287 research outputs found
The Nuker model for galactic nuclei
The Nuker profile, characterised by an inner and outer power-law profile smoothly merged around a break radius, is a very popular model to describe the surface brightness profile of galactic nuclei. A disadvantage of this model for dynamical studies is that the spatial density distribution that corresponds to this surface brightness profile cannot be written in terms of elementary or regular special functions. We derive a compact and elegant analytical expression for the density of the Nuker model, based the Mellin integral transform method. We use this expression to discuss the general behaviour and asymptotic expansion of the density. We also discuss the special subclass of Nuker models with an infinitely sharp break and demonstrate that these models are always characterised by non-monotonous and hence unphysical density profile. We extend our study to the dynamical structure of spherical isotropic galactic nuclei with a Nuker surface brightness profile. Based on this analysis, we extend and refine the classification of spherical isotropic galactic nuclei introduced by Tremaine et al. (1994, AJ, 107, 634). We demonstrate that both the inner density slope and the sharpness of the break between the inner and outer profiles critically determine the consistency and stability of the Nuker models
Stellar systems following the R^1/m luminosity law, IV : the total energy and the central concentration of galaxies
We expand our previous analytical and numerical studies of the family of SĂ©rsic models, which are routinely used to describe early-type galaxies and the bulges of spiral galaxies. In particular, we focus on the total energy budget, an important dynamical property that has not been discussed in detail in previous works. We use two different methods to calculate the total energy for the SĂ©rsic model family that result in two independent expressions that can be used along the entire sequence of SĂ©rsic models. We use these expressions to investigate whether the Spitzer concentration index is a reliable measure for the intrinsic 3D concentration of galaxies, and we conclude that it is not a very useful measure for the central concentration. The popular Third Galaxy Concentration index, on the other hand, is shown to be a reliable measure for the intrinsic 3D concentration, even though it is based on the surface brightness distribution and not on the intrinsic 3D density
The Failure of Monte Carlo Radiative Transfer at Medium to High Optical Depths
Computer simulations of photon transport through an absorbing and/or
scattering medium form an important research tool in astrophysics. Nearly all
software codes performing such simulations for three-dimensional geometries
employ the Monte Carlo radiative transfer method, including various forms of
biasing to accelerate the calculations. Because of the probabilistic nature of
the Monte Carlo technique, the outputs are inherently noisy, but it is often
assumed that the average values provide the physically correct result. We show
that this assumption is not always justified. Specifically, we study the
intensity of radiation penetrating an infinite, uniform slab of material that
absorbs and scatters the radiation with equal probability. The basic Monte
Carlo radiative transfer method, without any biasing mechanisms, starts to
break down for transverse optical depths above ~20 because so few of the
simulated photon packets reach the other side of the slab. When including
biasing techniques such as absorption/scattering splitting and path length
stretching, the simulated photon packets do reach the other side of the slab
but the biased weights do not necessarily add up to the correct solution. While
the noise levels seem to be acceptable, the average values sometimes severely
underestimate the correct solution. Detecting these anomalies requires the
judicious application of statistical tests, similar to those used in the field
of nuclear particle transport, possibly in combination with convergence tests
employing consecutively larger numbers of photon packets. In any case, for
transverse optical depths above ~75 the Monte Carlo methods used in our study
fail to solve the one-dimensional slab problem, implying the need for
approximations such as a modified random walk.Comment: Accepted for publication in the ApJ; 13 pages, 6 figure
SKIRT: the design of a suite of input models for Monte Carlo radiative transfer simulations
The Monte Carlo method is the most popular technique to perform radiative
transfer simulations in a general 3D geometry. The algorithms behind and
acceleration techniques for Monte Carlo radiative transfer are discussed
extensively in the literature, and many different Monte Carlo codes are
publicly available. On the contrary, the design of a suite of components that
can be used for the distribution of sources and sinks in radiative transfer
codes has received very little attention. The availability of such models, with
different degrees of complexity, has many benefits. For example, they can serve
as toy models to test new physical ingredients, or as parameterised models for
inverse radiative transfer fitting. For 3D Monte Carlo codes, this requires
algorithms to efficiently generate random positions from 3D density
distributions. We describe the design of a flexible suite of components for the
Monte Carlo radiative transfer code SKIRT. The design is based on a combination
of basic building blocks (which can be either analytical toy models or
numerical models defined on grids or a set of particles) and the extensive use
of decorators that combine and alter these building blocks to more complex
structures. For a number of decorators, e.g. those that add spiral structure or
clumpiness, we provide a detailed description of the algorithms that can be
used to generate random positions. Advantages of this decorator-based design
include code transparency, the avoidance of code duplication, and an increase
in code maintainability. Moreover, since decorators can be chained without
problems, very complex models can easily be constructed out of simple building
blocks. Finally, based on a number of test simulations, we demonstrate that our
design using customised random position generators is superior to a simpler
design based on a generic black-box random position generator.Comment: 15 pages, 4 figures, accepted for publication in Astronomy and
Computin
Stellar systems following the luminosity law. III. Photometric, intrinsic, and dynamical properties for all S\'ersic indices
The S\'ersic or model has become the de facto standard model to
describe the surface brightness profiles of early-type galaxies and the bulges
of spiral galaxies. The photometric, intrinsic, and dynamical properties of
this model have been investigated, but mainly for fairly large S\'ersic indices
. For small values of , appropriate for low-mass and dwarf ellipticals, a
detailed investigation of these properties is still lacking. In this study, we
used a combination of numerical and analytical techniques to investigate the
S\'ersic model over the entire range of S\'ersic parameters, focussing on the
small regime, where a number of interesting and surprising properties are
found. For all values , the model is characterised by a finite central
luminosity density, and for , even a central depression in the
luminosity density profile. This behaviour translates to the dynamical
properties: we show that all S\'ersic models with can be
supported by an isotropic velocity dispersion tensor, and that these isotropic
models are stable to both radial and non-radial perturbations. The models with
, on the other hand, cannot be supported by an isotropic velocity
dispersion tensor.Comment: 10 pages, 5 figures, accepted for publication in A&
Dynamical models for dusty disk galaxies
Disk galaxies contain a large amount of interstellar dust, which affects the
projection of kinematic quantities. We investigate in detail the effects of
dust extinction on the mean projected velocity and the projected velocity
dispersion. We use our results to construct a general strategy to determine the
dynamical structure of disk galaxies, with the aim to constrain their mass
distribution and dynamical history.Comment: to be published in the proceedings of "Galaxy Disks and Disk
Galaxies", Funes J.G. and Corsini E.M. eds., ASP Conference Serie
The nature of the UV halo around the spiral galaxy NGC 3628
Thanks to deep UV observations with GALEX and Swift, diffuse UV haloes have
recently been discovered around galaxies. Based on UV-optical colours, it has
been advocated that the UV haloes around spiral galaxies are due to UV
radiation emitted from the disc and scattered off dust grains at high
latitudes. Detailed UV radiative transfer models that take into account
scattering and absorption can explain the morphology of the UV haloes, and they
require the presence of an additional thick dust disc next the to traditional
thin disc for half of the galaxies in their sample. We test whether such an
additional thick dust disc agrees with the observed infrared emission in NGC
3628, an edge-on galaxy with a clear signature of a thick dust disc. We extend
the far-ultraviolet radiative transfer models to full-scale panchromatic
models. Our model, which contains no fine-tuning, can almost perfectly
reproduce the observed spectral energy distribution from UV to mm wavelengths.
These results corroborate the interpretation of the extended UV emission in NGC
3628 as scattering off dust grains, and hence of the presence of a substantial
amount of diffuse extra-planar dust. A significant caveat, however, is the
geometrical simplicity and non-uniqueness of our model: other models with a
different geometrical setting could lead to a similar spectral energy
distribution. More detailed radiative transfer simulations that compare the
model results to images from UV to submm wavelengths are a way to break this
degeneracy, as are UV polarisation measurements.Comment: 6 pages, 2 figures, accepted for publication in Astronomy &
Astrophysic
Using 3D Voronoi grids in radiative transfer simulations
Probing the structure of complex astrophysical objects requires effective
three-dimensional (3D) numerical simulation of the relevant radiative transfer
(RT) processes. As with any numerical simulation code, the choice of an
appropriate discretization is crucial. Adaptive grids with cuboidal cells such
as octrees have proven very popular, however several recently introduced
hydrodynamical and RT codes are based on a Voronoi tessellation of the spatial
domain. Such an unstructured grid poses new challenges in laying down the rays
(straight paths) needed in RT codes. We show that it is straightforward to
implement accurate and efficient RT on 3D Voronoi grids. We present a method
for computing straight paths between two arbitrary points through a 3D Voronoi
grid in the context of a RT code. We implement such a grid in our RT code
SKIRT, using the open source library Voro++ to obtain the relevant properties
of the Voronoi grid cells based solely on the generating points. We compare the
results obtained through the Voronoi grid with those generated by an octree
grid for two synthetic models, and we perform the well-known Pascucci RT
benchmark using the Voronoi grid. The presented algorithm produces correct
results for our test models. Shooting photon packages through the geometrically
much more complex 3D Voronoi grid is only about three times slower than the
equivalent process in an octree grid with the same number of cells, while in
fact the total number of Voronoi grid cells may be lower for an equally good
representation of the density field. We conclude that the benefits of using a
Voronoi grid in RT simulation codes will often outweigh the somewhat slower
performance.Comment: 9 pages, 7 figures, accepted by A
Self-consistent dynamical models with a finite extent -- I. The uniform density sphere
The standard method to generate dynamical models with a finite extent is to
apply a truncation in binding energy to the distribution function. This
approach has the disadvantages that one cannot choose the density to start
with, that the important dynamical quantities cannot be calculated
analytically, and that a fraction of the possible bound orbits are excluded a
priori. We explore another route and start from a truncation in radius rather
than a truncation in binding energy. We focus on the simplest truncated density
profile, the uniform density sphere. We explore the most common inversion
techniques to generate distribution functions for the uniform density sphere,
corresponding to a large range of possible anisotropy profiles. We find that
the uniform density sphere cannot be supported by the standard isotropic,
constant anisotropy or Osipkov-Merritt models, as all these models are
characterised by negative distribution functions. We generalise the Cuddeford
inversion method to models with a tangential anisotropy and present a
one-parameter family of dynamical models for the uniform density sphere. Each
member of this family is characterised by an anisotropy profile that smoothly
decreases from an arbitrary value at the centre to
completely tangential at the outer radius. All models have a positive
distribution function over the entire phase space, and a nonzero occupancy of
all possible bound orbits. This shows that one can generate nontrivial
self-consistent dynamical models based on preset density profile with a finite
extent.Comment: Accepted for publication in MNRA
Tracing the relation between black holes and dark haloes
We present new velocity dispersion measurements for a set of 12 spiral
galaxies and use them to derive a more accurate V_c - sigma relation which
holds for a wide morphological range of galaxies. Combined with the M_BH -
sigma relation, this relation can be used as a tool to estimate supermassive
black hole (SMBH) masses by means of the asymptotic circular velocity. Together
with the Tully-Fisher relation, it serves as a constraint for galaxy formation
and evolution models.Comment: 2 pages, 2 figures, to appear in Proc. IAU Symp. 220, "Dark Matter in
Galaxies" eds. S. Ryder, D.J. Pisano, M. Walker, & K. Freeman (San Francisco:
ASP
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