A Flexible Spherical Mixture Model for Gamma-Ray Burst Patterns Obtained from BATSE and FERMI Mission

Abstract The study encapsulates the investigation into the spherical distributional characteristics of parameters relevant to Gamma-Ray Bursts (GRBs), mainly focusing on their Galactic coordinates. The study utilized a mixture of von Mises Fisher spherical distributions to model the spatial distribution of GRBs in both BATSE and FERMI catalogs. Optimal numbers of mixture components were determined for different subsets of GRBs, including Long and Short GRBs. For the BATSE catalog, it turns out that a mixture of two spherical distributions provides a good fit for the whole data set and long and short GRBs. On the other hand, for the FERMI catalog, it turns out that a mixture of three spherical distributions provides a good fit for the whole data set, and a mixture of four distributions is adequate for both long and short GRBs. Additionally, an assessment was made to determine if the location parameter of GRBs follows any spherical distribution. Our flexible directional statistical modeling framework reveals that GRBs exhibit a non-uniform distribution on the celestial sphere, as evidenced by rejecting the null hypothesis of uniform distribution on a sphere using the Watson test. Our analysis statistically inquires the long-held assumption of their isotropic spread, especially in 2D projected spatial distributions of GRBs, suggesting that these cosmic events might not be uniformly scattered across the celestial sphere. The observed clumping of GRBs hints at the underlying cosmic scaffolding—the large-scale distribution of matter and star formation. Our results statistically asserts the explanation that the intrinsic GRB formation rate is typically tied to cosmic star formation rates with a delay time distribution, leading to a non-uniform rate as a function of redshift, demanding more nuanced calculations. However, this finding needs to consider potential biases introduced by the Milky Way’s obscuration and our heliocentric perspective.