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 Sérsic 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 Sérsic model family that result in two independent expressions that can be used along the entire sequence of Sérsic 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

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

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

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

Stellar systems following the R1/mR^{1/m} luminosity law. III. Photometric, intrinsic, and dynamical properties for all S\'ersic indices

The S\'ersic or $R^{1/m}$ 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 $m$. For small values of $m$, 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 $m$ regime, where a number of interesting and surprising properties are found. For all values $m<1$, the model is characterised by a finite central luminosity density, and for $m<\tfrac12$, even a central depression in the luminosity density profile. This behaviour translates to the dynamical properties: we show that all S\'ersic models with $m \geqslant\tfrac12$ 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 $m < \tfrac12$, on the other hand, cannot be supported by an isotropic velocity dispersion tensor.Comment: 10 pages, 5 figures, accepted for publication in A&

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

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

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 $\beta_0\leqslant0$ 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