We present an XMM-Newton time-resolved spectral analysis of the narrow-line Seyfert 1 galaxy Mrk 766. We analysed eight available observations taken between May 2000 and June 2005 with the EPIC-pn camera in order to investigate the X-ray spectral variability produced by changes in the mass accretion rate. The 0.2−10 keV spectra are extracted in time bins longer than 3 ks to have at least 3 × 10 4 net counts in each bin and then accurately trace the variations of the best-fit parameters of our adopted Comptonization spectral model. We tested a bulk-motion Comptonization (BMC) model which is in general applicable to any physical system powered by accretion onto a compact object, and assumes that soft seed photons are efficiently up-scattered via inverse Compton scattering in a hot and dense electron corona. The Comptonized spectrum has a characteristic power law shape, whose slope was found to increase for large values of the normalization of the seed component, which is proportional to the mass accretion rateṁ (in Eddington units). Our baseline spectral model also includes a warm absorber lying on the line of sight and radiation reprocessing from the accretion disc or from outflowing matter in proximity to the central compact object. Our study reveals that the normalization-slope correlation, observed in Galactic black hole sources (GBHs), also holds for Mrk 766: variations of the photon index in the range Γ ∼ 1.9−2.4 are indeed likely to be related to the variations ofṁ, as observed in X-ray binary systems. We finally applied a scaling technique based on the observed correlation to estimate the BH mass in Mrk 766. This technique is commonly and successfully applied to measure masses of GBHs, and this is the first time it has been applied in detail to estimate the BH mass in an AGN. We obtained a value of M BH = 1.26 +1.00 −0.77 × 10 6 M , which is in very good agreement with that estimated by the reverberation mapping.

We study the acceleration of electrons and positrons at an electromagnetically modified, ultrarelativistic shock in the context of pulsar wind nebulae (PWNe). We simulate the outflow produced by an obliquely rotating pulsar in proximity of its termination shock with a two-fluid code which uses a magnetic shear wave to mimic the properties of the wind. We integrate electron trajectories in the test-particle limit in the resulting background electromagnetic fields to analyse the injection mechanism. We find that the shock-precursor structure energizes and reflects a sizeable fraction of particles, which becomes available for further acceleration. We investigate the subsequent first-order Fermi process sustained by small-scale magnetic fluctuations with a Monte Carlo code. We find that the acceleration proceeds in two distinct regimes: when the gyro-radius r g exceeds the wavelength of the shear λ, the process is remarkably similar to first-order Fermi acceleration at relativistic, parallel shocks. This regime corresponds to a low density wind which allows the propagation of superluminal waves. When r g < λ, which corresponds to the scenario of driven reconnection, the spectrum is softer.

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