Gravitational Wave Emission by Cataclysmic Variables: numerical models of semi-detached binaries

Gravitational wave emission is considered to be the driving force for the evolution of short-period cataclysmic binary stars, making them a potential test for the validity of General Relativity. In spite of continuous refinements of the physical description, a 10% mismatch exists between the theoretical minimum period ($P_{\rm turn} \simeq 70$ min) and the short-period cut-off ($P_{\rm min} \simeq 80$ min) observed in the period distribution for cataclysmic variable binaries. A possible explanation for this mismatch was associated with the use of the Roche model. We here present a systematic comparison between self-consistent, numerically constructed sequences of hydrostatic models of binary stars and Roche models of semi-detached binaries. On the basis of our approach, we also derive a value for the minimum period of cataclysmic variable binaries. The results obtained through the comparison indicate that the Roche model is indeed very good, with deviations from the numerical solution which are of a few percent at most. Our results therefore suggest that additional sources of angular momentum loss or alternative explanations need to be considered in order to justify the mismatch.Comment: 7pages, 4figures. To appear in MNRA

Phase Structure of Thermal QED Based on the Hard Thermal Loop Improved Ladder Dyson-Schwinger Equation --a "Gauge Invariant" Solution--

Based on the hard-thermal-loop resummed improved ladder Dyson-Schwinger quation for the fermion mass function, we study how we can get the gauge invariant solution in the sense it satisfies the Ward identity. Properties of the ``gauge-invariant'' solutions are discussed.Comment: 3figures, Proceedins of SCGT06 (Nagoya University, Japan, November 2006

Chiral Phase Transitions in QED at Finite Temperature: Dyson-Schwinger Equation Analysis in the Real Time Hard-Thermal-Loop Approximation

In order for clarifying what are the essential thermal effects that govern the chiral phase transition at finite temperature, we investigate, in the real-time thermal QED, the consequences of the Hard-Thermal-Loop (HTL) resummed Dyson-Schwinger equation for the physical fermion mass function $\Sigma_R$. Since $\Sigma_R$ is the mass function of an ``unstable'' quasi-particle in thermal field theories, it necessarily has non-trivial imaginary parts together with non-trivial wave function renormalization constants. In the present analysis we correctly respect this fact, and study, in the ladder approximation, the effect of HTL resummed gauge boson propagator. Our results with the use of numerical analysis, show the two facts; i) The chiral phase transition is of second order, since the fermion mass is dynamically generated at a critical value of the temperature $T_c$, or at the critical coupling constant $\alpha_c$, without any discontinuity, and ii) the critical temperature $T_c$ at fixed value of $\alpha$ is significantly lower than the previous results, namely the restoration of chiral symmetry occurs at lower temperature than previously expected. The second fact shows the importance of correctly taking the essential thermal effect into the analysis of chiral phase transition, which are, in the previous analyses, neglected due to the inappropriate approximations. The procedure how to maximally respect the gauge invariance in the present approximation, is also discussed.Comment: Revtex4 with 6 figures, 11 page