Models of Diffusion of Galactic Cosmic Rays From Superbubbles

Abstract

Superbubbles are shells in the interstellar medium produced by the simultaneous explosions of many supernova remnants. The solutions of the mathematical diffusion and of the Fourier expansion in 1D, 2D and 3D were deduced in order to describe the diffusion of nucleons from such structures. The mean number of visits in the the case of the Levy flights in 1D was computed with a Monte Carlo simulation. The diffusion of cosmic rays has its physical explanation in the relativistic Larmor gyro-radius which is energy dependent. The mathematical solution of the diffusion equation in 1D with variable diffusion coefficient was computed. Variable diffusion coefficient means magnetic field variable with the altitude from the Galactic plane. The analytical solutions allow us to calibrate the code that describes the Monte Carlo diffusion. The maximum energy that can be extracted from the superbubbles is deduced. The concentration of cosmic rays is a function of the distance from the nearest superbubble and the selected energy. The interaction of the cosmic rays on the target material allows us to trace the theoretical map of the diffuse Galactic continuum gamma-rays. The streaming of the cosmic rays from the Gould Belts that contains the sun at its internal was described by a Monte Carlo simulation. Ten new formulas are derived.

Anomalous Transport of High-Energy Cosmic Rays in Galactic Superbubbles. I. Numerical Simulations

“…On the one hand, the superbubble origin of GCR is made more compelling by a number of disparate observations and interpretations: from energetics and acceleration efficiency (Casse et al 2001;Butt & Bykov 2008;Butt 2009Butt , 2011 to elemental (Silich et al 2001;Rauch et al 2009;Ohira & Ioka 2011) and isotopic (Binns et al 2001) composition of both the progenitors (Higdon et al 1998;Lingenfelter & Higdon 2007;Ogliore et al 2009), as well as those of the arriving GCRs (Alibes et al 2002;Lingenfelter et al 2003;Prantzos 2010). In addition, there appears to be further supporting evidence from, e.g., the presumed superbubble origin of dust particles in the interstellar medium (ISM; Westphal & Bradley 2004) to the mathematical and statistical characters (Tsallis et al 2003;Beck 2004Beck , 2009Otsuka & Hada 2006;Zaninetti 2007) of cosmic-ray transport and acceleration in general. On the other, the notion of a superbubble origin of GCR is not without some "technical" problems (Tatischeff & Kiener 2011) such as those related to the source abundance ratio of some crucial isotopes (Prantzos 2012) deduced from the recent Fermi-LAT γ -ray observations (Mizuno et al 2011).…”

The Giants Arcs as Modeled by the Superbubbles

“…The physical parameters concerning the Gould Belt as deduced in [57], are reported in Table 5. The total energy is such as to produce results comparable with the observations and the kinematic age is the same as in [57,58]. In order to obtain E tot = 6.…”