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&

The dynamical structure of isotropic spherical galaxies with a central black hole

We discuss the kinematical structure of a two-parameter family of isotropic models with a central black hole. The family contains the slope of the central density cusp and the relative black hole mass as parameters. Most of the basic kinematical quantities of these models can be expressed analytically. This family contains three distinct models where also the distribution function, differential energy distribution and spatial LOSVDs can be expressed completely analytically. Each of these models show a drastically different behaviour of the distribution function. Although the effect of a black hole on the distribution function is very strong, in particular for models with a shallow density cusp, the differential energy distribution is only marginally affected. We discuss in detail the effects of a central black hole on the LOSVDs. The projected velocity dispersion increases with black hole mass at small projected radii, but the effect of a black hole on the shape of the LOSVDs (characterized by the h4 parameter) is less straightforward to interpret. Too much reliance on the wings of the LOSVDs and the value of the h4 parameter to determine black hole masses might hence be dangerous.Comment: 12 pages, 3 figures, accepted for publication in A&

Radial stability of a family of anisotropic Hernquist models with and without a supermassive black hole

We present a method to investigate the radial stability of a spherical anisotropic system that hosts a central supermassive black hole (SBH). Such systems have never been tested before for stability, although high anisotropies have been considered in the dynamical models that were used to estimate the masses of the central putative supermassive black holes. A family of analytical anisotropic spherical Hernquist models with and without a black hole were investigated by means of N-body simulations. A clear trend emerges that the supermassive black hole has a significant effect on the overall stability of the system, i.e. an SBH with a mass of a few percent of the total mass of the galaxy can prevent or reduce the bar instabilities in anisotropic systems. Its mass not only determines the strength of the instability reduction, but also the time in which this occurs. These effects are most significant for models with strong radial anisotropies. Furthermore, our analysis shows that unstable systems with similar SBH but with different anisotropy radii evolve differently: highly radial systems become oblate, while more isotropic models tend to form into prolate structures. In addition to this study, we also present a Monte-Carlo algorithm to generate particles in spherical anisotropic systems.Comment: 16 pages, 12 figures, accepted for publication in MNRAS (some figures have a lowered resolution

G2C2-III: Structural parameters for Galactic globular clusters in SDSS passbands

We use our Galactic Globular Cluster Catalog (G2C2) photometry for 111 Galactic globular clusters (GC) in g and z, as well as r and i photometry for a subset of 60 GCs and u photometry for 22 GCs, to determine the structural parameters assuming King (1962) models. In general, the resulting core radii are in good comparison with the current literature values. However, our half-light radii are slightly lower than the literature. The concentrations (and therefore also the tidal radii) are poorly constrained mostly because of the limited radial extent of our imaging. Therefore, we extensively discuss the effects of a limited field-of-view on the derived parameters using mosaicked SDSS data, which do not suffer from this restriction. We also illustrate how red giant branch (RGB) stars in cluster cores can stochastically induce artificial peaks in the surface brightness profiles. The issues related to these bright stars are scrutinised based on both our photometry and simulated clusters. We also examine colour gradients and find that the strongest central colour gradients are caused by central RGB stars and thus not representative for the cluster light or colour distribution. We recover the known relation between the half-light radius and the Galactocentric distance in the g-band, but find a lower slope for redder filters. We did not find a correlation between the scatter on this relation and other cluster properties. We find tentative evidence for a correlation between the half-light radii and the [Fe/H], with metal-poor GCs being larger than metal-rich GCs. However, we conclude that this trend is caused by the position of the clusters in the Galaxy, with metal-rich clusters being more centrally located.Comment: 17 pages, 23 figures, 3 tables. Accepted to MNRAS. The online appendix includes the structural parameters and the SB profile fits for all the sample cluster

Large and small-scale structures and the dust energy balance problem in spiral galaxies

The interstellar dust content in galaxies can be traced in extinction at optical wavelengths, or in emission in the far-infrared. Several studies have found that radiative transfer models that successfully explain the optical extinction in edge-on spiral galaxies generally underestimate the observed FIR/submm fluxes by a factor of about three. In order to investigate this so-called dust energy balance problem, we use two Milky Way-like galaxies produced by high-resolution hydrodynamical simulations. We create mock optical edge-on views of these simulated galaxies (using the radiative transfer code SKIRT), and we then fit the parameters of a basic spiral galaxy model to these images (using the fitting code FitSKIRT). The basic model includes smooth axisymmetric distributions along a S\'ersic bulge and exponential disc for the stars, and a second exponential disc for the dust. We find that the dust mass recovered by the fitted models is about three times smaller than the known dust mass of the hydrodynamical input models. This factor is in agreement with previous energy balance studies of real edge-on spiral galaxies. On the other hand, fitting the same basic model to less complex input models (e.g. a smooth exponential disc with a spiral perturbation or with random clumps), does recover the dust mass of the input model almost perfectly. Thus it seems that the complex asymmetries and the inhomogeneous structure of real and hydrodynamically simulated galaxies are a lot more efficient at hiding dust than the rather contrived geometries in typical quasi-analytical models. This effect may help explain the discrepancy between the dust emission predicted by radiative transfer models and the observed emission in energy balance studies for edge-on spiral galaxies.Comment: 9 pages, 5 figures, accepted for publication in A&

A low-frequency study of recently identified double-double radio galaxies

In order to understand the possible mechanisms of recurrent jet activity in radio galaxies and quasars, which are still unclear, we have identified such sources with a large range of linear sizes (220 $-$ 917 kpc), and hence time scales of episodic activity. Here we present high-sensitivity 607-MHz Giant Metrewave Radio Telescope (GMRT) images of 21 possible double-double radio galaxies (DDRGs) identified from the FIRST survey to confirm their episodic nature. These GMRT observations show that none of the inner compact components suspected to be hot-spots of the inner doubles are cores having a flat radio spectrum, confirming the episodic nature of these radio sources. We have indentified a new DDRG with a candidate quasar, and have estimated the upper spectral age limits for eight sources which showed marginal evidence of steepening at higher frequencies. The estimated age limits (11 $-$ 52 Myr) are smaller than those of the large-sized ($\sim$ 1 Mpc) DDRGs.Comment: Accepted for publication in MNRAS. 14 pages, 7 figure

Radiative equilibrium in Monte Carlo radiative transfer using frequency distribution adjustment

The Monte Carlo method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. The main drawback of the standard Monte Carlo radiative equilibrium methods is that they require iteration, which makes them numerically very demanding. Bjorkman & Wood recently proposed a frequency distribution adjustment scheme, which allows radiative equilibrium Monte Carlo calculations to be performed without iteration, by choosing the frequency of each re-emitted photon such that it corrects for the incorrect spectrum of the previously re-emitted photons. Although the method appears to yield correct results, we argue that its theoretical basis is not completely transparent, and that it is not completely clear whether this technique is an exact rigorous method, or whether it is just a good and convenient approximation. We critically study the general problem of how an already sampled distribution can be adjusted to a new distribution by adding data points sampled from an adjustment distribution. We show that this adjustment is not always possible, and that it depends on the shape of the original and desired distributions, as well as on the relative number of data points that can be added. Applying this theorem to radiative equilibrium Monte Carlo calculations, we provide a firm theoretical basis for the frequency distribution adjustment method of Bjorkman & Wood, and we demonstrate that this method provides the correct frequency distribution through the additional requirement of radiative equilibrium. We discuss the advantages and limitations of this approach, and show that it can easily be combined with the presence of additional heating sources and the concept of photon weighting. However, the method may fail if small dust grains are included... (abridged)Comment: 17 pages, 2 figures, accepted for publication in New Astronom

Photo-centric variability of quasars caused by variations in their inner structure: Consequences on Gaia measurements

We study the photocenter position variability due to variations in the quasar inner structure. We consider variability in the accretion disk emissivity and torus structure variability due to different illumination by the central source. We discuss possible detection of these effects by Gaia. Observations of the photocenter variability in two AGNs, SDSS J121855+020002 and SDSS J162011+1724327 have been reported and discussed. With investigation of the variations in the quasar inner structure we explore how much this effect can affect the position determination and whether it can be (or not) detected with Gaia mission. We used (a) a model of a relativistic disk, including the perturbation that can increase brightness of a part of the disk, and consequently offset the photocenter position, and (b) a model of a dusty torus which absorbs and re-emits the incoming radiation from accretion disk. We estimated the value of the photocenter offset due to these two effects. We found that perturbations in the inner structure can significantly offset the photocenter. It depends on the characteristics of perturbation and accretion disk and structure of the torus. In the case of two considered QSOs the observed photocenter offsets cannot be explained by variations in the accretion disk and other effects should be considered. We discussed possibility of exploding stars very close to the AGN source, and also possibility that there are two variable sources in the center of these two AGNs that may indicate a binary super-massive black hole system on a kpc (pc) scale. The Gaia mission seems to be very perspective, not only for astrometry, but also for exploring the inner structure of AGNs. We conclude that variations in the quasar inner structure can affect the observed photocenter (up to several mas). There is a chance to observe such effect in the case of bright and low-redshifted QSOs.Comment: 12 pages, 8 figures, 3 tables. Accepted for publication in Astronomy and Astrophysics. Language improved, typos correcte

G2C2 II: Integrated colour-metallicity relations for Galactic Globular Clusters in SDSS passbands

We use our integrated SDSS photometry for 96 globular clusters in $g$ and $z$, as well as $r$ and $i$ photometry for a subset of 56 clusters, to derive the integrated colour-metallicity relation (CMR) for Galactic globular clusters. We compare this relation to previous work, including extragalactic clusters, and examine the influence of age, present-day mass function variations, structural parameters and the morphology of the horizontal branch on the relation. Moreover, we scrutinise the scatter introduced by foreground extinction (including differential reddening) and show that the scatter in the colour-metallicity relation can be significantly reduced combining two reddening laws from the literature. In all CMRs we find some low-reddening young GCs that are offset to the CMR. Most of these outliers are associated with the Sagittarius system. Simulations show that this is due less to age than to a different enrichment history. Finally, we introduce colour-metallicity relations based on the infrared Calcium triplet, which are clearly non-linear when compared to $(g^\prime-i^\prime)$ and $(g^\prime-z^\prime)$ colours.Comment: Accepted for publication in MNRAS. 17 pages, 18 figure

Far-infrared and dust properties of present-day galaxies in the EAGLE simulations

The Evolution and Assembly of GaLaxies and their Environments (EAGLE) cosmological simulations reproduce the observed galaxy stellar mass function and many galaxy properties. In this work, we study the dust-related properties of present-day EAGLE galaxies through mock observations in the far-infrared and submm wavelength ranges obtained with the 3D dust radiative transfer code SKIRT. To prepare an EAGLE galaxy for radiative transfer processing, we derive a diffuse dust distribution from the gas particles and we re-sample the star-forming gas particles and the youngest star particles into star-forming regions that are assigned dedicated emission templates. We select a set of redshift-zero EAGLE galaxies that matches the K-band luminosity distribution of the galaxies in the Herschel Reference Survey (HRS), a volume-limited sample of about 300 normal galaxies in the Local Universe. We find overall agreement of the EAGLE dust scaling relations with those observed in the HRS, such as the dust-to-stellar mass ratio versus stellar mass and versus NUV–r colour relations. A discrepancy in the f250/f350 versus f350/f500 submm colour–colour relation implies that part of the simulated dust is insufficiently heated, likely because of limitations in our sub-grid model for star-forming regions. We also investigate the effect of adjusting the metal-to-dust ratio and the covering factor of the photodissociation regions surrounding the star-forming cores. We are able to constrain the important dust-related parameters in our method, informing the calculation of dust attenuation for EAGLE galaxies in the UV and optical domain