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1.
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В. А. Гаген-Торн 《Astrophysics and Space Science》1980,73(2):279-294
J 287 1972–1976. , . . J ( ), () . (0=80°) . J 287 ¶ . p=42.8%, 0=101°. (50%). 相似文献
3.
4.
- . , - . -. 相似文献
5.
А. П. Маркеев 《Celestial Mechanics and Dynamical Astronomy》1973,8(2):307-322
. . ,e, , . . e, . , .
Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.相似文献
6.
Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K
g
, =
g
c
2.Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density
g
to the central density
gc
,
g
/
gc
; pressureP to the
gc
,P/
gc
; and the metric componente
–, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r
2
P
*(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c
2 to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P
c
, binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986 相似文献
7.
TS. G. Tsvetkov 《Astrophysics and Space Science》1988,150(2):223-234
On the basis of observational data for the absolute R and relative R/R amplitudes of variations in radius of galactic classical cepheids (55 stars from Balona and Stobie (1979) and 30 stars from Sollazzoet al. (1981)), four kinds of empirical linear relations are obtained: log(P V)–logR, logP–logR, log(P V)–log(R/R), and logP–log(R/R);P, R, and V are the pulsation periods, the mean stellar radii, and the amplitudes of light variations, respectively. Three groups of stars are considered: short-period cepheids (SPC)-with logP1.1; long-period cepheids (LPC)-with logP>1.1; and s-cepheids (sC). Both the R values and the R/R values increase withP andP V, for a given group of variables. A comparison is performed with our results obtained from data in other sources (Kurochkin, 1966; Gieren, 1982; etc.). The investigated relations can be applied for determining R and R/R of galactic classical cepheids, by using their observedP and V. All studied galactic classical cepheids have R/R<0.35, R<10R
for SPC and 10R
<R60R
for LPC. The sC have smaller R and R/R values than other classical cepheids, at the same periods (the difference is about 2 times for R and 1.4–2.8 times for R/R); the studied sC have R/R in the range 0.025–0.075 and R in the range 1–3R
(only Y Oph has R8R
). 相似文献
8.
The exact geometry of the Roche curvilinear coordinates (, , ) in which corresponds to the zero-velocity surfaces is investigated numerically in the plane, as well as in the spatial, case for various values of the mass-ratio between the two point-masses (m
1,m
2) constituting a binary system.The geometry of zero-velocity surfaces specified by -values at the Lagrangian points are first discussed by taking their intersections with various planes parallel to thexy-, xz- andyz-planes. The intersection of the zero-velocity surface specified by the -value at the Lagrangian equilateral-triangle pointsL
4,5 with the planex=1/2 discloses two invariable curves passing through the pointsL
4,5 and situated symmetrically with respect to thexy-plane whose form is independent of the mass-ratio.The geometry of the remaining two coordinates (, ) orthogonal to the zero-velocity surfaces is investigated in thexy- andxz-planes from extensive numerical integrations of differential equations generated from the orthogonality relations among the coordinates. The curves (x, y)=constant in thexy-plane are found to be separated into three families by definite envelopes acting as boundaries whose forms depend upon the mass-ratio only: the inner -constant curves associated with the masspointm
1, the inner -constant curves associated with the mass-pointm
2 and the outer -constant curves. All the -constant curves in thexy-plane coalesce at either of the Lagrangian equilateraltriangle pointsL
4,5, except for a limiting case coincident with thex-axis. The curves (x, z)=constant in thexz-plane are also separated by definite envelopes depending upon the mass-ratio into different families: the inner -constant curves associated with the mass-pointm
1, the inner -constant curves associated with the mass-pointm
2 and the outer -constant curves on both sides out of the envelopes. For larger values ofz, the curves =constant tend asymptotically to the line perpendicular to thex-axis and passing through the centre of mass of the system, except for a limiting case coincident with thex-axis. The geometrical aspects of the envelopes for the curves (x, y)=constant in thexy-plane and the curves (x, z)=constant in thexz-plane are also discussed independently.In the three-dimensional space, the Roche coordinates can be conveniently defined in such a way as to correspond to the polar coordinates in the immediate neighbourhood of the origin, and to the cylindrical coordinates at great distances. From numerical integrations of simultaneous differential equations generating spatial curves orthogonal to the zero-velocity surfaces, the surfaces (x, y, z)=constant and the surfaces (x, y, z)=constant are constructed as groups of such spatial curves with common values of some parameters specifying the respective surfaces.On leave of absence from the University of Tokyo as an Honorary Fellow of the Victoria University of Manchester. 相似文献
9.
The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR
eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR
eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR
eff one obtains the amounts of actionA
c(M), the effective densities eff(M)=(M)3(M), the densities of action and of energy (or mean presures in the stellar interior)a
c(M),e
c(M), and the potential energiesE
p(M).The amounts of action areA
cM
k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M
–1.81, (M)M0.6.The cases for the M stars (e
c(M)M
–1) and for the A and earlier stars (betweena
c(M)=constant and eff(M)M
–1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M
M25M
.With all this, one can build dynamical HR diagrams withA
c(M), Ep(M), eff
M
–p
, etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA
c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE
p(M)M
–p according to the stellar models used here and the observed frequency function (MM
–q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE
p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA
c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed. 相似文献
10.
The shifts of Fraunhofer lines of different chemical elements in a homogeneous medium with a plane monochromatic progressive adiabatic sound waves are derived. The calculations indicate that lines of neutral elements (6 0 14) with lower excitation potentials 0
i= 0–2 eV are red shifted, those with excitation potential 0
i= 4–12 eV are blue shifted, and with 0
i= 3 eV are both blue and red shifted. The lines of ions are shifted toward the blue. The shifts of Fraunhofer lines are found to decrease from the centre of the solar disk to the limb. These results agree qualitatively and quantitatively with observations. 相似文献
11.
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
12.
Amos Yahil 《Astrophysics and Space Science》1994,217(1-2):243-260
Comparison of the large-scale density and velocity fields in the local universe shows detailed agreement, strengthening the standard paradigm of the gravitational origin of these structures. Quantitative analysis can determine the cosmological density parameter, , and biasing factor,b; there is virtually no sensitivity in any local analyses to the cosmological constant,. Comparison of the dipole anisotropy of the cosmic microwave background with the acceleration due to theIRAS galaxies puts the linear growth factor in the range 0.6 /b = 0.6
–0.3
+0.7
(95% confidence). A direct comparison of the density and velocity fields of nearby galaxies gives = 1.3
–0.6
+0.7
, and from nonlinear analysis the weaker limit > 0.45 forb > 0.5 (again 95% confidence). A tighter limit, > 0.3 (4–6), is obtained by a reconstruction of the probability distribution function of the initial fluctuations from which the structures observed today arose. The last two methods depend critically on the smooth velocity field determined from the observed velocities of nearby galaxies by thePOTENT method. A new analysis of these velocities, with more than three times the data used to obtain the above quoted results, is now underway and promises to tighten the uncertainties considerably, as well as reduce systematic bias. 相似文献
13.
Theoretical Ca X electron temperature sensitive emission line ratios, derived using electron excitation rates interpolated from accurateR-matrix calculations, are presented forR
1 =I(419.74 )/I(574.02 ,),R
2 =I(411.65 )/I(574.02 ),R
3 =I(419.74 )/I(557.75 ), andR
4 =I(411.65 )/I(557.75 ). A comparison of these with observational data for three solar flares, obtained by the Naval Research Laboratory's S082A slitless spectrograph on boardSkylab, reveals good agreement between theory and observation forR
1 andR
3 in one event, which provides limited support for the accuracy of the atomic data adopted in the analysis. However, in the other flares the observed values ofR
1 –R
4 are much larger than the theoretical high-temperature limits, which is probably due to blending of the 419.74 line with Civ 419.71 , and 411.65 with possibly Ciii 411.70 . 相似文献
14.
-- () ., , , , , . , , . , . 相似文献
15.
In the framework of non-linear fluid theory we use a lower hybrid (LH) wave of the form
as a pump which interacts with the small fluctuations with the low-frequency vibrations
i
or =0, where
i
, is the hydrogen ion-cyclotron (HIC) gyrofrequency. The ponderomotive force generated by the beating of the high-frequency pump wave 0 and the sideband LH waves (±0) produces a non-linear coupling between the high- and low-frequency motions of electrons and ions. Under certain conditions the HIC waves and the zero-frequency waves both become parametrically unstable and start to grow. These excited waves then heat the ions by stochastic acceleration in the transverse direction, thus explaining the formation of ion comics along the auroral field lines. Electrons would be heated in the parallel direction directly by the pump field as well as by low-frequency waves. Thus a single mechanism can explain the existence of ion-cyclotron waves, zero-frequency waves, ion conics, and energetic electrons along the auroral field lines. 相似文献
16.
A three-component fluid model of the Universe during the recombination era is analysed for =
c
(
c
is the critical density). In addition to the well-known instability of the Jeans mode at 109
M
, we find two more unstable modes at 1012
M
. 相似文献
17.
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
18.
The aim of the present paper is to prove that the system of partial differential equations, which define a set of curvilinear coordinates , , that are orthogonal to the Roche equipotentials (r, , ) incorporating the effects of both rotationaland tidal distortion, does not admit of any formal integrals; and can be solved only numerically in an asymptotic manner. This fact is related with analytic properties of the problem of three bodies, in which represents the potential. 相似文献
19.
R. Caimmi 《Astrophysics and Space Science》1988,140(1):1-32
An approximate analytical method of solving the polytropic equilibrium equations, first developed by Seidov and Kuzakhmedov (1978), has been extended and generalized to equilibrium configurations of axisymmetric systems in rigid rotation, with polytropic index,n =n
p
+
n
, nearn
p
=0, 1, and 5. Though the details of the method depend on the value ofn
p
, acceptable results are obtained for |
n
| 0.5 to describe slowly rotating configurations in the range 0n1.5, 4.5n5. In the limit of rotational equilibrium configurations, when the distorsion may be large enough, a satisfactory approximation holds only in the range 0n, 1n1.5, 4.5n5. 相似文献
20.
Paul S. Wesson 《Astrophysics and Space Science》1976,42(2):285-330
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