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    {\small\rm\zihao{6}\songti\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
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    {\small\rm \zihao{6}\songti suppl.\hfill J.-H. Zhao: Radio Variability of the Supermassive
Black Hole at The Galactic Center%%（作者：题目名称）
    \vspace{1.5mm}
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    \normalsize\rm
\zihao{5}\songti

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    \zihao{6}\songti
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    Vol.44~ Suppl.
    \hfill\hspace{8mm} %%% if ``October/January'' then \hspace{8/10 mm} July
    \small ACTA ASTRONOMICA SINICA
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      Feb.,~2003 \\[-1.5 true mm] %%January
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\vs\vs\vs \bc {\Large\bf Radio Variability of the Supermassive
Black Hole at  Galactic Center:\\[2mm] Double Quasi-Periodic
Oscillation in Radio Flux \\[2mm] Density
and Flares at 1 Millimeter Wavelength    %%（文题）
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize Jun-Hui Zhao}  %%（本文作者）

\vs ({\footnotesize {\it Harvard-Smithsonian Center for
Astrophysics,
60 Garden St., MS 78, MA 02138, USA}}) \\%%（本文作者单位）
\vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
With the densely sampled  light curves observed with the Very
Large Array (VLA) over the past two years, we have confirmed the
previous finding of the periodic signals with a period of 100 d
from the VLA archival data. In addition, we have found an
additional periodic signal with a period of 2.4-2.5 times longer
than the short period, revealing the nature of double periodic
oscillation  in flux density of Sgr~A*. Our observations also
suggest that the individual oscillation periods of the double
features are  drifting in time while the ratio of the periods
appears to remain in a constant. The double periodic oscillation
of Sgr~A* suggests that a dynamic system consisting  of a
supermassive black hole, an accretion flow,  and an orbiting
object is subject to an orbital resonance which may periodically
trigger central activities. The observed drifts in the periods
suggest that this dynamic system (or the Sgr~A* system) must have
been substantially disturbed
 by a nearby
 gravitational source.

With the partially finished Sub-millimeter Array on Mauna Kea, a
total of 25 epochs of observations were carried out over the past
15 months. Noticeable variations in flux density at 1.3 mm were
observed showing three ``flares''. The SMA observations suggest
that Sgr A* is highly peaked towards sub-millimeter wavelengths
during a flare suggesting the presence of a break wavelength
around 3 mm. A cross-correlation of the SMA data at 1 mm with the
data obtained with the VLA at 1 cm shows a global delay of two
weeks, suggesting that sub-millimeter wavelengths tend to peak
first. The SMA observations suggest that Sgr A*
 might have been regularly powered via the flares. Any periodicity
 in flares at 1 mm needs to be confirmed with  further better sampled
 observations.

 %\vn
 %\no{\bf Key words}~~  pulsar-mode  change-spectrum
\end{quotation}

\para{\large\bf{1}~~ Introduction}

\vs\vs Sgr~A*, a compact radio source,   is believed to be
associated with the supermassive black hole at the Galactic center
(Eckart \& Genzel 1997; Ghez et al., 1998). The inferred
bolometric luminosity (L$\sim10^{-8.5}$ L$_{\rm Edd}$) is far
below the Eddington luminosity assuming that the mass of the black
hole is $\sim$2.6$\times10^6$ M$_\odot$. Sgr~A* represents an
extremely dim galactic nucleus. Because of its compactness, we
have known little about its intrinsic structure. The apparent
structure at radio wavelengths up to 3 mm appears to be  mainly
dominated by the scattering structure due to  the ISM. Its
intrinsic size measured at 3 mm is less than 0.27 mas (Doeleman et
al.~2001) suggesting that a characteristic source size at 3 mm is
$\sim$ 40 Schwarzchild radii (${\rm R_{sc}}$ hereafter).

The compactness of the source  appears to be just beyond
our  current capability to image its detailed structure
using the available telescopes.
Alternatively, a promising way to explore this
extremely compact source
is to monitor the variations of the emitting flux density
at multi-wavelengths from radio to
X-ray.

In this invited talk, we summarize the new results from the  VLA
monitoring program and the observations with the SMA.

\begin{figure}[h]
%\center {\includegraphics [bb=0 103 408 475,scale=0.8]{fig1.ps}}
\center {\includegraphics[bb=60 176 571 648,scale=0.75]{fig1.ps}}
   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize

      Fig.\,1~~ The SMA light curves at 1.3 mm observed in
2001-03  and 2002-05 for the calibrators (upper panel) and Sgr~A*
(middle panel). Bottom panel: the densely sampled VLA light curves
at 1.3 and 2 cm were observed in the same period (McGary 2002).}

    \end{figure}


\para{\large\bf{2}~~New Observations \& Radio Light Curves}

\vs\vn{\bf{2.1~~ VLA observations}}

We  briefly reported the preliminary results in the AAS Meeting
199 (Bower et al. 2002). The details of the reduction procedure
along with data and more results will be reported elsewhere (Zhao
et al. 2002a; McGary et al. 2002). A part of the VLA light curves
at 1.3 and 2 cm is shown in Fig. 1 (the bottom panel). Multiple
``flares'' are seen when the flux density of Sgr~A* rises by at
least 30\%.  Sgr~A* now appears to be in a relatively quiet mode
as compared to that in the period of 1980's and early 1990's (Zhao
et al. 2001).


\vn{\bf{2.2~~SMA Observations}}

We observed Sgr A* at 1.3\,mm and 0.87\,mm using the partially
finished SMA with three or four antennas and baselines ranging
from 7 to 55 kilo wavelengths at 1.3\,mm. The details of data
reduction are  described in Zhao et al. (2002b).


Fig. 1 shows the SMA light curve at 1.3\,mm suggesting that Sgr~A*
varies significantly. The light curve of Sgr~A* appears to be
characterized with a few ``flares'' while the calibrators show
secular variations with opposite drifts in flux density over the
past year (see the upper panel of Fig. 1). Three ``flares'' were
observed over a 1-year period. Both  the 2001-March and
2002-February flares (Flare 1 and Flare 3 as marked in Fig. 1)
were partially observed in  their dropping phase while the
2001-July flare (Flare 2) was observed covering its entire cycle
from its rising to maximum and then a slow decrease. Flare 1
 (started from 4.1$\pm$0.5\,Jy
after an unseen peak and decreased to 1.1 $\pm$ 0.15\,Jy in three
months) appeared to be relatively stronger than others. The rising
time for Flare 2 was about 2 weeks, reaching a peak of
$3.2\pm0.3$\,Jy on 2001 July 10. Then, a slow decrease lasted
about 3 months. We were not able to observe Sgr~A* for next 3
months due to the solar avoidance restricted by the current SMA
system. The monitoring program was resumed in early 2002 February.
A tail of a possible flare (Flare 3) appeared to be observed in
early 2002.

\vspace{-4cm}\begin{figure}[tbph] \center {\includegraphics [bb=19
39 575 691,scale=0.6]{fig2.ps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
  \vspace{-11cm}
   \footnotesize
 Fig.\,2~~ Left panel: the PSD derived from
the VLA archival data over the period between 1990 March to 1993
October (Right panel) using Lomb PSD  Algorithm. Two significant
PSD features at 1.16$\times10^{-7}$\,Hz (or 100 d) and
0.48$\times10^{-7}$\,Hz (or 240 d) can be identified. The
horizontal lines mark the significant levels.}

    \end{figure}

 \vspace{-5cm}
 \para{\large\bf{3}~~Data Analysis and Results}

\vs\vn{\bf{3.1~~Power Spectral Density (PSD) Analysis And Periodic
Signals}}

In the initial discovery paper (Zhao et al. 2001), we identified
a periodic signal in the power spectral density (PSD)
using maximum entropy (all poles) method (MEM). We used the lower
resolution (or a smaller number (N=10) of poles) MEM to find the
106 day period in  the archived data. The advantage
of lower resolution MEM is  suppression of  the noise and improved
S/N for the dominant features. However, the MEM
requires  re-griding of  the unevenly sampled light curve to an evenly
separated  grid which might artificially introduce an uncertainty in the
reconstruction of the light curves. Also, weak features close  to
the dominant signal  can be blended in
the lower resolution PSD.


Instead, we now search for  periodic signals in the power spectral
density (PSD) of Sgr\,A*'s light curves with the Lomb Algorithm
(Press et al. 1992). The Lomb PSD method is designed for unevenly
sampled time series data and provides reliable results with
significance level based on Monte Carlo simulation. The PSD
results throughout this paper are derived using Lomb algorithm.

We calculated the PSD  of the light curve of the VLA data observed
at 1.3\,cm during 1990 March to 1993 October over a 1300-d period
(lower panel, published in Zhao et al. 2001). The mean sampling
interval during this period is 28 d which is less than the Nyquist
sampling limit for a periodic signal with a period of 100\,d. In
addition to the strong feature at  $\sim$100\,d, there is a weak
periodic signal at $\sim$240\,d (see Fig.\,2).

We have also derived the PSD  of the light curve of the VLA data
observed at 1.3\,cm during 2000 June to 2002 August over an 800-d
period (Zhao et al 2002a). This PSD reveals the double periodic
signals with a ratio of $\sim$2.5 in period. The long period
oscillation in flux density can be clearly seen in the densely
sampled light curves at 1.3\,cm over a period of more than 2
complete 335-d cycles. This signal is very strong  and completely
dominates the PSD of the light curve. In addition,  weak flares
appear also  to  present on top of the long periodic modulation.

In short, the periodic signal at 100\,discovered from the VLA
archival data is confirmed with the Lomb algorithm and also
persists in the new data taken from this monitoring program over
the past two years. In addition, a new periodic feature at a
period 2.4---2.5 times longer has also been revealed in both the
archival data and the new light curves. The periods of the
individual signals appear to drift to longer values over time but
the ratio of the double periods appears to remain  constant.
\begin{figure}[ht]
\center {\includegraphics [bb=91 190 601 571,scale=0.6]{fig3.ps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize

      Fig.\,3~~ A spectrum of Sgr\,A* made from the observations near the
peak of Flare 1. The 0.87 and 1.3\,mm measurements were made with
the SMA. The measurements at 3\,mm were obtained from observations
with the Nobeyama Millimeter Array (NMA) (Tsutsumi et al.~2002).
The data at 0.7, 1.3 and 2\,cm were from McGary et al.~(2002 ). }
    \end{figure}

\vn{\bf{3.2~~Flares at Short-/Sub-millimeter}}

\no {3.2.1~~Spectrum During A ``Flare''}

The SMA monitoring project is highly motivated by the fact that
the sub-millimeter wavelengths can penetrate more deeply into the
source and the radiation at the short wavelengths reflects the
activities occurring in the inner region of the accretion disk
near the supermassive black hole.

Fig.\,2 shows that the SMA light curve at 1.3\,mm is characterized
by a few ``flares'',  suggesting that Sgr\,A* varies
significantly. During the ``Flare 1'' (2001-March), the VLA,
Nobeyama Millimeter Array (NMA) and the SMA observed Sgr\,A*
within a period of two weeks. A spectrum (see Fig. 3) constructed
using the mean flux densities measured at wavelengths ranging from
2\,cm to 0.87\,mm near the peak of Flare 1 shows a break frequency
at 100\,GHz (or a break wavelength at $\sim$ 3\,mm). The intensity
of the flare appeared to be highly peaked towards sub-millimeter
wavelength, suggesting that flares at sub-millimeter wavelengths
are more prominent.


\no {3.2.2~~Cross Correlation and Global Delay}

  We have found
that flares at centimeter wavelengths appear to be correlated with
increased flux densities at 1.3\,mm (Zhao et al. 2002b). Fig.~2
shows a comparison of the light curves observed with the SMA at
1.3\,mm and with the VLA at 1.3 and 2\,cm. A quantitative analysis
of cross-correlation  properties  between the light curves at
1.3\,cm and 1.3\,mm have been carried out. A global delay between
1.3\,cm and 1.3\,mm light curves has been searched using the
z-transformed discrete correlation function (ZDCF) (Alexander
1997; Edelson \& Krolik 1988). With no prior models assumed, the
ZDCF is an efficient method in searching for delay in unevenly
sampled sparse data. Fig.~4 shows the cross  correlation function
between SMA and VLA light curves at 1.3\,mm and 1.3\,cm. The peak
in the correlation function corresponds to a lag of 4$_{-1}^{+2}$
d while the correlation coefficient weighted mean of the hump near
zero lag suggests a global delay of 14$\pm$8\,d. This global delay
indicates that flares at 1.3\,mm starts first. In addition, the
cross correlation function tends to show a periodic oscillation.
With Lomb PSD analysis of the ZDCF, we derived a period of
134$\pm$5\,d which appears to be consistent with what has been
found from the VLA light curve at 1.3\,cm. The periodic
oscillation in the ZDCF suggests that the SMA data might contain
the periodic signal. Any periodic signals at 1\,mm needs to be
confirmed with better sampled observations.

\begin{figure}[h]
\center {\includegraphics [bb=40 135 577 577,scale=0.6]{fig4.ps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize

      Fig.\,4~~ The z-transformed discrete cross-correlation function (ZDCF)  of
the SMA data at 1.3 mm with the VLA data at 1.3 cm. The peak of
ZDCF corresponds to a delay of 4$^{+2}_{-1}$ d and global delay of
14$\pm$8d is inferred from a correlation coefficient weighted mean
of the hump near the zero lag. }

    \end{figure}

\no {3.2.3~~X-ray Flares}

 In 2000 October, an X-ray
flare of Sgr~A* was observed with {\it Chandra} (Baganoff, 2001).
Following the X-ray flare, Sgr~A* was observed to brighten at all three of
our observed wavelengths and to peak in flux density on 2000 November 5, showing
a delay of 10 days. The VLA monitoring data provides critical
evidence for supporting the idea that the X-ray flare arises from the
inner region of the accretion disk near the supermassive black hole
 instead of from other possible origins such as star-star
collisions.


In addition, during the 1\,mm Flare 2 (2001 July), Chandra
observed Sgr~A* on 2001 July 14, a few days past the 1\,mm peak,
showing no X-ray flares. The X-ray flux level was consistent with
that of a quiescent state (Baganoff 2001, private communication).

More recently, both the SMA and the VLA participated in
coordinated observations with Chandra, OVRO, ATNF,  VLBA, Keck,
VLT and other telescopes to observationally study the emission
mechanism of the X-ray flares (Baganoff, Morris et al. 2002). The
VLA monitoring project was used to schedule the observations based
on our best estimate of the most likely time for a flare to occur.
Several significant flares at X-ray wavelengths were observed
during the week long campaign.  Although we observed no
significant flares at both 1\,cm and 1\,mm during the coordinated
observations, a small flare was observed on ~10 June 2002. The VLA
data again shows a significant lag in flare as is compared to the
X-ray data. In addition,  the significant  X-ray flares and no
significant changes in the VLA flux density at centimeter and the
SMA flux density at 1\,mm during the multi-wavelength campaign
appear to provide a critical information in distinguishing various
emission models for the X-ray flares.



\para{\large\bf{4}~~Astrophysical Implication and Discussion}

\vs\vn{\bf{4.1~~Low Luminosity Nature and ADAF}}

The low luminosity nature of Sgr~A* as a galactic nuclear source
has been successfully explained
by the low efficiency radiative ADAF model (Narayan et al. 1998).
In the ADAF model, the high temperature protons that carry with the most of the
energy and angular moment are advected all the way to the event horizon
 with little radiation.
The emission from low temperature electrons in the advection
dominated accretion flow make the main contribution to illuminate
the source. However, the ADAF alone
 appears to be difficult in explaining the
detailed activities observed at the wavelengths ranging
from radio to X-ray.

\vn{\bf{4.2~~Intrinsic Activity and Jet-ADAF}}

Alternatively, recent work by Yuan, Markoff \& Falcke (2002)
provides a model to link
a jet outflow (Falcke et al. 1993) with the ADAF
(Narayan et al. 1998). The jet-ADAF model appears to fit
reasonably well to the overall spectrum of Sgr~A* from radio, sub-millimeter,
IR to the X-ray. In the Jet-ADAF model, the sub-millimeter excess is thought
to be the result of a sum of the synchrotron radiation from both the ADAF
and the nozzle of the jet.

    On the other hand, from the observations with the VLA, SMA and other
interferometer arrays,  further constraints on the models can be
discussed. The global delay of 2 weeks determined from the
cross-correlation between the SMA and VLA light curves and the
source size of 40 R$_{\rm SC}$, suggest a small expansion velocity
of V$_{\exp}\sim$ 200\,km\,s$^{-1}$ or 0.001\,c which is far below
the escaped velocity of 0.1\,c required to form a visible jet. In
addition, the break wavelength around 3\,mm also indicates that a
large fraction of flaring plasma might well be confined within the
characteristic radius at 3\,mm although the possible outflow
driven by the central activities tends to expand to a large scale.

\vn{\bf{4.3~~Periodic Oscillation and Disk Precession}}

The existence of periodic fluctuation cycle around a period of
$\sim$ 100\,d appears to have been established with the extensive
analysis of the VLA archival data and the densely sampled VLA
observations in the new monitoring program. In addition, the two
states (flare and quiescent) can be separated in the folded light
curve  with a module of 100 to 120\,d based on the irregularly
sampled data taken with the NMA at 3\,mm over the past six years
(Tsutsumi et al. 2002). The 3\,mm result appears to be consistent
with the centimeter data observed with the VLA. In addition, the
global cross-correlation analysis of the VLA data at 1.3\,cm and
the SMA data at 1.3\,mm has revealed a quasi-periodic oscillation
in the cross-correlation function with a mean separation in lags
between the cross-correlation peaks. Such a cross-correlation
feature is a good evidence for the fact that the SMA sparse data
does contain the periodic signal as observed at 1.3 cm with  the
VLA although the SMA data alone is not sufficient to extract such
a signal due to a poor data sampling.

 A model to interpret such an interesting periodic signal has been proposed
 by  Liu and Melia (2002) in an assumption of both a small Keplanian
 accretion disk (with an out
 radius of ${\rm R_o}$) and a Kerr black hole with a specific spin of a/M.
 If the rotation axis of the disk offsets from the spin axis, then the spin
 black hole places an intrinsic torque on the accretion disk and causes
 the disk precession around the spin axis. The wabbling, opaque disk
 shadows the radio emission  and produces periodic modulation in the radio
 light curves. Linking the disk precession period to the observed
 100 day period  ${\rm P_{100d}}$, then the black hole spin can be inferred:

       $${\rm {a\over M} \sim 0.1 \left[ R_o\over 30R_{SC}\right]^{2.5}/ P_{100d}
\sim 0.1\,.}$$
A small black hole spin (10\% of a perfect Kerr
black hole) is therefore inferred in this model.

\vn{\bf{4.4~~Double Periodic Oscillation and Orbital Resonance}}

The discovery of double quasi-periodic oscillation in the VLA data
suggests that
the nature of the Sgr~A* system is more complicated than originally thought.
The mode of the double oscillation appears to vary in the following way:

1) The short periodic oscillation (${\rm P_1}\sim 100$\,d) that
dominated in early 1990's has been weakened and the long periodic
oscillation  (${\rm P_2}$) now dominates in the radio light
curves.

2) The periods of both oscillations drifts to long periods with a
fractional period change rate of $\dot P/P\sim0.0129$\,yr$^{-1}$
while the ratio of the two oscillation period ($P_2/P_1$) keeps
nearly constant (in a range of 2.4 to 2.5).

The constant ratio of the two oscillation periods suggests that an
orbital resonance phenomenon might  indeed occur in the Sgr~A*
system. If the P$_2$ corresponds to  a modulation period of a
tidal bulge in the emitting plasma surrounding the supermassive
black hole due to an orbiting object, the mean orbital radius of
2200 $\rm R_{SC}$ (110\,AU) is inferred. The orbiting object
interacting with the accretion flow triggers a wave such as an
epicyclic oscillation through parametric resonance instabilities
(Kluzniak \& Abramowicz 2001, 2002). The growing wave propagates
inwards and periodically triggers the central activity in a
resonant frequency of 2.5 times faster than the oribtal frequency
of the orbiting object. This resonance system must be perturbed by
a nearby gravitational source in order to explain for the
oscillation frequency drifts.


\vn{\bf{4.5~~Origin of the X-ray Flares}}

The  lack of strong flares on a short time scales at  the
short-/sub-millimeter wavelengths
 places a critical constraint on the hypothesis
of the inverse Compton scattering as is proposed for the emission
mechanism for the short lived X-ray flares (Falcke \& Markoff 2000).
Alternatively, the
X-ray flares can be naturally excited by the inward growing resonance wave
triggered by the orbital star. The flares at the sub-millimeter to
radio wavelengths might be a result of a collective mass ejections associated
with the X-ray flares.

\vs\vn{\bf ACKNOWLEDGEMENTS}~~ The author thank McGary, Bower and
Goss for carrying out the VLA monitoring program and the SMA staff
from both the SAO and the ASIAA for supporting the SMA
observations. The SMA is a collaborative project of the
Smithsonian Astrophysical Observatory and the Academia Sinica
Institute of Astronomy \& Astrophysics. The Very Large Array is
operated by the National Radio Astronomy Observatory (NRAO). The
NRAO is a facility of the National Science Foundation operated
under cooperative agreement by Associated Universities, Inc.

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

\nref Alexander T.,  in Astronomical Time Series, eds. D. Maoz, A.
Sternberg, E. Leibowitz (Dordrect: Kluwer), 1997, p.163
\nref Baganoff F.K., et al.  Nature, 2001, 413, 45
\nref Baganoff F.K.,
Morris M., et al.   GC Workshop 2002, 2002
\nref Bower G.C.,
McGary R.S., Zhao J.H., et al.,  American Astronomical Society
meeting, Washington, DC, 2002
\nref Doeleman S., Shen Z., Rogers
A.E.E., et al.,  AJ, 2001, 121, 2610
\nref Eckart A., Genzel R.,
MNRAS, 1997, 28, 576
\nref Edelson R.A., Krolik J.H., ApJ, 1988,
333, 646
\nref Falcke H., Mannheim K., Biermann P. L.,  A\&A,
1993, 278, L1
\nref Falcke H., Markoff S.,  A\&A, 2000, 362, 113
\nref Ghez A.M., Klein B.L., Morris M.,et al., , ApJ, 1998 509,
678
\nref Kluzniak W., Abramowicz M.A.,  APP B32/11, 2001, p.3605
\nref Kluzniak W., Abramowicz M.A.,  astro-ph 0203314, 2002
\nref Liu S., Melia F.,  ApJ, 2002, 573, L23
\nref McGary R., et al., 2002, in preparation
\nref Narayan R., Mahadevan R., Grindly J.E.,
    et al., ApJ, 1998, 492, 554
\nref Press William, et al., Numerical Recipes in C, The Art of
Scientific Computing, Second Edition, Cambridge University Press,
1992
\nref Tsutsumi T., Miyazaki A., Tsuboi M., AAS Meeting 200,
\#44.09, 2002
\nref Yuan F., Markoff S., Falcke H., A\&A, 2002,
  383, 854
\nref Zhao J.H., Bower G.C., Goss W.M., ApJ,  2001, 547, L29 \nref
Zhao J.H., Pegg J., McGary R.S., et al., 2002a, in preparation
\nref Zhao J.H., Young K.H.,
 McGary R.S., et al. 2002b, in preparation for ApJ Letter

%\end{CJK}
\end{document}
