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Register a new userMagnetised Accretion Discs in Kerr Spacetimes II: Hot Spots
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Authors
Federico Garcia
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Context. Quasi-periodic variability has been observed in a number of X-ray binaries harboring black hole candidates. In general relativity, black holes are uniquely described by the Kerr metric and, according to the cosmic censorship conjecture, curvature singularities always have to be clothed by an event horizon. Aims. In this paper, we study the effect of an external magnetic field on the observed light curves of orbiting hot spots in thin accretion discs around Kerr black holes and naked singularities. Methods. We employ a ray-tracing algorithm to calculate the light curves and power spectra of such hot spots as seen by a distant observer for uniform and dipolar magnetic field configurations assuming a weak coupling between the magnetic field and the disc matter. Results. We show that the presence of an external dipolar magnetic field leads to potentially observable modifications of these signals for both Kerr black holes and naked singularities, while an external uniform magnetic field has practically no effect. In particular, we demonstrate that the emission from a hot spot orbiting near the innermost stable circular orbit of a naked singularity in a dipolar magnetic field can be significantly harder than the emission of the same hot spot in the absence of such a magnetic field. Conclusions. The comparison of our model with observational data may allow us study the geometry of magnetic fields around compact objects and to test the cosmic censorship conjecture in conjunction with other observables such as thermal continuum spectra and iron line profiles.
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In standard accretion discs, outward angular momentum transfer by viscous forces is compensated by the inward motion of the accreting matter. However, the vertical structure of real accretion discs leads to meridional circulation with comparable amplitudes of poloidal velocities. Using thin-disc approximation, we consider different regimes of disc accretion with different vertical viscosity scalings. We show that, while gas-pressure-dominated discs can easily have a midplane outflow, standard thin radiation-pressure-dominated disc is normally moving inwards at all the heights. However, quasi-spherical scaling for pressure ($ppropto varpi^{-5/2}$) leads to a midplane outflow for a very broad range of parameters. It particular, this may lead to a reversed, outward heat advection in geometrically thick discs when the temperature decreases rapidly enough with height. While the overall direction of heat advection depends on the unknown details of vertical structure and viscosity mechanisms, existence of the midplane counterflow in quasi-spherical flows is a robust result weakly dependent on the parameters and the assumptions of the model. Future models of thick radiatively inefficient flows should take meridional circulation into account.
The tools of Kerr/CFT correspondence are applied to the Kerr black hole embedded in an axial external magnetic field. Its extremal near horizon geometry remains a warped and twisted product of $AdS_2times S^2$. The central charge of the Virasoro algebra, generating the asymptotic symmetries of the near horizon geometry, is found. It is used to reproduce, via the Cardy formula, the Bekenstein-Hawking entropy of the magnetised Kerr black hole as the statistical microscopic entropy of a dual CFT. The presence of the background magnetic field makes available also a second dual CFT picture, based on the $U(1)$ electromagnetic symmetry, instead of the only rotational one of the standard non-magnetised Kerr spacetime. A Meissner-like effect, where at extremality the external magnetic field is expelled out of the black hole, allows us to infer the value of the mass for these magnetised extremal black holes. The generalisation to the CFT dual for the magnetised extreme Kerr-Newman black hole is also presented.
Hydromagnetic stresses in accretion discs have been the subject of intense theoretical research over the past one and a half decades. Most of the disc simulations have assumed a small initial magnetic field and studied the turbulence that arises from the magnetorotational instability. However, gaseous discs in galactic nuclei and in some binary systems are likely to have significant initial magnetisation. Motivated by this, we performed ideal magnetohydrodynamic simulations of strongly magnetised, vertically stratified discs in a Keplerian potential. Our initial equilibrium configuration, which has an azimuthal magnetic field in equipartion with thermal pressure, is unstable to the Parker instability. This leads to the expelling of magnetic field arcs, anchored in the midplane of the disc, to around five scale heights from the midplane. Transition to turbulence happens primarily through magnetorotational instability in the resulting vertical fields, although magnetorotational shear instability in the unperturbed azimuthal field plays a significant role as well, especially in the midplane where buoyancy is weak. High magnetic and hydrodynamical stresses arise, yielding an effective $alpha$-value of around 0.1 in our highest resolution run. Azimuthal magnetic field expelled by magnetic buoyancy from the disc is continuously replenished by the stretching of a radial field created as gas parcels slide in the linear gravity field along inclined magnetic field lines. This dynamo process, where the bending of field lines by the Parker instability leads to re-creation of the azimuthal field, implies that highly magnetised discs are astrophysically viable and that they have high accretion rates.
Accretion discs are ubiquitous in the universe and it is a crucial issue to understand how angular momentum and mass are being radially transported in these objects. Here, we study the role played by non-linear spiral patterns within hydrodynamical and non self-gravitating accretion disc assuming that external disturbances such as infall onto the disc may trigger them. To do so, we computed self-similar solutions that describe discs in which a spiral wave propagates. Such solutions present both shocks and critical sonic points that we carefully analyze. For all allowed temperatures and for several spiral shocks, we calculated the wave structure. In particular we inferred the angle of the spiral patern, the stress it exerts on the disc as well as the associated flux of mass and angular momentum as a function of temperature. We quantified the rate of angular momentum transport by means of the dimensionless $alpha$ parameter. For the thickest disc we considered (corresponding to $h/r$ values of about 1/3), we found values of $alpha$ as high as $0.1$, and scaling with the temperature $T$ such that $alpha propto T^{3/2} propto (h/r)^3$. The spiral angle scales with the temperature as $arctan(r/h)$. The existence of these solutions suggests that perturbations occurring at disc outer boundaries, such as for example perturbations due to infall motions, can propagate deep inside the disc and therefore should not be ignored, even when considering small radii.
We examine the properties of strongly magnetized accretion discs in a global framework, with particular focus on the evolution of magnetohydrodynamic instabilities such as the magnetorotational instability (MRI). Work by Pessah and Psaltis showed that MRI is stabilized beyond a critical toroidal field in compressible, differentially rotating flows and, also, reported the appearance of two new instabilities beyond this field. Their results stemmed from considering geometric curvature effects due to the suprathermal background toroidal field, which had been previously ignored in weak-field studies. However, their calculations were performed under the local approximation, which poses the danger of introducing spurious behavior due to the introduction of global geometric terms in an otherwise local framework. In order to avoid this, we perform a global eigenvalue analysis of the linearized MHD equations in cylindrical geometry. We confirm that MRI indeed tends to be highly suppressed when the background toroidal field attains the Pessah-Psaltis limit. We also observe the appearance of two new instabilities that emerge in the presence of highly suprathermal toroidal fields. These results were additionally verified using numerical simulations in PLUTO. There are, however, certain differences between the the local and global results, especially in the vertical wavenumber occupancies of the various instabilities, which we discuss in detail. We also study the global eigenfunctions of the most unstable modes in the suprathermal regime, which are inaccessible in the local analysis. Overall, our findings emphasize the necessity of a global treatment for accurately modeling strongly magnetized accretion discs.
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