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2.
Albert P. Linnell 《Astrophysics and Space Science》1977,48(1):185-190
A linear approximating equation exists for the boundary of a uniformly rotating polytrope. The equation in η=(ξ1−ξ)/ξ1 permits rapid calculation of the polytrope radius for any latitude, and is accurate for angular velocities of rotation nearly
to critical rotation. Data in this paper apply to a polytrope indexn=3.0. 相似文献
3.
A theory has been developed for obtaining the potential energy of two interpenetrating spherically symmetric galaxies of unequal dimensions due to their mutual gravitational interaction. The mass distribution in both the galaxies is assumed to be that of a polytrope of integral index. A basic function that occurs in the theory has been tabulated for the cases of polytropes of indicesn=0 and 4 for four ratios of the radii. 相似文献
4.
Martin Beech 《Astrophysics and Space Science》1988,147(2):219-227
The existence of a maximum isothermal core mass fraction (q
max), the Schoenberg-Chandrasekhar limit, is one of the classic results from the theory of stellar structure. This limit can be demonstrated through a simplified composite polytrope model in which an isothermal core is surrounded by ann=1 polytrope envelope. While this model underestimatesq
mas by 25% in the homogeneous case, it is accurate to within 5% in the more realistic inhomogeneous situation. 相似文献
5.
The oscillations of a gaseous polytrope with a magnetic field having both a toroidal and a poloidal component are examined using the second-order tensor virial equations on the assumption that the magnetic energy is small compared with the gravitational energy. The frequencies of oscillation of the transverse shear, the toroidal and the coupled pulsation modes are tabulated for polytropic indicesn=1, 1.5, 2, 3 and 3.5. It is found that the magnetic field decreases the frequency of oscillation of (i) the transverse shear mode and (ii) the mode which starts as a radial pulsation in the absence of a magnetic field while it increases the frequency of oscillation of (i) the toroidal mode and (ii) the Kelvin mode. In all cases the shift in frequency decreases with increasingn. 相似文献
6.
The equilibrium general magnetic field inside a magneto-rotating star, assumed to be a polytrope, has been determined more accurately, for large general magnetic field. Furthermore the effect of such field on the structure and oscillations of a slowly rotating polytrope has been studied forn=1,0, 1.5, 2.0, and 3.0. 相似文献
7.
P. M. S. Namboodiri 《Celestial Mechanics and Dynamical Astronomy》2000,76(1):69-77
Oscillations in galaxies have been investigated by numerical simulations. The various models used have density distributions
corresponding to that of polytrope of index n in the range 0 ≤ n ≤ 4 and their evolution has been followed for more than 70 crossing times. The kinetic energy shows regular and smooth oscillations
for models with n = 0, 1 and 2 whereas in other models it shows noisy oscillation. The oscillation in kinetic energy is observed to have a
period of 3 crossing time irrespective of the density and size of the galaxy. The amplitude of oscillation is seen to decrease
as the central density of the galaxy increases.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
Zero-velocity curves perpendicular to the orbital plane are computed for a close pair of interacting galaxies having density distribution that of a polytrope of indexn=4. An analytical formulation for computing the zero-velocity surfaces is suggested. 相似文献
9.
Albert P. Linnell 《Astrophysics and Space Science》1975,37(1):57-72
Analytic expressions are presented which approximate the Emden function θ, and the associated Emden functions,ψ o andψ 2, and their derivatives, near the first zero of θ,ξ o. The range of accurate representation extends toξ= 1.5ξ 1. This range is sufficient to encompass the boundary of a critically rotating polytrope. 相似文献
10.
In order to specify the structure of a rapidly and differentially rotating gaseous polytrope, we extend Chandrasekhar's perturbation theory to include third-order terms in the perturbation parameter. In the present paper, the theory developed is required for a subsequent numerical treatment of the structure-determination.This research was supported by the Research Development Project of the University of Patras, Greece. 相似文献
11.
Albert P. Linnell 《Astrophysics and Space Science》1981,80(2):501-511
This paper develops algebraic expressions for the volume and surface area of a uniformly rotating polytrope. The expressions depend on an analytic theory for boundary shape developed in previous papers. A comparison with the calculations of James indicates the present theory improves on the original Chandrasekhar theory by a factor 10 or more. 相似文献
12.
R. Caimmi 《Astrophysics and Space Science》1980,71(2):415-457
The basic theory on polytorpes is revisited and EC polytropes are defined. The first-order approximation theory of Chandrasekhar (1933a, b, c) and Chandrasekhar and Lebovitz (1962) is reviewed, refined and extended in such a way that better results are obtained without involving hard analytical or numerical techniques. A more precise equation is given in defining non-outer equipotential surfaces, and a new method is adopted in determining the explicit expression of the gravitational potential. This method essentially consists in equating the expression of the gravitational potential and its first radial derivative determined by accounting for the equilibrium condition, with the corresponding expression of the gravitational potential and its first radial derivative determined by accounting for mass distribution. Such expressions are to be calculated at convenient points — for instance, at the centre and at the pole of the system. In this way, an infinity of exact solutions is derived for the special casesn=0 andn=1, and we then have the problem: ‘Which of the infinite number of solutions available leads to the most stable configuration?’ The simplest of these solutions is taken into account in detail for bothn=0 andn=1; results relative to the latter case allow us to solve the Kopal (1937) problem. EC polytropes withn=5 are found to consist of an inner massive non-rotating component and an outer zero-density rotating atmosphere. It is seen that they are equivalent in some respects to Roche systems, and the corresponding exact solution is derived. Explicit expressions for characteristic physical parameters are also determened in the general case, relative to sequences of equilibrium states characterized by constant masses and angular momenta. Detailed results are given for the special casesn=0, 1 and 5. Finally, some properties of both EC polytropes and R polytropes withn=0 (i.e., generalized Roche systems) are reported and discussed. The conclusions of this paper make it highly desirable to have an extension of the method used here to general values ofn. 相似文献
13.
R. Louise 《Earth, Moon, and Planets》1982,26(1):93-96
The revised Titius-Bode law (Balsano and Hughes, 1979) giving distances of planets from the Sun shows integers that recall the Bohr law in the early quantum theory of hydrogen atom. The author searchs for a formalism, similar to the Sommerfeld's one accounting for the planetary distribution of the solar system. It is shown that such a formalism might be started with the assumed relation $$\int_{r_0 }^{r_n } {U(r)dr = nk,} $$ whereU(r) stands for the gravitation potential created by the Sun at distancer,k=cte,r o=cte,r n=distance of then th planet andn=1, 2, 3... Although the inspiration of the present note came from the early quantum theory, it is emphasized that there is no connection between the above assumed equation and the Sommerfeld quantum rule, but a pure formal similarity. the true significance of that equation is still unknown. It is either a fortuitous coincidence leading to the T-B law or any possible unsuspected property of gravitation. 相似文献
14.
A number of small, cyclic molecules containing several carbon atoms in their ring structure has been identified in different astrophysical environments. It is the aim of this work to study important molecular properties of such heterocyclic species bearing an iron atom, which is one of the most abundant cosmic elements. Quantum theoretical calculations based on a density functional approach have been employed to investigate physical properties of six small cyclic carbon and hydrocarbon molecules containing iron as a hetero atom, viz. FeC2H n and FeC3H n (n=0,2,4). The full geometry optimisation at the chosen level of electronic structure theory (B3LYP/6-31G(d)) including vibrational anharmonicities and non-rigidity, has furnished values for the rotational constants of these species to an expected accuracy of about one per cent. We present structural, electronic, vibrational, and rotational molecular properties including line frequencies, line strengths, and transition probabilities. These results may be helpful for identifying these molecules in future laboratory experiments in view of tentative astronomical observations. 相似文献
15.
We have determined the real and imaginary indices of refraction (n and k) for six iron oxide/oxyhydroxide phases—magnetite, maghemite, goethite, lepidocrocite, akaganéite, and ferrihydrite. A single crystal of magnetite was used to derive bulk n and k values from 100-2000 cm−1 (5-100 μm). Synthetic nanocrystalline samples of maghemite, goethite, lepidocrocite, akaganéite, and ferrihydrite were pressed into compact pellets used to determine bulk n and k values from 100-1200 cm−1 (8.33-100 μm). All values of n and k (the optical constants) were determined from specular reflectance spectra acquired at 2 cm−1 spectral sampling using classical Lorentz-Lorenz dispersion theory. In this paper, we present the optical constants of all six minerals and the oscillator parameters with which they were modeled. Use of these optical constants could aid in radiative transfer models of terrestrial dust as well as Mars, the Moon, and airless bodies in the Solar System. 相似文献
16.
Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R n (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new. 相似文献
17.
We examine the non-radial modes of oscillation, belonging to spherical harmonics of ordersl=1 andl=3, of a gaseous polytrope with a toroidal magnetic field. We find that a toroidal magnetic field increases the growth rate of convective instability for deformations belonging to the spherical harmonicl=1 whereas it decreases the growth rate of convective instability for deformations belonging to the harmonicsl=2 andl=3. The frequencies of the ‘acoustic’ mode and the ‘Kelvin’ mode are decreased by the presence of the toroidal magnetic field. 相似文献
18.
The earlier work on classification of galactic collisions for identical galaxies is extended to the situations where the two colliding galaxies differ in mass and dimension. We consider collisions between galaxies of masses 107, 109, 1011 and 1013
M
and let their radii be 0.1, 1, 10 and 100 kpc, respectively. The density distribution in both galaxies is represented by that of a polytrope of indexn=4. The type of collision is determined for head-on collisions for initial relative velocities 500, 1000, 2000 and 3000 km s–1. The corresponding final velocities are also indicated. 相似文献
19.
《Icarus》1987,70(2):334-347
The Laplace resonance among the inner three Galilean satellites (mean motions n1 − 3n2 + 2n3 = 0) has stable configurations in “deep resonance,” i.e., where mean motions taken by pairs are in ratios very close to 2:1. The present satellite configuration, with the resonance variable φ ≡ λ1 − 3λ2 + 2λ3 stable at 180°, is unstable near this exact commensurability. But there is a continuous path of stable conditions branching from φ = 180° to higher and lower values of φ and toward very deep resonance, according to a theory extended to third order in orbital eccentricity. This path provides a track for tidal evolution of the system. Thus, scenarios involving evolution (probably episodic) from deep resonance are viable, and eliminate the requirement by the alternative equilibrium hypothesis for rapid tidal dissipation in Jupiter. Evolution out from deep resonance is consistent with the free eccentricity of Ganymede, the free libration of φ, and observational constraints on Io's secular acceleration. Also, the relatively large forced eccentricities in deep resonance may have controlled geophysical processes in the satellites by much greater tidal heating and global stress than at present. 相似文献
20.
The possibility of H3+ playing a role as a sink for noble gases has been investigated in the case of Argon. Elaborate quantum methods (ab initio Coupled Cluster and density functional BH&HLYP levels of theory) have been shown to reproduce the rotational constants within 0.3% together with the only known IR frequency on the test case of Ar…D3+. Dissociation energies of (Ar)n…H3+ as a function of cluster size, i.e. 7.2 (n=1), 3.7 (n=2), 3.6 (n=3), 1.6 (n=4), 1.7 (n=5) kcal/mol, follow the pattern established experimentally for (Ar)n…H3+ and (H2)n…H3+ series. Rotational constants and harmonic frequencies of (Ar)n…H3+ (n=1-3) are presented. 相似文献