Self-similar solutions for the interaction of relativistic ejecta with an ambient medium

We find self-similar solutions to describe the interaction of spherically symmetric ejecta expanding at relativistic speeds with an ambient medium having a power law density distribution. Using this solution, the time evolution of the Lorentz factor of the outer shock is derived as a function of the explosion energy, the mass of the ejecta, and parameters for the ambient medium. These solutions are an ultra-relativistic version of the solutions for the circumstellar interaction of supernova ejecta obtained by Chevalier and extensions of the relativistic blast wave solutions of Blandford & Mckee.Comment: 12 pages, 1 figure, accepted for publication in Ap

Self-Similar Evolution of Relativistic Shock Waves Emerging from Plane-Parallel Atmospheres

We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the distance from the surface, there is a self-similar motion of the fluid before and after the shock emergence. The time evolution of the Lorentz factor of the shock front is assumed to follow a power law when the time is measured from the moment at which the shock front reaches the surface. The power index is found to be determined by the condition for the flow to extend through a critical point. The energy spectrum of the ejected matter as a result of the shock breakout is derived and its dependence on the strength of the explosion is also deduced. The results are compared with the self-similar solution for the same problem with non-relativistic treatment.Comment: 9 pages, 4 figures, To appear in The Astrophysical Journal Corrected typo

Roles of Supernova Ejecta in Nucleosynthesis of Light Elements, Li, Be, and B

Explosions of type Ic supernovae (SNe Ic) are investigated using a relativistic hydrodynamic code to study roles of their outermost layers of the ejecta in light element nucleosynthesis through spallation reactions as a possible mechanism of the "primary" process. We have confirmed that the energy distribution of the outermost layers with a mass fraction of only 0.001 % follows the empirical formula proposed by previous work when the explosion is furious. In such explosions, a significant fraction of the ejecta ($>$0.1 % in mass) have the energy greater than the threshold energy for spallation reactions. On the other hand, it is found that the outermost layers of ejecta become more energetic than the empirical formula would predict when the explosion energy per unit ejecta mass is smaller than \sim 1.3\times 10^{51}{ergs/}\Msun. As a consequence, it is necessary to numerically calculate explosions to estimate light element yields from SNe Ic. The usage of the empirical formula would overestimate the yields by a factor of \gtsim 3 for energetic explosions such as SN 1998bw and underestimate the yields by a similar factor for less energetic explosions like SN 1994I. The yields of light elements Li, Be, and B (LiBeB) from SNe Ic are estimated by solving the transfer equation of cosmic rays originated from ejecta of SNe Ic and compared with observations.Comment: 10 pages, 6 figures, 2 tables, to appear in The Astrophysical Journa

Self-similar solutions for relativistic shocks emerging from stars with polytropic envelopes

We consider a strong ultrarelativistic shock moving through a star whose envelope has a polytrope-like density profile. When the shock is close to the star's outer boundary, its behavior follows the self-similar solution given by Sari (2005) for implosions in planar geometry. Here we outline this solution and find the asymptotic solution as the shock reaches the star's edge. We then show that the motion after the shock breaks out of the star is described by a self-similar solution remarkably like the solution for the motion inside the star. In particular, the characteristic Lorentz factor, pressure, and density vary with time according to the same power laws both before and after the shock breaks out of the star. After emergence from the star, however, the self-similar solution's characteristic position corresponds to a point behind the leading edge of the flow rather than at the shock front, and the relevant range of values for the similarity variable changes. Our numerical integrations agree well with the analytic results both before and after the shock reaches the star's edge.Comment: 18 pages, 5 figures, submitted to Ap

High pressure Ca-VI phase between 158-180 GPa: Stability, electronic structure and superconductivity

We have performed ab initio calculations for new high-pressure phase of Ca-VI between 158-180 GPa. The study includes elastic parameters of mono- and poly-crystalline aggregates, electronic band structure, lattice dynamics and superconductivity. The calculations show that the orthorhombic Pnma structure is mechanically and dynamically stable in the pressure range studied. The structure is superconducting in the entire pressure range and the calculated Tc (~25K) is maximum at ~172 GPa, where the transfer of charges from 4s to 3d may be thought to be completed.Comment: 8 pages, 4 figures; PACS number(s): 74.70.Ad, 62.20.de, 71.20.-b, 74.20.Pq, 74.25.Kc, 74.62.Fj; Keywords: Calcium; High pressure; Electronic band structure; Phonon spectrum; Elastic constants; Superconducto