共查询到20条相似文献，搜索用时 593 毫秒
1.
We study the Sunyaev–Zeldovich effect for clusters of galaxies. We explore the relativistic corrections to the Kompaneets equation in terms of two different expansion approximation schemes, namely, the Fokker–Planck expansion approximation and delta function expansion approximation. We show that two expansion approximation formalisms are equivalent under the Thomson approximation, which is extremely good approximation for the CMB photon energies. This will clarify the situation for existing theoretical methods to analyse observation data. 相似文献
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3.
Harold Willis Milnes 《Celestial Mechanics and Dynamical Astronomy》1973,7(3):295-300
An exact, closed-form solution of the problem of the motion of a satellite in the equatorial plane of an oblate body is obtained. It is shown that the classic formula for the motion of the perihelion is a first order approximation to the exact formula. 相似文献
4.
Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two‐dimensions, followed by others for three dimensions, have presented formulae of the form 〈b2〉 = f(RM) . Such “Zeldovich relations” have sometimes been interpreted to provide steady‐state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function f that depends on spatial dimension and a magnetic Reynolds number RM. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. In 3D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of RM and the initially imposed , as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re‐analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady‐states of large RM MHD turbulence. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Pablo Fosalba & Enrique Gaztañaga 《Monthly notices of the Royal Astronomical Society》1998,301(2):503-523
We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, ξJ , for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S J = ξ J /ξ J −1 2 . We compare our analytic results with N -body simulations, which turn out to be in very good agreement up to scales where σ ≈ 1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime. 相似文献
6.
We have classified orbits in a stationary triaxial stellar system created from a cold dissipationless collapse of 100,000 particles. In order to integrate the orbits, two potential approximations with different fitting functions were used in turn. We found that the relative amount of chaotic versus regular orbits does depend on the chosen approximation of potential, even though both models resulted in very good fits of the underlying exact potential. On the other hand, the content of regular orbits, i.e., its distribution among main families, does not strongly depend of the potential approximation, being therefore a more robust signature of the gravitational system under study. 相似文献
7.
We investigate the multiple scattering of radiation in semi-infinite homogeneous atmosphere when the sources of the radiation are distributed inhomogeneous, for example, are created by restricted beams penetrating into the medium. The case of isotropic scattering is considered. It is shown that the density of radiation and the intensity of outgoing radiation for any forms of the sources can be represented as some integrals with the real and imaginary parts of the universal H-function, which satisfies the nonlinear integral equation. We calculated the intensity of radiation emerging from the surface after multiple scattering for the case when a beam with a finite radius incident perpendicular on the medium surface. The results allowed us to estimate quantitatively when the intensity of outgoing radiation in the center of a beam coincides with that for the classical case of unbounded flux (the case considered by Chandrasekhar et al.). We compared our exact solutions with those in the diffusion approximation. For conservative medium the difference is ?20–30%, depending on the particular forms of the radiation sources. For absorbing medium the difference is much larger. Our exact semi-analytical solution can be generalized for the cases of multiple anisotropic scattering of the polarized beams. The presented simple theory can be used at the consideration of close binary systems, flare stars etc. 相似文献
8.
The study of Einstein's field equations describing Robertson-Walker cosmological models with massive scalar field and viscous fluid representing the matter has been made. The problem has been investigated with and without the source density in the wave equation. Corresponding exact solutions of the field equations have been obtained under different physical equations of state: namely, (i) dust distribution, (ii) Zeldovich fluid distribution, (iii) disordered distribution of radiation subject to physically realistic conditions. The physical interpretations of the physically realistic solutions has been investigated. It has been found that physically realistic solutions has been obtained for closed cosmological models only. 相似文献
9.
L.C. Garcia de Andrade 《Astronomische Nachrichten》2008,329(6):583-586
A filamentary non‐holonomic dynamo solution of self‐induction magnetic field equation is found by considering highly conducting filaments. It is shown that planar filaments cannot support dynamo action since the flow along the filament vanishes for torsion‐free filaments. This is a generalization of the Zeldovich theorem for linear magnetic dynamo filaments. The flow of filament is proportionally to the product between Frenet torsion and curvature. This shows that filamentary dynamos must possess Frenet torsion. A well‐known example of this result is the α ‐dynamo in solar physics. Magnetic helicity and magnetic energy for this filamentary dynamo are computed. Magnetic helicity vanishes by construction and the magnetic field decays with torsion energy in helicoidal dynamos. The approach considered here is useful for the investigation of anisotropic turbulent cascades. As a particular simple example it is shown that under certain constraints the solution can be reduced to the Arnold cat dynamo map solution where the non‐holonomic directional mixed derivative, would play the role of the Lyapunov exponent which appears on stretching the magnetic field in Riemannian space. The solution seems to describe marginal slow dynamos when the velocities involved in the dynamo flows are constants. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution. 相似文献
11.
I. Lerche 《Astrophysics and Space Science》1971,13(1):48-52
We critically discuss the three approximations which have been employed to estimate the influence of interstellar fluctuations in both electron density and magnetic field on Faraday rotation measure and signal dispersion measure in the radio band. We demonstrate that: (i) the geometrical optics approximation employed by Ginzburg and Eruhimov (1971) relies on the unproven assertion thatall ray paths are essentially the same as the geometrical distance between source and observer; (ii) the exact solution is physically meaningless; (iii) the purported proof of Ginzburg and Eruhimov that earlier work by Lerche is in error, is itself in error and also self-contradictory; (iv) the first order smoothing theory employed earlier by Lerche gives the exact correction to the phase of the ordered field provided only that theirreducible part of a three-point correlation function is negligible.Receipt delayed by postal strike in Great Britain. 相似文献
12.
Robert L. Oldershaw 《Astrophysics and Space Science》2007,311(4):431-433
The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the
discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened in order
to accommodate this form of discrete conformal invariance, and a further generalization of relativity theory is required. 相似文献
13.
For radiative transfer in plane-parallel emitting, absorbing, and scattering media, the two-stream approximation, and its various modifications or related methods, is probably mathematically the most simple to use. Unfortunately this physical approximation produces errors that are neither analytically known nor controllable. For externally (Sun) driven problems, many error studies exist for reflectivity, transmissivity, and certain defined albedos. A two-stream accuracy study for internally (thermal) driven problems is presented in this paper by comparison with a recently developed “exact” adding/doubling method. The resulting errors in external (or boundary) radiative intensity and flux are usually larger than those for the externally driven problems and vary substantially with the radiative parameters. Error predictions for a specific problem are difficult. An unexpected result was that the exact method is computationally as fast as the two-stream approximation for nonisothermal media. Although the adding/doubling method is mathematically and conceptually more complex, it may be used as a developed code with no essential sacrifice in computing time. 相似文献
14.
M. S. Ruderman 《Solar physics》2014,289(7):2473-2485
We consider kink oscillations of thin magnetic tubes with the equilibrium density discontinuous in the axial direction. The aim is to find out what boundary conditions have to be used at a contact discontinuity where the equilibrium density jumps. At a contact discontinuity perturbations of all quantities but the density have to be continuous. However, in the thin-tube approximation, all these conditions cannot be satisfied simultaneously. It is shown that in the thin-tube approximation, there is a boundary layer with the thickness of the order of the tube radius that embraces the contact discontinuity. In this boundary layer the variation of the loop displacement and its axial derivative is negligible. In contrast, the total pressure variation in the boundary layer is very strong. Hence, the correct boundary conditions at a contact discontinuity in the thin-tube approximation are the continuity of the tube displacement and its axial derivative. 相似文献
15.
An appropriate generalization of the Jacobi equation of motion for the polar moment of inertia I is considered in order to study the N-body problem with variable masses. Two coupled ordinary differential equations governing the evolution of I and the total energy E are obtained. A regularization scheme for this system of differential equations is provided. We compute some illustrative
numerical examples, and discuss an average method for obtaining approximate analytical solutions to this pair of equations.
For a particular law of mass loss we also obtain exact analytical solutions. The application of these ideas to other kind
of perturbed gravitational N-body systems involving drag forces or a different type of mass variation is also considered.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
Surajit Chattopadhyay Ujjal Debnath Goutami Chattopadhyay 《Astrophysics and Space Science》2008,314(1-3):41-44
In this letter, we have assumed that the Universe is filled in tachyonic field with potential, which gives the acceleration
of the Universe. For certain choice of potential, we have found the exact solutions of the field equations. We have shown
the decaying nature of potential. From recently developed statefinder parameters, we have investigated the role of tachyonic
field in different stages of the evolution of the Universe. 相似文献
17.
Przemysław Bartczak Sławomir Breiter Przemysław Jusiel 《Celestial Mechanics and Dynamical Astronomy》2006,96(1):31-48
Simple models of potential based on material points and material segments are confronted with a homogeneous ellipsoid potential.
A spheroid is approximated with a pair of material points or with one material segment. The segment model proves to be more
accurate. For a triaxial ellipsoid, two models are considered: one with five material points and one with two material segments
and a point. When their parameters are determined with the fourth sectorial harmonic ignored, both simple models have a similar
approximation error. Numerical tests indicate that the approximate models of a triaxial ellipsoid are 5 to 10 times faster
than exact formulation, whereas for a spheroid the approximate models are at most twice as fast as the exact formulae. 相似文献
18.
Naoki Yoshida † Ravi K. Sheth Antonaldo Diaferio 《Monthly notices of the Royal Astronomical Society》2001,328(2):669-677
We use numerical simulations of a (480 Mpc h −1 )3 volume to show that the distribution of peak heights in maps of the temperature fluctuations from the kinematic and thermal Sunyaev–Zeldovich (SZ) effects will be highly non-Gaussian, and very different from the peak-height distribution of a Gaussian random field. We then show that it is a good approximation to assume that each peak in either SZ effect is associated with one and only one dark matter halo. This allows us to use our knowledge of the properties of haloes to estimate the peak-height distributions. At fixed optical depth, the distribution of peak heights resulting from the kinematic effect is Gaussian, with a width that is approximately proportional to the optical depth; the non-Gaussianity comes from summing over a range of optical depths. The optical depth is an increasing function of halo mass and the distribution of halo speeds is Gaussian, with a dispersion that is approximately independent of halo mass. This means that observations of the kinematic effect can be used to put constraints on how the abundance of massive clusters evolves, and on the evolution of cluster velocities. The non-Gaussianity of the thermal effect, on the other hand, comes primarily from the fact that, on average, the effect is larger in more massive haloes, and the distribution of halo masses is highly non-Gaussian. We also show that because haloes of the same mass may have a range of density and velocity dispersion profiles, the relation between halo mass and the amplitude of the thermal effect is not deterministic, but has some scatter. 相似文献
19.
S. D. Katore K. S. Adhav A. Y. Shaikh M. M. Sancheti 《Astrophysics and Space Science》2011,333(1):333-341
We consider a self-consistent system of Plane symmetric cosmology and binary mixture of perfect fluid and dark energy. The
perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding
Einstein’s field equations are obtained as a quadrature. The cases of Zeldovich Universe, Dust Universe and Radiation Universe
and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic. 相似文献
20.
A. R. Bestman 《Astrophysics and Space Science》1991,179(2):217-222
The flow in the boundary layer of a very hot two-component plasma is analysed when the radiative heat flux is given by the exact integral equation expression. The basic nonlinear integro-differential equation is solved by perturbing it about the differential approximation for radiation. In this way some light is shed on the order of accuracy of the differential approximation of radiation. In fact an error of about 4% may be incurred by invoking the differential approximation. 相似文献