelength range at the Trieste Astronomical Observatory, was analyzed using a Fourier transform technique in order to accurately determine the decay constant of the exponential phase and to derive the exciter time profile. The decay constant () was found to be correlated with the exciter duration (D _e ), suggesting that the damping of plasma waves is not of collisional origin and confirming results obtained by previous authors at lower frequencies. In particular, two distributions can be identified in the ( – D _e ) plane and fitted by two nearly parallel lines, which could be the signature of different decay processes. Moreover, the damping constant observed at higher frequencies (327 and 408 MHz) has the same dependence on exciter duration as that at the lower frequency (237 MHz), also in disagreement with the collisional hypothesis.     

Annihilation of antimatter meteors

Antimatter meteors probably enter the Earth's atmosphere. If they have the ability to escape complete vaporization during their infall flight, it may be possible, that a fraction of their original mass could survive for short or long time, depending on the mechanisms of ablation. In case of ablation through the annihilation process only, the lifetime of such an object is following the simple relation = (N _L R)/(rA), where andA are the density and the atomic weight of the antimatter fragment respectively,R is its radius,r is the rate of annihilation per cm² of its surface, and N _L is the Loschmidt number.     

Absolute wavelengths of Fraunhofer lines: Convective motions in the solar photosphere and the gravitational red shift

Absolute wavelengths for Fraunhofer lines are compared with laboratory measurements for several atomic and molecular spectra. The wavelength differences are shown to be consistent with the proposal that the deeper layers of the photosphere are in convective motion: _e -3 km/sec for log ₀> -1.0. Convective motions in the outer layers (log₀< - 1.0) are shown to be very small. Wavelength shifts of Fraunhofer lines formed in these outer layers are in good quantitative agreement with the predictions of the General Theory of Relativity.     

The inclination changes in the problem of two triaxial rigid spheroids

The first-order perturbations of a system of two triaxial rigid spheroids under Hori-Lie transformation are investigated. The time dependence of the configuration of the three angular momentum vectors, two rotational and one orbital, is studied. The problem is simplified by the introduction of a new time parameter , such thatt is the hyperelliptic function of . The projectionsH ₁ andH ₂ of the rotational momentum vectors into the direction of the total angular momentum vector of the system are then harmonic or exponential functions of . The trajectory in theH ₁,H ₂ plane is a part of an ellipse or hyperbola respectively. If this conical section intersects a certain critical contourC, the system is bounced back along the original trajectory. The motion of the relative configuration of the angular momentum vectors is periodical except in a special aperiodic case. The expressions for the periods are given.     

Coronal Leaky Tube Waves and Oscillations Observed with Trace

Leaky tube waves are examined in the context of kink oscillations in coronal loops, observed in recent years using TRACE. It is pointed out that the standard (non-leaky) principal kink mode has a leaky bifurcated counterpart with decay time 4^–4(L/R)² P, where R and L are the loop radius and length, and P is the oscillation period. This is somewhat too long to explain the observed decays, except for very short or thick loops, but may be implicated in the initial excitation. Higher harmonics decay much more rapidly. The external solution takes the form of a wave running nearly parallel to the tube, but with a small outward component. In addition, a number of other leaky modes are described which decay on timescales of seconds, =Ra _e/a ², where a and a _e are the loop and external Alfvén speeds respectively, and which can be identified as being almost radially propagating fast magnetoacoustic waves. These are outside the currently observable range, but are likely to be important energetically.     

Gravitational radiation and spiralling time of close binary systems (V)

Forty-six binary systems with their primary component masses between 2M and 3M have been considered for gravitational radiation study. Power output by gravitational radiation (P _B ) and spiral time ₀ for all individual systems have been evaluated. A relation has been given betweenP _B and ₀. The rate of decrease of orbital period (P) has also been given for 10 eccentric orbit systems.     

Transformations to extend the range of application of power series solutions of differential equations of motion

Let the solution of a differential equation, expanded in powers of the independent variablet, have radius of convergenceT. let , wheret=t(), be a new independent variable, and let the corresponding power series in have radius of convergenceS. Thent(S) will not in general be equal toT. Ift(S)>T, then the series in powers of may have advantages over those in powers oft. Mathematical consequences of this distinction have been appreciated since the time of Poincaré. In this note the practical applications of some transformations are investigated.     

Singular points of the polarization tensor

The problem to compute the magnetic field above the chromosphere using data of the vector = B _t/Bt that gives the projected field direction can be solved with different approximations. The field of direction vectors is, however, not the only field accessible to observations. The Stokes parameters, which are components of the radiation tensor, can be measured at each point of the image plane. The directions of the eigenvectors of the radiation tensor define two mutually orthogonal systems of integral curves in the image plane. These families of curves have singular points, which are generally of different type than those of the vector field. When the morphology of H chromospheric fibrils are used to infer the topology of the magnetic field, a similar problem is met, suggesting that singular points should also be present there.     

A new time element for a general time transformation

The paper introduces a new time element to be used with a general time transformation for satellite equations of motion. The purpose of this time element is to reduce the growth of the numerical errors with respect to the time integration. It is characteristic for the new time element , that the relation between the timet and the element does not depend on the independent variables.     

Physical Properties of Dust in the Martian Atmosphere: Analysis of Contradictions and Possible Ways of Their Resolution

Atmospheric aerosols play an important role in forming the Martian climate. However, the basic physical properties of the Martian aerosols are still poorly known; there are many contradictions in their estimates. We present an analytical overview of the published results and potentialities of various methods. We consider mineral dust. Zonally averaged data obtained from mapping IR instruments (TES and IRTM) give the optical thickness of mineral aerosols ₉ = 0.05–0.1 in the 9-m band for quite atmospheric conditions. There is a problem of comparing these estimates with those obtained in the visible spectral range. We suggest that the commonly used ratio _vis/₉ >2 depends on the interpretation and it may actually be smaller. The ratio _vis/₉ 1 is in better agreement with the IRIS data (materials like montmorillonite). If we assume that _vis/₉ = 1 and take into account the nonspherical particle shape, then the interpretation of ground-based integrated polarimetric observations ( < 0.04) can be reconciled with IR measurements from the orbit. However, for thin layers, the sensitivity of both methods to the optical thickness is poorly understood: on the one hand, polarimetry depends on the cloud cover and, on the other hand, the interpretation of IR measurements requires that the atmospheric temperature profile and the surface temperature and emissivity be precisely known. For quite atmospheric conditions, the local optical-thickness estimates obtained by the Bouguer–Lambert–Beer method and from the sky brightness measured from Viking 1 and 2 and Mars Pathfinder landers are much larger: = 0.3–0.6. Estimates of the contrasts in images from theVikingorbiters yield the same values. Thus, there is still a factor of 3 to 10 difference between different groups of optical-thickness estimates for the quiet atmosphere. This difference is probably explained by the contribution of condensation clouds and/or by local/time variations.     

Structure and physics of solar faculae

Taking into account the effect of roughness (or local departures from sphericity) of the emitting layers in the chromosphere-corona transition zone (CCT) allows one to determine the optical depths of layers responsible for resolved structures in Cii, Ciii, Oiv, and Ovi lines. The result, at the top of the irregularities, is of the order of respectively ₁ 3.5,2.0, 1.6,0.5, and for the bottom of these irregularities, ₂ = 0.7, 0.4, 0.3, 0.25. The characteristic angle of these irregularities is, respectively, of the order of 35 °, 33 °, 35 °, and 41 °. For unresolved structures of Civ and Ovi (already analyzed in the spherical symmetry hypothesis in Paper III), one finds ₁ 0.6; 0.9 and ₂ 0.12; 0.2 in the case of quiet areas; in the case of active areas, the range is broader for Civ and Ovi, from 1.0 to 1.7 for ₁ and from 0.2 to 0.9 for ₂. The values obtained from Ovi are in reasonable agreement with each other for resolved and unresolved structures. And the obtained values of ₁ and ₂ correspond not too badly with the determinations made in Paper III, by methods not exceedingly influenced by the spherical symmetry hypothesis.