------------------------------------------------------------------------ From: acoil@mars.berkeley.edu (Alison Coil) To: gcnews@aoc.nrao.edu Subject:astro-ph/9809068: Infalling Gas Towards the Galactic Center MIME-Version: 1.0 %astro-ph/9809068 \documentstyle[12pt,aasms4]{article} \def\solar{\ifmmode_{\mathord\odot}\;\else$_{\mathord\odot}\;$\fi} \begin{document} \raggedright \addtolength{\oddsidemargin}{0.3in} \addtolength{\evensidemargin}{0.3in} \title{\center Infalling Gas Towards the Galactic Center} \author{Alison L. Coil} \author{Paul T.P. Ho} \affil{Harvard-Smithsonian Center for Astrophysics \\ 60 Garden St. MS-78\\ Cambridge, MA 02138\\ e-mail: acoil@cfa.harvard.edu; pho@cfa.harvard.edu \\} \begin{abstract} \ \ \ \ \ VLA maps of ammonia emission were made for the Galactic Center region. The NH$_3$(1,1) and NH$_3$(2,2) transitions were observed in three 2$'$$\times$2$'$ fields covering Sgr A$^*$ and the region 3$'$ immediately south of it. In the central 3 parsecs surrounding Sgr A$^*$ we find emission which appears to be associated with the circumnuclear disk (CND), both morphologically and kinematically. This central emission is connected to a long, narrow 2 pc$\times$10 pc streamer of clumpy molecular gas located towards the south, which appears to be carrying gas from the nearby 20 km sec$^{-1}$ giant molecular cloud (GMC) to the circumnuclear region. We find a velocity gradient along the streamer, with progressively higher velocities as the gas approaches Sgr A$^*$. The streamer stops at the location of the CND, where the line width of the NH$_3$ emission increases dramatically. This may be the kinematic signature of accretion onto the CND. The ratio of the NH$_3$(2,2)/NH$_3$(1,1) emission indicates that the gas is heated at the northern tip of the streamer, located inside the eastern edge of the CND. The morphology, kinematics and temperature gradients of the gas all indicate that the southern streamer is located at the Galactic Center and is interacting with the circumnuclear region. \end{abstract} \keywords{Galaxy : center --- ISM : clouds} \section{Introduction} \ \ \ \ \ Our Galactic Center has been under increasingly intensive study of late as more sensitive instruments with higher angular resolutions are brought to bear on the region. Recent data suggest that many galactic nuclei harbor massive black holes (\cite{kor95}; \cite{fer96}; \cite{kor96}; \cite{kom96}; \cite{van97}), and there is mounting evidence that Sgr A$^*$, the strong compact radio source at the dynamical center of the Milky Way, is also a black hole with a mass of $\sim$2 10$^6$ M$\solar$ (\cite{mor96}; \cite{eck97}; \cite{gen97}). Immediately surrounding Sgr A$^*$, arc-shaped ionized gas streamers converge at the location of the proposed black hole. These streamers may originate from the inner edge of the circumnuclear disk (CND) (\cite{gen85}; \cite{har85}; \cite{ser86}; \cite{gat86}; \cite{gus87}; \cite{sut90}; \cite{mar93}; \cite{mar95}), where the gas on the inner edge is photoionized and stripped off the disk, falling in towards the nucleus. The CND is dense (10$^5$ cm$^{-3}$), clumpy, and turbulent with large line widths ($\geq$40 km sec$^{-1}$). Its inner edge is located 1.5 - 2 pc from Sgr A$^*$, and it extends beyond 7 pc. The gas is predominantly moving in a circular orbit, rotating around the nucleus at a velocity of $\sim$110 km sec$^{-1}$. However, non-circular motions are also present, and as the disk appears to be only semi-complete and the gas is highly clumped, the CND does not appear to be in equilibrium. The CND may be feeding the nucleus through the ionized streamers (\cite{gus87}), which might be infall from the CND. The question remains as to how the disk itself is fed. \newline \ \ \ \ \ Two giant molecular clouds (GMCs) lie near the Galactic Center, the ``20 km sec$^{-1}$ cloud'' (M-0.13-0.08) and the ``50 km sec$^{-1}$ cloud'' (M-0.02-0.07) (\cite{gus81}). These clouds are physically near the Galactic Center, and various studies have attempted to establish the interactions of the GMCs, the continuum Sgr A gas complex, and the CND and ionized gas streamers surrounding Sgr A$^*$ (\cite{hoe85}; \cite{lis85}; \cite{oku89}; \cite{gen90}; Zylka, Mezger, \& Wink 1990; \cite{hoe91}; \cite{ser92}; \cite{den93}; \cite{mar95}). Ho et al. (1991) map in NH$_3$(3,3) a long gas streamer which connects the 20 km sec$^{-1}$ cloud to the location of the CND. They propose that this gas streamer feeds the circumnuclear region with gas from the 20 km sec$^{-1}$ cloud. No velocity gradient along the streamer is detected within their spectral resolution of 10 km sec$^{-1}$, and no increase in line width is seen, prompting an interpretation that the gas is moving towards Sgr A$^*$ across the line of sight. Hints of this streamer are also seen in HCN (Marr et al. 1995) and submillimeter continuum emission (\cite{den93}). However, these studies also find no clear velocity gradient in the streamer along the line of sight. \newline \ \ \ \ \ In this paper we investigate the interactions between the 20 km sec$^{-1}$ cloud and the circumnuclear region in order to question how gas is drawn into the CND. We also compare the HCN information on the CND with our NH$_3$ findings. Section 2 of this paper details our NH$_3$(1,1) and NH$_3$(2,2) observations and data reduction. The results are presented in Section 3 and discussed in Section 4, while Section 5 outlines our conclusions. \newline \section{Observations and Data Reduction} \ \ \ \ \ We observed the (J,K)=(1,1) and (2,2) metastable transitions of NH$_3$ emission on the night of February 10 of 1995 with the Very Large Array (VLA) in C/D configuration.\footnote{The VLA is operated by NRAO and the Associated Universities Inc., under cooperative agreement with the National Science Foundation.} Our observing frequencies were 23.694495GHz and 23.722633GHz. We made three pointings with one field centered at ($\alpha$, $\delta$)=(17$^h$42$^m$29$^s$.3, -28$^\circ$$59'$$17''$.0), the position of Sgr A$^\ast$, and two fields centered at ($\alpha$, $\delta$)=(17$^h$42$^m$29$^s$.3, -29$^\circ$$00'$$18''$.6) and ($\alpha$, $\delta$)=(17$^h$42$^m$29$^s$.3, -29$^\circ$$02'$$18''$.6), roughly one and three arcminutes south of the first field. Our total spectral bandwidth is 12 MHz, centered at $v_{LSR}$= -10.56 km $s^{-1}$ for the northern and central field and $v_{LSR}$= 31.14 km $s^{-1}$ for the southern field. At $\lambda$=1.3 cm the field-of-view is $2'$ as determined by the primary beam of the individual antennas. The full resolution of our synthesized images is $\sim$$3''.6$$\times$$2''.1$ with a position angle of 44$^{\circ}$. Our spectral resolution is 4.9 km sec$^{-1}$. \newline \ \ \ \ \ We reduced the data within AIPS, flagging potentially bad data surrounding the amplitude and phase discontinuities in the calibrators. Our flux calibrator was 3C286, and we tracked the antenna gain and phase responses with the phase calibrator 1730-130. After calibrating the broadband data, we applied the calibration tables to the line data, using the strong quasar 1226+023 as our bandpass calibrator. The continuum emission in the northern two fields was subtracted from the line data by averaging the {\it u,v} data in several off-line channels and subtracting this from the {\it u,v} data of all of the line channels. \newline \ \ \ \ \ The data were imaged and analyzed with the MIRIAD software package. To emphasize the extended emission in our images we heavily tapered the {\it u,v} data by convolving with a Gaussian function, resulting in a beam size of $\sim$14$''$$\times$9$''$ with a position angle of 12$^{\circ}$. In order to avoid CLEANing regions of the ``negative bowl'' artifically caused by the lack of short spacing information in the {\it u,v} plane and to help the deconvolution algorithm interpolate through the central hole in the {\it u,v} plane, we added a flat offset from zero of 50 mJy across all of the spectral images to bias the CLEANing towards positive emission. This flat offset was subtracted out after CLEANing, and we compared our data cube with images made without zero spacing flux to check that source structure did not change as a result of this process and did not depend on the amount of zero spacing flux introduced. A variation of this procedure using AIPS is described in detail by Wiseman (1991) and Wiseman \& Ho (1998) who provide sample maps made with different amounts of added zero spacing flux as well as with different deconvolution techniques. This process does not intend to correct for the true value of zero spacing flux in the source, and as a result we estimate that as much as 1/2 to 2/3 of the total flux may be missing in our maps due to extended structure not adequately sampled because of the lack of short spacing data. \newline \ \ \ \ \ The {\it u,v} data from the northern two fields were imaged and deconvolved simultaneously as one image with two pointings. When performing a joint mosaic, the imaging software in MIRIAD corrects for primary beam attenuation to within a certain noise limit, as set by the theoretical noise of the individual pointings. As a result, while most of the image is primary beam corrected, there is residual attenuation at the edges of the mosaic. The far southern field has a different v$_{LSR}$ and an offset velocity coverage from the northern two fields, so the data from the southern field were imaged and deconvolved separately. To mosaic the subset of the data with overlapping velocity channels in all three fields, we de-mosaiced the northern two fields using the task DEMOS and then applied a linear mosaic of all three fields in the image plane using the task LINMOS with the taper option, which creates final images which have significant attenuation at the edges (\cite{sau96}). \newline \section{Results} \subsection{Velocity-Integrated Map} \ \ \ \ \ Figure \ref{fig.color.mom0} presents the velocity-integrated NH$_3$(1,1) and NH$_3$(2,2) emission from all three fields in contours overlaid on a false color HCN map of the inner part of the CND. The scale of this image is $\sim$9 pc$\times$16 pc (using R$_\circ$=8.5 kpc), and there is significant attenuation at the edges of this mosaic so that only the highest signal-to-noise features are seen here. The HCN emission (\cite{mar93}) has a beam size of 12$''$$\times$6$''$, while the NH$_3$ line emission has a beam size of 14$''$$\times$9$''$, as seen in the lower left corner of each image. A long narrow north-south streamer can be seen in both NH$_3$ maps. The southern half of this streamer extends into the 20 km sec$^{-1}$ GMC, and the streamer ends to the north at the location of the CND, precisely where little or no HCN emission is seen (\cite{mar93}; \cite{jac93}). A semi-complete ring is mapped in NH$_3$(1,1) around the CND, extending roughly 2-4 pc from Sgr A$^*$. The NH$_3$(2,2) map shows a less-complete ring of emission which closely follows the curve of the HCN emission on the eastern and western sides. Most of the northern half of the CND is missing in the NH$_3$ maps, and this is almost certainly due to the limited spectral window of this experiment. The HCN data show that emission in the northeastern quadrant is predominantly at v$_{LSR}$$\sim$100 km sec$^{-1}$, which falls outside of our velocity coverage. \newline \ \ \ \ \ The size of the entire southern streamer connecting the 20 km sec$^{-1}$ GMC to the circumnuclear region is about $\sim$2 pc$\times$10 pc, with many smaller clumps about 1 pc to 2 pc in diameter. It is immediately clear from Figure \ref{fig.color.mom0} that the greatest morphological differences between the NH$_3$(1,1) and NH$_3$(2,2) emission is in the immediate neighborhood of Sgr A$^*$ and the CND. The NH$_3$(1,1) emission is fluffier than the NH$_3$(2,2), extending further out from the CND as defined by the HCN emission. The NH$_3$(2,2) gas appears in projection to be concentrated near the inner edge of the disk. In both maps the streamer has a large clump in the north where the streamer meets the disk. The northern tip of the streamer extends further into the interior of the disk in the NH$_3$(2,2) map. Both maps also show a dense region of gas along the western side of the disk, near the densest part of the CND itself. The NH$_3$(1,1) emission continues on around the ring to the northwest at a larger radial distance before sharply stopping where the CND has two dense spots, one to the north of the other, where little NH$_3$(2,2) emission is seen. \newline \ \ \ \ \ Figure \ref{fig.bw.mom0.spiral} overlays the same NH$_3$(1,1) and NH$_3$(2,2) contours from the northern half of the streamer onto a greyscale map of the ionized gas streamers which form a mini-spiral centered at Sgr A$^*$ (\cite{loe83}). It has been proposed that the western streamer is the inner photo-ionized edge of the CND and that the northern and eastern streamers are infalling gas which has been stripped off of the disk (\cite{lac91}). The northern part of the streamer reaches up past the eastern arm of the mini-spiral. In the NH$_3$(2,2) map the small clump at the tip of the streamer resides in the hollow area between the eastern and northern ionized gas streamers. This is the same location as that of the ionized gas and dust `tongue' which is thought to be falling in towards Sgr A$^*$ (\cite{cha97} and references therein). On the western side of the spiral the NH$_3$(2,2) emission follows the outer edge of the western arm, which is also the location of the inner edge of the CND. In the NH$_3$(1,1) map the northern part of the emission around the CND reaches down in between the western and northern ionized gas streamers. We find little emission in NH$_3$(1,1) and NH$_3$(2,2) in the central parsec of the Galaxy. \newline \subsection{Velocity-Integrated Map of the NH$_3$(2,2)/NH$_3$(1,1) Ratio} \ \ \ \ \ The rotation temperature of the gas can be determined by comparing the observed brightness temperatures of the two NH$_3$ transitions, using the optical depth measured in the NH$_3$(1,1) line. For a given optical depth, a higher ratio of the NH$_3$(2,2) to NH$_3$(1,1) observed brightness temperatures implies hotter gas. While in section 3.6 we calculate the rotation temperature for specific locations along the streamer where we can directly measure the optical depth of the NH$_3$(1,1) gas, here we present a spatial representation of the NH$_3$(2,2) to NH$_3$(1,1) line ratio seen in this region. In Figure \ref{fig.22.11mom0} the contours map the NH$_3$(2,2) velocity-integrated emission in the northern part of the streamer. This image has been primary-beam corrected to within the theoretical noise limits, and we present this map in order to investigate the low-level emission around the CND, where the signal to noise is not as high as in Figure \ref{fig.color.mom0}. The NH$_3$(2,2)/NH$_3$(1,1) line ratio is shown in greyscale emission, with the dark regions tracing higher ratios where the gas is hotter. One can see that the northern tip of the streamer is the darkest area on the map, indicating that this gas is heated near the nuclear region. There are also dark regions around the inner edge of the northwestern part of the CND, and a somewhat dark area in between the two largest clumps in the streamer. Inter-clump heating of gas is commonly seen, where the gas is externally heated (\cite{wis98}). Figure \ref{fig.22.11heat} presents the same greyscale map of the NH$_3$(2,2)/NH$_3$(1,1) line ratio overlaid with contours of both the ionized gas mini-spiral and the disk as mapped in HCN. The heated tip of the NH$_3$ streamer lies in between the eastern and northern ionized gas streamers in the mini-spiral and is clearly located in projection inside the CND, near the inner northeast edge of the disk. There is another dark area of heated emission near the northeastern side of the CND, though the signal-to-noise is lower in this area of the map. \newline \subsection{Spectra} \ \ \ \ \ To investigate the kinematics of the gas surrounding the CND, Figure \ref{fig.11.spec} presents selected NH$_3$(1,1) spectra. The NH$_3$(1,1) velocity-integrated map shown here only includes the northern two fields and has been corrected for primary beam attenuation so that the signal-to-noise is lower at the edges. We use this primary-beam corrected map in order to probe the fainter emission around the nuclear region, and we show spectra of several interesting features around the CND. The semi-complete ring of NH$_3$(1,1) emission is clearly seen in the upper part of the map, while the southern half of the streamer is cut off to the south due to the edge of the primary beam in the lower field. We note that in removing the continuum emission, we subtracted the {\it u,v} data averaged over the velocity range of -35 km sec$^{-1}$ to -75 km sec$^{-1}$ from all the spectral channels. It is possible therefore that our resulting line-only data may be missing some emission in this velocity range. \newline \ \ \ \ \ One can see from the spectra that the highest flux and signal-to-noise are found along the southern streamer. Spectra J, K and L reveal that the gas in the streamer is centered around a velocity of 25 km sec$^{-1}$, with FWHMs of 30-40 km sec$^{-1}$. These three FWHM measurements may be overestimated due to blending with hyperfine structures, which we will discuss shortly when we present the position-velocity diagrams in Section 3.4. In this figure, as we approach the CND in spectrum M, the gas becomes much more spread out in velocity space, with a FWHM $\geq$50 km sec$^{-1}$. All of the other spectra which are near the CND or within 1$'$ of Sgr A$^*$ show emission with very large FWHMs. It is quite likely that some of the linewidths in the nuclear region are underestimated in our experiment due to our limited velocity range. HCN spectra from the CND show that in the southwest region lines peak from -60 km sec$^{-1}$ to -120 km sec$^{-1}$, while in the northeast lines peak from 80 km sec$^{-1}$ to 110 km sec$^{-1}$. These velocities are predominantly outside of our observed range, and this appears to be the principal reason why our data do not completely trace the CND. However, HCN spectra from these regions also include broad wings of emission at higher and lower velocities, and our spectra show emission from these broad wings. \newline \ \ \ \ \ NH$_3$(2,2) spectra from the two northern fields are presented in Figure \ref{fig.22.spec}. Here again the strongest emission is in the southern streamer, where the central velocity feature is around 20-35 km sec$^{-1}$. As also seen in the NH$_3$(1,1) emission, NH$_3$(2,2) spectra near the nuclear region show an excess of emission with broad linewidths. Most of the FWHM measurements in the NH$_3$(2,2) spectra are not affected by hyperfine blending, as the satellite lines are resolved with our spectral resolution. A dramatic increase in the FWHM of the spectra can easily be seen near the CND. To investigate low-level emission we present spectra from features at one and two contour levels in the velocity-integrated images. Features seen at two contour levels seem to have more significance than those at one contour, based upon their spectra. \newline \ \ \ \ \ In order to verify that our continuum subtraction has been successful and that the passband correction is reliable, we present spectra in Figure \ref{fig.base.spec} taken from randomly-selected areas where there is no emission seen in the velocity-integrated maps. These spectra, plotted to the same scale as in Figures \ref{fig.11.spec} and \ref{fig.22.spec}, do not show any residual emission, thus it appears that our continuum subtraction was successful. \newline \subsection{Position-Velocity Diagrams} \ \ \ \ \ Position-velocity diagrams are presented in Figure \ref{fig.psvl}. The locations of three position-velocity cuts are shown in the NH$_3$(2,2) velocity-integrated map at the left. The diagrams for these cuts are presented for both the NH$_3$(1,1) and NH$_3$(2,2) data, along with the NH$_3$(2,2)/NH$_3$(1,1) line ratio to examine the kinematics of the heated gas. Position-velocity diagrams for cut `a' taken north to south along the northern half of the streamer are presented in the top two rows, where the second row of diagrams has been smoothed in the R.A. direction to bring out the extended, tenuous emission. The top `a' row and the diagrams for cuts `b' and `c' have had no smoothing applied. \newline \ \ \ \ \ In both the smoothed and unsmoothed data for cut `a', one can see a dramatic increase in linewidth in the upper half of the diagrams. The gas approaches the nuclear region at 30-35 km sec$^{-1}$ with narrow linewidths, $\sim$10-15 km sec$^{-1}$ as seen in the NH$_3$(2,2) data. As mentioned before, the NH$_3$(1,1) emission has a hyperfine line 7 km sec$^{-1}$ away from the main line which causes artificial line broadening. The NH$_3$(2,2) emission more accurately reflects the inherent linewidths of the gas, as the hyperfine structures are clearly resolved. Gas in the northern tip of the streamer at the location of the CND has very large linewidths, with emission seen across the entire sampled velocity range from 60 km sec$^{-1}$ to -25 km sec$^{-1}$. This extended emission is more clearly seen for the NH$_3$(2,2) transition than the NH$_3$(1,1). The smoothed NH$_3$(2,2)/NH$_3$(1,1) position-velocity diagram indicates that the warmer part of the gas (dark in the greyscale image) with large line widths is at negative velocities from 0 km sec$^{-1}$ to -20 km sec$^{-1}$. In the unsmoothed `a' diagrams the region in between the two dense clumps of gas in the streamer is seen at a higher flux level in the NH$_3$(2,2) data. This is reflected in the NH$_3$(2,2)/NH$_3$(1,1) divided position-velocity diagram where there is a dark region, indicating heated gas, at that location. In the smoothed NH$_3$(2,2)/NH$_3$(1,1) diagram this region is not as dark, probably because cooler gas surrounding this narrow region of heating has been included in the smoothed diagram. \newline \ \ \ \ \ The next row shows diagrams from cut `b' taken northeast to southwest along the southern part of the streamer. An overall redshift can be seen in both transitions, moving from the southern part of the streamer up to the north. In the NH$_3$(2,2) diagram the southern part of the streamer connects with the northern section at a velocity of 30 km sec$^{-1}$. This connection is stronger in the NH$_3$(2,2) image than in the NH$_3$(1,1) diagram, as was seen in the velocity-integrated map Figure \ref{fig.color.mom0}, where this inter-clump gas may be externally heated. At the lower edge of the diagram a `C' structure is visible in the gas, where the central region of the cloud is blue-shifted along the line of sight compared to the northern and southern parts of the cloud. This feature can also be seen in the next row of diagrams. \newline \ \ \ \ \ The bottom row is from cut `c' taken east to west across the southern edge of the streamer, in the 20 km sec$^{-1}$ GMC. The `C' feature is prominent here in both the NH$_3$(1,1) and NH$_3$(2,2) diagrams. This may be indicating expansion where the central portion of the cloud is blue-shifted towards the observer relative to the gas to the east and west of it. The NH$_3$(2,2)/NH$_3$(1,1) diagram shows that the blue-shifted gas in the center of the cloud and the gas at the eastern edge of the cloud is hotter than the gas along the western edge. Ho et al. (1985) suggest that a supernova remnant may lie in the region south of the Sgr A East continuum emission (roughly at RA=17$^h$42$^m$30$^s$ and Dec=-29$^\circ$$03'$), just east of the bottom of the streamer. They find evidence for an interaction such as a shock front, which could be propagating into the molecular gas. Our position-velocity diagrams are consistent with this proposed idea. The gas in this region is clearly being disrupted and heated, as our position-velocity diagrams show, and the gas may become destabilized by the disruption. The immense gravitational pull of Sgr A$^*$ and the central stellar cluster would then be able to strip the gas off of the 20 km sec$^{-1}$ cloud and pull it in towards the nucleus along the streamer. \newline \ \ \ \ \ Hyperfine structures are clearly present in these position-velocity diagrams. While the first hyperfine line for NH$_3$(1,1) emission is blended with the central line, the second hyperfine line is located 19 km sec$^{-1}$ away from the central line and can be seen in these diagrams, most clearly in the `a' and `c' cuts. Hyperfine lines for the NH$_3$(2,2) transition are located 17 km sec$^{-1}$ and 26 km sec$^{-1}$ away from the central line and can be seen in the `c' (and to some extent in the `b') diagrams. Hyperfine features are also apparent in the spectra presented earlier (Figures \ref{fig.11.spec} and \ref{fig.22.spec}). \newline \subsection{Velocity Dispersion Map} \ \ \ \ \ Figure \ref{fig.mom2} presents velocity dispersion maps for both the NH$_3$(1,1) and NH$_3$(2,2) emission. These maps indicate the dispersion of the gas around the central velocity feature and therefore trace the line width of the emission, where the darker regions have greater line widths. In both transitions the FWHM of the gas is largest in the northernmost area around the CND, where emission from both the western and eastern sides of the CND has large line widths. This same increase in line width in the nuclear region was seen in both the spectra and position-velocity diagrams. Here we present a spatial map of this feature, which can be seen to span the entire nuclear region. The gas at the lower edge of the streamer, in the 20 km sec$^{-1}$ cloud, also shows an increase in line width. This is the region where we discussed in section 3.4 a possible disruption of the gas by a nearby supernova remnant. \newline \subsection{Derived Parameters} \ \ \ \ \ We derive several physical parameters for the gas along the streamer, where the signal to noise is high and there is good agreement between the NH$_3$(1,1) and NH$_3$(2,2) maps. We also compare our derived parameters with those found by Okumura et al. (1989) for the northern part of the 20 km sec$^{-1}$ cloud. Optical depths can be directly measured from the spectra, using the relative intensity of the main and hyperfine lines. The optical depth of the main line, $\tau$$_m$(J,K), is derived with the following equation (see \cite{hoe83}), \begin{equation} \frac {\Delta T_a^{*}(J,K,m)}{\Delta T_a^{*}(J,K,s)} = \frac {1-exp[-\tau_m (J,K)]}{1-exp[-\tau_s(J,K)]}, \end{equation} where $\Delta$$T_a$$^{*}$ is the observed brightness temperature, {\it m} and {\it s} refer to the main and satellite components, and $\tau$$_s$(J,K)=$a\tau$$_m$(J,K) is the optical depth of the satellite, where $a$ is the known ratio of the intensity of the satellite compared with the main component. This equation assumes equal beam-filling factors and excitation temperatures for the different hyperfine components. \newline \ \ \ \ \ We derive optical depths for the NH$_3$(1,1) transition in each of the large cloud clumps along the streamer where hyperfine lines are clearly seen in NH$_3$(1,1) spectra. We will refer to the northernmost clump, located at the southeast edge of the CND where the streamer ends to the north, as the northern cloud. The roughly spherical clump (as seen in NH$_3$(1,1)) directly below the northern cloud we will refer to as the central cloud, while the larger elongated southern half of the steamer will be called the southern cloud. The southern cloud has two peaks of emission, and this cloud corresponds to the northern part of the 20 km sec$^{-1}$ cloud. We derive optical depths for 44 locations in the southern cloud, 28 locations in the central cloud and 10 locations in the northern cloud, as seen in Figure \ref{fig.Trot}. The individual optical depths are reported in Table \ref{rottab}, while the mean values are shown in Table \ref{tab1}, where we derive the mean for the northern cloud using only the 5 optically thick estimates of the optical depth. The error bars for the optical depth calculations vary across the cloud, as the signal to noise changes. Near the peak emission of each cloud, where the signal to noise is highest, the error bars are roughly $\pm$0.2, whereas at the edge of the cloud the error bars are $\pm$0.9. Our optical depths for the lower edge of the southern cloud agree well with the those derived for the 20 km sec$^{-1}$ cloud by Okumura et al. (1989). \newline \ \ \ \ \ Rotation temperatures for the gas can be derived if two or more NH$_3$ transitions are observed. The ratio of the observed brightness temperatures from the NH$_3$(1,1) and NH$_3$(2,2) transitions are related to the rotation temperature as follows (Equation 4 in \cite{hoe83}), \begin{equation} T_R(2,2;1,1) = -41.5 \div \ln\left[ \frac{-0.282}{\tau_m(1,1)} \ln\left( 1 - \frac{\Delta T_a^{*}(2,2,m)}{\Delta T_a^{*}(1,1,m)} \times (1-e^{-\tau_m(1,1)}) \right)\right]. \end{equation} This equation assumes equal beam-filling factors and excitation temperatures for the NH$_3$(1,1) and NH$_3$(2,2) transitions. We calculate rotation temperatures for the locations where we have derived optical depths and report the values in Table \ref{rottab}. For both the southern and central clouds we find a mean rotation temperature of 22 K, while for the northern cloud the mean is 32 K. Error bars on these mean values are difficult to determine, as the equation is non-linear and the rotation temperature is highly sensitive to the ratio of the NH$_3$(2,2)/NH$_3$(1,1) brightness temperatures. From the spread of the values of $T_R$(2,2:1,1) reported in Table \ref{rottab}, we estimate rough error bars of -5K and +30K for $T_R$(2,2:1,1). Our values for $T_R$ for the southern cloud are consistent with those found by Okumura et al. (1989). \newline \ \ \ \ \ From the rotation temperature we can estimate a gas kinetic temperature, $T_K$, using the $T_K$ - $T_R$ relation of Danby et al. (1988). This $T_K$ - $T_R$ relation is calculated for a `standard' cloud and is not very sensitive to cloud density or ammonia abundance, however, relations like these may be highly model dependent. For the southern and central clouds, where $T_R$ is roughly 15 K to 25 K, the corresponding values for $T_K$ are 17 K to 35 K. For the northern cloud, where $T_R$ varies from 15 K to 60 K, $T_K$ ranges from 17 K up to 300 K, where $T_K$ becomes asymptotically large as $T_R$ approaches 60 K. Our estimates of the gas temperature for the southern cloud agree well with values reported by others for the 20 km sec$^{-1}$ cloud, which range from 20 K to 120 K (\cite{oku89} and references therein). The kinetic gas temperature in the 20 km sec$^{-1}$ cloud seems to be greater than the dust temperature (\cite{mez86}; \cite{zyl90}), so that there may be a difference in how the dust and gas are heated. There are some locations where we can not derive rotation temperatures. In these cases, the NH$_3$(1,1) optical depth is large and the $\Delta$ $T_a^{*}(2,2,m)$ to $\Delta$ $T_a^{*}(1,1,m)$ ratio is greater than one. In the optically thick case, $T_R$ becomes asymptotically sensitive to this brightness temperature ratio, and we believe that noise is our limiting factor for these few cases where we are unable to derive $T_R$. \newline \ \ \ \ \ The excitation temperature of the gas is derived using the following standard radiative transfer equation, \begin{equation} \Delta T_a^{*} = \Phi[J_{\nu}(T_{ex}) - J_{\nu}(T_{bg})](1-e^{-\tau}), \end{equation} where $T_{ex}$ is the excitation temperature, $T_{bg}$ is the background temperature, and $J_{\nu}$ is the Planck function. The brightness and excitation temperatures for the peak emission in each cloud is shown in Table \ref{tab1}, where the error bars on $\Delta$$T_a$$^{*}$ are roughly $\pm$0.2 K, and the error bars on $T_{ex}$ are $\pm$0.4-1.0 K. In the equation used to derive $T_{ex}$, $\Phi$ is the beam-filling factor, which is $\sim$1 for an extended source but may be $<$1 if there exists structure in the clouds on a scale smaller than the synthesized beam. There is some indication that full-resolution maps of our data (beam size 3.8$''$$\times$1.7$''$) show small structures at the peaks of the clouds; therefore the beam-filling factor may be $<$1 and our values for $T_{ex}$ may be underestimated.\newline \ \ \ \ \ The column density, $N$(J,K), can be derived from the observed optical depth and excitation temperature. Townes \& Schawlow (1955) relate $\tau$, $T_{ex}$ and the column density in the upper level of the transition, $N_1$, as \begin{equation} \tau(\nu) = \frac{c^2 h A_{1-0} f(\nu) N_1}{8 \pi \nu k J_{\nu}(T_{ex})}, \end{equation} where $A_{1-0}$ is the Einstein coefficient for spontaneous emission (1.67 10$^{-7}$ s$^{-1}$ for (J,K)=(1,1) and 2.23 10$^{-7}$ for (2,2)) and $f(\nu$) = (4$\ln$2/$\pi$)$^{1/2}$($\Delta$$\nu$)$^{-1}$ is the line profile function for a Gaussian. We then assume that $N$(J,K)=2$N_1$(J,K), which should be valid because the inversion doublet is only separated by $\sim$ 1K so that any excitation should equilibrate between the two levels. Using the usual partition function, with $T_R$=20K-30K, we can estimate the amount of NH$_3$ gas in each transition and determine $N$(NH$_3$) from $N$(J,K). If we then assume that $N$(H$_2$)=10$^8 N$(NH$_3$) (\cite{seg86}), we can roughly estimate the molecular hydrogen column density and use the spatial scale of the emission to find the mass of the streamer. To estimate these parameters we use the mean optical depth and peak excitation temperature of each cloud. The results are shown in Table \ref{tab1}, where the values for the mass are only rough estimates. Our derived parameters for the southern cloud agree well with those reported by Zylka et al. (1990), who find a mass for the 20 km sec$^{-1}$ of $\sim$3 10$^5$ M$_{\solar}$. The good agreement in masses implies that our assumed abundances are normal. They report a column density of $\sim$3-8 10$^{23}$ cm$^{-2}$, which is slightly lower than our value. \newline \ \ \ \ \ It is encouraging that our derived parameters for the southern cloud agree well with several other reports of the 20 km sec$^{-1}$ cloud. Studies of NH$_3$, CO, and dust emission in the region all yield similiar numbers, indicating that there are not unusual chemical abundance effects present and that the derived numbers are robust. NH$_3$ emission in particular is able to clearly detect discrete sources and dense cloud clumps in this region, whereas often CO, HCN, and dust maps include fluffy, extended emission which confuses source structure, especially on fine scales. \newline \section{Discussion} \ \ \ \ \ Our results agree well with the general morphology found by many other studies of the Galactic Center. The morphology of the streamer as mapped in NH$_3$(3,3) (\cite{hoe91}) is similiar to our NH$_3$(1,1) and NH$_3$(2,2) maps. We find little or no emission in NH$_3$(1,1) and NH$_3$(2,2) at the location of Sgr A$^*$ and in the central parsec (Figure \ref{fig.bw.mom0.spiral}). Ho et al. (1991) also find a 1.5-2 pc cavity surrounding Sgr A$^*$ with no NH$_3$(3,3) emission in the nuclear region, and Jackson et al. (1993) confirm that molecular gas is not found in this cavity. The key results in this paper concern the approach of molecular material toward this central cavity. \newline \subsection{The Case for Infalling Gas} \ \ \ \ \ Ho et al. (1991) discuss the possibility of gas feeding the CND from the 20 km s$^{-1}$ cloud via the southern streamer. Other studies have since imaged the same streamer, but none have found any kinematical or direct evidence to support the suggestion of infall or accretion (Marr et al. 1995; \cite{den93}). Whether this gas streamer is seen only in projection against the Galactic Center or whether it is actually approaching the central mass concentration can only be determined if we detect direct effects of the deepening gravitational potential well on the purported infalling feature. Our new data support this accretion theory with morphological, thermal, and kinematic evidences: \newline \ \ \ \ \ (1) Our velocity-integrated maps show a long, narrow streamer connecting the northern part of the 20 km sec$^{-1}$ GMC with the CND region (Figure \ref{fig.color.mom0}). It is of special significance that the streamer $stops$ at the CND. This can be seen not only in the velocity-integrated map, but also in the position-velocity diagrams for cut `a' (Figure \ref{fig.psvl}), where the gas moving into the region at 30-35 km sec$^{-1}$ clearly stops to the north, while the gas above it has much larger line widths. The comparison of the different NH$_3$ transitions suggests that the termination of the streamer is $not$ a temperature effect. The morphology of the streamer in NH$_3$(1,1) and NH$_3$(2,2) agrees well with NH$_3$(3,3), HCN and sub-millimeter continuum studies. \newline \ \ \ \ \ (2) We find that the northern tip of the streamer, located nearest to Sgr A$^*$ in projection, is stronger in NH$_3$(2,2) emission than in NH$_3$(1,1), indicating that the gas is heated (Figure \ref{fig.22.11mom0}). Other locations of heating appear around the CND. This would seem to indicate the gas is located at the distance of the Galactic Center and is being heated by nuclear processes. \newline \ \ \ \ \ (3) A velocity gradient is detected along the streamer. In the northern part of the streamer we observe a gradient of $\sim$5 km sec$^{-1}$ arcmin$^{-1}$ (Figure \ref{fig.psvl}). Along the southern half of the streamer (located in declination from -29$^\circ$01$'$ to -29$^\circ$03$'$) the gradient is $\sim$5-8 km sec$^{-1}$ arcmin$^{-1}$ seen across $\sim$5 pc. This is in good agreement with the southwest to northeast gradient of 5 km sec$^{-1}$ arcmin$^{-1}$ seen in the 20 km sec$^{-1}$ cloud by Okumura et al. (1989) and the 11 km sec$^{-1}$ arcmin$^{-1}$ gradient seen by Zylka et al. 1990. The expected gradient at a radius of 5 pc for a central mass of 10$^7$ M$\solar$ (including the central compact source and stellar population, see \cite{mor96}; \cite{hal96}) is $\sim$9 km sec$^{-1}$ pc$^{-1}$, roughly 3 or 4 times more than we observe. Thus, our detected gradient suggests that if this motion is infall, the bulk of the motion is across the line of sight, with the geometry such that the streamer is more to the side of Sgr A$^*$ than along our particular line of sight. The difference in the size of the gradient seen in the northern part of the streamer as opposed to the southern part may indicate a tilting in the streamer, so that projection effects may result in the lower gradient seen to the north. There may also be forces other than gravity which need to be taken into account, such as increased turbulence from supernovae and winds as well as magnetic effects. \newline \ \ \ \ \ (4) Another handle on the kinematics is the velocity dispersion of the observed motions. The streamer ends to the north at the location of the CND, where we see in the position-velocity diagrams that the line width increases dramatically (Figures \ref{fig.11.spec}, \ref{fig.22.spec}, \ref{fig.psvl}). This increase in line width has not been seen before. Other studies of the southern streamer have coarser spectral resolutions than our 5 km sec$^{-1}$. It is expected that if the gas is moving from the 20 km sec$^{-1}$ cloud to the nuclear region, it would interact with the CND and become disrupted, resulting in an increase in the line width of the gas, regardless of whether the motion is predominantly along or across the line of sight. The disk is known to have inherently large line widths around $\geq$ 40 km sec$^{-1}$. Our detection and measurement of a component with increased line widths concretely place the northern tip of the streamer at the location of the CND and are consistent with the gas in the southern streamer accreting onto the CND. This kinematic evidence does not reflect chemistry or abundance effects and is the strongest argument for the streamer transporting gas to the nuclear region along the southern streamer. The morphology and velocity gradient we see do not argue alone that the streamer is falling in towards the nuclear region; it is only when combined with the heating seen and the increase in line width at the northern tip of the streamer that the argument becomes strong. \newline \subsection{Other Nearby Streamers?} \ \ \ \ \ Hints in our data show that there may be more than one streamer flowing toward the nuclear region. The 20 km sec$^{-1}$ cloud has a tuning-fork morphology which may be indicating the presence of two streamers. The southern edge of streamer which dips into the 20 km sec$^{-1}$ cloud has two separate elongated lobes of emission. These two `fingers' pointing into the GMC can be seen clearly in the velocity dispersion maps (Figure \ref{fig.mom2}), where the dark regions at the southern part of the map seem to separate into two distinct regions of gas. There are also hints in the velocity-integrated maps (Figure \ref{fig.color.mom0} and the NH$_3$(2,2) contours in Figure \ref{fig.22.11mom0}) that there may be a second streamer connecting the northern section of this double-lobed part of the 20 km sec$^{-1}$ cloud to the nuclear region. Along the western edges of the maps (e.g. RA=17$^h$42$^m$26$^s$) there are hints of a narrow line of gas originating from the northwest of the 20 km sec$^{-1}$ cloud and moving up towards the southwestern quadrant of the CND. Both this second western streamer as well as the main southern streamer have been imaged in dust emission at 1.3mm by Zylka et al. (1997), where their maps show remarkable agreement with our NH$_3$ emission. \newline \ \ \ \ \ Another feature at the one contour level in the velocity integrated map which seems to be a real structure is the small spot of emission to the east of the 20 km sec$^{-1}$ seen in both the NH$_3$(1,1) and NH$_2$(2,2) maps (RA=17$^h$42$^m$32$^s$). Spectra from this location indicate a central velocity of $\sim$15-25 km sec$^{-1}$. It is also worth noting that this feature is seen clearly in the NH$_3$(3,3) data of Ho et al. (1991), where it is part of a ridge of gas connecting the 20 km sec$^{-1}$ with the 50 km sec$^{-1}$ cloud. The higher intensity of this feature in the NH$_3$(3,3) line suggests that it must be fairly warm. \newline \section{Conclusions} \ \ \ \ \ Investigating connections between molecular material in the nucleus of the Galaxy and the nearby 20 km sec$^{-1}$ GMC, NH$_3$(1,1) and NH$_3$(2,2) were observed with the VLA using three overlapping 2$'$ fields at the Galactic Center, surrounding Sgr A$^*$ and the region directly south of it. We map a streamer which appears to be feeding the nuclear region with molecular gas from the 20 km sec$^{-1}$ cloud. The long, narrow streamer is about 2 pc east to west and 10 pc north to south and originates from the northeastern edge of the 20 km sec$^{-1}$ cloud, south of Sgr A West. The streamer ends to the north at the location of the CND, in the area where the least amount of HCN disk flux is seen, just southeast of Sgr A$^*$. We detect a clear velocity gradient along its length of $\sim$5-8 km sec$^{-1}$ arcmin$^{-1}$. The line widths of the gas increase substantially in the northern portion of the streamer, with FWHMs of $\geq$50 km sec$^{-1}$, possibly signalling accretion onto the CND. The gas at the location of the CND also appears to be heated, as indicated by the ratio of the NH$_3$(2,2)/NH$_3$(1,1) velocity-integrated emission. Additional faint streamers also appear to be link the 20 km sec$^{-1}$ cloud to the CND, suggesting possible other paths of accretion. Our morphological, kinematical, and thermal data strongly support the thesis that gas is falling in towards the circumnuclear region from the 20 km sec$^{-1}$ cloud along the southern streamer and accreting onto the CND. \newline \ \ \ \ \ We would like to thank Mel Wright for providing the HCN maps of the CND. The image of the ionized gas spiral in Sgr A West was made by D. A. Roberts and W. M. Goss and was downloaded from the Astronomy Digital Image Library maintained by the NCSA. 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These images have significant primary beam attenuation at the edges, and the noise level across the central region of the image is .05 Jy beam$^{-1}$ km sec$^{-1}$. The solid contours are at integer levels of .4 Jy beam$^{-1}$ km sec$^{-1}$, and the 14$''$$\times$9$''$ synthesized beam is in the lower left corner. \label{fig.color.mom0}} \figcaption[fig_mom0.a+as+1/spiral.bw.mom0.ps]{Northern two fields of the velocity-integrated NH$_3$(1,1) and NH$_3$(2,2) emission in contours overlaid on a greyscale image of the mini-spiral of ionized gas surrounding Sgr A$^*$. The contour levels are the same as in Figure \ref{fig.color.mom0}. \label {fig.bw.mom0.spiral}} \figcaption[fig_22.11mom0.a+as+1/22.11.mom0.both.ps]{NH$_3$(2,2) primary-beam corrected emission is shown in contours overlaid on the NH$_3$(2,2)/NH$_3$(1,1) line intensity ratio in greyscale. The NH$_3$(2,2)/NH$_3$(1,1) line ratio indicates heating, where the darker areas correspond to hotter gas. The hottest area is at the northern tip of the streamer, where it reaches the CND. The greyscales are 0 to 50 Jy beam$^{-1}$ km sec$^{-1}$ for the NH$_3$(2,2) emission and a ratio of 0.5 to 6 for the divided NH$_3$(2,2)/NH$_3$(1,1) emission. \label{fig.22.11mom0}} \figcaption[fig_heat.spiral.a+as+1/heat.spiral+disk.ps]{The NH$_3$(2,2)/NH$_3$(1,1) line intensity ratio (the same as in Figure \ref{fig.22.11mom0}) is shown in greyscale with contours of the ionized gas mini-spiral on the left and the CND as seen in HCN on the right. \label{fig.22.11heat}} \figcaption[fig_11spec.a+as/11.spec.fig.ps]{Selected NH$_3$(1,1) spectra with Gaussian fits; the positions of the spectra are shown in the primary-beam corrected map. The line widths of the spectra increase as the gas is located near the CND. \label{fig.11.spec}} \figcaption[fig_22spec.a+as/22.spec.fig.ps]{Selected NH$_3$(2,2) spectra with Gaussian fits from a primary-beam corrected map. \label{fig.22.spec}} \figcaption[fig_basespec.a+as/base.spec.ps]{Test of baseline subtraction using random NH$_3$(1,1) and NH$_3$(2,2) spectra from low-emission regions; there is no residual emission above zero. \label{fig.base.spec}} \figcaption[fig_psvl.a+as+1/22.11.psvl.ps]{Position-velocity diagrams for NH$_3$(1,1), NH$_3$(2,2) and NH$_3$(2,2)/NH$_3$(1,1) emission; the second row for the cut `a' has been smoothed in the R.A. direction, while the other diagrams have no smoothing applied. North is up in the `a' and `b' diagrams, while east is up for the `c' diagrams. The NH$_3$(2,2)/NH$_3$(1,1) greyscale ranges from a ratio of 0.5 (light) to 3 (dark) with contours at 0.5 intervals, and the contour levels for the NH$_3$(1,1) and NH$_3$(2,2) diagrams are at .2 Jy beam$^{-1}$. \label{fig.psvl}} \figcaption[fig_mom0.a+as+1/bw.mom2.ps]{Velocity dispersion maps which trace line width gradients in the gas, where the darker areas indicate broader line widths. The line widths increase in the nuclear area in both the NH$_3$(1,1) and NH$_3$(2,2) gas, as well as at the southern tip of the long, narrow southern streamer. The greyscale is 0 km sec$^{-1}$ (white) to 40 km sec$^{-1}$ (dark). \label{fig.mom2}} \figcaption[fig_mom0.a+as+1/bw.Trot.ps]{The locations used to derive optical depths and rotation temperatures listed in Table 1 are labelled on a grey-scale velocity-integrated map of the NH$_3$(1,1) emission. \label{fig.Trot}} \pagebreak \small \begin{deluxetable}{ccccc} \tablewidth{350pt} \tablecolumns{5} \tablecaption{Derived Physical Parameters \label{rottab}} \tablehead{ \colhead{Location}\tablenotemark{a} & \colhead{$\tau$(1,1,m)} & \colhead{$\Delta$ $T_a^{*}(1,1,m)$} & \colhead{$\Delta$ $T_a^{*}(2,2,m)$ } & \colhead{$T_R$(2,2:1,1)} \\ \colhead{} & \colhead{$(K)$} & \colhead{$(K)$} & \colhead{$(K)$} } \startdata A & $\ll$1 & 1.5 & 2.7 & 58 \\ B & 3.4 & 0.9 & 1.4 & \ \ $ ^b$ \\ C & $\ll$1 & 1.9 & 2.7 & 46 \\ D & $\ll$1 & 2.5 & 2.7 & 36\\ E & $\ll$1 & 1.9 & 1.6 & 29\\ F & 2.3 & 1.7 & 1.7 & 34 \\ G & 1.3 & 2.5 & 2.1 & 26 \\ H & 1.4 & 2.7 & 2.0 & 23 \\ I & 3.7 & 1.9 & 1.5 & 19 \\ J & 5.6 & 0.6 & 0.4 & 15 \\ K & 1.7 & 0.9 & 0.7 & 21 \\ L & 1.9 & 1.5 & 1.1 & 22 \\ M & 2.2 & 1.4 & 1.4 & 36 \\ N & 1.9 & 1.4 & 1.8 & \ \ $ ^b$ \\ O & 2.0 & 0.9 & 0.9 & 32 \\ P & 2.1 & 1.6 & 1.5 & 26 \\ Q & 2.2 & 2.4 & 1.9 & 23 \\ R & 2.5 & 2.4 & 2.0 & 23 \\ S & 1.3 & 2.2 & 1.7 & 25 \\ T & 2.0 & 2.0 & 2.0 & 32 \\ U & 2.3 & 3.2 & 2.7 & 24 \\ V & 1.6 & 3.4 & 2.5 & 22 \\ W & 0.9 & 3.0 & 1.9 & 22 \\ \tablebreak X & 1.7 & 3.5 & 2.6 & 23 \\ Y & 2.2 & 3.8 & 2.6 & 20 \\ Z & 3.4 & 3.5 & 2.2 & 16 \\ a & 2.9 & 2.9 & 2.1 & 19 \\ b & 4.0 & 3.4 & 2.6 & 18 \\ c & 5.8 & 3.4 & 2.6 & 15 \\ d & 5.0 & 3.2 & 2.3 & 15 \\ e & 3.3 & 2.4 & 1.5 & 17 \\ f & 2.0 & 1.1 & 0.6 & 17 \\ g & 3.0 & 1.7 & 1.0 & 17 \\ h & 1.8 & 2.4 & 1.7 & 21 \\ i & 1.9 & 3.0 & 2.7 & 27 \\ j & 2.9 & 3.2 & 3.1 & 29 \\ k & 0.3 & 2.9 & 2.6 & 31 \\ l & 1.3 & 2.2 & 1.5 & 22 \\ m & 3.1 & 1.2 & 0.8 & 18 \\ n & 6.3 & 0.8 & 0.8 & 21 \\ o & 4.0 & 1.1 & 0.8 & 16 \\ p & 4.1 & 1.1 & 0.8 & 16 \\ q & 4.2 & 1.3 & 1.1 & 19 \\ r & 4.1 & 1.5 & 1.0 & 16 \\ s & 6.0 & 1.4 & 0.9 & 14 \\ t & 6.2 & 1.0 & 0.9 & 18 \\ \tablebreak u & 9.8 & 0.8 & 0.8 & 19 \\ v & 7.1 & 1.4 & 0.9 & 13 \\ w & 3.7 & 1.9 & 1.7 & 24 \\ x & 7.2 & 1.7 & 1.9 & \ \ $ ^b$ \\ y & 6.2 & 1.9 & 2.3 & \ \ $ ^b$ \\ z & 4.3 & 1.1 & 1.3 & \ \ $ ^b$ \\ $A$ & 6.1 & 1.2 & 1.2 & 20 \\ $B$ & 4.4 & 2.2 & 2.3 & \ \ $ ^b$ \\ $C$ & 4.2 & 2.2 & 2.4 & \ \ $ ^b$ \\ $D$ & 4.8 & 2.3 & 2.5 & \ \ $ ^b$ \\ $E$ & 3.6 & 2.6 & 2.6 & 29 \\ $F$ & 6.1 & 1.5 & 2.1 & \ \ $ ^b$ \\ $G$ & 5.1 & 2.4 & 2.0 & 17 \\ $H$ & 4.0 & 2.3 & 2.3 & \ \ $ ^b$ \\ $I$ & 3.9 & 3.8 & 2.9 & 18 \\ $J$ & 1.8 & 4.4 & 5.6 & \ \ $ ^b$ \\ $K$ & 1.9 & 5.0 & 6.3 & \ \ $ ^b$ \\ $L$ & 3.4 & 3.7 & 2.3 & 16 \\ $M$ & 2.3 & 3.6 & 3.0 & 23 \\ $N$ & 3.3 & 4.4 & 3.1 & 18 \\ $O$ & 2.5 & 4.8 & 4.6 & 29 \\ $P$ & 2.3 & 5.3 & 5.0 & 29 \\ \tablebreak $Q$ & 1.7 & 5.0 & 4.6 & 28 \\ $R$ & 1.3 & 2.4 & 2.7 & 39 \\ $S$ & 1.2 & 2.1 & 2.3 & 40 \\ $T$ & 2.2 & 3.1 & 3.4 & 60 \\ $U$ & 2.9 & 2.1 & 2.1 & 34 \\ $V$ & 2.3 & 3.0 & 2.5 & 23 \\ $W$ & 2.1 & 3.2 & 3.8 & \ \ $ ^b$ \\ $X$ & 0.9 & 1.7 & 2.1 & 48 \\ $Y$ & 0.8 & 1.6 & 1.7 & 35 \\ $Z$ & 0.9 & 1.4 & 1.2 & 26 \\ $a$ & 0.8 & 1.3 & 1.2 & 28 \\ $b$ & 1.5 & 1.0 & 1.2 & 61 \\ $c$ & 0.8 & 1.5 & 1.6 & 34 \\ $d$ & 1.2 & 1.4 & 1.8 & 90 \\ $e$ & 1.2 & 1.5 & 1.8 & 53 \\ \enddata \tablenotetext{a}{The positions for each location listed here are shown in Figure 10} \tablenotetext{b}{Rotation temperature can not be derived (see section 3.6 for discussion)} \end{deluxetable} \begin{deluxetable}{lcccccc} \tablecolumns{7} \tablecaption{NH$_3$(1,1) Column Density and Mass Estimates \label{tab1}} \tablehead{ \colhead{Cloud} & \colhead{Mean $\tau$$_m$} & \colhead{Peak $\Delta$$T_a$$^{*}$} & \colhead{Peak $T_{ex}$} & \colhead{$N(J,K)$} & \colhead{$N$(H$_2$)} & \colhead{Mass} \\ \colhead{} & \colhead{} & \colhead{$(K)$} & \colhead{$(K)$} & \colhead{($10^{15}$ $cm^{-2}$)} & \colhead{($10^{24}$ $cm^{-2}$)} & \colhead{($10^4$ $M_{\solar}$)} } \startdata Northern & 2.7 & 3.2 & 6.1 & 3.4 & 0.85 & 5.5 \\ Central & 2.4 & 3.8 & 6.9 & 3.4 & 0.81 & 6.2 \\ Southern & 3.5 & 5.3 & 8.2 & 6.0 & 1.4 & 23 \\ \enddata \end{deluxetable} \end{document}