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 deguchi.tex PASJ, Feb 2002, in press
From: Shuji deguchi <deguchi@nro.nao.ac.jp>
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\documentclass{pasj00}
%\draft

\begin{document}
\SetRunningHead{Deguchi et al.}{SiO Maser Sources near the Galactic 
Center}
\Received{2001/05/17}%{yyyy/mm/dd}
\Accepted{2001/10/24}%{yyyy/mm/dd}
%\comment{(version: 2001/11/01)}

\title{Observations of SiO Maser Sources within a Few Parsecs
from the Galactic Center}

%%% begin:list of authors
\author{Shuji \textsc{Deguchi}%
   }
\affil{Nobeyama Radio Observatory, National Astronomical Observatory,\\
Minamimaki, Minamisaku, Nagano 384-1305}
\email{deguchi@nro.nao.ac.jp}

\author{Takahiro  \textsc{Fujii}
%\thanks{Present Address; xxxxxxxxxx}
}
\affil{Institute of Astronomy,
University of Tokyo, Mitaka, Tokyo 181-8588
}
\email{fujii@mtk.ioa.s.u-tokyo.ac.jp}

\author{Makoto  \textsc{Miyoshi}}
\affil{VERA Office, National Astronomical Observatory,
Mitaka, Tokyo 181-8588
}
\email{miyoshi@miz.nao.ac.jp}

\and
\author{Jun-ichi {\sc Nakashima}}
\affil{Department of Astronomical Science, The Graduate University for 
Advanced
Studies,\\
Nobeyama Radio Observatory,
Minamimaki, Minamisaku, Nagano 384-1305}
\email{junichi@nro.nao.ac.jp}

\author{ \\(PASJ 54, No. 1 in press)}
%%% end:list of authors

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%% `\KeyWords{}' always has to be placed before `\maketitle'.
\KeyWords{Galaxy:center --- Galaxy: nucleus ---
  Masers --- Stars: late-type} %Do NOT move this preamble from here!

\maketitle

\begin{abstract}
Mapping and monitoring observations of the SiO maser sources
near the Galactic center were made with the Nobeyama 45-m telescope
at 43 GHz. Rectangular mapping an area of approximately
$200'' \times 100''$ in a 30$''$ grid,
and triangular mapping in a 20$''$ grid toward the Galactic center,
resulted in 15 detections of SiO sources; positions of the sources
were obtained with errors of 5--10$''$ except for a few weak sources.
Three-year monitoring observations
found that the component at $V_{lsr}=-27$ km s$^{-1}$
of IRS 10 EE flared to about 1.5 Jy during 2000 March--May, which was
a factor of more than 5 brighter than its normal intensity.
Using the radial velocities and positions of the SiO sources,
we identified 5 which are counterparts of the previously observed
OH 1612 MHz sources. The other 10 SiO sources have no OH counterparts,
but two were previously detected with VLA, and four are located
close to the positions of large-amplitude variables
observed at near-infrared wavelengths. A least-square fit to a
plot of velocities versus Galactic longitudes gives a rather high
speed for rotation of the star cluster around the Galactic center.
The observed radial-velocity dispersion is roughly consistent with
the value obtained before. It was found that all the SiO sources
with OH 1612 MHz counterparts have periods of light variation
longer than 450 days, while SiO sources without
OH masers often have periods shorter than 450 days. This fact
suggests that lower-mass AGB stars are more often
detected in SiO masers than in the OH 1612 MHz line.
\end{abstract}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Section 1 %%%%%%%%%%%%%%%%%%%
\section{Introduction}
The  Galactic-center star cluster consists of mixed
stellar populations (\cite{kra95}; \cite{mor96}). It involves a number
of late-type stars which are potential candidates for
OH/SiO maser emitters. Deep surveys in OH 1612 MHz, H$_{2}$O 22 GHz
and SiO 43 GHz masers (\cite{win96}; \cite{sjo98a}; \cite{men97}; 
\cite{izu98})
have been made; a dozen sources have been detected
within a few parsec of the Galactic center.
The accurate H$_{2}$O/SiO maser positions of these sources
observed by the Very Large Array (VLA) provided a precise alignment 
between
the near-infrared and radio coordinate frames
(\cite{men97}), enabling the position of Sgr A*  to be pinpointed
with accuracy better than 0.1$''$
on near-infrared images. Detections of accelerating motions of
stars near the Galactic center fixed the mass of the cental object
at about $3 \times 10^{6} M_{\odot}$ (\cite{ghe00}).
Because radio interferometers have a potential of
measuring the proper motions of stars relative to Sgr A*
[e.g., \citet{sjo98b}] more accurately than
the present optical/infrared telescopes (\cite{gen96}; \cite{eck97}),
to detect more SiO maser sources near the Galactic center and
to investigate their properties will be quite important.

Using the  45-m telescope at Nobeyama,
\citet{izu98} detected 14 SiO sources around the Galactic center.
This observation (by a beam width of about 40$''$)
proved that SiO maser source density is peaked at the Galactic center.
Because this was a set of pointed observations toward the Galactic center
and two one-beam offset positions, the SiO source positions were not
determined with accuracy better than the beam size.
To remedy the positional uncertainties to some degree,  we made
new mapping observations of SiO masers near the Galactic center
using the 45-m telescope in the year 2000.
The present mapping observations on a 30$''$ grid
can be used to derive the source positions with an uncertainty
of about 5--10$''$ depending on the signal-to-noise ratio.
Also because the intensities of SiO masers are
expected to vary strongly in a time scale of a year,
we monitored the intensities of SiO masers toward the Galactic center
during 1999--2001.
During the three-year monitoring observations, we found
an SiO maser flare in the $-27$ km s$^{-1}$ component of IRS 10 EE
in March--June 2000. We present the details
of these observations in this paper.

\section{Observations}
Simultaneous observations in the SiO $J=1$--0, $v=1$ and 2 transitions 
at 42.122
and 42.821 GHz, respectively, were made with the 45-m radio telescope at 
Nobeyama
on 1999 June 8--12, 2000 May 20--29, and 2001 February 9. A cooled SIS
receiver (S40) with a bandwidth of about 0.4 GHz was used, and the 
system temperature
(including atmospheric noise) was 200--250 K (SSB).
The aperture efficiency of the telescope was
0.60 at 43 GHz. The half-power beam width (HPBW) was about 38$''$ at 43 
GHz.
A factor of 2.9 Jy K$^{-1}$ was used to convert antenna temperature to 
flux
density. An acousto-optical spectrometer array of low resolution (AOS-W) 
was
used. Each spectrometer has 250 MHz bandwidth and 2048 channels, giving a
velocity coverage of about 1700 km s$^{-1}$ and a spectral resolution of 
1.7
km s$^{-1}$ (per two binned channels). Observations were made in a 
position
switching mode, and the off-position was chosen 10$'$ away from the
Galactic center in azimuth. The telescope pointing was checked using a 
strong SiO
maser source, OH$2.6-0.4$. The calibration of the telescope antenna 
temperature
was made by observing the intensities of the $^{29}$SiO (thermal),
H52$\alpha$ (recombination), U42.767, and SiO $J=1$--0, $v=1$ (maser)
lines toward Sgr B2 MD5 [e.g., \citet{shi97}]. Total on-source 
integration time was
approximately 2 hours per day.

In the 1999 June observations, only the direction toward Sgr A* was 
observed;
(R.A., Decl., epoch)=($17^{h}42^{m}29.314^{s}, -28^{\circ}59'18.3''$, 
1950)
(\cite{rog94}).
At this time, we spent three days looking for extreme velocity components
  ($|V_{lsr}|>350$ km s$^{-1}$) ; no extreme velocity component above 0.04
  and 0.03 K for $J=1$--0, $v=1$ and 2 transitions, respectively,
was detected in the frequency range between 42.73--43.35 GHz
(approximate velocity range of $-2200$--2700 km s$^{-1}$
for the SiO $J=1$--0 $v=1$ transitions). In fact, several
unidentified lines have been found in the spectra toward Sgr B2 MD5
in this frequency range: U42.767, U43.018, U43.026, and U43.178.
These U-lines should appear at the $V_{lsr}=$378 km s$^{-1}$
for the $J=1$--0 $v=2$ transition,
and $V_{lsr}=723$,  668, and $-390$ km s$^{-1}$ for the  $J=1$--0 $v=1$ 
transition,
if the circumnuclear molecular ring (cf., \cite{wri01}) contains
enough of the molecules responsible for these U-lines.
The spectra toward the Galactic center
above $|V_{lsr}|>$ 350 km s$^{-1}$ were carefully checked  for
contamination by these lines, but we found no such feature
at the corresponding velocities (except weak features due to
$^{29}$SiO, H52$\alpha$, and U42.767 at several
$10'$ offset positions from Sgr A*).

%%%%%%%%%%%%%%%%%%%%% Figure 1 %%%%%%%%%%%%%
\begin{figure}
   \begin{center}
       \hspace{2cm}
     \FigureFile(75mm,100mm){fig1.eps}
     %%% \FigureFile(width,height){filename}
   \end{center}
   \caption{The mapped positions of the telescope (top),  positions of 
the 15
   detected sources with error bars (middle), and position-velocity 
diagram of
   the detected sources (bottom). The coordinates, $\Delta$l and 
$\Delta$b,
   indicates position differences from Sgr A* in Galactic coordinates in 
unit of
   arcminute. The extreme sources with $|V_{lsr}|>300$ km s$^{-1}$
   are shown as open circle in the middle and bottom panels. The numbers 
in the
   middle panel correspond to the SiO source number in Tables 1 and 2.
   The solid and broken lines
   in the bottom panel are the least-square linear fits for all sources 
and for
   all but the extreme sources, respectively.}\label{fig:l-b.map}
\end{figure}

In the 2000 May observations, we made mapping observations
in an area covering approximately $200''\times 100''$ centered toward 
Sgr A*.
Two different modes of mapping were used: 3-point (triangular) mapping
with 20$''$ separation toward Sgr A*, and 9-point ($3\times 3$ square)
mappings toward $(\Delta l, \Delta b)=(0$ or $\pm 60''$, 0$''$) on a 
30$''$ grid.
The 9-point mapping mode was utilized to obtain
a reasonably high level of signals in one run of
typical mapping time about two hours (approximately 10-minutes 
integration
per point).
The mapped points are shown in the top panel of Figure 1.
The large circle in Figure 1 indicates the effective beam of the 
telescope
($HPBW \sim 40''$).
Because the telescope pointing has been known to be influenced
strongly by the wind, we made the 3-point mapping on the days with wind
speed less than 5 m s$^{-1}$, when the telescope pointing was excellent
(error $\lesssim 5''$ accuracy), and the 9-point mapping
on relatively windy days of the wind speed between 5 and 10 m s$^{-1}$
(approximately $\lesssim  10''$ accuracy). Because the grid separation is
larger than HPBW in the 9-point mapping, the relative intensities of SiO 
maser
components in the grid points were supposed to be kept constant
even though the wind velocity was slightly high.
In the 2001 February observations, we could manage a-few-hours 
observation
time only and we made observations in the 3-point mapping mode toward 
Sgr A*;
the signal-to-noise ratio of the spectra obtained
was not very high. Therefore, we averaged the spectra of three
positions (a half-beam width each away). They are
shown at the bottom in Figure 2.

A shallow survey of SiO sources
in the Galactic center area was also made with the 45-m telescope
using a multibeam receiver (S40M) prior to the present observations
(March--April 2000).
This shallow observation detected 9 sources in the  $7'\times 13'$ area
toward the Galactic center (\cite{miy01}). The present observations 
concentrated
on a smaller and much closer area to the Galactic
center with longer integration time per point and
using a more sensitive single-beam receiver, S40.

As noted in \citet{izu98}, the  AOS-W spectra toward the strong 
continuum source,
Sgr A* ($\sim 11$ Jy at 43 GHz; \cite{sof86} ; \cite{bec96}), exhibited 
a baseline
distortion of about 0.3 K at the maximum,
and ripples due to a standing wave in the telescope system.
The ripples in the velocity range of $\pm$ 350 km s$^{-1}$ were 
relatively weak.
In order to remove these complex ripple features from the spectra, we 
took
running means of the spectra (average of about 100 channels, or about 80 
km
s$^{-1}$ width), and the averaged spectra were subtracted from the 
originals. With
this procedure, the baselines of the resulting spectra became quite 
flat. Because
the SiO maser lines are quite narrow (width less than 10 km s$^{-1}$) 
and weak
($T_{a} <0.2$ K), this method seems to work well except a strong line of 
$T_{a}
\sim 0.5$ K at $-27$ km s$^{-1}$  (No. 6 in Table 1). An additional 
baseline
adjustment was made by taking a parabolic fit to the trough
between $\pm$ 40 km s$^{-1}$ near this strong feature.
The resulting three-year spectra toward Sgr A* [$(\Delta l, \Delta 
b)$=(0,0)] are shown
in Figure 2.

Detections were judged by criteria similar to those given in 
\citet{izu98}.
All the peaks for a single channel with $S/N>3$ and features for
several channels with  $(S/N)_{broad} >5$ were treated as detection 
candidates.
Then, all the features were checked as to whether or not they were 
detected
in the spectra of both the $v=1$ and 2 transitions of SiO,
at nearby positions, or at different epochs of observations.
Dubious features were discarded.
After these careful checks, we selected 15 SiO spectral components
as confident detections which are listed in Table 1; the number,
telescope positions (relative to Sgr A*), $V_{lsr}$, peak antenna 
temperatures,
integrated intensities, rms noise values, and signal-to-noise ratios
integrated over the emission profile, are given. We show the spectra of
the detected sources in Figures 3, 4 and 5. The components at $-117$ and
$-337$ km s$^{-1}$ were quite weak and only slightly above the critical 
level
of detections in May 2000.
These components were detected at several different positions
and epochs. They were, in fact, more clearly detected previously;
the $-117$ km s$^{-1}$ component
in 1999, and the $-338$ km s$^{-1}$ component in 1997 (\cite{izu98}).
For the $-117$ km s$^{-1}$ component (No. 9) in Figure 3,
the spectra taken in 1999 are shown.


%%%%%%%%%%%%%%%%% Figure 2 %%%%%%%%%%
\begin{figure}
   \begin{center}
       \hspace{2cm}
     \FigureFile(75mm,100mm){fig2.eps}
     %%% \FigureFile(width,height){filename}
   \end{center}
   \caption{Time variation of the SiO maser spectra toward Sgr A*.
   The data were taken on 1999 June 8 (top), 2000 May 25 (middle),
   and 2001 February 9 (bottom). In fact, the bottom spectra are averages
  over the three 12$''$-offset spectra taken in the 3-point mapping mode 
to improve S/N.}
   \label{fig:time.variation}
\end{figure}
%%%%%%%%%%%%%%%%% Figure 3 %%%%%%%%%%%%
\begin{figure}
   \begin{center}
     \FigureFile(75mm,100mm){fig3.eps}
     %%% \FigureFile(width,height){filename}
   \end{center}
   \caption{SiO maser spectra of detected sources. The source number 
shown on the upper left
   of each panel corresponds to the number in Tables 1 and 2. The 
observed positions
   (in unit of $''$ from Sgr A*) are shown
   in the parenthesis.}\label{fig:spectra}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% table 1 %%%%%%%%%%%%%%
\begin{table*}
   \caption{Observed Line Parameters}\label{tab:table1}
   \begin{tabular}{rrrrrrrrrrrrl}
   \hline\hline
   & & \multicolumn{5}{c}{$J=1$--0, $v=1$}&\multicolumn{5}{c}{$J=1$--0, 
$v=2$}\\
  \cline{3-7} \cline{8-12} \\
No&($\Delta l, \Delta b)_{\rm obs}^{1}$&$V_{\rm lsr}$&$T_{\rm
a}$&$F$&$T_{\rm rms}$&$S/N$
&$V_{\rm lsr}$&$T_{a}$&$F$&$T_{\rm rms}$&$S/N$&Date\\
  &($''$, $''$)&{\scriptsize (km s$^{-1}$)}&(K)&{\tiny (K km s$^
{-1}$)}&(K)& &{\scriptsize(km
  s$^{-1}$})&(K)&{\tiny (K km
  s$^{-1}$)}&(K)& &{\scriptsize (yymmdd)}\\
	\hline
1&
($-$90,30)&$-$26.0&0.096&0.368&0.019&7.4&$-$27.4&0.084&0.496&0.021&7.2&000530\
\
2&
($-$90,$-$30)&$-$308.0&0.668&2.764&0.018&55.1&$-$308.3&0.403&2.173&0.021&33.
3&000530\\
3&
($-$90,0)&$-$110.2&0.172&0.700&0.019&13.6&$-$110.1&0.144&0.775&0.023&10.7&
000530\\
4&($-$60,0)&6.3&0.109&0.436&0.018&8.8&7.4&0.087&0.296&0.014&8.5&000530\\
5&(0,0)&$-$335.8&0.031&0.123&0.009&5.2&$-$335.7&0.044&0.314&0.014&6.1&000525\
\
6&(0,$-$12)&$-$27.8&0.349&1.228&0.008&59.8&$-$27.4&0.583&1.732&0.010&72.3&
000526\\
7&(0,0)&$-$60.8&0.102&0.206&0.012&9.0&$-$62.0&0.109&0.243&0.014&8.6&000525\
\
8&(0,-12)&85.2&0.073&0.265&0.008&12.4&84.8&0.046&0.103&0.010&5.0&000526\\
9&(10,6)&---&---&---&0.009&---&$-$117.3&0.036&0.160&0.010&5.5&000526\\
10&
($-$10,6)&$-$12.5&0.051&0.157&0.010&6.9&$-$13.7&0.044&0.288&0.007&11.8&000526\
\
11&(30,30)&71.7&0.302&1.027&0.022&18.8&71.3&0.249&1.151&0.028&14.4&000530\
\
12&(30,30)&37.7&0.092&0.161&0.014&6.4&37.7&0.078&0.260&0.014&7.4&000530\\
13&(30,$-$30)&51.1&0.202&0.951&0.022&15.1&54.4&0.160&0.852&0.025&11.0&000531\
\
14&(90,0)&23.3&0.311&1.037&0.021&20.5&23.2&0.416&1.690&0.026&24.3&000531\\
15&(90,0)&86.9&0.161&0.686&0.021&12.1&86.5&0.152&0.915&0.026&10.8&000531\\
\hline
\end{tabular}
$^{1}$ Observed telescope position.
\end{table*}
%%%%%
%% change 5-5,8-6,10-7,9-8,7-10,6-9
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Table 2 %%%%%%%%%%%%%%%%%%%%

%\begin{longtable}{rrrrrrrrllrr}
\begin{table*}
   \caption{Obtained positions and identifications to the previously 
detected objects}\label{tab:table2}
   \begin{tabular}{rrrrrrrrllrr}
   \hline\hline
No&l&b&$\Delta l$&$\Delta b$&$(\Delta l)_{er}$&$(\Delta b)_{er}$
&$V_{lsr}^{SiO}$&Ref$^{1}$&Identification$^{2}$&$V_{lsr}^{Ref}$
&$\Delta r$\\
  & ($\circ$) &($\circ$) & ($''$)&($''$)&($''$)&($''$)& {\scriptsize (km 
s$^{-1}$)} &
  &{\scriptsize (km s$^{-1}$)}&{\scriptsize (km s$^{-1}$)}&($''$) \\
	\hline
1&359.915&$-$0.041&$-$105&18&7&5&$-$26.7&3&3--57&&6\\
2&359.919&$-$0.055&$-$92&$-$32&5&5&$-$308.1&1,3&359.918$-$0.055,3--2855&$-$307.
9&5\\
3&359.921&$-$0.047&$-$84&$-$3&5&5&$-$110.1&2,3&M4&$-$105.1&\\
4&359.930&$-$0.045&$-$47&0&5&7&6.9&2,3&M3,3--88&17.5&6\\
5&359.944&$-$0.045&0&4&10&9&$-$335.8&2&C7&$-$341.9&\\
6&359.945&$-$0.047&2&-2&11&11&$-$27.6&1,2,4&359.946$-$0.048,C4&$-$26.4&6\\
&&&&&&&&&,IRS10EE&&\\
7&359.945&$-$0.045&2&3&14&12&$-$61.4&2  &C5 &$-$69.6&\\
8&359.946&$-$0.046&5&$-$1&18&13&85.0& & & & \\
9&359.946&$-$0.047&5&$-$4&12&8&$-$117.3&2,4&C6,IRS7&$-$121&7\\
10&359.946&$-$0.045&6&3&13&15&$-$13.1&2,4&C2,IRS15NE&$-$14.6&5\\
11&359.952&$-$0.040&28&22&8&5&71.5&1,2&359.954$-$0.041,P1&70.6&10\\
12&359.953&$-$0.032&30&52&6&30&37.7&3&3--885&&8\\
13&359.957&$-$0.051&46&$-$19&5&5&52.8&1,2,3,5&359.956$-$0.050,P2,3--5&48.5&
8\\
14&359.970&$-$0.043&93&10&8&5&23.3&3&3--6&&3\\
15&359.973&$-$0.048&105&$-$8&12&5&86.7&1,3&359.970$-$0.049,3--3&88.8&8\\
\hline
\\
\end{tabular}
$^{1}$ References: 1---\citet{sjo98a}, 2---\citet{izu98}, 
3---\citet{gla01},
4---\citet{men97}, 5---\citet{lev95}.\\
$^{2}$ The names, 3--57, etc. (indicating the survey field and the star 
number)
refer to the large-amplitude variables in \citet{gla01}.
The names of the sources in \citet{izu98} are designated as
Mn, Cn, and Pn, where M, C, and P stand the telescope positions
at ($-40''$,0), ($0''$, $0''$), and ($+40''$,0), respectively,
relative to Sgr A*, and n the number given to the detected SiO source
in \citet{izu98}.  \\
$^{3}$ A slightly dubious identification is in a parenthesis with a 
``?'' mark.
\end{table*}
%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%% section 3
\section{Discussion}
%
\subsection{Source positions and identifications}
Because most of the components were detected at more than one telescope 
position,
we computed the most likely positions of the SiO features from the 
relative intensities
at the several observed positions. We assumed that antenna temperature
of a SiO maser component varies with angular separation from the 
telescope pointing center
according to a Gaussian beam shape with $HPBW=40''$ (which is taken 
slightly larger
than the nominal HPBW because of pointing fluctuation due to wind).
The most likely position of a component was calculated by minimizing the 
sum, $\Sigma
[(F_{\rm obs}-F_{\rm exp})/T_{\rm rms}]_{\rm i}^{2}$,
where the sum was made over the detected and undetected
($F_{\rm obs}=0$) positions, $i$, and $F_{\rm obs}$, $F_{\rm exp}$,
and $T_{\rm rms}$ are the observed integrated intensity of the component,
the expected integrated intensity of the component
at the observed position assuming the Gaussian beam
shape, and the rms noise temperature, respectively.
The errors in $\Delta l$ and $\Delta b$ are also calculated from
the distance which gives twice the minimum value of the above sum.
The resulting most-likely positions obtained are shown in Table 2;
the component number, Galactic longitude and latitude, the relative 
positions
from Sgr A*, errors of positions,
SiO radial velocity (averaged in $J=1$--0, $v=$1 and 2
transitions), the reference and name of the previously detected sources,
the radial velocity in the literature, and the separation of the 
positions
from the identified source were given. The positions obtained were 
plotted
in the middle panel in figure 1 with uncertainty bars.

The identifications were made by using both positions
and radial velocities. A list of the previously detected OH 1612 MHz 
sources
near the Galactic center (\cite{sjo98a}) was used for
the identification. The positions for these OH sources are known
to an accuracy better than $\sim 1''$. Previous identifications of SiO 
sources
with OH sources were also made by \citet{izu98}.
No. 6 in table 2 is the OH/IR source, 359.946$-$0.048 (IRS 10 EE; 
\cite{men97}),
which has a radial velocity of $-27$ km s$^{-1}$. The location of this
source is well known from the near-infrared, OH,
and SiO maser observations (\cite{men97}; \cite{sjo98a}).
The position obtained in the present paper
agrees well with the OH position within an accuracy of about 6$''$.
The high signal-to-noise ratio of this component confirms
that this method for determing the positions of SiO masers works nicely.
Source No. 10 with $V_{lsr}=-13$ km s$^{-1}$
has been identified as IRS 15 NE (\cite{men97}) with the VLA;
the VLA position agrees with the position obtained in the present paper
within an error of 5$''$.
The positions of the other 4 weaker sources, No. 2, 11, 13, and 15,
also coincide well with the positions of identified OH sources
within accuracies of 3--10$''$, thus
verifying this method for the weaker sources.

The radial velocity of the SiO source No. 4, $V_{lsr}=7$ km s$^{-1}$, is
close to the center velocity of the OH 1612 MHz double peaks of
OH359.931$-$0.050, (\cite{sjo98a}) at $V_{lsr}=17.5$ km s$^{-1}$
(the expansion velocity is about 14 km s$^{-1}$).
Because the SiO position obtained is separated
from the OH position by 11$''$,
it is probably a different source.
%unless the OH double-peak velocities
%listed (\cite{sjo98a}) are in error.
The  position of SiO source No. 8 (85 km s$^{-1}$)
agrees well with that of OH359.947$-$0.046, which is known to
an accuracy of 4$''$,
(but note that there is a large uncertainty in the SiO position).
However, the radial velocity of the SiO masers, 85 km s$^{-1}$,
is slightly outside the
OH double peak velocities (89.4 and 105.3 km s$^{-1}$).
Therefore, we left these two SiO sources unassigned.

It is not surprising that more than half of the  SiO maser sources
have no OH 1612 MHz counterpart.
Previous studies of
SiO masers near the Galactic center (\cite{lin91})
and in the inner bulge (e.g., Deguchi et al.
2000ab) revealed that approximately 2/3 of the SiO sources
have not been detected previously in spite of a very sensitive
OH 1612 MHz survey (\cite{lin92b}; \cite{sev97}) with the VLA and the 
ATCA.
%The positions of the SiO sources, No. 6, 9, and 10, were measured
%accurately with VLA in the 43 GHz SiO line
%and were identified to the Infrared objects,
%IRS 10 EE, IRS 7, and IRS 15 NE,  respectively (\cite{men97}).
%The latter two sources are known to have no OH 1612 MHz
%counterparts.

Large-amplitude variables (including long-period and semiregular 
variables,
as well as supergiants) are potential candidates for SiO maser emitters.
We  compared the positions of SiO sources
without OH identification with the known
positions of the large-amplitude variables within
12$'$ of the Galactic center (\cite{gla01}).
The positions of these variables were measured
with the K-band array camera and are of a few arcsec accuracy.
We found that 4 SiO sources, No. 1, 4, 12, and 14, are located
near to these long-period variables within the estimated positional 
uncertainty.
These identifications are given in the columns 9 and 10 in Table 2.
Because the radial velocities
of these large-amplitude variables are not known,
the identifications of these sources may be slightly
less certain than OH identifications.
So far, SiO sources No. 3, 5, 7, and 8, have no OH 1612 MHz counterpart
and no corresponding large-amplitude variable; nevertheless, these were
detected before in SiO by \citet{izu98}.

We also checked the corresponding near-infrared objects
in the 2MASS image server for unidentified sources. However,
because the star density within 30$''$ of the Galactic center is too
high [e.g., \citet{blu96}], it is quite difficult to identify
the SiO sources in this region.
On the 2MASS images,  we could only find
one red candidate ($\sim$10 mag in the $K$ band ) for the source No. 3
within a 5$''$ error circle.
This red star, however, accompanies a faint extended ($\sim 5''$) feature
which is considerably elongated in galactic longitude,
probably because of coalescence of several stars due
to the low spatial resolution of the 2MASS images).

%%%%%%%%%%%%%%%%% Figure 4 %%%%%%%%%%%%
\begin{figure}
   \begin{center}
     \FigureFile(75mm,100mm){fig4.eps}
     %%% \FigureFile(width,height){filename}
   \end{center}
   \caption{SiO spectra in the $J=1$--0, $v=1$ transition
   at the three $12''$-offset positions around Sgr A*. The position 
offsets
   from Sgr A* in unit of $''$ are shown on the right side. The component 
number
   in in this figure corresponds to the number given in Tables 1 and 2.
   }\label{fig:three.V1}
\end{figure}

%%%%%%%%%%%%%%%%% Figure 5 %%%%%%%%%%%%
\begin{figure}
   \begin{center}
     \FigureFile(75mm,100mm){fig5.eps}
     %%% \FigureFile(width,height){filename}
   \end{center}
   \caption{The same as Figure 4 but in the $J=1$--0, v=2 transition.
   }\label{fig:three.V2}
\end{figure}

%
\subsection{Velocity distribution of the SiO masers sources}
The bottom panel of Figure 1 shows the longitude-velocity diagram
for the 15 detected sources. The positions given
in Table 2 were used for making this diagram.
A linear fit to the SiO radial velocities was made
and the result is given in the first row of Table 3.
There are two extreme sources with
very large negative velocities, $-336$ and $-308$ km s$^{-1}$.
It is possible that the sources with very large radial velocities
are bulge stars with very small angular momentum,
rather than stars in the Galactic-center stellar cluster
(\cite{van93}; \cite{izu95}). They may be located far
from the Galactic center in distance but happen to be seen
near to it in projection, though this possibility is small.
We also made a linear fit excluding these two sources.
The result are also given in the second row of Table 3.

The slope of about 1.1 ($\pm$0.5) km s$^{-1}$ per arcsec
(or 3890 km s$^{-1}$ deg$^{-1}$, or a rotation period
of $2.3 \times 10^{5}$ yr around the Galactic center)
is a factor of a few larger than the previously obtained values
from SiO and OH maser observations on much larger scales
[e.g., \citet{miy01}].
Even for the sample excluding
the 2 extreme-velocity sources, the slope is
$\sim$2290 km s$^{-1}$ deg$^{-1}$.
The present value of the slope
is not compatible with the previously obtained low value
by \citet{izu98} ($\sim$0.09 km s$^{-1}$ per arcsec), probably because
the positions of the sample in \citet{izu98} were not
known with accuracy better than the telescope beam size
of about $40''$; the positional accuracy
is considerably better in this paper.
The obtained high rotational speed of the SiO maser cluster
is, however, simply a slope of the least squares fit and
must be interpreted very carefully.
Non-circular motions of stars and
the gravitational potential made from
the central compact mass and the nuclear star cluster
are responsible for the observed velocity structure.
The high rotational speed of these stars is comparable with
the rotational velocity of the circumnuclear gas ring
which has been observed in various molecular lines
[e.g., \citet{wri01}]. It is possible that these rapidly rotating
AGB stars were born as a result of
star formation in the circumnuclear ring
(\cite{lev95}).

The velocity dispersion from the average linear fit
is approximately 108 km s$^{-1}$
(or 54 km s$^{-1}$ excluding the extreme sources).
This value gives the mass
of the Galactic center (integrated to 100$''$; $\sim$ 4.1 pc) as
$\sim 1 \times  10^{7} M_{\odot}$,
when we use the Virial theorem, and
is consistent with the previous estimates of the mass
of the Galactic center region
(\cite{kra95}; \cite{mor96}).
The radial velocity dispersion obtained for SiO maser sources, 110 km 
s$^{-1}$,
is slightly smaller than the value 154 km s$^{-1}$
for the late-type stars
within 12$''$ from the Galactic center (\cite{kra95}).
In fact,  if we take only the SiO sources only within a 20$''$ radius
from the Galactic center in our sample
(No. 5--10; including the extreme source No. 5),
we get a velocity dispersion of 133 km s$^{-1}$,
giving a reasonable agreement with the \citet{kra95} result.

A simple judgement
on whether or not a particular star is dynamically bound to the
Galactic-center massive compact object can be obtained from
the characteristic binding energy per unit mass,
$E_{c}=(1/2)V_{l.o.s.}^{2}-G M/r_{p}$.
Here, $V_{l.o.s.}$, $r_{p}$,
$G$, and $M$ are the observed radial velocity, the projected radius
from the galactic center,
the gravitational constant, and the mass of the central compact object
(for which we adopt $2.8\times 10^{6}$ M$_{\odot}$; \cite{ghe00}; 
\cite{gen00})
, respectively.
Considering a perpendicular velocity component and
some depth along the line of sight, the characteristic binding energy, 
$E_{c}$,
gives a lower limit to the real binding energy when the central mass 
dominates
the gravitational field.
For the SiO sources, No. 2, 3, and 15, the characteristic binding 
energies are
positive. Therefore, these sources are not dynamically bound to
the central compact object.

Because the SiO intensity of the extreme object No. 5 was quite weak
in the year 2000, the position uncertainty given in the present paper
is quite large. The characteristic binding energy
of the object No. 5 could be positive if the true position is a few 
arcsec further
away from the Galactic center than that observed. The SiO intensity of 
this component
was much stronger in 1997 (\cite{izu98}). Therefore, a more accurate
position should be obtained at a future date.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Table 3 %%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*}
   \caption{Fitting results}\label{tab:table3}
   \begin{tabular}{lccr}
   \hline\hline

Sample & Number  &  best fit  & rms  \\
    &   of sources   &    (km s$^{-1}$) &(km s$^{-1}$) \\
\hline
   &&&\\
All sources &  15  & $-42.0(\pm 30.0) + 1.07 (\pm 0.51) [\Delta 
l$($''$)] & 108.4 \\
(including extreme sources)&&&\\
Low-velocity sources only &  13  & $-3.7(\pm16.3) + 0.67 (\pm 
0.28)[\Delta
l$($''$)]  & 53.9\\
(excluding extreme sources)  &&&\\
\hline
\\
\end{tabular}
\end{table*}
%%%
%
\subsection{Time variation}
The intensities of SiO maser lines  change significantly on a time scale 
of a year.
Though the number of SiO sources detected in this paper is similar to
the number given previously (\cite{izu98}), the two lists are not
completely the same; 9 objects in the SiO spectra in 2000 are
inferred to be the same as those found in 1997
because of the velocity coincidences.
The identifications are given in the columns 9 and 10 in Table 2.
If we compare figure 1 in the present paper with the middle panel of 
figure 1
of \citet{izu98}, we can recognize significant variations in SiO maser 
intensities
in the last 5 years.

We noticed in March 2000 that the SiO masers of the source No. 6
(the $-27$ km s$^{-1}$ component, known as IRS 10 EE; \cite{men97})
had flared up to more than $T_{a}\simeq$0.5 K ($\sim$ 1.5 Jy).
The SiO maser intensities of the source No. 6  are plotted against time 
in figure 6.
We took the 1996 and 1997 data from \citet{men97} and \citet{izu98}, 
respectively,
and the March--April 2000 data from \citet{miy01}. The peak and 
integrated
intensities
of the $-27$ km s$^{-1}$ component of \citet{miy01}
agree quite well with the present results at May 2000.
Therefore, the flare lasted for more than  two months,
from the end of March 2000 to the end of May 2000.
Because we did not observe the Galactic center in 1998,
it is not known if there was a brightening in 1998.
Near-infrared monitoring observations of
this source over 4 years (\cite{woo98}; assigned as LWHM65)
gave a period of 736 days for the light variation.
Extrapolating the fit of the light curve given
in \citet{woo98}, we estimate that the infrared maxima
of this source came around 1998 mid November and 2000
late November. However, because the observed light curve
  (\cite{woo98}) has a large ambiguity, the estimated
time of the light maximum is quite uncertain. It may
occur in advance by several months before November 2000
(in fact, March-June 2000), if we assume the light  maximum
occurs at the same time as the SiO maser intensity maximum.

%%%%%%%%%%%%%%%%% Figure 6 %%%%%%%%%%%%
\begin{figure}
   \begin{center}
     \FigureFile(75mm,50mm){fig6.eps}
     %%% \FigureFile(width,height){filename}
   \end{center}
   \caption{Time variation of the SiO lines from No. 6 (IRS 10 EE).
   The data of 1996 and 1997 were taken from \citet{men97} and
   \citet{izu98}. The data of March 2000 were taken from
   \citet{miy01}. Filled and unfilled circles indicate the
   SiO $J=1$--0, $v=1$ and 2 lines, respectively.
   The line fluxes in 1997 and 1999 were scaled by a factor of
   1.4 because IRS 10 EE is located at the off-set of
   about 10$''$ from  Sgr A*.
   }\label{time.variation.IRS10}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The intensities of the SiO lines from IRS 10 EE, $T_{a}\simeq 0.5$ K
(about 1.5 Jy), in 2000 May were comparable with the intensity of
the SiO $J=1$--0 $v=1$ maser from Sgr B2 MD5 (\cite{shi97};\cite{mor92}).
If they are scaled to the distance to 500 pc ($\sim 400$ Jy),
it is comparable with the intensities of the Orion SiO masers.
Therefore, the SiO maser flare of IRS 10 EE may indicate that
the mass loss rate of this star is temporarily enhanced to rates
comparable with these from Orion IRc2 and Sgr B2 MD5.
If the flare of IRS 10 EE is repeated periodically, it is probably 
associated
with pulsation activity of the central star.
If it is irregular,  it is possible to consider another mechanism,
for example, a wind-wind collision between nearby massive stars
(\cite{yus92}). In addition, a tidal effect due to a close encounter
between nearby stars might not be negligible, because
the density of stars in the central star cluster is
quite high.
%As noted in \citet{izu98}, the tidal force due to the
%central compact object also cannot be neglected.

For the 8 SiO sources, No. 1, 2, 4, 6, 12, 13, 14, and 15,
the periods of light variation are known (\cite{blo98}; \cite{woo98}; 
\cite{gla01}).
A histogram of the periods is shown in figure 7. Because the sample
involve only 8 stars, we divided the sample into two bins,
i.e., above and below 450 days. It is worth to mention that
all the sources with OH counterparts have periods more than 450 days
(see Figure 7). Note that the average period of the sample
of 412 large-amplitude variables
near the Galactic center given by \citet{gla01} is 427 day.
Therefore, the Galactic-center SiO source sample is probably weighted 
more
toward the variables with longer period than the average.
SiO masers are, however, occasionally detected in stars
with shorter periods than those in which OH masers were found.
Considering the mass--luminosity--period
relation [e.g., \citet{vas93}], we conclude that
lower-mass AGB stars are more often detected in SiO maser observations
than  in OH 1612 MHz observations. Because the size of the sample
is a bit small, the conclusion may not be free from statistical
fluctuations.  However, the present conclusion is quite
consistent with the finding by \citet{gla01}
that the OH 1612 MHz sources have longer periods
than the average period in their sample.
According to an SiO maser study
of the Galactic disk IRAS sources (\cite{nak01}),
stars with bluer colors in terms of the IRAS 25/12 $\mu$m intensity ratio
(relatively thin dust envelope) tend to be detected
in SiO masers more often than in OH 1612 MHz masers. This fact also 
seems to
agree qualitatively with the above result
for the Galactic-center AGB stars, though the IRAS 25/12 $\mu$m colors
do not necessarily correlate well with
the periods of AGB stars (\cite{whi92}; \cite{nak00}).

%%%%%%%%%%%%%%%%% Figure 7 %%%%%%%%%%%%
\begin{figure}
   \begin{center}
     \FigureFile(75mm,100mm){fig7.eps}
     %%% \FigureFile(width,height){filename}
   \end{center}
   \caption{Histogram of the periods for the SiO detected sources.
   The blank and shadow parts indicate the SiO sources with and without
   OH counterparts. All the SiO sources with OH counterparts
   are stars with periods above 450 days.
   }\label{P-histogram}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The total number of SiO sources detected in the present paper is
15. If we include all the SiO sources which were detected in 
\citet{izu98}
and in the present paper, the total number of SiO maser stars
in the region of 200$'' \times 100''$ from the Galactic center
is 20.  Further monitoring observations of the SiO maser intensities of
the these Galactic center SiO sources are definitely required.

\section{Conclusion}
We have made mapping and monitoring observations of SiO maser sources
near the Galactic center and have detected 15 SiO sources. Approximate
positions were obtained with accuracies of about 5--10$''$;
five sources are identified with the previously observed
OH 1612 MHz sources. Among the sources
without OH counterparts, four are close to the positions
of the large-amplitude variable stars observed at near-infrared
wavelengths and two to previously detected SiO sources
with accurate positions from the VLA. Three-year monitoring observations
of these objects found that SiO masers from IRS 10 EE flared up by a 
factor
of more than 5 during March-May 2000. A least squares linear fit of
velocities to the Galactic longitude in the longitude-velocity diagram
gives a  high rotational speed for the star cluster
around the Galactic center.

The authors thank I. Glass for stimulating discussions
and reading the manuscript.
They also thank M. Morris, H. Izumiura, H. Imai, and A. Miyazaki for 
comments.
This research was partly supported by Scientific Research Grant
(C2) 12640243 of Japan Society for Promotion of Sciences.


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% Books
%\bibitem[Author(2001)]{key-3}
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%......
% Editorial Books
%\bibitem[Author(2001)]{key-n}
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%   ed Editor D.\ Editor(Publisher, Tokyo) page0
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