\hfill
  \caption{
The initial apastron is
    $r_a=30M$. Left column, from the top, frame 1:  $L=4.10$ and
    the orbit rapidly moves through zoom-whirl cycles precessing by
    $>\pi$ ($q\sim 1/2$) between apastra. The orbit rapidly loses
    eccentricity but still merges with non-zero eccentricity. 
    Frame 2: $L=3.95$ and the orbit
    precesses by nearly$> 2\pi$ ($q\sim 1$) in the first radial cycle
    before merging.
    Frame 3:
    $L=3.915$ and the orbit is very nearly homoclinic, precessing by
    $\sim 4\pi$ ($q\sim 2$)  around the unstable circular orbit before 
    radiative losses cause merger. 
    Right Column:  The gravitational waveforms versus simulation time were extracted
    at a
    finite radius of $60M$. 
}
\label{NR}
\end{figure}


The runs in Fig.\ \ref{NR} were simulated using the Georgia Tech 
\texttt{MayaKranc} code that uses the same computational infrastructure
and methodology as in previous studies
\cite{2008arXiv0802.2520W,2007ApJ...661..430H,2007CQGra..24...33H,2009arXiv0905.3914H,2009PhRvL.102d1101H}, 
namely a Baumgarte-Shapiro-Shibata-Nakamura code with moving puncture gauge conditions \cite{campanelli2006,baker2005}
using the \texttt{Kranc} code generator~\cite{Husa:2004ip}.  
The black-hole encounters are initiated with Bowen-York initial 
data~\cite{Bowen:1980yu}.  The black holes are located on the 
$x$-axis: bh$_\pm$ are located at $x_+ = 7.5 M$ and $x_- = -22.5 M$ 
where $m_+ =3 M/4$ 
and $m_-= M/4$.  The spatial finite differencing is sixth order.  We 
used eleven levels of refinement with Carpet~\cite{Schnetter-etal-03b}, 
a mesh refinement package in Cactus~\cite{cactus_web}.  The finest 
resolution is $M/143$ and the outer boundary is at $287M$.  The total 
initial orbital angular momentum, is varied between the 
values of $3.9$ and $4.1$. The range is shifted from the conservative
PN value as expected, yet zoom-whirl behavior was comfortably found
given that initial prediction.

Fig.\ \ref{NR} shows three different orbits and their waveforms
corresponding to different initial
values of $L$. The largest value of $L$ shows zoom-whirl behavior
characterized by
$q\sim 1/2$ before merging. The middle value of $L$ has a $q\sim 1$ 
while the smallest value of $L$ we show is very close to the
separatrix and whirls nearly twice. 
We caution that we are only loosely reading off
these values since $q$ is changing so rapidly during inspiral.

As expected, the pairs merge by rolling over the top of the
effective potential (Fig.\ \ref{Vm.25Sm8}).
We emphasize that 
the nearly circular pattern of 
the whirl phase is not equivalent to full circularization of the
orbit. In other words, quite importantly, the orbits shown in
Fig.\ \ref{NR} do not merge through the ISCO but rather roll over the
top of the potential, merging through a whirl. To compare with the
language in a previous paper \cite{Hinder:2007qu}, some of
those eccentric orbits were circular because they merged
through a whirl phase and not because they merged through the ISCO.
This could be relevant for initial conditions for the ringdown phase.

\begin{comment}
Also notice, from the effective potential picture, that the angular
momentum at plunge is smallest for the ISCO. Therefore, all orbits 
that do not circularize before merger must have more angular momentum
at merger than a quasi-circular orbit that rolls through the
ISCO. Since the remaining angular momentum all goes into the spin of
the final black hole, the zoom-whirl mergers result in a faster
spinning black hole.
Since they have not shed enough angular momentum, the
anti-aligned zoom-whirl pairs (spins pointing down relative to the
initial orbital angular momentum) experience a spin
flip in the formation of the final black hole (final spin pointing up).
\end{comment}

The waveforms show distinctly quiet phases during the highly
elliptical zooms followed by louder glitches during the nearly
circular whirls. The distinctive spikes of zoom-whirls are directly
related to their rational number $q$. This suggests that zoom-whirl
orbits could be dug out of the data using algorithms suited for burst
searches, perhaps in conjunction with more targeted template
searches. 

Fig.\ \ref{relsep} plots the relative orbital separation 
of the black holes versus phase for our three
cases of
$L$.  The plot illustrates the rapid merger
of the
black holes as $L$ decreases. The figure also
shows that
inspiral ends and plunge begins in the simulations for 
radii $\sim 5M$.
In line with the numerical results, 
the effective potential picture in Fig. \ref{Vm.25Sm8}
predicts whirls
around periastron, $\sim 5M$,
which is much less than the PN predicted value of the ISCO,
$r_{ISCO}\sim 8.8M$, for a mass ratio of 1/3 and these spins. 
The figure therefore confirms that the zoom-whirl pair merge near a
whirl phase and not near the ISCO.
The
top line, corresponding to $L=4.1$, shows the three zooms before
merger that we see in frame 1 of Fig.\ \ref{NR}.   The bottom line,
corresponding to $L=3.915$ and frame 3 of Fig.\ \ref{NR} is almost
homoclinic with no zooms, precessing around the unstable circular
orbit before merging.

In general, we conclude from the PN approximation that
zoom-whirl behavior has better odds at surviving
dissipation and leaving a mark in the gravitational waveform for (1)
more disparate values of $m_2/m_1$ because of the slower dissipation
time, 
(2) larger spin magnitudes, all else being equal, because of
the greater frame dragging effect, (3)
larger initial apastra because of the longer orbital lifetime. 
There is less zoom-whirl behavior in equal-mass nonspinning pairs, hence the
importance of sticking closer to the separatrices 
\cite{pretorius2007}. Yet more generally, zoom-whirl orbits
ought to extend down below the separatrices.
In the future, we intend to
extend this work by pushing the numerical simulations to
large mass ratio and extracting a measure of $\dot q$.

For any zoom-whirl pair, the glitchy waveforms followed by longer
quiescent phases are highly distinctive and beg for tailored search
algorithms.
Furthermore, the loud glitches could 
nudge these highly
precessing orbits into an optimistic position for early direct detection.


\begin{figure}[t]
\centering
\includegraphics[width=50mm,angle=-90]{rel_sepvph.eps}
\hfill
\caption{The relative orbital separation in units of M plotted
  versus the orbital phase for the series of $L$ in Fig.\ \ref{NR}.
}
\label{relsep}
\end{figure}

{\bf Acknowledgements:} The authors wish to acknowledge NSF grants
AST-0908365, PHY-0925345,  PHY-0653303 and TG-PHY060013N that supported this work.
We also thank Ian Hinder, Frank Herrmann,Tanja Bode and Pablo Laguna for
contributions to the \texttt{MayaKranc} code.

\bibliographystyle{aip}
Design Patterns Explained See more Webinars and Podcasts Provide Feedback October 4, 2007 Al Shalloway | Recording This webinarThe filters are still the worst visual design for a game I've ever seen. Watching back some older videos before they were put in feels downright pleasant by comparison.

I don't really get much eye strain from it anymore, but I just feel disoriented and never like I fully understand where everything is, I'm checking the map constantly for where the enemy *and* myself are instead of being able to just read it all off the view alone. The detached camera doesn't help either since the orientation keeps moving too.

You'd think after 6.0, WG understood how important familiarity is to the players, but nope.