1,063 research outputs found
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 āthe fundamental transformationā), 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
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