Molecular hydrogen production from amorphous solid water during low energy electron irradiation.

This work investigates the production of molecular hydrogen isotopologues (H2, HD, and D2) during low energy electron irradiation of layered and isotopically labelled thin films of amorphous solid water (ASW) in ultrahigh vacuum. Experimentally, the production of these molecules with both irradiation time and incident electron energy in the range 400 to 500 eV is reported as a function of the depth of a buried D2O layer in an H2O film. H2 is produced consistently in all measurements, reflecting the H2O component of the film, though it does exhibit a modest reduction in intensity at the time corresponding to product escape from the buried D2O layer. In contrast, HD and D2 production exhibit peaks at times corresponding to product escape from the buried D2O layer in the composite film. These features broaden the deeper the HD or D2 is formed due to diffusion. A simple random-walk model is presented that can qualitatively explain the appearance profile of these peaks as a function of the incident electron penetration.

Analysis of the fractional relativistic polytropic gas sphere.

Many stellar configurations, including white dwarfs, neutron stars, black holes, supermassive stars, and star clusters, rely on relativistic effects. The Tolman-Oppenheimer-Volkoff (TOV) equation of the polytropic gas sphere is ultimately a hydrostatic equilibrium equation developed from the general relativity framework. In the modified Riemann Liouville (mRL) frame, we formulate the fractional TOV (FTOV) equations and introduce an analytical solution. Using power series expansions in solving FTOV equations yields a limited physical range to the convergent power series solution. Therefore, combining the two techniques of Euler-Abel transformation and Padé approximation has been applied to improve the convergence of the obtained series solutions. For all possible values of the relativistic parameters ([Formula: see text]), we calculated twenty fractional gas models for the polytropic indexes n = 0, 0.5, 1, 1.5, 2. Investigating the impacts of fractional and relativistic parameters on the models revealed fascinating phenomena; the two effects for n = 0.5 are that the sphere's volume and mass decrease with increasing [Formula: see text] and the fractional parameter ([Formula: see text]). For n = 1, the volume decreases when [Formula: see text] = 0.1 and then increases when [Formula: see text] = 0.2 and 0.3. The volume of the sphere reduces as both [Formula: see text] and [Formula: see text] increase for n = 1.5 and n = 2. We calculated the maximum mass and the corresponding minimum radius of the white dwarfs modeled with polytropic index n = 3 and several fractional and relativistic parameter values. We obtained a mass limit for the white dwarfs somewhat near the Chandrasekhar limit for the integer models with small relativistic parameters ([Formula: see text], [Formula: see text]). The situation is altered by lowering the fractional parameter; the mass limit increases to Mlimit = 1.63348 M⊙ at [Formula: see text] and [Formula: see text].