Dipole and quadrupole tests of the isotropy of gamma-ray burst locations

view Abstract Citations (56) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dipole and Quadrupole Tests of the Isotropy of Gamma-Ray Burst Locations Briggs, Michael S. Abstract Dipole and quadrupole tests of the isotropy of locations on the sphere are discussed. The statistics (cos theta), the dipole moment to the Galactic center, and mean (sin-squared b - 1/3), the quadrupole moment about the Galactic plane, can be used to search for significant anisotropies in galactic coordinates. Such coordinate-system-based tests are the most powerful tests of dipole and quadrupole anisotropies in the particular coordinate system. Two statistics which have not been previously applied to gamma-ray burst data are described. The Rayleigh-Watson statistic measures the size of the dipole moment of the locations and the Bingham statistic measures the deviation of the eigenvalues of a quadrupole-like matrix from the values expected for isotropy. Tests based upon these two statistics search for dipole and quadrupole moments in spherical location data in a coordinate-system-independent, and thus model-independent, manner. They can detect an anisotropy in any direction and yield an analytic statistical significance to any detected anisotropy. The statistical tests are demonstrated herein using a variety of data sets. Publication: The Astrophysical Journal Pub Date: April 1993 DOI: 10.1086/172498 Bibcode: 1993ApJ...407..126B Keywords: Gamma Ray Astronomy; Gamma Ray Bursts; Statistical Analysis; Astronomical Models; Milky Way Galaxy; Spherical Coordinates; Space Radiation; GAMMA RAYS: BURSTS full text sources ADS |