Object cross-identification in multiple observations is often complicated by the uncertainties in their astrometric calibration. Due to the lack of standard reference objects, an image with a small field of view can have significantly larger errors i
n its absolute positioning than the relative precision of the detected sources within. We present a new general solution for the relative astrometry that quickly refines the World Coordinate System of overlapping fields. The efficiency is obtained through the use of infinitesimal 3-D rotations on the celestial sphere, which do not involve trigonometric functions. They also enable an analytic solution to an important step in making the astrometric corrections. In cases with many overlapping images, the correct identification of detections that match together across different images is difficult to determine. We describe a new greedy Bayesian approach for selecting the best object matches across a large number of overlapping images. The methods are developed and demonstrated on the Hubble Legacy Archive, one of the most challenging data sets today. We describe a novel catalog compiled from many Hubble Space Telescope observations, where the detections are combined into a searchable collection of matches that link the individual detections. The matches provide descriptions of astronomical objects involving multiple wavelengths and epochs. High relative positional accuracy of objects is achieved across the Hubble images, often sub-pixel precision in the order of just a few milli-arcseconds. The result is a reliable set of high-quality associations that are publicly available online.
We discuss a novel approach to identifying cosmic events in separate and independent observations. In our focus are the true events, such as supernova explosions, that happen once, hence, whose measurements are not repeatable. Their classification an
d analysis have to make the best use of all the available data. Bayesian hypothesis testing is used to associate streams of events in space and time. Probabilities are assigned to the matches by studying their rates of occurrence. A case study of Type Ia supernovae illustrates how to use lightcurves in the cross-identification process. Constraints from realistic lightcurves happen to be well-approximated by Gaussians in time, which makes the matching process very efficient. Model-dependent associations are computationally more demanding but can further boost our confidence.
Sky coverage is one of the most important pieces of information about astronomical observations. We discuss possible representations, and present algorithms to create and manipulate shapes consisting of generalized spherical polygons with arbitrary c
omplexity and size on the celestial sphere. This shape specification integrates well with our Hierarchical Triangular Mesh indexing toolbox, whose performance and capabilities are enhanced by the advanced features presented here. Our portable implementation of the relevant spherical geometry routines comes with wrapper functions for database queries, which are currently being used within several scientific catalog archives including the Sloan Digital Sky Survey, the Galaxy Evolution Explorer and the Hubble Legacy Archive projects as well as the Footprint Service of the Virtual Observatory.
We present a detailed study of the Galaxy Evolution Explorers photometric catalogs with special focus on the statistical properties of the All-sky and Medium Imaging Surveys. We introduce the concept of primaries to resolve the issue of multiple dete
ctions and follow a geometric approach to define clean catalogs with well-understood selection functions. We cross-identify the GALEX sources (GR2+3) with Sloan Digital Sky Survey (DR6) observations, which indirectly provides an invaluable insight about the astrometric model of the UV sources and allows us to revise the band merging strategy. We derive the formal description of the GALEX footprints as well as their intersections with the SDSS coverage along with analytic calculations of their areal coverage. The crossmatch catalogs are made available for the public. We conclude by illustrating the implementation of typical selection criteria in SQL for catalog subsets geared toward statistical analyses, e.g., correlation and luminosity function studies.
We present a novel technique to overcome the limitations of the applicability of Principal Component Analysis to typical real-life data sets, especially astronomical spectra. Our new approach addresses the issues of outliers, missing information, lar
ge number of dimensions and the vast amount of data by combining elements of robust statistics and recursive algorithms that provide improved eigensystem estimates step-by-step. We develop a generic mechanism for deriving reliable eigenspectra without manual data censoring, while utilising all the information contained in the observations. We demonstrate the power of the methodology on the attractive collection of the VIMOS VLT Deep Survey spectra that manifest most of the challenges today, and highlight the improvements over previous workarounds, as well as the scalability of our approach to collections with sizes of the Sloan Digital Sky Survey and beyond.
We present a rigorous mathematical solution to photometric redshift estimation and the more general inversion problem. The challenge we address is to meaningfully constrain unknown properties of astronomical sources based on given observables, usuall
y multicolor photometry, with the help of a training set that provides an empirical relation between the measurements and the desired quantities. We establish a formalism that blurs the boundary between the traditional empirical and template-fitting algorithms, as both are just special cases that are discussed in detail to put them in context. The new approach enables the development of more sophisticated methods that go beyond the classic techniques to combine their advantages. We look at the directions for further improvement in the methodology, and examine the technical aspects of practical implementations. We show how training sets are to be constructed and used consistently for reliable estimation.
We present a general probabilistic formalism for cross-identifying astronomical point sources in multiple observations. Our Bayesian approach, symmetric in all observations, is the foundation of a unified framework for object matching, where not only
spatial information, but physical properties, such as colors, redshift and luminosity, can also be considered in a natural way. We provide a practical recipe to implement an efficient recursive algorithm to evaluate the Bayes factor over a set of catalogs with known circular errors in positions. This new methodology is crucial for studies leveraging the synergy of todays multi-wavelength observations and to enter the time-domain science of the upcoming survey telescopes.
