On the Nature of Black Holes in Loop Quantum Gravity

A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain the black hole thermodynamical properties. As for all quantum systems, a quantum realization of black holes requires an operator algebra of the fundamental observables of the theory which is introduced in this study based on aspects of loop quantum gravity. From the eigenvalue spectra of the quantum operators for the black hole area, charge and angular momentum, it is demonstrated that a strict bound on the extensive parameters, different from the relation arising in classical general relativity, holds, implying that the extremal black hole state can neither be measured nor can its existence be proven. This is, as turns out, a result of the specific form of the chosen angular momentum operator and the corresponding eigenvalue spectrum, or rather the quantum measurement process of angular momentum. Quantum mechanical considerations and the lowest, non-zero eigenvalue of the loop quantum gravity black hole mass spectrum indicate, on the one hand, a physical Planck scale cutoff of the Hawking temperature law and, on the other hand, give upper and lower bounds on the numerical value of the Immirzi parameter. This analysis provides an approximative description of the behavior and the nature of quantum black holes

Synchrotron self-Compton flaring of TeV blazars

A theoretical radiation model for the flaring of TeV blazars is discussed here for the case of a nonlinear electron synchrotron cooling in these sources. We compute analytically the optically thick and thin synchrotron radiation intensities and photon density distributions in the emission knot as functions of frequency and time followed by the synchrotron self-Compton intensity and fluence in the optically thin frequency range using the Thomson approximation of the inverse Compton cross section. At all times and frequencies, the optically thin part of the synchrotron radiation process is shown to provide the dominant contribution to the synchrotron self-Compton quantities, while the optically thick part is always negligible. Afterwards, we compare the linear to the nonlinear synchrotron radiation cooling model using the data record of PKS 2155-304 on MJD 53944 favouring a linear cooling of the injected monoenergetic electrons. The good agreement of both the linear and the nonlinear cooling model with the data supports the relativistic pickup process operating in this source. Additionally, we discuss the synchrotron self-Compton scattering, applying the full Klein-Nishina cross section to achieve the most accurate results for the synchrotron self-Compton intensity and fluence distributions

Synchrotron self-Compton flaring of TeV blazars

The vast improvement of the sensitivity of modern ground-based air Cherenkov telescopes, together with the sensitive flux measurements at lower frequencies, requires accurate elaborations of the theoretical radiation models for flaring blazars. Here the flaring of TeV blazars due to the synchrotron-self Compton (SSC) process is considered. We assume that, at the moment $t=t_0$, a flare in the emission knot occurs due to the instantaneous injection of monoenergetic (E0) ultrarelativistic electrons. The ultrarelativistic electrons are injected uniformly over the knot volume and at later times are subject to linear synchrotron radiation cooling in a magnetic field whose strength remains constant during the time evolution of the relativistic electrons. The generated synchrotron photons are subject to multiple Thomson-scattering off the cold electrons in the source giving rise to spatial photon diffusion. Optically thick and thin synchrotron radiation intensities and photon density distributions in the emission knot as functions of frequency and time are analytically determined. The synchrotron photons serve as target photons for the SSC process, which is calculated in the optically thin frequency range using the Thomson approximation of the inverse Compton cross section. It is shown that the optically thick part of the synchrotron radiation process provides a negligible contribution to the resulting SSC intensity at all frequencies and times. Because the high-energy TeV photons undergo no elastic multiple Compton scatterings, we neglect the influence of photon diffusion in the calculation of the SSC intensity and fluence distribution with energy. The SSC fluence exhibits a break at $E_f=15.8b^{-1/3}$ GeV from a $\propto$$E_s^{-1/4}$-power law spectrum at lower photon energies $E_t\le E_s\le E_f$ to a $\propto$$E_s^{-2}[1-(E_s/E_0)^{7/3}]$-distribution at high energies $E_f\le E_s\le E_0$. The application to the observed TeV fluence spectrum of the flare of PKS 2155-304 on July 28, 2006 yields $\delta b^{-1/3}=27.1\pm 6.5$. The emergent SSC light curve is independent of spatial photon diffusion and determined by the temporal variations on the relativistic electron density distribution and the synchrotron photon density. The comparison of the observed with the theoretical monochromatic synchrotron light curve determines the photon escape distribution

Predicting the future from observable sequences of events in astrophysics I. Maximum Likelihood Estimation for a fixed number of parameters

International audienceUsing analytical and numerical methods, estimates are given of future predictions in astrophysics that can be gathered from a sequence of observed events, for example for ?-ray bursts. Some general probability considerations are provided and then a maximum likelihood estimation, together with an approximation for the large number limit of possible events. Illustrations are given of the numerical maximum likelihood estimation programs in the situations of both a large number and a finite number of events. The effects of data uncertainty are also considered. Numerical calculations and comparisons with theoretical expectations are presented too