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1.
Using a new approach, we have obtained a formula for calculating the rotation period and radius of planets. In the ordinary gravitomagnetism the gravitational spin (S) orbit (L) coupling, $\vec{L}\cdot\vec{S}\propto L^{2}$ , while our model predicts that $\vec{L}\cdot\vec{S}\propto\frac{m}{M}L^{2}$ , where M and m are the central and orbiting masses, respectively. Hence, planets during their evolution exchange L and S until they reach a final stability at which MS∝mL, or $S\propto\frac{m^{2}}{v}$ , where v is the orbital velocity of the planet. Rotational properties of our planetary system and exoplanets are in agreement with our predictions. The radius (R) and rotational period (D) of tidally locked planet at a distance a from its star, are related by, $D^{2}\propto\sqrt{\frac{M}{m^{3}}}R^{3}$ and that $R\propto\sqrt{\frac {m}{M}}a$ .  相似文献   

2.
The analytical techniques of the Nekhoroshev theorem are used to provide estimates on the coefficient of Arnold diffusion along a particular resonance in the Hamiltonian model of Froeschlé et al. (Science 289:2108–2110, 2000). A resonant normal form is constructed by a computer program and the size of its remainder ||R opt || at the optimal order of normalization is calculated as a function of the small parameter ${\epsilon}$ . We find that the diffusion coefficient scales as ${D \propto ||R_{opt}||^3}$ , while the size of the optimal remainder scales as ${||R_{opt}|| \propto {\rm exp}(1/\epsilon^{0.21})}$ in the range ${10^{-4} \leq \epsilon \leq 10^{-2}}$ . A comparison is made with the numerical results of Lega et al. (Physica D 182:179–187, 2003) in the same model.  相似文献   

3.
We obtain an approximate solution $\tilde{E}=\tilde{E}(e,M)$ of Kepler’s equation $E-e\sin (E)=M$ for any $e\in [0,1)$ and $M\in [0,\pi ]$ . Our solution is guaranteed, via Smale’s $\alpha $ -theory, to converge to the actual solution $E$ through Newton’s method at quadratic speed, i.e. the $n$ -th iteration produces a value $E_n$ such that $|E_n-E|\le (\frac{1}{2})^{2^n-1}|\tilde{E}-E|$ . The formula provided for $\tilde{E}$ is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near $e=1$ and $M=0$ , where a single cubic root is used. We also show that the root operation is unavoidable, by proving that no approximate solution can be computed in the entire region $[0,1)\times [0,\pi ]$ if only rational functions are allowed in each branch.  相似文献   

4.
This paper deals with the existence of libration points and their linear stability when the more massive primary is radiating and the smaller is an oblate spheroid. Our study includes the effects of oblateness of $\bar{J}_{2i}$ (i=1,2) with respect to the smaller primary in the restricted three-body problem. Under combining the perturbed forces that were mentioned before, the collinear points remain unstable and the triangular points are stable for 0<μ<μ c , and unstable in the range $\mu_{c} \le\mu\le\frac{1}{2}$ , where $\mu_{c} \in(0,\frac{1}{2})$ , it is also observed that for these points the range of stability will decrease. The relations for periodic orbits around five libration points with their semimajor, semiminor axes, eccentricities, the frequencies of orbits and periods are found, furthermore for the orbits around the triangular points the orientation and the coefficients of long and short periodic terms also are found in the range 0<μ<μ c .  相似文献   

5.
Using γ-ray data detected by Fermi Large Area Telescope (LAT) and multi-wave band data for 35 TeV blazars sample, we have studied the possible correlations between different broad band spectral indices ( $\alpha_{\rm r.ir}$ , $\alpha_{\rm{r.o}}$ , $\alpha_{\rm r.x}$ , $\alpha_{\rm r.\gamma}$ , $\alpha_{\rm{ir.o}}$ , $\alpha_{\rm ir.x}$ , $\alpha_{\rm ir.\gamma}$ , $\alpha_{\rm o.x}$ , $\alpha_{\rm o.\gamma}$ , $\alpha_{\rm r.x}$ , $\alpha_{\rm x.\gamma}$ ) in all states (average/high/low). Our results are as follows: (1) For our TeV blazars sample, the strong positive correlations were found between $\alpha_{\rm r.ir}$ and $\alpha_{\rm{r.o}}$ , between $\alpha_{\rm r.ir}$ and $\alpha_{\rm r.x}$ , between $\alpha_{\rm r.ir}$ and $\alpha_{\rm r.\gamma}$ in all states (average/high/low); (2) For our TeV blazars sample, the strong anti-correlations were found between $\alpha_{\rm r.ir}$ and $\alpha_{\rm x.\gamma}$ , between $\alpha_{\rm{r.o}}$ and $\alpha_{\rm ir.\gamma}$ , between $\alpha_{\rm{r.o}}$ and $\alpha_{\rm o.\gamma}$ , between $\alpha_{\rm{r.o}}$ and $\alpha_{\rm x.\gamma}$ , between $\alpha_{\mathrm{ir.o}}$ and $\alpha_{\rm o.\gamma}$ , between $\alpha_{\rm r.x}$ and $\alpha_{\rm x.\gamma}$ , between $\alpha_{\rm ir.x}$ and $\alpha_{\rm x.\gamma}$ in all states (average/high/low). The results suggest that the synchrotron self-Compton radiation (SSC) is the main mechanism of high energy γ-ray emission and the inverse Compton scattering of circum-nuclear dust is likely to be a important complementary mechanism for TeV blazars. Our results also show that the possible correlations vary from state to state in the same pair of indices, Which suggest that there may exist differences in the emitting process and in the location of the emitting region for different states.  相似文献   

6.
The influence of free static spherically symmetric quintessence on particle motion in the Schwarzschild-quintessence space-time has been studied by numerical calculation. In the Schwarzschild space-time, the particle motion can be determined by an effective potential. However, this potential is dependent on the quintessence’s state parameter w q . We find that when the quintessence’s state parameter w q is in the range of $[-\frac{1}{3},0]$ , the massive particle’s motion is just like that in the Schwarzschild space-time. And when $-1\leqslant w_{q}<-\frac{1}{3}$ , a maximum unstable circular orbit exists for every L, and no matter how small L is, the scattering state exists, which leads to the accelerating expansion of our universe. The exists of the maximum orbit can even explain why galaxies is in a ball.  相似文献   

7.
Magneto-curvature stresses could deform magnetic field lines giving rise to back reaction and restoring magnetic stresses (Tsagas in Phys. Rev. Lett., 2001). Barrow and Tsagas (Phys. Rev. D, 2008) have shown that in Friedman universe the expansion slows down in its spatial section of negative Riemann curvature. Earlier, Chicone and Latushkin (Proc. Am. Math. Soc. 125(11):3391, 1995) proved that fast dynamos in compact 2D manifold implies negatively constant Riemannian curvature. Here one applies the Barrow-Tsagas ideas to cosmic dynamos of negative curvature. Fast dynamo, covariant stretching of Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection term on dynamo equations (Clarkson and Marklund in Mon. Not. R. Astron. Soc., 2005) is considered. In advection absence, slow dynamos are also obtained. It is shown the viscous and restoring forces on stretching particles decrease, as magnetic rates increase. From COBE data ( $\frac{{\delta}B}{B}\approx{10^{-5}}$ ), one is able to compute the stretching $\frac{{\delta}V^{y}}{V^{y}}=1.5\frac{{\delta}B}{B}\approx{1.5{\times}10^{-5}}$ . Zeldovich et al. have computed the maximum magnetic growth rate as γ max ≈8.0×10?1 t ?1. From COBE data a lower growth rate as γ COBE ≈6.0×10?6 t ?1, is well-within Zeldovich et al estimate. Instead of Harrison value $B\approx{t^{\frac{4}{3}}}$ one obtains a lower primordial field B≈10?6 t which yields B≈10?6 G at 1 s Big Bang time.  相似文献   

8.
In this work, we explore a sample of 362 flat-spectrum radio quasars (FSRQs) to investigate the jet formation. We find that the fundamental plane for our FSRQs can be expressed as $L_{\rm 5~GHz}\propto M_{\rm bh}^{-0.19}L_{\rm 2~keV}^{1.08}$ . We also find that the 5?GHz luminosities are tightly related to both black hole mass and Eddington ratio, which is established as $L_{\rm 5~GHz}\propto M_{\rm bh}^{0.67}(L_{\rm bol}/ L_{\rm EDD})^{1.32}$ .  相似文献   

9.
We investigate the dynamics of two satellites with masses $\mu _s$ and $\mu '_s$ orbiting a massive central planet in a common plane, near a first order mean motion resonance $m+1{:}m$ (m integer). We consider only the resonant terms of first order in eccentricity in the disturbing potential of the satellites, plus the secular terms causing the orbital apsidal precessions. We obtain a two-degrees-of-freedom system, associated with the two critical resonant angles $\phi = (m+1)\lambda ' -m\lambda - \varpi $ and $\phi '= (m+1)\lambda ' -m\lambda - \varpi '$ , where $\lambda $ and $\varpi $ are the mean longitude and longitude of periapsis of $\mu _s$ , respectively, and where the primed quantities apply to $\mu '_s$ . We consider the special case where $\mu _s \rightarrow 0$ (restricted problem). The symmetry between the two angles $\phi $ and $\phi '$ is then broken, leading to two different kinds of resonances, classically referred to as corotation eccentric resonance (CER) and Lindblad eccentric Resonance (LER), respectively. We write the four reduced equations of motion near the CER and LER, that form what we call the CoraLin model. This model depends upon only two dimensionless parameters that control the dynamics of the system: the distance $D$ between the CER and LER, and a forcing parameter $\epsilon _L$ that includes both the mass and the orbital eccentricity of the disturbing satellite. Three regimes are found: for $D=0$ the system is integrable, for $D$ of order unity, it exhibits prominent chaotic regions, while for $D$ large compared to 2, the behavior of the system is regular and can be qualitatively described using simple adiabatic invariant arguments. We apply this model to three recently discovered small Saturnian satellites dynamically linked to Mimas through first order mean motion resonances: Aegaeon, Methone and Anthe. Poincaré surfaces of section reveal the dynamical structure of each orbit, and their proximity to chaotic regions. This work may be useful to explore various scenarii of resonant capture for those satellites.  相似文献   

10.
S.-X. Chen  B. Li  L.-D. Xia  Y.-J. Chen  H. Yu 《Solar physics》2014,289(5):1663-1681
Fundamental standing modes and their overtones play an important role in coronal seismology. We examine the effects of a significant field-aligned flow on standing modes that are supported by coronal loops, which are modeled here as cold magnetic slabs. Of particular interest are the period ratios of the fundamental to its (n?1)th overtone [P 1/nP n ] for kink and sausage modes, and the threshold half-width-to-length ratio for sausage modes. For standing kink modes, the flow significantly reduces P 1/nP n in general, the effect being particularly strong for higher n and weaker density contrast [ $\rho_{0}/\rho_{\rm e}$ ] between loops and their surroundings. That said, even when $\rho_{0}/\rho_{\rm e}$ approaches infinity, this effect is still substantial, reducing the minimal P 1/nP n by up to 13.7?% (24.5?%) for n=2 (n=4) relative to the static case, when the Alfvén Mach number [M A] reaches 0.8, where M A measures the loop flow speed in units of the internal Alfvén speed. Although it is not negligible for standing sausage modes, the flow effect in reducing P 1/nP n is not as strong. However, the threshold half-width-to-length ratio is considerably higher in the flowing case than in its static counterpart. For $\rho_{0}/\rho_{\rm e}$ in the range [9,1024] and M A in the range [0,0.5], an exhaustive parameter study yields that this threshold is well fitted by $(d/L)_{\rm cutoff, fit} = \frac{1}{2}\sqrt{\frac{1}{\rho_{0}/\rho_{\rm e}-1}} \exp (3.7 M_{\mathrm{A}}^{2} )$ , which involves the two parameters in a simple way. This allows one to analytically constrain the combination $(\rho_{0}/\rho_{\rm e}, M_{\mathrm {A}})$ for a loop with a known width-to-length ratio when a standing sausage oscillation is identified. It also allows one to examine the idea of partial sausage modes in more detail, and the flow is found to significantly reduce the spatial extent where partial modes are allowed.  相似文献   

11.
We study the effects of winds on advection dominated accretion flows in the presence of a global magnetic field under a self-similar treatment. The disk gas is assumed to be isothermal. For a steady state structure of such accretion flows a set of self similar solutions are presented. We consider the wind in a general magnetic field with three components (r,φ,z) in advection-dominated accretion flows. The mass-accretion rate $\dot{M}$ decreases with radius r as $\dot{M}\propto r^{s+1/2}$ , where s is an arbitrary constant. We will see, by increasing the wind parameter s, radial and rotational velocities increase.  相似文献   

12.
A statistical study is carried out on the photospheric magnetic nonpotentiality in solar active regions and its relationship with associated flares. We select 2173 photospheric vector magnetograms from 1106 active regions observed by the Solar Magnetic Field Telescope at Huairou Solar Observing Station, National Astronomical Observatories of China, in the period of 1988??C?2008, which covers most of the 22nd and 23rd solar cycles. We have computed the mean planar magnetic shear angle ( $\overline{\Delta\phi}$ ), mean shear angle of the vector magnetic field ( $\overline{\Delta\psi}$ ), mean absolute vertical current density ( $\overline{|J_{z}|}$ ), mean absolute current helicity density ( $\overline{|h_{\mathrm{c}}|}$ ), absolute twist parameter (|?? av|), mean free magnetic energy density ( $\overline{\rho_{\mathrm{free}}}$ ), effective distance of the longitudinal magnetic field (d E), and modified effective distance (d Em) of each photospheric vector magnetogram. Parameters $\overline{|h_{\mathrm{c}}|}$ , $\overline{\rho_{\mathrm{free}}}$ , and d Em show higher correlations with the evolution of the solar cycle. The Pearson linear correlation coefficients between these three parameters and the yearly mean sunspot number are all larger than 0.59. Parameters $\overline {\Delta\phi}$ , $\overline{\Delta\psi}$ , $\overline{|J_{z}|}$ , |?? av|, and d E show only weak correlations with the solar cycle, though the nonpotentiality and the complexity of active regions are greater in the activity maximum periods than in the minimum periods. All of the eight parameters show positive correlations with the flare productivity of active regions, and the combination of different nonpotentiality parameters may be effective in predicting the flaring probability of active regions.  相似文献   

13.
We propose a relativistic model for: quintessence stars with the combination of an anisotropic pressure corresponding to normal matter and a quintessence dark energy having a characteristic parameter ω q such that $-1<\omega_{q}< -\frac{1}{3}$ . We discuss various physical features of the model and show that the model satisfies all the regularity conditions and can provide stable equilibrium configurations.  相似文献   

14.
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15.
Long-slit grating spectrometers in scanning mode and Fabry–Perot interferometers as tunable filters are commonly used to perform integral wide-field spectroscopy on extended astrophysical objects as HII regions and nearby galaxies. The goal of this paper is to demonstrate, by comparison, through a thorough review of the imaging Fourier transform spectrometer (IFTS) properties, that this instrument represents another interesting solution. After a brief recall of the performances, regarding FOV and spectral resolution, of the grating spectrometer, without and with integral field units (IFU), and of the imaging Fabry–Perot, it is demonstrated that for an IFTS the product of the maximum resolution R by the entrance beam étendue U is equal to $2.6\,N\times S_I$ with $N\,\times \,N$ the number of pixels of the detector array and S $_I$ the area of the interferometer beamsplitter. As a consequence, the IFTS offers the most flexible choice of field size and spectral resolution, up to high values for both parameters. It also presents on a wide field an important multichannel advantage in comparison to integral field grating spectrometers, even with multiple IFUs. To complete, the few astronomical IFTSs, built behind ground-based telescopes and in space, for the visible range up to the sub-millimetric domain, are presented. Through two wide-field IFTS projects, one in the visible, the other one in the mid-infrared, the question is addressed of the practical FOV and resolution limits, set by the optical design of the instrument, which can be achieved. Within the 0.3 to $\sim $ 2.5 $\upmu$ m domain, a Michelson interferometer with wide-field diopric collimators provides the easiest solution. This design is illustrated by a $11^{\prime}\times 11^{\prime}$ -field IFTS in the 0.35–0.90 $\upmu$ m range around an off-axis interferometer, called SITELLE, proposed for the 3.6-m CFH Telescope. At longer wavelengths, an all-mirror optics is required, as studied for a spaceborne IFTS, H2EX, for the 8–29 $\upmu$ m range, a $20^{\prime} \times 20^{\prime}$ field, and a high resolution of $\simeq 3\times 10^4$ at 10 $\upmu$ m. To comply with these characteristics, the interferometer is designed with cat’s eye retroreflectors. In the same domain and up to the far infrared, if the instrument aims only at a low spectral resolution (few thousands) and a smaller field (few arcmins $^2$ ), roof-top or corner cube mirrors, as for the IFTS SPIRE on the Herschel space telescope, are usable. At last, perspectives are opened, behind an ELT in the visible and the near infrared with the SITELLE optical combination, in the 2–5 $\upmu$ m on the Antarctic plateau or in space up to longer wavelengths, with the H2EX design, to provide the missing capability of global high spectral resolution studies of extended sources, from comets to distant galaxy clusters.  相似文献   

16.
In a cosmological model developed by the author in previous articles the universe starts in a geometrical phase transition in Minkowski space. Here the source of the gravitational field is a Higgs-like scalar field $\bar{\phi}$ . A relation of this cosmological field $\bar{\phi}$ with the Higgs-field ? H in the gauge theory of electroweak interaction is established. This relation leads to two dimensionless constants. One of them is interpreted as a characteristic constant of the phase transition and is connected with the volume of huge bubbles of open universes.  相似文献   

17.
In this paper we give a short analytical proof of the inequalities proved by Albouy–Moeckel through computer algebra, in the cases $n=5$ and $n=6$ . These inequalities guarantee that, in the $n$ -body problem, the family of mass vectors making a given collinear configuration a central configuration is 2-dimensional. The induction techniques here may be used to prove the inequalities for general $n$ with more subtle estimation but currently the inequalities still remains unproved for $n\ge 7$ .  相似文献   

18.
A popular model of a cometary plasma is hydrogen (H+) with positively charged oxygen (O+) as a heavier ion component. However, the discovery of negatively charged oxygen (O?) ions enables one to model a cometary plasma as a pair-ion plasma (of O+ and O?) with hydrogen as a third ion constituent. We have, therefore, studied the stability of the ion-acoustic wave in such a pair-ion plasma with hydrogen and electrons streaming with velocities $V_{d\mathrm{H}^{+}}$ and V de , respectively, relative to the oxygen ions. We find the calculated frequency of the ion-acoustic wave with this model to be in good agreement with the observed frequencies. The ion-acoustic wave can also be driven unstable by the streaming velocity of the hydrogen ions. The growth rate increases with increasing hydrogen density $n_{\mathrm{H}^{+}}$ , and streaming velocities $V_{d\mathrm{H}^{+}}$ and V de . It, however, decreases with increasing oxygen ion densities $n_{\mathrm{O}^{+}}$ and $n_{\mathrm{O}^{-}}$ .  相似文献   

19.
In the present investigation, Electron acoustic solitons in a plasma consisting of cold electrons, superthermal hot electrons and stationary ions are studied. The basic properties of small but finite amplitude solitary potential structures that may exist in a given plasma system have been investigated theoretically using reductive perturbation technique. It has been found that the profile of electron acoustic solitary wave structures is very sensitive to relative hot electron density, $\alpha(=\frac{n_{h0}}{n_{c0}})$ , temperature of hot to cold electrons, $\theta(=\frac{T_{h}}{T_{c}})$ and the spectral index κ. The implications of the present study may be applied to explain some features of large amplitude localized structures that may occur in the plasma sheet boundary layer.  相似文献   

20.
The number of equivalence classes of central configurations of $n \le 4$ bodies of positive mass is known to be finite, but it remains to be shown if this is true for $n \ge 5$ . By allowing one mass to be negative, Gareth Roberts constructed a continuum of inequivalent planar central configurations of $n = 5$ bodies. We reinterpret Roberts’ example and generalize the construction of his continuum to produce a family of continua of central configurations, each with a single negative mass. These new continua exist in even dimensional spaces $\mathbb R ^k$ for $k \ge 4$ .  相似文献   

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