Is J enough? Comparison of gravitational waves emitted along the total
  angular momentum direction with other preferred orientations
  The gravitational wave signature emitted from a merging binary depends on the
orientation of an observer relative to the binary. Previous studies suggest
that emission along the total initial or total final angular momenta leads to
both the strongest and simplest signal from a precessing compact binary. In
this 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 the
gravitational 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 $<L_a
L_b>_M$. Using several diagnostics, we show that the suggested preferred
directions are not representative. For example, only for a handful of other
directions (< 15%) will the gravitational wave signal have comparable shape to
the one extracted along each of these fiducial directions, as measured by a
generalized overlap (>0.95). We conclude that the information available in just
one direction (or mode) does not adequately encode the complexity of
orientation-dependent emission for even short signals from merging black hole
binaries. Future investigations of precessing, unequal-mass binaries should
carefully explore and model their orientation-dependent emission.
