On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable character for the generalized oscillator system is investigated from the points of view of a quadratic invariance algebra.Comment: 13 pages, Latex file. Submitted for publication to Yadernaya Fizik

Superintegrability on the two dimensional hyperboloid II

This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C.P.Boyer, E.G.Kalnins and P.Winternitz, which haven't yet been studied. We give an example of an interbasis expansion and work out the structure of the quadratic algebra generated by the integrals of motion.Comment: 18 pages, LaTex; 1 figure (eps

Searching for solar siblings among the HARPS data

The search for the solar siblings has been particularly fruitful in the last few years. Until now, there are four plausible candidates pointed out in the literature: HIP21158, HIP87382, HIP47399, and HIP92831. In this study we conduct a search for solar siblings among the HARPS high-resolution FGK dwarfs sample, which includes precise chemical abundances and kinematics for 1111 stars. Using a new approach based on chemical abundance trends with the condensation temperature, kinematics, and ages we found one (additional) potential solar sibling candidate: HIP97507.Comment: 4 pages, 2 figures, 1 table. Accepted in A&

From stellar to planetary composition: Galactic chemical evolution of Mg/Si mineralogical ratio

The main goal of this work is to study element ratios that are important for the formation of planets of different masses. We study potential correlations between the existence of planetary companions and the relative elemental abundances of their host stars. We use a large sample of FGK-type dwarf stars for which precise Mg, Si, and Fe abundances have been derived using HARPS high-resolution and high-quality data. A first analysis of the data suggests that low-mass planet host stars show higher [Mg/Si] ratios, while giant planet hosts present [Mg/Si] that is lower than field stars. However, we found that the [Mg/Si] ratio significantly depends on metallicity through Galactic chemical evolution. After removing the Galactic evolution trend only the difference in the [Mg/Si] elemental ratio between low-mass planet hosts and non-hosts was present in a significant way. These results suggests that low-mass planets are more prevalent around stars with high [Mg/Si]. Our results demonstrate the importance of Galactic chemical evolution and indicate that it may play an important role in the planetary internal structure and composition.Comment: Accepted by A&A (Letter to the Editor

Exploring the alpha-enhancement of metal-poor planet-hosting stars. The Kepler and HARPS samples

Recent studies showed that at low metallicities Doppler-detected planet-hosting stars have preferably high alpha-content and belong to the thick disk. We used the reconnaissance spectra of 87 Kepler planet candidates and data available from the HARPS planet search survey to explore this phenomena. Using the traditional spectroscopic abundance analysis methods we derived Ti, Ca, and Cr abundances for the Kepler stars. In the metallicity region -0.65 < [Fe/H] < -0.3 dex the fraction of Ti-enhanced thick-disk HARPS planet harboring stars is 12.3 +/- 4.1 % and for their thin-disk counterparts this fraction is 2.2 +/- 1.3 %. The binomial statistics gives a probability of 0.008 that this could have occurred by chance. Combining the two samples (HARPS + Kepler) reinforces the significance of this result (P ~ 99.97 %). Since most of these stars are harboring small-mass/size planets we can assume that, although terrestrial planets can be found at low-iron regime, they are mostly enhanced by alpha-elements. This implies that early formation of rocky planets could get started in the Galactic thick disk, where the chemical conditions for their formation were more favorable.Comment: 5 pages, 3 figure