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

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 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

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&

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 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

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

Hierarchical octree and k-d tree grids for 3D radiative transfer simulations

A crucial ingredient for numerically solving the 3D radiative transfer problem is the choice of the grid that discretizes the transfer medium. Many modern radiative transfer codes, whether using Monte Carlo or ray tracing techniques, are equipped with hierarchical octree-based grids to accommodate a wide dynamic range in densities. We critically investigate two different aspects of octree grids in the framework of Monte Carlo dust radiative transfer. Inspired by their common use in computer graphics applications, we test hierarchical k-d tree grids as an alternative for octree grids. On the other hand, we investigate which node subdivision-stopping criteria are optimal for constructing of hierarchical grids. We implemented a k-d tree grid in the 3D radiative transfer code SKIRT and compared it with the previously implemented octree grid. We also considered three different node subdivision-stopping criteria (based on mass, optical depth, and density gradient thresholds). Based on a small suite of test models, we compared the efficiency and accuracy of the different grids, according to various quality metrics. For a given set of requirements, the k-d tree grids only require half the number of cells of the corresponding octree. Moreover, for the same number of grid cells, the k-d tree is characterized by higher discretization accuracy. Concerning the subdivision stopping criteria, we find that an optical depth criterion is not a useful alternative to the more standard mass threshold, since the resulting grids show a poor accuracy. Both criteria can be combined; however, in the optimal combination, for which we provide a simple approximate recipe, this can lead to a 20% reduction in the number of cells needed to reach a certain grid quality. An additional density gradient threshold criterion can be added that solves the problem of poorly resolving sharp edges and... (abridged).Comment: 10 pages, 6 figures. Accepted for publication in A&

Testing baryon-induced core formation in Λ\LambdaCDM: A comparison of the DC14 and coreNFW dark matter halo models on galaxy rotation curves

Recent cosmological hydrodynamical simulations suggest that baryonic processes, and in particular supernova feedback after bursts of star formation, can alter the structure of dark matter haloes and transform primordial cusps into shallower cores. To assess whether this mechanism offers a solution to the cusp-core controversy, simulated haloes must be compared to real dark matter haloes inferred from galaxy rotation curves. For this purpose, two new dark matter density profiles were recently derived from simulations of galaxies in complementary mass ranges: the DC14 halo ($10^{10} < M_{\text{halo}}/M_{\odot} < 8 \times 10^{11}$) and the coreNFW halo ($10^{7} < M_{\text{halo}}/M_{\odot} < 10^{9}$). Both models have individually been found to give good fits to observed rotation curves. For the DC14 model, however, the agreement of the predicted halo properties with cosmological scaling relations was confirmed by one study, but strongly refuted by another. A next question is whether the two models converge to the same solution in the mass range where both should be appropriate. To investigate this, we tested the DC14 and cNFW halo models on the rotation curves of a selection of galaxies with halo masses in the range $4 \times 10^{9}$ - $7 \times 10^{10}$ $M_{\odot}$. We further applied the DC14 model to a set of rotation curves at higher halo masses, up to $9 \times 10^{11}$ $M_{\odot}$, to verify the agreement with the cosmological scaling relations. We find that both models are generally able to reproduce the observed rotation curves, in line with earlier results, and the predicted dark matter haloes are consistent with the cosmological $c-M_{\text{halo}}$ and $M_{*}-M_{\text{halo}}$ relations. The DC14 and cNFW models are also in fairly good agreement with each other, even though DC14 tends to predict slightly less extended cores and somewhat more concentrated haloes than cNFW.Comment: 19 pages, 12 figures, accepted for publication in A&