Theoretical models of planetary system formation: mass vs. semi-major axis

Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims: In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods: We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results: We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ~5 M⊕, simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.

Early repolarization, left ventricular diastolic function, and left atrial size in professional soccer players

Recent data have suggested a relation among long-term endurance sport practice, left atrial remodeling, and atrial fibrillation. We investigated the influence of an increased vagal tone, represented by the early repolarization (ER) pattern, on diastolic function and left atrial size in professional soccer players. Fifty-four consecutive athletes underwent electrocardiography, echocardiography, and exercise testing as part of their preparticipation screening. Athletes were divided into 2 groups according to presence or absence of an ER pattern, defined as a ST-segment elevation at the J-point (STE) > or =0.1 mm in 2 leads. For linear comparisons average STE was calculated. Mean age was 24 +/- 4 years. Twenty-five athletes (46%) showed an ER pattern. Athletes with an ER pattern had a significant lower heart rate (54 +/- 9 vs 62 +/- 11 beats/min, p = 0.024), an increased E/e' ratio (6.1 +/- 1.2 vs 5.1 +/- 1.0, p = 0.002), and larger volumes of the left atrium (25.6 +/- 7.3 vs 21.8 +/- 5.0 ml/m(2), p = 0.031) compared to athletes without an ER pattern. There were no significant differences concerning maximum workload, left ventricular dimensions, and systolic function. Univariate regression analysis revealed significant correlations among age, STE, and left atrial volume. In a stepwise multivariate regression analysis age, STE and e' contributed independently to left atrial size (r = 0.659, p <0.001). In conclusion, athletes with an ER pattern had an increased E/e' ratio, reflecting a higher left atrial filling pressure, contributing to left atrial remodeling over time.

Regulation of endothelial cell cytoskeletal reorganization by a secreted frizzled-related protein-1 and frizzled 4- and frizzled 7-dependent pathway: role in neovessel formation

Consistent with findings of Wnt pathway members involved in vascular cells, a role for Wnt/Frizzled signaling has recently emerged in vascular cell development. Among the few Wnt family members implicated in vessel formation in adult, Wnt7b and Frizzled 4 have been shown as involved in vessel formation in the lung and in the retina, respectively. Our previous work has shown a role for secreted Frizzled-related protein-1 (sFRP-1), a proposed Wnt signaling inhibitor, in neovascularization after an ischemic event and demonstrated its role as a potent angiogenic factor. However the mechanisms involved have not been investigated. Here, we show that sFRP-1 treatment increases endothelial cell spreading on extracellular matrix as revealed by actin stress fiber reorganization in an integrin-dependent manner. We demonstrate that sFRP-1 can interact with Wnt receptors Frizzled 4 and 7 on endothelial cells to transduce downstream to cellular machineries requiring Rac-1 activity in cooperation with GSK-3beta. sFRP-1 overexpression in endothelium specifically reversed the inactivation of GSK-3 beta and increased neovascularization in ischemia-induced angiogenesis in mouse hindlimb. This study illustrates a regulated pathway by sFRP-1 involving GSK-3beta and Rac-1 in endothelial cell cytoskeletal reorganization and in neovessel formation.