Elliptic curves with j = 0, 1728 and low embedding degree

Elliptic curves over a finite field Fq with j-invariant 0 or 1728, both supersingular and ordinary, whose embedding degree k is low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree with respect to a subgroup of prime order . For k = 1, 2, these conditions give parameterizations of q in terms of and two integers m, n. We show several examples of families with infinitely many curves. Similar parameterizations for k ? 3 need a fixed kth root of the unity in the underlying field. Moreover, when the elliptic curve admits distortion maps, an example is provided

New chemical profiles for the asteroseismology of ZZ Ceti stars

We compute new chemical profiles for the core and envelope of white dwarfs appropriate for pulsational studies of ZZ Ceti stars. These profiles are extracted from the complete evolution of progenitor stars, evolved through the main sequence and the thermally-pulsing asymptotic giant branch (AGB) stages, and from time-dependent element diffusion during white dwarf evolution. We discuss the importance of the initial-final mass relationship for the white dwarf carbon-oxygen composition. In particular, we find that the central oxygen abundance may be underestimated by about 15% if the white dwarf mass is assumed to be the hydrogen-free core mass before the first thermal pulse. We also discuss the importance for the chemical profiles expected in the outermost layers of ZZ Ceti stars of the computation of the thermally-pulsing AGB phase and of the phase in which element diffusion is relevant. We find a strong dependence of the outer layer chemical stratification on the stellar mass. In particular, in the less massive models, the double-layered structure in the helium layer built up during the thermally-pulsing AGB phase is not removed by diffusion by the time the ZZ Ceti stage is reached. Finally, we perform adiabatic pulsation calculations and discuss the implications of our new chemical profiles for the pulsational properties of ZZ Ceti stars. We find that the whole $g-$mode period spectrum and the mode-trapping properties of these pulsating white dwarfs as derived from our new chemical profiles are substantially different from those based on chemical profiles widely used in existing asteroseismological studies. Thus, we expect the asteroseismological models derived from our chemical profiles to be significantly different from those found thus far.Comment: 12 pages, 11 figures, 1 table. To be published in Ap

Evolution of white dwarf stars with high-metallicity progenitors: the role of 22Ne diffusion

Motivated by the strong discrepancy between the main sequence turn-off age and the white dwarf cooling age in the metal-rich open cluster NGC 6791, we compute a grid of white dwarf evolutionary sequences that incorporates for the first time the energy released by the processes of 22Ne sedimentation and of carbon/oxygen phase separation upon crystallization. The grid covers the mass range from 0.52 to 1.0 Msun, and it is appropriate for the study of white dwarfs in metal-rich clusters. The evolutionary calculations are based on a detailed and self-consistent treatment of the energy released from these two processes, as well as on the employment of realistic carbon/oxygen profiles, of relevance for an accurate evaluation of the energy released by carbon/oxygen phase separation. We find that 22Ne sedimentation strongly delays the cooling rate of white dwarfs stemming from progenitors with high metallicities at moderate luminosities, whilst carbon/oxygen phase separation adds considerable delays at low luminosities. Cooling times are sensitive to possible uncertainties in the actual value of the diffusion coefficient of 22Ne. Changing the diffusion coefficient by a factor of 2, leads to maximum age differences of approx. 8-20% depending on the stellar mass. We find that the magnitude of the delays resulting from chemical changes in the core is consistent with the slow down in the white dwarf cooling rate that is required to solve the age discrepancy in NGC 6791.Comment: 10 pages, 6 figures, to be published in The Astrophysical Journa

Estudio de valoración del dolor en pacientes con fractura-luxación de Lisfranc

Objetivo: Cuantificar la presencia de dolor y pérdida de calidad de vida secundaria a la fractura-luxación de Lisfranc. Material y Métodos: Realizamos un estudio de cohortes transversal de 83 pacientes con diagnostico de fractura-luxación de Lisfranc. La presencia de dolor en reposo y en actividad se valoró mediante la aplicación de la Escala Visual Analógica (EVA) y el cuestionario de calidad de vida Espiditest. Resultados: La edad media de los pacientes estudiados fue de 38,36 años. No se detectaron diferencias en las puntuaciones por sexo y edad. No se encontró asociación entre calidad de vida en Espiditest y el tipo de tratamiento empleado, la cirugía precoz y su duración. Existía mayor consumo de analgésicos para control del dolor y más dificultad para regresar a su empleo o actividad laboral previa a la lesión en pacientes que presentaban peor calidad de vida en Espiditest. El grado de satisfacción por parte de los pacientes fue concordante con la calidad de vida. Conclusiones: La fractura-luxación de Lisfranc a pesar de ser una lesión incapacitante, no es tan limitante para la calidad de vida por causa del dolor.Objetives: To quantify the presence of pain and to determine loss of quality of life after a Lisfranc fracture-dislocation. Material and methods: We conducted a cross-sectional cohort study in 83 patients diagnosed with Lisfranc fracture-dislocation. The presence of pain at rest and during activity was assessed by means of a visual analogy scale (VAS) and the quality of life questionnaire Espiditest. Results: Patients in the study have a mean age of 38,36 years. The study results are not skewed by sex or gender of participants. No association whatsoever was found between the quality of life - according to the Espiditest - and the type of treatment being used, neither the early surgery nor the length of it. Patients with poorer quality of life - as shown in Espiditest - have a higher consumption of analgesics used for pain relief and more difficulty returning to their job or work activity prior to the injury. The degree of satisfaction by patients was consistent with the quality of their life. Conclusions: The Lisfranc fracture-dislocation, despite being a disabling injury, does not limit the quality of life because of pain

An upper limit to the secular variation of the gravitational constant from white dwarf stars

A variation of the gravitational constant over cosmological ages modifies the main sequence lifetimes and white dwarf cooling ages. Using an state-of-the-art stellar evolutionary code we compute the effects of a secularly varying G on the main sequence ages and, employing white dwarf cooling ages computed taking into account the effects of a running G, we place constraints on the rate of variation of Newton's constant. This is done using the white dwarf luminosity function and the distance of the well studied open Galactic cluster NGC 6791. We derive an upper bound G'/G ~ -1.8 10^{-12} 1/yr. This upper limit for the secular variation of the gravitational constant compares favorably with those obtained using other stellar evolutionary properties, and can be easily improved if deep images of the cluster allow to obtain an improved white dwarf luminosity function.Comment: 15 pages, 4 figures, accepted for publication in JCA

The white dwarf cooling sequence of NGC 6791: a unique tool for stellar evolution

NGC 6791 is a well-studied, metal-rich open cluster that is so close to us that can be imaged down to luminosities fainter than that of the termination of its white dwarf cooling sequence, thus allowing for an in-depth study of its white dwarf population. We use a Monte Carlo simulator that employs up-to-date evolutionary cooling sequences for white dwarfs with hydrogen-rich and hydrogen-deficient atmospheres, with carbon-oxygen and helium cores. The cooling sequences for carbon-oxygen cores account for the delays introduced by both Ne^22 sedimentation in the liquid phase and by carbon-oxygen phase separation upon crystallization. We do not find evidence for a substantial fraction of helium-core white dwarfs, and hence our results support the suggestion that the origin of the bright peak of the white dwarf luminosity function can only be attributed to a population of unresolved binary white dwarfs. Moreover, our results indicate that the number distribution of secondary masses of the population of unresolved binaries has to increase with increasing mass ratio between the secondary and primary components of the progenitor system. We also find that the observed cooling sequence appears to be able to constrain the presence of progenitor sub-populations with different chemical compositions and the fraction of non-DA white dwarfs. Our simulations place interesting constraints on important characteristics of the stellar populations of NGC 6791. In particular, we find that the fraction of single helium-core white dwarfs must be smaller than 5%, that a sub-population of stars with zero metallicity must be <12%, while if the adopted metallicity of the sub-population is solar the upper limit is ~8%. Finally, we also find that the fraction of non-DA white dwarfs in this particular cluster is surprinsingly small <6%.Comment: 9 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

The diffusion-induced nova scenario. CK Vul and PB 8 as possible observational counterparts

We propose a scenario for the formation of DA white dwarfs with very thin helium buffers. For these stars we explore the possible occurrence of diffusion-induced CNO- flashes, during their early cooling stage. In order to obtain very thin helium buffers, we simulate the formation of low mass remnants through an AGB final/late thermal pulse (AFTP/LTP scenario). Then we calculate the consequent white dwarf cooling evolution by means of a consistent treatment of element diffusion and nuclear burning. Based on physically sounding white dwarf models, we find that the range of helium buffer masses for these diffusion-induced novas to occur is significantly smaller than that predicted by the only previous study of this scenario. As a matter of fact, we find that these flashes do occur only in some low-mass (M < 0.6M) and low metallicity (Z_ZAMS <0.001) remnants about 10^6 - 10^7 yr after departing from the AGB. For these objects, we expect the luminosity to increase by about 4 orders of magnitude in less than a decade. We also show that diffusion-induced novas should display a very typical eruption lightcurve, with an increase of about a few magnitudes per year before reaching a maximum of M_V ~ -5 to -6. Our simulations show that surface abundances after the outburst are characterized by logNH/NHe ~ -0.15...0.6 and N>C>O by mass fractions. Contrary to previous speculations we show that these events are not recurrent and do not change substantially the final H-content of the cool (DA) white dwarf. (Abridged)Comment: 16 pages, 8 figures, 3 tables. Replaced to match the final version published by MNRAS. The definitive version is available at http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291365-296

The impact of chemical differentiation of white dwarfs on thermonuclear supernovae

Gravitational settling of 22Ne in cooling white dwarfs can affect the outcome of thermonuclear supernovae. We investigate how the supernova energetics and nucleosynthesis are in turn influenced by this process. We use realistic chemical profiles derived from state-of-the-art white dwarf cooling sequences. The cooling sequences provide a link between the white dwarf chemical structure and the age of the supernova progenitor system. The cooling sequence of a 1 M_sun white dwarf was computed until freezing using an up-to-date stellar evolutionary code. We computed explosions of both Chandrasekhar mass and sub-Chandrasekhar mass white dwarfs, assuming spherical symmetry and neglecting convective mixing during the pre-supernova carbon simmering phase to maximize the effects of chemical separation. Neither gravitational settling of 22Ne nor chemical differentiation of 12C and 16O have an appreciable impact on the properties of Type Ia supernovae, unless there is a direct dependence of the flame properties (density of transition from deflagration to detonation) on the chemical composition. At a fixed transition density, the maximum variation in the supernova magnitude obtained from progenitors of different ages is ~0.06 magnitudes, and even assuming an unrealistically large diffusion coefficient of 22Ne it would be less than ~0.09 mag. However, if the transition density depends on the chemical composition (all other things being equal) the oldest SNIa can be as much as 0.4 magnitudes brighter than the youngest ones (in our models the age difference is 7.4 Gyr). In addition, our results show that 22Ne sedimentation cannot be invoked to account for the formation of a central core of stable neutron-rich Fe-group nuclei in the ejecta of sub-Chandrasekhar models, as required by observations of Type Ia supernovae.Comment: 8 pages, 8 figures, 3 tables, accepted for Astronomy and Astrophysics. Revised version with corrected typo

Grasping the dialogical nature of acculturation

In this interesting article, Andreouli (2013). Identity and acculturation: The case of naturalised citizens in Britain. Culture & Psychology, 19, 1–47) presents a dialogical perspective on acculturation. To support this perspective, the author integrates the Dialogical Self Theory and the Social Representations Theory. Drawing on her theoretical explanation, we develop a conceptual review focused on two pairs of constructs – social representations/I-positions and polyphasia/polyphonia. Andreouli’s empirical study allowed her to operationalize some critiques about the two-dimensional perspective and its strategies on acculturation. Nevertheless, it seems that the author ends up replicating a more conventional and dual way of thinking. Their results give us privileged access to the negotiation of meanings and activation of promoter signs or, in other words, to the dialogical dynamics between I-positions. In this respect, we suggest that the assumption of a more dialogic and semiotic lens could be an interesting further development to this study

New phase diagrams for dense carbon-oxygen mixtures and white dwarf evolution

Cool white dwarfs are reliable and independent stellar chronometers. The most common white dwarfs have carbon-oxygen dense cores. Consequently, the cooling ages of very cool white dwarfs sensitively depend on the adopted phase diagram of the carbon-oxygen binary mixture. A new phase diagram of dense carbon-oxygen mixtures appropriate for white dwarf interiors has been recently obtained using direct molecular dynamics simulations. In this paper, we explore the consequences of this phase diagram in the evolution of cool white dwarfs. To do this we employ a detailed stellar evolutionary code and accurate initial white dwarf configurations, derived from the full evolution of progenitor stars. We use two different phase diagrams, that of Horowitz et al. (2010), which presents an azeotrope, and the phase diagram of Segretain & Chabrier (1993), which is of the spindle form. We computed the evolution of 0.593 and 0.878M_sun white dwarf models during the crystallization phase, and we found that the energy released by carbon-oxygen phase separation is smaller when the new phase diagram of Horowitz et al. (2010) is used. This translates into time delays that are on average a factor about 2 smaller than those obtained when the phase diagram of Segretain & Chabrier (1993) is employed. Our results have important implications for white dwarf cosmochronology, because the cooling ages of very old white dwarfs are different for the two phase diagrams. This may have a noticeable impact on the age determinations of very old globular clusters, for which the white dwarf color-magnitude diagram provides an independent way of estimating their age.Comment: 7 pages, 7 figures, accepted for publication in Astronomy and Astrophysic