The physical origin of the X-ray power spectral density break timescale in accreting black holes

X-ray variability of active galactic nuclei (AGN) and black hole binaries can be analysed by means of the power spectral density (PSD). The break observed in the power spectrum defines a characteristic variability timescale of the accreting system. The empirical variability scaling that relates characteristic timescale, black hole mass, and accretion rate ($T_B \propto M_{BH}^{2.1}/\dot{M}^{0.98}$) extends from supermassive black holes in AGN down to stellar-mass black holes in binary systems. We suggest that the PSD break timescale is associated with the cooling timescale of electrons in the Comptonisation process at the origin of the observed hard X-ray emission. We obtain that the Compton cooling timescale directly leads to the observational scaling and naturally reproduces the functional dependence on black hole mass and accretion rate ($t_C \propto M_{BH}^{2}/\dot{M}$). This result simply arises from general properties of the emission mechanism and is independent of the details of any specific accretion model.Comment: 4 pages, accepted for publication in Astronomy and Astrophysics, Letters to the Edito

The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1 wave equation with a potential $V$, on a field $\Psi_z$. For smooth metric perturbations $\Psi_z$ is singular at $r_s=-6M/(\ell-1)(\ell+2)$, $\ell$ the mode harmonic number, and $V$ has a second order pole at $r_s$. This is irrelevant to the black hole exterior stability problem, where $r>2M>0$, and $r_s <0$, but it introduces a non trivial problem in the naked singular case where $M0$, and the singularity appears in the relevant range of $r$. We solve this problem by developing a new approach to the evolution of the even mode, based on a {\em new gauge invariant function}, $\hat \Psi$ -related to $\Psi_z$ by an intertwiner operator- that is a regular function of the metric perturbation {\em for any value of $M$}. This allows to address the issue of evolution of gravitational perturbations in this non globally hyperbolic background, and to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for suitably chosen initial data.Comment: typos corrected, references adde

Synchrotron radio emission in radio-quiet AGNs

The basic mechanism responsible for radio emission in radio-loud active galactic nuclei (AGNs) is assumed to be synchrotron radiation. We suggest here that radio emission in radio-quiet objects is also due to synchrotron radiation of particles accelerated in shocks. We consider generic shocks and study the resulting synchrotron properties. We estimate the synchrotron radio luminosity and compare it with the X-ray component produced by inverse Compton emission. We obtain that the radio to X-ray luminosity ratio is much smaller than unity, with values typical of radio-quiet sources. The predicted trends on source parameters, black hole mass and accretion rate, may account for the anticorrelation between radio-loudness and Eddington ratio observed in different AGN samples.Comment: 5 pages, accepted for publication in Astronomy and Astrophysic

The Quantum Spacetime of c>0 2d Gravity

We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c>0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on the value of the Hausdorff dimension d_H obtained from scaling properties of two point functions defined in terms of geodesic distance. Further insight to the fractal structure of spacetime is obtained from the study of the loop length distribution function which reveals that the 0<c<= 1 system has similar geometric properties with pure gravity, whereas the branched polymer structure becomes clear for c >= 5.Comment: LaTeX2e, 3 pages, 3 figure

On the Quantum Geometry of Multi-critical CDT

We discuss extensions of a recently introduced model of multi-critical CDT to higher multi-critical points. As in the case of pure CDT the continuum limit can be taken on the level of the action and the resulting continuum surface model is again described by a matrix model. The resolvent, a simple observable of the quantum geometry which is accessible from the matrix model is calculated for arbitrary multi-critical points. We go beyond the matrix model by determining the propagator using the peeling procedure which is used to extract the effective quantum Hamiltonian and the fractal dimension in agreement with earlier results by Ambjorn et al. With this at hand a string field theory formalism for multi-critical CDT is introduced and it is shown that the Dyson-Schwinger equations match the loop equations of the matrix model. We conclude by commenting on how to formally obtain the sum over topologies and a relation to stochastic quantisation.Comment: 15 pages, 2 figures, improved discussion, some new results regarding Hausdorff dimension, as publishe

An Exact Bosonization Rule for c=1 Noncritical String Theory

We construct a string field theory for c=1 noncritical strings using the loop variables as the string field. We show how one can express the nonrelativistic free fermions which describes the theory, in terms of these string fields.Comment: 17 pages, to appear in JHE

X-ray power law spectra in active galactic nuclei

X-ray spectra of active galactic nuclei (AGN) are usually described as power law spectra, characterized by the spectral slope $\alpha$ or photon index $\Gamma$. Here we discuss the X-ray spectral properties within the framework of clumpy accretion flows, and estimate the power law slope as a function of the source parameters. We expect harder spectra in massive objects than in less massive sources, and steeper spectra in higher accretion rate systems. The predicted values of the photon index cover the range of spectral slopes typically observed in Seyfert galaxies and quasars. The overall trends are consistent with observations, and may account for the positive correlation of the photon index with Eddington ratio (and the possible anticorrelation with black hole mass) observed in different AGN samples. Spectral properties are also closely related to variability properties. We obtain that shorter characteristic time scales are associated with steeper spectra. This agrees with the observed `spectral-timing' correlation.Comment: 6 pages, 1 figure, Astronomy and Astrophysics, accepte

Statistical switching kinetics in ferroelectrics

By assuming a more realistic nucleation and polarization reversal scenario we build a new statistical switching model for ferroelectrics, which is different from either the Kolmogorov-Avrami-Ishibashi (KAI) model or the Nucleation-Limited-Switching (NLS) model. After incorporating a time-dependent depolarization field this model gives a good description about the retardation behavior in polycrystalline thin films at medium or low fields, which can not be described by the traditional KAI model. This model predicts correctly n=1 for polycrystalline thin films at high Eappl or ceramic bulks in the ideal case

On Phase Transition of NH4H2PO4NH_{4}H_{2}PO_{4}-Type Crystals by Cluster Variation Method

The Cluster Variation Method (CVM) is applied to the Ishibashi model for ammonium dihydrogen phosphate ($\rm NH_{4}H_{2}PO_{4}$) of a typical hydrogen bonded anti-ferroelectric crystal. The staggered and the uniform susceptibility without hysteresis are calculated at equilibrium. On the other hand, by making use of the natural iteration method (NIM) for the CVM, hysteresis phenomena of uniform susceptibility versus temperature observed in experiments is well explained on the basis of local minimum in Landau type variational free energy. The polarization $P$ curves against the uniform field is also calculated.Comment: 14 pages, 10 figure

The Factorization Method for Monte Carlo Simulations of Systems With a Complex Action

We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. In some cases, like in the IKKT matrix model, a finite size scaling extrapolation can provide results for systems whose size would make it prohibitive to simulate directly.Comment: Lattice2003(nonzero), 3 pages, 4 figures, Proceedings for Lattice 2003, July 2003, Tsukuba, Japa