This paper summarizes the limits on propagation of ultra high energy particles in the Universe, set up by their interactions with cosmic background of photons and neutrinos. By taking into account cosmic evolution of these backgrounds and considering
appropriate interactions we derive the mean free path for ultra high energy photons, protons and neutrinos. For photons the relevant processes are the Breit-Wheeler process as well as the double pair production process. For protons the relevant reactions are the photopion production and the Bethe-Heitler process. We discuss the interplay between the energy loss length and mean free path for the Bethe-Heitler process. Neutrino opacity is determined by its scattering off the cosmic background neutrino. We compute for the first time the high energy neutrino horizon as a function of its energy.
We derive and solve by the spectral method the equations for a neutral system of ultra-relativistic electrons that are compressed to the radius of the nucleus and subject to a driving force. This driving force can be thought of as originating from a
nuclear breathing mode, a possibility we discuss in detail.
Optically thick energy dominated plasma created in the source of Gamma-Ray Bursts (GRBs) expands radially with acceleration and forms a shell with constant width measured in the laboratory frame. When strong Lorentz factor gradients are present withi
n the shell it is supposed to spread at sufficiently large radii. There are two possible mechanisms of spreading: hydrodynamical and thermal ones. We consider both mechanisms evaluating the amount of spreading that occurs during expansion up to the moment when the expanding shell becomes transparent for photons. We compute the hydrodynamical spreading of an ultrarelativistically expanding shell. In the case of thermal spreading we compute the velocity spread as a function of two parameters: comoving temperature and bulk Lorentz factor of relativistic Maxwellian distribution. Based on this result we determine the value of thermal spreading of relativistically expanding shell. We found that thermal spreading is negligible for typical GRB parameters. Instead hydrodynamical spreading appears to be significant, with the shell width reaching $sim10^{10}$ cm for total energy $E=10^{54}$ erg and baryonic loading $B=10^{-2}$. Within the fireshell model such spreading will result in the duration of Proper Gamma-Ray Bursts up to several seconds.
We consider the formation of photon spectrum at the photosphere of ultrarelativistically expanding outflow. We use the Fokker-Planck approximation to the Boltzmann equation, and obtain the generalized Kompaneets equation which takes into account anis
otropic distribution of photons developed near the photosphere. This equation is solved numerically for relativistic steady wind and the observed spectrum is found in agreement with previous studies. We also study the photospheric emission for different temperature dependences on radius in such outflows. In particular, we found that for $Tpropto r^{-2}$ the Band low energy photon index of the observed spectrum is $alphasimeq -1$, as typically observed in Gamma Ray Bursts.
In this paper we reexamine the optical depth of ultrarelativistic spherically symmetric outflows and reevaluate the photospheric radius for each model during both the acceleration and coasting phases. It is shown that for both the wind and the shell
models there are two asymptotic solutions for the optical depth during the coasting phase of the outflow. In particular we show that quite counterintuitively a geometrically thin shell may appear as a thick wind for photons propagating inside it. For this reason we introduce notions of photon thick and photon thin outflows, which appear more general and better physically motivated with respect to winds and shells. Photosphere of relativistic outflow is a dynamic surface. We study its geometry and find that the photosphere of photon thin outflow has always a convex shape, while in the photon thick one it is initially convex (there is always a photon thin layer in any outflow) and then it becomes concave asymptotically approaching the photosphere of an infinitely long wind. We find that both instantaneous and time integrated observed spectra are very close to the thermal one for photon thick outflows, in line with existing studies. It is our main finding that the photospheric emission from the photon thin outflow produces non thermal time integrated spectra, which may be described by the Band function well known in the GRB literature. We find that energetic GRBs should produce photon thin outflows with photospheric emission lasting less than one second for the total energy $E_0leq10^{54}$ erg and baryonic loading parameter $Bleq10^{-2}$. It means that only time integrated spectra may be observed from such GRBs.
We present the self-consistent treatment of the simplest, nontrivial, self-gravitating system of degenerate neutrons, protons and electrons in $beta$-equilibrium within relativistic quantum statistics and the Einstein-Maxwell equations. The impossibi
lity of imposing the condition of local charge neutrality on such systems is proved, consequently overcoming the traditional Tolman-Oppenheimer-Volkoff treatment. We emphasize the crucial role of imposing the constancy of the generalized Fermi energies. A new approach based on the coupled system of the general relativistic Thomas-Fermi-Einstein-Maxwell equations is presented and solved. We obtain an explicit solution fulfilling global and not local charge neutrality by solving a sophisticated eigenvalue problem of the general relativistic Thomas-Fermi equation. The value of the Coulomb potential at the center of the configuration is $eV(0)simeq m_pi c^2$ and the system is intrinsically stable against Coulomb repulsion in the proton component. This approach is necessary, but not sufficient, when strong interactions are introduced.
The isothermal Tolman condition and the constancy of the Klein potentials originally expressed for the sole gravitational interaction in a single fluid are here generalized to the case of a three quantum fermion fluid duly taking into account the str
ong, electromagnetic, weak and gravitational interactions. The set of constitutive equations including the Einstein-Maxwell-Thomas-Fermi equations as well as the ones corresponding to the strong interaction description are here presented in the most general relativistic isothermal case. This treatment represents an essential step to correctly formulate a self-consistent relativistic field theoretical approach of neutron stars.
The recent formulation of the relativistic Thomas-Fermi model within the Feynman-Metropolis-Teller theory for compressed atoms is applied to the study of general relativistic white dwarf equilibrium configurations. The equation of state, which takes
into account the beta-equilibrium, the nuclear and the Coulomb interactions between the nuclei and the surrounding electrons, is obtained as a function of the compression by considering each atom constrained in a Wigner-Seitz cell. The contribution of quantum statistics, weak, nuclear, and electromagnetic interactions is obtained by the determination of the chemical potential of the Wigner-Seitz cell. The further contribution of the general relativistic equilibrium of white dwarf matter is expressed by the simple formula $sqrt{g_{00}}mu_{rm ws}$= constant, which links the chemical potential of the Wigner-Seitz cell $mu_{rm ws}$ with the general relativistic gravitational potential $g_{00}$ at each point of the configuration. The configuration outside each Wigner-Seitz cell is strictly neutral and therefore no global electric field is necessary to warranty the equilibrium of the white dwarf. These equations modify the ones used by Chandrasekhar by taking into due account the Coulomb interaction between the nuclei and the electrons as well as inverse beta-decay. They also generalize the work of Salpeter by considering a unified self-consistent approach to the Coulomb interaction in each Wigner-Seitz cell. The consequences on the numerical value of the Chandrasekhar-Landau mass limit as well as on the mass-radius relation of $^4$He, $^{12}$C, $^{16}$O and $^{56}$Fe white dwarfs are presented. All these effects should be taken into account in processes requiring a precision knowledge of the white dwarf parameters.
Based on the Thomas-Fermi approach, we describe and distinguish the electron distributions around extended nuclear cores: (i) in the case that cores are neutral for electrons bound by protons inside cores and proton and electron numbers are the same;
(ii) in the case that super charged cores are bare, electrons (positrons) produced by vacuum polarization are bound by (fly into) cores (infinity).
We evidence the existence of plasma oscillations of electrons-positron pairs created by the vacuum polarization in an uniform electric field with E < Ec. Our general treatment, encompassing also the traditional, well studied case of E > Ec, shows the
existence in both cases of a maximum Lorentz factor acquired by electrons and positrons and allows determination of the a maximal length of oscillation. We quantitatively estimate how plasma oscillations reduce the rate of pair creation and increase the time scale of the pair production. These results are particularly relevant in view of the experimental progress in approaching the field strengths E < Ec.
