The internal structure of neutron stars and white dwarfs, and the Jacobi virial equation. II

In a previous paper we have shown that the function \Gamma(M, EOS)=\alpha\beta_{GR}/\Lambda^{0.9}(R) is constant (~ 0.4) for pre main-sequence stars (PMS), white dwarfs (WD) and for some neutron star (NS) models, where \alpha_{GR} and \beta_{GR} are the form-factors of the gravitational potential energy and of the moment of inertia. To investigate the structural evolution of another type of celestial bodies, we use the MESA code to extend these calculations to gaseous planets. We show that this function is conserved for all models during the whole planetary evolution and is independent of the planet mass. We also analyse the cases for which this function is not conserved during some stellar evolutionary phases. For the PMS to the WD cooling sequences, we have found a connection between the strong variations of \Gamma(M, EOS) during the intermediary evolutionary phases and the specific nuclear power. A threshold for the specific nuclear power was determined. Below this limit this function is invariant (~ 0.4) for these models, i.e., at the initial and final stages (PMS and WD). Concerning NS, we study the influence of the equation of state (EOS) on this function and refine the exponent of the auxiliary function \Lambda(R) to be ~ 0.8. It is shown that the function \Gamma(M, EOS) is also invariant (~ 0.4) and is independent of the EOS and of the stellar mass. Therefore, we confirm that regardless of the final products of the stellar evolution, NS or WD, they recover the initial value of \Gamma(M, EOS) ~ 0.4 acquired at the PMS. Finally, we have introduced a macroscopic stability "criterion" for neutron star models based on the properties of the relativistic product \alpha\beta_{GR}.Comment: 6 pages, 5 figures, v3: editorial changes, identical to published versio

Combined effects of tidal and rotational distortions on the equilibrium configuration of low-mass, pre-main sequence stars

In close binary systems, rotation and tidal forces of the component stars deform each other and destroy their spherical symmetry. We present new models for low-mass, pre-main sequence stars that include the combined distortion effects of tidal and rotational forces on the equilibrium configuration of stars. We investigate the effects of interaction between tides and rotation on the stellar structure and evolution. The Kippenhahn & Thomas (1970) approximation, along with the Clairaut-Legendre expansion for the gravitational potential of a self-gravitating body, is used to take the distortion effects into account. We obtained values of internal structure constants for low-mass, pre-main sequence stars from stellar evolutionary models that consider the combined effects of rotation and tidal forces due to a companion star. We also derived a new expression for the rotational inertia of a tidally and rotationally distorted star. Our distorted models were successfully used to analyze the eclipsing binary system EK Cep, reproducing the stellar radii, effective temperature ratio, lithium depletion, rotational velocities, and the apsidal motion rate in the age interval of 15.5-16.7 Myr. In the low-mass range, the assumption that harmonics greater than j=2 can be neglected seems not to be fully justified, although it is widely used when analyzing the apsidal motion of binary systems. The non-standard evolutionary tracks are cooler than the standard ones, mainly for low-mass stars. Distorted models predict more mass-concentrated stars at the zero-age main-sequence than standard models

1970, 1925, 2009. Whistling in the stadium as a form of protest

The discovery and documentation of a clandestine handbill dating from the end of Franco's regime calling on supporters to whistle in protest at the dictator at the Camp Nou provides the departure point for a revision of the relation between football as the game of the masses and citizen protest in the case of Catalan political (and sporting) culture of the twentieth and twenty-first centuries. It is based on antecedents and more recent cases of protests at big sporting events, in view of the continuing use of whistling at anthems or government authorities under different political regimes

Industrial engineering in Spain, the challenge of a new liberal profession in the nineteenth century

Industrial engineering was established in Spain in 1850. Despite the initial difficulties, the profession found its role in the process of the industrialization of Spain. The industrial engineers were the first free professionals in the world of engineerin g, given that there was not a State Corps linked to them. In this sense, there are some similarities between the Spanish industrial engineers and the French Centraliens . Moreover, the educational system developed in Spain in the nineteenth century gave lit tle autonomy to the engineering schools, and this was a major difference from the French onesPostprint (published version

Theoretical isochrones for the Delta a photometric system

We have calculated theoretical isochrones for the photometric Delta a system to derive astrophysical parameters such as the age, reddening and distance modulus for open clusters. The Delta a system samples the flux depression at 520 nm which is highly efficient to detect chemically peculiar (CP) objects of the upper main sequence. The evolutionary status of CP stars is still a matter of debate and very important to test, for example, the dynamo and diffusion theories. In fact, the dynamo or fossil origin of the magnetic fields present in this kind of stars it still not clear. Using the stellar evolutionary models by Claret (1995), a grid of isochrones with different initial chemical compositions for the Delta a system was generated. The published data of 23 open clusters were used to fit these isochrones with astrophysical parameters (age, reddening and distance modulus) from the literature. As an additional test, isochrones with the same parameters for Johnson UBV data of these open clusters were also considered. The fits show a good agreement between the observations and the theoretical grid. We find that the accuracy of fitting isochrones to Delta a data without the knowledge of the cluster parameters is between 5 and 15%.Comment: 5 pages, 4 figures, accepted by A&

Stellar Limb-Darkening Coefficients for CoRot and Kepler

Transiting exoplanets provide unparalleled access to the fundamental parameters of both extrasolar planets and their host stars. We present limb-darkening coefficients (LDCs) for the exoplanet hunting CoRot and Kepler missions. The LDCs are calculated with ATLAS stellar atmospheric model grids and span a wide range of Teff, log g, and metallically [M/H]. Both CoRot and Kepler contain wide, nonstandard response functions, and are producing a large inventory of high-quality transiting lightcurves, sensitive to stellar limb darkening. Comparing the stellar model limb darkening to results from the first seven CoRot planets, we find better fits are found when two model intensities at the limb are excluded in the coefficient calculations. This calculation method can help to avoid a major deficiency present at the limbs of the 1D stellar models.Comment: Accepted for publication in A&A. 4 pages, 2 figures, 2 tables. Full versions of tables 1 and 2 containing limb-darkening coefficients available at http://vega.lpl.arizona.edu/~sing