Spherical Harmonic Expansion of Gamma Ray Burst Distributions: Probing Large Scale Structure?

Abstract

We have laid down the formalism and techniques necessary for computing the multipole components in a spherical harmonic expansion for bursting sources given any specific power spectrum of density perturbations. Using this formalism we have explicitly computed and tabulated the expected first few multipole components for the GRB distribution using a Cold Dark Matter power spectrum. Unfortunately, our analysis leads us to expect that an anisotropy signal for this model of structure formation will be below the shot noise level for the foreseeable future. Earlier studies by others had claimed that it may be possible within a decade or so to probe structure formation using the angular distribution of GRBs. We find that while it may be possible to probe the dipole due to our motion with respect to the cosmic rest-frame, it does not seem feasible to probe the multipole components due to intrinsic fluctuations if the actual power spectrum is fixed to within an order of magnitude by the Cold Dark Matter model of structure formation.