Twin peaks kHz QPOs: mathematics of the 3:2 orbital resonance

Using the method of multiple scales, one can derive an analytic solution that describes the behaviour of weakly coupled, non-linear oscillations in nearly Keplerian discs around neutron stars or black holes close to the 3:2 orbital epicyclic resonance. The solution obtained agrees with the previous numerical simulation. Such result may be relevant to the kilohertz quasi-periodic variability in X-ray fluxes observed in many Galactic black hole and neutron star sources. With a particular choice of tunable parameters, the solution fits accurately the observational data for Sco X-1.Comment: Published (25 June 2004) on PASJ, 56, 55

Impact of supermassive black holes on galaxy clusters

In the semi-analytical work presented here the feedback from supermassive black holes on galaxy clusters is investigated. In particular we aim at providing simple diagnostics tools to constrain the characteristic velocities and spatial scales of the hot Intra Cluster Medium (ICM) motions. In the so-called "cold core'' clusters these motions are believed to be driven by the activity of a central black hole. The methods developed here, together with present-day and future observations, are designed to help to solve the puzzle of cooling flow clusters (see section $1.3$) and understand better the AGN/gas interaction in smaller systems (down to individual galaxies).\\ Clusters of galaxies are the largest gravitationally bound systems in the Universe: they are composed of hundreds to thousands of galaxies, moving in a deep potential well set by the dominating dark matter. The whole volume of clusters is filled with hot (temperature $\sim 10^7-10^8$~K) and rarefied (electron density $10^{-4}-10^{-1} {\rm cm^{-3}}$) gas. In such a high-temperature regime even heavy elements (e.g. silicon, sulfur, iron etc.) are highly ionized up to [H]- or [He]-like ions and they emit in bright lines with energies from $\sim 0.7$ to $\sim 8$ keV. Using X-ray observations one can reliable measure all the major gas properties: the temperature, density and abundance of heavy elements.\\ A significant fraction of clusters (called "cool core'' clusters) show distinct signatures in the central region: the gas temperature drops inward, while the gas density increases. The central gas radiative cooling time in such clusters is much shorter than the age of the cluster and without any external source of energy the gas would cool well below X-ray temperatures. However observations suggest that the gas temperature drops only to 1-2 keV. One plausible explanation of this problem is that the activity of a central supermassive black hole deposits large amounts of mechanical energy into the cluster gas and that this balances the gas radiative losses. A direct implication of this hypothesis is that the hot gas is not at rest, but it is continuously stirred by the AGN activity.\\ The same class of cool core clusters is characterized by a centrally peaked distribution of the heavy elements abundance (usually measured using the He-like iron 6.7 keV line). The peaked abundance profiles are likely associated with the metals ejection by the stars of very massive elliptical galaxies, that are always present at the centers of these clusters. However the observed abundance distributions are significantly broader than the central galaxy light profiles, suggesting that some gas motions are spreading the metals ejected from the galaxy. We treat this process in a diffusion approximation to derive, from the X-ray observations, constraints on the characteristic velocities and spatial scales of the gas motions for a sample of cool core clusters and groups (Chapters $2$ and $3$). The parameters derived from a simple semi-analytic model are then compared with the results of numerical simulations of the AGN/gas interaction in the cluster core (Chapter $4$).\\ In Chapter $5$ we discuss the impact of the gas motions on the width of the strongest X-ray emission lines. Since the characteristic thermal velocities of heavy ions (e.g. iron) are much smaller than the sound speed of the gas, the width of the lines sensitively depends on the presence of gas motions. We show that both the absolute value of the linewidth and its dependence on the projected distance from the cluster center provide valuable diagnostics of the gas motions. Such measurements will soon become possible with the launch of X-ray micro-calorimeters in space.\\ This work has been done in collaboration with E.Churazov, R.Sunyaev, H.B\"ohringer, M.Br\"uggen, W.Forman and E.Roediger

Epicyclic oscillations of fluid bodies Paper II. Strong gravity

Fluids in external gravity may oscillate with frequencies characteristic of the epicyclic motions of test particles. We explicitly demonstrate that global oscillations of a slender, perfect fluid torus around a Kerr black hole admit incompressible vertical and radial epicyclic modes. Our results may be directly relevant to one of the most puzzling astrophysical phenomena -- high (hundreds of hertz) frequency quasiperiodic oscillations (QPOs) detected in X-ray fluxes from several black hole sources. Such QPOs are pairs of stable frequencies in the 3/2 ratio. It seems that they originate a few gravitational radii away from the black hole and thus observations of them have the potential to become an accurate probe of super-strong gravity.Comment: submitted to Classical and Quantum Gravit

Non-linear resonance in nearly geodesic motion in low-mass X-ray binaries

We have explored the ideas that parametric resonance affects nearly geodesic motion around a black hole or a neutron star, and that it may be relevant to the high frequency (twin) quasi-periodic oscillations occurring in some low-mass X-ray binaries. We have assumed the particles or fluid elements of an accretion disc to be subject to an isotropic perturbation of a hypothetical but rather general form. We find that the parametric resonance is indeed excited close to the radius where epicyclic frequencies of radial and meridional oscillations are in a 2:3 ratio. The location and frequencies of the highest amplitude excitation vary with the strength of the perturbation. These results agree with actual frequency ratios of twin kHz QPOs that have been reported in some black hole candidates, and they may be consistent also with correlation of the twin peaks in Sco X-1.Comment: 5 pages; accepted for publication in PAS

Kinematic Density Waves in Accretion Disks

When thin accretion disks around black holes are perturbed, the main restoring force is gravity. If gas pressure, magnetic stresses, and radiation pressure are neglected, the disk remains thin as long as orbits do not intersect. Intersections would result in pressure forces which limit the growth of perturbations. We find that a discrete set of perturbations is possible for which orbits remain non-intersecting for arbitrarily long times. These modes define a discrete set of frequencies. We classify all long-lived perturbations for arbitrary potentials and show how their mode frequencies are related to pattern speeds computed from the azimuthal and epicyclic frequencies. We show that modes are concentrated near radii where the pattern speed has vanishing radial derivative. We explore these modes around Kerr black holes as a possible explanation for the high-frequency quasi-periodic oscillations of black hole binaries such as GRO J1655-40. The long-lived modes are shown to coincide with diskoseismic waves in the limit of small sound speed. While the waves have long lifetime, they have the wrong frequencies to explain the pairs of high-frequency quasi-periodic oscillations observed in black hole binaries.Comment: 28 pages, 6 figures; extended comparison with diskoseismology; added reference to astro-ph/060368

Difficulties with the QPOs Resonance Model

High frequency quasi-periodic oscillations (HFQPOs) have been detected in microquasars and neutron star systems. The resonance model suggested by Kluzniak & Abramowicz (2000) explains twin QPOs as two weakly coupled nonlinear resonant epicyclic modes in the accretion disk. Although this model successfully explains many features of the observed QPOs, it still faces difficulties and shortcomings. Here we summarize the aspects of the theory that remain a puzzle and we briefly discuss likely developments.Comment: To appear in New Astronomy Review, Proceedings of "Jean-Pierre Lasota, X-ray binaries, accretion disks and compact stars" (October 2007); Ed. M. Abramowic

The origin and evolution of cluster magnetism

Random motions can occur in the intergalactic gas of galaxy clusters at all stages of their evolution. Depending on the poorly known value of the Reynolds number, these motions can or cannot become turbulent, but in any case they can generate random magnetic fields via dynamo action. We argue that magnetic fields inferred observationally for the intracluster medium require dynamo action, and then estimate parameters of random flows and magnetic fields at various stages of the cluster evolution. Polarization in cluster radio halos predicted by the model would be detectable with the SKA.Comment: 4 pages, 1 figure, to be published by Astronomische Nachrichten (proceedings of "The Origin and Evolution of Cosmic Magnetism", 29 August - 2 September 2005, Bologna, Italy); version updated to match the accepted tex