Revisiting the correlation between stellar activity and planetary surface gravity

Aims: We re-evaluate the correlation between planetary surface gravity and stellar host activity as measured by the index log($R'_{HK}$). This correlation, previously identified by Hartman (2010), is now analyzed in light of an extended measurements dataset, roughly 3 times larger than the original one. Methods: We calculated the Spearman's rank correlation coefficient between the two quantities and its associated p-value. The correlation coefficient was calculated for both the full dataset and the star-planet pairs that follow the conditions proposed by Hartman (2010). In order to do so, we considered effective temperatures both as collected from the literature and from the SWEET-Cat catalog, which provides a more homogeneous and accurate effective temperature determination. Results: The analysis delivers significant correlation coefficients, but with a lower value than those obtained by Hartman (2010). Yet, the two datasets are compatible, and we show that a correlation coefficient as large as previously published can arise naturally from a small-number statistics analysis of the current dataset. The correlation is recovered for star-planet pairs selected using the different conditions proposed by Hartman (2010). Remarkably, the usage of SWEET-Cat temperatures leads to larger correlation coefficient values. We highlight and discuss the role of the correlation betwen different parameters such as effective temperature and activity index. Several additional effects on top of those discussed previously were considered, but none fully explains the detected correlation. In light of the complex issue discussed here, we encourage the different follow-up teams to publish their activity index values in the form of log($R'_{HK}$) index so that a comparison across stars and instruments can be pursued.Comment: 11 pages, 3 figures, accepted for publication in A&

Granular mixtures modeled as elastic hard spheres subject to a drag force

Granular gaseous mixtures under rapid flow conditions are usually modeled by a multicomponent system of smooth inelastic hard spheres with constant coefficients of normal restitution. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. The Navier--Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman--Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.Comment: The title has been changed, 4 figures, and to be published in Phys. Rev.

Third and fourth degree collisional moments for inelastic Maxwell models

The third and fourth degree collisional moments for $d$-dimensional inelastic Maxwell models are exactly evaluated in terms of the velocity moments, with explicit expressions for the associated eigenvalues and cross coefficients as functions of the coefficient of normal restitution. The results are applied to the analysis of the time evolution of the moments (scaled with the thermal speed) in the free cooling problem. It is observed that the characteristic relaxation time toward the homogeneous cooling state decreases as the anisotropy of the corresponding moment increases. In particular, in contrast to what happens in the one-dimensional case, all the anisotropic moments of degree equal to or less than four vanish in the homogeneous cooling state for $d\geq 2$.Comment: 15 pages, 3 figures; v2: addition of two new reference

Creation of discrete solitons and observation of the Peierls-Nabarro barrier in Bose-Einstein Condensates

We analyze the generation and mobility of discrete solitons in Bose-Einstein condensates confined in an optical lattice under realistic experimental conditions. We discuss first the creation of 1D discrete solitons, for both attractive and repulsive interatomic interactions. We then address the issue of their mobility, focusing our attention on the conditions for the experimental observability of the Peierls-Nabarro barrier. Finally we report on the generation of self-trapped structures in two and three dimensions. Discrete solitons may open alternative routes for the manipulation and transport of Bose-Einstein condensates.Comment: 7 pages, 6 eps figure

Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of $B$ splines and $B$ polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization of the scattered light are investigated as a function of scattering angle and photon energy. Analytical expressions are derived for the polarization-dependent angular distribution which can be used for scattering by both hydrogenic as well as many-electron systems. Detailed computations are performed for Rayleigh scattering by atomic hydrogen within the incident photon energy range 0.5 to 10 keV. Particular attention is paid to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction.Comment: 8 pages, 5 figure

Switching of Magnetic Moments of Nanoparticles by Surface Acoustic Waves

We report evidence of the magnetization reversal in nanoparticles by surface acoustic waves (SAWs). The experimental system consists of isolated magnetite nanoparticles dispersed on a piezoelectric substrate. Magnetic relaxation from a saturated state becomes significantly enhanced in the presence of the SAW at a constant temperature of the substrate. The dependence of the relaxation on SAW power and frequency has been investigated. The effect is explained by the effective ac magnetic field generated by the SAW in the nanoparticles.Comment: Accepted in Europhysics Letter