A Spheroidal Harmonic Picture for GWs from Binary Black Holes

Central to gravitational wave detection and the inference of source parameters is the representation of gravitational radiation in terms of multipole moments. By construction, these functions of time or frequency allow the radiation's angular dependence to be given by spin weighted harmonic functions. This leaves the radiation itself to be represented as a sum over harmonic functions, whereby each term is weighted by a different multipole moment. The choice of representation, namely the choice of which harmonic functions to use, is not unique. Only the radiation's spin weight must be respected. And while there are multiple appropriate spin weighted functions, only one set of harmonic functions corresponds to the physical system's natural modes. In this talk I will discuss recent and ongoing work regarding a new set of functions that are naturally suited to the modes of astrophysical gravitationally radiating systems. I will outline the mathematical nature of these functions, and comment on their potential use in gravitational wave theory and data analysis.