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Register a new user3D Extinction Mapping Using Hierarchical Bayesian Models
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S. E. Sale
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The Galaxy and the stars in it form a hierarchical system, such that the properties of individual stars are influenced by those of the Galaxy. Here, an approach is described which uses hierarchical Bayesian models to simultaneously and empirically determine the mean distance-extinction relationship for a sightline and the properties of stars which populate it. By exploiting the hierarchical nature of the problem, the method described is able to achieve significantly improved precision and accuracy with respect to previous 3D extinction mapping techniques. This method is not tied to any individual survey and could be applied to any observations, or combination of observations available. Furthermore, it is extendible and, in addition, could be employed to study Galactic structure as well as factors such as the initial mass function and star formation history in the Galaxy.
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Selection effects can bedevil the inference of the properties of a population of astronomical catalogues, unavoidably biasing the observed catalogue. This is particularly true when mapping interstellar extinction in three dimensions: more extinguished stars are fainter and so generally less likely to appear in any magnitude limited catalogue of observations. This paper demonstrates how to account for this selection effect when mapping extinction, so that accurate and unbiased estimates of the true extinction are obtained. We advocate couching the description of the problem explicitly as a Poisson point process, which allows the likelihoods employed to be easily and correctly normalised in such a way that accounts for the selection functions applied to construct the catalogue of observations.
We present a method to simultaneously infer the interstellar extinction parameters $A_0$ and $R_0$, stellar effective temperature $T_{rm eff}$, and distance modulus $mu$ in a Bayesian framework. Using multi-band photometry from SDSS and UKIDSS, we train a forward model to emulate the colour-change due to physical properties of stars and the interstellar medium for temperatures from 4000 to 9000 K and extinctions from 0 to 5 mag. We introduce a Hertzsprung-Russel diagram prior to account for physical constraints on the distribution of stars in the temperature-absolute magnitude plane. This allows us to infer distances probabilistically. Influences of colour information, priors and model parameters are explored. Residual mean absolute errors (MAEs) on a set of objects for extinction and temperature are 0.2 mag and 300 K, respectively, for $R_0$ fixed to 3.1. For variable $R_0$, we obtain MAEs of 0.37 mag, 412.9 K and 0.74 for $A_0$, $T_{rm eff}$ and $R_0$, respectively. Distance moduli are accurate to approximately 2 mag. Quantifying the precisions of individual parameter estimates with $68%$ confidence interval of the posterior distribution, we obtain 0.05 mag, 66 K, 2 mag and 0.07 for $A_0$, $T_{rm eff}$, $mu$ and $R_0$, respectively, although we find that these underestimate the accuracy of the model. We produce two-dimensional maps in extinction and $R_0$ that are compared to previous work. Furthermore we incorporate the inferred distance information to compute fully probabilistic distance profiles for individual lines of sight. The individual stellar AP estimates, combined with inferred 3D information will make possible many Galactic science and modelling applications. Adapting our method to work with other surveys, such as Pan-STARRS and Gaia, will allow us to probe other regions of the Galaxy.
Context. While Gaia enables to probe in great detail the extended local neighbourhood, the thin disk structure at larger distances remains sparsely explored. Aims. We aim here to build a non-parametric 3D model of the thin disc structures handling both the extinction and the stellar density simultaneously. Methods. We developed a Bayesian deconvolution method in two dimensions: extinction and distance. It uses a reference catalogue which completeness information defines the selection function. It is designed so that any complementary information from other catalogues can be added. It has also been designed to be robust to outliers, frequent in crowded fields, and differential extinction. The prior information is designed to be minimal: only a reference H-R diagram. We derived for this an empirical H-R diagram of the thin disk using Gaia DR2 data and synthetic isochrone-based H-R diagrams can also be used. Results. We validated the method on simulations and real fields using 2MASS and UKIDSS data complemented by Gaia DR2 photometry and parallaxes. We detail the results of two test fields: a 2MASS field centred around the NGC 4815 open cluster which shows an over-density of both extinction and stellar density at the cluster distance, and a UKIDSS field at $l=10^{circ}$ where we recover the position of the Galactic bar.
We present a scheme for using stellar catalogues to map the three-dimensional distributions of extinction and dust within our Galaxy. Extinction is modelled as a Gaussian random field, whose covariance function is set by a simple physical model of the ISM that assumes a Kolmogorov-like power spectrum of turbulent fluctuations. As extinction is modelled as a random field, the spatial resolution of the resulting maps is set naturally by the data available; there is no need to impose any spatial binning. We verify the validity of our scheme by testing it on simulated extinction fields and show that its precision is significantly improved over previous dust-mapping efforts. The approach we describe here can make use of any photometric, spectroscopic or astrometric data; it is not limited to any particular survey. Consequently, it can be applied to a wide range of data from both existing and future surveys.
(Abridged) We present maps for various Galactic longitudes and latitudes at 1.4 GHz, which is the frequency where deep SKA surveys are proposed. The maps are about 1.5 deg in size and have an angular resolution of about 1.6 arcsec. We analyse the maps in terms of their probability density functions (PDFs) and structure functions. Total intensity emission is more smooth in the plane than at high latitudes due to the different contributions from the regular and random magnetic field. The high latitude fields show more extended polarized emission and RM structures than those in the plane, where patchy emission structures on very small scales dominate. The RM PDFs in the plane are close to Gaussians, but clearly deviate from that at high latitudes. The RM structure functions show smaller amplitudes and steeper slopes towards high latitudes. These results emerge from the fact that much more turbulent cells are passed through by the line-of-sights in the plane. Although the simulated random magnetic field components distribute in 3D, the magnetic field spectrum extracted from the structure functions of RMs conforms to 2D in the plane and approaches 3D at high latitudes. This is partly related to the outer scale of the turbulent magnetic field, but mainly to the different lengths of the line-of-sights.
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