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 extinguishe
d 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 for obtaining the likelihood function of distance and extinction to a star given its photometry. The other properties of the star (its mass, age, metallicity and so on) are marginalised assuming a simple Galaxy model. We demonstra
te that the resulting marginalised likelihood function can be described faithfully and compactly using a Gaussian mixture model. For dust mapping applications we strongly advocate using monochromatic over bandpass extinctions, and provide tables for converting from the former to the latter for different stellar types.
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 th
e 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.
We present a three dimensional map of extinction in the Northern Galactic Plane derived using photometry from the IPHAS survey. The map has fine angular ($sim 10$ arcmin) and distance (100 pc) sampling allied to a significant depth ($gtrsim 5$ kpc).
We construct the map using a method based on a hierarchical Bayesian model as previously described by Sale (2012). In addition to mean extinction, we also measure differential extinction, which arises from the fractal nature of the ISM, and show that it will be the dominant source of uncertainty in estimates of extinction to some arbitrary position. The method applied also furnishes us with photometric estimates of the distance, extinction, effective temperature, surface gravity, and mass for $sim 38$ million stars. Both the extinction map and the catalogue of stellar parameters are made publicly available via http://www.iphas.org/extinction .
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 de
termine 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.
The determination of reliable distances to Planetary Nebulae (PNe) is one of the major limitations in the study of this class of objects in the Galaxy. The availability of new photometric surveys such as IPHAS covering large portions of the sky gives
us the opportunity to apply the extinction method to determine distances of a large number of objects. The technique is applied to a sample of 137 PNe located between -5 and 5 degrees in Galactic latitude, and between 29.52 and 215.49 degrees in longitude. The characteristics of the distance-extinction method and the main sources of errors are carefully discussed. The data on the extinction of the PNe available in the literature, complemented by new observations, allow us to determine extinction distances for 70 PNe. A comparison with statistical distance scales from different authors is presented.
This study is an investigation of the stellar density profile of the Galactic disc in the Anticentre direction. We select over 40,000 early A stars from IPHAS photometry in the Galactic longitude range 160 < l < 200 close to the equatorial plane (-1
< b < +1). We then compare their observed reddening-corrected apparent magnitude distribution with simulated photometry obtained from parameterised models in order to set constraints on the Anticentre stellar density profile. By selecting A stars, we are appraising the properties of a population only ~100 Myrs old. We find the stellar density profile of young stars is well fit to an exponential with length scale of (3020 pm 120_{statistical} pm 180_{systematic}) pc, which is comparable to that obtained in earlier studies, out to a Galactocentric radius of R_T = (13.0 pm 0.5_{statistical} pm 0.6_{systematic}) kpc. At larger radii the rate of decline appears to increase with the scale length dropping to (1200 pm 300_{statistical} pm 70_{systematic}) pc. This result amounts to a refinement of the conclusions reached in previous studies that the stellar density profile is abruptly truncated. The IPHAS A star data are not compatible with models that propose a sudden change in metallicity at R_G = 10 kpc.
We present an algorithm ({scshape mead}, for `Mapping Extinction Against Distance) which will determine intrinsic ($r - i$) colour, extinction, and distance for early-A to K4 stars extracted from the IPHAS $r/i/Halpha$ photometric database. These dat
a can be binned up to map extinction in three dimensions across the northern Galactic Plane. The large size of the IPHAS database ($sim 200$ million unique objects), the accuracy of the digital photometry it contains and its faint limiting magnitude ($r sim 20$) allow extinction to be mapped with fine angular ($ sim 10 $ arcmin) and distance ($sim 0.1$ ~kpc) resolution to distances of up to 10 kpc, outside the Solar Circle. High reddening within the Solar Circle on occasion brings this range down to $sim 2$ kpc. The resolution achieved, both in angle and depth, greatly exceeds that of previous empirical 3D extinction maps, enabling the structure of the Galactic Plane to be studied in increased detail. {scshape mead} accounts for the effect of the survey magnitude limits, photometric errors, unresolved ISM substructure, and binarity. The impact of metallicity variations, within the range typical of the Galactic disc is small. The accuracy and reliability of {scshape mead} are tested through the use of simulated photometry created with Monte-Carlo sampling techniques. The success of this algorithm is demonstrated on a selection of fields and the results are compared to the literature.
