Dynamical invariants and diffusion of merger substructures in time-dependent gravitational potentials

This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the explicit time-dependence from the Hamiltonian of the system. By referring the phase-space locations of particles to a coordinate frame in which the potential remains `static' the dynamical effects introduced by the time evolution vanish. It follows that dynamical invariants correspond to the integrals of motion for the static potential expressed in the transformed coordinates. The main difficulty of the method reduces to solving the differential equations that define the canonical transformation, which are typically coupled with the equations of motion. We discuss a few examples where both sets of equations can be exactly de-coupled, and cases that require approximations. The construction of dynamical invariants has far-reaching applications. These quantities allow us, for example, to describe the evolution of (statistical) microcanonical ensembles in time-dependent gravitational potentials without relying on ergodicity or probability assumptions. As an illustration, we follow the evolution of dynamical fossils in galaxies that build up mass hierarchically. It is shown that the growth of the host potential tends to efface tidal substructures in the integral-of-motion space through an orbital diffusion process. The inexorable cycle of deposition, and progressive dissolution, of tidal clumps naturally leads to the formation of a `smooth' stellar halo.Comment: 13 pages, 5 figures. Accepted to MNRA

High resolution in z-direction: The simulation of disc-bulge-halo galaxies using the particle-mesh code SUPERBOX

SUPERBOX is known as a very efficient particle-mesh code with highly-resolving sub-grids. Nevertheless, the height of a typical galactic disc is small compared to the size of the whole system. Consequently, the numerical resolution in z-direction, i.e. vertically with respect to the plane of the disc, remains poor. Here, we present a new version of SUPERBOX that allows for a considerably higher resolution along z. The improved code is applied to investigate disc heating by the infall of a galaxy satellite. We describe the improvement and communicate our results. As an important application we discuss the disruption of a dwarf galaxy within a disc-bulge-halo galaxy that consists of some 10^6 particles.Comment: Comments: 4 pages, 5 figures, pre-peer reviewed version. In: Galactic and stellar dynamics in the era of high-resolution surveys, Boily C., Combes F., Hensler G., eds., Strasbourg (France), March 2008, in press (Astronomische Nachrichten

A statistical method for measuring the Galactic potential and testing gravity with cold tidal streams

We introduce the Minimum Entropy Method, a simple statistical technique for constraining the Milky Way gravitational potential and simultaneously testing different gravity theories directly from 6D phase-space surveys and without adopting dynamical models. We demonstrate that orbital energy distributions that are separable (i.e. independent of position) have an associated entropy that increases under wrong assumptions about the gravitational potential and/or gravity theory. Of known objects, `cold' tidal streams from low-mass progenitors follow orbital distributions that most nearly satisfy the condition of separability. Although the orbits of tidally stripped stars are perturbed by the progenitor's self-gravity, systematic variations of the energy distribution can be quantified in terms of the cross-entropy of individual tails, giving further sensitivity to theoretical biases in the host potential. The feasibility of using the Minimum Entropy Method to test a wide range of gravity theories is illustrated by evolving restricted N-body models in a Newtonian potential and examining the changes in entropy introduced by Dirac, MONDian and f(R) gravity modifications.Comment: Accepted for publication in ApJ. 11 pages 6 figure

Specific investments and coordination failures

This note presents a new result on incomplete contracts. We show that if the different degrees of relation-specificity of the partnerts' investments determines their ex post bargaining position (what Williamson (1985) calls “the fundamental transformation”), it will appear a potential coordination failure. Under plausible conditions, the parties will coordinate in the more inefficient but less risky equilibrium, that is, in the risk-dominant equilibrium in the sense of Harsanyi and Selten (1988).

Constraining the distribution of dark matter in dwarf spheroidal galaxies with stellar tidal streams

We use high-resolution N-body simulations to follow the formation and evolution of tidal streams associated to dwarf spheroidal galaxies (dSphs). The dSph models are embedded in dark matter (DM) haloes with either a centrally-divergent 'cusp', or an homogeneous-density 'core'. In agreement with previous studies, we find that as tides strip the galaxy the evolution of the half-light radius and the averaged velocity dispersion follows well-defined tracks that are mainly controlled by the amount of mass lost. Crucially, the evolutionary tracks behave differently depending on the shape of the DM profile: at a fixed remnant mass, dSphs embedded in cored haloes have larger sizes and higher velocity dispersions than their cuspy counterparts. The divergent evolution is particularly pronounced in galaxies whose stellar component is strongly segregated within their DM halo and becomes more disparate as the remnant mass decreases. Our analysis indicates that the DM profile plays an important role in defining the internal dynamics of tidal streams. We find that stellar streams associated to cored DM models have velocity dispersions that lie systematically above their cuspy counterparts. Our results suggest that the dynamics of streams with known dSph progenitors may provide strong constraints on the distribution of DM on the smallest galactic scales.Comment: 5 pages, 4 figure