The bulk Lorentz factor crisis of TeV blazars : evidence for an inhomogeneous pileup energy distribution ?

There is growing evidence that the estimations of the beaming Doppler factor in TeV BL Lac object based on the Self Synchrotron Compton (SSC) models are in strong disagreement with those deduced from the unification models between blazars and radio galaxies. When corrected from extragalactic absorption by the diffuse infrared background (DIrB), the SSC one-zone models require very high Lorentz factor (around 50) to avoid strong gamma-gamma absorption. However, the statistics on beamed vs. unbeamed objects, as well as the luminosity contrast, favors much lower Lorentz factor of the order of 3. In this paper, we show that for the special case of Markarian 501, the need for very high Lorentz factor is unavoidable for all one-zone models where all photons are assumed to be produced at the same location at the same time. Models assuming a double structure with two different beaming patterns can partially solve the problem of luminosity contrast, but we point out that they are inconsistent with the statistics on the number of detected TeV sources. The only way to solve the issue is to consider inhomogeneous models, where low energy and high energy photons are not produced at the same place, allowing for much smaller Lorentz factors. It implies that the jet is stratified, but also that the particle energy distribution is close to a monoenergetic one, and that pair production is likely to be significant. The implications on relativistic jet physics and particle acceleration mechanism are discussed.Comment: 31 pages, 5 figures. Accepted for publication in Ap

Variation of bulk Lorentz factor in AGN jets due to Compton rocket in a complex photon field

Radio-loud active galactic nuclei are among the most powerful objects in the universe. In these objects, most of the emission comes from relativistic jets getting their power from the accretion of matter onto supermassive black holes. However, despite the number of studies, a jet's acceleration to relativistic speeds is still poorly understood. It is widely known that jets contain relativistic particles that emit radiation through several physical processes, one of them being the inverse Compton scattering of photons coming from external sources. In the case of a plasma composed of electrons and positrons continuously heated by the turbulence, inverse Compton scattering can lead to relativistic bulk motions through the Compton rocket effect. We investigate this process and compute the resulting bulk Lorentz factor in the complex photon field of an AGN composed of several external photon sources. We consider various sources here: the accretion disk, the dusty torus, and the broad line region. We take their geometry and anisotropy carefully into account in order to numerically compute the bulk Lorentz factor of the jet at every altitude. The study, made for a broad range of parameters, shows interesting and unexpected behaviors of the bulk Lorentz factor, exhibiting acceleration and deceleration zones in the jet. We investigate the patterns of the bulk Lorentz factor along the jet depending on the source sizes and on the observation angle and we finally show that these patterns can induce variability in the AGN emission with timescales going from hours to months.Comment: 12 pages, 16 figures, accepted to A&

Time dependent modelisation of TeV blazars by a stratified jet model

We present a new time-dependent inhomogeneous jet model of non-thermal blazar emission. Ultra-relativistic leptons are injected at the base of a jet and propagate along it. We assume continuous reacceleration and cooling, producing a relativistic quasi-maxwellian (or "pile-up") particle energy distribution. The synchrotron and Synchrotron-Self Compton jet emissivity are computed at each altitude. Klein-Nishina effects as well as intrinsic gamma-gamma absorption are included in the computation. Due to the pair production optical depth, considerable particle density enhancement can occur, particularly during flaring states.Time-dependent jet emission can be computed by varying the particle injection, but due to the sensitivity of pair production process, only small variations of the injected density are required during the flares. The stratification of the jet emission, together with a pile-up distribution, allows significantly lower bulk Lorentz factors, compared to one-zone models. Applying this model to the case of PKS 2155-304 and its big TeV flare observed in 2006, we can reproduce simultaneously the average broad band spectrum of this source from radio to TeV, as well as TeV light curve of the flare with bulk Lorentz factor lower than 15

Job Turnover, Unemployment and Labor Market Institutions

This paper studies the role of labor market institutions on unemployment and on the cyclical properties of job flows. We construct an intertemporal general equilibrium model with search unemployment and endogenous job turnover, and examine the consequences of introducing an unemployment benefit, a firing cost and a downward wage rigidity. The simulations suggest that downward wage rigidities, rather than unemployment benefit or firing cost, may well play a dominant role in explaining both the high unemployment rate and the job flows dynamics of such an economy.Unemployment, Job flows dynamics, Institutions

Picking the one that does not fit - A matter of logical proportions

National audienceQuiz or tests about reasoning capabilities often pertain to the perception of similarity and dissimilarity between situations. Thus, one may be asked to complete a series of entities $A$, $B$, $C$ by an appropriate $X$, or to pick the one that does not fit in a list. It has been shown that the first problem can receive a solution by solving analogical proportion equations between the representations of the entities in a logical setting, where we assume that $X$ should be such that $A$ is to $B$ as $C$ is to $X$. In this paper, we focus on the second problem, and we show that it can be properly handled by means of heterogeneous proportions that are the logical dual of the homogeneous proportions involved in the modeling of analogical proportions and related proportions. Thus, the formal setting of logical proportions, to which homogeneous and heterogeneous proportions belong, provides an appropriate framework for handling the two problems in a coherent way. As it already exists for homogeneous proportions, a particular multiple-valued logic extension of heterogeneous proportions is discussed (indeed being an intruder in a group may be a matter of degree)