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.     

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.     

The galactic diffuse component of soft X-rays and its source function

A new model for the source distribution of galactic soft X-ray (B and C band) emission is presented. From the mean dependence of count rates on galactic latitudeb (i.e., the brightness distribution), we derive the soft X-ray source functionQ as function of the optical depth by solving the equation of radiative transfer with the aid of a Laplace transform. Contrary to older Heaviside step models,Q is found to increase strongly, but not abruptly, in the range 1.5<<2.5, indicating a noticeable emission of X-rays from beyond theHi scale height. Using standard X-ray absorption cross-sections for the interstellar medium, we find that the B band X-ray emission coefficient is non-zero within theHi disk and has a maximum at az-value slightly above the Hi scale height. In the C band, the emission coefficient slightly decreases with increasingz, at least up to theHi scale height. A non-zero source function near the galactic plane implies that the interstellar medium (ISM) within theHi scale height is not only an absorbing layer but is mixed with X-ray emitting regions. The so-called local hot bubble is adopted as one of these regions. The maximum of the B band emission coefficient, together with the sharp increase ofQ, is strong evidence for the existence of a galactic soft X-ray halo, and, moreover, give rise to the assumption of a general intergalactic X-ray background. The effective absorption cross-sections given in the literature, based on an (pure) exponential dependence in the negative correlation between count rates andHi column densities, were biased to be too small, in particular in the B band. In replacing the Heaviside step (in the ISM) by a smoothed transition region, these inconsistencies become spurious.     

WR stars with the Ovi λλ3811, 3834 emission doublet

The catalog of the classical WR stars which have the emission doublet Ovi 3811, 3834 in their optical spectra (the catalog of the WR-Ovi stars) and the results of the spectroscopic investigations of the WR-Ovi stars HD 16523, HD 17638, and HD 192103 are presented. Rapid spectral variability of the emission doublet Ovi 3811, 3834 in the spectra of WR-Ovi stars HD 16523, HD 17638, and of the emission band 3680-3780 Å in the spectra of the WR-Ovi star HD 16523 is observed. It is shown that spectral sub-types of the stars HD 16523 and HD 17638 as estimated from different criteria are uncertain. We argue that the WR-Ovi stars HD 16523 and HD 17638, the optical spectra of which display emission doublet Ovi 3811, 3834, may be considered as WO5 stars. The sub-type WO5 is proposed for the first time. Classification criteria of the WO5 sub-type are represented. The possible contribution of the ions Heii to the emission at 3811 Å and 3834 Å is investigated. Thez-distributions of WR-Ovi stars and WR stars with the probable relativistic companions are found to be similar.     

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.     

Pulsar dispersion measures and the mean and mean-squared interstellar electron density

Theoretical distributions of pulsar dispersion measures (times sinb ^II) are computed for various assumed pulsar spatial distributions above (and below) the galactic plane, assuming a distribution for the ionized gas. The statistics on the twelve high-latitude pulsars lead to the conclusion that the pulsar distribution inz is at least as broad as the distribution of the ionized gas. The value derived for the local mean interstellar electron density in the galactic plane is 0.12 cm^–3 and is interpreted to be due to a uniform ionized intercloud medium.Interstellar absorption of radio waves at low frequencies and cosmic X-rays at low energies are considered with regard to irregularities in the distribution of ionized gas. It is shown that if the obervations are made with a wide angle receiver the effective absorption optical deph is –²/2 where is the mean value and is the dispersion in . This relation assumes is much larger than . Analysis of recent low-frequency radio measurements from a satellite-borne receiver, however, leads to the conclusion that effects of irregulatirities are large.     

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.     

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.     

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.     

Distribution of polarization and intensity of radiation across the stellar disk and numberical values of atmospheric characteristics governing this distribution

Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT _eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT _eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT _eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.     

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.     

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.     

Compton scattering in sources with synchrotron reabsorption

By considering the consecutive effects of synchrotron reabsorption, Compton scattering and other kinds of energy losses of relativistic electrons, it may be possibile to form a universal distribution of electrons in the region of reabsorption (synchrotron reactor). This will be either a power law with a power index of the energy spectrumn _r=3–5, or a relativistic Maxwell distribution with an electron temperatureT _e=4T _b(1+), where is the ratio of Compton (or other losses) to synchrotron losses, andT _bis the brightness temperature of the radiation. Since the total energy losses of electrons in the reactor is equal to zero, this ensures the continuous existence and accumulation of relativistic electrons in the region of reabsorption and their associated hard scattered radiation. Multiple Compton scattering produces a specific stepped power distribution of scattered radiation by which we can identify the reactor. In the nuclei of quasars W _Hand, therefore,n _r=3; hence the spectral index of scattered radiation in the corresponding ranges (optical, UV, X- and -ray) is .Consideration of other kinds of losses and gains of energy by electrons can lead to the dependencen =3–5(E) — where (E) may have either positive or negative values—which, in turn, leads to the frequency dependence of the spectral index of scattered radiation = 1 – (), |()| < 1, |(E)| < 1.Within the framework of the model being considered, the physical parameters of the nucleus of quasar 3C 273 are calculated.     

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.     

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.     

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.     

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.     

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.     

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).