Effect of ionic radii on the Curie temperature in Ba1-x-ySrxCayTiO3 compounds

<p>A series of Ba_1-x-ySr_xCa_yTiO₃ compounds were prepared with varying average ionic radii and cation disorder on A-site. All samples showed typical ferroelectric behavior. A simple empirical equation correlated Curie temperature, <em>T_C</em>, with the values of ionic radii of A-site cations. This correlation was related to the distortion of TiO₆ octahedra observed during neutron diffraction studies. The equation was used for the selection of compounds with predetermined values of <em>T_C</em>. The effects of A-site ionic radii on the temperatures of phase transitions in Ba_1-x-ySr_xCa_yTiO₃ were discussed. </p

On the interpretation of echelle diagrams for solar-like oscillations. Effect of centrifugal distortion

This work aims at determining the impact of slow to moderate rotation on the regular patterns often present in solar-like oscillation spectra. We focus on the well-known asteroseismic diagnostic echelle diagrams, examining how rotation may modify the estimates of the large and small spacings, as well as the identification of modes. We illustrate the work with a real case: the solar-like star $\eta$ Bootis. The modeling takes into account rotation effects on the equilibrium models through an effective gravity and on the oscillation frequencies through both perturbative and non-perturbative calculations. We compare the results of both type of calculations in the context of the regular spacings (like the small spacings and the scaled small spacings) and echelle diagrams. We show that for echelle diagrams the perturbative approach remains valid for rotational velocities up to 40-50 km/s. We show that for the rotational velocities measured in solar-like stars, theoretical oscillation frequencies must be corrected up to the second-order in terms of rotation rate, including near degeneracy effects. For rotational velocities of about 16 km/S and higher, diagnostics on large spacings and on modal identification through echelle diagrams can be significantly altered by the presence of the $m\neq0$ components of the rotationally split modes. We found these effects to be detectable in the observed frequency range. Analysis of the effects of rotation on small spacings and scaled small spacings reveals that these can be of the order of, or even larger than surface effects, typically turbulence, microscopic diffusion, etc. Furthermore, we show that scaled spacings are significantly affected by stellar distortion even for small stellar rotational velocities (from 10-15 km/s) and therefore some care must be taken when using them as indicators for probing deep stellar interiors.Comment: 10 pages,5 figures, accepted for publication in ApJ; http://iopscience.iop.org/0004-637X/721/1/537

Numerical constraints on the model of stochastic excitation of solar-type oscillations

Analyses of a 3D simulation of the upper layers of a solar convective envelope provide constraints on the physical quantities which enter the theoretical formulation of a stochastic excitation model of solar p modes, for instance the convective velocities and the turbulent kinetic energy spectrum. These constraints are then used to compute the acoustic excitation rate for solar p modes, P. The resulting values are found ~5 times larger than the values resulting from a computation in which convective velocities and entropy fluctuations are obtained with a 1D solar envelope model built with the time-dependent, nonlocal Gough (1977) extension of the mixing length formulation for convection (GMLT). This difference is mainly due to the assumed mean anisotropy properties of the velocity field in the excitation region. The 3D simulation suggests much larger horizontal velocities compared to vertical ones than in the 1D GMLT solar model. The values of P obtained with the 3D simulation constraints however are still too small compared with the values inferred from solar observations. Improvements in the description of the turbulent kinetic energy spectrum and its depth dependence yield further increased theoretical values of P which bring them closer to the observations. It is also found that the source of excitation arising from the advection of the turbulent fluctuations of entropy by the turbulent movements contributes ~ 65-75 % to the excitation and therefore remains dominant over the Reynolds stress contribution. The derived theoretical values of P obtained with the 3D simulation constraints remain smaller by a factor ~3 compared with the solar observations. This shows that the stochastic excitation model still needs to be improved.Comment: 11 pages, 9 figures, accepted for publication in A&

Effect of local treatments of convection upon the solar p-mode excitation rates

We compute, for several solar models, the rates P at which the solar radial p modes are expected to be excited. The solar models are computed with two different local treatments of convection : the classical mixing-length theory (MLT hereafter) and Canuto, Goldmann and Mazzitelli(1996, CGM hereafter)'s formulation. For one set of solar models (EMLT and ECGM models), the atmosphere is gray and assumes Eddington's approximation. For a second set of models (KMLT and KCGM models), the atmosphere is built using a T(tau) law which has been obtained from a Kurucz's model atmosphere computed with the same local treatment of convection. The mixing-length parameter in the model atmosphere is chosen so as to provide a good agreement between synthetic and observed Balmer line profiles, while the mixing-length parameter in the interior model is calibrated so that the model reproduces the solar radius at solar age. For the MLT treatment, the rates P do depend significantly on the properties of the atmosphere. On the other hand, for the CGM treatment, differences in P between the ECGM and the KCGM models are very small compared to the error bars attached to the seismic measurements. The excitation rates P for modes from the EMLT model are significantly under-estimated compared with the solar seismic constraints. The KMLT model results in intermediate values for P and shows also an important discontinuity in the temperature gradient and the convective velocity. On the other hand, the KCGM model and the ECGM model yield values for P closer to the seismic data than the EMLT and KMLT models. We conclude that the solar p-mode excitation rates provide valuable constraints and according to the present investigation cleary favor the CGM treatment with respect to the MLT.Comment: 4 pages, 3 figures, proceedings of the SOHO14/GONG 2004 workshop "Helio- and Asteroseismology: Towards a Golden Future" from July 12-16 2004 at New Haven CT (USA

Influence of local treatments of convection upon solar p mode excitation rates

We compute the rates P at which acoustic energy is injected into the solar radial p modes for several solar models. The solar models are computed with two different local treatments of convection: the classical mixing-length theory (MLT hereafter) and Canuto et al (1996)'s formulation (CGM hereafter). Among the models investigated here, our best models reproduce both the solar radius and the solar luminosity at solar age and the observed Balmer line profiles. For the MLT treatment, the rates P do depend significantly on the properties of the atmosphere whereas for the CGM's treatment the dependence of P on the properties of the atmosphere is found smaller than the error bars attached to the seismic measurements. The excitation rates P for modes associated with the MLT models are significantly underestimated compared with the solar seismic constraints. The CGM models yield values for P closer to the seismic data than the MLT models. We conclude that the solar p-mode excitation rates provide valuable constraints and according to the present investigation clearly favor the CGM treatment with respect to the MLT, although neither of them yields values of P as close to the observations as recently found for 3D numerical simulations.Comment: 11 pages, 7 figures, accepted for publication in Astronomy & Astrophysic

Wave chaos in rapidly rotating stars

Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens new perspectives for rapidly rotating star seismology and also provides a new and potentially observable manifestation of wave chaos in a large scale natural system.Comment: 5 pages, 3 figures; accepted for publication in Phys. Rev.