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1.
Chaos appears in various problems of Relativity and Cosmology. Here we discuss (a) the Mixmaster Universe model, and (b) the motions around two fixed black holes. (a) The Mixmaster equations have a general solution (i.e. a solution depending on 6 arbitrary constants) of Painlevé type, but there is a second general solution which is not Painlevé. Thus the system does not pass the Painlevé test, and cannot be integrable. The Mixmaster model is not ergodic and does not have any periodic orbits. This is due to the fact that the sum of the three variables of the system (α + β + γ) has only one maximum for τ = τm and decreases continuously for larger and for smaller τ. The various Kasner periods increase exponentially for large τ. Thus the Lyapunov Characteristic Number (LCN) is zero. The "finite time LCN" is positive for finite τ and tends to zero when τ → ∞. Chaos is introduced mainly near the maximum of (α + β + γ). No appreciable chaos is introduced at the successive Kasner periods, or eras. We conclude that in the Belinskii-Khalatnikov time, τ, the Mixmaster model has the basic characteristics of a chaotic scattering problem. (b) In the case of two fixed black holes M1 and M2 the orbits of photons are separated into three types: orbits falling into M1 (type I), or M2 (type II), or escaping to infinity (type III). Chaos appears because between any two orbits of different types there are orbits of the third type. This is a typical chaotic scattering problem. The various types of orbits are separated by orbits asymptotic to 3 simple unstable orbits. In the case of particles of nonzero rest mass we have intervals where some periodic orbits are stable. Near such orbits we have order. The transition from order to chaos is made through an infinite sequence of period doubling bifurcations. The bifurcation ratio is the same as in classical conservative systems. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

2.
As stars close to the galactic centre have short orbital periods it has been possible to trace large fractions of their orbits in the recent years. Previously the data of the orbit of the star S2 have been fitted with Keplerian orbits corresponding to a massive black hole (MBH) with a mass of MBH = 3–4 × 106M⊙ implying an insignificant cusp mass. However, it has also been shown that the central black hole resides in a ∼1″ diameter stellar cluster of a priori unknown mass. In a spherical potential which is neither Keplerian nor harmonic, orbits will precess resulting in inclined rosetta shaped trajectories on the sky. In this case, the assumption of non‐Keplerian orbits is a more physical approach. It is also the only approach through which cusp mass information can be obtained via stellar dynamics of the cusp members. This paper presents the first exemplary modelling efforts in this direction. Using positional and radial data of star S2, we find that there could exist an unobserved extended mass component of several 105M⊙ forming a so‐called ‘cusp’ centered on the black hole position. Considering only the fraction of the cusp mass Mequation/tex2gif-inf-4.gif within the apo‐center of the S2 orbit we find as an upper limit that Mequation/tex2gif-inf-6.gif/(MBH + Mequation/tex2gif-inf-9.gif) ≤ 0.05. A large extended cusp mass, if present, is unlikely to be composed of sub‐solar mass constituents, but could be explained rather well by a cluster of high M/L stellar remnants, which we find to form a stable configuration. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
We examine the disc-jet connection in stellar mass and supermassive black holes by investigating the properties of their compact emission in the hard X-ray and radio bands. We compile a sample of ∼100 active galactic nuclei with measured mass, 5 GHz core emission, and 2–10 keV luminosity, together with eight galactic black holes with a total of ∼50 simultaneous observations in the radio and X-ray bands. Using this sample, we study the correlations between the radio (LR) and the X-ray (LX) luminosity and the black hole mass (M). We find that the radio luminosity is correlated with both M and LX, at a highly significant level. We show how this result can be used to extend the standard unification by orientation scheme to encompass unification by mass and accretion rate.  相似文献   

4.
Empirical evidence for both stellar mass black holes (M •<102  M ⊙) and supermassive black holes (SMBHs, M •>105  M ⊙) is well established. Moreover, every galaxy with a bulge appears to host a SMBH, whose mass is correlated with the bulge mass, and even more strongly with the central stellar velocity dispersion σ c , the M •–σ relation. On the other hand, evidence for “intermediate-mass” black holes (IMBHs, with masses in the range 100–105 M ⊙) is relatively sparse, with only a few mass measurements reported in globular clusters (GCs), dwarf galaxies and low-mass AGNs. We explore the question of whether globular clusters extend the M •–σ relationship for galaxies to lower black hole masses and find that available data for globular clusters are consistent with the extrapolation of this relationship. We use this extrapolated M •–σ relationship to predict the putative black hole masses of those globular clusters where existence of central IMBH was proposed. We discuss how globular clusters can be used as a constraint on theories making specific predictions for the low-mass end of the M •–σ relation.  相似文献   

5.
We show that density spikes begin to form from dark matter particles around primordial black holes immediately after their formation at the radiation-dominated cosmological stage. This stems from the fact that in the thermal velocity distribution of particles there are particles with low velocities that remain in finite orbits around black holes and are not involved in the cosmological expansion. The accumulation of such particles near black holes gives rise to density spikes. These spikes are considerably denser than those that are formed later by the mechanism of secondary accretion. The density spikes must be bright gamma-ray sources. Comparison of the calculated signal from particle annihilation with the Fermi-LAT data constrains the present-day cosmological density parameter for primordial black holes with masses M BH ≥ 10?8 M ⊙ from above by values from ΩBH ≤ 1 to ΩBH ≤ 10?8, depending on MBH. These constraints are several orders of magnitude more stringent than other known constraints.  相似文献   

6.
The possibility of identifying some of Galactic gamma-ray sources as clusters of primordial black holes is discussed. The known scenarios of supermassive black hole formation indicate the multiple formation of lower-mass black holes. Our analysis demonstrates that due to Hawking evaporation the cluster of black holes with masses about 1015 g could be observed as a gamma-ray source. The total mass of typical cluster is ∼10 M⊙. Detailed calculations have been performed on the basis of specific model of primordial black hole formation.  相似文献   

7.
The X-ray spectral and timing properties of ultraluminous X-ray sources (ULXs) have many similarities with the very high state of stellar-mass black holes (power-law dominated, at accretion rates greater than the Eddington rate). On the other hand, their cool disk components, large characteristic inner-disk radii and low characteristic timescales have been interpreted as evidence of black hole masses ～1000 M ⊙ (intermediate-mass black holes). Here we re-examine the physical interpretation of the cool disk model, in the context of accretion states of stellar-mass black holes. In particular, XTE J1550–564 can be considered the missing link between ULXs and stellar-mass black holes, because it exhibits a high-accretion-rate, low-disk-temperature state (ultraluminous branch). On the ultraluminous branch, the accretion rate is positively correlated with the disk truncation radius and the bolometric disk luminosity, while it is anti-correlated with the peak temperature and the frequency of quasi-periodic-oscillations. Two prototypical ULXs (NGC?1313 X-1 and X-2) also seem to move along that branch. We use a phenomenological model to show how the different range of spectral and timing parameters found in the two classes of accreting black holes depends on both their masses and accretion rates. We suggest that ULXs are consistent with black hole masses ～50–100 M ⊙, moderately inefficiently accreting at ≈20 times Eddington.  相似文献   

8.
The hydrodynamics of stellar models in the tidal field of a massive black hole is calculated numerically under certain simplifying assumptions. It is found that solar type stars are totally disrupted only when falling toward a black hole whose mass does not exceed 106–107 M . Red giants lose their entire envelope for all black hole masses studied.Our findings strengthen the view that tidal disruption is not an important source of gas in AGN's.  相似文献   

9.
The present research paper discusses the derivation for the change in entropy of Non- spinning black holes with respect to the change in the radius of event horizon applying the first law of black hole mechanics ( $\delta M = \frac{\kappa}{8\pi} \delta A + \varOmega\delta J - \upsilon\delta Q$ ) with the relation for the change in entropy δS=8πMδM. When the work is further extended with proper operation, the entropy of black hole is obtained almost the same as the Bekenstein-Hawking entropy of black hole. This is the entirely new method to obtain the change in entropy of Non-spinning black holes w.r.t. the radius of event horizon and Hawking entropy of black hole. We have also calculated their values for different types of test non-spinning black holes having masses 5–20M ⊙ found in X-ray binaries (Narayan, gr-qc/0506078v1, 2005).  相似文献   

10.
Possible manifestations of small mass black holes (M BH<M ) in cosmic bodies (stars, millisecond pulsars, planets, etc.) are considered. The formation of millisecond pulsars in the early proposed pulsar's model goes onto a small black hole in the centre due to accretion of neutron star matter. Within the framework of a model under consideration, the following is predicted: millisecond pulsars withP min=0.5 ms, single optical and X-ray pulsars with the negative derivative derivative of period. Small black holes can be applied to make models of anomalies in planetary bodies (gravitational, heat, etc.). The vulcan model with radiation of a microblack hole in a magnetic void (M BH1015 g) as the source of energy is considered. At the Earth's surface, near a vulcan, the neutrino flow from a microblack hole is estimated.  相似文献   

11.
In this paper, the orbital dynamics of the gravitational field in Bardeen space-time are investigated. The equations of the particle’s orbital motion are given by solving the Lagrangian equation, and the stability and types of orbits are studied by means of analysing the effective potential of particles. Also, with the help of phase-plane method, the closed and non-closed orbits of test particle are analysed. We find that the stability and types of orbits in the Bardeen space-time are determined not only by the particles’ energy but also by the angular momentum. And for q=0.5M and b<3.3731M, absorbed by the black hole is the only fate of the test particle. We also find that the position of the innermost stable circular orbit of Bardeen black hole occurs at r min =5.5722M.  相似文献   

12.
We compare families of simple periodic orbits of test particles in the Newtonian and relativistic problems of two fixed centers (black holes). The Newtonian problem is integrable, while the relativistic problem is highly non-integrable.The orbits are calculated on the meridian plane through the fixed centersM 1 (atz=+1) andM 2 (atz=–1) for energies smaller than the escape energyE=1. We use prolate spheroidal coordinates (, , =const) and also the variables =cosh and =–cos . The orbits are inside a curve of zero velocity (CZV). The Newtonian orbits are also limited by an ellipse and a hyperbola, or by two eillipses. There are 3 main types of periodic orbits (1) elliptic type (around both centers), (2) hyperbolic-type, and (3) resonant-type.The elliptic type orbits are stable in the Newtonian case and both stable and unstable in the relativistic case. From the stable orbits bifurcate double period orbits both symmetric and asymmetric with respect to thez-axis. There are also higher order bifurcations. The hyperbolic-type orbits are unstable. The Newtonian resonant orbits are defined by the ratiot µ/t =n/m of oscillations along and during one period, and they are all marginally unstable. The corresponding relativistic orbits are stable, or unstable. The main families are figure eight orbits aroundM 1, or aroundM 2 (3/1 orbits); gamma, or inverse gamma orbits (4/2); higher resonant families 5/1,7/1,...,8/2,12/2,...;, more complicated orbits, like 5/3, and bifurcations from the above orbits. Satellite orbits aroundM 1, orM 2, and their bifurcations (e.g. double period) exist in the relativistic case but not in the Newtonian case. The characteristics of the various families are quite different in the Newtonian and the relativistic cases. The sizes of the orbits and their stabilities are also quite different in general. In the Appendix we study the various types of straight line orbits and prove that some subcases introduced by Charlier (1902) are impossible.  相似文献   

13.
We report three new or updated techniques for probing the parameters of active galaxies based on the masses of their central black holes MBH). First, we derived a near-IR analog of the bulge luminosity versus MBH relationship. The low scatter makes it a promising new tool to study the black hole demographics. Next, we present relations between MBH and the10 μm and 2-10 keV nuclear luminosity. They may help to study the MBH evolution over wide redshift ranges. Finally, we measured MBH in quasars from z ∼ 3.4 to z ∼ 0.3 to search directly for MBH growth. Surprisingly, we found no evidence for growth implying that the majority of quasar host galaxies have undergone their last major merger at z ≥ 3. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

14.
Small perturbations of spherical star clusters around massive black holes are studied. The presence of a black hole gives rise to peculiar distributions that have no stars with low angular momenta (falling into the so-called “loss cone”). The stability of such a distribution has been found to depend significantly on whether it monotonically increases with angular momentum L (from the loss cone up to L = L circ in circular orbits) or has a maximum at some intermediate L = L *. In the case of spherical systems under consideration, the loss-cone instability is shown to be possible only for nonmonotonic distributions.  相似文献   

15.
I use the fact that the radiation emitted by the accretion disk of supermassive black hole can heat up the surrounding gas in the protogalaxy to achieve hydrostatic equilibrium during the galaxy formation. The correlation between the black hole mass M BH and velocity dispersion σ thus naturally arises. The result generally agrees with empirical fittings from observational data, even with M BH ≤106 M ⊙. This model provides a clear picture on how the properties of the galactic supermassive black holes are connected with the kinetic properties of the galactic bulges.  相似文献   

16.
We consider a cosmological model in which part of the Universe, Ωh～10?5, is in the form of primordial black holes with masses of ～ 105 M ⊙. These primordial black holes were the centers for growing protogalaxies, which experienced multiple mergers with ordinary galaxies and with each other. The galaxy formation is accompanied by the merging and growth of central black holes in the galactic nuclei. We show that the recently discovered correlations between central black hole masses and galactic bulge parameters naturally arise in this scenario.  相似文献   

17.
We study the structure of chaos in a simple Hamiltonian system that does no have an escape energy. This system has 5 main periodic orbits that are represented on the surface of section by the points (1)O(0,0), (2)C 1,C 2(±y c, 0), (3)B 1,B 2(O,±1) and (4) the boundary . The periodic orbits (1) and (4) have infinite transitions from stability (S) to instability (U) and vice-versa; the transition values of are given by simple approximate formulae. At every transitionS U a set of 4 asymptotic curves is formed atO. For larger the size and the oscillations of these curves grow until they destroy the closed invariant curves that surroundO, and they intersect the asymptotic curves of the orbitsC 1,C 2 at infinite heteroclinic points. At every transitionU S these asymptotic curves are duplicated and they start at two unstable invariant points bifurcating fromO. At the transition itself the asymptotic curves fromO are tangent to each other. The areas of the lobes fromO increase with ; these lobes increase even afterO becomes stable again. The asymptotic curves of the unstable periodic orbits follow certain rules. Whenever there are heteroclinic points the asymptotic curves of one unstable orbit approach the asymptotic curves of another unstable orbit in a definite way. Finally we study the tangencies and the spirals formed by the asymptotic curves of the orbitsB 1,B 2. We find indications that the number of spiral rotations tends to infinity as . Therefore new tangencies between the asymptotic curves appear for arbitrarily large . As a consequence there are infinite new families of stable periodic orbits that appear for arbitrarily large .  相似文献   

18.
We propose a classification of supermassive black holes (SMBHs) based on their efficiency in the conversion of infalling mass in emitted radiation. We use a theoretical model that assumes a conservation of angular momentum between the gas falling inside the hole and the photons emitted outwards, and suggests the existence of the scaling relation M•‐Reσ3, where M• is the mass of the central SMBH, whereas Re and σ are the effective radius and velocity dispersion of the host galaxies (bulges), respectively. We apply our model on a data set of 57 galaxies of different morphological types and with M• measurements, obtained through the analysis of Spitzer /IRAC 3.6‐µ m images. In order to find the best fit of the corresponding scaling law, we use the FITEXY routine to perform a least‐squares regression of M• on Reσ3 for the considered sample of galaxies. Our analysis shows that the relation is tight and our theoretical model allows to easily estimate the efficiency of mass conversion into radiation of the central SMBHs. Finally we propose a new appealing way to classify the SMBHs in terms of this parameter. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

19.
We consider the possibility of detecting intermediate-mass (103–104 M ⊙) black holes, whose existence at the centers of globular clusters is expected from optical and infrared observations, using precise pulse arrival timing for the millisecond pulsars in globular clusters known to date. For some of these pulsars closest to the cluster centers, we have calculated the expected delay times of pulses as they pass in the gravitational field of the central black hole. The detection of such a time delay by currently available instruments for the known pulsars is shown to be impossible at a black hole mass of 103 M ⊙ and very problematic at a black hole mass of 104 M ⊙. In addition, the signal delay will have a negligible effect on the pulsar periods and their first derivatives compared to the current accuracy of their measurements.  相似文献   

20.
In the framework of ‘microscopic’ theory of black holes (J. Phys. Soc. Jpn. Suppl. B 70, 84, 2001; Astrophys. USSR 4, 659, 1996; 35, 335, 1991, 33, 143, 1990, 31, 345, 1989a; Astrophys. Space Sci. 1, 1992; Dokl. Akad. Nauk USSR 309, 97, 1989b), and references therein, we address the ‘pre-radiation time’ (PRT) of neutrinos from black holes, which implies the lapse of time from black hole’s birth till radiation of an extremely high energy neutrinos. For post-PRT lifetime, the black hole no longer holds as a region of spacetime that cannot communicate with the external universe. We study main features of spherical accretion onto central BH and infer a mass accretion rate onto it, and, further, calculate the resulting PRT versus bolometric luminosity due to accretion onto black hole. We estimate the PRTs of AGN black holes, with the well-determined masses and bolometric luminosities, collected from the literature by Woo Jong-Hak and Urry (Astrophys. J. 579, 530, 2002) on which this paper is partially based. The simulations for the black holes of masses M BH ≃(1.1⋅106 ÷4.2⋅109) M ⊙ give the values of PRTs varying in the range of about T BH ≃(4.3⋅105 ÷5.6⋅1011) yr. The derived PRTs for the 60 AGN black holes are longer than the age of the universe (∼13.7 Gyr) favored today. At present, some of remaining 174 BHs may radiate neutrinos. However, these results would be underestimated if the reservoir of gas for accretion in the galaxy center is quite modest, and no obvious way to feed the BHs with substantial accretion.  相似文献   

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