------------------------------------------------------------------------ GCH30aSMA.tex ApJ (2010), Vol. 722 (October 20, 2010), in press X-MailScanner-Information: Please contact the postmaster@aoc.nrao.edu for more information X-MailScanner: Found to be clean X-MailScanner-SpamCheck: not spam, SpamAssassin (not cached, score=-4, required 5, autolearn=disabled, RCVD_IN_DNSWL_MED -4.00) X-MailScanner-From: jzhao@cfa.harvard.edu X-Spam-Status: No %% LATEX this file (not TEX) %% Beginning of file 'sample.tex' %% This is a sample manuscript marked up using the %% AASTeX v5.0 LaTeX 2e macros. %% The first piece of markup in an AASTeX v5.0 document %% is the \documentclass command. LaTeX will ignore %% any data that comes before this command. %% The command below calls the default manuscript style, %% which will produce a double-spaced document on one column. %% Examples of commands for other substyles follow. Use %% whichever is most appropriate for your purposes. %%\documentclass{aastex} %% preprint produces a one-column, single-spaced document: %%\documentclass[preprint2]{aastex} \documentclass[10pt,preprint2]{aastex} %\usepackage{emulateapj5} %\usepackage{graphicx,apjfonts,emulateapj5,onecolfloat5} %% preprint2 produces a double-column, single-spaced document: %\documentclass[preprint2]{aastex} %% If you want to create your own macros, you can do so %% using \newcommand. Your macros should appear before %% the \begin{document} command. %% %% If you are submitting to a journal that translates manuscripts %% into SGML, you need to follow certain guidelines when preparing %% your macros. See the AASTeX v5.0 Author Guide %% for information. \newcommand{\vdag}{(v)^\dagger} \newcommand{\myemail}{skywalker@galaxy.far.far.away} \hyphenation{off-line} %command added by Carolann on 3/1/10 \hyphenation{mini-spiral} %% You can insert a short comment on the title page using the command below. \def\etal{{\it et al.~}} \def\ds{\displaystyle} %% If you wish, you may supply running head information, although %% this information may be modified by the editorial offices. %% The left head contains a list of authors, %% usually a maximum of three (otherwise use et al.). The right %% head is a modified title of up to roughly 44 characters. Running heads %% will not print in the manuscript style. \shorttitle{The Ionized ISM in The Central Parsec of the Galaxy} \shortauthors{Zhao et al.} %% This is the end of the preamble. Indicate the beginning of the %% paper itself with \begin{document}. \begin{document} \title{ The High-Density Ionized Gas in the Central Parsec of the Galaxy} %% Use \author, \affil, and the \and command to format %% author and affiliation information. %% Note that \email has replaced the old \authoremail command %% from AASTeX v4.0. You can use \email to mark an email address %% anywhere in the paper, not just in the front matter. %% As in the title, you can use \\ to force line breaks. \author{Jun-Hui Zhao\footnote{jzhao@cfa.harvard.edu}, Ray Blundell, James M. Moran} \affil{Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS 78, Cambridge, MA 02138} \author{Dennis Downes, Karl F. Schuster} \affil{Institut de Radio Astronomie Millim\'etrique, 38406 Saint Martin d'H\`eres, France} \author{Daniel P. Marrone\footnote{Hubble Fellow}} \affil{Department of Astronomy \& Astrophysics, University of Chicago, Chicago, IL 60637} \email{} \begin{abstract} We report a study of the H30$\alpha$ line emission at 1.3 mm from the region around Sgr~A* made with the Submillimeter Array at a resolution of 2\arcsec\ over a field of 60\arcsec\ (2~parsec) and a velocity range of --360 to +345 \kms. This field encompasses most of the Galactic center's ``minispiral.'' With an isothermal homogeneous HII model, we determined the physical conditions of the ionized gas at specific locations in the Northern and Eastern Arms from the H30$\alpha$ line data along with Very Large Array data from the H92$\alpha$ line at 3.6~cm and from the radio continuum emission at 1.3~cm. The typical electron density and kinetic temperature in the minispiral arms are 3-21$\times10^4$~cm$^{-3}$ and 5,000--13,000~K, respectively. The H30$\alpha$ and H92$\alpha$ line profiles are broadened due to the large velocity shear within and along the beam produced by dynamical motions in the strong gravitational field near Sgr~A*. We constructed a 3D model of the minispiral using the orbital parameters derived under the assumptions that the gas flows are in Keplerian motion. The gas in the Eastern Arm appears to collide with the Northern Arm flow in the ``Bar" region, which is located 0.1--0.2 parsec south of and behind Sgr~A*. Finally, a total Lyman continuum flux of $3\times10^{50}$ photons s$^{-1}$ is inferred from the assumption that the gas is photoionized and the ionizing photons for the high-density gas in the minispiral arms are from external sources, which is equivalent to $\sim250$ O9-type zero-age-main-sequence stars. \end{abstract} \keywords{Galaxy: center --- ISM: individual (Sgr~A) --- ISM: kinematics and dynamics --- ISM: recombination line --- radio lines: ISM} \section{INTRODUCTION} The Galactic center harbors a supermassive black hole (SMBH) with a mass of about $4.2\times10^6~M_\odot$ \citep{Ghez08,gill09} at the position of the radio source Sgr~A*. The inner parsec of the Galactic center region contains a rich cluster of stars, including at least 55 OB stars within the central 0.5 pc \citep{paum06}. There are several theories to explain how these stars got there. In~situ formation, as in giant molecular clouds, is improbable because of the stars' large velocity dispersion. The accretion sequence may or may not include the formation of an intermediate mass black hole in a super-dense stellar cluster that stabilizes the cluster against tidal disruption \citep{hans03}. The mystery of the formation of these stars is closely linked to the balance of mass inflow and outflow toward the Galactic center and its interaction with the source Sgr~A*. Infall of interstellar material may lead to star formation up to a certain radius from the SMBH, and the subsequent feedback from stellar mass loss may suppress further star formation. Both phenomena may determine whether Sgr~A* is in a quiescent state of the active galactic nuclei cycle \citep{loeb04}. Earlier radio recombination line (RRL) studies \citep{schw89,rob93,rob96} revealed complex structures of ionized gas, including the ``minispiral'' and ``Bar," whose dynamics remain unclear. Parts of these structures have been modeled as gas orbiting Sgr~A* \citep{schw89,sand98,paum04,voll00,lisz03, muzic07,zhao09} while other parts of the structures may be gravitationally unbound \citep{yusef98}. Another possibility is that some of the nearby stellar clusters (IRS 13 and IRS 16) have powerful winds that, with the help of gravitational focusing, create large-scale, unbound flows (e.g., \citealt{lutz93}). There are a number of limitations in the existing spectral line observations of these structures. In the~cm--radio images made with the Very Large Array (VLA),\footnote{The Very Large Array (VLA) 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.} the recombination line strength is low, the line-to-continuum ratio is low, and the bandwidth is limited, making high-velocity line wings especially difficult to detect. In the infrared, the picture given by the emission lines from the ionized gas is subject to corrections for dust extinction of $\sim$3 mag in the central parsec \citep{scov03,buch09,scho10}. A few key questions about the ionized medium associated with Sgr~A* are: \\ \noindent 1) Is the ionized material related to stars or star formation? \\ \noindent 2) Is the ionized material streaming freely in the central gravitational potential, or do other mechnisms such as stellar winds and shocks influence the dynamics? \\ \noindent 3) What are the column densities (or emission measures), densities, kinetic temperatures, and dynamics of the HII gas in the vicinity of Sgr~A* itself? In this paper, we present new observational results on the ionized gas in the central parsec of the Galaxy based on observations of the H30$\alpha$ line made with the Submillimeter Array (SMA)\footnote{The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica.} and we interpret them in combination with previous H92$\alpha$ and continuum measurements made with the VLA. Section 2 discusses the observations and data reduction. Section 3 presents our results and the modeling of the physical conditions and dynamics of the ionized gas in the vicinity of Sgr~A*. Section 4 discusses the ionizing properties and possible links to the massive star formation in the central parsec, and Section 5 summarizes the results and conclusions. We assume a distance of 8~kpc to Sgr~A* throughout the paper. At this distance, 1~pc corresponds to $24''$. \section{OBSERVATIONS AND DATA REDUCTION} \subsection{{\it SMA H30$\alpha$ Line Data}} The H30$\alpha$ line observations reported here were obtained with the SMA as part of a key project on the Galactic center in the period of 2006-2008. Our data comprise eleven tracks (Table~1). In all cases, the pointing center was the position of Sgr~A*, and the half-power beam width at the 231.901~GHz frequency of the H30$\alpha$ recombination line was 53\arcsec\ (2~parsec at the distance of Galactic center). The 2~GHz bandwidth of the SMA correlator corresponds to a velocity range of $\pm1300$ km~s$^{-1}$. Six tracks were taken in the compact array configuration, where the synthesized beam was $5.1''\times3.2''$. Five higher-resolution tracks were also acquired, four in the extended configuration ($1.5''\times1.1''$ resolution) and one in the very extended configuration ($0.7''\times0.4''$). Calibrations of the data were carried out in Miriad \citep{stw95} with the specific implementation for SMA data reduction.\footnote{http://www.cfa.harvard.edu/sma/miriad} The system temperature correction was made in post-processing to compensate for amplitude attenuation owing to the Earth's atmosphere. Using the calibrators listed in Table~1, we determined the antenna-based bandpass solutions for each observing track, and the bandpass corrections were applied to the visibility data. The flux density scale was determined from observations of planets. Phase corrections were made using the point source model of Sgr~A*, conveniently located at the center of the field, based on self-calibrations. The continuum emission was subtracted from the spectral data using the Miriad task UVLIN for both the point source ($\sim$3 Jy) and the extended emission ($\sim$3 Jy). We constructed the H30$\alpha$ line image cube with robust weighting ($R=2$) \citep{dsb95}. The synthesized FWHM beam was $1.9''\times1.5''$ (PA = 26\arcdeg). In order to compare the SMA images with the VLA images of the H92$\alpha$ line and 22~GHz continuum emission, the SMA image cube was convolved to a circular beam of 2\arcsec. The intrinsic resolution of the correlator was 3.2~MHz, or 4.2~\kms. We smoothed the spectra to a resolution of 15~\kms\ with a Miriad task. For this paper, we selected the velocity range of --360 to +345~\kms\ for analysis. We found no significant emission beyond this range. The rms noise level of each channel image was 7 mJy. The image of the integrated H30$\alpha$ line is shown in Figure 1 along with spectra in the directions of known infrared sources. Figure 2 shows the distribution of radial velocities determined from fitting the peak velocities of the H30$\alpha$ line profile in the central $40''$ of the field. Notice the large velocity gradients along the Northern and Eastern Arms. The Western Arc does not show well in the SMA H30$\alpha$ data because most of the line emission is below the SMA's 4$\sigma$ sensitivity limit. It is detected, however, in single-dish H30$\alpha$ data taken with the IRAM 30m telescope. \subsection{\it VLA H92$\alpha$ Line Data} The detailed calibrations and imaging of the H92$\alpha$ line data have been described by \cite{zhao09}. They used the line image cube convolved to a circular beam ($\theta_{\rm FWHM}=2$\arcsec), the same size as that of the H30$\alpha$ line cube. Figure~3 shows a comparison of the spectra of the H92$\alpha$ and H30$\alpha$ lines toward selected regions containing IR sources. Table 2 lists the line fluxes and their ratios in these spectra. \subsection{{\it Continuum Data at 22~GHz}} The continuum image at 22~GHz was obtained with the VLA high-resolution (A and B arrays) data set of 2005 described in \cite{zhao09} and the VLA archival data sets observed in C and D arrays during 2004 and 2005. The data reduction procedure described in \cite{zhao09} was followed. Sgr~A* and the X-ray transient source (J174540.0290031) 3\arcsec~south of Sgr~A* were removed from the visibility data prior to imaging. The image of continuum emission was constructed from the visibility data with a long-baseline cutoff ($\le100~{\rm k}\lambda$) to achieve a synthesized FWHM beam of $1.95''\times1.41''$. The dirty image was cleaned with the Clark--Steer hybrid algorithm and convolved to a FWHM beam of $2''$, for comparison with other data at the same resolution. \subsection{{\it IRAM H30$\alpha$ Line Data}} We also used additional H30$\alpha$ data taken with the HERA multibeam receiver on the IRAM 30m telescope, with 11\arcsec\, beams, in order to calculate the global parameters for the region. Based on the intensity of integrated H30$\alpha$ line emission in a lower-angular-resolution ($\sim4''$) image constructed by combining the SMA data with the IRAM 30m data, we separated Sgr~A West into two components: A, the bright minispiral features of the Northern and Eastern Arms ($\int S_{{\rm H}30\alpha}dV\ge5$ Jy beam$^{-1}$ \kms) that trace the high-density ionized gas, and B, the residuals of Sgr~A West after subtracting the emission from A. These results are in Table~2. \section{RESULTS} \subsection{{\it Physical Conditions of the Ionized Gas in the Central Parsec}} The overall radio properties of the observed region (Sgr~A West; $80''\times45''$) determined from the H30$\alpha$, H92$\alpha$, and 22-GHz continuum images are summarized in Table 2. \subsubsection{Distribution of H30$\alpha$ Line Emission and IR Sources} Figures 1 and 2 show the H30$\alpha$ line data in the central parsec. Figure~3 shows a comparison between the SMA H30$\alpha$ and the VLA H92$\alpha$ line spectra in the direction of selected IR sources. For optically thin gas in local thermodynamic equilibrium (LTE) with no pressure broadening, the ratio of line peak intensity is $\displaystyle {R^{\rm H30\alpha}_{\rm H92\alpha}\equiv {S_{\rm H30\alpha}/ S_{\rm H92\alpha}} \approx {\nu_{\rm H30\alpha}/\nu_{\rm H92\alpha}}} \approx 28$. A detailed comparison of the H30$\alpha$ line spectra from the SMA and the H92$\alpha$ line spectra observed with the VLA yields line ratios in most of the regions that are close to the expected LTE ratio, suggesting that the ionized gas in the central parsec is optically thin and under LTE conditions. In some regions, however (e.g., IRS 1W, 10W, 16 and 33), the observed ratios show significant departure from the expected LTE ratio. \subsubsection{Distribution of T$_e^*$} The equivalent electron temperature, $T_{e}^*$, derived from the ratio of line-to-continuum emission under the assumption that the optically thin gas is in LTE, can be estimated from our measurements. In order to avoid contamination from both the dust emission, which becomes dominant at higher frequencies, and significant synchrotron emission at lower frequencies, we used the continuum data at 22~GHz, where the contributions from both the synchrotron and thermal dust emission are negligible relative to the free-free emission. Figures 4a and 4b show the integrated H30$\alpha$ line image and radio continuum image at 22~GHz, respectively. We assume that the continuum emission at 22~GHz is entirely due to optically thin free-free emission and scale its intensity to 231.9~GHz, according to the power law $\nu^{-0.1}$, i.e., a factor of 0.79. Using Equation (1) below \citep{wils09}, we determined the value of $T_e^*$, \begin{eqnarray} {T_e^*\over K} &=&\Bigg[ {6985 \over a(\nu, T_e)} \left(\nu\over {\rm~GHz}\right)^{1.1} {1\over {1+N(He)/N(H)}} \nonumber \\ & &\left(S_{C}\over {S_{L} \Delta V_{{\rm FWHM}}} \right) \Bigg]^{0.87}~~, \end{eqnarray} where $\nu$ is the frequency; $S_L$ is the line flux density; $S_C$ is the continuum flux density; $\Delta V_{\rm FWHM}$ is the line width (FWHM), and only Doppler broadening is involved; $N(He)/N(H)$ is the number density ratio, which we take to be 0.08; and $\alpha(\nu, T_e)\sim0.97$ (at $\nu=22$~GHz and $T_e$, the electron temperature, $\sim10^4$~K) is the correction to the \cite{mezger67} power-law approximation. The angular distribution of $T^*_e$ is shown in Figure~4c. $T^*_e$ varies from 7,000 K to 10,000 K in most regions of Sgr~A West. However, in the Bar region (e.g., IRS~2L, IRS~12N, IRS~13E, IRS~33), 3\arcsec~SE of Sgr~A*, $T^*_e$ increases to $\sim15,000$~K. The significant increase of $T^*_e$ in the Bar has also been derived from line observations of H92$\alpha$ \citep{rob93} and H66$\alpha$ \citep{schw89}. \subsubsection{Isothermal Homogeneous HII Model} Since the observed quantities of line and continuum intensities depend on the density, temperature, and path length of HII gas, we can construct a model and fit the data to it over a wide frequency range in order to determine the parameters of the ionized gas. In particular, with the high-resolution data obtained from interferometer observations, uncertainties due to variations in structure and the physical parameters across the source are substaintially reduced. Thus, the results from such an analysis become more reliable. Models for RRL emission from the nuclear region of external galaxies have been discussed by \cite{pux91,ana93,ana00,zhao96,zhao97,pho98}; and \cite{rodr04}. They found that the main constraints for the models are the integrated RRL strength at multiple frequencies and the observed radio continuum spectrum. The observed quantities (line and continuum intensities) depend in a nonlinear way on the distribution of $T_e$ and $n_e$, the electron density, both along the line of sight and across the telescope beam. In the cases of the extragalactic nuclear regions, at a given frequency, the line emission often arises from HII components under the physical conditions that are particularly favorable at this particular frequency. Usually, multiple collections of HII regions with different physical parameters are required to fit the observations. Both the SMA and VLA data achieve angular resolution (2\arcsec, $\sim0.1$~pc) adequate to resolve the $\sim1$~pc minispiral structure. The effects due to changes of physical parameters across the source are therefore less significant. However, the electron temperature and density could possibly change along the line of sight; $T_e$ and $n_e$ derived from the simple isothermal and homogeneous model correspond, therefore, to average physical properties of the HII gas in the telescope beam. If the HII gas in the beam along the path length is isothermal and homogeneous, then the line and continuum flux densities from a region subtending a solid angle $\Omega$ are given by (e.g., \cite{shaver75}), \begin{eqnarray} S_L&=&{2k\nu^2\over c^2} \Omega T_e \Bigg[\left(\tau_L/\beta_n +\tau_C \over \tau_L + \tau_C \right) \nonumber \\ & &\left(1-e^{-(\tau_L+\tau_C)}\right) -(1- e^{-\tau_C})\Bigg]~~, \end{eqnarray} and \begin{equation} S_C = {2k\nu^2\over c^2} \Omega T_e(1- e^{-\tau_C})~~, \end{equation} \noindent where $k$ is Boltzmann's constant, $c$ is the speed of light, and the line ($\tau_L$) and continuum ($\tau_C$) optical depths are given by \begin{eqnarray} \displaystyle \tau_L &\approx& 575 b_n\beta_n \left(\nu\over {\rm~GHz}\right)^{-1} \left(n_e\over {\rm~cm}^{-3}\right)^2 \nonumber \\ & &\left(Lf_V \over {\rm pc}\right)\left(T_e\over {\rm K}\right)^{-5/2} \left(\Delta V_{{\rm D}}\over {\rm km~s}^{-1}\right)^{-1} \nonumber \\ & &\left(1+1.48{{\Delta V_P}\over{\Delta V_D}}\right)^{-1}~~, \end{eqnarray} \noindent and \begin{eqnarray} \displaystyle \tau_C &\approx& 0.08235 \left(n_e\over {\rm~cm}^{-3}\right)^2 \left(Lf_V\over {\rm pc}\right) \left(\nu\over {\rm~GHz}\right)^{-2.1} \nonumber \\ & & \left(T_e\over {\rm K}\right)^{-1.35} a(\nu,T_e)~~, \end{eqnarray} \noindent respectively. $b_n$ and $\beta_n$ are the population departure coefficients; $n_e$ is the electron density; $\Delta V_{\rm D}$ and $\Delta V_{\rm P}$ are the FWHM Doppler and pressure line widths in \kms, respectively; $L$ is the path length; and $f_V$ is the volume filling factor. Note that the last factor in Equation (4) provides a convenient approximation for the transition between the pure Doppler and pure pressure-broadened cases. The Doppler broadening has a thermal and turbulent component and is given by \begin{equation} \displaystyle \Delta V_{\rm D} = \sqrt{{8{\rm ln(2)}kT_e\over M_{\rm H}}+ (\Delta V_t)^2}~~, \end{equation} \noindent where $M_{\rm H}$ is the mass of hydrogen, and $\Delta V_t$ is the turbulent width, which here includes microscopic turbulence and dynamical velocity gradients. In the central parsec, the thermal width ($\Delta V_{\rm th}=\sqrt{{8{\rm ln(2)}kT_e\over M_{\rm H}}}$) is less than the turbulent width ($\Delta V_t$). The line width due to pressure broadening, computed by \cite{brock71}, is given by \begin{equation} \displaystyle \Delta V_{\rm P} = 1.7\times10^{-18} {n_e\over T_e^{0.1}} N^{7.4}~{\rm km~s^{-1}}~~, \end{equation} where $N$ is the principal quantum number of the transition. The total line width is approximately the quadratic sum of $\Delta V_{\rm D}$ and $\Delta V_{\rm P}$, \begin{equation} \Delta V_{\rm FWHM} \cong \sqrt{(\Delta V_{\rm D})^2 + (\Delta V_{\rm P})^2}~~. \end{equation} $\Delta V_{\rm FWHM}$ is an observable quantity. We solved for the parameters $T_e$, $n_e$, $\Delta V_t$, and $Lf_V$ for each point in the image in the following way. Since $\Delta V_{\rm P}\ll\Delta V_{\rm th}<\Delta V_t$ for reasonable values of $T_e$ and $n_e$, we assume initial values of $T_e$ and $n_e$, and solve for $\Delta V_t$ via Equations (6)--(8). We computed the values for $b_n$ and $\beta_n$ for the assumed values of $T_e$ and $n_e$ using the NLTE code of \cite{gordon02}, which followed the analysis of \cite{walmsley90}. We then formed the flux density ratios $\displaystyle {R^{\rm H30\alpha}_{\rm 22GHz}\equiv {S_{\rm H30\alpha}/ S_{\rm 22GHz}}}$, $\displaystyle {R^{\rm H92\alpha}_{\rm 22GHz}\equiv {S_{\rm H92\alpha}/ S_{\rm 22GHz}}}$, and $\displaystyle {R^{\rm H30\alpha}_{\rm 92\alpha}\equiv {S_{\rm H30\alpha}/ S_{\rm H92\alpha}}}$. The use of these ratios eliminates the solid angle $\Omega$ in Equations (2) and (3). At each point in the image, we used these ratios to solve for $T_e$, $n_e$, and $Lf_V$. We then iterated the process, i.e., solved for a new estimate of $\Delta V_t$ with these values of $T_e$ and $n_e$. The process converged in a few iterations. The parameters derived for the line of sight for each of the regions are summarized in Table 3. Instead of $Lf_V$, we report the emission measure ($EM= n_e^2Lf_V$). The ratio $T_e/T_e^*$ is given in column 6, which mainly corrects for the effect due to underpopulated electrons at the level $N=30$ as compared to that expected under the LTE; the ratio $\Delta V_t / \Delta V_{\rm FWHM}$ in column 7; and $\Delta V_{\rm P}^{\rm H92\alpha} / \Delta V_{\rm D}^{\rm TH}$, the ratio of the H92$\alpha$ line width of pressure broadening to that of thermal Doppler broadening, in column 8. The pressure broadening term ($\Delta V_{\rm P}^{\rm H30\alpha}$) is negligible. The uncertainties in the physical parameters mainly come from the uncertainties in the measurements. Although the relation between the physical parameters and observable quantities is nonlinear, we assess the errors through linear approximation. We use the optically thin assumption, which appears to be valid at the frequencies used in this paper. The fractional uncertainty in $T_e$, which is proportional to the fractional uncertainties of the measured ratios, $\displaystyle {R^{\rm H30\alpha}_{\rm 22GHz}}$ and $\displaystyle R^{\rm H30\alpha}_{\rm H92\alpha}$, lies in the range from 7\% for IRS 1W to 39\% for IRS 12N. The fractional uncertainty in $n_e$ is dominated by those of observed line ratios $\displaystyle R^{\rm H30\alpha}_{\rm H92\alpha}$ and ranges from 6\% for IRS~1W to 36\% for IRS~12N. The variations of the H30$\alpha$ line intensities reflect the changes of excitation conditions in the region. Our model fitting suggests that, given similar solutions in $n_e$ and $T_e$, the large difference in the H30$\alpha$ line intensity between the two extreme regions (IRS 1W and IRS 7) is mainly due to the difference of the emission measure (EM) or the path length along the line of sight (see Table 3). In short, the line ratio of H30$\alpha$ to H92$\alpha$ varies from 15$\pm$4 to 32$\pm$4. The derived mean values of the line optical depth are $\overline{\tau}_L{\rm (H30\alpha)} = -0.001$ and $\overline{\tau}_L{\rm (H92\alpha)} = -0.006$ with standard deviations of $\sigma_{\tau_L{\rm (H30\alpha)}}=0.0004$ and $\sigma_{\tau_L{\rm (H92\alpha)}}=0.005$ from the corresponding emission regions. The free-free optical depth at the H30$\alpha$ line frequency $\tau_C{\rm (231.9~GHz)}$ varies from 1$\times10^{-4}$ to 1$\times10^{-5}$ while $\tau_C{\rm (8.3~GHz)}$ is in the range between 0.16 and 0.01. Because of the small optical depths in both line and continuum, the non LTE effects in the minispiral, in general, are not critical. There is a diffuse nonthermal synchrotron component in the central parsec region \citep{ekers83}. Based on the flux density of 22 Jy at 20~cm in the central $40''\times70''$ from \citet{ekers83}, we estimated that the contribution to the continuum flux density in a 2\arcsec~beam is $\sim$10 mJy under the assumption that the nonthermal spectral index $\alpha\sim-0.5$ ($S_\nu\propto\nu^\alpha$) and the emission are evenly distributed. The optical depth of the H92$\alpha$ line is small ($\tau_L\sim -0.01$). The contribution from the stimulated H92$\alpha$ emission of $\sim0.1$ mJy is insignificant in the regions discussed in this paper. The contribution from the stimulated line emission by the dust emission at 232~GHz is negligible because of the small optical depth of the H$30\alpha$ line. The observed line widths of the HII gas in the minispiral arms at the Galactic center are dominated by $\Delta V_t$, which is consistent with velocity gradients due to gas motion around Sgr~A* or the SMBH being primarily responsible for the broadening in the line profiles observed in the 2\arcsec\ beam. \subsubsection{Northern and Eastern Arms} The ionized gas of the high-density components in the Northern and Eastern Arms has a mean kinetic temperature of $\overline T_e\approx 6\times10^3$ K and an electron density of $ n_e$ in the range of $10^{4-5}$~cm$^{-3}$, which is consistent with the values ($10^4$~cm$^{-3}$) derived from Pa$\alpha$ line emission at 1.87 $\mu$m \citep{scov03} for a given uncertainty in extinction corrections in the near IR. The HII gas properties in the Northern and Eastern Arms are similar to these in HII regions around young and/or evolved massive stars. \subsubsection {The Bar} We confirm that the ionized gas in the Bar (e.g., IRS~2L, IRS~12N, IRS~13E, and IRS~33 in Table 3) appears to have a higher kinetic temperature in the range of $8.5\times10^3$K $\le T_e\le1.3\times10^4$K, as suggested by earlier RRL observations \citep{rob93}. The electron density shows a range from a few times 10$^4$ to a few times 10$^5$~cm$^{-3}$. The heating process may be complicated in the Bar because of complex gas interactions. There are several energy sources in the region. First, strong winds from the central stellar clusters such as IRS 16 and IRS 13 could provide kinetic energy to compress the ionized gas in this region. The heating due to the interaction between the winds and the ionized gas in the Bar likely occurs in the regions localized to the cluster sources. In addition, the well-known minicavity (marked with the gray circle in Figures 4a and 4b), a region depressed of radio continuum, is located 3.5\arcsec~SW of Sgr~A* \citep{yusef89}. This region is likely created by a fast wind outflow from the sources in the vicinity sweeping up the gas in the orbiting ionized streams, as suggested by the morphology of a bright [FeIII] line in the infrared \citep{lutz93}. However, the minicavity is a few arcsec displaced from the high-kinetic-temperature region, which in fact is best seen as a depression associated with H30$\alpha$ line emission. The minicavity can also be explained by \cite{melia96} as a downstream, focuced flow due to the accretion by the SMBH at Sgr A*. Alternatively, the high temperature in the Bar could result from a collision between two ionized orbiting flows, as suggested in the dynamical model of \cite{zhao09}. A computation using their Keplerian orbital model (see Section 3.2) shows that the specific kinetic energy reaches a maximum (see Figure~4d) in the Bar region where high kinetic temperatures (see Figure~4c) are observed. The distribution of specific kinetic energy (Figure~4d) shows a substantial increase from $2\times10^{14}$ erg~g$^{-1}$ at a region near IRS~5 in the Northern Arm to $12\times10^{14}$ erg~g$^{-1}$ at IRS~33 in the Bar. However, we note that a high kinetic energy of the orbiting flow does not have to correspond to a high kinetic temperature; the ionized flows can release their kinetic energy to shocks if the ionized flows collide with each other. If they collide with the strong stellar winds from the clusters of stars in the Bar area, then the gas could be heated by the shocks to higher temperatures. In addition, the model also shows that the ionized flows of the Northern and Eastern Arms do collide at the region with high kinetic temperatures (see Figure~21d of \cite{zhao09} and the 3D structure of the minispiral arms in Figure~5). The observed high kinetic temperatures in the Bar suggest that the ionized gas could be further heated by the shocks generated from the collision. \subsection{{\it Kinematics and Dynamics}} Kinematics of the ionized gas in both the Northern Arm and Western Arc have been explained as Keplerian circular motion of a circumnuclear ring \citep{schw89,lacy91,voll00,lisz03}. Based on the VLA observations of H92$\alpha$, \cite{rob93} found that the ionized ring consists of three separated kinematic components, the Western Arc, Northern Arm, and Bar. The radial velocities of the Western Arc can be fitted with a Keplerian model with circular motion. Using the observations of the Brackett-$\gamma$ line, \cite{paum04} found that the kinematics of the ionized gas in the Northern Arm can be explained as a bundle of elliptical orbits. In addition, the Eastern Arm may be interrupted by a high-velocity component ``tip''. Also, the Bar component extends to the IRS6/34 region which is affected by two other kinematic features, the ``Western Bridge'' and the ``Bar Overlay.'' The VLA observations of the H92$\alpha$ line suggest that the loci of the three minispiral arms can be fitted with three families of elliptical orbits; the orbits of both the Northern and Eastern Arms have high eccentricities while the Western Arc is in nearly circular motion \citep{zhao09}. The VLA measurements of the proper motions and the radial velocity resolved the degeneracies in the inclination angles, suggesting that the two ionized flows from the Northern and Eastern Arms collide in the Bar region. On the other hand, \cite{muzic07} suggested that the non-Keplerian motions might be important in the kinematics of the filaments observed near Sgr A*. In addition, \cite{voll00} noticed that a substantial amount of velocity dispersion along with additional inwards radial motion is required in order to fit the observed velocities of the ionized flows with their Keplerian circular-orbit model. \subsubsection{3D View of the Minispiral Structure and the Circumnuclear Disk} Using the Keplerian model described in \cite{zhao09} along with the orbital parameters derived from fitting the VLA H92$\alpha$ data and proper motion measurements, we recomputed the 3D locations of the three ionized arms. Figure~5 shows a 3D visualization of the three ionized flows in the Northern, Eastern, and Western Arms (Arc), which illustrates that the Northern Arm and Western Arc are nearly coplanar based on the similar longitudes of their ascending nodes ($\Omega$) and inclination angles ($i$) derived from fitting the loci of the ionized flows. The mean values of the two orbital angles, $\overline \Omega=71\arcdeg\pm6$\arcdeg~and $\overline i=119\arcdeg\pm3$\arcdeg, are inferred for the two coplanar orbits (Northern Arm and Western Arc), which form the ionized ring. The orbital plane of the ionized flows appears to be aligned with the plane of the circumnuclear disk (CND) derived by \cite{gust87} from molecular line observations. If the fitted parameters from both the molecular lines \citep{gust87} and hydrogen recombination lines \citep{schw89,lacy91,rob93,voll00,lisz03,zhao09} are correct, the Keplerian motions dominate the kinematics in the central parsec, and the plane of the main nuclear gaseous disk or the CND can be described by the mean orbital angles inferred above. Therefore, the orbital plane of the Eastern Arm ($i=122\arcdeg\pm5\arcdeg$ and $\Omega=-42\arcdeg\pm11\arcdeg$) is nearly perpendicular to that of the CND. Figure~5 shows that the Eastern Arm flow runs into the CND from the northeast and the near side with respect to Sgr~A* and collides with the Northern Arm flow in the region located south and behind Sgr~A*. \subsubsection{Kinematics and Keplerian Motions} Figure~6 shows the spectra taken from 12 positions along each of the two ionized arms (shown in Figure~7). The observed spectra are compared with the radial velocities (green bars) derived from the Keplerian model. Note that we assume that the LSR velocity of the black hole, $V_z$, is 0 to within $\pm$ 5 km s$^{-1}$ (see discussion in \cite{gill09}). In general, the kinematics of the ionized gas follow the Keplerian orbital motion expected for the gravity of the SMBH ($4.2\times10^6~M_\odot$) at Sgr~A*. Models of the enclosed mass (see \citealt{okf09}) show that the added enclosed mass starts to rise above the black hole's mass starting at a radius of 0.3 pc (7\arcsec) from Sgr A*. At a radius of 1 pc (24\arcsec) from Sgr A*, near the tip of the minispiral seen in projection, the enclosed mass has nearly doubled, to about $8\times10^6~M_\odot$. Thus, for a given circular orbit with a radius of 1 pc the actual orbital velocity would be about 1.4 times higher than in a pure Keplerian approximation based on the mass of the black hole only. Apart from this effect, however, in several regions the radial velocities deviate even more significantly from those predicted from the Keplerian model. \subsubsection{Non-Keplerian Components} In the northwest end of the Eastern Arm near the location E17 (Figure~7a), a feature with radial velocities blue-shifted up to $\sim -200$~\kms\ shows a large deviation from the value of $\sim-100$~\kms\ predicted by the Keplerian model (Figure~6). From \cite{paum06}, we find that at least five massive stars---IRS 34W (Ofpe/WN9), IRS 34E (O9--9.5I), IRS 34NW (WN7), IRS 7SW (WN8), and IRS 3E (WC5/6)---are located in a region with a radius of 2.2\arcsec\ (indicated with a large black circle near region E16 in Figure~7a), referred to as IRS 34 hereafter. Except for IRS 3E, which has no proper motion measurements, the proper motion data of the remaining four stars \citep{paum06} show that the stars all move southwest toward the ionized flow with a mean transverse velocity of 185 \kms\ (PA = --134\arcdeg) (as shown by an arrow in Figure~7a). We compare the radial velocity of the stars with the spectrum (inset c in Figure~7a) of the H30$\alpha$ line emission integrated from the IRS 34 region. The four stars besides IRS 3E show negative radial velocities in the range \hbox{--150} \kms\ to \hbox{--340} \kms, which is blue-shifted with respect to the peak velocity ($-146\pm4$ \kms) of the broad ($\Delta V_{\rm FWHM}=160\pm8$ \kms) spectral feature. The stellar winds from the Wolf-Rayet (WR) stars, evolved from early type O-stars with mass loss rate of 10$^{-5}~M_\odot$ yr$^{-1}$, appear to play a considerable role in the local kinematics. The strong stellar winds with velocities up to a few times 10$^{3}$ \kms~could sweep up the ionized flow of the Eastern Arm, causing the peculiar velocities and the velocity gradient across the Eastern Arm at the northwest end. In fact, the motions of the filaments associated with the minispiral found by \citep{muzic07} in infrared also suggest that a model of purely Keplerian motions of the gas is inadequate and the filaments could be due to the interaction of a fast wind with the minispiral. In the tip region \citep{paum04} with peculiar radial velocity that deviates signficantly from the Keplarian velocity by +150 \kms\ (see panel E12 in Figure~6 and Figures 7a and 7b), there is also a WN8 star, IRS 9W. The radial velocity (+140 \kms) of IRS 9W \citep{paum04} is similar to that of ionized gas in the Eastern Arm. A comparison between the stellar transverse velocity of 215 \kms\ (PA = 51\arcdeg) and that of 304 \kms\ (PA = --67\arcdeg) predicted from the Keplerian model for the ionized flow at the location of IRS 9W suggests that the star does not follow the orbit of the Eastern Arm but may run across the Eastern Arm. Then, the high-radial velocity tip is likely to be the part of the gas in the ionized flow that is compressed and accelerated by the suspected strong wind from the IRS 9W star. The velocity discontinuity at the tip may be evidence for the presence of shocks in the region. In addition, deviations from Keplerian motions are also observed in the Bar region. The non-Keplerian kinematics could be attributed both to the interaction between the ionized flows in the Northern and Eastern Arms and to the interaction of the ionized flows with the strong winds from the massive star clusters (the IRS 16 and IRS 13 clusters, for example). Well-organized polarized emission from magnetically aligned dust grains in the central parsec has been observed \citep{aitk91,aitk98,glas03} suggesting a magnetic field strength of $\geq$2 mG. The corresponding energy densities in the magnetic fields are $\sim1.6\times10^{-7}$ erg cm$^{-3}$, about twice larger than the thermal energy densities in the ionized gas ($T_e\sim7\times10^{3}$ K and $n_e\sim6\times10^{4}$ cm$^{-3}$ at IRS 1W) but two orders of magnitude less than the kinetic energy densities of the orbital motions. The magnetic fields frozen in the ionized streamers can not substantially alter the bulk motions of the gas but produce some cumulative magnetohydrodynamic (MHD) effects, such as orbital compression of the streamers as implied from the observed evidence for the convergence of field lines near Sgr A* \citep{glas03}, and a helix of a natural morphology for a twisted magnetic field frozen into a plasma as observed in the Northern Arm \citep{yusef89,zhao09}. In the region close to Sgr~A*, the magnetic field probably becomes stronger, and the MHD effects may also play a significant role in the kinematics of the ionized flows. An interesting anomalous feature located $\sim2''$~northwest of Sgr~A* can be seen in the integrated H30$\alpha$ line intensity image (Figure~1). The radial-velocity image (Figure~2) indicates a large velocity gradient across this feature. The H30$\alpha$ line spectrum (inset d in Figure~7) suggests that this feature is composed of at least three spectral components ($\geq4\sigma$) at radial velocities of 160 \kms, 39 \kms, and --250 \kms, with a line width of $\sim50$~\kms, a typical velocity width of the ionized gas in the minispiral arms. We note that there is a compact continuum source called $\varepsilon$ \citep{yusef91}, located 1\arcsec~south of this anomalous feature, corresponding to a hole in the H30$\alpha$ line images (e.g., Figure~7a and Figure 1). The source $\varepsilon$ appears to be moving away from Sgr~A* with a transverse velocity of 340 km s$^{-1}$ \citep{zhao09}, which has been interpreted as the confluence of gravitationally focussed winds from the IRS 16 cluster \citep{ward92}. The H30$\alpha$ line property of the anomalous feature appears to be consistent with the focused-wind model, suggesting that the velocity components in the anomalous feature correspond to ionized blobs of the minispiral arms that have been blown out of the region $\varepsilon$ due to the high pressure of the confluent stellar winds. However, given the closeness to Sgr~A*, the detection of this feature needs to be further confirmed with higher-sensitivity observations. Finally, in the locations with large angular offsets from Sgr~A*, we noticed that the deviations in radial velocity from the Keplerian motions become significant for the Northern Arm ($>50$ \kms), as shown in both Figures 6 and 7, while for the Eastern Arm, the deviations are less significant. The difference in the deviation of the observed radial velocities from the Keplerian velocities between the Northern and Eastern Arms suggests that the distribution of mass has a preference for the plane of the CND. \section{IONIZATION} \subsection{\it The High-Density Gas in the Northern and Eastern Arms} We have shown that the H30$\alpha$ lines observed with the SMA are excellent tracers of the high-density HII components in the Northern and Eastern Arms. Based on the observations and derived physical parameters, we can estimate the ionizing photon rate ($Q=n_e^2\alpha_BV$) required for maintaining the ionizations in these regions for the case where the ionized gas is optically thick in the Lyman lines and where $\alpha_B$ is the ionization coefficient, and $V\approx\Omega D^2Lf_V$ is the volume of the ionized clumps. The ionizing photon rate can be written as \begin{eqnarray} Q(H) &=& 1.31\times10^{45} \left[\alpha_B(T_e)\over\alpha_B(10^4~{\rm K})\right] \nonumber \\ &&\left[\theta_B\over {\rm ~arcsec}\right]^2 \left[n_e \over 10^4 {\rm ~cm^{-3}}\right]^2 \left[D \over 8 {\rm ~kpc}\right]^2 \nonumber \\ && \left[Lf_V\over 10^{-3} {\rm ~pc}\right]~{\rm phot.~s}^{-1} ~~, \end{eqnarray} where $\theta_B$ is the resolution of the observations (beam) with the assumption that source fills the beam; and $\alpha_B(T_e)$, the total recombination coefficient to excited levels, is given by \cite{humm63}. We calculated the values of the inferred ionizing photon flux required to maintain the ionization of the high-density components in the Northern and Eastern Arms as well as the HII mass ($M_{\rm HII}$) and excitation parameter ($U$). On the assumption that the HII gas is internally ionized, the equivalent zero-age main sequence (ZAMS) star that is the ionizing source was estimated. The internal-ionization model requires at least $\sim25$ O9-type stars embedded and roughly evenly distributed in both the Northern and Eastern Arms. \subsection{Ionizing Sources} We now examine where the known OB stars lie in the region. Figure~8 shows the 90 massive stars within a radius of 14\arcsec~(0.5 pc) of Sgr~A* identified by \cite{paum06}, among which 55 are OB stars. The 14 OB stars within a radius of 0.85\arcsec\ (0.03 pc) from Sgr~A* are known as S stars. No obvious correlations appear between the location of 41 OB stars outside the radius of 0.85\arcsec~and the distribution of the high-density HII gas in the minispiral arms on the projected plane. If we assume the average solid angle for the minispiral subtended to be $\Omega_s$, then the required number of ionizing photons from the stars will be \begin{eqnarray} Q^*(H)=Q(H)(4\pi/\Omega_s)~~. \end{eqnarray} If we assume $4\pi/\Omega_s\sim10$, then 250 O9-type stars are required. For the lower-density ($\overline {n}_e\sim 8\times10^2$~cm$^{-3}$) component B, the ionized mass of $\sim340~M_\odot$ is inferred, requiring a Lyman photon flux of $1.2\times 10^{50}$ phot. s$^{-1}$ or $\sim$100 O9-type stars (ZAMS). The 250 O9-type stars required for externally maintaining the ionization of the minispiral appear to be adequate in supplying the leaking Lyman photons from the minispiral to further ionize the lower density component that pervasively distributes in the region. Thus, the ionizing source to maintain the ionization state of Sgr~A West is equivalent to $\sim$250 O9-type stars (ZAMS). Considering that a substantial amount of the ionizing photons can be produced by the hot evolved massive stars and the survey of \cite{paum06} is incomplete, there may be enough stars to ionize the region. The origin of the ionized minispiral arms and the birthplace of the massive stars found in the central parsec are still matters of conjecture. There are two possible models that may explain the presence of the massive stars near the SMBH. First, the stars formed elsewhere outside the central parsec and migrated to the Galactic center \citep{gerh01}. However, compared with the age of the massive stars in the central parsec, it takes too long for stars to move to the center from several parsec away by losing their orbital energy through dynamical friction \citep{porte03,kim03}. Alternatively, the stars may have formed near the SMBH by an unusual astrophysical process, such as the fragmentation of a massive disk rotating near the SMBH \citep{nayak07}. Recent modeling and numerical simulations \citep{nayak07,ward08,br08} show that for an infalling giant molecular cloud (10$^{4-5}~M_\odot$) interacting with an SMBH (\hbox{1--$3\times10^6~M_\odot$}), a small fraction of the gas cloud becomes bounded to the black hole, forming an eccentric disk that quickly fragments to form stars. The tidal disruption of the self-graviting clouds formed coherent spiral structures, i.e., the minispiral arms, which are ionized by the Lyman continuum photons produced from the newly formed massive stars. \section{SUMMARY AND CONCLUSION} We report results from the SMA observations of the H30$\alpha$ line emission from the Galactic center at a resolution of 2\arcsec. We measured the velocity profiles over the central $60''$ (2 parsec) region around Sgr~A*. We carried out an analysis of the line and continuum data based on an isothermal homogeneous HII model for each component. With the constraints from the SMA H30$\alpha$ data at 1.3 mm and the VLA H92$\alpha$ data at 3.6~cm and continuum data at 1.3~cm, we determined the physical conditions of ionized gas in the Northern and Eastern Arms of the minispiral. We found that the typical electron density and kinetic temperature in the arms are \hbox{3--$21\times10^4$~cm$^{-3}$} and 5,000--13,000 K, respectively. The highest density of $2.1\times10^5$~cm$^{-3}$ occurs in the IRS 13 region. Higher temperatures up to 13,000 K are found in the Bar region. Both the H30$\alpha$ and H92$\alpha$ line profiles are broadened due to large velocity gradients along the line of sight and across the $2''$ beam produced by the dynamical motions near Sgr~A*. For the H92$\alpha$ line, the line width due to pressure broadening appears to be comparable to that of thermal Doppler broadening, while for the H30$\alpha$ lines, the pressure broadening is negligible. Using the orbital parameters derived under the assumption that the three minispiral flows are in Keplerian motion, we calculated the 3D geometry of the minispiral structure. We showed that the ionized flows of Northern Arm and Western Arc are almost coplanar, and the plane of the ionized flow in the Eastern Arm is nearly perpendicular to that of the Northern Arm and Western Arc. The Eastern Arm flow collides with the Northern Arm flow in the Bar region located 0.1--0.2 parsec south of and behind Sgr~A*. The high kinetic temperature gas in the Bar is probably due to the heat in shocks generated by collisions. We compared observed radial velocities in the Northern and Eastern Arms with those computed from the Keplerian model with a mass of $4.2\times10^6~M_\odot$ of the SMBH at the position of Sgr~A*. We show that Keplerian motion dominates the kinematics of the minispiral arms. In some regions, significant deviations exist between the observed radial velocities and those computed from the Keplerian model. Near the IRS 9W and IRS 34 regions, the observed peculiar velocities in the minispiral are likely a result of the ionized gas being swept up by the strong stellar winds from nearby WR stars. A total Lyman continuum flux of $3\times10^{50}$ phot.~s$^{-1}$ is needed to maintain the ionization of the gas in Sgr~A West with an inferred ionized mass of 350~$M_\odot$, which requires $\sim$250 O9-type (ZAMS) stars. About 10\% of the total number of UV photons is required to externally maintain the ionization of the high-density gas in the Northern and Eastern Arms, which have an ionized mass of 12~$M_\odot$, less than 5\% of the total ionized mass \citep{lisz03}. \acknowledgments We are grateful to Carolann Barrett for her careful editing of our manuscript. We also thank Harvey Liszt for discussing aspects of his 2003 Keplerian model and for encouraging us to make these SMA observations. The research has made use of NASA's Astrophysics Data System. Support for DPM was provided by NASA through Hubble Fellowship grant HST-HF-51259.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. \begin{thebibliography}{} \bibitem[Aitken et al. (1991)]{aitk91} Aitken, D. K., Gezari, D., Smith, C. H., McCaughrean, M. \& Roche, P. F. 1991, \apj, 380, 419 \bibitem[Aitken et al. (1998)]{aitk98} Aitken, D. K., Smith, C. H., Moore, T. J. T. \& Roche, P. F. 1998, \mnras, 299, 743 \bibitem[Anantharamaiah et al.\ (2000)]{ana00} Anantharamaiah, K. R., Viallefond, F., Mohan, N. R., Goss, W. M., \& Zhao, J.-H. 2000, \apj, 537, 613 \bibitem[Anantharamaiah et al.\ (1993)]{ana93} Anantharamaiah, K. R., Zhao, J.-H., Goss, W. M., \& Viallefond, F. 1993, \apj, 410, 110 \bibitem[Bonnell \& Rice (2008)]{br08} Bonnell, L. A., \& Rice, W. K. M. 2008, Science, 321, 1060 \bibitem[Briggs (1995)]{dsb95} Briggs, D. S. 1995, PhD thesis, NMIMT \bibitem[Brocklehurst \& Leeman (1971)]{brock71} Brocklehurst, M., \& Leemanm, S. 1971, \apj, 9, 35 \bibitem[Buchholz, Sch\"odel \& Eckart (2009)]{buch09} Buchholz, R. M., Sch\"odel, R,\& Eckart, A. 2009, A\&A, 499, 483 \bibitem[Ekers et al.\ (1983)]{ekers83} Ekers, R. D., van Gorkom, J. H., Schwarz, U. J., \& Goss, W. M. 1983, \aap, 122, 143 \bibitem[Gerhard et al.\ (2001)]{gerh01} Gerhard, O., Kronawitter, A., Saglia, R. P., \& Bender, R. 2001, AJ, 121, 1936 \bibitem[Ghez et al.\ (2008)]{Ghez08} Ghez, A. M., et al.\ 2008, ApJ, 689, 1044 \bibitem[Gillessen et al.\ (2009)]{gill09} Gillessen, S., et al.\ 2009, \apj, 692, 1075 \bibitem[Glasse, Aitken \& Roche (2003)]{glas03} Glasse, A. C. H., Aitken, D .K. \& Roche, P. F. 2003, Astron. Nachr. 324, No. S1, 563 \bibitem[Gordon \& Sorochenko (2002)]{gordon02} Gordon, M. A., \& Sorochenko, R. L. 2002, Radio Recombination Lines. Their Physics and Astronomical Applications (Dordrecht: Kluwer) \bibitem[G\"usten et~al.\ (1987)]{gust87} G\"usten, R., Genzel, R., Wright, M. C. H., Jaffe, D. T., Stutzki, J., \& Harris, A. I. 1987, \apj, 318, 124 \bibitem[Hansen \& Milosavljevic (2003)]{hans03} Hansen, B. M. S., \& Milosavljevic, M. 2003, \apj, 593, L77 \bibitem[Hummer \& Seaton (1963)]{humm63} Hummer, D. G., \& Seaton, M. J. 1963, \mnras, 125, 437 \bibitem[Kim \& Morris (2003)]{kim03} Kim, S. S., \& Morris, M. 2003, \apj, 597, 312 \bibitem[Lacy, Achtermann, \& Serabyn (1991)]{lacy91} Lacy, J. H., Achtermann, J. M., \& Serabyn, E. 1991, \apjl, 380, L71 \bibitem[Liszt (2003)]{lisz03} Liszt, H. S. 2003, A\&A, 408, 1009 \bibitem[Loeb (2004)]{loeb04} Loeb, A. 2004, MNRAS, 350, 725 \bibitem[Lutz, Krabbe, \& Genzel (1993)]{lutz93} Lutz, D., Krabbe, A., \& Genzel, R., 1993, \apjl, 418, L244 \bibitem[Melia, Coker, \& Yusef-Zadeh (1996)]{melia96} Melia, F, Coker, R. F., \& Yusef-Zadeh, F.\ 1996, \apjl, 460, L33 \bibitem[Mezger \& Henderson (1967)]{mezger67} Mezger, P. G., \& Henderson, A. P. 1967, \apj, 147, 471 \bibitem[Muzic et al.\ (2007)]{muzic07} Muzic, K., Eckart, A., Sch\"odel, R., Meyer, L., \& Zensus, A. 2007, \apj, 469, 993 \bibitem[Nayakshin, Guadra, \& Springel (2007)]{nayak07} Nayakshin, S., Guadra, J., \& Springel, V. 2007, \mnras, 379, 21 \bibitem[Oh, Kim, \& Figer (2009)]{okf09} Oh, S., Kim, K. K., \& Figer, D. F.\ 2009, JKAS, 42, 17 \bibitem[Paumard et al.\ (2006)]{paum06} Paumard, T., et al.\ 2006, ApJ, 643, 1011 \bibitem[Paumard, Maillard, \& Morris \ (2004)]{paum04} Paumard, T., Maillard, J. P., \& Morris, M. 2004, \aap, 426, 81 \bibitem[Phookun, Anantharamaiah, \& Goss (1998)]{pho98} Phookun, B., Anantharamaiah, K. R., \& Goss, W. M. 1998, \mnras, 295, 156 \bibitem[Portegies Zwart, McMillan, \& Gerhard (2003)]{porte03} Portegies Zwart, S. F., McMillan, S. L. W., \& Gerhard, O. 2003, \apj, 593, 352 \bibitem[Puxley et~al.\ (1991)]{pux91} Puxley, P. J., Brand, P. W. J. L., Moore, T. J. T., Mountain, C. M., \& Nakai, N. 1991, \mnras, 248, 585 \bibitem[Roberts \& Goss (1993)]{rob93} Roberts, D. A., \& Goss, W. M. 1993, \apjs, 86, 133 \bibitem[Roberts, Yusef-Zadeh, \& Goss (1996)]{rob96} Roberts, D. A., Yusef-Zadeh, F., \& Goss, W. M. 1996, \apj, 459, 627 \bibitem[Rodriguez-Rico et al.\ (2004)]{rodr04} Rodriguez-Rico, C. A., Viallefond, F., Zhao, J.-H., Goss, W. M., \& Anantharamaiah, K. R. 2004, \apj, 616, 783 \bibitem[Sanders (1998)]{sand98} Sanders, R. H. 1998, MNRAS, 294, 35 \bibitem[Sault, Teuben, \& Wright (1995)]{stw95} Sault, B., Teuben, P., \& Wright, M. 1995, in ASP Conf. 77, ADASS IV, ed. R. Shaw, H. E. Payne, \& J. J. E. Hayes, 433 \bibitem[Sch\"odel et al.\ (2010)]{scho10} Sch\"odel, R., Najarro, F., Muzic, K., \& Eckart, A. 2010, A\&A, 511, A18 \bibitem[Schwarz, Bregman, \& van Gorkom (1989)]{schw89} Schwarz, U. J., Bregman, J. D., \& van Gorkom, J. H. 1989, A\&A, 215, 33 \bibitem[Scoville et al.\ (2003)]{scov03} Scoville, N. Z., et al.\ 2003, ApJ, 594, 294 \bibitem[Shaver (1975)]{shaver75} Shaver, P. A. 1975, Pramana, 5, 1 \bibitem[Vollmer \& Duschl (2000)]{voll00} Vollmer, B., \& Duschl, W. J. 2000, New Astronomy, 4, 581 \bibitem[Walmsley (1990)]{walmsley90} Walmsley, C. M. 1990, A\&A Suppl. Ser., 82, 201 \bibitem[Wardle \& Yusef-Zadeh (1992)]{ward92} Wardle, M., \& Yusef-Zadeh, F. 1992, Nature, 357, 308 \bibitem[Wardle \& Yusef-Zadeh (2008)]{ward08} Wardle, M., \& Yusef-Zadeh, F. 2008, \apj, 683, 37 \bibitem[Wilson, Rohlfs, \& H\"uttemeister (2009)]{wils09} Wilson, T. L., Rohlfs, K., \& H\"uttemeister, S. 2009, Tools of Radio Astronomy, 5th ed. (Berlin: Springer), 369 \bibitem[Yusef-Zadeh \& Morris (1991)]{yusef91} Yusef-Zadeh, F., \& Morris, M. 1991, \apjl, 371, L59 \bibitem[Yusef-Zadeh, Morris, \& Ekers (1989)]{yusef89} Yuzef-Zadeh, F., Morris, M., \& Ekers, R. 1989, in IAU Symp. 136, The Center of the Galaxy, ed. M. Morris (Norwell: Kluwer), 443 \bibitem[Yusef-Zadeh, Roberts, \& Biretta (1998)]{yusef98} Yusef-Zadeh, F., Roberts, D. A., \& Biretta, J. 1998, ApJ, 499, L159 \bibitem[Zhao et al.\ (1996)]{zhao96} Zhao, J.-H., Anantharamaiah, K. R., Goss, W. M., \& Viallefond, F. 1996, \apj, 472, 54 \bibitem[Zhao et al.\ (1997)]{zhao97} Zhao, J.-H., Anantharamaiah, K. R., Goss, W. M., \& Viallefond, F. 1997, \apj, 482, 186 \bibitem[Zhao et al.\ (2009)]{zhao09} Zhao, J.-H., Morris, M. R., Goss, W. M., \& An, T. 2009, ApJ, 699, 186 \end{thebibliography} \clearpage \onecolumn \include{figures} \include{table1} \include{table2} \include{table3} %%\include{table4} \end{document} %% %% End of file `sample.tex'.