Formation of Gyrs old black holes in the centers of galaxies within the Lema?tre–Tolman model

In this article we present a model of formation of a galaxy with a black hole in the center. It is based on the Lema?tre–Tolman solution and is a refinement of an earlier model. The most important improvement is the choice of the interior geometry of the black hole allowing for the formation of Gyrs old black holes. Other refinements are the use of an arbitrary Friedmann model as the background (unperturbed) initial state and the adaptation of the model to an arbitrary density profile of the galaxy. Our main interest was the M87 galaxy (NGC 4486), which hosts a supermassive black hole of mass 3.2 × 10⁹ M⊙. It is shown that for this particular galaxy, within the framework of our model and for the initial state being a perturbation of the ΛCDM model, the age of the black hole can be up to 12.7 Gyrs. The dependence of the model on the chosen parameters at the time of last scattering was also studied. The maximal age of the black hole as a function of the Ω _m and Ω_Λ parameters for the M87 galaxy can be 3.717 or 12.708 Gyr.     

The SMBH mass versus <Emphasis Type="Italic">M</Emphasis><Subscript>G</Subscript><Emphasis Type="Italic">σ</Emphasis><Superscript>2</Superscript> relation: a comparison between real data and numerical models

The relation between the mass of supermassive black holes located in the center of the host galaxies and the kinetic energy of random motions of the corresponding bulges can be reinterpreted as an age–temperature diagram for galaxies. This relation fits the experimental data better than the M _•−M _G, M _•−L _G, and M _•−σ laws. The validity of this statement has been confirmed by using three samples extracted from different catalogues of galaxies. In the framework of the ΛCDM cosmology our relation has been compared with the predictions of two galaxy formation models based on the Millennium Simulation.     

Estimate of the black-hole mass in NGC 6814 from a relativistic accretion disk scenario

Summary By using a fully relativistic model for the spectral line produced by a Keplerian disk orbiting a Schwarzschild black hole, we study the temporal behaviour of the line intensity in response to a continuum variation at an extended central source. We compare our results with the observed properties of the Seyfert galaxy NGC 6814, whose X-ray flux has been observed to decrease by a factor of two in ≈ 50 s, while the iron line intensity variations lag continuum variations by 250 s, at the most. Taking the stationary values of the iron line centroid energy and width, and assuming that the line comes from high-ionisation stages of iron (as several indications suggest) we derive that the inner radius of the line-emitting region is between 6 and 30r _g (r _g =GM/c ²), the inclination is ≤40°, while the mass of the central object is constrained to 8·10⁴ L ₄₃<M<3.9·10⁶ M _⊙(L ₄₃ is the accretion luminosity in units of 10⁴³ erg s⁻¹). Paper presented at the 6th Cosmic Physics National Conference, Palermo, 3–7 November 1992. Affiliated to ICRA.     

Gravity waves accompanying supernova explosions

Gravitational radiation arising during the formation of a protoneutron star is studied. Here it is mainly large-scale nonuniformities that develop inside the star. The entropy and density profiles of such nonuniformities resemble the “mushroom cloud” of a nuclear explosion. A bubble of hot neutron matter floats to the surface of the star, like the “mushroom cloud” of an explosion in the earth’s atmosphere. Depending on the symmetry of the problem, from two to six bubbles can float upward at the same time. The characteristic masses of such bubbles are 0.01M _⊗ and the radial velocities reach ∼0.1c. The energy radiated in the form of gravitational waves in one cycle of bubbles floating to the surface is ∼10⁻² M _⊗ c ²−10⁻¹⁰ M _⊗ c ². Such cycles occur repeatedly as the neutron star cools. This phase can last up to seconds. The total energy radiated in the form of gravitational radiation can reach 10⁻¹ M _⊗ c ². Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 817–822 (25 December 1996)     

Chandra observations of the H2O megamaser galaxy Mrk1210

We present the first Chandra X-ray observations of the H₂O megamaser galaxy Mrk1210 (UGC4203), a Seyfert 2 galaxy at an approximate distance of D ∼ 57.6 Mpc. The Chandra X-ray image, with by far the highest angular resolution (∼1″), displays an unresolved compact core toward the nuclear region of Mrk1210. Comparisons with the previous X-ray observations in the nuclear emission and the spectral shape indicate a fairly stable phase between 2001 (BeppoSAX and XMM-Newton) and 2004 (Chandra) after a dramatic variation since 1995 (ASCA). The best-fit model of Chandra X-ray spectrum consists of two components. The soft scattered component can be best fitted by a moderately absorbed power-law model adding a spectral line at ∼0.9 keV (possibly a Ne-Kα fluorescent line), while the hard nuclear component can be well reproduced by a heavily absorbed power-law model (N _H ∼ 2×10²³ cm⁻²) with an additional line at ∼6.19 keV (close to the Fe-Kα fluorescent line). The derived absorption-corrected X-ray luminosity implies that the dramatic variation of spectral properties is caused by significant changes of the absorbing column density along the line-of-sight, while the intrinsic nuclear X-ray luminosity remains stable. In this case, the absorbers should be anisotropic and its size can be constrained to be less than 0.0013 pc. In addition, we also estimate the mass of central engine, the disk radius and the accretion rate of the accretion disk to be 10^7.12±0.31 M _⊙, ∼1 pc and 0.006, respectively. Supported by the National Natural Science Foundation of China (Grant No. 10633010) and the Natural Science Foundation of Guangdong Province, China (Grant No. 8451009101001047) Recommended by Zhou YouYuan     

Black holes associated with galaxies

A small and a large black hole are naturally associated with a galaxy of total massM and spherical halo radiusR. Also of massM, the large black hole is a spatial contraction of the galaxy down to its Schwarzschild radius,r r, with=2GM/c ²R, whereG/c ²=4.78×10^–17 kpc/M is Newton's gravitational constant divided by the speed of light squared. The small black hole is ther r contraction of the large hole, i.e., the iterated double contraction of the galaxy itself, with the resulting massm=M=2GM ²/c²R. In the case of the Milky Way (M=7.0×10¹¹ M andR=15 kpc) the latter equation for the small black hole mass yieldsm=3.1×10⁶ M , which is close to the observed value for the mass of the black hole at the center of the Milky Way. Black holes of the small type may evolve to the large by mass accretion, perhaps during a quasar phase. Vast regions of the universe may in fact be populated by large black holes—missing mass—which validates the cosmological principle and effects the closure of the universe.     

Entropy function approach to charged BTZ black hole

We find solution to the metric function f(r) = 0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M _e (Q) = Q ²(1 − ln Q ²). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS₂ × S¹ represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald’s Noether formalism to reproduce the entropy of the extremal charged BTZ black hole without normalization when using the dilaton gravity approach.     

Constraints on Vector Unparticle Physics from Cosmic Censorship

Vector unparticle couplings to standard model fields produce repulsive corrections to gravity. From a general relativistic perspective, this leads to an effective Reissner-Nordstr?m-like metric whose “charge” is a function of the unparticle coupling constant λ, and therefore can admit naked singularities. Requiring the system to respect cosmic censorship provides a new method of constraining the value of λ. These limits are extremely loose for stellar-mass black holes, but commensurate with existing bounds for primordial black holes. In the case of theoretical low-mass black holes, the bounds on λ are much stricter than those derived from astrophysical and accelerator phenomenology. Additional constraints on the lower limit of λ are used to estimate the mass of the smallest possible black hole M_BH^minM_{\mathrm {BH}}^{\mathrm{min}} that can be formed in the unparticle framework, as a function of the unparticle parameters (L_U,M_U,d_U,d_BZ\Lambda_{{\mathcal{U}}},M_{{\mathcal{U}}},{d_{\mathcal{U}}},{d_{\mathit{BZ}}}).     

Inflationary scenario in the supersymmetric economical 3-3-1 model

We construct the supersymmetric economical 3-3-1 model which contains inflationary scenario and avoids the monopole puzzle. Based on the spontaneous symmetry breaking pattern (with three steps), the F-term inflation is derived. The slow-roll parameters ∈ and η are calculated. By imposing as experimental five-year WMAP data on the spectral index n, we have derived a constraint on the number of e-folding N _Q to be in the range from 25 to 50. The scenario for large-scale structure formation implied by the model is a mixed scenario for inflation and cosmic string, and the contribution to the CMBR temperature anisotropy depends on the ratio M _X /M _Pl. From the COBE data, we have obtained the constraint on the M _X to be M _X ∈ [1.22 × 10¹⁶, 0.98 × 10¹⁷] GeV. The upper value M _X ≃ 10¹⁷ GeV is a result of the analysis in which the inflationary contribution to the temperature fluctuations measured by the COBE is 90%. The coupling α varies in the range: 10⁻⁷−10⁻¹. This value is not so small, and it is a common characteristics of the supersymmetric unified models with the inflationary scenario. The spectral index n is a little bit smaller than 0.98. The SUGRA corrections are slightly different from the previous consideration. When ξ ≪ 1 and α lies in the above range, the spectral index gets the value consistent with the experimental five-year WMAP data. Comparing with string theory, one gets ξ < 10⁻⁸. Numerical analysis shows that α ≈ 10⁻⁶. To get inflation contribution to the CMBR temperature anisotropy ≈90%, the mass scale M _X < 3.5 × 10¹⁴ GeV.     

Kinetics of triplet-triplet absorption of anionic water-soluble porphyrins

It was established that in aqueous solutions of anionic porphyrins the processes of triplet-triplet (T-T) annihilation are absent (K₂<2.5·10⁵ M⁻¹ sec⁻¹), while a delayed annihilation fluorescence can be detected for these porphyrins in methanol (K₂≊3.5·10⁷ M⁻¹ sec⁻¹) and for their lipophilic analogs in organic solutions (K ₂≊2.5·10⁹ M⁻¹ sec⁻¹), and the kinetics of absorption of the latter porphyrins in triplet states is dependent on the intensity of the exciting radiation. The extremely small constant of T-T annihilation of anionic porphyrins can be due to the formation of a relatively dense solvate shell consisting of water molecules around the charged groups of the porphyrin molecules, which increases steric barriers and thus prevents an exchange-resonance transfer of energy between triplet excited molecules in aqueous solutions. It is also shown that porphyrin molecules can electrostatically repel one another when in their structure there are charged groups. To whom correspondence should be addressed. Deceased. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70 F. Skorina Ave., Minsk, 220072, Belarus; e-mail: llum@imaph.bas-net.by. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 6, pp. 791–795, November–December, 1999.     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

Phenomenology of a realistic accelerating universe using tracker fields

We present a realistic scenario of tracking of scalar fields with varying equation of state. The astrophysical constraints on the evolution of scalar fields in the physical universe are discussed. The nucleosynthesis and the galaxy formation constraints have been used to put limits on Ω_φ and estimate ɛ during cosmic evolution. Interpolation techniques have been applied to estimate ɛ ⋍0.772 at the present epoch. The epoch of transition from matter to quintessence dominated era and consequent onset of acceleration in cosmic expansion is calculated and taking the lower limit Θ _n ^/0 =0.2 as estimated from SN _e I _a data, it is shown that the supernova observations beyond redshift z=1 would reveal deceleration in cosmic expansion.     

Steady State and Time-Resolved Fluorescence Studies of a Hemagglutinin from Moringa oleifera

The saccharide binding and conformational characterization of a hemagglutinin, a low molecular weight protein from the seeds of Moringa oleifera was studied using steady state and time resolved fluorescence. The lectin binds sugars LacNAc (K _a = 1380 M⁻¹) and fructose (K _a = 975 M⁻¹), as determined by the fluorescence spectroscopy. It has a single tryptophan per monomer which is exposed on the surface and is in a strong electropositive environment as revealed by quenching with iodide. Quenching of the fluorescence by acrylamide involved both static (K _s = 0.216 M⁻¹) and collisional (K _sv = 8.19 M⁻¹) components. The native protein showed two different lifetimes, τ ₁ (1.6 ns) and τ ₂ (4.36 ns) which decrease and get converted into a single one, (2.21 ns) after quenching with 0.15 M acrylamide. The bimolecular quenching constant, k _q was 7.55 × 10¹¹ M⁻¹ s⁻¹. ANS binding studies showed that the native protein has exposed hydrophobic patches which get further exposed at extreme acidic or alkaline pH. However, they get buried in the interior of the protein in presence of 1 M GdnHCl or urea.     

The formation of primary galactic nuclei during phase transitions in the early universe

A new mechanism describing the formation of protogalaxies is proposed, based on the second-order phase transition in the inflation stage and the domain wall formation upon the end of inflation. The presence of closed domain walls with the size markedly exceeding the cosmological horizon at the instant of their formation and the wall collapse in the postinflation epoch (when the wall size becomes comparable with the cosmological horizon) lead to the formation of massive black hole clusters that can serve as nuclei for the future galaxies. The black hole mass distributions obtained do not contradict the available experimental data. The number of black holes with M ～ 100 solar masses (M _⊙) and above is comparable with the number of galaxies in the visible Universe. Development of the proposed approach gives grounds for a principally new scenario of galaxy formation in the model of a hot Universe.     

Unraveling the f<Subscript>0</Subscript> nature by connecting KLOE and BABAR data through analyticity

We define a general procedure, based on analyticity and dispersion relations, to estimate low-energy amplitudes for processes like: φ→e ⁺ e ^- M and φ→γM, starting from cross-section data on e ⁺ e ^-→φM, where M is a generic light scalar or pseudoscalar meson. In particular this procedure is constructed to obtain predictions on the radiative decay rate which are crucially linked on the assumed quark structure for the meson M under consideration. Three cases are analyzed: M = η, M = f ₀(qˉ) and M = f ₀(qqˉ). While in the η case the estimate of the branching fraction for the radiative decay φ→ηγ is in agreement with the data, in the case of f ₀, such agreement is obtained only under the hypothesis of a tetraquark scalar meson.     

Galaxy formation just after the recombination period

A scenario of galaxy formation is outlined which is based essentially on the fact that the cosmic matter about 10⁶yr after the end of the recombination period is a general relativistic Boltzmann gas very close to equilibrium. In this scenario the observed very small inhomogeneities of the background radiation lead to very sharply edged gas clouds in the centres of the inhomogeneities. The universe between the clouds is completely swept clean of matter. If one assumes the centres of the inhomogeneities to be axially symmetric, the mass spectrum of the clouds extends from the smallest globular clusters withM 10⁵ M as the lower limit (spherical symmetry) up to the big spiral galaxies withM 10¹¹ M as the upper limit (maximal flattening). The upper limit masses are extremely thin pancakes which contract within a time interval of about 2 · 10⁹ years to the proportions of an ordinary spiral galaxy of today.     

Method of Quantum Characters in Equivariant Quantization

 Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸 _h (M) is a 𝕌 _h (g)-equivariant quantization of the function algebra 𝔸(M) on M. We develop a method of building 𝕌 _h (g)-equivariant quantization on G-orbits in M as quotients of 𝔸 _h (M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌^* _h (g) and quotients of 𝔸 _h (M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸 _h (M). We specialize our approach to the situation g=gl(n,ℂ), M=End(ℂ ⁿ ), and 𝔸 _h (M) the so-called reflection equation algebra associated with the representation of 𝕌 _h (g) on ℂ ⁿ . For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the 𝕌(g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits. Received: 28 April 2002 / Accepted: 3 October 2002 Published online: 24 January 2003 RID="*" ID="*" This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01. Communicated by L. Takhtajan     

Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Short pulse width UV laser at 355 nm based on pulse LD side-pumped ceramic Nd:YAG and BBO electro-optical Q-switched

355 nm UV laser was obtained with a pulse width of less than 5 ns and a peak power at megawatt level by adopting the 808 nm pulse laser diode (LD) side-pumped ceramic Nd:YAG and BBO crystal electrooptical Q-switched. The single-pulse energy was measured to be 24.3 mJ with 4.86 ns pulse width and 5.11 MW peak power at a repetition rate of 1Hz under a 120 A pump current. Using a volume of beam splitting mirrors, wavelength outputs at 1064, 532, and 355 nm pulse laser was obtained simultaneously with a respective average output power of 656.6, 357.1, and 260.5 mW, the beam quality factor M ₂ are (M _{x − 1064}² = 5.83, M _{y − 1064}² = 5.61), (M _{x − 532}² = 4.25, M _{y − 532}² = 4.08) and (M _{x − 355}² = 6.32, M _{y − 355}² = 6.15), corresponding to a conversion efficiency at 11% from 1064 to 355 nm.     

The magnetic properties of nanosized La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> (0.5 ≤ <Emphasis Type="Italic">x</Emphasis> ≤ 0.8)

Magnetic properties of La_1−x Ca _x MnO₃ (0.5 ≤ x ≤ 0.8) samples with an equivalent average particle size ~50 nm prepared by a sol–gel method were investigated. The charge ordering (CO) transition that is observed in the bulks disappears and the ferromagnetic (FM) transition occurs in all the prepared samples. For all the samples, the spontaneous magnetization (M _S) value is much lower than the corresponding theoretic value, which shows that the majority of the sample is antiferromagnetic (AFM). However, the M _S value is much larger than the corresponding value reported by some other groups. The invisible of CO transition and the large M _S value can be attributed to the good connection among the adjacent particles. Moreover, the exchange bias (EB) phenomenon is observed except the x = 0.5 sample. With x increasing, the M _S value decreases and the EB field increases, which can be understood by considering the coexistence of FM phase with Mn³⁺–Mn⁴⁺ spin clusters in the shell and the AFM phase in the core of the nanoparticles.