Effects of metal abundances on the evolutionary period changes of classical Cepheids

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values _i = _i + _i ,v _i = _i + v _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,² =v ² = 10^–8) grow many times in marginally-stable state.     

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.     

On the solar oblateness: The combined effect of a pole-equator difference in effective temperature and mechanical heating

With the help of a model atmosphere of the Sun we evaluate the pole-equator difference in flux (as measured by Dicke and Goldenberg) assuming the following type of pole-equator temperature difference (T=T _e –T _p ): (a) T 2K for > ₀ (₀ 0.05); (b) T 10K for < ₀.The small T at all optical depths given by (a) could, for example, be due to a pole-equator difference in effective temperatures. At small optical depths a difference in mechanical heating could give rise to the larger temperature difference given by (b). We compare the results of our calculations with Dicke and Goldenberg's observations.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Dimensional Analysis of the Flare Distribution Problem

Dimensional analysis is used to derive the distribution of solar flare energies,p() = A-^3/2, in accordance with recent observational and numerical results. Several other scalings, notably _fl ² , where _fl is the flare duration, are obtained as well.     

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.     

High order symplectic integrators for perturbed Hamiltonian systems

A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(^p + ²²), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(^p +⁴²). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.     

Микрофлуктуации электрического поля на фронте ударной волны в модельном эксперименте

, . , , . . . . . , , .     

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.     

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.     

Emission cores in H and K lines

Profiles of the H and K lines of Mgii and the K line of Ca ii are computed using a two-level atom for five model atmospheres distinguished from each other mainly by the location of the temperature minimum. In the five models the temperature minimum and the chromospheric temperature are adjusted to give best agreement between computed and observed profiles. The parameters and r ₀ are prescribed as functions of from a density model of the atmosphere. By comparing computed and observed profiles of the K₃, K₂ and inner K₁ components of the lines we determine both the approximate depth variation of _D and the best of the temperature models. We find that the Doppler width increases rapidly with height in the chromosphere beginning from a value of 1.6 km/sec at ₀ 10^–2. This latter value corresponds closely to the thermal velocity of Mg atoms in the upper photosphere. The preferred temperature model is one for which the temperature minimum occurs near ₀( 2800) 10^–4–10^–5 with a value T _min 4200 ° and which has a temperatu near 7000 ° at ₀ = 10^–6 where K₂ is formed. The intensity in K₃ is determined largely by d _D/d in the K₂ and K₃ regions.     

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.     

Particle lifetimes in strong diffusion

The mean lifetime of a particle distribution, driven to isotropy by intense pitch-angle diffusion, is calculated by analytical means for conditions applicable to the Earth's magnetosphere. The resulting algebraic expressions reduce to [64La/35v _c ² (1–)] in the limit of a small equatorial loss cone (half-angle _c ), wherev is the particle speed,L is the magnetic shell parameter,a is the radius of the Earth, and is the particle albedo from the atmosphere at either foot of the field line. Distinction is made in the full expressions for between complete isotropy (caused by strong pitch-angle diffusion all along the field line) and incomplete isotropy (caused by strong diffusion that is localized at the magnetic equator) over the upward hemisphere in velocity space.     

General integral transform of the exponential integrals

General integral transform of the exponential integralsE _n is considered and will be denoted asB _(k) ⁿ (). Different expressions and the equations satisfied byB _(k) ⁿ are developed. Two-term recurrence formula forB _(k) ⁿ (0) and three-term recurrence formula forB _(k) ⁿ (); 0 will be established for a givenk1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy     

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.     

A simplified model solar atmosphere

A simplified representation of the temperature distribution in the solar photosphere is proposed: ( ₀) = ₀ - ₁ log ₀. An expression is derived for the emergent continuous spectrum from the simple model. The limitations and applications of the simple model are discussed.     

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.     

εлектроны космических лучей радиогало галактики

,      

The Bilderberg model of the photosphere and low chromosphere

From 17 through 21 April 1967, an international study week was held in the Bilderberg near Arnhem, Netherlands, with the aim of obtaining an internationally acceptable model of the solar photosphere and low chromosphere. It was found that such a model, based on observed intensities and center-to-limb observations of the solar continuous spectrum, could indeed be established. This model, henceforth called the Bilderberg Continuum Atmosphere (BCA), is shown in Table I, which gives the temperature, gas and electron pressures, and other data as functions of the continuous optical depth at 5000 Å between 5000 = 10^–7 and 25. The model is characterized by a flat temperature minimum of 4600 °K between 5000 10^–2 to 10^–4. The model is homogeneous, and in hydrostatic equilibrium. A hydrogen-helium ratio of 10 has been assumed.Much divergence remains in the interpretation of line-profile observations with regard to the establishment of a photospheric model (Section 4). It proved to be as yet impossible to obtain reliable information on the variation with depth of the following functions: temperature fluctuations, turbulence velocities, convective velocities, and vibrational velocity amplitudes (Section 5). Provisionally, it is assumed that _macro = 2 km/sec and _micro = 1 km/sec, isotropic and independent of depth.     

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.