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1.
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.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
The results of daily monitoring of the Ca K flux variations of integrated sunlight during the period 1 July 1979–18 February 1980 are presented, and the data analyzed by both power spectrum and autocorrelation methods. The latter method is found to be superior; in it the autocorrelation function is fit to a model having three parameters, viz. the maximum long-term autocorrelation c 1, the rotational period 0 and an effective lifetime 1. Values of c 1 = 0.26, 0 = 25.9 days, and 1 = 500 days are obtained for the Ca K flux ratio; somewhat different values of c 1 = 0.77, 0 = 28.0 days, and 1 = 89 days are obtained for the sunspot number for the same period. Rotational modulation is clearly evident for the relatively weak chromosphere of the Sun and should be even more easily observed for more active stars.  相似文献   

6.
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.  相似文献   

7.
Litvinenko  Yuri E. 《Solar physics》1998,180(1-2):393-396
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.  相似文献   

8.
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.  相似文献   

9.
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.  相似文献   

10.
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.  相似文献   

11.
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:  相似文献   

12.
Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn 0=108 cm–3 andT 0=104 K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×1033 erg s–1, which primarily arises from the optical surface (1) ofT104 K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10.  相似文献   

13.
A re-analysis of the diffuse far UV radiation ( 1350–1480 Å) observed in the sky region ofl II180° and 0°b II40° is presented, as a revised version of a paper by Hayakawaet al. (1969). In comparison with the previous one, the value of the half optical depth of the Galazxy in our wavelength region is reduced, and the values of the albedo coefficient and the forward phase functiong are not well determined. If, however, we combine our results with the theoretical model of interstellar grains by Gilra, the value of is given by 0.13(5)0.18(5).  相似文献   

14.
Twenty-seven typical binary systems have been investigated to study their power-output by gravitational radiation (P B ) and spiralling time (0) relation. It was found that these binary systems form two distinct groups. New relations have been given betweenP B and 0 for each group.  相似文献   

15.
In the previously published Parts I and II of the paper, the author has constructed a formal long-periodic solution for the case of 11 resonance in the restricted problem of three bodies to 0(m 3/2), wherem is the small mass parameter of the system. The time-dependencet(, ,m), where is the mean synodic longitude and is related to the Jacobi constant, has been expressed by ahyperelliptic integral. It is shown here that with the approximationm=0 in the integrand, the functiont(, , 0) can be expanded in a series involving standardelliptic functions. Then the problem of inversion can be formally solved, yielding the function (t, , 0).Similarly, the normalized period (,m) of the motion can be approximated by theHagihara hyperelliptic integral (, 0), corresponding tom=0. This integral is also expanded into elliptic functions. Asymptotic forms for (, 0) are derived for 0 and for 1, corresponding to the extreme members of thetadpole branch of the family of orbits.  相似文献   

16.
Three different asymptotic branches of the two-fluid equations are found with e m , p n , where, is the inverse distance from the Sun, with (m, n) = (2/7, 2/7), (2/7, 6/7), (4/3, 4/3); other special solutions are also found but they correspond to special choices of density and temperature at the corona. In all the (4/3, 4/3) solutions, the electron and proton temperatures tend to equality at large distances.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

17.
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.  相似文献   

18.
The Hall effect on the unsteady hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrical-conducting liquid through a porous medium past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean skin friction, and mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Ekman numberE, and permeability parameterK * on the flow field are discussed with the help of graphs and tables.Nomenclature C p specific heat at constant pressure - C the species concentration inside the boundary layer - C w the species concentration at porous plate - C the species concentration of the fluid at infinite - C dimensionless species concentration - D chemical molecular diffusivity - E Ekman number - Ec Eckert number - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - H 0 applied magnetic field - (J x, Jy, Jz) components of current density - M magnetic parameter - m Hall parameter - P Prandtl number - q m mean rate of heat transfer - Sc Schmidt number - t time - t dimensionless time - T temperature of fluid - T w temperature of the plate - T temperature of fluid at infinite - T dimensionless temperature - (u, v, w) components of the velocityq - w 0 suction velocity - (x, y, z) Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - * coefficient of thermal expansion with concentration - frequency - dimensionless frequency - k thermal conductivity - K * permeability parameter - dinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - e magnetic permeability - angular velocity - electrical conductivity of the fluid - m mean skin friction - mn mean skin friction in the direction ofx - mv mean skin friction in the direction ofy  相似文献   

19.
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.  相似文献   

20.
McKenzie  D. E.  Mullan  D. J. 《Solar physics》1997,176(1):127-145
We have applied time-series analysis to sequences of coronal loop images obtained with the Yohkoh soft X-ray telescope (SXT). Using images obtained in fast-cadence mode ( t = 4 s), we have generated X-ray light curves and power spectra for multiple subregions of a number of coronal loops. Our analysis indicates that out of 544 spectra of loops which range in length L from 40 Mm to 150 Mm, there are 16 cases where the X-ray brightness is modulated periodically with 99.5% confidence. The periods range from 9.6 s to 61.6 s, and the amplitudes range from 0.4% to 1.8%. Our result is statistically significant at the 8 level.The observed periods can hardly be due to fluctuations in gas pressure: temperatures estimated from image ratios indicate sound speeds of 200–280 km s-1, with loop crossing times of hundreds of seconds. On the other hand, the ratio 2 L/ yields velocities of 2–14 Mm s-1: these overlap with published estimates of Alfvén speeds v A in coronal loops, 3.5–37 Mm s-1 (Schmelz et al., 1994). Now, in the context of coronal loop heating by resonant absorption of MHD waves, the period g 2L/v A plays a key role: loops which are oscillating in their global mode (with period g) are maximally efficient at absorbing energy (Steinolfson and Davila, 1993). We suggest that the loops which we have found to be modulated periodically are oscillating in their global mode. With this interpretation, we find that the plasma beta in the loops lies in the range p = 0.001–0.045. According to the oscillating loop model of Zaitsev and Stepanov (1989), loops with such p values should be modulated with amplitudes of 1.1% or less: our data are consistent with at least the upper limit of this prediction.  相似文献   

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