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1.
The two degree-of-freedom system in rotating coordinates: \.u – 2 nv = V
x, \.v + 2 nu = V
y, \.x = u, \.y = v and its Jacobi integral define a time-dependent velocity field on a differentiable, two-dimensional manifold of integral curves. Explicit time dependence is determined by the dynamical system, coordinate frame, and initial conditions. In the autonomous cases, orbits are level curves of an autonomous function satisfying a second-order, quasi-linear, partial differential equation of parabolic type. Important aspects of the theory are illustrated for the two-body problem in rotating coordinates. 相似文献
2.
We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general
relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively.
These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their
ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density
ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature
of these solutions, one of the solution (I 1) is studied extensively. The solution (I 1) gives us wide range of Schwarzschild parameter u (0.138≤ u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of
Neutron star is maximized with all degree of suitability and by assuming the surface density ρ
b
=2×10 14 g/cm 3. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M
Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well
known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of
constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these
solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved
model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming
the surface density; ρ
b
=2×10 14 g/cm 3, the maximum mass of Neutron star comes out to be 1.34 M
Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively. 相似文献
3.
Various models are considered with metric type flat FRW i.e. with k = 0 whose energy-momentum tensor is described by a perfect fluid whose generic equation of state is p = ωρ and taking into account the conservation principle div(T
i
j
) = 0, but considering some of the‘constants’ as variable. A set of solutions through dimensional analysis is trivially found.
The numeric calculations carried out show that the results obtained are not discordant with those presently observed for cosmological
parameters together with the electromagnetic and quantum quantities.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
In this paper we present a detailed study of BCT Ist solution Tewari (Astrophys. Space Sci. 149:233, 1988) representing time dependent balls of perfect fluid with matter-radiation in general relativity. Assuming the life time of
quasar 10 7 years our model has initial mass≈10 8
M
Θ with an initial linear dimension≈10 15 cm. Our model is radiating the energy at a constant rate i.e. L
∞=10 47 ergs/sec with the gravitational red shift, z=0.44637. In this model we have 2 GM( u)/ c
2
R
S
( u))=0.3191 i.e. the model is horizon free. 相似文献
5.
Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier
et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative
of the angular velocity of Galactic rotation Ω′ 0 and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that
the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within
the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R
0 = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components ( u
⊙, v
⊙, ω
⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s −1; (2) the Galactic rotation parameters Ω 0 = −31.5 ± 0.9 km s −1 kpc −1, Ω′ 0 = +4.49 ± 0.12 km s −1 kpc −2, Ω″ 0 = −1.05 ± 0.38 km s −1 kpc −3 (the corresponding Oort constants are A = 17.9 ± 0.5 km s −1 kpc −1, B = −13.6 ± 1.0 km s −1 kpc −1 and the circular rotation velocity of the solar neighborhood is | V
0| = 252 ± 14 km s −1); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components,
respectively, f
R
= −12.5±1.1 km s −1 and f
ϑ
= 2.0 ± 1.6 km s −1; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x
⊙ = −91° ± 4°. 相似文献
6.
A possible correlation between the magnetic and velocity fields has been analyzed based on the SOHO/MDI magnetograms and Dopplergrams.
It is found that the observed large-scale weak magnetic field (weaker than 50 G (gauss)) is correlated with the velocity statistically.
The curves of u⋅ b with latitude, where u and b are the velocity and magnetic fields in a rectangular region (±15 ○ in longitude, ±45 ○ in latitude) on the Sun, show the same patterns in the years 2000, 2004, and 2007. The patterns indicate that u and b are positively correlated near the equator but are anti-correlated at the middle latitudes. For a strong magnetic field between
50 G and 3000 G, the curves of u⋅ b with latitude show the same tendencies at the middle latitudes. Near the equator, however, the slope of the curve is positive
in 2000 and is negative in 2004 and 2007. In addition, we give an estimation for the amplitude of the cross helicity h
χ
( hc=[`( u· b)]h_{\chi}=\overline{\mathbf{u}\cdot\mathbf{b}}) inferred from the MDI data, which is of the order of 10 3 G m s −1 near the center of the solar disk. 相似文献
7.
It is shown that the equation of motion Du
j/ Ds = ( e/ mc
2) F
ji
u
i , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx
j [jpi] = 0 or L
v
p
i = 0, where p
i is the conjugate momentum 4-vector and v a vector determined by the condition p
i
v
i, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors. 相似文献
8.
Stochastic temperatures and turbulence are characterized by average velocities u
th
and < u
turb
> ≡ u
0 and fluctuations u￠th {u'_{th}} and u′ (<u′ > = 0). Thus, the Doppler width of a line also has a fluctuating component Dl￠D \Delta {\lambda '_D} . Observed spectra correspond to the radiative flux averaged over time and over a star’s surface, <Hλ>. Usually, only the average velocities u
th
and u
0 are taken into account in photospheric models and these yield the Doppler width DlD(0) \Delta \lambda_D^{(0)} of a line in the customary way. The fluctuations Dl￠D \Delta {\lambda '_D} mean that near a line center the average absorption coefficient < αλ > is larger than the usual αλ, which depends only on the average velocities u
th
and u
0. This enhances the absorption line near the center and is not explained by the photospheric models. This new statistical
effect depends on the wavelength of the line. A comparison of observed lines with model profiles yields an estimate for the
average level of fluctuations in the Doppler width, h =
á | Dl￠D |
ñ | / |
DlD(0) \eta = {{{\left\langle {\left| {\Delta {{\lambda '}_D}} \right|} \right\rangle }} \left/ {{\Delta \lambda_D^{(0)}}} \right.} , which characterizes the average stochasticity of a photosphere and is important for understanding the physics of photospheres.
The depths of lines in synthetic spectra of stars are often greater than the observed values. The observed disagreement between
the theoretical and actually observed depths of lines can be corrected by introducing an additional parameter, the fluctuation
level η. Then it is possible to obtain estimates of η for a number of stars. 相似文献
9.
Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using
the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations
the expansion θ in the model is considered as proportional to the eigen value s 2 2\sigma^{2}_{~2} of the shear tensor s j i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing
function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early
stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string
at the late time. Some physical and geometric properties of the model are also discussed. 相似文献
10.
The features of a homogeneous scalar field ϕ with classical Lagrangian L = ϕ ;i
ϕ ;i
/2 − V(ϕ) and tachyon field Lagrangian L = − V(ϕ)√1 − ϕ ;i
ϕ ;i
causing the observable accelerated expansion of the Universe are analyzed. The models with constant equation-of-state parameter
w
de = p
de/ρ de < −1/3 are studied. For both cases the fields ϕ( a) and potentials V( a) are reconstructed for the parameters of cosmological model of the Universe derived from the observations. The effect of
rolling down of the potential V(ϕ) to minimum is shown.
Published in Ukrainian in Kinematika i Fizika Nebesnykh Tel, 2008, Vol. 24, No. 5, pp. 345–359.
The article was translated by the authors. 相似文献
11.
E × B-drifting jets have been generally ignored for the past 25 years even though they may well describe all the astrophysical
jet sources, both on galactic and stellar scales. Here we present closed-form solutions for their joint field-and-particle
distribution, argue that the observed jets are near equipartition, with extremely relativistic, monoenergetic e ±-pairs of bulk Lorentz factor γ ≲ 10 4, and are first-order stable. We describe plausible mechanisms for the jets’ ( i) formation, ( ii) propagation, and ( iii) termination. Wherever a beam meets with resistance, its frozen-in Poynting flux transforms the delta-shaped energy distribution
of the pairs into an almost white power law, E
2
N
E ∼ E
−∫ with ∫ ≳ 0, via single-step falls through the huge convected potential. 相似文献
12.
It is shown (1) that the coefficients Ai of the limb darkening functions I(μ)/ Icenter = P5 (μ) = ∑ Ai μ i ( i = 0... 5; μ = cos ϑ), which had been published by Neckel and Labs ( Solar Phys. 153, 91, 1994), can well be approximated by analytical functions of wavelength λ, and (2) that at first sight purely formal extrapolation
of the functions P5(μ) to the very limb (μ = 0.0) is not meaningless: in combination with absolute intensities for the disk center these functions
yield ‘limb intensities’ which all correspond to almost the same ‘limb temperature’, Tlimb≈4746 K. Together these results lead to ‘reference functions’ which can quickly yield rather reliable values of the Sun's
continuum intensities, for any values of μ and λ. 相似文献
13.
We analyze the three-dimensional kinematics of about 82 000 Tycho-2 stars belonging to the red giant clump (RGC). First, based
on all of the currently available data, we have determined new, most probable components of the residual rotation vector of
the optical realization of the ICRS/HIPPARCOS system relative to an inertial frame of reference, ( ω
x
, ω
y
, ω
z
) = (−0.11, 0.24, −0.52) ± (0.14, 0.10, 0.16) mas yr −1. The stellar proper motions in the form μ α cos δ have then be corrected by applying the correction ω
z
= −0.52 mas yr −1. We show that, apart from their involvement in the general Galactic rotation described by the Oort constants A = 15.82 ± 0.21 km s −1 kpc −1 and B = −10.87 ± 0.15 km s −1 kpc −1, the RGC stars have kinematic peculiarities in the Galactic yz plane related to the kinematics of the warped stellar-gaseous Galactic disk. We show that the parameters of the linear Ogorodnikov-Milne
model that describe the kinematics of RGC stars in the zx plane do not differ significantly from zero. The situation in the yz plane is different. For example, the component of the solid-body rotation vector of the local solar neighborhood around the
Galactic x axis is M
32− = −2.6 ± 0.2 km s −1 kpc −1. Two parameters of the deformation tensor in this plane, namely M
23+ = 1.0 ± 0.2 km s −1 kpc −1 and M
33 − M
22 = −1.3 ± 0.4 km s −1 kpc −1, also differ significantly from zero. On the whole, the kinematics of the warped stellar-gaseous Galactic disk in the local
solar neighborhood can be described as a rotation around the Galactic x axis (close to the line of nodes of this structure) with an angular velocity −3.1 ± 0.5 km s −1 kpc −1 ≤ Ω W ≤ −4.4 ± 0.5 km s −1 kpc −1. 相似文献
14.
We consider the Newtonian planar three-body problem with positive masses m
1, m
2, m
3. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian
orbit besides three exceptional cases ∑ m
i
m
j
/(∑ m
k
) 2 = 1/3, 2 3/3 3, 2/3 2 where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis
of the three-body problem started in papers [Tsygvintsev, A.: Journal für die reine und angewandte Mathematik N 537, 127–149
(2001a); Celest. Mech. Dyn. Astron. 86(3), 237–247 (2003)] and based on the Morales–Ramis–Ziglin approach. 相似文献
15.
We present results of a study of the so-called “stickiness” regions where orbits in mappings and dynamical systems stay for very long times near an island and then escape to the surrounding chaotic region. First we investigated the standard map in the form xi+1 = xi+ yi+1 and yi+1 = yi+ K/2π · sin(2π xi) with a stochasticity parameter K = 5, where only two islands of regular motion survive. We checked now many consecutive points—for special initial conditions of the mapping—stay within a certain region around the island. For an orbit on an invariant curve all the points remain forever inside this region, but outside the “last invariant curve” this number changes significantly even for very small changes in the initial conditions. In our study we found out that there exist two regions of “sticky” orbits around the invariant curves: A small region I confined by Cantori with small holes and an extended region II is outside these cantori which has an interesting fractal character. Investigating also the Sitnikov-Problem where two equally massive primary bodies move on elliptical Keplerian orbits, and a third massless body oscillates through the barycentre of the two primaries perpendicularly to the plane of the primaries—a similar behaviour of the stickiness region was found. Although no clearly defined border between the two stickiness regions was found in the latter problem the fractal character of the outer region was confirmed. 相似文献
16.
It is well known that the parallel cuts of the parallel and perpendicular electric field in electron phase-space holes (electron
holes) have bipolar and unipolar structures, respectively. Recently, electron holes in the Earth’s plasma sheet have been
observed by THEMIS satellites to have detectable fluctuating magnetic field with regular structures. Du et al. ( 2011) investigated the evolution of a one-dimensional (1D) electron hole with two-dimensional (2D) electromagnetic particle-in-cell
(PIC) simulations in weakly magnetized plasma (Ω
e
< ω
pe
, where Ω
e
and ω
pe
are the electron gyrofrequency and electron plasma frequency, respectively), which initially exists in the simulation domain.
The electron hole is unstable to the transverse instability and broken into several 2D electron holes. They successfully explained
the observations by THEMIS satellites based on the generated magnetic structures associated with these 2D electron holes.
In this paper, 2D electromagnetic particle-in-cell (PIC) simulations are performed in the x– y plane to investigate the nonlinear evolution of the electron two-stream instability in weakly magnetized plasma, where the
background magnetic field ( B0 = B0[( e)\vec] x)(\mathbf{B}_{0} =B_{0}\vec{\mathbf{e}} _{x}) is along the x direction. Several 2D electron holes are formed during the nonlinear evolution, where the parallel cuts of E
x
and E
y
have bipolar and unipolar structures, respectively. Consistent with the results of Du et al. ( 2011), we found that the current along the z direction is generated by the electric field drift motion of the trapped electrons in the electron holes due to the existence
of E
y
, which produces the fluctuating magnetic field δB
x
and δB
y
in the electron holes. The parallel cuts of δB
x
and δB
y
in the electron holes have unipolar and bipolar structures, respectively. 相似文献
17.
We analyze the properties of galaxy clusters in the region of the Leo supercluster using observational data from the SDSS
and 2MASS catalogs. We have selected 14 galaxy clusters with a total dynamical mass of 1.77 × 10 15
M
⊙ in the supercluster region 130 by 60 Mpc in the plane of the sky ( z ≃ 0.037). The composite luminosity function of the supercluster is described by a Schechter function with parameters that,
within the error limits, correspond to field galaxies and does not differ from the luminosity function of the richer Ursa
Major (UMa) supercluster for the same luminosity range (the bright end). The luminosity functions of early-type and late-type
galaxies in Leo at the faint end are characterized by a sharp decrease ( α = −0.60±0.08) and a steep increase ( α = −1.44± 0.10) in the number of galaxies, respectively. In the virialized cluster regions, the fraction of early-type galaxies
selected by the u- r color, bulge contribution, and concentration index among the galaxies brighter than M
K
* + 1 is, on average, 62%. This fraction is smaller than that in the UMa supercluster at a 2–3 σ level. The near-infrared luminosities of galaxy clusters down to a fixed absolute magnitude correlate with their masses almost
in the same way as for other samples of galaxy clusters ( L
200,K
∝ M
2000.63±0.11)). 相似文献
18.
Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants (SNRs) is used to investigate the properties
of Kepler’s SNR and, in particular, to predict the γ-eay spectrum expected from this SNR. Observations of the nonthermal radio and X-ray emission spectra as well as theoretical
constraints for the total supernova (SN) explosion energy E
sn are used to constrain the astronomical and particle acceleration parameters of the system. Under the assumption that Kepler’s
SN is a type Ia SN we determine for any given explosion energy E
sn and source distance d the mass density of the ambient interstellar medium (ISM) from a fit to the observed SNR size and expansion speed. This makes
it possible to make predictions for the expected γ-eay flux. Exploring the expected distance range we find that for a typical explosion energy E
sn=10 51 erg the expected energy flux of TeV γ-rays varies from 2×10 −11 to 10 −13 erg/(cm 2 s) when the distance changes from d=3.4 kpc to 7 kpc. In all cases the γ-eay emission is dominated by π
0-decay γ-rays due to nuclear CRs. Therefore Kepler’s SNR represents a very promising target for instruments like H.E.S.S., CANGAROO
and GLAST. A non-detection of γ-rays would mean that the actual source distance is larger than 7 kpc. 相似文献
19.
Some Bianchi type-I viscous fluid string cosmological models with magnetic field are investigated. The viscosity coefficient
of bulk viscous fluid is assumed to be a power function of mass density ξ( t)= ξ
0
ρ
m
, where ξ
0 and m are constants. To get a determinate model, we assume conditions ρ=(1+ ω) λ, where ρ is rest energy density, ω a positive constant and λ the string tension density and expansion θ is proportional to eigen value σ
11 of the shear tensor σ
j
i
. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is discussed.
相似文献
20.
In the first part the number of independent non-vanishing components of the 3-index torsion tensor Q
jk
i
is reduced from 24 (in general case) to 12 — for the case of cylindrical symmetry of the underlying manifold. In the second part of the paper we have obtained an exact solution of Einstein-Cartan-Maxwell equations representing a static cylinder of perfect fluid with an axial magnetic field H and non-zero spin density K. 相似文献
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