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Register a new userProbabilistic positional association of catalogs of astrophysical sources: the Aspects code
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Michel Fioc
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We describe a probabilistic method of cross-identifying astrophysical sources in two catalogs from their positions and positional uncertainties. The probability that an object is associated with a source from the other catalog, or that it has no counterpart, is derived under two exclusive assumptions: first, the classical case of several-to-one associations, and then the more realistic but more difficult problem of one-to-one associations. In either case, the likelihood of observing the objects in the two catalogs at their effective positions is computed and a maximum likelihood estimator of the fraction of sources with a counterpart -- a quantity needed to compute the probabilities of association -- is built. When the positional uncertainty in one or both catalogs is unknown, this method may be used to estimate its typical value and even to study its dependence on the size of objects. It may also be applied when the true centers of a source and of its counterpart at another wavelength do not coincide. To compute the likelihood and association probabilities under the different assumptions, we developed a Fortran 95 code called Aspects ([asp{epsilon}], ASsociation PositionnellE/ProbabilistE de CaTalogues de Sources in French); its source files are made freely available. To test Aspects, all-sky mock catalogs containing up to 10^5 objects were created, forcing either several-to-one or one-to-one associations. The analysis of these simulations confirms that, in both cases, the assumption with the highest likelihood is the right one and that estimators of unknown parameters built for the appropriate association model are reliable.
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We describe a simple probabilistic method to cross-identify astrophysical sources from different catalogs and provide the probability that a source is associated with a source from another catalog or that it has no counterpart. When the positional uncertainty in one of the catalog is unknown, this method may be used to derive its typical value and even to study its dependence on the size of objects. It may also be applied when the true centers of a source and of its counterpart at another wavelength do not coincide. We extend this method to the case when there are only one-to-one associations between the catalogs.
Aspects ([asp{epsilon}], ASsociation PositionnellE/ProbabilistE de CaTalogues de Sources in French) is a Fortran 95 code for the cross-identification of astrophysical sources. Its source files are freely available. Given the coordinates and positional uncertainties of all the sources in two catalogs K and K, Aspects computes the probability that an object in K and one in K are the same or that they have no counterpart. Three exclusive assumptions are considered: (1) Several-to-one associations: a K-source has at most one counterpart in K, but a K-source may have several counterparts in K; (2) One-to-several associations: the same with K and K swapped; (3) One-to-one associations: a K-source has at most one counterpart in K and vice versa. To compute the probabilities of association, Aspects needs the a priori (i.e. ignoring positions) probability that an object has a counterpart. The code obtains estimates of this quantity by maximizing the likelihood to observe all the sources at their effective positions under each assumption. The likelihood may also be used to determine the most appropriate model, given the data, or to estimate the typical positional uncertainty if unknown.
Detection of point sources in images is a fundamental operation in astrophysics, and is crucial for constraining population models of the underlying point sources or characterizing the background emission. Standard techniques fall short in the crowded-field limit, losing sensitivity to faint sources and failing to track their covariance with close neighbors. We construct a Bayesian framework to perform inference of faint or overlapping point sources. The method involves probabilistic cataloging, where samples are taken from the posterior probability distribution of catalogs consistent with an observed photon count map. In order to validate our method we sample random catalogs of the gamma-ray sky in the direction of the North Galactic Pole (NGP) by binning the data in energy and Point Spread Function (PSF) classes. Using three energy bins spanning $0.3 - 1$, $1 - 3$ and $3 - 10$ GeV, we identify $270substack{+30 -10}$ point sources inside a $40^circ times 40^circ$ region around the NGP above our point-source inclusion limit of $3 times 10^{-11}$/cm$^2$/s/sr/GeV at the $1-3$ GeV energy bin. Modeling the flux distribution as a power law, we infer the slope to be $-1.92substack{+0.07 -0.05}$ and estimate the contribution of point sources to the total emission as $18substack{+2 -2}$%. These uncertainties in the flux distribution are fully marginalized over the number as well as the spatial and spectral properties of the unresolved point sources. This marginalization allows a robust test of whether the apparently isotropic emission in an image is due to unresolved point sources or of truly diffuse origin.
We lay the foundations of a statistical framework for multi-catalogue cross-correlation and cross-identification based on explicit simplified catalogue models. A proper identification process should rely on both astrometric and photometric data. Under some conditions, the astrometric part and the photometric part can be processed separately and merged a posteriori to provide a single global probability of identification. The present paper addresses almost exclusively the astrometrical part and specifies the proper probabilities to be merged with photometric likelihoods. To select matching candidates in n catalogues, we used the Chi (or, indifferently, the Chi-square) test with 2(n-1) degrees of freedom. We thus call this cross-match a chi-match. In order to use Bayes formula, we considered exhaustive sets of hypotheses based on combinatorial analysis. The volume of the Chi-test domain of acceptance -- a 2(n-1)-dimensional acceptance ellipsoid -- is used to estimate the expected numbers of spurious associations. We derived priors for those numbers using a frequentist approach relying on simple geometrical considerations. Likelihoods are based on standard Rayleigh, Chi and Poisson distributions that we normalized over the Chi-test acceptance domain. We validated our theoretical results by generating and cross-matching synthetic catalogues. The results we obtain do not depend on the order used to cross-correlate the catalogues. We applied the formalism described in the present paper to build the multi-wavelength catalogues used for the science cases of the ARCHES (Astronomical Resource Cross-matching for High Energy Studies) project. Our cross-matching engine is publicly available through a multi-purpose web interface. In a longer term, we plan to integrate this tool into the CDS XMatch Service.
We describe the magnetohydrodynamics (MHD) code CRONOS, which has been used in astrophysics and space physics studies in recent years. CRONOS has been designed to be easily adaptable to the problem at hand, where the user can expand or exchange core modules or add new functionality to the code. This modularity comes about through its implementation using a C++ class structure. The core components of the code include solvers for both hydrodynamical (HD) and MHD problems. These problems are solved on different rectangular grids, which currently support Cartesian, spherical, and cylindrical coordinates. CRONOS uses a finite-volume description with different approximate Riemann solvers that can be chosen at runtime. Here, we describe the implementation of the code with a view toward its ongoing development. We illustrate the codes potential through several (M)HD test problems and some astrophysical applications.
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