G. Bao

General Relativistic Effects on the Spectrum Reflected by Accretion Disks around Black Holes

Making the usual assumption that the relatively cold matter within the central engine of an active galactic nucleus (or galactic black hole candidate) is in the form of a relativistic accretion disk, we compute the composite spectrum of the original disk plus a primary X-ray power-law source illuminating it from above, as well as the reflected emission from the disk. All special and general relativistic effects on both infalling photons and outgoing photons are considered in a Schwarzschild geometry. The strength, shape, and broadening of the reflected spectrum depend on the direction of the X-ray source relative to the disk and the observers viewing angle. The reflected photons extract energy and angular momentum from the relativistically rotating accretion disk and are beamed in the direction of the disk velocity. The reflection hump could essentially disappear if viewed far from the symmetry axis because the X-ray photons are affected by gravity both approaching and leaving the disk. This may produce a difference between X-ray spectra for Seyfert 1 and Seyfert 2 galaxies. For a given observation angle, the reflection hump is most sensitive to the inclination of the source relative to the accretion disk. Thus the spectral shape may also shed light on the location of the primary X-ray source, which is probably either in a jet or in a corona; however, additional computations involving distributed sources will be necessary before detailed comparisons with observations are feasible.

Models for Accretion-Disk Fluctuations through Self-Organized Criticality Including Relativistic Effects

The possibility that some of the observed X-ray and optical variability in active galactic nuclei and galactic black hole candidates is produced in accretion disks through the development of a self-organized critical state is reconsidered. New simulations, including more complete calculations of relativistic effects, do show that this model can produce light-curves and power-spectra for the variability which agree with the range observed in optical and X-ray studies of AGN and X-ray binaries. However, the universality of complete self-organized criticality is not quite achieved. This is mainly because the character of the variations depend quite substantially on the extent of the unstable disk region. If it extends close to the innermost stable orbit then a physical scale is introduced and the scale-free character of self-organized criticality is vitiated. Significant dependence of the power spectrum density slope on the type of diffusion within the disk and a weaker dependence on the amount of differential rotation are noted. When general relativistic effects are incorporated in the models, additional substantial differences are produced if the disk is viewed from directions far from the accretion disk axis.

Energy Extraction from a Relativistic Accretion Disk by Reflection Effect

Reprocessing of the light radiated from a companion star by the inner part of an accretion disk around a Schwarzschild black hole is modeled. Because of the aberration between the local static frame and the comoving frame of the disk, the infalling photons are seen by the disk to come mainly from the direction of the vertex of orbital motion, and the reradiated light is beamed into the direction of the disks velocity. As in the case of inverse Compton scattering, the frequency of the reflected photons can be increased and the energy (and angular momentum) from the disk can be extracted. The efficiency of this process is dependent on the geometry of the system. The infalling flux can be amplified by a factor of order unity in the vicinity of the marginally stable orbit. Despite the fact that the loss of energy is negligible for realistic intensities of the infalling flux, the effect is interesting in principle, and it can play a role in the modeling of observable effects in accreting systems like low-mass X-ray binaries, as well as active galactic nuclei.

The Flux Ratio of a Jet to Its Counterjet Revisited

A general relativistic formula for the flux density ratio of a nuclear jet to its counterjet is obtained. The key general relativistic effect, i.e., light bending by the black hole, favors the visibility of the counterjet. The formula is significantly different from the one that considers only Doppler effects when the angle between a line of sight and the jet, i, is small, say, i 16° and on the spectral index of α < 1.6.

On the Variability Coherence Observed in Black Hole Candidates at Different X-Ray Energies

The bright spot model explains in a natural way the variability coherence observed in black hole candidates at different X-ray energies.

Energy conservation: A theory of L2 ultimate attainment

Abstract The current theoretical landscape of second language acquisition (SLA) features abundance, disunity, and fragmentation. As early as 1993, Long counted 68 theories. That number, for sure, has only multiplied in the ensuing years, though what exactly counts as a theory has remained conceptually unsettled. Extant theories are diverse and disparate; they do not seem to gravitate toward a coherent understanding of SLA. In this article, we argue that a way to make theoretical headways is by engaging critical, well-established phenomena, a theoretical path that has long been noted but has remained intact. Using ultimate attainment, one of such phenomena, as an object of theorizing, we propose a new theory to both complement the theoretical spectrum in SLA and provide for a more holistic understanding of the phenomenon at hand.

Line Profiles Radiated by Orbiting Matter Around Black Holes

Emission-line profiles from both narrow eccentric rings and an extended disk around a black hole are presented. In both cases, a black-hole signature appears when the inclination of the emitting orbit is larger than 80°.