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1.
A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) T and T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.  相似文献   

2.
An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R –2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R –, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.  相似文献   

3.
We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec2 at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C min the H- 1.5 Å image (C m 0.1 type I, C m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C m- A scatter diagram, in H and H wings, indicates a wide range of variability for C m in correspondence with very narrow range of variability for A.  相似文献   

4.
The time transformation dt/ds=r is studied in detail and numerically stablized differential equations are obtained for =1,2, and 3/2. The case =1 corresponds to Baumgarte's results.  相似文献   

5.
The area preserving mapping x = x + a(y – y 3), y = y – a(x – x3), for 0.3 a 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).  相似文献   

6.
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   

7.
Extinction efficiency of grains is calculated from the Mie formula on the premise that the grains are of organic composition. The optical constants adopted for the calculations are those ofE. coli, polystyrene and bovine albumin. The grain radiusa is assumed to obey a distribution of the formN(a) a – and the value of is chosen so as to make the calculated extinction curve match the observed interstellar extinction curve. Although the calculated curve gives a reasonably good fit to the observed extinction curve for wavelength less than 2100 Å, at longer wavelength region agreement is poor. It is concluded that another component is required for the organic model to be viable.  相似文献   

8.
The aim of the present paper has been two-fold. In the first part (Sections 1–2), closed algebraic formulae will be set up furnishing the momentsA of the light curves of arbitrary index , and, due to arbitrary type of eclipses, in terms of the coefficientsa of Fourier cosine series obtained by least-squares fit to the given data; and the uncertainty of the momentsA deduced from that of thea 's.In the second part (Sections 3–4) we shall establish the explicit forms of the lincar functions r 1,2, (cosi) and L 1 for the variation of the respective elements expressible likewise in terms of the Fourier coefficientsa . The probable errors of these elements can then be identified with those of the respective linear functions, and are obtainable from the same matrix of coefficients which furnished the most probable values of the elements.  相似文献   

9.
One component of a three-fluid adiabatic plasma is under certain conditions contained in a restricted region of space by a large-scale electrostatic field generated within the plasma. The containment is discussed here for plasma consisting of ions and two populations of electrons characterized by different pitch angle distribution functions.The bouncing motion of electrons along open fieldlines between a magnetic mirror and an electrostatic mirror produces a velocity distribution function similar to that generated by bouncing particles on closed fieldlines.  相似文献   

10.
Using the results of numerical simulations of the solar atmospheric response to heating by nonthermal electron beams during solar flares, we have calculated the spatial and temporal evolution of both (i) the direct (beam-target) nonthermal bremsstrahlung and (ii) the thermal bremsstrahlung arising from the hot plasma energized by the electron beam. Typically, we find that below a certain cross-over energy E *, the emission is dominated by the thermal component, while at higher energies the direct bremsstrahlung component becomes more important. This cross-over energy is dependent on the position within the loop, generally increasing with height.We have also investigated the dependence of the cross-over energy E * on the parameters of the electron energy input. At the time of peak electron flux injection the cross-over energy E * can, for plausible parameters, be as high as 52 keV at the top 1 pixel, and as low as 16 keV at the bottom 1 pixel. We conclude that a possible reassessment of SMM HXIS data as an indicator of the thermal or nonthermal character of the primary energy release (based primarily on the geometric properties of the hard X-ray source) is required. Our results also point to the minimum photon energy that future instruments should observe (where practical, giving due consideration to detector sensitivity) in order to be sure that, in the context of the thick-target interpretation, the nonthermal component is not swamped by the self-consistent thermal counterpart created by the beam heating.  相似文献   

11.
An approximate metric is found which represents a sphere of matter embedded in a background of dust. The use of this metric in conjunction with the Friedmann equations gives values of for the three possible values ofk as +6×10–36 (k=+1), +3×10–35 (k=0), +10–36 (k=–1). These values depend on data regarding clusters of galaxies, and are probably accurate to within an order of magnitude given the correctness of the assumptions on which their derivation rests.  相似文献   

12.
Vibrational transition probabilities, namely Franck—Condon factors and -centroids have been evaluated by an approximate analytical method for the (A–X), (A–X), and (A–X) system of YO molecule. Morse potential energy curves forX 2+,A 22,A22, andA22, states of YO have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to decrease linearly with the corresponding wavelengths. We show results for two new transitions of (A–X) and (A–X) and five new bands of (A–X) of YO in the umbral spectrum of the Sun.  相似文献   

13.
We derive upper limits to the radiation temperaturesT t(k) for emission near the fundamental and second harmonic of the electron plasma frequency in terms of the effective temperature for plasma wavesT l(k). We findT t(k)(c/(3)1/2 V e)3 T l(k) for emission near the fundamental which differs from the result of Melrose (1970b) by the factor in parentheses. This factor can exceed 4×104 in some plasmas. The conditions under which this limit could be reached are delinated. For emission near the second harmonicT t(k)T l(k) since the absorption coefficient in this case can only be positive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

14.
According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q : above mentioned series converge for all bodies if q < q . Using Liapunov's algorithm and symbolic calculus tools we have calculated q = 0.000370916. Evidently, convergence radius q 0 may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q 0 for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q 0 = 0.337 for Maclaurin ellipsoids.  相似文献   

15.
The diagramV - log(1 +z e ) as function of (, ) is considered for the quasars. HereV is the apparent visual magnitude,z e is the emission line redshift, and are the equatorial coordinates. Two opposite extreme spots NE and SE are observed on the sky, where the inclination of the straight line fitting the dependenceV - log(1 +z e ) is maximum and minimum. The coordinates of the centres of these extreme spots are ( NE, NE) = (282°, +42°) and ( SE, SE) = (70°, -38°) with errors 5°. A hypothesis of the Superattractor (SA) is proposed to explain such an effect. Two independent tests of this hypothesis are realized. First, the dependence or the frequency a of the absorbers in QSO spectra on (, ) is investigated. A region of the larger a is found. The coordinates of its centre are (, ) = (82°, - 10°) with error 5°. Second, the cases ofz a >z e are plotted in the Mercatorial projection (, ). The most of the casesz -z e > 0.02 are concentrated within the circle with radiusR = 34° and centre (, ) = (50°, - 15°). The both anomalous regions overlap the Southern extreme spot around SE. The SA direction is (, ) = (67°, -21°) with errors about 12°. The redshift of SA isz SA = 1.7 ± 0.3 that corresponds to the distancer SA = (3100 ± 300)h –1 Mpc for the Hubble constantH 0 = 75h kms–1 Mpc–1. The SA mass isM SA ~ 1018-1020 M . The orientation of the normal to the quasiperiodical large-scale sheet structure on the sky occurs near SA.  相似文献   

16.
We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval i << f , f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > f .  相似文献   

17.
This investigation indicates an ambiguity in interpreting the results of applying the apparatus of the correlation gamma function [(r) and *(r)] to analyze the spatial distribution of objects from some sample. The presence of a linear section in the dependences of log() on log(r) and of log(*) on log(r) proves to be insufficient to state that the distribution has fractal properties (self-similarity). It is shown that a change in the geometrical boundaries of the sample may influence the form of the dependences of log() on log(r) and of log(*) on log(r).  相似文献   

18.
The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C jk n (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin2t - i inclination of the orbit - J n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S jk n (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M++m) (gravitational constant times the sum of the masses of Earth and satellite) - n,k coefficients ofR component of disturbing acceleration (funtions off) - n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X 0 n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node  相似文献   

19.
, . N/E, E r, (E r)=1. , (, ) . .  相似文献   

20.
A study is made of Lyman continuum observations of solar flares, using data obtained by the Harvard College Observatory EUV spectroheliometer on the Apollo Telescope Mount. We find that there are two main types of flare regions: an overall mean flare coincident with the H flare region, and transient Lyman continuum kernels which can be identified with the H and X-ray kernels observed by other authors. It is found that the ground level hydrogen population in flares is closer to LTE than in the quiet Sun and active regions, and that the level of Lyman continuum formation is lowered in the atmosphere from a mass column density m 5/sx 10–6 g cm–2 in the quiet Sun to m 3/sx 10–4 g cm–2 in the mean flare, and to m 10–3g cm–2 in kernels. From these results we derive the amount of chromospheric material evaporated into the high temperature region, which is found to be - 1015g, in agreement with observations of X-ray emission measures. A comparison is made between kernel observations and the theoretical predictions made by model heating calculations, available in the literature; significant discrepancies are found between observation and current particle-heating models.  相似文献   

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