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The gravitational wave signature emitted from a merging binary depends on theorientation of an observer relative to the binary. Previous studies suggestthat emission along the total initial or total final angular momenta leads toboth the strongest and simplest signal from a precessing compact binary. Inthis paper we describe a concrete counterexample: a binary with $m_1/m_2=4$,$a_1=0.6 \hat{x} = -a_2$, placed in orbit in the x,y plane. We extract thegravitational wave emission along several proposed emission directions,including the initial (Newtonian) orbital angular momentum; the final (~initial) total angular momentum; and the dominant principal axis of $<L_aL_b>_M$. Using several diagnostics, we show that the suggested preferreddirections are not representative. For example, only for a handful of otherdirections (< 15%) will the gravitational wave signal have comparable shape tothe one extracted along each of these fiducial directions, as measured by ageneralized overlap (>0.95). We conclude that the information available in justone direction (or mode) does not adequately encode the complexity oforientation-dependent emission for even short signals from merging black holebinaries. Future investigations of precessing, unequal-mass binaries shouldcarefully explore and model their orientation-dependent emission.

Is J enough? Comparison of gravitational waves emitted along the total angular momentum direction with other preferred orientations