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We analyze the directional dependence of the gravitational wave (GW) emissionfrom 15 3D neutrino radiation hydrodynamic simulations of core-collapsesupernovae. Using spin weighted spherical harmonics, we develop a new analytictechnique to quantify the evolution of the distribution of GW emission over allangles. We construct a physics-informed toy model that can be used toapproximate GW distributions for general ellipsoid-like systems, and use it toprovide closed form expressions for the distribution of GWs for different CCSNphases. Using these toy models, we approximate the PNS dynamics during multipleCCSN stages and obtain similar GW distributions to simulation outputs. Whenconsidering all viewing angles, we apply this new technique to quantify theevolution of preferred directions of GW emission. For nonrotating cases, thisdominant viewing angle drifts isotropically throughout the supernova, set bythe dynamical timescale of the protoneutron star. For rotating cases, duringcore bounce and the following tens of ms, the strongest GW signal is observedalong the equator. During the accretion phase, comparable -- if not stronger --GW amplitudes are generated along the axis of rotation, which can be enhancedby the low T/|W| instability. We show two dominant factors influencing thedirectionality of GW emission are the degree of initial rotation and explosionmorphology. Lastly, looking forward, we note the sensitive interplay between GWdetector site and supernova orientation, along with its effect on detectingindividual polarization modes.

Characterizing the Directionality of Gravitational Wave Emission from Matter Motions within Core-collapse Supernovae