62 research outputs found
A new code for orbit analysis and Schwarzschild modelling of triaxial stellar systems
We review the methods used to study the orbital structure and chaotic
properties of various galactic models and to construct self-consistent
equilibrium solutions by Schwarzschild's orbit superposition technique. These
methods are implemented in a new publicly available software tool, SMILE, which
is intended to be a convenient and interactive instrument for studying a
variety of 2D and 3D models, including arbitrary potentials represented by a
basis-set expansion, a spherical-harmonic expansion with coefficients being
smooth functions of radius (splines), or a set of fixed point masses. We also
propose two new variants of Schwarzschild modelling, in which the density of
each orbit is represented by the coefficients of the basis-set or spline
spherical-harmonic expansion, and the orbit weights are assigned in such a way
as to reproduce the coefficients of the underlying density model. We explore
the accuracy of these general-purpose potential expansions and show that they
may be efficiently used to approximate a wide range of analytic density models
and serve as smooth representations of discrete particle sets (e.g. snapshots
from an N-body simulation), for instance, for the purpose of orbit analysis of
the snapshot. For the variants of Schwarzschild modelling, we use two test
cases - a triaxial Dehnen model containing a central black hole, and a model
re-created from an N-body snapshot obtained by a cold collapse. These tests
demonstrate that all modelling approaches are capable of creating equilibrium
models.Comment: MNRAS, 24 pages, 18 figures. Software is available at
http://td.lpi.ru/~eugvas/smile
Dark matter annihilation near a black hole: plateau vs. weak cusp
Dark matter annihilation in so-called ``spikes'' near black holes is believed
to be an important method of indirect dark matter detection. In the case of
circular particle orbits, the density profile of dark matter has a plateau at
small radii, the maximal density being limited by the annihilation
cross-section. However, in the general case of arbitrary velocity anisotropy
the situation is different. Particulary, for isotropic velocity distribution
the density profile cannot be shallower than r^{-1/2} in the very centre.
Indeed, a detailed study reveals that in many cases the term ``annihilation
plateau'' is misleading, as the density actually continues to rise towards
small radii and forms a weak cusp, rho ~ r^{-(beta+1/2)}, where beta is the
anisotropy coefficient. The annihilation flux, however, does not change much in
the latter case, if averaged over an area larger than the annihilation radius.Comment: 4 pages, 3 figures. Matches published versio
Applying Schwarzschild's orbit superposition method to barred or non-barred disc galaxies
We present an implementation of the Schwarzschild orbit superposition method
which can be used for constructing self-consistent equilibrium models of barred
or non-barred disc galaxies, or of elliptical galaxies with figure rotation.
This is a further development of the publicly available code SMILE; its main
improvements include a new efficient representation of an arbitrary
gravitational potential using two-dimensional spline interpolation of Fourier
coefficients in the meridional plane, as well as the ability to deal with
rotation of the density profile and with multicomponent mass models. We compare
several published methods for constructing composite axisymmetric
disc--bulge--halo models and demonstrate that our code produces the models that
are closest to equilibrium. We also apply it to create models of triaxial
elliptical galaxies with cuspy density profiles and figure rotation, and find
that such models can be found and are stable over many dynamical times in a
wide range of pattern speeds and angular momenta, covering both slow- and
fast-rotator classes. We then attempt to create models of strongly barred disc
galaxies, using an analytic three-component potential, and find that it is not
possible to make a stable dynamically self-consistent model for this density
profile. Finally, we take snapshots of two N-body simulations of barred disc
galaxies embedded in nearly-spherical haloes, and construct equilibrium models
using only information on the density profile of the snapshots. We demonstrate
that such reconstructed models are in near-stationary state, in contrast with
the original N-body simulations, one of which displayed significant secular
evolution.Comment: 15 pages, 9 figures; MNRAS, 450, 2842. The software is available at
http://td.lpi.ru/~eugvas/smile
- …