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\title{Searching for a cosmic string through the graviational lens
       effect: Japanese Virtual Observatory science use case}
\titlemark{Searching for a cosmic string on the JVO}

%-----------------------------------------------------------------------
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\author{ 
   Y. Shirasaki, Y. Mizumoto, M. Ohishi, N. Yasuda, M. Tanaka,
   S. Honda, H. Yahagi, M. Nagashima, G. Kosugi, N. Kashikawa
}
\affil{National Astronomical Observatory of Japan, Mitaka, Tokyo,
   Japan}

\author{E. Matsuzaki, F. Kakimoto, S. Ogio}
\affil{Tokyo Institute of Technology, Meguro,
Tokyo, Japan}



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\contact{Yuji Shirasaki}
\email{yuji.shirasaki@nao.ac.jp}

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\paindex{Shirasaki, Y.}
\aindex{Mizumoto, Y.}
\aindex{Ohishi, M.}
\aindex{Yasuda, N.}
\aindex{Tanaka, M.}
\aindex{Honda, S.}
\aindex{Yahagi, H.}
\aindex{Nagashima, M.}
\aindex{Kosugi, G.}
\aindex{Kashikawa, N.}
\aindex{Matsuzaki, E.}
\aindex{Kakimoto, F.}
\aindex{Ogio, S.}

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\authormark{Shirasaki et al.}

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% "radio" as the minor keyword.  The colon is used to introduce another
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\keywords{cosmic string, pattern recognition, surveys, JVO}

%-----------------------------------------------------------------------
%			       Abstract
%-----------------------------------------------------------------------
% Type abstract in the space below.  Consult the User Guide and Latex
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\begin{abstract}          % Leave intact
% Place the text of your abstract here - NO BLANK LINES
%
   This paper describes a method to search for cosmic strings using 
   their unique gravitational effect, and its implementation to the
   Japanese Virtual Observatory (JVO).
%
   Grand unified theory predicts that super-heavy cosmic strings with
   linear mass density of 10$^{22}$ g/cm were produced at a phase transition 
   in the early universe.
%
   The lensing effect by a long straight object can be characterized 
   by undistorted double images which are almost co-aligned
   in a direction of the string network and distributed 
   in a very large scale.
%
   Because of its large scale nature, wide field deep survey is crucial 
   for its discovery, and also the automatic detection system is
   required to survey the large amount of deep sky data.
%
   We have constructed databases of Subaru Suprime-Cam catalog/image for
   selected areas and applied our search method on the JVO prototype.
%
\end{abstract}

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\section{Introduction}

The standard theory of particle physics predicts a symmetry breaking
in the early universe and, as a result, the production of topological 
defects (Vilenkin and Shellard 2000).
%
If the defects were generated at the GUT energy, the cosmic string
can be observed as an origin of gravitation lensing (Vilenkin 1984)
and its detection can be an observational confirmation of the standard
theory.
%
The recent observations of cosmic microwave background radiation rule
out pure topological defects model as the origin of large scale
structure of the universe, however, they
still do not rule out the existence of the defects (Pogosian et al. 2003).
%
So it is of great importance to constrain the existence experimentally.

Several gravitational lens candidates by a cosmic string
have been reported (e.g. Sahzin et al. 2003), however, none of them
have not been confirmed yet.
%
Huterer and Vachaspati (2003) pointed out that a deeper observation of the
vicinity of the candidate event reveals several additional lensing
events.
%
They predicts that, for a string located nearby ($z < 0.5$), future
wide-field surveys such as SNAP and LSST find 5 objects lensed by a
string in 1 arcmin$^{2}$ region, compared to 0.1 lensed by conventional
sources.
%

The Subaru Suprime-Cam has also a great advantage in observing the wide
field of view (30$\times$30 arcmin$^{2}$) with high sensitivity (R$<$26
400s exposure), so it is suitable for this research.
%
At present, three and half years of Suprime-Cam data are publicly
available, so it is interesting to search for a cosmic string in 
the archived data.
%
In addition, the Japanese Virtual Observatory (JVO) project has been
started and will provide automatic access to the Subaru Suprime-Cam 
database and also provide unified environment for the DB access and data
analysis (Mizumoto et al. 2003, Ohishi et al. 2004).
%
We are now developing tools to search for a cosmic string on the
JVO system.
%
The current status of such activity is presented here.

\section{Search Strategy}

Features of a string lens event are characterized as non-distorted
equal-brightness double images which are aligned in the direction of
the string network.
%
So the search strategy is simply summarized as follows:
%
0) Prepare an object catalog for given images using a source detection
   software such as the SExtractor.
%
1) Select closely located pair objects of similar brightness, color, and
   morphology.
%
   Use the following parameters for selection of the pair objects:
   separation angle,
   maximum difference of brightness for each band,
   maximum difference of color, and
   reduced chi-square for a difference of the pair images.
%
2) Calculate a degree of positional and directional coherence $C_{obs}$
   for a set of pair objects. 
   The coherence is defined as $C = \sum_{i} \sum_{j \neq i}
   W_{i,j}$ where $W_{i,j}$ is calculated as shown in 
   Fig.~\ref{P1-9:fig:DefinitionW}.
%
\begin{figure}
   \parbox[b]{0.35\textwidth}{
      \epsscale{.33}
      \plotone{P1-9_1.eps}
   }
   \parbox[b]{0.65\textwidth}{
      \caption{Definition of the weight parameter $W_{i,j}$.
      A pair of the solid circles represents an object lensed by a
      cosmic
      string. The expected directions of a cosmic string for each pair
      are shown with solid lines. $\theta_{i,j}$ is an angle between
      the two expected string directions for object $i$ and $j$.
      $\varphi_{i,j}$ is an angle between the string direction for $i$ and
      the line from $i$ to $j$. If $\varphi_{i,j}  < \theta_{i,j}$, 
      $W_{i,j} = e^{-\theta_{i,j}/\theta_{0}}$. Otherwise,
      $W_{i,j} = e^{-(\pi - \theta_{i,j})/\theta_{0}}$.
      } 
      \label{P1-9:fig:DefinitionW}
   }
\end{figure}
%
3) Calculate chance probability for $C_{obs}$.
%
   This can be estimated by simulating 1000 sets of pair objects whose
   separation directions are randomized to the observational ones and
   by obtaining the distribution of the degrees of coherence for them.
%


\begin{figure}
      \epsscale{.47}
      \plotone{P1-9_2.eps}
      \epsscale{.42}
      \plotone{P1-9_3.eps}
      \caption{Left: String configuration tested for the string detection
               method presented here.
               Right: Maximum redshift of the cosmic string detected
               by this method as a function of limiting magnitude (R
               band) of observations.}
      \label{P1-9:fig:simulation}
\end{figure}


\section{Simulation and Application to the Observational Data}

We examined ability of the proposed method by simulating lens effect
by a cosmic string.
%
The assumed string model is described as follows:
%
1) Three kinds of configuration as shown in
   Fig.~\ref{P1-9:fig:simulation}~(Left).
%
2) Mass density is assumed to be 10$^{22}$ g/cm which corresponds to
   the maximum separation angle of 5$''$.
%
3) The string direction is perpendicular to the line of sight.
%
%
A model of background galaxies is provided by the Numerical Galaxy Catalog
($\nu$GC) based on a N-body/semi-analytic model with a $\Lambda$-CDM
cosmology, $\Omega_{\lambda} = 0.7$, $\Omega_{m} = 0.3$, $\sigma_{8} =
1$.

In Fig.~\ref{P1-9:fig:simulation}~(Right),
maximum redshift, where cosmic string can be proved by the proposed
method in 99\% confidence limit, are calculated according to the
sensitivity of the observation.
%
We applied this method to the data of Subaru-XMM Deep Survey (SXDS), 
Subaru Deep Field (SDF), AGASA 10$^{20}$ eV Field, and 2 deg$^2$ Field.
%
No candidates of the string lens events were detected.

\section{Cosmic String Search on the JVO}

Since the detection rate of the GL candidates by a cosmic string is
expected to be very small, a survey of large amount of data is crucial
and development of the automatic detection system is required.
%
The Japanese Virtual Observatory (JVO) is now being constructed at
National Astronomical Observatory of Japan and it will provide an
interface to the Subaru Suprime-Cam database, which enable us to do an
automatic search on the whole Suprime-Cam image data.
%

We developed several tools to implement a GL search on the JVO
prototype.
%
The following tools were developed:
%
(1) JVO Query Language Editor specialized for GL search.
(2) GL candidate viewer.
(3) GL candidate search engine.
%
In Fig.~\ref{P1-9:fig:GLSearchDemoArc}, schematic diagram of cosmic string
search system is shown.
%
A search request is written in JVO Query Language (JVOQL, Mizumoto et
al. 2003) and the results are returned in VOTable and FITS format.
%
JVOQL can be generated by a JVOQL editor
(Fig~\ref{P1-9:fig:GLSearchDemoDisplay}), which uses a web browser as an
input method.
%
On the JVOQL editor, one can browse meta data of registered DBs and can
select a DB, a table and columns you want.
%
The requested table is retrieved from a DB server and
pair objects are selected on the JVO system server, and the result
is saved as a VOTable.
%
Image data are also retrieved for the pair objects as a FITS format
and the FITS images are converted to JPEG images.
%
User can access to the VOTable, FITS image and JPEG images through the
VOTable viewer shown in Fig~\ref{P1-9:fig:GLSearchDemoDisplay}.
%
A color-color diagram, a SED plot and a three-color composite image are
also generated in accordance with a user's request.
%
Although the search procedure described in section~2 is still not fully
introduced in the current JVO prototype, complete implementation will
be done in the second version of the JVO prototype.

\begin{figure}
   \parbox[t]{0.45\textwidth}{
      \epsscale{.45}
      \plotone{P1-9_4.eps}
      \caption{A schematic diagram of the cosmic string search system.} 
      \label{P1-9:fig:GLSearchDemoArc}
   }
   \parbox[t]{0.55\textwidth}{
      \epsscale{.55}
      \plotone{P1-9_5.eps}
      \caption{JVOQL Editor (left), VOTable viewer (right top), GL
               candidate viewer (right bottom)}
      \label{P1-9:fig:GLSearchDemoDisplay}
   }
\end{figure}

%\section{Summary}

%
%-----------------------------------------------------------------------
%			      References
%-----------------------------------------------------------------------
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%           \reference H\'enon, M.\  1961, Ann.d'Ap., 24, 369
%           \reference King, I.\ R.\  1966, \aj, 71, 276
%           \reference King, I.\ R.\  1975, in Dynamics of Stellar 
%                Systems, ed.\ A.\ Hayli (Dordrecht: Reidel), 99
%           \reference Tody, D.\  1998, \adassvii, 146
%           \reference Zacharias, N.\ \& Zacharias, M.\ 2003,
%                \adassxii, \paperref{P7.6}
% 
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\acknowledgements

This research was supported by Grant-in-aid "Information Science"
carried out by the MEXT (14019092 and 15017289).

\begin{references}

\reference  Huterer, D., \& Vachaspat, T.\ 2003, Phys.\ Rev.\ D68 041310

\reference Mizumoto, Y. et al.\ 2003, \adassxii, 96

\reference Ohishi, M. et al.\ 2004, \adassxiii, \paperref{P3-11}

\reference  Pogosian, L. et al.\ 2003, Phys.\ Rev.\ D68 023506

\reference  Sazhin, M., et al. \ 2003, Mon.\ Not.\ Roy.\ Astron.\ Soc.\ 343 353

\reference  Vilenkin, A.\ 1984, ApJ 282, L51 %%FO

\reference  Vilenkin, A., \& Shellard, E.\ P.\ S.\ 2000,
           {\it Cosmic Strings and Other Topological Defects, 
                Cambridge University Press}

\end{references}

% Do not place any material after the references section

\end{document}  % Leave intact
