1,991 research outputs found

    Relativistic Winds from Compact Gamma-ray Sources: I. Radiative Acceleration in the Klein-Nishina Regime

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    We consider the radiative acceleration to relativistic bulk velocities of a cold, optically thin plasma which is exposed to an external source of gamma-rays. The flow is driven by radiative momentum input to the gas, the accelerating force being due to Compton scattering in the relativistic Klein-Nishina limit. The bulk Lorentz factor of the plasma, Gamma, derived as a function of distance from the radiating source, is compared with the corresponding result in the Thomson limit. Depending on the geometry and spectrum of the radiation field, we find that particles are accelerated to the asymptotic Lorentz factor at infinity much more rapidly in the relativistic regime; and the radiation drag is reduced as blueshifted, aberrated photons experience a decreased relativistic cross section and scatter preferentially in the forward direction. The random energy imparted to the plasma by gamma-rays can be converted into bulk motion if the hot particles execute many Larmor orbits before cooling. This `Compton afterburn' may be a supplementary source of momentum if energetic leptons are injected by pair creation, but can be neglected in the case of pure Klein-Nishina scattering. Compton drag by side-scattered radiation is shown to be more important in limiting the bulk Lorentz factor than the finite inertia of the accelerating medium. The processes discussed here may be relevant to a variety of astrophysical situations where luminous compact sources of hard X- and gamma-ray photons are observed, including active galactic nuclei, galactic black hole candidates, and gamma-ray bursts.Comment: LateX, 20 pages, 5 figures, revised version accepted for publication in the Ap

    Quantifying overdispersion effects in count regression data

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    The Poisson regression model is often used as a first model for count data with covariates. Since this model is a GLM with canonical link, regression parameters can be easily fitted using standard software. However the model requires equidispersion, which might not be valid for the data set under consideration. There have been many models proposed in the literature to allow for overdispersion. One such model is the negative binomial regression model. In addition, score tests have been commonly used to detect overdispersion in the data. However these tests do not allow to quantify the effects of overdispersion. In this paper we propose easily interpretable discrepancy measures which allow to quantify the overdispersion effects when comparing a negative binomial regression to Poisson regression. We propose asymptotic α\alpha-level tests for testing the size of overdispersion effects in terms of the developed discrepancy measures. A graphical display of p-values curves can then be used to allow for an exact quantification of the overdispersion effects. This can lead to a validation of the Poisson regression or a discrimination of the Poisson regression with respect to the negative binomial regression. The proposed asymptotic tests are investigated in small samples using simulation and applied to two examples
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