
\newpage

\section{Executive summary}

%\vspace*{2mm}
%\noindent
%{\bf Purpose and Recommendations}

The purpose of this working group is to investigate and to make recommendations on
the interferometer optical configuration design of LCGT and its observation 
band for gravitational waves.
%In the baseline design, LCGT has a RSE (Resonant Sideband Extraction)
%interferometer configuration.
%With this design, it is possible to optimize and tune the observation 
%frequency band for target gravitational-wave (GW) sources, 
%by choosing suitable optical parameters.
Advantages and disadvantages of candidate interferometer 
configurations have been surveyed
from viewpoints of scientific possibilities,
technical feasibilities, and project strategy.
As a result, we recommend the following interferometer design and observation strategy.

\begin{center}
\begin{itembox}[l]{\bf Recommendations}
%\vspace*{2mm}
%\noindent
%\begin{quote}
%{\bf Recommendations}
\begin{itemize}
\item The optical configuration of LCGT should be VRSE:
      a RSE (resonant-sideband extraction) 
      with variable observation band.
\item In the first observation phase, LCGT interferometer
      should be operated with a detuned mode, VRSE (D), 
      for earlier detection of gravitational-wave signals.
      After the first detections, the variable configuration provides the option 
      to change the observation band to broadband, VRSE (B), so as to obtain more 
      scientific information. 
\end{itemize}
%\end{quote}
\end{itembox}
\end{center}


\vspace*{5mm}
\noindent
{\bf Candidate configurations}
\vspace*{2mm}

In the baseline design, LCGT has a RSE (Resonant Sideband Extraction)
interferometer configuration.
With this design, it is possible to optimize and tune the observation 
frequency band for target gravitational-wave sources, 
by choosing suitable optical parameters.
So as to determine the optical parameters, we define three candidate
parameter sets: broadband RSE ({\bf BRSE}), detuned RSE ({\bf DRSE}), 
and variable RSE ({\bf VRSE}) configurations.
In DRSE, the detector observation band is optimized 
by means of a detuning technique%
\footnote{Detuning is a technique to increase detector sensitivity
only in a slightly narrow frequency band. 
It is realized by controlling the signal-extraction-cavity length between
resonance and anti-resonance condition for the carrier laser beam.},
to have maximum sensitivity for neutron-star inspiral events, which are the primary targets of LCGT.
The parameters of BRSE are also optimized for these events, but with
broadband (tuned) configuration.
On the other hand, VRSE is designed to have good sensitivity both with 
tuned and detuned operation, and to switch observation bands depending on 
the observation purposes and targets%
\footnote{In this investigation, the VRSE configuration is designed so that the 
detuned/broadband modes would be switched with minimum observation dead times,
without replacing or moving mirrors.}. 
%The purpose of this report is to survey advantages and disadvantages of these three 
%configurations, and to make recommendation on which configuration to be adopted in LCGT.

The detector sensitivity curves are estimated with the current best-estimated boundary 
conditions of LCGT: an input laser power, suspension and mirror thermal noises, seismic noise,
and optical readout noises.
The estimated sensitivity curves are shown in Fig.\,\ref{fig:candidates0}.
The DRSE configuration (green curve) has the best floor-level sensitivity at around 100\,Hz,
and  the best observable distance of 132\,Mpc for neutron-star inspiral events%
\footnote{Here, observable distance is defined as the range within which events are detected 
with higher signal-to-noise ratio than 8.
Detector antenna pattern and wave polarizations are all-sky-averaged.
Details are described in Section 3.}.
The BRSE configuration (red curve) has wider observation band to cover various sources, 
and moderate observable range of 114\,Mpc for neutron-star inspirals.
The blue and sky-blue curves are for the VRSE configuration
with a detuned mode {\bf VRSE (D)} and with a broadband mode {\bf VRSE (B)}, respectively.
They have slightly narrower and wider observation bands than the BRSE (red curve) configuration,
respectively.


\begin{figure}[t]
\begin{center}
\includegraphics*[height=5.5cm]{candidates.eps}
\caption{Sensitivity curves of the candidate configurations: 
BRSE (red curve), DRSE (green curve), and VRSE (B/D) with sky-blue/blue curves.}
\label{fig:candidates0}
\end{center}
\end{figure}


\vspace*{2mm}
\noindent
{\bf Comparisons between the candidates}
\vspace*{2mm}

Firstly, these candidate configurations are compared from a viewpoint of
expected scientific outcomes (details are describes in Section 3).
The purposes of LCGT are (1) to detect gravitational waves as soon as possible, 
and (2) to obtain astrophysical prospects from the observed waves.
For these purposes, a neutron-star binary inspiral event is set to be the primary target 
of LCGT, because it is a confident source with known waveform and event rate. 
The observable ranges for this event are 114\,Mpc for BRSE, 112/123\,Mpc for VRSE (B/D), 
and 132\,Mpc for DRSE (Fig.\,\ref{fig_bw_summary}).
These ranges are interpreted from scientific outcomes. 
We set the first minimum success criteria of LCGT as 'to detect at least one event
in one-year observation'.
For this criteria, the success probabilities are more than 99\% for all configurations,
which are estimated with expected value of event rate and Poisson distribution.
Considering another criteria 'to detect the first event as soon as possible',
we estimated the required observation time for the first detection with 90\% probability.
The results are 5.1 months for BRSE, 5.3/4.0 months for VRSE (B/D), 
and 3.4 months for DRSE.
This result shows that the detuned configurations have advantages in the first detection 
and expected number of events.
On the other hand, broadband configurations are favorable to extract information 
from observed waveforms, in accuracy of estimated binary parameters, the arrival time,
and so on, because wider band provides longer observation duration for an inspiral event.
The difference in the accuracy is around a factor of 2 to 4.
In addition, broadband configurations have advantages in observation of variety of 
GW sources, such as signals from supernovae, pulsars, and so on.

\begin{figure}[p]
\begin{center}
 \includegraphics*[width=16cm]{bw_summary.eps}
 \caption{Summary of survey results for the candidate configurations.}
\label{fig_bw_summary}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
 \includegraphics*[width=15cm]{bw_comp.eps}
 \caption{Comparison of the candidate configurations.}
 \label{fig-comp}
\end{center}
\end{figure}


Secondary, the candidate configurations are compared from the viewpoint of technical 
feasibility in constructing and operating the detector.
In the optical design, BRSE and VRSE configurations require higher laser 
power (810\,kW) in arm cavities than that of DRSE configuration (360\,kW).
Since the power in arm cavities is limited by optical loss in mirrors,
higher quality mirrors are required in BRSE and VRSE configurations.
As for the control of the interferometer, signal extraction and control schemes 
for BRSE and DRSE have been established with prototype interferometers, as well as 
investigations with analytical calculations and numerical simulations.
VRSE would require additional complexity in signal extraction scheme to be capable both 
of broadband and detuned configurations.
In the interferometer control, DRSE has slightly tight requirement on the noises introduced 
by controlling interferometer auxiliary degree of freedom; the DRSE configuration 
has better sensitivity in low frequency band, which can be easily affected by these control noises
without careful design of control loops.
As described above, each configuration requires some additional technologies and complexities.
However, as results of investigations detailed in Section 4, the differences in technical
difficulties, the differences in commissioning times, additional complexities 
are not critical in these configurations.

\vspace*{2mm}
\noindent
{\bf Discussions and conclusions}
\vspace*{2mm}

As a result of investigations described above, there is no critical or deciding factor;
every configuration would be suitable for the purpose LCGT, and would be technically feasible.
With this situation, we recommend the following strategy.
We should construct and operate LCGT at first with a VRSE (D) configuration
(a variable RSE configuration with a detuned mode),
aiming at earlier detection of gravitational-wave signals.
There would be no critical difference in technical difficulties and commissioning times.
After the first a few or several detections, the variable configuration provides the possibility to 
change the observation band to broadband, VRSE (B), so as to obtain more information from waveforms,
and to observe various targets other than neutron-star inspirals, such as supernovae, pulsars,
and so on. 
In a detector technical point of view, the variable-band configuration is favorable in adding 
redundancies for unexpected technical difficulties, and in having additional measurement 
options in noise hunting and diagnostics of the interferometer 
during commissioning and operation of the detector,
at the cost of a little additional complexities in the interferometer control scheme.

In case of technical difficulties in interferometer control system
which may be recognized in further investigations, we set BRSE as a backup plan.
The BRSE configuration has slightly better sensitivity than VRSE(B),
and is considered to have higher technical feasibility.
 
