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1.
The Machian models of isotropic expanding universes according to the “inertia-free” gravo-dynamics imply the equations between the instantan values H0 and q0 of the HUBBLE parameter H, the acceleration q, and the matter density o. Therefore, in Machian universes with linear expansion q0 = 0 the energy integral E = -1/2ϵc2 is zero and the matter density becomes (with H02R02 = c2/3) (f0 the Newtonian gravitational constant). This is the critical density in general relativistic cosmology.  相似文献   

2.
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3.
The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric gik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads hiA(xl) as neutrino-current vectors, firstly. Then, the metric gik is defined by the equation gik = ηAB hiAhηB according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential hiA with the matter Tιi is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric gik by four WEYL spinors we are able to construct a conformal flat metric ĝik = ϕ2ηik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric gik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 1018 times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 1018 times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c2: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝik = ϕ2ηik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.  相似文献   

4.
Under the assumption of a power-law between the expansion factor of the Universe, and the scalar field (a n=c=const.) tensor theory with cosmological constant are reduced to quadrature. Several exact solutions are obtained, among them inflationary universes that have barotropic equation of state.  相似文献   

5.
We formulate the canonical equations of motion for particles with an (post-HEWTON ian) interaction potential and the HAMILTON ian form of our MACH ian dynamics without inertia.  相似文献   

6.
The maximum volume of the closed Friedmann universe is further investigated and is shown to be 22 R 3 (t), instead of 2 R 3 (t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, there exists the maximum volume at any cosmic timet in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the timet m of the maximum scale factorR(t m ). The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as it should be. It will lead to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.  相似文献   

7.
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   

8.
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   

9.
Using the 3-dimensional ASH code, we have studied numerically the instabilities that occur in stellar radiation zones in presence of large-scale magnetic fields, rotation and large-scale shear. We confirm that some configurations are linearly unstable, as predicted by Tayler and collaborators, and we determine the saturation level of the instability. We find that rotation modifies the peak of the most unstable wave number of the poloidal instability but not its growth rate as much as in the case of the m = 1 toroidal instability for which it is changed to σ = /Ω. Further in the case with rotation and shear, we found no sign of the dynamo mechanism suggested recently by Spruit even though we possess the essential ingredients (Tayler's m = 1 instability and a large scale shear) supposedly at work. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

10.
In this paper, we improve the previous work on the MHD Alfvén wave oscillation model for the neutron star (NS) kHz quasi‐periodic oscillations (QPOs), and compare the model with the updated twin kHz QPO data. For the 17 NS X‐ray sources with the simultaneously detected twin kHz QPO frequencies, the stellar mass M and radius R constraints are given by means of the derived parameter A in the model, which is associated with the averaged mass density of the star as 〈ρ 〉 = 3M /(4πR3) ≃ 2.4 × 1014 (A /0.7)2 g/cm3, and we also compare the M ‐R constraints with the stellar equations of state. Moreover, we also discuss the theoretical maximum kHz QPO frequency and maximum twin peak separation, and some expectations on SAX J1808.4–3658 are mentioned, such as its highest kHz QPO frequency ∼ 870 Hz, which is about 1.4–1.5 times less than those of the other known kHz QPO sources. The estimated magnetic fields for both Z sources (about Eddington accretion rate ) and Atoll sources (∼ 1% ) are approximately ∼109 G and ∼108 G, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

11.
A cosmological model describing the different stages of the universe, i.e.: inflation, radiation dominated period and matter dominated (Friedmann-like) period is shown. The model consists of the usual gravitational lagrangian with a R 2 term, and, for the matter content, the lagrangian of a massive conformally coupled scalar field. The effect of backreaction is evaluated by means of an extremum condition on the entropy at each time. The differential equation, obtained when the lowest quantum order is considered, describes all the periods of evolution of the universe. For a range of values of, inflation is unstable and the universe can reach the following regime.  相似文献   

12.
A general method is proposed to solve in the linear approximation the fourth-order gravitational equations, which stem from Lagrangians $ \text{Q} = 1 ‐ g\left( {R + \frac{1}{2}aR^2 + bR_{av} R^{av} } \right) ‐ x\text{Q}. $ The metric of a static spherically symmetric body and the metric of a straight infinitely thin cosmic string are given.  相似文献   

13.
Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr arrbwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr a andr b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr o , Examples of Green's functions are given for the caser a =0,r b = and derived for the cases of finiter a andr b . The diffusion coefficient is assumed of the form = o(p)r b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.  相似文献   

14.
Observations in polarized emission reveal the existence of large‐scale coherent magnetic fields in a wide range of spiral galaxies. Radio‐polarization data show that these fields are strongly inclined towards the radial direction, with pitch angles up to 35° and thus cannot be explained by differential rotation alone. Global dynamo models describe the generation of the radial magnetic field from the underlying turbulence via the so called α ‐effect. However, these global models still rely on crude assumptions about the small‐scale turbulence. To overcome these restrictions we perform fully dynamical MHD simulations of interstellar turbulence driven by supernova explosions. From our simulations we extract profiles of the contributing diagonal elements of the dynamo α ‐tensor as functions of galactic height. We also measure the coefficients describing vertical pumping and find that the ratio between these two effects has been overestimated in earlier analytical work, where dynamo action seemed impossible. In contradiction to these models based on isolated remnants we always find the pumping to be directed inward. In addition we observe that depends on whether clustering in terms of superbubbles is taken into account. Finally, we apply a test field method to derive a quantitative measure of the turbulent magnetic diffusivity which we determine to be ∼2 kpckms–1. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

15.
A direct approach of the dynamical equation for the evolution of the two-point density correlation function is given in an expanding flat Friedmann Universe in the Newtonian approximation. If the third and higher moments are neglected, a wave-like equation of third-order for the two-point density correlation function is found. The exact solution of this equation shows, in the large time limit, the usual Jeans instability t 4/3. It is suggested that the highern-point correlation function of the density grow liket 2n/3 in the same approximation. This indicates that every truncation procedure of the hierarchy of the equations is inapplicable at least for large timest.  相似文献   

16.
The neutrino-pair radiation by electrons in a non-quantizing magnetic field B is investigated. For a relativistic degenerate electron gas the emissivity of this process is mainly given by \documentclass{article}\pagestyle{empty}\begin{document}$ \varepsilon _r = 5 \times 10^{15} (pF/mc)^{4/3} \,B_{13}^{2/3} T_y^{12/8} \,{\rm erg} \times {\rm cm}^{ - 3} \times {\rm sec}^{- 1} $\end{document} where pF is the electron Fermi momentum. Under typical neutron star conditions at B ∼ 1013G neutrino synchrotron radiation appears to be one of the most effective mechanisms of neutrino energy loss in the envelopes of neutron stars; this mechanism may also compete with other known neutrino production mechanisms in the neutron star cores if pion condensate or quark matter is absent.  相似文献   

17.
D.G. Korycansky  Erik Asphaug 《Icarus》2009,204(1):316-329
We present the results of additional calculations involving the collisions of km-scale rubble piles. In new work, we used the Open Dynamics Engine (ODE), an open-source library for the simulation of rigid-body dynamics that incorporates a sophisticated collision-detection and resolution routine. We found that using ODE resulted in a speed-up of approximately a factor of 30 compared with previous code. In this paper we report on the results of almost 1200 separate runs, the bulk of which were carried out with 1000-2000 elements. We carried out calculations with three different combinations of the coefficients of friction η and (normal) restitution ?: low (η=0,?=0.8), medium (η=0,?=0.5), and high (η=0.5,?=0.5) dissipation.For target objects of ∼1 km in radius, we found reduced critical disruption energy values in head-on collisions from 2 to 100 J kg−1 depending on dissipation and impactor/target mass ratio. Monodisperse objects disrupted somewhat more easily than power-law objects in general. For oblique collisions of equal-mass objects, mildly off-center collisions (b/b0=0.5) seemed to be as efficient or possibly more efficient at collisional disruption as head-on collisions. More oblique collisions were less efficient and the most oblique collisions we tried (b/b0=0.866) required up to ∼200 J kg−1 for high-dissipation power-law objects. For calculations with smaller numbers of elements (total impactor or 200 elements) we found that collisions were more efficient for smaller numbers of more massive elements, with values as low as for low-dissipation cases. We also analyzed our results in terms of the relations proposed by Stewart and Leinhardt [Stewart, S.T., Leinhardt, Z.M., 2009. Astrophys. J. 691, L133-L137] where where QR is the impact kinetic energy per unit total mass mi+mT. Although there is a significant amount of scatter, our results generally bear out the suggested relation.  相似文献   

18.
Howard and Harvey (1970) analyzed Mt. Wilson Doppler shifts to obtain a daily measure of the Sun's differential rotation. The data were fitted to give an angular velocity of the form = a + b sin2 B + c sin4 B (B = heliographic latitude). Changes in a, b, c were found to be correlated (Howard and Harvey, 1970). Yoshimura (1972) used the anticorrelation of the b and c parameters to infer the existence of large-scale convection. Wolff (1975) used the b-c anticorrelation and a weak correlation between a and b to infer that variations of the Sun's polar and equatorial rotation rates are anticorrelated. In this paper, the anticorrelation of b and c is shown to be due to numerical coupling.  相似文献   

19.
We have derived a model of the Kuiper belt luminosity function exhibited by a broken power-law size distribution. This model allows direct comparison of the observed luminosity function to the underlying size distribution. We discuss the importance of the radial distribution model in determining the break diameter. We determine a best-fit break-diameter of the Kuiper belt size-distribution of 30<Db<90 km via a maximum-likelihood fit of our model to the observed luminosity function. We also confirm that the observed luminosity function for m(R)∼21-28 is consistent with a broken power-law size distribution, and exhibits a break at .  相似文献   

20.
The Franck-Condon factors and r-centroids, which are very closelyrelated to relative vibrational transition probabilities, have beenevaluated by the more reliable numerical integration procedure forthe bands of c 1 - a 1 and f 1 - a 1 systems of CN + and C 2 + u- X 2 + g and D 2 g- A 2 u systems of N + 2 molecular ions of astrophysical interest,using a suitable potential.  相似文献   

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