The synchrotron-self-Compton spectrum of relativistic blast waves at large Y

Recent analyses of multiwavelength light curves of gamma-ray bursts afterglows point to values of the magnetic turbulence well below the canonical $\sim1\,$\% of equipartition, in agreement with theoretical expectations of a micro-turbulence generated in the shock precursor, which then decays downstream of the shock front through collisionless damping. As a direct consequence, the Compton parameter $Y$ can take large values in the blast. In the presence of decaying micro-turbulence and/or as a result of the Klein-Nishina suppression of inverse Compton cooling, the $Y$ parameter carries a non-trivial dependence on the electron Lorentz factor, which modifies the spectral shape of the synchrotron and inverse Compton components. This paper provides detailed calculations of this synchrotron-self-Compton spectrum in this large $Y$ regime, accounting for the possibility of decaying micro-turbulence. It calculates the expected temporal and spectral indices $\alpha$ and $\beta$ customarily defined by $F_\nu\,\propto\,t_{\rm obs}^{-\alpha}\nu^{-\beta}$ in various spectral domains. This paper also makes predictions for the very high energy photon flux; in particular, it shows that the large $Y$ regime would imply a detection rate of gamma-ray bursts at $>10\,$GeV several times larger than currently anticipated.Comment: 13 pages, 6 figures, to appear in MNRA

The Growth-Volatility Relationship: New Evidence Based on Stochastic Volatility in Mean Models

This paper models the relationship between growth and volatility for G7 economies in the time period 1960-2009. It delivers for the first time estimates of this relationship based on a logarithm variant of stochastic volatility in mean (SV-M) models. The relationship appears significantly positive in Germany and Italy, but insignificant in other countries. We also show that output volatility has increased in all countries since the beginning of the financial crisis, which illustrates the end of the great moderation. For comparison, the paper also delivers estimates based on a logarithm variant of GARCH in mean (log-GARCH-M) models, the class of time series models previously used in the literature to estimate the growth-volatility relationship. We show that SV-M models deliver results preferable to those of log-GARCH-M models, despite the high computational cost of their estimation. SV-M models fit generally better data than log-GARCH-M ones. As their residuals do not violate distribution assumptions, they do not deliver dubious conclusions concerning the significance of the relationship, which is the case of the log-GARCH-model for France, the UK and the US. Finally, SV-M models suggest a positive impact of unexpected volatility on output growth, which is not taken into account by log-GARCH-M models.Growth, Volatility, Sequential Monte-Carlo Methods.

Corrugation of relativistic magnetized shock waves

As a shock front interacts with turbulence, it develops corrugation which induces outgoing wave modes in the downstream plasma. For a fast shock wave, the incoming wave modes can either be fast magnetosonic waves originating from downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting through the shock. Using linear perturbation theory in relativistic MHD, this paper provides a general analysis of the corrugation of relativistic magnetized fast shock waves resulting from their interaction with small amplitude disturbances. Transfer functions characterizing the linear response for each of the outgoing modes are calculated as a function of the magnetization of the upstream medium and as a function of the nature of the incoming wave. Interestingly, if the latter is an eigenmode of the upstream plasma, we find that there exists a resonance at which the (linear) response of the shock becomes large or even diverges. This result may have profound consequences on the phenomenology of astrophysical relativistic magnetized shock waves.Comment: 14 pages, 9 figures; to appear in Ap

Centaurus A as the Source of ultra-high energy cosmic rays?

We present numerical simulations for energy spectra and angular distributions of nucleons above 10^{19} eV injected by the radio-galaxy Centaurus A at a distance 3.4 Mpc and propagating in extra-galactic magnetic fields in the sub-micro Gauss range. We show that field strengths B~0.3 micro Gauss, as proposed by Farrar and Piran, cannot provide sufficient angular deflection to explain the observational data. A magnetic field of intensity ~1 micro Gauss could reproduce the observed large-scale isotropy and could marginally explain the observed energy spectrum. However, it would not readily account for the E=320 plusminus 93 EeV Fly's Eye event that was detected at an angle 136 degrees away from Cen-A. Such a strong magnetic field also saturates observational upper limits from Faraday rotation observations and X-ray bremsstrahlung emission from the ambient gas (assuming equipartition of energy). This scenario may already be tested by improving magnetic field limits with existing instruments. We also show that high energy cosmic ray experiments now under construction will be able to detect the level of anisotropy predicted by this scenario. We conclude that for magnetic fields B~0.1-0.5 micro Gauss, considered as more reasonable for the local Supercluster environment, in all likelihood at least a few sources within ~10 Mpc from the Earth should contribute to the observed ultra high energy cosmic ray flux.Comment: 7 latex pages, 7 postscript figures included; for related numerical simulations see also http://www.iap.fr/users/sigl/r2e.htm

Measuring the NAIRU: a complementary approach

Estimates of the Nairu generally suffer from a large uncertainty, which can be reduced by adopting a bivariate framework and assuming that shifts of the Phillips curve share a common trend with the unemployment rate. We consider in this paper if this common trend assumption is empirically relevant or not for seven economies over the sample 1973-2010. First, it appears that the Nairu can substantially differ from the unemployment trend. Second, relaxing the common trend assumption improves the fit of the inflation equation. Third, this assumption is necessary for getting an important reduction of uncertainty in a bivariate framework.Nairu, inflation, uncertainty.