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Published July 15, 2009 | public
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The 2pt+: an enhanced 2 point correlation function

Ave, M.
Cazon, L.
Cronin, J.
de Mello Neto, J. R. T.
Olinto, A. V.
Pavlidou, V.
Privitera, P.
Siffert, B. B.
Schmidt, F.
Venters, T.
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Abstract

We introduce a new method for testing departure from isotropy of points on a sphere based on an enhanced form of the two-point correlation function that we named 2pt+. This method uses information from the two extra variables that define the vector between two points on a sphere. We show that this is a powerful method to test departure from isotropy of a distribution of points on a sphere especially when the number of events is small. We apply the method to a few examples in astronomy and discuss the relevance for limited datasets, such as the case of ultra-high energy cosmic rays.

Additional Information

Copyright © IOP Publishing Ltd and SISSA 2009. Received 15 May 2009, accepted for publication 9 June 2009. Published 15 July 2009. We thank the Pierre Auger Collaboration for inspiring this work and for many discussions about testing isotropy with sparsely sample spherical datasets. This work was supported in part by NSF PHY-0758017 and by the KICP under NSF PHY-0551142 at the University of Chicago. VP acknowledges support by NASA through the GLAST Fellowship Program, NASA Cooperative Agreement: NNG06DO90A. TV acknowledges support by the NSF Graduate Research Fellowship Program.

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