首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 25 毫秒
1.
We solved the equation of radiative transfer in spherically-symmetric shells with arbitrary internal sources. We integrated the equation of transfer on the discrete grid of angle and radius given by [j–1, j] [ri–1, ri]. The size in the angle coordinates is determined by the roots of a quadrature formula where as the size in the radial coordinate is determined by the non-negativity of the reflection and transmission operators. We considered two cases of variation of the Planck function. (1) Constant throughout the medium and (2) varying as 1/r 2. We find that in the inner shells, the radiation directed toward the centre of the sphere is more than that directed away from the centre of the sphere. In the outer shells the converse is true.  相似文献   

2.
We have calculated the changes that would occur in mean intensity due to the presence of aberration and advection terms in radiative transfer equation. We have considered an absorbing medium with velocities 1000, 2000, 3000, 4000, and 5000 km s–1 (-0.0033, 0.017, where =V/C,V is the velocity of the medium andC is the velocity of the light). Calculations have been done in a comoving frame with monochromatic radiation field. We have calculated the deviation in mean intensity defined as 0)]/J(V = 0)]$$ " align="middle" border="0"> , whereJ is the mean intensity. We have taken two types of absorbing media (1) with a source of constant emission and (2) with emission source. As the emission decreases as 1/n 2 wheren is the number of layer, wheren=1 corresponds to max and n=N corresponds to =0We find that for a total optical depth of one, the maximum change is about 2% whenB(r)=1 and about 6%, whenB(r)1/n 2 whereB(r) is the Planck function. When the optical depth increases to 5 the maximum change in the case of the constant source function falls to 1.5%, where as in the other case in which the Planck function changes as 1/r 2 the maximum changes remains at 6%. Further increase of the optical depth will reduce the changes to less than 2%. The amplification factor in the case of the Planck function varying as 1/r 2 is more than when the emission sources are constant.  相似文献   

3.
The possibility that the cosmological term is proportional toGU, whereG is the gravitational coupling andU is the mass density of the universe is proposed and discussed. WithG = constant, a cosmological model is obtained, which avoids the flatness and horizon problems and does not affect the well known predictions on the cosmic helium abundance which come from standard big bang cosmology. In such model, the deceleration parameter is a null constant, there is matter creation process throughout the universe at the rate 10–47 g cm–3 s–1 and the cosmological term varies asH 2 =t –2, whereH is the Hubble constant andt is the cosmic time.The possibility of a time-dependentG is then considered. The main consequence of this is that there is a mass creation process on the local scale; the rate of mass creation inside a body of massM is dM/dt =M H. In Section 6 it is suggested that the new matter might be in the form of neutrinos. This suggestion leads to an interesting consequence in celestial mechanics: the radius of a binary system should depend on time according to the nature of the components (the radius of a binary star should decrease, the radius of a planet-moon system should expand, and the orbital radius of a planet should stay constant).  相似文献   

4.
To calculate structural parameters of stellar systems such as an effective radius and central space (or surface) density, the method of characteristic functions is suggested. The characteristic function of the system is a Fourier image of their normalized space density profile f3(r). In the case of spherical symmetry the probability distribution of r (Q3(r) = (3/a3)r2f3(r)) and its orthogonal projections have the same characteristic functions. This fact is used to calculate the effective radii of a few star cluster models (King law, Plummer model and Gausian profile). It is shown, that the characteristic function for King law clusters tends to a finite generalised function if the concentration parameter c is large. The expression for the effective radius (at c ≫ 1) is given. The formula of the effective radius in the Plummer model as well as the relation between the one-dimensional central velocity dispersion and the root mean square velocity are obtained. It is shown, that in the Gaussian model and for King law clusters the effective radius (half-mass visual radius) can differ from the effective (harmonic) radius a few times. This fact should be taken into account in estimating the mass-to-light ratio from the virial mass of such systems using the King radius.  相似文献   

5.
We present arguments to show that torsion-coupling constant (which depends on energy asE –2) can pass through the values of the coupling constants of the other interactions during the evolution of the Universe. An energy-dependent torsion-coupling constant helps in a natural way to understand the ratios of the coupling strengths of the different fundamental interactions.  相似文献   

6.
We have treated formation of spectral lines in a commoving frame where photoionization is predominant over collisional processes. We have assumed that the radiation field for causing photoionization is a function of Planck function. We have also considered the situation in which the continuum contributes to the radiation in the line. In all the models the quantityB/A (ratio of outer to inner radii) is kept equal to 10 and the total optical depth is taken to be 103. The velocity is assumed to be varying according to the lawdV/dτ ∼ < 1/τ whereτ is the optical depth (τ > 0) in the given shell. The velocities at the innermost radius (r =A) are set equal to 0 and at the outermost radius (r =B), the maximum velocities are taken to be 0, 1, 3 and 10 Doppler units. The calculated line profiles are those seen by an observer at infinity.P Cygni-type profiles are observed in the case of a medium with no continuum absorption. For a medium with continuum absorption double peaked asymmetric profiles are noticed when the velocities are small; the two emission peaks merge into a single asymmetric peak for larger velocities.  相似文献   

7.
The partial frequency redistribution function for zero natural line width with dipole scattering (RI) has been considered in obtaining the simultaneous solution of the statistical equilibrium and line transfer equations in the comoving frame of the expanding gas. We have considered a non-LTE two level atom in an expanding spherical medium whose outer radii are 3, 10 and 20 times the stellar radius with a total optical depthT ≃ 2 × 103. In all the cases, we have calculated the population ratio of the two levels N2/N1 and compared these results with those obtained by using different expansion velocities and geometrical extensions. Initially, the upper level population (N2) is set equal to zero. The converged simultaneous solution shows that the upper level population is enhanced considerably from the initial value. Variation in velocity gradients seem to have little effect on the ratio N2/N1 when the geometrical thickness of the medium is 3 or 10 times the stellar radius. However, when the thickness is increased to 20 times the central radius, the velocity gradients change the ratio N2/N1 considerably in the region where log T ≤ 2. The effect of variation of geometrical thickness is to reduce the N2/N1 ratio atτ = 0.  相似文献   

8.
In Sections 1–6, we determine an approximate analytical model for the density and temperature distribution in the protoplanetary could. The rotation of the planets is discussed in Section 7 and we conclude that it cannot be determined from simple energy conservation laws.The velocity of the gas of the protoplanetary cloud is found to be smaller by about 5×103 cm s–1 in comparison to the Keplerian circular velocity. If the radius of the planetesimals is smaller than a certain limitr 1, they move together with the gas. Their vertical and horizontal motion for this case is studied in Sections 8 and 9.As the planetesimals grow by accretion their radius becomes larger thanr 1 and they move in Keplerian orbits. As long as their radius is betweenr 1 and a certain limitr 2 their gravitational interaction is negligible. In Section 10, we study the accretion for this case.In Section 11, we determine the change of the relative velocities due to close gravitational encounters. The principal equations governing the late stages of accretion are deduced in Section 12, In Section 13 there are obtained approximate analytical solutions.The effect of gas drag and of collisions is studied in Sections 14 and 15, respectively. Numerical results and conclusions concerning the last and principal stage of accretion are drawn in Section 16.  相似文献   

9.
Kuhn  J. R.  O'Hanlon  Michael 《Solar physics》1983,87(2):207-219
Medium resolution CCD-spectrograph observations have been obtained that are suitable for studying long spatial wavelength 5-min oscillations. We find evidence that at wavelengths of order one solar radius the oscillation field is not isotropic. It is also not well described by modes of uniform excitation. The velocity power density per spherical harmonic increases with decreasing l to 1.1 × 103 cm2 s–2 per 3.5 × 10–4 Hz angular frequency bandwidth at l = 4. These results are inconsistent with the data of Fossat and Ricort (1975) as analyzed by Christensen-Dalsgaard and Gough (1982), who found a substantially constant modal amplitude at intermediate l values. It is interesting that other calculations have seen a similar dependence at small l in the growth rate of p-modes due to the -mechanism.Visiting Astronomer, Sacramento Peak Observatory.  相似文献   

10.
The effects of partial redistribution of frequency on the formation of spectral lines in a static and spherically symmetric media have been investigated. The partial redistribution functionsR I andR II (Hummer, 1962) have been employed to calculate the lines for a two-level atom in non-LTE in a spherically symmetric medium with homogenous physical characteristics whose ratiosB/A (of outer to inner radii) are equal to 2 and 10. These results are compared with those formed in a plane-parallel medium withB/A=1. Two types of atmosphere are treated: (1) a pure scattering medium with =0 and =0, and (2) an atmosphere with a constant source of emission =10–4 and =0, where is the probability per scatter that a photon will be destroyed by collisional de-excitation and is the ratioK c/K l of opacity due to continuous absorption per unit interval of frequency to that in the line. Lines formed in complete redistribution also have been calculated for the sake of comparison, and the total optical depth in all cases has been taken to be 103 at the line centre.Vast differences have been found between the lines formed by complete and partial redistribution functions (which, for the sake of simplicity, we shall hereafter refer to as CRD and PRD, respectively). In the case of a purely scattering medium, a small amount of emission is observed in the wings for all cases of scattering functions in the spherical medium as a result of the combined effects of curvature and physical scattering. In the scattering medium, more photons are scattered into the cores of the lines by PRD than in the case of CRD. The lines formed in the medium with internal sources show emission in all cases with small absorption in the cores, except those lines formed by the angle-dependent PRD functions which again depend on the geometrical extension of the medium.  相似文献   

11.
Spectral lines formed in a rotating and expanding atmosphere have been computed in the frame of the observer at infinity. Two kinds of velocity laws are employed: (i) a uniform radial velocity of the gas and (ii) velocity increasing with radius (i.e. velocity gradients). The atmosphere has been assumed to be rotating with constant velocity. We have considered maximum radial and rotational velocities to be 10 and 3 mean thermal units respectively in an atmosphere whose geometrical thickness is 10 times the stellar radius. The total radial optical depth at line centre is taken to be about 100. In all cases, Doppler profile and a source function which is varying as 1/r 2 have been used. Generally, the lines are broadened when rotation is introduced. However, when radial motion is also present, broadening becomes asymmetric and the red emission and blue absorption are enhanced.  相似文献   

12.
Dust grains of radiir g 3×10–6 cm, injected into the intercloud medium at speeds in the range 107–108 cm s–1, may be stochastically accelerated to speeds 0.1c due to scattering by irregularities in the galactic magnetic field.  相似文献   

13.
This work is divided into 13 sections and 2 appendices, and aims to elucidate the accretion mechanism, which operates via image-theory forces, whenever two interstellar dust grains come close together. Section 1 is an introduction. Section 2 proposes that the distribution of interstellar grains be taken asn(r) r –4 to avoid distortion of the 3K microwave background by radiation from spinning grains. Section 3 examines each of three types of image force accretion processes, finding them to be dominant compared to radiation or gravitational forces by at least a factor of 1019. Section 4 states that only grains made of conducting material (e.g., graphite, ice, iron) are involved in image theory. Section 5 presents reasons for believing that two grains should coalesce on impact. Section 6 examines the motion of charged interstellar grains in Hi and Hii regions. Section 7 demonstrates, by way of four examples involving dust grains ofr=10–7 cm up tor=10–4 cm, that the image effects on conducting grains are not trivial, and that the dynamics involved is not to be compared at all with elementary Coulomb interaction of two changes. Section 8 concludes that accretion with not take place in Hi clouds if thermal (equipartition) velocities prevail among the dust particles. section 9 examines grain interactions in Hii regions: here, following an argument due to Spitzer, consideration is given to the case of a population of dust grains all streaming in the direction of the local magnetic field B at velocities of order 0.1 km s–1. It is shown that accretion takes place effectively, leading to the formation of interstellar grit, meaning grains of mass 10–8 to 10–7 gm, radius 0.1 mm; and leaving also a population ofr10–6 cm grains, which are observed in polarization and extinction measurements. The existence of the latter is now a deduction and not an ad hoc postulate, as previously, and implies a distribution of the general formn(r) r mean –3 , in approximate agreement with that of Section 2. Section 10 considers the accretion mechanism as a cascade process. Section 11 shows that the existence of grains in space ofr 10–6 cm rules out an origin in supernova or galactic explosions, and supports a passive origin, perhaps in red giants or Mira variables. Section 12 discusses the implications of the results found for polarization observations and cosmogony, the latter being given a new foundation in which planets of different composition form automatically from a solar nebula. Section 13 is a conclusion.  相似文献   

14.
The rate equations of a restricted set of gas-phase chemical reactions occuring in an expanding circumstellar envelope are integrated numerically on the assumption that no chemical evolution has occurred in the stellar atmosphere. Abundances of all species are found to peak at a time on the order ofr 0/u 0, wherer 0 is the initial radius andu 0 the expansion velocity. After this time geometrical dilution dominates. For an initial density of 108 cm–3, on the order of 1% of hydrogen is converted to H2, and CH and CO have comparable densities of 10–6 relative to H, OH and O2 remain very low in abundance. For higher initial densities, H and H2 are more nearly comparable, and nearly all carbon is in CO, CH, OH and O2 remain low in abundance. The relevance of these results to M giants and other objects is discussed.  相似文献   

15.
A two-stage model of the propagation of 1–50 MeV solar-flare cosmic rays is presented. The first stage consists of a thin spherical shell of radius r a near the Sun which feeds particles into interplanetary space (the second stage) where they propagate along the Archimedean mean interplanetary magnetic field under the influences of anisotropic diffusion, convection, and energy changes. To calculate the time dependence at a fixed point in space, account is taken of the corotation of flux tubes past the observer.It is shown that the well-known east-west effect of the time-to-maximum cannot be obtained if the injection from the first stage is impulsive and thus a time and longitude dependent release for the second stage is essential. This is achieved by treating the first stage as a thin, spherical, diffusing shell of radius r a with diffusion coefficient s, from which particles leak into interplanetary space at a rate determined by the leakage coefficient .With this model we are able to reproduce simultaneously four principal features of solar events observed at r = 1 AU: (i) the east-west effect, i.e. the time-to-maximum as a function of flare longitude; (ii) the three phases of the anisotropy vector variation; (iii) the time-to-convective-phase as a function of flare longitude; and (iv) the longitudinal distribution of the differential intensity. Our best estimates of the parameters of the near-Sun propagation are that 0.01 hr–1 s/r a 2 0.02 hr–1 and 1/15 hr–1 1/10 hr–1. For the interplanetary propagation we estimate /V - 1.2AU with , the effective cosmic-ray diffusion coefficient and V, the solar-wind speed.  相似文献   

16.
Some analytical relations for the phase space functions of a self-consistent spherical stellar system are derived. The integral constraints on the distribution function by imposing a given (r) density distribution andN(E) fractional energy distribution are determined. For the case of radially-anisotropic velocity distribution in theE0 limit the constraint by an exponentialN(E) implies thatf(E, J 2) tends to zero in the order (–E)3/2. This lends analytical support to the use of the Stiavelli and Bertin (1985) distribution function for modeling elliptical galaxies. Maximum phase space density constraint confirms the necessity of high collapse factors to produce such a distribution function. Limits on the steepness of an exponentialN(E) for the case when (r) resembles the emissivity law of ellipticals are also derived.  相似文献   

17.
We present the results of solving the radiative transfer equation for the Stokes vector in the case of light scattering by spherical forsterite dust particles in an axisymmetric circumstellar envelope of a red giant. We have assumed that the surfaces of constant scattering-particle density are prolate or oblate spheroids, the particle density decreases with radius as N d ∝ r −2, and the dust particles at the inner boundary of the envelope are in thermal equilibrium with the stellar emission at solid-phase evaporation temperature T ev = 800 K. In the wavelength range 0.27 μm ≤ λ ≤ 1 μm, particles with radii 0.03 μm ≲ a ≲ 0.2 μm make a major contribution to the linear polarization of the stellar emission. The increase in scattering efficiency factor with decreasing wavelength λ is mainly responsible for the growth of polarization toward the short wavelengths known from observations. However, at a mean number of scatterings 1.2 ≤ N sca ≤ 1.6, the polarization ceases to grow due to depolarization effects and decreases rapidly as the wavelength decreases further. The wavelength of the polarization maximum is determined mainly by two quantities: the particle radius and the mass loss rate. The upper limits for the degree of linear polarization in the case of light scattering in circumstellar dust envelopes with the geometries of prolate and oblate spheroids are p ≈ 3 and 5%, respectively. The polarization for light scattering by enstatite particles is higher than that for light scattering by forsterite particles approximately by 0.3%. Original Russian Text ? Yu.A. Fadeyev, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 2, pp. 123–133.  相似文献   

18.
We have analyzed luminosity profiles of E galaxies studied by Strom and Strom in six clusters of galaxies. We have found a relationship between radius, luminosity, and surface brightness for galaxies in each of the clusters. A dependence of the zero point of the relation with the local projected density of galaxies is likewise found:r e proj –0.14 L 0.445 I e –0.413 . This relationship implies (i) that there is not a universal luminosity profile for elliptical galaxies, (ii) the environmental variation of radius is larger than that produced by mergers of galaxies, (iii) distance to a galaxy can be estimated from apparent magnitude, surface brightness, angular size, and apparent local projected density of galaxies.  相似文献   

19.
Colliding comets in the Solar System may be an important source of gamma ray bursts. The spherical gamma ray comet cloud required by the results of the Venera Satellites (Mazets and Golenetskii, 1987) and the BATSE detector on the Compton Satellite (Meeganet al., 1992a, b) is neither the Oort Cloud nor the Kuiper Belt. To satisfy observations ofN(>P max) vsP max for the maximum gamma ray fluxes,P max > 10–5 erg cm–2 s–1 (about 30 bursts yr–1), the comet density,n, should increase asn a 1 from about 40 to 100 AU wherea is the comet heliocentric distance. The turnover above 100 AU requiresn a –1/2 to 200 AU to fit the Venera results andn a 1/4 to 400 AU to fit the BATSE data. Then the masses of comets in the 3 regions are from: 40–100 AU, about 9 earth masses,m E; 100–200 AU about 25m E; and 100–400 AU, about 900m E. The flux of 10–5 erg cm–2 s–1 corresponds to a luminosity at 100 AU of 3 × 1026 erg s–1. Two colliding spherical comets at a distance of 100 AU, each with nucleus of radiusR of 5 km, density of 0.5 g cm–3 and Keplerian velocity 3 km s–1 have a combined kinetic energy of 3 × 1028 erg, a factor of about 100 greater than required by the burst maximum fluxes that last for one second. Betatron acceleration in the compressed magnetic fields between the colliding comets could accelerate electrons to energies sufficient to produce the observed high energy gamma rays. Many of the additional observed features of gamma ray bursts can be explained by the solar comet collision source.  相似文献   

20.
We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R , the major axis scattering angle is 0.7 at =6 cm and it varies with heliocentric distance asR –1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized to =20 cm, has a value 20±7 at 5R and varies with heliocentric distance asR –3. Comprison with earlier results suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scales sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are 1 km at 2R and 4 km at 13R . These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号