An alpha-stable approach to the study of the P(D) distribution of unresolved point sources in CMB sky maps

Abstract

We present a new approach to the statistical study and modelling of number counts of faint point sources in astronomical images, i.e. counts of sources whose flux falls below the detection limit of a survey. The approach is based on the theory of alpha-stable distributions. We show that the non-Gaussian distribution of the intensity fluctuations produced by a generic point source population -- whose number counts follow a simple power law -- belongs to the alpha-stable family of distributions. Even if source counts do not follow a simple power law, we show that the alpha-stable model is still useful in many astrophysical scenarios. With the alpha-stable model it is possible to totally describe the non-Gaussian distribution with a few parameters which are closely related to the parameters describing the source counts, instead of an infinite number of moments. Using statistical tools available in the signal processing literature, we show how to estimate these parameters in an easy and fast way. We demonstrate that the model proves valid when applied to realistic point source number counts at microwave frequencies. In the case of point extragalactic sources observed at CMB frecuencies, our technique is able to successfully fitting the P(D) distribution of deflections and to precisely determining the main parameters which describe the number counts. In the case of the Planck mission, the relative errors on these parameters are small either at low and at high frequencies. We provide a way to deal with the presence of Gaussian noise in the data using the empirical characteristic function of the P(D). The formalism and methods here presented can be very useful also for experiments in other frequency ranges, e.g. X-ray or radio Astronomy.

arXiv comment16 pages, 6 figures, final version to appear in A&A (in press)

References in corpus (18)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission
• A Physical Model for the Co-evolution of QSOs and of their Spheroidal Hosts
• Cosmic Microwave Background Anisotropies
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
• The Anisotropy of the Microwave Background to l = 3500: Deep Field Observations with the Cosmic Background Imager
• Semi-analytic modelling of galaxy evolution in the IR/submm range
• Extragalactic Source Counts and Contributions to the Anisotropies of the Cosmic Microwave Background. Predictions for the Planck Surveyor mission
• Joint Formation of QSOs and Spheroids: QSOs as clocks of star formation in Spheroids
• The star-formation history of the universe - an infrared perspective
• Point Source Detection using the Spherical Mexican Hat Wavelet on simulated all-sky Planck maps
• The effect of point sources on satellite observations of the cosmic microwave background
• First results from the Very Small Array -- II. Observations of the CMB
• Contributions of point extragalactic sources to the Cosmic Microwave Background bispectrum
• Discriminating between unresolved point sources and "negative" SZ clusters in CMB maps
• Confusion noise at far-IR to millimeter wavelengths
• Radio Wavelength Constraints on the Sources of the Far Infrared Background
• Point sources in the MAP sky maps

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• Astrophysics in 2005
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