On the occurrence and detectability of Bose-Einstein condensation in helium white dwarfs

It has been recently proposed that helium white dwarfs may provide promising conditions for the occurrence of the Bose-Einstein condensation. The argument supporting this expectation is that in some conditions attained in the core of these objects, the typical De Broglie wavelength associated with helium nuclei is of the order of the mean distance between neighboring nuclei. In these conditions the system should depart from classical behavior showing quantum effects. As helium nuclei are bosons, they are expected to condense. In order to explore the possibility of detecting the Bose-Einstein condensation in the evolution of helium white dwarfs we have computed a set of models for a variety of stellar masses and values of the condensation temperature. We do not perform a detailed treatment of the condensation process but mimic it by suppressing the nuclei contribution to the equation of state by applying an adequate function. As the cooling of white dwarfs depends on average properties of the whole stellar interior, this procedure should be suitable for exploring the departure of the cooling process from that predicted by the standard treatment. We find that the Bose-Einstein condensation has noticeable, but not dramatic effects on the cooling process only for the most massive white dwarfs compatible with a helium dominated interior (\approx 0.50 M_\odot) and very low luminosities (say, Log(L/L_\odot) < -4.0). These facts lead us to conclude that it seems extremely difficult to find observable signals of the Bose-Einstein condensation. Recently, it has been suggested that the population of helium white dwarfs detected in the globular cluster NGC 6397 is a good candidate for detecting signals of the Bose-Einstein condensation. We find that these stars have masses too low and are too bright to have an already condensed interior.Comment: 13 pages, 3 figures, 2 tables, accepted for publication in the Journal of Cosmology and Astroparticle Physics (JCAP

An evolutionary model for the gamma-ray system PSR J1311-3430 and its companion

The most recent member of the millisecond pulsar with very low-mass companions and short orbital periods class, PSR J1311-3430 (Pletsch et al. 2012) is a remarkable object in various senses. Besides being the first discovered in gamma-rays, its measured features include the very low or absent hydrogen content. We show in this Letter that this important piece of information leads to a very restricted range of initial periods for a given donor mass. For that purpose, we calculate in detail the evolution of the binary system self-consistently, including mass transfer and evaporation, finding the features of the new evolutionary path leading to the observed configuration. It is also important to remark that the detailed evolutionary history of the system naturally leads to a high final pulsar mass, as it seems to be demanded by observations.Comment: 5 pages, 5 figures, 1 table. Accepted for publication in MNRAS Letter

Positive operator valued measures covariant with respect to an irreducible representation

Given an irreducible representation of a group G, we show that all the covariant positive operator valued measures based on G/Z, where Z is a central subgroup, are described by trace class, trace one positive operators.Comment: 9 pages, Latex2

Group Theoretical Quantum Tomography

The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.Comment: 13 pages, no figure, Latex2e. Submitted to J.Math.Phy

PREDICTION MODELS FOR FREESTYLE PERFORMANCE TIMES IN MASTER SWIMMERS

This study was designed to define the most important factors to predict freestyle performance times in 135 elite master swimmers by prediction models which include age, anthropometric and strength variables. To cross validate these equations found for Elite swimmers, we used a group composed by 126 lower technical level age - and experience - matched master swimmers. Results demonstrated that age, height and hand grip strength were the best predictors in short events, whereas age and height predict middle and long events. The corresponding coefficients of determination (R2) of performance times were 0.84 in 50m, 0.73 in 100m, 0.75 in 200m, 0.66 in 400m and 0.63 in the 800m events. A good correlation have been found when these models have been applied in 126 non-elite master swimmers demonstrating to be useful in all Master swimmers