Accreting compact object systems such as X-ray binaries (XRBs; neutron stars and black holes up to tens of solar masses) and active galactic nuclei (AGN; supermassive black holes up to 1e9 solar masses) exhibit variability in their luminosity on many timescales ranging from milliseconds to hundreds of days. Current studies on accretion disks seek to determine how the changes in black hole mass, the rate at which mass accretes onto the central black hole, and the internal and external disk environment affect the observed variability in various bandwidths of light. The fundamental structure of the accretion flow process itself, how it changes and results in the observed variability is not well known. This thesis employs novel methods from nonlinear dynamics to connect the ubiquitously complex variability of XRBs and AGN to the accretion properties and emission and probe commonalities across decades of mass. The methodologies used surpass the capabilities of traditional time series analysis techniques commonly used in astrophysics, such as the power density spectrum and other second order measures of variability, to probe the underlying dynamics. We study the longest light curves to date of XRBs by combining data from multiple all-sky monitors in the 2-20 keV bandpass; the most well-sampled and high precision optical light curves of AGN from the Kepler satellite; and the largest samples to date of long-term monitoring in the hard X-ray of AGN with the Swift/BAT telescope. We find evidence for chaos in a neutron star XRB connected to its superorbital period of 120 days and possibly related to a precession in the accretion disk. We similarly find higher levels of determinism correlate with specific spectral states of XRBs. Among AGN, we find that Type 1 AGN are more likely to exhibit nonlinear behavior than Type 2, obscured AGN are more likely to exhibit stochastic behavior than unobscured AGN, and radio loud sources are more deterministic than radio quiet, with a possible anti-correlation between increased luminosity and nonlinearity. Overall, we hypothesize that specific configurations of the accretion flow onto a compact object result in specific modulations of the emission that can be characterized as deterministic (e.g., possibly related to the presence of a jet-like process), nonlinear (e.g., due to a modulating warp or precession in the accretion disk), or stochastic (e.g., possibly related to the presence of strong outflows or hard X-ray coronal component).

(Cont.) to the XPS in SNR RCW 103. The multiple IR band measurements of 1E 1048.1-5937 provide marginal evidence for spectral flattening, and cannot rule out an accretion disk scenario for AXPs.

The work developed in this thesis addresses very important and relevant issues of accretion processes around black holes. Beginning by studying the time variation of the evolution of inviscid accretion discs around black holes and their properties, the author investigates the change of the pattern of the flows when the strength of the shear viscosity is varied and cooling is introduced. He succeeds to verify theoretical predictions of the so called Two Component Advective Flow (TCAF) solution of the accretion problem onto black holes through numerical simulations under different input parameters. TCAF solutions are found to be stable. And thus explanations of spectral and timing properties (including Quasi-Period Oscillations, QPOs) of galactic and extra-galactic black holes based on shocked TCAF models appear to have a firm foundation.

The most luminous compact objects are powered by accretion of mass. Accretion disks are the one common and fundamental element of these sources on widely different scales, ranging from close stellar binaries, galactic black holes and X-ray pulsars to active galactic nuclei (AGN). Key new developments in theory and observations, reviewed by experts in the field, are presented in this book. The contributions to the workshop cover the puzzles presented by the X-UV spectra of AGN and their variability, the recent numerical simulations of magnetic fields in disks, the remarkable behavior of the superluminal source 1915+105 and the "bursting pulsar" 1744-28, to mention a few of the topics.

In this thesis, I study hydrodynamical models of slim accretion disks - advective, optically thick disks which generalize the standard models of radiatively efficient thin disks to all accretion rates. I start with a general introduction to the theory of accretion onto compact objects. It is followed by a derivation of the commonly-used standard models of thin disks. In the subsequent section I introduce the equations describing slim disks, explain the numerical methods I used to solve them and discuss properties of such solutions. I also give a general derivation of non-stationary equations and present the time evolution of thermally unstable accretion disks. I introduce a state-of-the-art approach coupling the radial and vertical structures of an advective accretion disk and discuss the improvements it brings to vertically-averaged solutions. I also present a numerical model of self-illuminated slim accretion disks. Finally, I present and discuss applications of slim accretion disks.

All papers have been peer-reviewed. These proceedings contain research papers from the participants of the astrophysics conference “Cool discs, hot flows”. The main focus of the conference was on physical processes of accreting compact objects. Topics covered include wind-fed accretion, neutron stars and white dwarfs, ultraluminous X-ray sources and temporal variability.

The most luminous compact objects are powered by accretion of mass. Accretion disks are the one common and fundamental element of these sources on widely different scales, ranging from close stellar binaries, galactic black holes and X-ray pulsars to active galactic nuclei (AGN). Key new developments in theory and observations, reviewed by experts in the field, are presented in this book. The contributions to the workshop cover the puzzles presented by the X-UV spectra of AGN and their variability, the recent numerical simulations of magnetic fields in disks, the remarkable behavior of the superluminal source 1915+105 and the "bursting pulsar" 1744-28, to mention a few of the topics.