An Application of Lorentz Invariance Violation in Black Hole Thermodynamics

In this paper, we have applied the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) with the dimensionless parameter n = 2 and the "sign of LIV" {\eta}_+ = 1, to phenomenologically study the effect of quantum gravity in the strong gravitational field. Specifically, we have studied the effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole thermodynamics. The result shows that the effect of the LIV-DR induced quantum gravity speeds up the black hole evaporation, and its corresponding black hole entropy undergoes a leading logarithmic correction to the "reduced Bekenstein-Hawking entropy", and the ill defined situations (i.e. the singularity problem and the critical problem) are naturally bypassed when the LIV-DR effect is present. Also, to put our results in a proper perspective, we have compared with the earlier findings by another quantum gravity candidate, i.e. the generalized uncertainty principle (GUP). Finally, we conclude from the inert remnants at the final stage of the black hole evaporation that, the GUP as a candidate for describing quantum gravity can always do as well as the LIV-DR by adjusting the model-dependent parameters, but in the same model-dependent parameters the LIV-DR acts as a more suitable candidate.Comment: 18 pages, 7 figure

A Bayesian Approach to Estimate the Size and Structure of the Broad-line Region in Active Galactic Nuclei Using Reverberation Mapping Data

This is the first paper in a series devoted to systematic study of the size and structure of the broad-line region (BLR) in active galactic nuclei (AGNs) using reverberation mapping (RM) data. We employ a recently developed Bayesian approach that statistically describes the variabibility as a damped random walk process and delineates the BLR structure using a flexible disk geometry that can account for a variety of shapes, including disks, rings, shells, and spheres. We allow for the possibility that the line emission may respond non-linearly to the continuum, and we detrend the light curves when there is clear evidence for secular variation. We use a Markov Chain Monte Carlo implementation based on Bayesian statistics to recover the parameters and uncertainties for the BLR model. The corresponding transfer function is obtained self-consistently. We tentatively constrain the virial factor used to estimate black hole masses; more accurate determinations will have to await velocity-resolved RM data. Application of our method to RM data with Hbeta monitoring for about 40 objects shows that the assumed BLR geometry can reproduce quite well the observed emission-line fluxes from the continuum light curves. We find that the Hbeta BLR sizes obtained from our method are on average ~20% larger than those derived from the traditional cross-correlation method. Nevertheless, we still find a tight BLR size-luminosity relation with a slope of alpha=0.55\pm0.03 and an intrinsic scatter of ~0.18 dex. In particular, we demonstrate that our approach yields appropriate BLR sizes for some objects (such as Mrk 142 and PG 2130+099) where traditional methods previously encountered difficulties.Comment: 17 pages, 10 figures, 2 tables; minor reversion to match the published versio

A New Approach to Constrain Black Hole Spins in Active Galaxies Using Optical Reverberation Mapping

A tight relation between the size of the broad-line region (BLR) and optical luminosity has been established in about 50 active galactic nuclei studied through reverberation mapping of the broad Hbeta emission line. The R_blr-L relation arises from simple photoionization considerations. Using a general relativistic model of an optically thick, geometrically thin accretion disk, we show that the ionizing luminosity jointly depends on black hole mass, accretion rate, and spin. The non-monotonic relation between the ionizing and optical luminosity gives rise to a complicated relation between the BLR size and the optical luminosity. We show that the reverberation lag of Hbeta to the varying continuum depends very sensitively to black hole spin. For retrograde spins, the disk is so cold that there is a deficit of ionizing photons in the BLR, resulting in shrinkage of the hydrogen ionization front with increasing optical luminosity, and hence shortened Hbeta lags. This effect is specially striking for luminous quasars undergoing retrograde accretion, manifesting in strong deviations from the canonical R_blr-L relation. This could lead to a method to estimate black hole spins of quasars and to study their cosmic evolution. At the same time, the small scatter of the observed R_blr-L relation for the current sample of reverberation-mapped active galaxies implies that the majority of these sources have rapidly spinning black holes.Comment: 6 pages, 5 figures, to appear in ApJ

Graphene quantum dot modified g-C3N4 for enhanced photocatalytic oxidation of ammonia performance

In this study, graphene quantum dot (GQD) modified g-C3N4 (GQDs/CN) composite photocatalysts were prepared. The photocatalytic ammonia degradation properties of the GQDs/CN composites were much higher than that of pure g-C3N4. When the amount of GQDs added reached 0.5 wt% the GQDs/CN composite showed the best performance for photocatalytic total ammonia nitrogen (TAN) removing, and a 90% TAN removing rate was achieved in 7 hours under visible light illumination (200 mW cm−2), which is approximately 3 times higher than that of pure g-C3N4. The increased photocatalytic property was contributed by the photon adsorption ability and electron transfer capacity, which were improved after GQD modification. The main photocatalytic end-product of TAN was NO3− which is a type of environmentally green ion. Further results indicated that the oxygen concentration and pH value of the reaction solution were very important for the photocatalytic ammonia degradation process. A better performance could be achieved under a higher oxygen concentration and pH value