Taking apart the dynamical clock. Fat-tailed dynamical kicks shape the blue-straggler star bimodality

In globular clusters, blue straggler stars are heavier than the average star, so dynamical friction strongly affects them. The radial distribution of BSS, normalized to a reference population, appears bimodal in a fraction of Galactic GCs, with a density peak in the core, a prominent zone of avoidance at intermediate radii, and again higher density in the outskirts. The zone of avoidance appears to be located at larger radii the more relaxed the host cluster, acting as a sort of dynamical clock. We use a new method to compute the evolution of the BSS radial distribution under dynamical friction and diffusion. We evolve our BSS in the mean cluster potential under dynamical friction plus a random fluctuating force, solving the Langevin equation with the Mannella quasi symplectic scheme. This amounts to a new simulation method which is much faster and simpler than direct N-body codes but retains their main feature: diffusion powered by strong, if infrequent, kicks. We compute the radial distribution of initially unsegregated BSS normalized to a reference population as a function of time. We trace the evolution of its minimum, corresponding to the zone of avoidance. We compare the evolution under kicks extracted from a Gaussian distribution to that obtained using a Holtsmark distribution. The latter is a fat tailed distribution which correctly models the effects of close gravitational encounters. We find that the zone of avoidance moves outwards over time, as expected based on observations, only when using the Holtsmark distribution. Thus the correct representation of near encounters is crucial to reproduce the dynamics of the system. We confirm and extend earlier results that showed how the dynamical clock indicator depends both on dynamical friction and effective diffusion powered by dynamical encounters.Comment: 8 pages, 6 figures. Version accepted in Astronomy & Astrophysic

Wage incentive profiles in dual labour markets

We propose a modified version of the Shapiro-Stiglitz’s (1984) efficiency wage model by introducing temporary contracts in the standard setup. New theoretical insights emerge on the incentive problem faced by workers and firms. We argue that the existence of temporary contracts broaden the incentive menu available to employers and that the optimal incentive structure can be sustained as an equi- librium outcome only if permanent contracts do not disappear. We also provide an alternative explanation of the wage penalty suffered by temporary workers even if standard models of efficiency wages would predict higher compensations for workers facing a higher job loss risk.Dual labour market, efficiency wages, wage differentials

Radially anisotropic systems with r−αr^{-\alpha} forces. II: radial-orbit instability

We continue to investigate the dynamics of collisionless systems of particles interacting via additive $r^{-\alpha}$ interparticle forces. Here we focus on the dependence of the radial-orbit instability on the force exponent $\alpha$. By means of direct $N$-body simulations we study the stability of equilibrium radially anisotropic Osipkov-Merritt spherical models with Hernquist density profile and with $1\leq\alpha<3$. We determine, as a function of $\alpha$, the minimum value for stability of the anisotropy radius $r_{as}$ and of the maximum value of the associated stability indicator $\xi_s$. We find that, for decreasing $\alpha$, $r_{as}$ decreases and $\xi_s$ increases, i.e. longer-range forces are more robust against radial-orbit instability. The isotropic systems are found to be stable for all the explored values of $\alpha$. The end products of unstable systems are all markedly triaxial with minor-to-major axial ratio $>0.3$, so they are never flatter than an E7 system.Comment: 12 pages, 6 figure