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1.
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   

2.
We compute the ultra-high energy (UHE) neutrino fluxes from plausible accreting supermassive black holes closely linking to the 377 active galactic nuclei (AGNs). They have well-determined black hole masses collected from the literature. The neutrinos are produced via simple or modified URCA processes, even after the neutrino trapping, in superdense proto-matter medium. The resulting fluxes are ranging from: (1) (quark reactions)— $J^{q}_{\nu\varepsilon}/(\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1})\simeq8.29\times 10^{-16}$ to 3.18×10?4, with the average $\overline{J}^{q}_{\nu\varepsilon}\simeq5.53\times 10^{-10}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ , where ε d ～10?12 is the opening parameter; (2) (pionic reactions)— $J^{\pi}_{\nu\varepsilon} \simeq0.112J^{q}_{\nu\varepsilon}$ , with the average $J^{\pi}_{\nu\varepsilon} \simeq3.66\times 10^{-11}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ ; and (3) (modified URCA processes)— $J^{URCA}_{\nu\varepsilon}\simeq7.39\times10^{-11} J^{q}_{\nu\varepsilon}$ , with the average $\overline{J}^{URCA}_{\nu\varepsilon} \simeq2.41\times10^{-20} \varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ . We conclude that the AGNs are favored as promising pure neutrino sources, because the computed neutrino fluxes are highly beamed along the plane of accretion disk, peaked at high energies and collimated in smaller opening angle θ～ε d .  相似文献   

3.
The quintessence dark energy model with a kinetic coupling to gravity within the Palatini formalism is studied in this paper. Two different coupling forms: $\hat{R}\partial^{\mu}\phi\partial_{\mu}\phi$ and $\hat {R}_{\mu\nu}\partial^{\mu}\phi\partial^{\nu}\phi$ are analyzed, respectively. We find that both the model with the $\hat{R}\partial^{\mu}\phi\partial_{\mu}\phi$ coupling and the one with the $\hat{R}_{\mu\nu}\partial^{\mu}\phi\partial^{\nu}\phi$ coupling can realize the phantom divide line crossing from phantom to quintessence at late time for its effective equation-of-state. Furthermore, the former can behave like phantom. These features are different from those found in the $\hat {R}\phi^{2}$ coupling case.  相似文献   

4.
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   

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.
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   

7.
We constrain holographic dark energy (HDE) with time varying gravitational coupling constant in the framework of the modified Friedmann equations using cosmological data from type Ia supernovae, baryon acoustic oscillations, cosmic microwave background radiation and X-ray gas mass fraction. Applying a Markov Chain Monte Carlo (MCMC) simulation, we obtain the best fit values of the model and cosmological parameters within 1σ confidence level (CL) in a flat universe as: $\varOmega_{b}h^{2}=0.0222^{+0.0018}_{-0.0013}$ , $\varOmega_{c}h^{2}=0.1121^{+0.0110}_{-0.0079}$ , $\alpha_{G}\equiv \dot{G}/(HG) =0.1647^{+0.3547}_{-0.2971}$ and the HDE constant $c=0.9322^{+0.4569}_{-0.5447}$ . Using the best fit values, the equation of state of the dark component at the present time w d0 at 1σ CL can cross the phantom boundary w=?1.  相似文献   

8.
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   

9.
We analyzed the luminosity-temperature-mass of gas (L X ?T?M g ) relations for a sample of 21 Chandra galaxy clusters. We used the standard approach (β?model) to evaluate these relations for our sample that differs from other catalogues since it considers galaxy clusters at higher redshifts (0.4<z<1.4). We assumed power-law relations in the form $L_{X} \sim(1 +z)^{A_{L_{X}T}} T^{\beta_{L_{X}T}}$ , $M_{g} \sim(1 + z)^{A_{M_{g}T}} T^{\beta_{M_{g}T}}$ , and $M_{g} \sim(1 + z)^{A_{M_{g}L_{X}}} L^{\beta_{M_{g}L_{X}}}$ . We obtained the following fitting parameters with 68 % confidence level: $A_{L_{X}T} = 1.50 \pm0.23$ , $\beta_{L_{X}T} = 2.55 \pm0.07$ ; $A_{M_{g}T} = -0.58 \pm0.13$ and $\beta_{M_{g}T} = 1.77 \pm0.16$ ; $A_{M_{g}L_{X}} \approx-1.86 \pm0.34$ and $\beta_{M_{g}L_{X}} = 0.73 \pm0.15$ , respectively. We found that the evolution of the M g ?T relation is small, while the M g ?L X relation is strong for the cosmological parameters Ω m =0.27 and Ω Λ =0.73. In overall, the clusters at high-z have stronger dependencies between L X ?T?M g correlations, than those for clusters at low-z. For most of galaxy clusters (first of all, from MACS and RCS surveys) these results are obtained for the first time.  相似文献   

10.
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   

11.
We analyzed 186 binary pulsars (BPSRs) in the magnetic field versus spin period (B-P) diagram, where their relations to the millisecond pulsars (MSPs) can be clearly shown. Generally, both BPSRs and MSPs are believed to be recycled and spun-up in binary accreting phases, and evolved below the spin-up line setting by the Eddington accretion rate ( $\dot{M}{\simeq}10^{18}~\mbox{g/s}$ ). It is noticed that most BPSRs are distributed around the spin-up line with mass accretion rate $\dot{M}=10^{16}~\mbox{g/s}$ and almost all MSP samples lie above the spin-up line with $\dot{M}\sim10^{15}~\mbox{g/s}$ . Thus, we calculate that a minimum accretion rate ( $\dot{M}\sim10^{15}~\mbox{g/s}$ ) is required for the MSP formation, and physical reasons for this are proposed. In the B-P diagram, the positions of BPSRs and their relations to the binary parameters, such as the companion mass, orbital period and eccentricity, are illustrated and discussed. In addition, for the seven BPSRs located above the limit spin-up line, possible causes are suggested.  相似文献   

12.
Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R n (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.  相似文献   

13.
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   

14.
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15.
Considering the host galaxy contribution, a spectral decomposition method is used to reanalyzed the archive data of optical spectra for a narrow line Seyfert 1 galaxy, NGC 4051. The light curves of the continuum f λ (5100 Å), and Hβ, He ii, Fe ii emission lines are given. We find strong flux correlations between line emissions of Hβ, He ii, Fe ii and the continuum f λ (5100 Å). These low-ionization lines (Hβ, Fe ii, He ii) have “inverse” intrinsic Baldwin effects. Using the methods of the cross-correlation function and the Monte Carlo simulation, we find the time delays, with respect to the continuum, are $3.45^{+12.0}_{-0.5}~\mbox{days}$ with the probability of 34 % for the intermediate component of Hβ, $6.45^{+13.0}_{-1.0}~\mbox{days}$ with the probability of 65 % for the intermediate component of He ii. From these intermediate components of Hβ and He ii, the calculated central black hole masses are $0.86^{+4.35}_{-0.33}\times 10^{6}$ and $0.82^{+3.12}_{-0.45}\times 10^{6}~M_{\odot }$ . We also find that the time delays for Fe ii are $9.7^{+3.0}_{-5.0}~\mbox{days}$ with the probability of 36 %, $8.45^{+1.0}_{-2.0}~\mbox{days}$ with the probability of 18 % for the total epochs and “subset 1” data, respectively. It seems that the Fe ii emission region is outside of the Hβ emission region.  相似文献   

16.
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   

17.
The restricted three-body problem (R3BP) possesses the property that some classes of doubly asymptotic (i.e., homoclinic or heteroclinic) orbits are limit members of families of periodic orbits, this phenomenon has been known as the “blue sky catastrophe” termination principle. A similar case occurs in the restricted four body problem for the collinear equilibrium point $L_{2}$ L 2 . In the restricted four body problem with primaries in a triangle relative equilibrium, we show that the same phenomenon observed in the R3BP occurs. We prove that there exists a critical value of the mass parameter $\mu _{b}$ μ b such that for $\mu =\mu _{b}$ μ = μ b a Hamiltonian Hopf bifurcation takes place. Moreover we show that for $\mu >\mu _{b}$ μ > μ b the stable and unstable manifolds of $L_{2}$ L 2 intersect transversally and the spectrum corresponds to a complex saddle. This proves that Henrard’s theorem applies at least for $\mu $ μ close to $\mu _{b}$ μ b . In particular there exists a family of periodic orbits having the homoclinic orbit as a limit.  相似文献   

18.
The radio tracking apparatus of the New Horizons spacecraft, currently traveling to the Pluto system where its arrival is scheduled for July 2015, should be able to reach an accuracy of 10 m (range) and 0.1  $\text{ mm } \text{ s }^{-1}$ mm s ? 1 (range-rate) over distances up to 50 au. This should allow to effectively constrain the location of a putative trans-Plutonian massive object, dubbed Planet X (PX) hereafter, whose existence has recently been postulated for a variety of reasons connected with, e.g., the architecture of the Kuiper belt and the cometary flux from the Oort cloud. Traditional scenarios involve a rock-ice planetoid with $m_\mathrm{X}\approx 0.7\,m_{\oplus }$ m X ≈ 0.7 m ⊕ at some 100–200 au, or a Jovian body with $m_\mathrm{X}\lesssim 5\,m_\mathrm{J}$ m X ? 5 m J at about 10,000–20,000 au; as a result of our preliminary sensitivity analysis, they should be detectable by New Horizons since they would impact its range at a km level or so over a time span 6 years long. Conversely, range residuals statistically compatible with zero having an amplitude of 10 m would imply that PX, if it exists, could not be located at less than about 4,500 au ( $m_\mathrm{X}=0.7\,m_{\oplus }$ m X = 0.7 m ⊕ ) or 60,000 au ( $m_\mathrm{X}=5\,m_\mathrm{J}$ m X = 5 m J ), thus making a direct detection quite demanding with the present-day technologies. As a consequence, it would be appropriate to rename such a remote body as Thelisto. Also fundamental physics would benefit from this analysis since certain subtle effects predicted by MOND for the deep Newtonian regions of our Solar System are just equivalent to those of a distant pointlike mass.  相似文献   

19.
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   

20.
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   

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