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1.
Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin p cos q which peaks near the equator (q p) will correspond to a cos n magnetic field at high latitudes only if p = 1 and m = n /R. Recent measurements of n 8 and 600 km2 s–1 would then give m 7 m s–1.  相似文献   

2.
Durney  Bernard R. 《Solar physics》2001,202(2):201-228
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3.
We semi-quantitatively calculate the distribution of energy in frequency and angle emitted from a sheet of charges that are moving out relativistically along dipolar magnetic field lines originating near the magnetic polar caps of a rotating neutron star. The angular distribution is conical with the angle of maximum intensity varying with frequency as –1/4 for c 2 c /(R M 2), whereRM is the initial angular radius of the charge sheet at the surface of the star of radiusR. At higher frequencies the width of the angular cone remains constant. The radiation is linearly polarized with the polarization vector in the plane of the line of sight and the magnetic axis. A sheet of uniform charge density and finite thickness has a frequency spectrum that varies from –3/2 to –4 for c and c , respectively. These features are in good general agreement with the observed characteristics of the intensity, pulse shape, and frequency spectrum of the radio pulses from pulsars.Operated by Associated Universities, Inc., under contract with the National Science Foundation.  相似文献   

4.
An expression is derived for the fluctuation (t) in emergent intensity (observed at some wavelength in a Fraunhofer line or the continuum) caused by a perturbation in temperature (z, t) in the Sun's atmosphere. If the contribution function for the observed intensity is single-peaked near z and if (z) and p(z) are not too rapidly varying, then (t) m (z , t)+N p(z , t) where m and N depend on the structure of the atmosphere. We compute M, N, and contribution functions for several values of and in the inner wings of the K line (13933 Caii).Presently on leave of absence from the Institute for Astronomy, Honolulu, Hawaii.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

5.
Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is =(p+q) jup –p–q, exact corotations are double resonant motions defined by the conditionsd/dt=0 andd(– jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev 5-resonance. This paper presents the symmetric solutions =0 (mod ), = jup (mod ). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as and are close to the equilibrium values.  相似文献   

6.
Thermal and electrical conductivities due to electron scattering on phonons are calculated for degenerate cores of white dwarfs and envelopes of neutron stars for wide ranges of density, temperature and ion charge. In the stellar zones, in which T pi(Z1/3e2/F) (piis the ion plasma frequency and F the Fermi velocity of electrons), the main contribution into scattering comes from the Umklapp processes. In the zones with lowerT, the Umklapp processes are frozen out, that results in a sharp growth of electrical and thermal conductivities. This, for instance, should make nuclear burning more stable in such zones.  相似文献   

7.
A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( i+1/ i [r i /r i+1] is approximately equal to the exponentN in a continuous density law (=aR –N) provided (r i /r i+1)3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c 2 R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s–1 Mpc–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c 2 R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R N ,N2); (j) for the Galaxy, theory predictsp G7×10–12 dyn cm–2, observation givesp G5×10–12 dyn cm–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 1012 g s–1, compared to 1011 g s–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×109 years for the Sun and 1010 years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN B of baryons; (o)N B1057N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L max1059 erg s–1); (r) larger bodies have longer time-scales of energy radiation atL max (10–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR –N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.  相似文献   

8.
In this paper of the series, elliptic expansions in terms of the sectorial variables j (i) introduced by the author in Paper IV (Sharaf, 1982) to regularize the highly oscillating perturbation force of some orbital systems will be established analytically and computationally for the ninth, tenth, eleventh, and twelfth categories according to our adopted scheme of presentation drawn up in Paper V (Sharaf, 1983). For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computation, and numerical results are included to provide test examples for constructing computational algorithms. Finally, the first collection of completed elliptic expansions in terms of j (i) so explored will be given in Appendix A for the guidance of the reader.  相似文献   

9.
As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U r(r,)=P 2(cos)2(r)/r 2+P 4(cos)4(r)/r 2 +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P 2(cos), P 4(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting 4(r)=–H2(r) with H–1.6, a constant. The value of 2(r) is negative, i.e., the P 2 flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.  相似文献   

10.
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   

11.
Free convection in a conducting liquid past an infinite porous vertical flat plate in a rotating frame of reference when the Hall current is present is considered. Exact solutions for the velocity and temperature fields have been derived. The effects ofM (Hartmann number),m (Hall parameter), andE (Ekman number) on the velocity field are discussed.Nomenclature C p specific heat at constant pressure - g acceleration due to gravity - E Ekman number - G Grashof number - H 0 applied magnetic field - j x ,j y ,j z components of the current densityJ - k thermal conductivity - M Hartmann number - m Hall parameter - P Prandtl number - Q heat flux per unit area - T temperature of the fluid near the plate - T w temperature of the plate - T temperature of the fluid in the free-stream - u, v, w components of the velocity fieldq - U uniform free-stream velocity - w 0 suction velocity - x, y, z Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - e cyclotron frequency - e electron collision time - u skin friction in the direction ofu - v skin friction in the direction ofv - dimensionless temperature - density of the fluid - kinematic viscosity - e magnetic permeability - electrical conductivity of the fluid - angular velocity  相似文献   

12.
The variation of radio luminosity with redshift and its effect on the analysis of the angular size-redshift ( –z) relation for a bright radio source sample (s 178 10Jy) has been investigated. By assuming a power law dependence of luminosity on redshift of the formP (1 +z), it was found that 4.4 (with correlation coefficientr 0.99) for at leastz 0.3. Correction for such a strongP – (1 +z) correlation when considering the –z data for the sample led to a steeper –z slope. This could be explained by assuming linear size evolution of the formD (1 +z)–n withn = 2.8 – 3.3 consistent with both theoretical results and those obtained for more homogeneous source samples.  相似文献   

13.
General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities 0, where 0 = 2.8×1014 g cm–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of –-hyperons at > c , where c 40. The electric resistivities along and acrossB, and , and the Hall resistivity H are calculated and fitted by simple analytical formulae at c and > c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If c , one has = [1 + (B/B 0)2] for the normal neutrons, and for the superfluid neutrons, while H = B/B e for both cases. HereB e 109 T 8 2 G,B 01011 T 8 2 G, andT 8 is temperature in units of 108 K. Accordingly for the normal neutrons atBB 0, the transverse resistivity suffers an enhancement, 1/4 1. When 50 andB varies from 0 toBB p 1013 T 8 2 G, increases by a factor of about 103–104 and H changes sign. WhenBB p , remains constant for the superfluid neutrons, and H B 2 for the normal neutrons, while H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.  相似文献   

14.
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   

15.
Techniques for generating large-order Y l m (, ) are discussed.  相似文献   

16.
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   

17.
A local geometric construction is proposed on thepartially ordered set of instantsI. A totally ordered subsetC(I)I is assumed to have 3-dimensional affine coordinate structure,without a specified metric, called the -space ofC(I). Guided by a strong analogy with analytical mechanics theT-configuration space (, ), a real parameter, is constructed where-upon the usual Hamilton-Jacobi theory establishes a simple geometrical construction, viz., the complete figure from the calculus of variations. The duration function, dur:C(I)R is associated withtemporally equidistant hypersurfaces through which pass a congruence of extremal curves to the fundamental integral.  相似文献   

18.
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   

19.
This paper discusses the methods used to analyse and interpret X-ray filtergrams obtained by solar soft X-ray telescopes such as the S-056 Skylab instrument. First, an appropriate definition of the line-of-sight emission measure L(T) is developed, and it is shown how the X-ray data may be analysed to obtain an approximation to L(T). The accuracy of this approximation is severely limited by the mathematical ill-conditioning of the problem, and additional constraints on the solutions must be imposed through the use of a specific model of the coronal region under study. Such a model is also required for the proper interpretation of the results in terms of coronal plasma processes. Examples of such models are provided and the forms of L(T) derived from them compared with other, semi-empirical forms.The filter ratio method (a simplified form of analysis in which the region under study is assumed isothermal) is discussed. It is shown that in the presence of line-of-sight temperature gradients, the values of effective temperature and emission measure yielded by this method cannot be directly related to the physical state of the plasma and so are of little utility in the study of coronal processes.Now at: Institute for Plasma Research, Stanford University, Via Crespi, Stanford, Calif. 94305, U.S.A.  相似文献   

20.
In this paper we consider almost integrable systems for which we show that there is a direct connection between symplectic methods and conventional numerical integration schemes. This enables us to construct several symplectic schemes of varying order. We further show that the symplectic correctors, which formally remove all errors of first order in the perturbation, are directly related to the Euler—McLaurin summation formula. Thus we can construct correctors for these higher order symplectic schemes. Using this formalism we derive the Wisdom—Holman midpoint scheme with corrector and correctors for higher order schemes. We then show that for the same amount of computation we can devise a scheme which is of order O(h 6)+(2 h 2), where is the order of perturbation and h the stepsize. Inclusion of a modified potential further reduces the error to O(h 6)+(2 h 4).This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

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