115 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
Fluctuations of the gravitational field generated by a random population of extended substructures
A large population of extended substructures generates a stochastic
gravitational field that is fully specified by the function , which
defines the probability that a tracer particle experiences a force
within the interval . This paper presents a
statistical technique for deriving the spectrum of random fluctuations directly
from the number density of substructures with known mass and size functions.
Application to the subhalo population found in cold dark matter simulations of
Milky Way-sized haloes shows that, while the combined force distribution is
governed by the most massive satellites, the fluctuations of the {\it tidal}
field are completely dominated by the smallest and most abundant subhaloes. In
light of this result we discuss observational experiments that may be
sufficiently sensitive to Galactic tidal fluctuations to probe the "dark"
low-end of the subhalo mass function and constrain the particle mass of warm
and ultra-light axion dark matter models.Comment: 16 pages, 9 figures, accepted to MNRAS after minor revisio
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
Measuring the slopes of mass profiles for dwarf spheroidals in triaxial CDM potentials
We generate stellar distribution functions (DFs) in triaxial haloes in order
to examine the reliability of slopes inferred by applying mass estimators of the form (i.e. assuming spherical symmetry, where and are
luminous effective radius and global velocity dispersion, respectively) to two
stellar sub-populations independently tracing the same gravitational potential.
The DFs take the form , are dynamically stable, and are generated within
triaxial potentials corresponding directly to subhaloes formed in cosmological
dark-matter-only simulations of Milky Way and galaxy cluster haloes.
Additionally, we consider the effect of different tracer number density
profiles (cuspy and cored) on the inferred slopes of mass profiles. For the
isotropic DFs considered here, we find that halo triaxiality tends to introduce
an anti-correlation between and when estimated for a variety of
viewing angles. The net effect is a negligible contribution to the systematic
error associated with the slope of the mass profile, which continues to be
dominated by a bias toward greater overestimation of masses for
more-concentrated tracer populations. We demonstrate that simple mass estimates
for two distinct tracer populations can give reliable (and cosmologically
meaningful) lower limits for , irrespective of the degree of
triaxiality or shape of the tracer number density profile.Comment: 5 pages, 4 figures, submitted to MNRA
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
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