148 research outputs found
Two Body Relaxation in Simulated Cosmological Haloes
This paper aims at quantifying discreetness effects, born of finite particle
number, on the dynamics of dark matter haloes forming in the context of
cosmological simulations. By generalising the standard calculation of two body
relaxation to the case when the size and mass distribution are variable, and
parametrising the time evolution using established empirical relations, we find
that the dynamics of a million particle halo is noise-dominated within the
inner percent of the final virial radius. Far larger particle numbers (~ 10^8)
are required for the RMS perturbations to the velocity to drop to the 10 %
level there. The radial scaling of the relaxation time is simple and strong:
t_relax ~ r^2, implying that numbers >> 10^8 are required to faithfully model
the very inner regions; artificial relaxation may thus constitute an important
factor, contributing to the contradictory claims concerning the persistence of
a power law density cusp to the very centre. The cores of substructure haloes
can be many relaxation times old. Since relaxation first causes their expansion
before recontraction occurs, it may render them either more difficult or easier
to disrupt, depending on their orbital parameters. It may thus modify the
characteristics of the subhalo distribution and effects of interactions with
the parent. We derive simple closed form formulas for the characteristic
relaxation times, as well as for the weak N-scaling reported by Diemand et al.
when the main contribution comes from relaxing subhaloes (abridged).Comment: 11 Pages, 7 figs, Monthly Notices styl
Dark Matter Annihilation and the PAMELA, FERMI and ATIC Anomalies
If dark matter (DM) annihilation accounts for the tantalizing excess of
cosmic ray electron/positrons, as reported by the PAMELA, ATIC, HESS and FERMI
observatories, then the implied annihilation cross section must be relatively
large. This results, in the context of standard cosmological models, in very
small relic DM abundances that are incompatible with astrophysical
observations. We explore possible resolutions to this apparent conflict in
terms of non-standard cosmological scenarios; plausibly allowing for large
cross sections, while maintaining relic abundances in accord with current
observations.Comment: 13 pages, 3 figures; published for publication in Physical Review
From cusps to cores: a stochastic model
The cold dark matter model of structure formation faces apparent problems on
galactic scales. Several threads point to excessive halo concentration,
including central densities that rise too steeply with decreasing radius. Yet,
random fluctuations in the gaseous component can 'heat' the centres of haloes,
decreasing their densities. We present a theoretical model deriving this effect
from first principles: stochastic variations in the gas density are converted
into potential fluctuations that act on the dark matter; the associated force
correlation function is calculated and the corresponding stochastic equation
solved. Assuming a power law spectrum of fluctuations with maximal and minimal
cutoff scales, we derive the velocity dispersion imparted to the halo particles
and the relevant relaxation time. We further perform numerical simulations,
with fluctuations realised as a Gaussian random field, which confirm the
formation of a core within a timescale comparable to that derived analytically.
Non-radial collective modes enhance the energy transport process that erases
the cusp, though the parametrisations of the analytical model persist.
In our model, the dominant contribution to the dynamical coupling driving the
cusp-core transformation comes from the largest scale fluctuations. Yet, the
efficiency of the transformation is independent of the value of the largest
scale and depends weakly (linearly) on the power law exponent; it effectively
depends on two parameters: the gas mass fraction and the normalisation of the
power spectrum. This suggests that cusp-core transformations observed in
hydrodynamic simulations of galaxy formation may be understood and parametrised
in simple terms, the physical and numerical complexities of the various
implementations notwithstanding.Comment: Minor revisions to match version to appear in MNRAS; Section~2.3
largely rewritten for clarit
Regular and chaotic motion in softened gravitational systems
The stability of the dynamical trajectories of softened spherical
gravitational systems is examined, both in the case of the full -body
problem and that of trajectories moving in the gravitational field of
non-interacting background particles. In the latter case, for ,
some trajectories, even if unstable, had exceedingly long diffusion times,
which correlated with the characteristic e-folding timescale of the
instability. For trajectories of systems this timescale
could be arbitrarily large --- and thus appear to correspond to regular orbits.
For centrally concentrated systems, low angular momentum trajectories were
found to be systematically more unstable. This phenomenon is analogous to the
well known case of trajectories in generic centrally concentrated non-spherical
smooth systems, where eccentric trajectories are found to be chaotic. The
exponentiation times also correlate with the conservation of the angular
momenta along the trajectories. For up to a few hundred, the instability
timescales of -body systems and their variation with particle number are
similar to those of the most chaotic trajectories in inhomogeneous
non-interacting systems. For larger (up to a few thousand) the values of
the these timescales were found to saturate, increasing significantly more
slowly with . We attribute this to collective effects in the fully
self-gravitating problem, which are apparent in the time-variations of the time
dependent Liapunov exponents. The results presented here go some way towards
resolving the long standing apparent paradoxes concerning the local instability
of trajectories of gravitational systems (abridged).Comment: 16 pages, 11 figures, Monthly Notices styl
Flat-Cored Dark Matter in Cuspy Clusters of Galaxies
Sand, Treu, & Ellis (2002) have measured the central density profile of
cluster MS2137-23 with gravitational lensing and velocity dispersion and
removed the stellar contribution with a reasonable M/L. The resulting dark
matter distribution within r<50 kpc was fitted by a density cusp of r^{-beta}
with beta=0.35. This stands in an apparent contradiction to the CDM prediction
of beta~1, and the disagreement worsens if adiabatic compression of the dark
matter by the infalling baryons is considered. Following El-Zant, Shlosman &
Hoffman (2001), we argue that dynamical friction acting on galaxies moving
within the dark matter background counters the effect of adiabatic compression
by transfering the orbital energy of galaxies to the dark matter, thus heating
up and softening the central density cusp. Using N-body simulations of massive
solid clumps moving in clusters we show that indeed the inner dark matter
distribution flattens (with beta approx 0.35 for a cluster like MS2137-23) when
the galaxies spiral inward. We find as a robust result that while the dark
matter distribution becomes core-like, the overall mass distribution preserves
its cuspy nature, in agreement with X-ray and lensing observations of clusters.Comment: 7 pages, 3 figures, to be published in Astrophysical Journal Letter
Long-Lived Double-Barred Galaxies: Critical Mass and Length Scales
A substantial fraction of disk galaxies is double-barred. We analyze the
dynamical stability of such nested bar systems by means of Liapunov
exponents,by fixing a generic model and varying the inner (secondary) bar mass.
We show that there exists a critical mass below which the secondary bar cannot
sustain its own orbital structure, and above which it progressively destroys
the outer (primary) bar-supporting orbits. In this critical state, a large
fraction of the trajectories (regular and chaotic) are aligned with either bar,
suggesting the plausibility of long-lived dynamical states when
secondary-to-primary bar mass ratio is of the order of a few percent.
Qualitatively similar results are obtained by varying the size of the secondary
bar, within certain limits, while keeping its mass constant. In both cases, an
important role appears to be played by chaotic trajectories which are trapped
around (especially) the primary bar for long periods of time.Comment: 7 pages, 1 figure, to be published in Astrophysical Journal Letters
(Vol. 595, 9/20/03 issue). Replaced by revised figure and corrected typo
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