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1.
We calculate in this paper the secular and critical terms arising from the principal part of the classical planetary Hamiltonian. This is the first step to establish a third order canonical planetary theory of Uranus-Neptune through the Hori-Lie technique. We truncate our expansions at the second degree of eccentricity-inclination. Our planetary theory is expressed in terms of the canonical variables of H. Poincaré.  相似文献   

2.
We present a second order secular Jupiter-Saturn planetary theory through Poincaré canonical variables, von Zeipel's method and Jacobi-Radau referential. We neglect in our expansions terms of power higher than the fourth with respect to eccentricities and sines of inclinations. We assume that the disturbing function is composed of secular and critical terms only. We shall deriveF 2si and writeF 2s in terms of Poincaré canonical variables in Part II of this problem.  相似文献   

3.
The observed values of the time-derivatives of the spin or orbital frequency of pulsars are affected by their dynamical properties. We derive thorough analytical expressions for such dynamical contributions in terms of the Galactic coordinates, the proper motion, the pulsar distance, and the radial velocity. We find that the effects of the dynamical terms in the second-derivative of frequencies or parameters based on such second derivatives, e.g., braking index, are usually negligible. However, unique pulsars for which the effects of the dynamical terms are significant can exist. In particular, dynamical effects can make the magnitude of the observed value of the braking index to be in the order of thousand while the true value of it is close to the theoretically expected value three, especially if the pulsars lie close to the Galactic centre. Dynamics can also affect the value of the second derivative of the orbital frequency of a binary pulsar at the first decimal place. We also emphasize the fact that our expressions provide more accurate results than pre-existing approximate ones that exclude some of the terms. Comparison with a set of pulsars showed that the median value of the difference between the results obtained by our method and a pre-existing method is about 50 percent.  相似文献   

4.
In this part we calculate the secular and critical terms arising from the indirect part of the classical planetary Hamiltonian for Uranus and Neptune. We neglect in our expansions powers higher than the second in the eccentricity-inclination. Our required results, are expressed in terms of Poincaré variables.  相似文献   

5.
We review in this part the outline of a third-order general planetary theory established through Von Zeipel's method and in terms of Poincaré's canonical variables We consider our system to consist of the Sun as the primary body, one disturbed planet, and one disturbing planet.  相似文献   

6.
We present a method to construct a mapping for perturbed systems, in which the perturbations do not need to be conservative. We use a variation of Wisdom and Holman's method, where the dissipative term is placed together with the other perturbative terms. The method is applied for two dissipative systems: one including gas drag and the other including Poynting-Robertson drag. We compare the results with those obtained by Malhotra's mapping. Because the dissipative part in our method is treated as a regular perturbative term, there is no need for analytical developments of the nonconservative terms. This is a great advantage in itself and this also allows for a fast performance of the integrator.  相似文献   

7.
In this part we expand the indirect part of the planetary perturbing function by Smart's method, via Taylor's theorem. We neglect, in our expansion, terms of degree higher than the fourth with regard to the eccentricities and tangents of the inclinations.  相似文献   

8.
Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.  相似文献   

9.
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10.
We consider the possibility of low-mass primordial black holes being formed in terms of the inflationary theory of the early Universe. We found a condition on the reheating temperature under which the relic remnants of primordial black holes had been formed by now. These relic remnants may account for a part of the dark matter in our Universe.  相似文献   

11.
A solution of the Uranus-Neptune planetary canonical equations of motion through the Von Zeipel technique is presented. A unique determinging function which depends upon mixed canonical variables, reduces the 12 critical terms of the Hamiltonian to the set of its secular terms. The Poincaré canonical variables are used. We refer to a common fixed plane, and apply the Jacobi-Radau set of origins. In our expansion we neglected terms of power higher than the fourth with respect to the eccentricities and sines of the inclinations.  相似文献   

12.
We expand the principal part of the planetary disturbing function, by Smart's method, using Taylor's theorem. In our expansion we neglect terms of degree higher than the fourth in the eccentricities and tangents of the inclinations.Now at the JPL Pasadena, California.  相似文献   

13.
We describe an efficient method of calculating the radiation pressure resulting from spectral lines, including all the terms in the velocity gradient tensor. We apply this method to calculate the two-dimensional, time-dependent structure of winds from luminous discs. Qualitative features of our new models are very similar to those we calculated including only the dominant terms in the tensor. In particular, we find that models which displayed unsteady behaviour in our earlier paper are also unsteady with the new method, and gross properties of the winds, such as mass-loss rate and characteristic velocity, are not changed by the more accurate approach. The largest change caused by the new method is in the disc-wind opening angle: winds driven only by the disc radiation are more polar with the new method, whilst winds driven by the disc and central object radiation are typically more equatorial. In the closing discussion, we provide further insight into the way the geometry of the radiation field and consequent flow determine the time properties of the flow.  相似文献   

14.
We investigate the effects of weak gravitational lensing in the standard cold dark matter cosmology, using an algorithm that evaluates the shear in three dimensions. The algorithm has the advantage of variable softening for the particles, and our method allows the appropriate angular diameter distances to be applied to every evaluation location within each three-dimensional simulation box. We investigate the importance of shear in the distance–redshift relation, and find it to be very small. We also establish clearly defined values for the smoothness parameter in the relation, finding its value to be at least 0.83 at all redshifts in our simulations. From our results, obtained by linking the simulation boxes back to source redshifts of 4, we are able to observe the formation of structure in terms of the computed shear, and also note that the major contributions to the shear come from a very broad range of redshifts. We show the probability distributions for the magnification, source ellipticity and convergence, and also describe the relationships amongst these quantities for a range of source redshifts. We find a broad range of magnifications and ellipticities; for sources at a redshift of 4, 97.5 per cent of all lines of sight show magnifications up to 1.39 and ellipticities up to 0.23. There is clear evidence that the magnification is not linear in the convergence, as might be expected for weak lensing, but contains contributions from higher order terms in both the convergence and the shear. Our results for the one-point distribution functions are generally different from those obtained by other authors using two-dimensional (planar) approaches, and we suggest reasons for the differences. Our magnification distributions for sources at redshifts of 1 and 0.5 are also very different from the results used by other authors to assess the effect on the perceived value of the deceleration parameter, and we briefly address this question.  相似文献   

15.
We investigate the environments and clustering properties of starburst galaxies selected from the 2dF Galaxy Redshift Survey (2dFGRS) in order to determine which, if any, environmental factors play a role in triggering a starburst. We quantify the local environments, clustering properties and luminosity functions of our starburst galaxies and compare to random control samples. The starburst galaxies are also classified morphologically in terms of their broad Hubble type and evidence of tidal merger/interaction signatures. We find the starburst galaxies to be much less clustered on large (5–15 Mpc) scales compared to the overall 2dFGRS galaxy population. In terms of their environments, we find just over half of the starburst galaxies to reside in low to intermediate luminosity groups, and a further ∼30 per cent residing in the outskirts and infall regions of rich clusters. Their luminosity functions also differ significantly from that of the overall 2dFGRS galaxy population, with the sense of the difference being critically dependent on the way their star formation rates are measured. In terms of pin-pointing what might trigger the starburst, it would appear that factors relating to their local environment are most germane. Specifically, we find clear evidence that the presence of a near neighbour of comparable luminosity/mass within 20 kpc is likely to be important in triggering a starburst. We also find that a significant fraction (20–30 per cent) of the galaxies in our starburst samples have morphologies indicative of either an ongoing or a recent tidal interaction and/or merger. These findings notwithstanding, there remain a significant portion of starburst galaxies where such local environmental influences are not in any obvious way playing a triggering role, leading us to conclude that starbursts can also be internally driven.  相似文献   

16.
We explore the capability of a method of mapping the depth distribution of a hydrogen-rich layer in the top meter of Mars from the neutron currents measured by the Mars Odyssey Neutron Spectrometer. Assuming the soil can be modeled by two layers of known composition having different hydrogen contents, simulations allow an inversion of the neutron data into knowledge of depth and hydrogen content of the lower layer. The determination of these variables is sensitive to the hypothesis of chemical composition of the soil. We quantify this contribution to the uncertainty in the method first in terms of individual chemical elements and then in terms of macroscopic absorption cross sections. To minimize this source of error, an average composition was inferred from Mars Exploration Rover data. Possible compositions having a wide range of macroscopic absorption cross sections were used to evaluate the uncertainty associated with our calculations. We finally compare our results to ice table depth estimates predicted by two published theoretical models at locations where the composition is relatively well known. The fit is excellent in the southern high latitudes but questionable in the northern high latitudes. Possible explanations of these differences include the high geographical variations of the neutron currents relative to the spatial width of the response function of the instrument and the overly simple model we, of necessity, used for surface layering.  相似文献   

17.
We analyse the stability of a magnetized medium consisting of a neutral fluid and a fluid of charged particles, coupled to each other through a drag force and exposed to differential body forces (for example, as the result of radiation forces on one phase). We consider a uniform equilibrium and simple model input physics, but do not arbitrarily restrict the relative orientations of the magnetic field, slip velocity and wavevector of the disturbance. We find several instabilities and classify these in terms of wave resonances. We briefly apply our results to the structure of SiO maser regions appearing in the winds from late-type stars.  相似文献   

18.
In a previous paper, we have shown that the classical definition of E+A galaxies excludes a significant number of post-starburst galaxies. We suggested that analysing broad-band spectral energy distributions (SEDs) is a more comprehensive method to select and distinguish post-starburst galaxies than the classical definition of measuring equivalent widths of (Hδ) and [O  ii ] lines.
In this paper, we will carefully investigate this new method and evaluate it by comparing our model grid of post-starburst galaxies to observed E+A galaxies from the MORPHS catalogue.
In the first part, we investigate the UV-optical-NIR (near-infrared) SEDs of a large variety in terms of progenitor galaxies, burst strengths and time-scales of post-starburst models and compare them to undisturbed spiral, S0 and E galaxies as well as to galaxies in their starburst phase. In the second part, we compare our post-starburst models with the observed E+A galaxies in terms of Lick indices, luminosities and colours. We then use the new method of comparing the model SEDs with SEDs of the observed E+A galaxies.
We find that the post-starburst models can be distinguished from undisturbed spiral, S0 and E galaxies and galaxies in their starburst phase on the basis of their SEDs. It is even possible to distinguish most of the different post-starbursts by their SEDs. From the comparison with observations, we find that all observed E+A galaxies from the MORPHS catalogue can be matched by our models. However, only models with short decline time-scales for the star formation rate are possible scenarios for the observed E+A galaxies in agreement with our results from the first paper.  相似文献   

19.
We present a new general procedure for determining a given set of quantities. To this end, we define a certain statistic, which we call 'modified  χ2' (χ2M)  , because of its similarity to the standard  χ2  . The terms of this  χ2M  are made up of the fluctuations of an unbiased estimator of some statistical quantities and certain weights. Only the diagonal terms of the covariance matrix appear explicitly in our statistic, while the full covariance matrix (and not its inverse) is included implicitly in the calculation of the weights. Choosing these weights, we may obtain, through minimizing  χ2M  , the estimator that provides the minimum rms, either for those quantities or for the parameters on which these quantities depend. In this paper, we describe our method in the context of cosmic microwave background experiments, in order to obtain either the statistical properties of the maps or the cosmological parameters. The test here is constructed out of some estimator of the two-point correlation function at different angles. For the problem of one-parameter estimation, we show that our method has the same power as the maximum-likelihood method. We have also applied this method to Monte Carlo simulations of the COBE -DMR data, as well as to the actual 4-yr data, obtaining consistent results with previous analyses. We also provide a very good analytical approximation to the distribution function of our statistic, which could also be useful in other contexts.  相似文献   

20.
In this paper the first variational equations of motion about the triangular points in the elliptic restricted problem are investigated by the perturbation theories of Hori and Deprit, which are based on Lie transforms, and by taking the mean equations used by Grebenikov as our upperturbed Hamiltonian system instead of the first variational equations in the circular restricted problem. We are able to remove the explicit dependence of transformed Hamiltonian on the true anomaly by a canonical transformation. The general solution of the equations of motion which are derived from the transformed Hamiltonian including all the constant terms of any order in eccentricity and up to the periodic terms of second order in eccentricity of the primaries is given.  相似文献   

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