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

Smart detectors for Monte Carlo radiative transfer

Many optimization techniques have been invented to reduce the noise that is inherent in Monte Carlo radiative transfer simulations. As the typical detectors used in Monte Carlo simulations do not take into account all the information contained in the impacting photon packages, there is still room to optimize this detection process and the corresponding estimate of the surface brightness distributions. We want to investigate how all the information contained in the distribution of impacting photon packages can be optimally used to decrease the noise in the surface brightness distributions and hence to increase the efficiency of Monte Carlo radiative transfer simulations. We demonstrate that the estimate of the surface brightness distribution in a Monte Carlo radiative transfer simulation is similar to the estimate of the density distribution in an SPH simulation. Based on this similarity, a recipe is constructed for smart detectors that take full advantage of the exact location of the impact of the photon packages. Several types of smart detectors, each corresponding to a different smoothing kernel, are presented. We show that smart detectors, while preserving the same effective resolution, reduce the noise in the surface brightness distributions compared to the classical detectors. The most efficient smart detector realizes a noise reduction of about 10%, which corresponds to a reduction of the required number of photon packages (i.e. a reduction of the simulation run time) of 20%. As the practical implementation of the smart detectors is straightforward and the additional computational cost is completely negligible, we recommend the use of smart detectors in Monte Carlo radiative transfer simulations.Comment: 7 pages, 5 figures, accepted for publication in MNRA

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

The Herschel Virgo Cluster Survey. VI. The far-infrared view of M87

The origin of the far-infrared emission from the nearby radio galaxy M87 remains a matter of debate. Some studies find evidence of a far-infrared excess due to thermal dust emission, whereas others propose that the far-infrared emission can be explained by synchrotron emission without the need for an additional dust emission component. We present Herschel PACS and SPIRE observations of M87, taken as part of the science demonstration phase observations of the Herschel Virgo Cluster Survey. We compare these data with a synchrotron model based on mid-infrared, far-infrared, submm and radio data from the literature to investigate the origin of the far-infrared emission. Both the integrated SED and the Herschel surface brightness maps are adequately explained by synchrotron emission. At odds with previous claims, we find no evidence of a diffuse dust component in M87, which is not unexpected in the harsh X-ray environment of this radio galaxy sitting at the core of the Virgo cluster

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&

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

Herschel-ATLAS: The dust energy balance in the edge-on spiral galaxy UGC4754

We use Herschel PACS and SPIRE observations of the edge-on spiral galaxy UGC4754, taken as part of the H-ATLAS SDP observations, to investigate the dust energy balance in this galaxy. We build detailed SKIRT radiative models based on SDSS and UKIDSS maps and use these models to predict the far-infrared emission. We find that our radiative transfer model underestimates the observed FIR emission by a factor of two to three. Similar discrepancies have been found for other edge-on spiral galaxies based on IRAS, ISO, and SCUBA data. Thanks to the good sampling of the SED at FIR wavelengths, we can rule out an underestimation of the FIR emissivity as the cause for this discrepancy. Instead we support highly obscured star formation that contributes little to the optical extinction as a more probable explanation

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