Ultra-high-energy cosmic rays (UHECRs) have been tried to be related to the most varied and powerful sources known in the universe. Gamma-ray bursts (GRBs) are natural candidates. Here, we argue that cosmic rays can be accelerated by large amplitude
electromagnetic waves (LAEMWs) when the MHD approximation of the field in the wind generated by the GRBs magnetized central engine breaks down. The central engine considered here is a strange star born with differential rotation from the accretion induced conversion of a neutron star into a strange star in a low-mass X-ray binary system. The LAEMWs generated this way accelerate light ions to the highest energies $E = qetaDeltaPhi_{max}$ with an efficiency $eta sim 10^{-1}$ that accounts for all plausible energy losses. Alternatively, we also consider the possibility that, once formed, the LAEMWs are unstable to creation of a relativistically strong electromagnetic turbulence due to an overturn instability. Under this assumption, a lower limit to the efficiency of acceleration is estimated to be about $eta sim 10^{-2.5}$. Due to their age, low mass X-ray binary systems can be located in regions of low interstellar medium density as, e.g., globular clusters or even intergalactic medium in case of high proper motion systems, and cosmic ray energy losses due to proton collisions with photons at the decelerating region are avoided, thus opening the possibility for particles to exploit the full voltage available, well beyond that currently observed.
Following a wave-mechanical treatment we calculate the drag force exerted by an infinite homogeneous background of stars on a perturber as this makes its way through the system. We recover Chandrasekhars classical dynamical friction (DF) law with a m
odified Coulomb logarithm. We take into account a range of models that encompasses all plausible density distributions for satellite galaxies by considering the DF exerted on a Plummer sphere and a perturber having a Hernquist profile. It is shown that the shape of the perturber affects only the exact form of the Coulomb logarithm. The latter converges on small scales, because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm this way earlier results based on the impulse approximation of small angle scatterings.
We present a rigorous calculation of the dynamical friction force exerted on a spherical massive perturber moving through an infinite homogenous system of field stars. By calculating the shape and mass of the polarization cloud induced by the perturb
er in the background system, which decelerates the motion of the perturber, we recover Chandrasekhars drag force law with a modified Coulomb logarithm. As concrete examples we calculate the drag force exerted on a Plummer sphere or a sphere with the density distribution of a Hernquist profile. It is shown that the shape of the perturber affects only the exact form of the Coulomb logarithm. The latter converges on small scales, because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm this way earlier results based on the impulse approximation of small angle scatterings.
We investigate the Jeans instability of a galactic disk embedded in a dynamically responsive dark halo. It is shown that the disk-halo system becomes nominally Jeans unstable. On small scales the instability is suppressed, if the Toomre stability ind
ex Q_T is higher than a certain threshold, but on large scales the Jeans instability sets invariably in. However, using a simple self-consistent disk-halo model it is demonstrated that this occurs on scales which are much larger than the system so that this is indeed only a nominal effect. From a practical point of view the Jeans instability of galactic disks is not affected by a live dark halo.
