Non-Gaussian statistics, maxwellian derivation and stellar polytropes

In this letter we discuss the Non-gaussian statistics considering two aspects. In the first, we show that the Maxwell's first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. The second one, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter $\kappa$ and stellar polytrope index $n$. We compare also the Kaniadakis relation $n=n(\kappa)$ with $n=n(q)$ proposed in the Tsallis framework.Comment: 10 pages, 1 figur

An approach for the detection of point-sources in very high resolution microwave maps

This paper deals with the detection problem of extragalactic point-sources in multi-frequency, microwave sky maps that will be obtainable in future cosmic microwave background radiation (CMB) experiments with instruments capable of very high spatial resolution. With spatial resolutions that can be of order of 0.1-1.0 arcsec or better, the extragalactic point-sources will appear isolated. The same holds also for the compact structures due to the Sunyaev-Zeldovich (SZ) effect (both thermal and kinetic). This situation is different from the maps obtainable with instruments as WMAP or PLANCK where, because of the smaller spatial resolution (approximately 5-30 arcmin), the point-sources and the compact structures due to the SZ effect form a uniform noisy background (the "confusion noise"). Hence, the point-source detection techniques developed in the past are based on the assumption that all the emissions that contribute to the microwave background can be modeled with homogeneous and isotropic (often Gaussian) random fields and make use of the corresponding spatial power-spectra. In the case of very high resolution observations such an assumption cannot be adopted since it still holds only for the CMB. Here, we propose an approach based on the assumption that the diffuse emissions that contribute to the microwave background can be locally approximated by two-dimensional low order polynomials. In particular, two sets of numerical techniques are presented containing two different algorithms each. The performance of the algorithms is tested with numerical experiments that mimic the physical scenario expected for high Galactic latitude observations with the Atacama Large Millimeter/Submillimeter Array (ALMA).Comment: Accepted for publication on "Astronomy & Astrophysics". arXiv admin note: substantial text overlap with arXiv:1206.4536 Replaced version is the accepted one and published in A&

DC magnetic field generation in unmagnetized shear flows

The generation of DC magnetic fields in unmagnetized plasmas with velocity shear is predicted for non relativistic and relativistic scenarios either due to thermal effects or due to the onset of the Kelvin-Helmholtz instability (KHI). A kinetic model describes the growth and the saturation of the DC field. The predictions of the theory are confirmed by multidimensional particle-in-cell simulations, demonstrating the formation of long lived magnetic fields ($t \sim 100s \omega_{pi}^{-1}$) along the full longitudinal extent of the shear layer, with transverse width on the electron length scale ($\sqrt{\gamma_0}c/\omega_{pe}$), reaching magnitudes $eB_{\mathrm{DC}}/m_ec\omega_{pe}\sim \beta_0\sqrt{\gamma_0}$

Electron-scale shear instabilities: magnetic field generation and particle acceleration in astrophysical jets

Strong shear flow regions found in astrophysical jets are shown to be important dissipation regions, where the shear flow kinetic energy is converted into electric and magnetic field energy via shear instabilities. The emergence of these self-consistent fields make shear flows significant sites for radiation emission and particle acceleration. We focus on electron-scale instabilities, namely the collisionless, unmagnetized Kelvin-Helmholtz instability (KHI) and a large-scale dc magnetic field generation mechanism on the electron scales. We show that these processes are important candidates to generate magnetic fields in the presence of strong velocity shears, which may naturally originate in energetic matter outburst of active galactic nuclei and gamma-ray bursters. We show that the KHI is robust to density jumps between shearing flows, thus operating in various scenarios with different density contrasts. Multidimensional particle-in-cell (PIC) simulations of the KHI, performed with OSIRIS, reveal the emergence of a strong and large-scale dc magnetic field component, which is not captured by the standard linear fluid theory. This dc component arises from kinetic effects associated with the thermal expansion of electrons of one flow into the other across the shear layer, whilst ions remain unperturbed due to their inertia. The electron expansion forms dc current sheets, which induce a dc magnetic field. Our results indicate that most of the electromagnetic energy developed in the KHI is stored in the dc component, reaching values of equipartition on the order of $10^{-3}$ in the electron time-scale, and persists longer than the proton time-scale. Particle scattering/acceleration in the self generated fields of these shear flow instabilities is also analyzed

Transverse electron-scale instability in relativistic shear flows

Electron-scale surface waves are shown to be unstable in the transverse plane of a shear flow in an initially unmagnetized plasma, unlike in the (magneto)hydrodynamics case. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroom-like electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. Macroscopic ($\gg c/\omega_{pe}$) fields are shown to be generated by these microscopic shear instabilities, which are relevant for particle acceleration, radiation emission and to seed MHD processes at long time-scales