Dissertations / Theses on the topic 'Accretion discs'

Accretion discs are commonplace around magnetic stars. They can be found in newly formed stars and in interacting binaries. The effects of the stellar magnetic field on these discs are manifold. For example it may act as a 'seed field' for the initiation of the magneto-rotational instability and thus drive viscosity. However this thesis explores the more direct effect of the stellar magnetic field on the global structure of circumstellar accretion discs, and how this structure may in turn influence the time dependent behaviour of the disc. This work is done through a combination of analytic and numerical techniques, by modelling a torque which represents the effect of the magnetic field.;Some young stellar objects exhibit disc outbursts, known as FU Orionis events, which are separated by recurrence times much longer than would be expected from the standard disc instability model. However, it is shown here that a moderate stellar magnetic field may truncate the accretion disc, and so stabilise the inner accretion disc against outbursts. This forces outbursts to begin in the outer disc where higher trigger densities must be reached, and so extends the recurrence time. This result is of great interest since planet formation may be strongly influenced by the structure of the protoplanetary disc.;The dwarf nova WZ Sagittae is unusual in that it also has very long recurrence times. In addition, a series of short echos have been observed to follow the main outburst. It has therefore been suggested that this object is surrounded by an accretion disc which is magnetically truncated in a similar manner to those around the FU Orionis stars. It is shown that such a truncated disc may, when placed within the binary Roche potential, exhibit echo outbursts.

Many galaxies in the Universe show evidence of a supermassive black hole at their dynamical centre. About 10-20% of these galaxies also contain an extremely bright, point-like continuum source in their nuclear region. These luminous objects are called active galactic nuclei (AGN), and are thought to be powered by material accreting onto the central black hole. The infalling gas loses its energy and angular momentum by passing through an accretion disc. The disc then radiates away this energy, and it is this radiation that is observed as an AGN. When observed in the X-ray waveband AGN are found to be very bright and rapidly variable (on timescales as small as 1000 s), implying that the emission must originate from the innermost regions of the central engine. X-ray spectra of AGN often exhibit distinct features that are attributed to radiation reflecting off of the accretion disc. Therefore, it is possible to use sensitive X-ray spectroscopic observations of AGN to directly probe the physics of accretion flows only a short distance away from the black hole. Comparing the results from AGN with different properties, such as luminosity or radio power, may allow general conclusions on the AGN phenomenon to be drawn. This thesis applies computations of X-ray reflection spectra to observations of different AGN in order to determine various properties of their accretion flows. The calculations take into account the ionization effects of the incident radiation and consider different density structures for the surface of the accretion disc. It was found that the model spectra were a good description of the observed X-ray data for many AGN between 1 and 10 keV. In particular, five narrow-line Seyfert 1 galaxies were well fit with reflection spectra from a highly ionized accretion disc, consistent with the idea that they contain rapidly accreting black holes. A similar result was found when fitting the data of 3C 120, a broad-line radio galaxy, which argues against the claim that radio-loud AGN have truncated accretion discs. On the other hand, a weakly ionized reflector proved to be a better fit to the Seyfert 1 galaxy MCG-6-30-15.

In this thesis we develop a mathematical model to describe the internal structure of an -accretion disc. The method is to consider the standard thin disc as a zero order approximation to a disc with vertical structure. The order of the approximation is controlled by the parameter 1/M2, where M is the Mach number of the azimuthal flow is a fiducial point. The theory is developed analytically as far as possible, using numerical solutions for the final system of ordinary differential equations only. The model expands upon the work of other authors by assuming a disc surface defined by the condition of pressure balance between the disc and its environment. Vertically transported angular momentum is extracted by coupling to these surroundings. In the absence of an external couple, the vertical transport of angular momentum is ignored, as in the standard thin disc. The internal structure and stability of the disc is investigated in both the gas and radiation pressure dominated regions, and the effects of including advection and the vertical transport of angular momentum is discussed. An application of the disc model is presented whereby external heating from X-rays associated with a radio jet are shown to induce mass loss from the disc surface. Such a configuration may undergo symmetry breaking to an asymmetric state in which one jet dominates. This is therefore a possible model for intrinsically one-sided radio sources.

The primary idea behind the work in this thesis is that accretion discs interacting with astrophysical bodies, from planets to supermassive black holes (SMBHs), can strongly affect the dynamical behaviour of those bodies. While this idea is by no means new, observational and theoretical developments in recent years provide fresh motivation to consider this effect across a number of astrophysical contexts. Of particular relevance to the work here are three observational measurements which I attempt to reconcile with theory by invoking interactions with accretion discs. Firstly, observations of giant exoplanets show that they prefer to inhabit eccentric orbits, which is unexpected given the predictions of planet formation theory. Conversely, Kepler’s discovery of planets with low eccentricities around moderately eccentric binaries goes against theoretical expectation that their orbits should be eccentric. In galactic centres, binary supermassive black holes are not observed despite theoretical expectations that their evolution should drive them to ~ parsec separations and leave them there. In this thesis I use high-resolution smoothed particle hydrodynamics simulations to investigate each of these problems involving planet- and binary-disc interactions. I show that these interactions are unable to solve the problem of eccentric giant exoplanets, but that they can cause damping of circumbinary planetary eccentricity and so are able to explain Kepler’s circumbinary planets. I use this latter to place a limit on the surface density in which Kepler-16b in particular can have formed. I also show that a disc formed from a gas cloud moving prograde with respect to a SMBH binary will fragment to form stars sooner than a similar retrograde disc. Consequently, a retrograde disc is able to drive stronger binary evolution than is the prograde disc. Allowing that a large number of such encounters would be expected in the aftermath of the galaxy merger that formed the binary, this process may be able to solve the ‘last parsec problem.’

One of the larger questions within the study of X-ray Binaries currently concerns the geometry of the accretion disc during the so called ’hard state’. A model involving a truncated disc is often used to explain the properties of the hard state, but there is still disagreement on the extent to which it is necessary. Presented in this thesis are three studies related to this issue. The first looks into the changes in the accretion geometry using an argument based around radiative efficiency. Periods of exponential decay before and after the soft- to hard-state transition are found. The e-folding times of these decays are measured and it is found that this value changes from ~12 days in the soft state to ~7 days in the hard state. This factor ~2 change would be expected if there is a change from a radiatively efficient regime to a radiatively inefficient regimee. The second concerns the treatment of absorption from the Interstellar Medium in studies of X-ray Binaries. Column densities for the most abundant elements are found and compared with previous results for a number of sources. Simulated data is also used to test the impact of using incorrect column densities and older X-ray absorption models on spectral analysis. It is found that the use of incorrect absorption parameters can have a large effect on the results of spectral fitting. The third directly tests for the presence of a truncated disc by fitting a model to energy spectra from the XMM-Newton/EPIC-pn instrument. The model assumes the accretion disc extends down to rISCO at all times, and is fit to a large range of observations in both the hard and soft states. In the majority of cases there is no explicit need for a truncated disc in either the soft or hard state.

Black hole jets and accretion discs are the most extreme objects in modern astrophysics whilst dark energy is undoubtedly the most mysterious. This thesis focuses on understanding these three topics. The majority of this thesis is dedicated to investigating the structure and properties of black hole jets by modelling their emission. I develop an inhomogeneous jet model with a magnetically dominated parabolic accelerating base, transitioning to a slowly decelerating conical jet, with a geometry set by radio observations of M87. This model is able to reproduce the simultaneous multiwavelength spectra of all 38 Fermi blazars with redshifts in unprecendented detail across all wavelengths. I constrain the synchrotron bright region of the jet to occur outside the BLR and dusty torus for FSRQs using the optically thick to thin synchrotron break. At these large distances their inverse-Compton emission originates from scattering CMB photons. I find an approximately linear relation between the jet power and the transition region radius where the jet first comes into equipartition, transitions from parabolic to conical and stops accelerating. The decreasing magnetic field strength and increasing bulk Lorentz factor with jet power are the physical reasons behind the blazar sequence. I calculate the conditions for instability in a thin accretion disc with an α parameter which depends on the magnetic Prandtl number, as suggested by MHD simulations. The global behaviour of the instability induces cyclic flaring in the inner regions of the disc, for parameters appropriate for X-ray binary systems, thereby offering a potential solution to a long standing problem. Finally, I calculate the effect of an interacting quintessence model of dark energy on cosmological observables. I find that a scalar-tensor type interaction in the dark sector results in an observable increase in the matter power spectrum and integrated Sachs-Wolfe effect at horizon scales.

In this thesis I have studied how discs around young stars evolve and disperse. In particular, I build models which combine viscous evolution with photoevaporation, as previous work suggests that photoevaporation can reproduce the observed disc evolution and dispersal time-scales. The main question this thesis attempts to address is: Can photoevaporation provide a dominant dispersal mechanism for the observed population of young stars? Photoevaporation arises from the heating that high energy (UV and X-ray) photons provide to the surface layers of a disc. Before I started this work, only photoevaporation from a pure EUV radiation field was described within a hydrodynamic framework. Therefore, I start by building a hydrodynamic solution to the pure X-ray photoevaporation problem, and then extend this solution to the entire high energy spectrum. This hydrodynamic model leads me to conclude that it is the X-ray radiation field that sets the mass-loss rates. These mass-loss rates scale linearly with X-ray luminosity, are independent of the underlying disc structure and explicitly independent of stellar mass. I build a radiation-hydrodynamic algorithm, based on previous work, to describe the process of X-ray heating in discs. I then use this algorithm to span the full range of observed parameter space, to fully solve the X-ray photoevaporation problem. I further extend the algorithm to roughly approximate the heating an FUV radiation field would have on the photoevaporative flow, as well as separately testing the effect an EUV radiation field will have. These numerical tests are in agreement with the hydrodynamic model derived. Specifically, it is the X-rays that are driving the photoevaporative flow from the inner disc. Armed with an accurate description of the photoevaporative mass-loss rates from young stars, I consider the evolution of a population of disc-bearing, young (

This thesis focuses on the evolution of zonal flows in self-gravitating accretion discs and their resulting effect on disc stability; it also studies the process of disc gravito-turbulence, with particular emphasis given to the way the turbulent state is able to extract energy from the background flow and sustain itself by means of a feedback. Chapters 1 and 2 provide an overview of systems involving accretion discs and a theoretical introduction to the theory of accretion discs, along with potential methods of angular momentum transport to explain the observed accretion rates. To address the issue of the gravito-turbulence self-sustenance, a compressible non-linear spectral code (dubbed CASPER) was developed from scratch in C; its equations and specifications are laid out in Chapter 3. In Chapter 4 an ideal (no viscosities or cooling) linear stability analysis to non-axisymmetric perturbations is carried out when a zonal flow is present in the flow. This yields two instabilities: a Kelvin-Helmholtz instability (active only if the zonal flow wavelength is sufficiently small) and one driven by self-gravity. A stability analysis of the zonal flow itself is carried out in Chapter 5 by means of an axisymmetric linear analysis, using non-ideal conditions. This considers instability due to both density wave modes (which give rise to overstability) and slow modes (which result in thermal or viscous instability) and, thanks a different perturbation wavelength regime, represents an extension to the classical theory of thermal and viscous instabilities. The slow mode instability is found to be aided by high Prandtl numbers and adiabatic index γ values, while quenched by fast cooling. The overstability is likewise stabilised by fast cooling, and occurs in a non-self-gravitational regime only if γ ≲ 1.305. Lastly, Chapter 6 illustrates the results of the non-linear simulations carried out using the CASPER code. Here the system settles into a state of gravito-turbulence, which appears to be linked to a spontaneously-developing zonal flow. Results show that this zonal flow is driven by the slow mode instability discussed in Chapter 5, and that the presence of zonal flows triggers a non-axisymmetric instability, as seen in Chapter 4. The role of the latter is to constrain the zonal flow amplitude, with the resulting zonal flow disruption providing a generation of shearing waves which permits the self-sustenance of the turbulent state.

Accretion discs are fluid-dynamical entities which surround many black holes. Observations reveal that these systems exhibit variability on a range of time scales. This thesis investigates phenomena occurring in black-hole accretion discs which are likely to induce high-frequency quasi-periodic variability. Two classes of pseudo-relativistic theoretical models are investigated. The first is based on the stability of transonic accretion flows and its connection to a disc instability that takes the form of propagating waves (viscous overstability). The time-dependent study looks at the conditions under which the transition between subsonic disc-like accretion, which occurs at large radii, and the supersonic flow characteristic of the immediate vicinity of the black hole is stable. In agreement with previous findings, results indicate that the system reaches a steady state for low viscosity. Above that threshold the transonic solutions are unstable to viscous overstability. The overstable inertial-acoustic waves appear to be excited near the maximum of the epicyclic frequency and are global in the sense that their frequency is maintained for a wide range of radii. The second class of models looks at accretion-disc oscillations which are trapped due to the non-monotonic variation of the epicyclic frequency in relativistic flows. In particular, it focuses on inertial waves trapped below the maximum of the epicyclic frequency which are excited in deformed, warped or eccentric, discs. The excitation mechanism involves a non-linear coupling between the global deformation, an intermediate wave and the inertial mode and results, under a variety of conditions, in growth of the latter. Excitationis only effective when global deformations are capable of reaching the inner disc with non-negligible amplitude. With that in mind, the conditions favourable to the propagation of warped and eccentric modes from the outer to the inner regions are analysed. Another aspect that is taken into account is the influence of a transonic background, ignored in the coupling calculations, on the propagation of modes in the disc. It is found that, under certain conditions, inertial waves may be severely affected or destroyed in this background. On the other hand, results indicate that the decay rate of inertial waves due to the presence of the radial inflow is small in sufficiently thin discs. In this case, the coupling mechanism can still work to excite trapped inertial modes.

I present the first two- and three-dimensional simulations of accretion disc-driven outbursts in cataclysmic variables and X-ray transients. A Smoothed Particle Hydrodynamics scheme is used to model the accretion disc, which is subject to the full tidal potential of a binary system. The scheme, which includes a time-varying viscosity, is applied to cataclysmic variables and X-ray transients with differing mass ratios and orbital periods. Simulations of the dwarf nova SS Cygni, with mass ratio q = 0.6, produce coherent outbursts and a wide range of other observationally testable results. When applied to the tidally unstable system Z Chamaeleontis (q = 0.15), the scheme reproduces superoutbursts and superhumps. The tidal and thermal instabilities are shown to be entirely decoupled: a superoutburst is simply a normal outburst in the presence of a 3:1 eccentric inner Lindblad resonance. The model is refined for X-ray transients to include a simple treatment of irradiation of the disc by the X-rays generated at the primary. In short periods systems with correspondingly small discs, if q is small tidal effects can influence the outburst behaviour. If a small region at the outer edge of the disc remains shielded from the X-rays, tidal forces can drive this gas inwards through the disc, producing the rebrightening that has been observed in several X-ray light curves of soft X-ray transient outbursts. At longer periods, the disc cannot ever entirely be heated by the X-rays and more complex outburst behaviour is possible. Simulations show that this behaviour is determined by competition between the variable size of the irradiated region and the thermal instability operating in the cool region.

This thesis explores aspects of the theory of accretion discs in two astrophysical environments; around young low-mass stars - T Tauri stars, and in mass transfer binaries. A particular aim is to consider the role that magnetic fields - including fields within the disc and those of the central star - may play in controlling the evolution of the star-disc system. T Tauri stars are known to be magnetically active, and the first part of the thesis considers the structure and evolution of discs around magnetic T Tauri stars. I extend prior models to examine the effect of time-varying magnetic fields on the disc, and show that some of the long-term photometric variability in T Tauri systems could be caused by the influence of magnetic cycles on the accretion disc. The evolution of the star-disc system on much longer timescales is then investigated by combining pre-main-sequence stellar evolution models with those for the disc. The resulting model is used to examine the rotation rates of magnetically braked T Tauri stars, and the possible influence of close binary companions on those rotation rates. The second part of the thesis considers accretion discs in interacting binary systems. A magnetic dynamo within the disc is a promising candidate mechanism for the origin of the viscosity in accretion discs, and I discuss the implications of an operating dynamo for observations of dwarf novae. A simple model is presented in which the prominent outbursts seen in these systems have a direct origin in the physics of the underlying disc dynamo. I also present the results of three dimensional simulations of the interaction between the gas stream from the mass-donating star and the accretion disc. The hydrodynamic calculations show that a significant fraction of the stream gas can ricochet off the outer rim of the disc and overflow towards smaller radii, and the implications of this for models and observations of Cataclysmic variables and low-mass X-ray binaries are discussed.

Doctor of Philosophy
We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and perturbations have vertical wavevectors only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, disc structure and configuration of the conductivity tensor. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conductivity discs. For the minimum-mass solar nebula model, incorporating cosmic ray and x-ray ionisation and assuming that charges are carried by ions and electrons only, perturbations grow at 1 AU for B < 8G. For a significant subset of these strengths (200mG < B < 5 G), the growth rate is of order the ideal MHD rate (0.75 Omega). Hall conductivity modifies the structure and growth rate of global unstable modes at 1 AU for all magnetic field strengths that support MRI. As a result, at this radius, modes obtained with a full conductivity tensor grow faster and are active over a more extended cross-section of the disc, than perturbations in the ambipolar diffusion limit. For relatively strong fields (e.g. B > 200 mG), ambipolar diffusion alters the envelope shapes of the unstable modes, which peak at an intermediate height, instead of being mostly flat as modes in the Hall limit are in this region of parameter space. Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B < 2 G. For strong fields, perturbations exhibit a kink at the height where x-ray ionisation becomes active. Finally, for R = 5 AU (10 AU), unstable modes exist for B < 800 mG (B < 250 mG) and the maximum growth rate is close to the ideal-MHD rate for 20 mG < B < 500 mG (2 mG < B < 50 mG). Similarly, perturbations incorporating Hall conductivity have a higher wavenumber and grow faster than solutions in the ambipolar diffusion limit for B < 100 mG (B < 10 mG). Unstable modes grow even at the midplane for B > 100 mG (B ~ 1 mG), but for weaker fields, a small dead region exists. When a population of 0.1 um grains is assumed to be present, perturbations grow at 10 AU for B < 10 mG. We estimate that the figure for R = 1 AU would be of order 400 mG. We conclude that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. An example of such magnetic activity is the generation of MRI unstable modes, which are supported at 1 AU for field strengths up to a few gauss. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 AU, in particular, it is crucial to incorporate the full conductivity tensor in the analysis of this instability, and more generally, in studies of the dynamics of astrophysical discs.

We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and perturbations have vertical wavevectors only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, disc structure and configuration of the conductivity tensor. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conductivity discs. For the minimum-mass solar nebula model, incorporating cosmic ray and x-ray ionisation and assuming that charges are carried by ions and electrons only, perturbations grow at 1 AU for B < 8G. For a significant subset of these strengths (200mG < B < 5 G), the growth rate is of order the ideal MHD rate (0.75 Omega). Hall conductivity modifies the structure and growth rate of global unstable modes at 1 AU for all magnetic field strengths that support MRI. As a result, at this radius, modes obtained with a full conductivity tensor grow faster and are active over a more extended cross-section of the disc, than perturbations in the ambipolar diffusion limit. For relatively strong fields (e.g. B > 200 mG), ambipolar diffusion alters the envelope shapes of the unstable modes, which peak at an intermediate height, instead of being mostly flat as modes in the Hall limit are in this region of parameter space. Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B < 2 G. For strong fields, perturbations exhibit a kink at the height where x-ray ionisation becomes active. Finally, for R = 5 AU (10 AU), unstable modes exist for B < 800 mG (B < 250 mG) and the maximum growth rate is close to the ideal-MHD rate for 20 mG < B < 500 mG (2 mG < B < 50 mG). Similarly, perturbations incorporating Hall conductivity have a higher wavenumber and grow faster than solutions in the ambipolar diffusion limit for B < 100 mG (B < 10 mG). Unstable modes grow even at the midplane for B > 100 mG (B ~ 1 mG), but for weaker fields, a small dead region exists. When a population of 0.1 um grains is assumed to be present, perturbations grow at 10 AU for B < 10 mG. We estimate that the figure for R = 1 AU would be of order 400 mG. We conclude that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. An example of such magnetic activity is the generation of MRI unstable modes, which are supported at 1 AU for field strengths up to a few gauss. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 AU, in particular, it is crucial to incorporate the full conductivity tensor in the analysis of this instability, and more generally, in studies of the dynamics of astrophysical discs.

Accretion discs efficiently transport angular momentum by a wide variety of as yet imperfectly understood mechanisms, with profound implications for the disc lifetime and planet formation. We discuss two different methods of angular momentum transport: first, generation of acoustic waves by mixing of inertial waves, and second, the generation of a self-sustaining magnetic field via the magnetorotational instability (MRI) which would be a source of dissipative turbulence. Previous local simulations of the MRI have shown that the dynamo changes character on addition of vertical stratification. We investigate numerically 3D hydrodynamic shearing waves with a conserved Hermitian form in an isothermal disc with vertical gravity, and describe the associated symplectic structure. We continue with a numerical investigation into the linear evolution of the MRI and the undular magnetic buoyancy instability in isolated flux regions and characterise the resultant quasi-linear EMFs as a function of height above the midplane. We combine this with an analytic description of the linear modes under an assumption of a poloidal-toroidal scale separation. Finally, we use RAMSES to perform full MHD simulations in a zero net flux shearing box, followed by spatial and a novel temporal averaging to reveal the essential structure of the dynamo. We find that inertial modes may be efficiently converted into acoustic modes for "bending waves", despite a fundamental ambiguity in the inertial mode structure. With our linear MRI and the undular magnetic buoyancy modes we find the localisation of the instability high in the atmosphere becomes determined by magnetic buoyancy rather than field strength for small enough azimuthal wavenumber, and that the critical Alfven speed below which the dynamo can operate increases with increasing distance from the midplane. We calculate analytically quasi-linear EMFs which predict both a vertical propagation of toroidal field and a method for creation of radial field. From our fully nonlinear calculations we find an electromotive force in phase with the toroidal field, which is itself 3π/2 out of phase with the radial (sheared) field at the midplane, and good agreement with our quasi-linear analytics. We have identified an efficient mechanism for generating acoustic waves in a disc. In our investigation of the accretion disc dynamo, we have reproduced analytically the EMFs calculated in our simulations, given arguments based on the phase of relevant quantities, several correlation integrals and the scalings suggested by our analytic work. Our analysis contributes significantly to an explanation for the dynamo in an accretion disc.

The standard paradigm of active galactic nuclei (AGN) postulates that their luminosity, L ~ 1039−48erg s−1, derives from the accretion of gas onto a supermassive black hole, mass M ~ 106−9M☉, at the centre of a host galaxy. Echo or reverberation mapping affords a method of relating flux variations at different wavelengths to determine the nature of the flux emitting regions, with μ-arcsecond resolution. The results of an intensive two-month campaign of ground based spectrophotometric monitoring of the Seyfert 1 galaxy NGC 7469, with a temporal resolution of ≤1 day, are presented. Application of echo mapping techniques reveal the virial mass of the central source to be MNGC 7469 ~106−7 M☉, and a compact broad Balmer line emitting region ~ 5 light days from the central source. Together, this evidence suggests the existence of a supermassive black hole in NGC 7469. Further, evidence for significant wavelength- dependent continuum time delays is presented, with optical continuum variations lagging those at UV wavelengths by about 1-2 days. The wavelength-dependent time delays, (λ), are consistent with the predicted T ∝ λ 4/ 3 relationship for an irradiated blackbody accretion disc with temperature structure T(R) ∝ R−3/4 and hence may represent the indirect detection of an accretion disc structure in NGC 7469. It is shown that wavelength-dependent time delays test the standard black-hole accretion disc paradigm of AGN, by measuring T(R) of the gaseous material surrounding the purported black hole. Moreover, a new direct method is presented that combines observed time delays and the spectral energy distribution of an AGN to derive a redshift-independent luminosity distance; assuming the observed time delays are indeed due to a classical accretion disc structure. The luminosity distance permits an estimate of the Hubble constant, H0-the expansion rate of the Universe. The first application of the method yields H0(cos i/0.7)1/2 = 38 ± 7km s−1 Mp −1. A more accurate determination of H0 requires either an independent accurate determination of the disc inclination i or statistical average of a moderate sample of active galaxies. This method permits determination of redshift-independent luminosity distances to AGNs, thereby, giving a new route to H0, and by extension to fainter objects at z ~ 1, q0.

Includes bibliographical references
Long-term optical spectroscopic monitoring of Galactic Be X-ray binaries (BeXBs) is performed using the Liverpool Telescope and the Southern African Large Telescope on northern and southern objects, respectively. Be disc size variations are presented to investigate their influence on mass accretion producing X-ray activity. Be disc variability is traced observationally through Balmer emission lines, the strongest and best studied being the Hα line. The peak separations of the double peaked Hα emission line are measured, and along with the mass of the Be star and the inclination of the disc obtained from literature, are used to determine the Be disc radius. For single peaked Hα profiles the peak separation cannot be obtained directly; however, using the empirically determined relationship between the equivalent width and the peak separation of the double peaked profiles, an estimate of the peak separation for the single peaked profiles is obtained. The work is done in the context of the viscous decretion disc model presented by Okazaki & Negueruela (2001), which predicts that the circumstellar discs around Be stars in binary systems are truncated by resonant torques from the neutron star in its orbit. The calculated disc radii are compared to the expected resonance radii from the viscous decretion disc model to determine how different truncation radii affect mass accretion producing X-ray outbursts. Type I outbursts are seen to occur when the disc is truncated close to/beyond the mean critical Roche lobe radius at periastron passage of the neutron star, in agreement with model predictions. Type II outbursts, however, do not show any correlation (or anticorrelation) with the disc size, as they are seen to occur both at relatively small and large sizes of the disc. Additional information on the Hα emission line profile variations, such as the line-shape variations of high-resolution spectra, is required to investigate the origin of type II outbursts in order to make reliable predictions of them. Spectroscopic follow-up of the gamma-ray binary system LSI +61 303 was also performed with the Liverpool Telescope and the Hα line profile variations are presented. In addition to data from the Liverpool Telescope monitoring campaign, published equivalent width measurements are used and timing analysis of the combined measurements is performed. The orbital period and super-orbital period are found, which are similar to those found at other wavelengths. The periodicities in the system can therefore be associated with circumstellar disc variations.

Emission from X-ray binaries is variable on a wide range of timescales. On long timescales, changes in mass accretion rate drive changes in spectral state. There is also rapid variability, the power spectrum of which consists of a low frequency quasi-periodic oscillation (QPO) superimposed on a broad band noise continuum. Here I investigate a model intended to quantitatively explain the observed spectral and variability properties. I consider a truncated disc geometry whereby the inner regions of an optically thick, geometrically thin accretion disc evaporate to form an optically thin, large scale height accretion flow. The QPO is driven by Lense-Thirring precession of the entire hot flow and the broad band noise is due to fluctuations in mass accretion rate which propagate towards the central object. Mass conservation ties these two processes together, enabling me to define a model for the QPO and broad band noise which uses only one set of parameters. I am thus able fit the model to data. The accretion rate fluctuations drive fluctuations in the precession frequency, giving rise to a quasi-periodic oscillation rather than a pure periodicity. The model thus predicts recent observations which show the QPO frequency to correlate with flux on short timescales. I then investigate a more unique model prediction. As the flow precesses, the patch of the disc preferentially illuminated by the flow rotates such that a non face on observer sees a quasi-periodic shift between blue and red shift in the iron K alpha line. An observation of such an effect would constitute excellent evidence for the model.

In this Thesis, we study the accretion of mass and angular momentum onto the disc of spiral galaxies from a global and a local perspective and comparing theory predictions with several observational data. First, we propose a method to measure the specific mass and radial growth rates of stellar discs, based on their star formation rate density profiles and we apply it to a sample of nearby spiral galaxies. We find a positive radial growth rate for almost all galaxies in our sample. Our galaxies grow in size, on average, at one third of the rate at which they grow in mass. Our results are in agreement with theoretical expectations if known scaling relations of disc galaxies are not evolving with time. We also propose a novel method to reconstruct accretion profiles and the local angular momentum of the accreting material from the observed structural and chemical properties of spiral galaxies. Applied to the Milky Way and to one external galaxy, our analysis indicates that accretion occurs at relatively large radii and has a local deficit of angular momentum with respect to the disc. Finally, we show how structure and kinematics of hot gaseous coronae, which are believed to be the source of mass and angular momentum of massive spiral galaxies, can be reconstructed from their angular momentum and entropy distributions. We find that isothermal models with cosmologically motivated angular momentum distributions are compatible with several independent observational constraints. We also consider more complex baroclinic equilibria: we describe a new parametrization for these states, a new self-similar family of solution and a method for reconstructing structure and kinematics from the joint angular momentum/entropy distribution.

In this Thesis, we study the accretion of mass and angular momentum onto the disc of spiral galaxies from a global and a local perspective and comparing theory predictions with several observational data. First, we propose a method to measure the specific mass and radial growth rates of stellar discs, based on their star formation rate density profiles and we apply it to a sample of nearby spiral galaxies. We find a positive radial growth rate for almost all galaxies in our sample. Our galaxies grow in size, on average, at one third of the rate at which they grow in mass. Our results are in agreement with theoretical expectations if known scaling relations of disc galaxies are not evolving with time. We also propose a novel method to reconstruct accretion profiles and the local angular momentum of the accreting material from the observed structural and chemical properties of spiral galaxies. Applied to the Milky Way and to one external galaxy, our analysis indicates that accretion occurs at relatively large radii and has a local deficit of angular momentum with respect to the disc. Finally, we show how structure and kinematics of hot gaseous coronae, which are believed to be the source of mass and angular momentum of massive spiral galaxies, can be reconstructed from their angular momentum and entropy distributions. We find that isothermal models with cosmologically motivated angular momentum distributions are compatible with several independent observational constraints. We also consider more complex baroclinic equilibria: we describe a new parametrization for these states, a new self-similar family of solution and a method for reconstructing structure and kinematics from the joint angular momentum/entropy distribution.

The circumnuclear disc (CND) orbiting the Galaxy's central black hole is a reservoir of material that can ultimately provide energy through accretion, or form stars in the presence of the black hole, as evidenced by the stellar cluster that is presently located at the CND's centre. In this paper, we report the results of a computational study of the dynamics of the CND. The results lead us to question two paradigms that are prevalent in previous research on the Galactic Centre. The first is that the disc's inner cavity is maintained by the interaction of the central stellar cluster's strong winds with the disc's inner rim, and secondly, that the presence of unstable clumps in the disc implies that the CND is a transient feature. Our simulations show that, in the absence of a magnetic field, the interaction of the wind with the inner disc rim actually leads to a filling of the inner cavity within a few orbital time-scales, contrary to previous expectations. However, including the effects of magnetic fields stabilizes the inner disc rim against rapid inward migration. Furthermore, this interaction causes instabilities that continuously create clumps that are individually unstable against tidal shearing. Thus the occurrence of such unstable clumps does not necessarily mean that the disc is itself a transient phenomenon. The next steps in this investigation are to explore the effect of the magnetorotational instability on the disc evolution and to test whether the results presented here persist for longer time-scales than those considered here.

Themain characters of this thesis are themagnetic field, the plasma velocity field, the turbulentmagnetic resistivity and the numerical codes. They act on two different stages and on two different levels and occasionaly there are other bit players, e.g. the α-effect, the quenching, the differential rotation, themagnetic streamfunction, themagnetic Reynolds number, the Interactive Data Language and even ZEUS. All of them are led by the same invisible hand with the purpose of understanding better the intricate topic of the magnetic field - plasma relation. The two stages of the scene could not be more different, in one case everything is done in less than a minute inside a proto-neutron star soon after a supernova explosion, in the other case there is no time evolution at all and an equilibrium configuration is looked for inside a disc ofmatter spiraling around a neutron star. Nevertheless the same set of equations can describe the behaviour of the characters on both stages, this set is composed of the equations of the electromagnetic field plus the fluid equations. However knowing that the answers to all of your questions are written inside only one book, does not mean that you are able to read that book ... It is at this moment that the numerical codes come into the scene, offering you a way of translating the book in a language that you know. Unfortunately they like playing tricks and you cannot trust their translations unless you take many precautions every time. Eventually, after the equations have been solved, comes the art of interpreting the results; a task that might seem quite simple in comparison with the difficulties overcome on the path to get there, but that requires a deep knowledge of what has already been done and a good intuition about what can possibly happen later on. We do not presume to have made big leaps forward in the process of understanding the behaviour of the magnetic field in the cases considered here, nonetheless thanks to our simplified models we were able to grasp the fundamental aspects of the phenomena being considered, to gain some insights and to propose new falsifiable ideas. At the same time we have also developed new tools for making our models more elaborate and realistic. Therefore we expect to find even more characters in the future Chapters of this analysis, but that is another story, and will be told another time.

I have carried out three-dimensional numerical simulations of self-gravitating discs to determine under what circumstances they fragment to form bound clumps that may grow into giant planets. Through radiation hydrodynamical simulations using a Smoothed Particle Hydrodynamics code, I find that the disc opacity plays a vital role in determining whether a disc fragments. Specifically, opacities that are smaller than interstellar Rosseland mean values promote fragmentation (even at small radii, R < 25AU) since low opacities allow a disc to cool quickly. This may occur if a disc has a low metallicity or if grain growth has occurred. Given that the standard core accretion model is less likely to form planets in a low metallicity environment, I predict that gravitational instability is the dominant planet formation mechanism in a low metallicity environment. In addition, I find that the presence of stellar irradiation generally acts to inhibit fragmentation (since the discs can only cool to the temperature defined by stellar irradiation). However, fragmentation may occur if the irradiation is sufficiently weak that it allows the disc to attain a low Toomre stability parameter. With specific reference to the HR 8799 planetary system, I find that it is only possible for fragments to form in the radial range where the HR 8799 planets are located (approximately 24-68 AU) if the disc is massive. In such a high mass regime, mass transport occurs in the disc causing the surface mass density to alter. Therefore, fragmentation is not only affected by the disc temperature and cooling, but also by any restructuring due to the gravitational torques. The high mass discs also pose a problem for the formation of this system because the protoplanets accrete from the disc and end up with masses greater than those inferred from observation and thus, the growth of planets would need to be inhibited. In addition, I find that further subsequent fragmentation at small radii also takes place. By way of analytical arguments in combination with hydrodynamical simulations using a parameterised cooling method, I explore the fragmentation criteria which in the past, has placed emphasis on the cooling timescale in units of the orbital timescale, beta. I find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. I find that for shallow surface mass density profiles (p<2, where the surface mass density is proportional to R^{-p}), fragments form in the outer regions of the disc. However for steep surface mass density profiles (p is greater than or similar to 2), fragments form in the inner regions of a disc. In addition, I find that the critical value of the cooling timescale in units of the orbital timescale, beta_crit, found in previous simulations is only applicable to certain disc surface mass density profiles and for particular disc radii and is not a general rule for all discs. I obtain an empirical fragmentation criteria between the cooling timescale in units of the orbital timescale, beta, the surface mass density, the star mass and the radius. Finally, I carry out crucial resolution testing by performing the highest resolution disc simulations to date. My results cast some serious doubts on previous conclusions concerning fragmentation of self-gravitating discs.

The reflection of the X-rays emitted from a corona of energetic particles surrounding an accreting black hole from the accretion disc is investigated in the context of probing the structure of the central regions as well as the physical processes that power some of the brightest objects seen in the Universe. A method is devised to measure the emissivity profile of the accretion disc, that is the reflected flux as a function of radius in the disc. This method exploits the variation in the Doppler and gravitational redshift of emission from different radii in the disc to fit the observed reflection spectrum as the sum of contributions from successive radii and is applied to X-ray spectra of the narrow line Seyfert 1 galaxies 1H 0707-495, IRAS 13224-3809 and MCG-6-30-15 as well as the Galactic X-ray binary, Cygnus X-1. This illumination pattern of the accretion disc is a sensitive probe of the geometry of the corona that is illuminating the disc. A formalism is developed in which systematic ray tracing simulations can be run between X-ray emitting coronae and the accretion disc for a range of source geometries and other physical parameters, allowing observable data products to be simulated that can be directly compared to data from astrophysical black holes, in order to determine how these parameters affect the observed data, allowing them to be constrained observationally. The measured emissivity profiles are found to be in agreement with those expected theoretically and it is also discovered that the measured emissivity profile can be used to determine the radial extent of the X-ray emitting corona above the accretion disc. The X-ray emitting coronae are located and their radial extents constrained in 1H 0707-495, IRAS 13224-3809 and MCG-6-30-15, while the insight gained into accretion disc emissivity profiles from ray tracing simulations allows the low flux state that 1H 0707-495 was seen to drop in to in January 2011 to be explained in terms of a collapse of the X-ray emitting corona to a confined region around the central black hole. The rapid variability of the X-ray emission from accreting black holes is exploited in the use of reverberation time lags, where variability in the continuum is seen to lead that in its reflection from the accretion disc, to measure the distances between the X-ray emitting corona and the reflector. Ray tracing calculations are developed to simulate lag spectra that can be measured in X-ray observations to provide a means of constraining the extent and geometry of the corona, complimentary to the use of the emissivity profiles. Combining these methods, the X-ray emitting coronae are constrained to extend radially outward a few tens of gravitational radii over the accretion disc, while extending vertically a few gravitational radii above the plane of the disc. Furthermore, it is demonstrated how measured lag spectra can be used to understand the propagation of luminosity fluctuations through the extent of the corona and techniques are developed for analysing energy-resolved variability analysis that will be possible with future generations of X-ray telescopes. Finally, these methods, along with theoretical insight gained form ray tracing simulations, are applied to X-ray spectra extracted from 1H 0707-495 during periods of low and high flux during the observations. Evidence is found for the expansion of the corona along with a drop in the average energy density as the X-ray luminosity increases followed by its contraction as the luminosity decreases on timescales of hours.

In this thesis, an assessment is made of the value of optical CMDs as a useful diagnostic of the accretion properties of young stars. An analysis has been made of the phenomena that we observe and their effect on the position of stars in the CMD. Limitations and potential biases have been identified and evaluated. Variability causes some luminosity spread at a given colour in optical CMDs. A detailed characterisation of variability has been performed which places strong constraints on the magnitudes and the timescales on which the variability is seen. On timescales 15 minutes, almost no variability is detected (at levels greater than ≈ 0.2%) in the i band for a sample of ≈ 700 disc-bearing young stellar objects (YSOs). This suggests that the variability predicted by some accretion shock models is either very weak or not present. On hours to days timescales the optical variability in most stars is well described by a simple power law. The amplitude of the variability, a ∝ f−k, where f is the frequency of the variability in days. Disc-bearing and discless YSOs exhibit median values of k of 0.85 ± 0.02 and 0.95 ± 0.03 respectively, the uncertainity being the error on the median. The power law is valid up to a certain timescale (tmax) at which point the variability amplitude does not increase any further. tmax is found to be 1.50 ± 0.07 days and 1.41 ± 0.10 days for disc-bearing and discless stars respectively. Disc-bearing stars show greater variability amplitudes than the discless stars. However, it is notable that the variability timescale and power spectrum exponent are remarkably similar. This implies that the amplitude of the variability is driven by the physics of the underlying process, but that the timescales are instead driven by geometric effects. For disc-bearing stars, the highest amplitude variables are the accreting stars, which often appear to vary in the CMD along lines that correspond to changes in accretion luminosity. Four disc-bearing stars (approximately 0.5% of the disc-bearing sample) in Cep OB3b show extreme variability on timescales of years. Three (possible EXor candidates), show long-timescale changes that have a dramatic effect on their CMD position. However their small numbers mean that the overall impact on the CMDs of young associations is small. Variability on timescales of the rotational period and shorter adds uncertainty to age estimates of individual stars that are calculated by comparison with PMS models. Having provided a detailed description of variability and its impact on the CMD, it is clear that there are further significant mechanisms that affect the positions of YSOs in the CMD. I show that the spread in luminosity seen in the Orion Nebula Cluster and NGC 2264 could not be explained by accretion at rates of M ̇ ≥ 5 × 10−4 M⊙ yr−1 occurring within the protostellar phase of YSO evolution. Thus it appears that CMDs are not a useful diagnostic for study of the accretion histories of YSOs. The wavelength dependence of the extinction by dust within the inner regions of YSO discs is shown to differ from that seen in the ISM. Typically the wavelength dependence of the extinction is given by RV ≈5-8, compared with the value of RV ≈3.1 typical of the ISM. The interpretation is that grain growth has occurred. The location of this material within the ‘snow line’ implies that grains have coalesced rather than simply gaining an ice mantle. This is evidence for the beginning of planet formation. The effect of the high value of RV on the CMD is to add additional uncertainty of 0.1 mag to photometric measurements that have been corrected for the effects of extinction. Accretion luminosity is shown to be the dominant signal in the luminosity spread seen in CMDs of young associations. Stars which exhibit excess flux in the U band or Hα are displaced in CMD space. The accretion vector is shown to be a significant blueward shift in colour accompa- nied by a modest brightening in the g, g − i CMD. Accretion results in a luminosity spread as stars are displaced blueward below the PMS locus. This effect is not seen in non-accreting disc-bearing stars. Examination of the underlying excess luminosity spectrum for 15 accreting stars shows that the colour of the emission excess is not consistent across the sample. Thus to quantify the effect of accretion luminosity on CMD positions for individual stars, moderate resolution spectra are required with a large range in wavelength. This accretion luminosity may systematically bias estimates of PMS ages. A simple mitigation is to exclude accreting stars from age analysis. U band and Hα flux excesses are shown to vary independently by ≈ 1 dex on timescales shorter than the rotation period of the star. The relation between U band flux excess and veiling at 7000Å also appears to be variable. This implies that single epoch measurements of these parameters will add an uncertainty of ≈ 1 dex on accretion rates derived from them. Accretion rates derived from either U or Hα excess should be calculated from a mean of several photometric measurements, separated by significant fractions of the rotation period of the star. In most stars, the veiling at 7000Å is shown not to be a good measure for the calculation of the accretion rate. Despite providing a detailed characterisation of phenomena that influence the positions of YSOs in the CMD, there exists some residual luminosity spread at a given Teff that cannot be explained by variability on any timescale, extinction uncertainties or accretion luminosity. This residual spread should provide an opportunity to study an as-yet uncharacterised aspect of young stars.

High-mass stars play a significant role in the evolution of the Universe and the process that leads to the formation of such objects is still an open question in Astrophysics. The details of the structures connected to the central sources, such as the circumstellar disks and the morphology of the jets at their launching points, still lack of observational evidence. In this thesis, the high-mass star forming process is investigated in terms of the evolution of high-mass clumps selected from the ATLASGAL survey based on their CO emission in the sub-millimetre. While single-dish sub-millimetre observations provide a large-scale view of the high-mass star formation process, higher angular resolution observations are required to disentangle the details of the protostars within the clumps. For this, three-dimensional infrared spectroscopy was obtained for a group of RMS sources to characterise the circumstellar environment of high-mass YSOs in linear scales of ~100-1000 AU. The ATLASGAL TOP100 sample offers a unique opportunity to analyse a statistically complete sample of high-mass clumps at different evolutionary stages. APEX data of three rotational J transitions of the CO (the CO(4-3), CO(6-5) and CO(7-6)) were used to characterise the properties of their warm gas (~155 K) content and to derive the relations between the CO and the clump properties. The CO line luminosities were derived and the analysis indicated that the CO emission increases as a function of the evolutionary stage of the clumps (from infrared-weak to HII regions) and as a function of the bolometric luminosity and mass of the sources. The comparison of the TOP100 with low-mass objects observed in the CO(6-5) and CO(7-6), together with CO(10-9) data observed for a complementary sample of objects indicated that the dependency of the CO luminosity with the bolometric luminosity of the sources gets steeper towards higher-J transitions. Although the CO luminosity of more luminous clumps are systematically larger than the values obtained for the less luminous sources, the individual analysis of each subsample suggests a similar dependency of the CO luminosity versus the bolometric luminosity for each luminosity regime. Finally, the presence of high-velocity CO emission observed for the TOP100 suggests that ~85% of the sources are driving molecular outflows. The selection of isolated high-mass objects undergoing mass accretion is fundamental to investigate if these objects are formed through an accretion disc or if they are formed by merging of low-mass YSOs. The near-infrared window provides one of the best opportunities to investigate the interior of the sub-mm clumps and study in details their individual members. Thanks to the relatively high-resolution obtained in the K-band and the moderate reddening effects in the K-band, a sample of eight (8) HMYSOs exhibiting large-scale H2 outflows were selected to follow-up K-band spectroscopic observations using the NIFS spectrometer (Gemini North). All sources exhibit extended continuum emission and exhibit atomic and molecular transitions typical of embedded objects, such as Brackett-gama, H2 and the CO lines. The H2 lines are tracing the launching point of the large-scale jets in scales of ~100 AU in five of eight sources (63%). The identification of jets at such small scales indicates that these objects are still undergoing mass accretion. The Brackett-gama emission probes the ionised gas around the HMYSOs. The analysis of the Brackett-gama spectro-astrometry at sub-pixel scales suggests that the line arises from the cavity of the outflows or from rotating structures perpendicular to the H2 jets (i.e., disc). Five sources also exhibit CO emission features (63%), and three HMYSOs display CO absorption features (38%), indicating that they are likely associated with circumstellar discs. By further investigating the kinematics of the spatially resolved CO absorption features, the Keplerian mass of three sources was estimated in 5±3, 8±5 and 30±10 solar masses. These results support that high-mass stars are formed through discs, similarly as observed towards low-mass stars. The comparison between the collimation degree of the molecular jets or outflows detected in the NIFS data with their large-scale counterparts indicate that these structures present a relatively wide range of collimation degrees.
Estrelas de alta massa têm grande impacto na evolução do Universo e o processo de formação destes objetos ainda é um problema em aberto na Astrofísica. Os detalhes das estruturas associadas às regiões mais próximas dos objetos centrais, tais como os discos circunstelares e a morfologia dos jatos próximos à base de lançamento, ainda não foram estudados em detalhe e carecem de evidências observacionais. Esta tese apresenta um estudo da formação de estrelas de alta massa em termos da evolução de glóbulos de alta massa (clumps), selecionados a partir do levantamento ATLASGAL, a partir de observações da molécula do CO na faixa espectral do sub-milimétrico. Enquanto observações \"single-dish\" no sub-milimétrico possibilitam o estudo em larga escala do processo de formação de estrelas de alta massa, observações com maior resolução angular são necessárias para investigar os detalhes das protoestrelas no interior dos glóbulos. Para isso, espectroscopia tri-dimensional no infra-vermelho próximo foi obtida para um grupo de fontes RMS para caracterizar o meio circunstelar de objetos estelares jovens e de alta massa (HMYSOs) em escalas lineares de ~100-1000 UA. A amostra TOP100 oferece uma oportunidade ímpar de analisar um conjunto estatisticamente completo de glóbulos de alta massa em diversas fases evolutivas. Observações realizadas com o radiotelescópio APEX de três transições rotacionais da molécula do CO (CO(4-3), CO(6-5) e CO(7-6)) foram utilizadas para estudar as propriedades do gás morno (~155 K) associado aos glóbulos, e obter as relações entre a emissão do CO e as propriedades físicas dos glóbulos. A luminosidade das diferentes transições do CO foi obtida e sua análise mostrou que a emissão do gás aumenta em função do estágio evolutivo dos glóbulos (de glóbulos com emissão fraca no infravermelho longínquo a regiões HII) e em função da luminosidade bolométrica e massa dos glóbulos. A comparação entre os glóbulos de alta massa presentes na amostra TOP100 com fontes de menor massa observadas nas transições do CO(6-5) e CO(7-6), juntamente com a análise de uma amostra complementar de fontes observadas na transição do CO(10-9) mostrou que a dependência da luminosidade do CO com a luminosidade bolométrica aumenta em função do número quântico J associado à transição do CO. Este estudo também mostrou que as relações entre a luminosidade do CO e dos clumps são dominadas pelas fontes de alta luminosidade presentes na amostra analisada. A análise individual de fontes de baixa e alta luminosidade sugerem que a dependência entreas luminosidades do CO e bolométrica é a mesma em ambos os regimes de luminosidade, embora as luminosidades do CO sejam sistematicamente maiores para os glóbulos de alta massa. Por fim, a análise da emissão do CO em altas-velocidades mostrou que ~85% dos glóbulos presentes na amostra TOP100 apresentam jatos moleculares. A seleção de objetos de alta massa isolados em estágio de acreção ativa é crucial para decidir se ela ocorre através de um disco de acreção e/ou via fusão de YSOs de menor massa. Para isso, observações no infra-vermelho próximo são ideais para se investigar o conteúdo dos glóbulos sub-milimétricos e resolver seus membros individuais. Devido a alta resolução espacial na banda K e a extinção interestelar moderada nesta faixa espectral, um conjunto de oito (8) HMYSOs associados a jatos em H2 em larga-escala foram selecionados para observações espectroscópicas na banda K utilizando o espectrômetro NIFS no Gemini Norte. Todos os objetos investigados com o NIFS apresentam emissão extendida no contínuo, bem como nas linhas espectrais típicas de fontes jovens, tais como o Brackett-gama, transições do H2 e a emissão nas bandas moleculares do CO. A emissão em H2 está associada aos jatos moleculares em escalas de ~100 UA em cinco das oito fontes (63%). A indentificação de jatos moleculares em escalas tão próximas ao objeto central indica que o processo de acreção de massa ainda está ativo nestes objetos. A emissão do Brackett-gama provém do gás ionizado nas regiões mais próximas das fontes centrais ou regiões de choque próximas aos jatos. A espectro-astrometria da linha do Brackett-gama em escalas de sub-píxeis, indica que a emissão do gás ocorre nas cavidades dos jatos moleculares ou delineiam estruturas alinhadas perpendicularmente aos jatos, tais como os discos de acreção. Cinco fontes também apresentam emissão nas bandas do CO (63%), e três HMYSOs apresentam linhas do CO em absorção (38%), indicando que estes objetos apresentam discos de acreção. A massa total do sistema \"disco e protoestrela\" foi determinada a partir do estudo da cinemática das linhas de absorção do CO, detectadas em três objetos. A partir de modelos de rotação Kepleriana, as massas das fontes foram estimadas em 5±3, 8±5 e 30±10 massas solares. Os resultados obtidos a partir da espectroscopia tri-dimensional no infravermelho corroboram a hipótese de que estrelas de alta massa são formadas a partir de acreção por discos, de maneira similar ao observado para estrelas de baixa massa. A comparação entre a morfologia dos jatos moleculares identificados nos campos do NIFS e das correspondentes contrapartidas em escalas maiores indicam que os jatos apresentam diferentes graus de colimação ao longo de suas estruturas, explicadas pela multiplicidade de fontes nas proximidades da base de lançamento dos jatos ou efeitos de precessão no objeto central.

In this thesis we analyse X-ray data of accretion powered low mass and high mass X-ray binaries to understand the nature of their accretion mechanisms by searching for some clues of viscous time-scales of their accretion discs, if they have, in their low frequency power density spectra created from their long-term X-ray observations, or by doing pulse timing analysis with much shorter X-ray data to detect the effects of torque fluctuations caused by the accreting material on the pulsar. The low mass and high mass X-ray binaries we analysed have breaks in their power density spectra, which are attributed to the role of viscosity in the formation of accretion discs. Although, the time-scales corresponding to these break frequencies are smaller than the predictions of the Standard theory of accretion discs, the sources give consistent results among themselves by displaying the expected correlation between their break and orbital frequencies. The correlation curve of LMXBs implies thicker appearing accretion discs than those assumed by the theory. The dichotomy of the HMXBs on this curve points out the different origins of accretion that these sources may have, and offers a way to distinguish the stellar-wind fed systems from the Roche-lobe overflow systems. The timing and spectral analysis of Swift J1626.6-5156 reveal a correlation between the spin-up rate and the luminosity of the source implying that the pulsar is accretion-powered. This correlation together with the characteristics of the X-ray spectra enables us to estimate the magnetic field and the distance of the source. The AXP 1E 2259+586 does not display any signs of viscous time-scale in its low frequency power density spectra, and its pulse timing analysis gives a much smaller torque noise value than that expected from accretion powered pulsars. In addition, the analysis results presented in this thesis reveal magnetar-like glitches which differ than those of radio pulsars, due to the presence of the strong magnetic field of the pulsar. These results eliminate the possibility that the AXP is an accretion-powered pulsar.

We investigate the origin of the parsec-scale radio emission from the changing-look active galactic nucleus (AGN) of Mrk 590, and examine whether the radio power has faded concurrently with the dramatic decrease in accretion rates observed between the 1990s and the present. We detect a compact core at 1.6 and 8.4 GHz using new Very Long Baseline Array observations, finding no significant extended, jet-like features down to similar to 1 pc scales. The flat spectral index (alpha(8.4)(1.6) = 0.03) and high brightness temperature (T-b similar to 10(8) K) indicate self-absorbed synchrotron emission from the AGN. The radio to X-ray luminosity ratio of log(L-R/L-X) similar to -5, similar to that in coronally active stars, suggests emission from magnetized coronal winds, although unresolved radio jets are also consistent with the data. Comparing new Karl G. Jansky Very Large Array measurements with archival and published radio flux densities, we find 46 per cent, 34 per cent, and (insignificantly) 13 per cent flux density decreases between the 1990s and the year 2015 at 1.4 GHz, 5 GHz and 8.4 GHz, respectively. This trend, possibly due to the expansion and fading of internal shocks within the radio-emitting outflow after a recent outburst, is consistent with the decline of the optical-UV and X-ray luminosities over the same period. Such correlated variability demonstrates the AGN accretion-outflow connection, confirming that the changing-look behaviour in Mrk 590 originates from variable accretion rates rather than dust obscuration. The present radio and X-ray luminosity correlation, consistent with low/hard state accretion, suggests that the black hole may now be accreting in a radiatively inefficient mode.

L’émission X associée à l’accrétion sur un objet compact présenter une important variabilit photométrique et spectroscopique. Quand l’accréteur est en orbite autour d’une étoile Supergéante, il capture une fraction du vent stellaire supersonique qui forme des chocs dans son voisinage. L’amplitude et la stabilité de cette focalisation gravitationnelle conditionnent le taux d’accrétion de masse responsable, in fine, de la luminosité X des Binaires X Supergéantes (SgXB). La capacité de ce flot à faible moment angulaire à former un disque susceptible de présenter des instabilités est en jeu.Grâce à des setups numériques sophistiqués, nous caractérisons la structure du flot de Bondi- Hoyle-Lyttleton sur un objet compact, depuis le choc jusqu’au voisinage de l’accréteur, typiquement 5 ordres de grandeur plus petit. L’évolution du choc détaché qui se forme autour de l’accréteur (structure transverse, angle d’ouverture, stabilité, profil de température) avec le nombre de Mach est détaillé. La fiabilité de ces simulations basées sur le code hautes performances MPI-AMRVAC est étayée par la topologie de la surface sonique, en accord avec le attentes théoriques.Nous développons un modèle synthétique de transfert de masse dans les SgXB qui couple le lancement du vent, les paramètres stellaires, l’évolution orbital du flot et l’accrétion. Nous montrons que la forme du flot est entièrement détermimée par les facteur de remplissage et d’Eddington, le rapport de masse et le multiplieur de force alpha. Avec les paramètres d’échelle, nous pouvons en déduire, eg, la luminosité X, le processus d’accrétion et le cisaillement du flot
X-ray emission associated to accretion onto compact objects displays important levels of photometric and spectroscopic time-variability. When the accretor orbits a Supergiant star, it captures a fraction of the supersonic radiatively-driven wind which forms shocks in its vicinity. The amplitude and stability of this gravitational beaming of the flow conditions the mass accretion rate responsible, in fine, for the X-ray luminosity of those Supergiant X-ray Binaries (SgXB). The capacity of this low angular momentum inflow to form a disc susceptible to be the stage of instabilities remains at stake.Using state-of-the-art numerical setups, we characterize the structure of a Bondi-Hoyle- Lyttleton flow onto a compact object, from the shock down to the vicinity of the accretor, typically five orders of magnitude smaller. The evolution of the bow shock which forms around the accretor (transverse structure, opening angle, stability, temperature profile...) with the Mach number of the flow is detailed. The robustness of those simulations based on the High Performance Computing MPI-AMRVAC code is supported by the topology of the inner sonic surface, consistent with theoretical expectations.We develop a synthetic model of mass transfer in SgXB which couples the launching of the wind the stellar parameters, the orbital evolution of the streamlines and the accretion process. We show that the shape of the permanent flow is entirely determined by the filling and Eddington factor, the mass ratio and the alpha force multiplier. Provided scales are known, we can trace back, eg, the X-ray luminosity, the accretion mechanism (stream or wind-dominated) and the shearing of the inflow

Protoplanetary discs, composed of gas and dust, usually surround young stellar objects and serve two main purposes: they determine the accretion of matter onto the central object and also represent sites of planet formation. The accretion proceeds through the transport of angular momentum outwards allowing the disc matter to fall towards the centre. A mechanism responsible for the transport can be turbulence, waves or other coherent structures originating from various instabilities in discs that could, in addition, play a role in the planet formation process. For an understanding of these instabilities, it is necessary to study perturbation dynamics in differentially rotating, or sheared media. Thus, this thesis focuses on new aspects in the perturbation dynamics in non-magnetised protoplanetary discs that arise due to their self-gravity and velocity shear associated with the disc’s differential rotation. The analysis is carried out in the framework of the widely employed local shearing box approximation. We start with 2D discs and then move on to 3D ones. In 2D discs, there are two basic perturbation types/modes – spiral density waves and vortices – that are responsible for angular momentum transport and that can also contribute to accelerating planet formation. First, in the linear regime, we demonstrate that the vortical mode undergoes large growth due to self-gravity and in this process generates density waves via shear-induced linear mode coupling phenomenon. This is noteworthy, because commonly only density waves are considered in self-gravitating discs. Then we investigate vortex dynamics in the non-linear regime under the influence of self-gravity by means of numerical simulations. It is shown that vortices are no longer well-organised and long-lived structures, unlike those occurring in non-self-gravitating discs. They undergo recurring phases (lasting for a few disc rotation periods) of formation, growth and eventual destruction. We also discuss the dust trapping capability of such transient vortices. Perturbation dynamics in 3D vertically stratified discs is richer, as there are more mode types. We first consider non-axisymmetric modes in non-self-gravitating discs and then only axisymmetric modes in the more complicated case when self-gravity is present. Specifically, in non-self-gravitating discs with superadiabatic vertical stratification, motivated by the recent results on the transport properties of incompressible convection, we show that when compressibility is taken into account, the non-axisymmetric convective mode excites density waves via the same shear-induced linear mode coupling mechanism mentioned above. These generated density waves transport angular momentum outwards in the trailing phase, and we suggest that they may aid and enhance the transport due solely to convection in the non-linear regime, where the latter becomes outward. In the final part of the thesis, we carry out a linear analysis of axisymmetric vertical normal modes in stratified self-gravitating discs. Although axisymmetric modes do not display shear-induced couplings, their analysis provides insight into how gravitational instabilities develop in the 3D case and their onset criterion. We examine how the structure of dispersion curves and eigenfunctions of 3D modes are influenced by self-gravity, which mode first becomes gravitationally unstable and thus determines the onset criterion and nature of the gravitational instability in stratified discs. We also contrast the more exact instability criterion obtained with our 3D model with that of density waves in 2D discs. Based on these findings, we discuss the origin of 3D behaviour of perturbations involving noticeable disc surface distortions, as seen in some numerical simulations of self-gravitating discs.

I buchi neri transienti (BHT) sono tra le sorgenti con emissione ai raggi X più luminose della galassia. Grazie all’elevato flusso in banda X e alla loro alta variabilità temporale. queste sorgenti offrono un’opportunità unica per studiare la fisica dell’accrescimento in straordinareie condizioni fisiche. I BHT mostrano episodici outburst caratterizzati da diverse luminosità in banda X e γ, diverse forme spettrali e proprietà della variabilità temporale. L’obiettivo di questa tesi è lo studio della geometria, dei meccanismi e dei processi fisici coinvolti nell’emissione del buco nero transiente GRS 716-249. Di seguito presento l’analisi spettrale e temporale delle osservazioni della GRS 1716-249 ai raggi X effettuate con il satellite Neil Gehrels Swift bservatory durante l’outburst verificatosi nel 2016-2017. Questi dati mi hanno permesso di studiare l’evoluzione dei parametri fisici durante tutta la durata dell’outburst e di studiare come varia la geometria della materia in accrescimento attraverso le transizioni spettrali. In particolare, coerentemente con lo scenario del disco di accrescimento troncato in cui il disco si avvicina all’oggetto compatto durante l’evoluzione dell’outburst, ho osservato che il disco di accrescimento della GRS 1716-249 potrebbe aver raggiunto l’ultima orbita stabile mentre la sorgente si trovava nello stato hard intermedio. Grazie al monitoraggio radio effettuato durante l’outburst ho potuto localizzare la sorgente sulla sempre più popolata correlazione radio/X degli "outliers" (o radioquieti) nel piano delle luminosità radio/X. Successivamente, mi sono concentrata sull’emissione ai raggi X/γ della sorgente. Questo mi ha permesso di osservare un eccesso nell’emissione alle alte energie, sopra a 200 keV, in aggiunta allo spettro di Comptonizzazione termica, nello spettro della GRS 1716-249. L’origine di questa componente può essere dovuta a processi di Compton inverso tra i fotoni soft del disco d’accrescimento e una popolazione di elettroni non-termici nella corona, o all’emissione di sincrotrone prodotta dagli elettroni energetici nel getto. Inizialmente ho modellando lo spettro X/γ della sorgente con modelli ibridi di Comptonizazione termica/non-termica: EQPAIR e BELM. In particolare, utilizzando BELM ho potuto stimare un limite superiore sull’intensità del campo magnetico nella corona. Infine, ho considerato la possibilità che l’eccesso di energia alle ate energie sia dovuto all’emissioni del jet. A tale scopo, ho prodotto la distribuzione d’energia spettrale della GRS 1716-249 usando le osservazioni multi-banda (dalla banda radio ai raggi γ) eseguite quando la sorgente era nello stato hard. Il flusso di accrescimento l’ho modellato con un modello di disco irradiato unito ad un modello di Comptonizzazine, mentre l’emissione del getto l’ho modellata con il modello Internal Schock Emission Model (ISHEM). Questo modello assume che le fluttuazioni di velocità del getto siano guidate dalla variabilità delle proprietà temporali del disco di accrescimento. Sebbene (ISHEM riproduce i dati radio e soft γ della sorgente GRS 1716-249, i risultati favoriscono lo scenario di Comptonizazione non termica nel flusso di accrescimento rispetto all’emissione di sincrotrone del getto oltre 200 keV.
Black hole transients (BHTs) are among the brightest X-ray sources in the Galaxy. Thanks to their high X-ray flux and short variability time scales they offer a unique opportunity to study the physics of the accretion under extraordinary physical conditions. These sources show episodic outbursts characterised by different X/γ-ray luminosities, spectral shapes and timing properties. The aim of this thesis is the understanding of the geometry, mechanisms and physical processes playing a role in the bright black hole X-ray transient GRS 1716-249. I present the spectral and timing analysis of X-ray observations performed with the Neil Gehrels Swift Observatory on GRS 1716-249 during the 2016-2017 outburst. These data gave me the opportunity to study the evolution of physical parameters and geometry variation of the accreting matter through the spectral transitions during the whole outburst. I found that the accretion disc could have reached the inner stable circular orbit during the hard intermediate state, coherently with the truncated accretion disc scenario in which the disc moves closer to the compact object. Then, the radio monitoring performed during the outburst let me locate the source on the ever more populated radio-quiet branch on the radio/X-ray luminosity plane. Thereafter, focusing on the soft γ-ray emission of the source, I observed a high energy excess, above 200 keV, in addition to the thermal Comptonisation spectrum. This component could be originate either through inverse Compton of the soft photons by non-thermal electrons in the corona, or from synchrotron emission of energetic electrons in the jet. First, I fitted the broad band X/γ-ray spectrum of GRS 1716-249 with hybrid Comptonisation thermal/non-thermal models: EQPAIR and BELM. Using BELM I obtained an upper limit on the magnetic field intensity in the corona. Finally, I investigated the possible origin of this high energy excess as due to jet emission. To this aim, I computed the Spectral Energy Distribution of GRS 1716-249 with the multi-wavelength observations (from the radio band to γ-rays) performed. I modelled the accretion flow with an irradiated disc plus Comptonisation model and the jet emission with the internal shock emission model (ISHEM). This model assumes that the jet velocity fluctuations are directly driven by the variability of X-ray timing proprieties of the accretion flow. Even though ISHEM reproduces the radio and soft γ-ray data of GRS 1716-249, the results seem to disfavour the jet scenario for the excess above 200 keV, in favour of non-thermal Comptonisation process.

Tidal Disruption Events (TDEs) occur when a star, wandering too close to a black hole (BH), is torn apart by BH tides. After the disruption, roughly half of the stellar debris is expected to circularize around the BH and eventually form an accretion disc. These events represent a unique way to detect BHs through the universe since they emit both electromagnetic (EM) radiation and gravitational waves (GWs). In fact, after returning to the pericenter, the stellar material accretes onto the central object, producing very luminous EM flares. To date, around 50 robust TDEs have been detected in different bands of the EM spectrum (optical, X-ray, radio). Furthermore, these events also produce GWs during the whole process: while the star is stretched and compressed by BH tides, when the star is disrupted at pericenter and during the circularization process. So far, these gravitational signals have been inaccessible to us since they are low-frequency signals. Hence, these events will be seen by the future space-based detectors (like LISA and deci-Hertz observatories). In the upcoming future, thanks to the synergy between the spatial GW observatories and new and more performant telescopes, we will observe these events both via GWs and EM radiation. This will provide us a unique and more complete way to study BHs. Given these premises, this Thesis aims to study the main features of TDE gravitational emission, both through analytical and numerical studies. In particular, I explore the signal from an individual TDE, focussing on the emission generated at later stages during the circularization of the debris. Then, I investigate the signal produced by the entire cosmic population of tidal disruptions. Finally, I illustrate a catalogue of gravitational waveforms from TDEs built with a numerical tool implemented by myself during the PhD.

Le champ magnétique vertical joue un rôle prépondérant dans la dynamique des disques d'accrétion. L'émission de jet par un disque ainsi que la turbulence qu'on suppose y exister sont tous deux fortement contraints par l'intensité de ce champ vertical. Ce champ évolue lui même suivant les mécanismes d'advection par la matière et de diffusion par la turbulence. Depuis plus de vingt ans, la question de l'évolution d'un tel champ dans un disque fait l'objet de nombreuses études, mais une modélisation globale de disque prenant en compte tous ces ingrédients n'avait encore jamais été réalisée. Je propose ici un modèle, considérant le transport d'un champ magnétique vertical par le disque, mais également la rétroaction de ce champ sur la dynamique du disque. Une résolution analytique de configurations homogènes est réalisée. Elle confirme les résultats des études précédentes, à savoir qu'en l'état actuel des connaissances des processus de transport, un disque turbulent ne peut advecter significativement le champ vertical pour permettre l'émission d'un jet. Elle met cependant en avant une configuration nouvelle de disque, mixte, dans laquelle les conditions d'éjection sont réunies non pas à l'intérieur du disque mais dans ses régions externes. La stabilité des configurations homogènes calculée a été réalisée, et de nouvelles instabilités sont mises en avant. L'effectivité de ces instabilités dépend des dépendances fonctionnelles employées pour quantifier la dynamique du disque. Une caractérisation, via des simulation locales, des ces dépendances fonctionnelles, permettrait de savoir si ces instabilités peuvent être effectives dans un disque d'accrétion. Enfin, les outils numériques développé permettent d'étudier les configurations envisagées. Les configurations homogènes stationnaires sont récupérées, et une étude dynamique de la configuration mixte permet de caractériser les conditions d'advection de la limite disque éjectant/disque standard
The vertical magnetic field plays a fundamental role in the dynamics of accretion discs. The jet launching, so as the turbulence that is supposed to exist in these discs are strongly constrained by the intensity of this field. This field evolves following the mechanisms of advection by the mater and diffusion by turbulence. The question of the evolution of such a field has been studied since more than 20 years, but a global modelisation, involving all these méchanisms wasn't done yet. I propose a model, taking into account the transport of a vertical magnetic field by the disc, and also the feedback of this field on the dynamics of the disc. Analytical solutions for standard configurations a calculated. It confirms previous studies in the sense that considering the state of the art, a turbulent disc can not advect a vertical field in order to allow a jet launching. However, a new configuration is rised, in wich the ejection conditions are realised in the outer radius of the disc. The stability of the standard configurations is calculated, and new instabilities are rised. The effectivity of such instabilities depends on the functionnal dependancies used to quantify the disc dynamics. A determination of such dependancies, via local simulations, would clarify if such instabilities could be effective in accretion discs. At last, the numerical tools developped allows to study the configurations. Standard one are found, and a dynamical study of the new configuration is done to determine the advection conditions for the limit ejecting disc/ standard disc

The main goal of my PhD Thesis was to investigate the nature of ULXs using their multiwave-length emission properties and to extend the treatment of the evolution of their binary systems including the effects of super-Eddington accretion. In this way we constrain the masses of the black holes and donor stars in these systems, and their accretion regime. To this end, we developed a code that enables us to constrain the properties of ULXs binaries from their position on the Color-Magnitude Diagram, from their multiwavelength SED and from additional information available on the systems (such as the age of its parent stellar population). A novelty of this present treatment is the inclusion of super-Eddington accretion, with the possibility to produce the output in the HST photometric system; the extension of the parameter space for BH and donor masses with a proper computation of the orbital angular momentum loss during super-critical accretion; the possibility to model the Multiwavelength emission of ULXs considering the effects of a Comptonzing corona covering the innermost regions of the disc.

This thesis describes efforts to improve the realism of numerical models of giant planet formation and migration in an attempt to better understand these processes. A new approach has been taken to the modelling of accretion, designed to mimic reality by allowing gas to accumulate upon a protoplanetary surface. Implementing this treatment in three-dimensional self-gravity radiation hydrodynamics calculations provides an excellent model for planet growth, allowing an exploration of the factors that affect accretion. Moreover, these calculations have also been extended to investigate the migration of protoplanets through their parent discs as they grow. When focusing on the growth of non-migrating protoplanets, the models are performed using small sections of disc, enabling excellent resolution right down to the core; gas structures and flow can be resolved on scales from ~ 10^4 to 10^11 metres. Using radiative transfer, these models reveal the importance of opacity in determining the accretion rates. For the low mass protoplanets, equivalent in mass to a giant planet core (~ 10 M⊕), the accretion rates were found to increase by up to an order of magnitude for a factor of 100 reduction in the grain opacity of the parent circumstellar disc. However, even these low opacities lead to growth rates that are an order of magnitude slower than those obtained in locally-isothermal conditions. For high mass protoplanets (>~ 100M⊕), the accretion rates show very little dependence upon opacity. Nevertheless, the rates obtained using radiative transfer are still lower than those obtained in locally-isothermal models by a factor of ~2, due to the release of accretion energy as heat. Only high mass protoplanets are found to be capable of developing circumplanetary discs, and this ability is dependent upon the opacity, as are the scaleheights of such discs. However, their radial extents were found to be independent of the opacity and the protoplanet mass, all reaching ≈ RH/3, inline with analytic predictions. Migration is investigated using global models, ensuring a self-consistently evolved disc. Using locally-isothermal calculations, it was found that the capture radius of an accreting sink particle, used to model a protoplanet without a surface, must be small (<< RH) to yield migration timescales consistent with linear theory of Type I migration. In the low mass regime of Type I migration, accreting sinks with such small radii yield timescales consistent with those models in which a protoplanetary surface is used. However, for high mass protoplanets, undergoing Type II migration, the surface treatment leads to faster rates of migration, indicating the importance of a realistic accretion model. Using radiative transfer, with high opacities, leads to a factor of ~ 3 increase in the migration timescale of the lowest mass protoplanets, improving their chances of survival. As suitable gas giant progenitors, their survival is key to understanding the growth of giant planets. An unexpected result of the radiative transfer was a reduction in the migration timescale of high mass planets. This appears to be a result of the less thoroughly evacuated gaps created by planets in non-locally-isothermal discs, which affects the corotation torque.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
Includes bibliographical references (leaves 61-64).
We consider geometrically thin accretion disks around millisecond X-ray pulsars. We start with the Shakura-Sunyaev thin disk model as a basis and modify the disk equations with a magnetic torque from the central neutron star. Disk solutions are computed for a range of neutron star magnetic fields. We also investigate the effect of different equations of state and opacities on the disk solutions. We show that there are indications of thermal instability in some of the disk solutions, especially for the higher values of 3M. We also explain how the time evolution of the disk solutions can be calculated.
by Antonia Stefanova Savcheva.
S.B.