------------------------------------------------------------------------ From: Tom Geballe tgeballe@gemini.edu To: gcnews@aoc.nrao.edu Subject: submit GC_h3p.tex ApJ, in press % astro-ph/0507463 \documentclass[12pt,preprint]{aastex} \begin{document} \title{Hot and Diffuse Clouds near the Galactic Center Probed by Metastable H$_3^+$} \author{Takeshi Oka} \affil{Department of Astronomy and Astrophysics, and Department of Chemistry, The Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 USA} \email{t-oka@uchicago.edu} \and \author{Thomas R. Geballe} \affil{Gemini Observatory, Hilo, Hawaii 96720 USA} \and \author{Miwa Goto} \affil{Max Planck Institute for Astronomy, Heidelberg, Germany} \and \author{Tomonori Usuda} \affil{Subaru Telescope, National Astronomical Observatory of Japan, Hilo, Hawaii 96720 USA} \and \author{Benjamin J. McCall} \affil{Department of Chemistry and Department of Astronomy, University of Illinois Urbana-Champaign, Urbana, IL 61801-3792 USA} \begin{abstract} We have observed a vast amount of high temperature ($T$ $\sim$ 250 K) and low density ($n$ $\sim$ 100 cm$^{-3}$) gas with a large velocity dispersion in the central 200 pc of the Galactic center (the Central Molecular Zone; CMZ) that has not previously been reported. We used the infrared spectrum of H$_3^+$ which is a sensitive probe of low density molecular gas. The observed large column density of H$_3^+$ in the ($J$, $K$) = (3, 3) metastable rotational level (361 K above the lowest (1, 1) level) gives evidence for high temperature, and the observed small column density in the (2, 2) level (210 K below (3, 3)), gives evidence for low density. This remarkable non-thermal rotational distribution is caused for a low density gas by the fact that the spontaneous emission from the (3, 3) level is rigorously forbidden by the selection rules while that for the (2, 2) $\rightarrow$ (1, 1) transition has a short lifetime of 27 days, corresponding to a low critical density of $\sim$ 200 cm$^{-3}$. Observed H$_3^+$ spectrum toward the brightest infrared source GCS 3-2, one of the Quintuplet Stars, has been analyzed in detail. Of the observed total H$_3^+$ column density of 4.3 $\times$ 10$^{15}$ cm$^{-2}$, approximately 3.1 $\times$ 10$^{15}$ cm$^{-2}$ with high velocity dispersion is inferred to be in the CMZ while 1.2 $\times$ 10$^{15}$ cm$^{-2}$ is in the intervening spiral arms. Almost all of H$_3^+$ in the CMZ are in diffuse clouds with high temperature. About a half of the gas has a velocity of $\sim$ $-$ 100 km s$^{-1}$ indicating that it is associated with the 180 pc Expanding Molecular Ring which approximately forms the boundary of the CMZ. The other half with lower velocities of $\sim$ $-$ 50 km s$^{-1}$ and $\sim$ 0 km s$^{-1}$ is thought to be closer to the Galactic center. CO do not exist much in those clouds. The non-thermal rotational distribution of H$_3^+$ has also been observed toward 7 other infrared sources within 40 pc of the Galactic center indicating that the hot and diffuse gas is ubiquitous in the CMZ. The spectrum toward GC IRS 3 near Sgr A* shows presence of the hot and diffuse gas in the ``50 km s$^{-1}$ cloud", the complex of giant molecular clouds which plays a central role in the discussion of Sgr A* and its environment. The hot and diffuse gas has not been observed toward any of the dense and diffuse clouds in the Galactic disk where we have observed large column densities of H$_3^+$ had been observed. The large observed H$_3^+$ column density suggests an ionization rate in the CMZ which is an on the order of magnitude higher than in the diffuse interstellar medium in the Galactic disk if the C/H ratio is indeed as high as reported. Also the fact that the observed H$_3^+$ in the CMZ are almost all in diffuse clouds, along with the reported relatively low visual extinctions ($A_V$ $\sim$ 25 - 40) and mass estimated from radio observations of molecules, indicate that dense clouds are more sparse than previously thought and the reported volume filling factor (f $\geq$ 0.1) is an overestimate by at least an order of magnitude. \end{abstract} \keywords{astrochemistry --- radiation mechanisms: non-thermal --- molecular processes --- ISM: clouds --- ISM: molecules --- Galaxy: center} : individual(\objectname{GCS 3-2}, \objectname{GC IRS 1W}, \objectname{GC IRS 3}, \objectname{GC IRS 21}, \objectname{NHS 21}, \objectname{NHS 22}, \objectname{NHS 25}, \objectname{NHS 42}) \section{Introduction} It is thought mainly from the radio observations of molecules, that the Central Molecular Zone (CMZ, also called the nuclear molecular disk) of the Galaxy, a region of radius $\sim$ 200pc, contains high density ($n$ $\geq 10^4$ cm$^{-3}$) molecular gas with a high volume filling factor and that the gas constitutes a sizable fraction of the total molecular gas content in the Galaxy \citep{mor96, dah98}. It has also been observed that a significant fraction of this gas has unusually high temperature ($\sim$ 200 K) and large velocity dispersion (15 $\sim$ 50 km s$^{-1}$) demonstrating the highly energetic, turbulent nature of the gas in the CMZ. Unlike the hot spots in the Galactic disk where a luminous star heats up the surrounding dust which in turn heats the gas and hence the extent of the high temperature is limited to the vicinity of the star, the hot gas in the CMZ extends over large distances and suggests a direct and widespread gas heating mechanism. On the other hand, dust in the same area has been observed to have low temperatures of $\leq$ 30 K from far-infrared \citep{ode84} and submillimeter \citep{pie00} measurements. Studies of the hot gas in the CMZ provide information vital for understanding the great activity near the nucleus of the Galaxy with non-thermal magnetic phenomena \citep{yus84}, extended X-ray emissions \citep{koy89, koy96} and their interaction with molecular clouds \citep{lis85, tsu97, oka01, yus02}. The most direct evidence for the high temperature of the gas has been obtained from radio observations of molecules in high rotational levels. \citet{wil82} observed inversion spectrum of NH$_3$ in absorption up to the ($J$, $K$) = (8, 8) and (9, 9) metastable levels, 680 K and 835 K above the ground level, respectively, toward Sgr B2 and reported an estimated temperature of $T$ = 200 K and cloud density of $n$ = 10$^4$ cm$^{-3}$. \citet{mau86} and \citet{hut93} extended the observation to many clouds in the CMZ using NH$_3$ emission lines up to the (7, 7) and (6, 6) metastable levels, respectively, and reported similar temperature and density. Recently, \citet{her02} reported similar results toward Sgr A. \citet{har85} used the $J = 7-6$ submillimeter emission line of CO in the central 10 pc of the Galaxy and reported $T$ $\sim$ 300 K and $n$ = 3 $\times 10^4$ cm$^{-3}$, although recent paper by \citet{kim02} reported lower mean density and temperature for larger regions. The high $J$ CO rotational transition corresponds to a high critical density of $n_{crit} \geq 10^6$ cm$^{-3}$ \citep{gre78} and probe dense regions of the CMZ. Recently, \citet{rod01} used \emph{ISO} H$_2$ rotational emission lines, $S$(0) - $S$(5), to probe 16 molecular clouds distributed in the central $\sim$ 500 pc of the Galaxy. Since critical densities of those transitions are lower, they are capable of probing low density clouds if sufficient quantity of H$_2$ exists. The ubiquity of H$_2$ makes it a most general probe to study widely in the area. They reported $T$ = 150 $\sim$ 600 K and $n$ = 10$^{3.5-4.0}$ cm$^{-3}$, similar to other works. Very recently, they reported observations of atomic fine structure lines which were interpreted to be from a photodissociation region with a density of $\sim$ 10$^3$ cm$^{-3}$ \citep{rod04}. Here we report our discovery of \emph{low} density ($n$ $\sim$ 100 cm$^{-3}$) and high temperature ($T$ $\sim$ 250 K) molecular gas in the CMZ using the infrared absorption line of H$_3^+$ in the (3, 3) metastable level. H$_3^+$ (protonated H$_2$) is a unique astrophysical probe in that it is observed with comparable column densities ($\sim 10^{14}$ cm$^{-2}$) in dense clouds \citep{geb96, mcc99, bri04} as well as in diffuse clouds \citep{mcc98a, geb99, mcc02}. Contrary to the expectation from chemical model calculations which predict orders of magnitude lower H$_3^+$ number density for diffuse clouds (because of the rapid dissociative recombination with electrons), observed column densities of H$_3^+$ per unit visual extinction is an order of magnitude \emph{higher} for diffuse clouds ($N$(H$_3^+$) $\sim 4.4 \times 10^{13}$ cm$^{-2}$ $A_V$) than for dense clouds (N(H$_3^+$) $\sim 3.6 \times 10^{12}$ cm$^{-2}$ $A_V$) \citep{geb99, mcc02, oka04b}. Since the heavy visual extinction of $A_V$ = 25 - 40 \citep{cot00} toward the Galactic center is caused mainly by diffuse clouds \citep{wil79, but86, oku90, pen94, whi97}, H$_3^+$ is a most powerful probe to study sightlines toward the Galactic center. Indeed the observed column densities of $N$(H$_3^+$) $\sim 3 - 5 \times 10^{15}$ cm$^{-2}$ toward GCS 3-2 and GC IRS 3 \citep{geb99, got02} are an order of magnitude higher than other sightlines in the Galactic disk. H$_3^+$ is also special for the study of the CMZ since, being a charged molecule, it is sensitive to ionization of molecular gas which is efficient in the CMZ with intense X-ray sources and high magnetohydrodynamic activities \citep{mor96}. In this work we have used the $R$(3, 3)$^l$ absorption line of H$_3^+$ at 2829.9 cm$^{-1}$ \citep{oka80} which starts from the (3, 3) metastable rotational level of ortho-H$_3^+$, 361 K above the lowest (1, 1) level. \citet{got02} discovered the spectral line toward the bright infrared star GCS 3-2 \citep{nag90, oku90}, one of the quintuplet stars approximately 30 pc from the Galactic nucleus, and GC IRS 3 very close to the nucleus \citep{bec78}. H$_3^+$ has a structure of an equilateral triangle like NH$_3$ but, being simpler, lighter and electrically charged, it has three salient features which is not found in NH$_3$. First, unlike NH$_3$ which is pyramidal, H$_3^+$ is planar. Thus the totally symmetric rotational levels like (0, 0), (2, 0) etc. are not allowed by the Pauli exclusion principle. This makes the (1, 1) level the rotational ground level. Second, the metastability of H$_3^+$ is similar to that of NH$_3$ qualitatively, but is very different quantitatively. The crucial difference relevant to this paper is that while NH$_3$ in the (2, 2) level takes $\sim$ 200 years to decay to the (1, 1) level by spontaneous emission \citep{oka71}, it takes only 27 days for H$_3^+$. The (2, 2) level is not metastable in H$_3^+$! On the other hand, the spontaneous emission from the (3, 3) level is rigorously forbidden by the dipole selection rules and the absence the (2, 0) level \citep{pan86}. This leads to a very non-thermal rotational distribution between the (3, 3) and (2, 2) levels for a low density gas. More details on the metastable level and non-thermal rotational distribution of H$_3^+$ can be found in \citet{oke04} (hereafter called Paper I). Here we simply emphasize that the spontaneous emission time of 27 days (2.35 $\times 10^6$ s) is a very reliable number with the uncertainty of at most 5 \% based on the ab initio calculation by \citet{nea96}, and it sets an accurate time standard for the thermalization of interstellar H$_3^+$. Other spontaneous emissions from higher levels such as (2, 1) $\rightarrow$ (2, 2) (20 days), (3, 2) $\rightarrow$ (2, 1) (16 hours), (3, 1) $\rightarrow$ (2, 2) (8 hours) etc. have even shorter life times. The spontaneous emission gets drastically faster with increasing $J$ and $K$ and rapidly cool rotationally hot H$_3^+$ except those in metastable levels, (4, 4), (5, 5), (6, 6) etc. This has an implication even for laboratory experiments \citep{kre04}. Third, the collision between H$_3^+$ and H$_2$ is qualitatively different from that between NH$_3$ and H$_2$. It is actually a chemical reaction H$_3^+$ + H$_2$ $\rightarrow$ (H$_5^+$)$^*$ $\rightarrow$ H$_3^+$ + H$_2$ in which the protons may scramble in the activated complex (H$_5^+$)$^*$ during its short lifetime \citep{Oka04a}. Therefore, unlike for NH$_3$ or other neutral molecules such as H$_2$O and H$_2$CO, ortho- and para- nuclear spin modifications are efficiently converted to each other by collisions with H$_2$ \citep{cor00}. Also the collision between H$_3^+$ and H$_2$ has higher cross section than between NH$_3$ and H$_2$ because of the long range r$^{-4}$ Langevin potential and this makes the critical densities for the H$_3^+$ collisions lower. If we assume that the collision rate constant between H$_3^+$ and H$_2$ is close to the Langevin rate constant, $k_L$ = 2$\pi$e($\alpha$/$\mu$)$^{1/2}$ = 1.9 $\times 10^{-9}$ cm$^3$ s$^{-1}$, (where $\alpha$ is the polarizability of H$_2$ and $\mu$ is the reduced mass of H$_3^+$ and H$_2$) \citep{rid04}, we see that the critical density for the (2, 2)$\rightarrow$ (1, 1) spontaneous emission is $\sim$ 200 cm$^{-3}$, comparable to the density of diffuse clouds. Therefore, the observed absence of H$_3^+$ in the (2, 2) level gives a definitive evidence for low density of the gas. The actual rate for the collision-induced transition from (1, 1) to (2, 2) is much less than the Langevin rate at low temperature because of the principle of detailed balancing. The value is also lower at very high temperatures because of dilution by collisional transitions from (1, 1) to other levels higher than (2, 2), but they are compensated for by the fact that the fast spontaneous emission will channel most of para-H$_3^+$ in high rotational levels to the (2, 2) $\rightarrow$ (1, 1) transition. Those are taken into account in the model calculations of Paper I. \section{Observations} %% In a manner similar to \objectname authors can provide links to dataset %% hosted at participating data centers via the \dataset{} command. The %% second curly bracket argument is printed in the text while the first %% parentheses argument serves as the valid data set identifier. Large %% lists of data set are best provided in a table (see Table 3 for an example). %% Valid data set identifiers should be obtained from the data center that %% is currently hosting the data. A log of the observations conducted by using three spectrometer/telescopes is given in Table 1. The Phoenix Spectrometer mounted on the 8 m Gemini South Telescope is the most suitable for the study because of its location in the southern hemisphere and the high spectral resolution (5 km s$^{-1}$) but its wavelength coverage is limited by the availability of filters. The Infrared Camera and Spectrograph (IRCS) on the 8 m Subaru Telescope is powerful for a survey because of its wide wavelength coverage based on a cross-dispersion grating, although its resolution is low (15 km s$^{-1}$). The Cold Grating Spectrometer-4 (CGS-4) on the 3.8 m United Kingdom Infrared Telescope (UKIRT) has resolution of 7 km s$^{-1}$ and can reach wavelengths widely in the L band. This had been the most productive machine for the study of H$_3^+$ until the recent advent of large diameter telescopes equipped with high resolution spectrometers, but it still is an extremely useful machine for our purposes. Details of operations of the spectrometers and data reduction are given in \citet{mcc02}, \citet{got02} and \citet{geb99}, respectively. Targets were chosen from bright young infrared stars with magnitude $L$ $\leq 7.5$ which have clean infrared continuum. Most of the bright stars near the Galactic center are late-type stars whose continuum is not smooth due to photospheric absorptions of atoms and molecules and are less appropriate for a detection of the weak absorption lines of H$_3^+$. For example, out of the 50 objects studied by \citet{nag93}, only 6 have been used so far. This could be partially overcome in the near future by subtracting standard photospheric absorptions from observed spectra. The infrared absorption spectroscopy has a disadvantage compared to radio observation that a mapping is difficult because observable sightlines are limited to directions of bright infrared sources. It has, however, advantages in high spatial resolution. Also the determination of column densities is more straightforward because of lower optical depths and availability of several transitions in the same wavelength region. \section{Results} Observed infrared absorption spectra toward GCS 3-2 corresponding to the $R$(1, 1)$^l$ , $R$(3, 3)$^l$, and $R$(2, 2)$^l$ transitions of H$_3^+$ in the L window and the $R$(1) transition of the $v$ = 2 - 0 overtone band of CO in the K window are compared in Fig. 1. GCS 3-2 is a young massive star bright in the infrared ($L$ = 3.03, $K$ = 6.19 \citep{nag93}). It is one of the quintuplet stars \citep{nag90, oku90} in the active star-forming region located approximately where the non-thermal Radio Arc crosses the Galactic plane at the Galactic coordinates $l$ = 10$\arcmin$, $b$ = $-$ 4$\arcmin$, close to the compact thermal structures of the Pistol and the Sickle \citep{gen94, cot00}. The intense and sharp absorptions with the velocity of $-$ 52 km s$^{-1}$, $-$ 33 km s$^{-1}$, $-$ 5 and +2 km s$^{-1}$, and + 19 km s$^{-1}$ and +23 km s$^{-1}$, that are clearly visible both in the H$_3^+$ $R$(1, 1)$^l$ and CO $R(1)$ spectra of Fig. 1 are known from the early days of the 21 cm HI spectroscopy and radio-observations of OH, H$_2$CO, and CO as due to clouds in the intervening spiral arms \citep{oor77}. The $-$ 52 km s$^{-1}$ absorption is due to the 3 kpc arm \citep{van57, rou60} and the $-$ 33 km s$^{-1}$ is due to the 4.5 kpc arm \citep{men70}. The absorption lines near 0 km s$^{-1}$, which are dominating and ubiquitous in the HI spectrum, is ascribed to the ``local" arms within a few kpc of the solar system. For CO and H$_3^+$, however, they may not be local because, unlike the HI line, they are not uniformly observed in all sightlines but only toward the Galactic center. \citet{whi79} suggested that some of them are near the Galactic center. Analyses and discussions of those sharp lines corresponding to the low temperature CO and H$_3^+$ are outside the scope of this paper and will be given in a separate paper. \subsection{Non-thermal Rotational Distribution Toward GCS 3-2} Here we focus our attention to the three broad absorption features with large equivalent widths at $-$ 123 km s$^{-1}$, $-$ 97 km s$^{-1}$ and $-$ 52 km s$^{-1}$ that are clearly visible in the $R$(3, 3)$^l$ spectrum of Fig. 1. These absorptions have been reported in our earlier paper with less clarity \citep{got02}. We now note also weaker broad absorptions at lower velocities. We argue in the following that these absorption features are due to ortho-H$_3^+$ in the ($J$, $K$) = (3, 3) metastable rotational level that exist abundantly in huge high temperature and low density turbulent clouds in the CMZ. First, note that the $R$(3, 3)$^l$ spectrum does not show any of the sharp features that are observed in the $R$(1, 1)$^l$ spectrum and in the $R$(1) CO spectrum. Note also that the CO spectrum does not show the broad features of the $R$(3, 3)$^l$ spectrum. Clearly the metastable H$_3^+$ and CO do not coexist. CO exist in relatively high density and low temperature areas with low velocity dispersion mostly in the intervening spiral arms, while the (3, 3) metastable H$_3^+$ exist in hotter, more turbulent regions in the CMZ. Second, note that the H$_3^+$ $R$(1, 1)$^l$ spectrum also shows the broad absorptions at $-$ 123 km s$^{-1}$, $-$ 97 km s$^{-1}$ and $-$ 52 km s$^{-1}$, although the $-$ 52 km s$^{-1}$ component is overlapped by the strong and sharp line of cold H$_3^+$ in the 3 kpc arm. The intensities (equivalent widths) of the three components are comparable between the $R$(1, 1)$^l$ and $R$(3, 3)$^l$ spectra indicating that the population in the (1, 1) ground level and the (3, 3) metastable level are comparable. Since the strength of the $R$(1, 1)$^l$ and $R$(3, 3)$^l$ transitions are $\mid \mu_{ij}\mid^2$ = 0.01407 D$^2$ and 0.01914 D$^2$, respectively, the same intensity means the population ratio of $N$(3, 3)/$N$(1, 1) = (14/3) exp ($-$ 361/$T$$_{ex}$) = 0.735, corresponding to the excitation temperature of $T$$_{ex}$ = 195 K. Because of spontaneous emissions between rotational levels of H$_3^+$, the kinetic temperature of the clouds $T$ is at least as high as $T_{ex}$ and is likely much higher. Third, note that the H$_3^+$ $R$(2, 2)$^l$ spectrum does not show any absorption for the $-$ 123 km s$^{-1}$ and $-$ 97 km s$^{-1}$ clouds ($\Delta$$I$ $\leq 0.3$ \%) although there seems to be a very weak absorption for the $-$ 52 km s$^{-1}$ cloud. These demonstrate a remarkably non-thermal H$_3^+$ rotational distribution in which the (3, 3) level 361 K above the ground level is highly populated while the (2, 2) level 151 K above the ground level is scarcely populated. This demonstrates that the cloud density is considerably lower than the critical density of the (2, 2) $\rightarrow$ (1, 1) spontaneous emission, $N_{crit}$ $\sim$ 200 cm$^{-3}$. Thus, the high temperature and low density of the clouds are established. The high negative velocities $\sim$$-$ 100 km s$^{-1}$ of the hot and diffuse clouds, peaking at $-$ 123 km s$^{-1}$ and $-$ 97 km s$^{-1}$, suggest that they are part of the colossal large-scale structure moving away from the Galactic center with a high speed that was initially proposed as the Expanding Molecular Ring (EMR) by \citet{kai72}, \citet{sco72} and \citet{kai74} on their ($l$-$V$) maps. It was later also interpreted as a parallelogram by \citet{bin91} and as an Expanding Molecular Shell (EMS) by \citet{sof95} based on the radio $^{13}$CO observations by \citet{bal87, bal88}. \citet{sof95} estimated that the total CO emission from the EMS amounts to 15 \% of the total emission from the CMZ. From a large-scale CO survey of the Galactic center, \citet{oka98a} pointed out the possibility that the EMR may consist of multiple arm-features that could be associated with different Lindblad resonances \citep{bin87} discussed by \citet{bin91} and \citet{bli93}. The observed double peak of the $R$(3, 3)$^l$ and $R$(1, 1)$^l$ spectrum must provide information on this issue. It is interesting to note that CO is observed for the $-$ 97 km s$^{-1}$ cloud but not for the $-$ 123 km s$^{-1}$ cloud. The small amount of CO in the cold and high density areas of those clouds in the particular direction of GCS 3-2 ($l$ = 10' and $b$ = $-$ 4') (Fig. 1) is in agreement with the observation of \citet{oka98a} (see their $l$-$V$ maps for $b$ = $-$ 4$\arcmin$ on page 493). The $R$(3, 3)$^l$ absorption at the velocity of $-$ 52 km s$^{-1}$ suggests that the hot and diffuse cloud also exists in the ``$-$ 50 km s$^{-1}$ cloud" that has been ascribed to the 3 kpc arm which merges into the corotating stars in the Galactic Stellar Bar of about 2.4 kpc \citep{bin91, wad94, mez96}. The radial location of the hot and diffuse gas is uncertain. However, the large velocity dispersion of the cloud suggests that it is in the CMZ. A comparison of the H$_3^+$ $R$(1, 1)$^l$ spectrum with the CO $R(1)$ spectrum shows that there is a wide and deep ``pedestal" in the former with velocities lower than $-$ 50 km s$^{-1}$, as already noted in our earlier work \citep{geb99, got02}. This will be discussed in more detail in the next section. Those cloud components are also weakly seen in the $R$(3, 3)$^l$ spectrum and demonstrate the presence of diffuse clouds without CO with lower temperature than those in the EMR. Probably all those clouds are located inside the CMZ closer to the Galactic center; their high velocity dispersion makes a sharp contrast to that of H$_3^+$ in many cold dense and diffuse clouds in the Galactic disk which always give sharp spectra \citep{geb96, mcc98a, geb99, mcc99, mcc02, mcc03, bri04}. Observations of many more sources distributed over a wider region of the CMZ under high spectroscopic resolution will be attempted in the near future to obtain a more detailed picture of those clouds. \subsection{Other Infrared Sources in the CMZ} The non-thermal distribution between the (3, 3) and (2, 2) rotational levels of H$_3^+$, demonstrating the presence of hot and diffuse clouds have also been observed toward other infrared sources in the CMZ. Fig. 2 shows the results of our Subaru observations of the $R$(1, 1)$^l$, $R$(3, 3)$^l$ and $R$(2, 2)$^l$ lines toward eight infrared sources; GC IRS 1W, GC IRS 3, and GC IRS 21 are near Sgr A* \citep{bec78, tol89} at the Galactic coordinates $l$ = 359.94$^{\circ}$ and $b$ = $-$ 0.05$^{\circ}$, while GCS 3-2, NHS 21, NHS 22, NHS 25, and NHS 42 are at nearly the same Galactic latitude but with higher longitudes ranging from $l$ = 0.10$^{\circ}$ to 0.16$^{\circ}$ \citep{nag90}. The relative positions of the stars are shown in Fig. 3 together with the VLA 90 cm image of the Galactic center by \citet{lar00}, which shows high magnetic activities in the region. In Fig. 2 we see in all targets the metastable $R$(3, 3)$^l$ absorption line which is the finger print of the high temperature, and the absence of the $R$(2, 2)$^l$ absorption which signifies the low density. Those observations demonstrate that the hot and diffuse gas exists widely in the CMZ. The velocity and location of the clouds, however, varies drastically depending on the individual sightline. Such a drastic dependence on the sightlines which are separated by only $\sim$ 1$\arcmin$-12$\arcmin$ provides a supporting evidence that those hot and diffuse gas are local in the CMZ and not in spiral arms closer to the solar system. Of particular interest is the pronounced broad $R$(3, 3)$^l$ absorption at v$_{LSR}$ $\sim$ 50 km s$^{-1}$ in the spectrum of GC IRS 3, which was noted also in our earlier work \citep{got02}. The strength of the $R$(3, 3)$^l$ absorption and the weakness or absence of the $R$(2, 2)$^l$ spectrum indicate that the hot and diffuse gas exists also in the region of the ``50 km s$^{-1}$ cloud", a complex of giant molecular clouds within 10 pc of the Galactic nuclei \citep{gus81}, that plays a central role in the discussion of Sagittarius A and its environment \citep{bro84, lis85}. From measurements of NH$_3$ emission and H$_2$CO absorption, \citet{gus81} and \citet{gus83} concluded that the 50 km s$^{-1}$ cloud is sandwiched between Sgr A West in the front and Sgr East in the back which is clearly confirmed in the recent CS observation by \citet{lan02} and the HI observation by \citet{lan04}. The observed $R$(3, 3)$^l$ spectrum demonstrates that GC IRS 3 is behind the 50 km s$^{-1}$ cloud and the Galactic nucleus. On the other hand, the same velocity component is not observed toward GC IRS 1W suggesting that this source is located in front of the nucleus. \citet{geb89} had the same situation in their infrared CO observation, where the 50 km s$^{-1}$ component was observed for GC IRS 3 and GC IRS 7, but not for GC IRS 1 and GC IRS 2. They tentatively concluded that the component is not due to the ``50 km s$^{-1}$ cloud" but due to the circumstellar molecular ring orbiting the nucleus at a radial; distance of $\sim$ 2 pc \citep{gen94} since otherwise the radial locations of the four stars are too far separated. Our present observation, however, indicates that the absorption is likely due to the ``50 km s$^{-1}$ cloud" since the circumnuclear molecular ring cannot have much extinction and it is surprising to detect H$_3^+$. Detailed analyses of the individual spectrum shown in Fig. 2 together with many more spectral lines observed at Subaru will be given in a separate paper. Here we simply emphasize that the hot and diffuse clouds are distributed widely in the CMZ. The drastic variation of the velocity and density of clouds within the Galactic latitude of 0.2$^{\circ}$ is not in disaccord with the CO observation by \citet{oka98a} (see their $l$-$V$ maps on page 493). Such spatial variation has also been reported in dust absorption by \citet{ada04}. \subsection{Infrared Sources in the Galactic disk} We have attempted to detect the $R$(3, 3)$^l$ metastable spectrum toward the many dense and diffuse clouds where large column densities of H$_3^+$ had been observed in the low (1, 1) and (1, 0) levels in order to check the possibility that those cold clouds are surrounded by hot and diffuse clouds containing metastable H$_3^+$. We have not been able to detect it in any of AFGL 2136 and W 33A \citep{geb96}, Cygnus OB2 12 \citep{mcc98a, geb99}, WR 118 and HD 183143 \citep{mcc02}, and StRS 217 and W51 IRS 1 (Geballe et al, in preparation). The hot and diffuse clouds seem unique for sightlines toward the Galactic center and to the CMZ. \section{Discussions} The semi-quantitative argument for the existence of hot and diffuse gas in the CMZ given in the previous section can be more quantified for the sightline of GCS 3-2 by comparing the observed data with the model calculation of the H$_3^+$ thermalization given in Paper I. According to the calculation, the population ratios $N$(3, 3)/$N$(1, 1) and $N$(3, 3)/$N$(2, 2) give crucial information on temperature and density of the cloud, respectively, as seen from the qualitative discussion in the previous section. Also, the excitation temperature determined from the population ratio $N$(1, 0)/$N$(1, 1) = 2 exp ($-$ 32.9/$T_{ex}$) gives independent (but less accurate) information on the temperature and the density of clouds. \subsection{Temperature and Density of Clouds toward GCS 3-2} Observed data for each cloud component toward GCS 3-2, that is, the local standard of rest velocity $v_{LSR}$, the $v_{LSR}$ range, the equivalent width $W_\lambda = \int (\Delta I(\lambda)/I)d\lambda$, and the corresponding H$_3^+$ column density in the lower level of absorption $N$(H$_3^+$)$_{level}$ = (3hc/8$\pi^3\lambda$)$W_\lambda$/$\mid\mu\mid^2$ are listed in Table 2. The wavelength $\lambda$ and the strength $\mid\mu\mid^2$ of the $R$(1, 1)$^l$, $R$(3, 3)$^l$, and $R$(2, 2)$^l$ transitions in D$^2$ are also given. As noted earlier, the $R$(1, 1)$^l$ spectrum is composed of sharp absorption lines due to H$_3^+$ in ``ordinary" clouds coexisting with a small amount of CO that are mostly in the intervening spiral arms, and broad features peaked at $v_{LSR}$ of $-$ 123 km s$^{-1}$, $-$ 97 km s$^{-1}$, and the ``pedestal" in the lower velocity region that are thought to be in the CMZ. They are separated as shown in Fig.~4, by using the close similarity between the sharp portion of the H$_3^+$ spectrum and the $R$(1) CO spectrum in Fig.~1. Measured values of $W_{\lambda}$ and $N$(H$_3^+$) are listed separately in Table 2. The values in parentheses are for sharp absorptions. The broad spectral features are unique for the sightlines toward the GC \citep{geb99, got02}; none of the ordinary dense and diffuse clouds observed so far in the Galactic disk \citep{geb96, mcc99, mcc02} has shown such velocity dispersion. We regard them as all in the CMZ and the following analysis is focussed on these broad absorption. Separating the broad spectrum into cloud components is difficult especially for the pedestal absorption, and we measured them for each $v_{LSR}$ range. For the $-$ 123 km s$^{-1}$ and $-$ 97 km s$^{-1}$ clouds where a deconvolution into gaussian components is feasible, the result was similar to the measurement by $v_{LSR}$ range. We separate the clouds with high velocity dispersions into three categories: (1) clouds with $v_{LSR}$ $\sim$ $-$ 100 km s$^{-1}$ (from $-$ 140 to $-$ 74 km s$^{-1}$ in Table 2) which are likely in the EMR, (2) the cloud with $v_{LSR}$ $\sim$ $-$ 50 km s$^{-1}$ (from $-$ 74 to $-$ 40 km s$^{-1}$) which is the velocity of the ``3 kpc arm", and (3) clouds with $v_{LSR}$ near 0 km s$^{-1}$ (from $-$ 40 to + 32 km s$^{-1}$) which gives the pedestal absorption. Observed values of $N$(H$_3^+$)$_{level}$ for the (1, 1), (3, 3), (2, 2), and (1, 0) rotational levels are listed in Table 3. They are the levels that are significantly populated apart from high metastable rotational levels ($J$, $J$) with $J$ = 4, 5, and 6. The values for the (1, 0) level are from our Subaru observations of the $Q$(1, 0) spectrum \citep{got02}; the separation of broad features from the sharp lines in this spectrum is not as clear as in the $R$(1, 1)$^l$ spectrum because of low resolution and the separation of $N$(H$_3^+$)$_{level}$ to sharp and broad features has high uncertainties for the second and the third clouds. In order to determine temperature and density of clouds, Fig. 4 of Paper I has been inverted to give $T$ and $n$ as a function of the observed population ratios $N$(3, 3)/$N$(1, 1) and $N$(3, 3)/$N$(2, 2) as shown in Fig. 5. Observed values of those ratios calculated from $N$(H$_3^+$)$_{level}$ listed in Table 3 gives the kinetic temperature and the density of clouds as shown in the last columns of Table 3. It is seen that all clouds have low densities of $\leq$ 200 cm$^{-3}$. Temperatures of the $-$ 100 km s$^{-1}$ and the $-$ 50 km s$^{-1}$ clouds are high, $\geq$ 250 K while that of the 0 km s$^{-1}$ clouds are lower but is still higher than those of ordinary diffuse clouds in the Galactic disk which have been determined from the observed values of $N$(1, 0)/$N$(1, 1) to be 25 - 50 K \citep{mcc02}. The excitation temperature $T_{ex}$ calculated from observed population ratio $N$(1, 0)/$N$(1, 1) provides an independent (but less direct) measure of cloud temperature when compared with Fig. 6 of Paper I. We note that it is $\sim$ 300 - 400 K for the $-$ 100 km s$^{-1}$ cloud and $\sim$ 200 - 250 K for the $-$ 50 km s$^{-1}$ cloud. Because of larger uncertainties in this method of determination both in the measurement and in the model calculations, we regard them as good agreement with those determined from $N$(3, 3)/$N$(1, 1). \subsection{Accuracy} The uncertainties of temperature and density listed in Table 3 are from standard deviation of our observations, but larger systematic errors are expected from inaccuracy of the model calculation of Paper I. Four assumptions were used in the calculation: (1) the steady state approximation, (2) the theoretical rates of spontaneous emissions, (3) the assumed rates of collision-induced rotational transitions given in Eq.(2) of Paper I, and (4) neglect of hydrogen atoms as collision partners. As noted in Paper I, we believe that errors introduced from (1) and (2) are at most 10 \% and are minor. Major sources of possible error are the assumptions (3) and (4) both of which introduce error mainly of the number density. Assumption (3) has three sources of errors: (a) the assumption of the completely random selection rules, (b) the formula given in Eq.(2), and (c) usage of the Langevin rate as the total collision rate. Out of these three, (c) is most liable to introduce large overall errors. The assumption is based on the microwave pressure broadening measurement of the HCO$^+$ - H$_2$ collision by \citet{and80} and the extensive experimental and theoretical studies of the collision by the group of de Lucia and Herbst \citep{pea95, lia96, oes01}. The latter papers show that the collision rate constant is close to the Langevin rate constant of 1.5 $\times$ 10$^{-9}$ cm$^3$ s$^{-1}$ for the temperature range of from 10 to 77 K both experimentally and theoretically. How well this applies to collisions of H$_3^+$ whose rotational energy separations are much larger than those of HCO$^+$ remains to be seen. Since experimental measurement of H$_3^+$ pressure broadening is next to impossible, theoretical calculations are awaited. Better still, a theoretical calculation of state to state transition probabilities induced by collisions will make the model calculation more accurate since it will eliminate errors caused from the assumptions (a) and (b) also. If the rate constant of the H$_3^+$ - H$_2$ collision is much lower than the Langevin rate, the number density of the cloud determined above will be an underestimate. We speculate that this error is within a factor of 2 at most especially at the high temperature of 250 K. A considerable fraction of hydrogen in the region of hot and diffuse gas may be in the atomic form due to photodissociation of H$_2$, although it has been noted that, because of the high volume density of the CMZ, even the intercloud hydrogen exists mainly in molecular form (\citet{bin94} quoted in \citet{mez96}). However, since the polarizability of H is comparable to that of H$_2$ (0.67 \AA$^3$ versus 0.79 \AA$^3$), the Langevin rate constants for the H$_3^+$ - H and H$_3^+$ - H$_2$ collisions are comparable (2.2 $\times$ 10$^9$ cm$^3$ s$^{-1}$ versus 1.9 $\times$ 10$^9$ cm$^3$ s$^{-1}$). Therefore, as long as we interpret the cloud density n as n(H$_2$) + n(H), the results of Paper I stand with good approximation. Overall we believe that the low cloud density on the order of 100 cm$^{-3}$ is secure. The claimed high temperature is less affected by the model calculation since it is simply based on the high energy value of the (3, 3) metastable level, unless there is some special pumping mechanism to cause the non-thermal distribution. We have not been able to find any. Unlike in H$_2$ or C$_2$, optical pumping is inconceivable since H$_3^+$ does not have stable electronic excited state. Infrared pumping is very unlikely since the H$_3^+$ vibrational transition is isolated in the middle of the L window from those of other molecules. Collisional pumping by the $J$ = 2 $\rightarrow$ 0 transition of H$_2$ at 510 K may discriminate the (3, 3) and (2, 2) levels to some extent but is unlikely to cause such a drastically non-thermal population. \subsection{Total H$_3^+$ Column Densities} According to the model calculation of Paper I, the (1, 1), (1, 0) and (3, 3) rotational levels accommodate most of the H$_3^+$ population with a very small fraction in the (2, 2) level at the temperature and density listed in Table 3. In addition, the higher metastable levels (4, 4), (5, 5), and (6, 6) accommodate non-negligible fraction of population. From Fig. 5 of Paper I we estimate the total column densities in the three high metastable levels to be 1.4 $\times$ 10$^{14}$ cm$^{-2}$, 0.4 $\times$ 10$^{14}$ cm$^{-2}$, and 0.1 $\times$ 10$^{14}$ cm$^{-2}$, for the $-$ 100 km s$^{-1}$, $-$ 50 km s$^{-1}$, and 0 km s$^{-1}$ cloud, respectively. The total H$_3^+$ column density toward GCS 3-2 including cold clouds in spiral arms is obtained by summing the total level column densities for the (1, 1), (3, 3) and (2, 2) levels given at the bottom of Table 2, the total H$_3^+$ column density for the (1, 0) level of (12.1 $\pm$ 1.5) $\times$ 10$^{14}$ cm$^{-2}$ determined from the $Q$(1, 0) line (see Table 3 of \citet{got02}), and the total column density of the high metastable levels estimated above, (1.9 $\pm$ 0.5) $\times$ 10$^{14}$ cm$^{-2}$ to be (4.3 $\pm$ 0.3) $\times$ 10$^{15}$ cm$^{-2}$ in agreement with our previous value of 4.6 $\times$ 10$^{15}$ cm$^{-2}$ \citep{got02}. The total H$_3^+$ column density in low rotational levels (1, 1) and (1, 0), (3.3 $\pm$ 0.3) $\times$ 10$^{15}$ cm$^{-2}$, is also in approximate agreement with our earlier value of 2.8 $\times$ 10$^{15}$ cm$^{-2}$ \citep{geb99}. Out of the total column density of (4.3 $\pm$ 0.3) $\times$ 10$^{15}$ cm$^{-2}$, 1.2 $\times$ 10$^{15}$ cm$^{-2}$ are due to H$_3^+$ in the cold cloud mostly in the intervening spiral arms while 3.1 $\times$ 10$^{15}$ cm$^{-2}$ are in hotter clouds in the CMZ. Visual extinction toward GCS 3-2 is calculated to be $A_V$ $\sim$ 30 from Fig. 20 of \citet{cot00}. How much of this is due to dense and diffuse clouds is not known. If the ratio is like toward Sgr A*, i.e., 1 to 2 \citep{whi97}, the amount of H$_3^+$ in dense clouds is nearly negligible since, as mentioned in Section 1, the H$_3^+$ column density per unit extinction in dense clouds is 10 times smaller than in diffuse clouds. Even if we assume that the clouds in the sightline are all diffuse clouds, which gives the maximum H$_3^+$ column density, the empirical formula for the Galactic disk of N(H$_3^+$) $\sim$ 4.4 $\times$ 10$^{13}$ cm$^{-2}$ $A_V$ gives 1.3 $\times$ 10$^{15}$. The observed H$_3^+$ column density toward GCS 3-2 is about 3 times greater. This is particularly surprising since the C/H ratio is reported to be higher near the Galactic center at least by a factor 3 \citep{sod95, ari96} which will make the H$_3^+$ number density lower as shown below. This suggests that the ionization rate in the CMZ is higher than in diffuse clouds in the Galactic disk by an order of magnitude. \subsection{Other Properties of the Clouds toward GCS 3-2} Many more observations are needed in order to elucidate the nature of the hot and diffuse gas in the CMZ other than their temperature and density. Nevertheless, we can speculate on some physical and chemical properties of the clouds based on the data obtained so far and the understanding of H$_3^+$ in the diffuse interstellar medium gained from our previous studies. One of the salient properties of H$_3^+$ as an astrophysical probe is the simplicity and generality of its chemistry. This allows us to express its number density in diffuse clouds in terms of the number densities of H$_2$ and electron as $n$(H$_3^+$) = ($\zeta$/$k_e$)[$n$(H$_2$)/n(e)], where $\zeta$ is the ionization rate of H$_2$ and k$_e$ is the rate constant of the dissociative recombination of H$_3^+$ with electrons \citep{mcc98a, mcc98b, geb99, mcc02}. This formula represents the remarkable property of $n$(H$_3^+$) that it is independent of the cloud density as long as the ratio $n$(H$_2$)/$n$(e) is approximately constant in the cloud. The H$_3^+$ column density can thus be expressed as $N$(H$_3^+$) = $n$(H$_3^+$)$L$ in terms of the column length $L$ in good approximation and we obtain $\zeta$$L$ = $k_e$ $N$(H$_3^+$)[$n$(e)/$n$(H$_2$)] = 2$k$$_e$$N$(H$_3^+$)($n_C$/$n_H$)/$f$, where it is assumed that carbons are mostly in the atomic form (which matches with the absence of broad CO line in Fig. 1) and are ionized due to its low ionization potential, and $f$ is the fraction of hydrogen atom in the molecular form $f$ = 2$n$(H$_2$)/[2$n$(H$_2$) + $n$(H)] $\leq$ 1. The carbon to hydrogen ratio ($n_C$/$n_H$) in the CMZ has been reported to be higher than 3.7 $\times$ 10$^{-4}$ of the solar vicinity by at least a factor of 3 \citep{sod95, ari96, mez96}. \subsubsection{The $-$ 100 km s$^{-1}$ cloud} The hot and diffuse clouds with velocities of $-$ 123 km s$^{-1}$ and $-$ 97 km s$^{-1}$ are most likely associated with the EMR. Those clouds summarily called ``the $-$ 100 km s$^{-1}$ cloud" have more than half of H$_3^+$ in the CMZ and provides the most definitive information since its spectrum is least interfered by that of cold H$_3^+$ in the intervening spiral arms. Using the total column density of (1.6 $\pm$ 0.2) $\times$ 10$^{15}$ cm$^{-2}$ listed in Table 3 and $k_e$ = 7.3 $\times 10^{-8}$ cm$^3$ s$^{-1}$ for $T$ = 270 K calculated from Eq. (7) of \citet{mcc04}, we obtain $\zeta$$L$ = 8.7 $\times 10^4$ $\Phi$/$f$ cm s$^{-1}$, where $\Phi$ = ($n_C$/$n_H$)$_{GC}$/($n_C$/$n_H$)$_{SV}$ is enhancement of metallicity near the Galactic center over that of solar vicinity. For the canonical value of the interstellar cosmic ray ionization rate of $\zeta = 3 \times 10^{-17}$ s$^{-1}$, this formula gives a huge value of $L$ $\sim 1$ kpc even for $f$ = 1 and $\Phi$ = 1 which is clearly unreasonable; this situation is the same as in the other ordinary diffuse clouds in the Galactic disk \citep{mcc98a, geb99, mcc02}. \citet{mcc03} used $\zeta$ = 1.2 $\times$ 10$^{-15}$ s$^{-1}$, 40 times higher than the canonical value of $\zeta$, for explaining the H$_3^+$ column density observed in the classic visible sightline toward $\zeta$ Per. This value of $\zeta$ gives $L$ $\sim$ 23$\Phi$/$f$ pc which is not as absurd but is still too high since $\Phi$$\geq$ 3 and $f$ $\leq$ 1. Based on the $^{13}$CO observations by \citet{bal87, bal88}, \citet{sof95} estimated the thickness of the EMS to be $\sim$ 15 pc. The value of $f$ is not known but the absence of HI absorption in the spectrum of the Arched Filament complex and small absorption in the Sickle near the sightline of the quintuplet by \citet{lan04} suggests that $f$ is perhaps between 1 and 1/2. If the value of $\Phi$ is 3 - 10 \citep{sod95}, the pathlength is calculated to be 70 - 230 pc even for $f$ = 1 which is clearly unreasonably high. This strongly suggest that the ionization rate $\zeta$ in the CMZ is much higher than that in the diffuse interstellar medium in the Galactic disk. In order to make the pathlength on the order of 20 pc, the value of the ionization rate must be on the order of 4 - 14 $\times$ 10$^{-15}$ s$^{-1}$. Such high ionization rate, however, will introduce all sort of other consequences discussed recently by \citet{lis03}. The simple formula given above need to be modified. \subsubsection{The $-$ 50 km s$^{-1}$ cloud} The radial location of this cloud, which has a slightly lower temperature and higher density than the $-$ 100 km s$^{-1}$ cloud, is uncertain. The broad absorption of the metastable $R$(3, 3)$^l$ spectrum and in the pedestal of the $R$(1, 1)$^l$ spectrum show that the hot and diffuse clouds are in the CMZ. Whether the agreement of their velocity and that of the 3 kpc arm is accidental or not remains to be seen. The 3 kpc spiral arm merges into the Galactic bar and reach the CMZ (Fig. 4 of \citet{mez96}) but how their velocity varies depending on their location is not known. Observations of many more infrared sources may provide clearer picture of this cloud. The total H$_3^+$ column density of the cloud is (7 $\pm$ 1) $\times$ 10$^{14}$ cm$^{-2}$. Therefore, we obtain the cloud path length of L = 10 $\Phi$/f pc. The chemical conditions of this cloud is likely similar to that of the $-$ 100 km s$^{-1}$ cloud. The ionization rate in this cloud must also be comparable to the value given above for the $-$ 100 km s$^{-1}$ cloud. \subsubsection{The 0 km s$^{-1}$ cloud} This is a complex of many clouds in the CMZ located at various distances from the Galactic nucleus with lower temperature and higher density than the $-$ 100 km s$^{-1}$ and $-$ 50 km s$^{-1}$ clouds. The temperature listed in Table 3 with a high uncertainty is an average value of those clouds. Some clouds may well have temperature outside the uncertainties in Table 3. There may also be some cloud with a density higher than 200 cm$^{-3}$. Nevertheless, the average value indicates that most clouds are diffuse and their temperatures are higher than the usual diffuse clouds in the Galactic disk. Observations of more sightlines toward infrared stars in the CMZ may enable us to separate some clouds. The total H$_3^+$ column density of this cloud is (8 $\pm$ 2) $\times$ 10$^{14}$ cm$^{-2}$, and the total cloud path length is $L$ = 10 $\Phi$/$f$ pc, which is too high. The quintuplet stars are young high mass stars with high intrinsic luminosity of $\sim$ 10$^5$ $L_{\bigodot}$ \citep{oku90} in an active star forming region and efficient photo-ionization is expected for the interstellar medium; also their location near the Radio Arc suggests high MHD activity. For clouds in the vicinity of such an area, the effective value of $\zeta$ may well be an order of magnitude higher than in diffuse clouds in the Galactic disk. The discussions of the cloud dimension $L$ and the ionization rate $\zeta$ in this section 4.4 are based on the dissociative rate constant $k_e$ reported by \citet{mcc03, mcc04}. While this value has also been supported theoretically by \citet{kok03a, kok03b}, there still is a possibility that the number is not final. Since laboratory experiment cannot be performed completely in the conditions of interstellar conditions, further theoretical confirmation is highly desirable. \subsection{Dense Clouds} The above analysis shows that almost all H$_3^+$ observed in the CMZ are in diffuse clouds with densities on the order of 100 cm$^{-3}$. This is primarily because the H$_3^+$ column density per unit visible extinction is ten times higher in diffuse clouds ($\sim$ 4.4 $\times$ 10$^{13}$ cm$^{-2}A_V$) than in dense clouds ($\sim$ 3.6 $\times$ 10$^{12}$ cm$^{-2}A_V$). Nevertheless, if indeed the CMZ contains high density gas ($\geq$ 10$^4$ cm$^{-3}$) with a high volume filling factor ($\geq$ 0.1) as mentioned in \citet{mor96}, we should have easily observed H$_3^+$ in dense clouds. Dense clouds in the Galactic disk surrounding AFGL 2136 and W 33A with a pathlength of 1.3 pc and 1.7 pc showed H$_3^+$ column densities of 3.8 $\times$ 10$^{14}$ cm$^{-2}$ and 5.2 $\times$ 10$^{14}$ cm$^{-2}$, respectively \citep{mcc99}. Therefore dense clouds with a pathlength of 20 pc will give a deep H$_3^+$ absorption even if the line is broad and the metallicity is high. Also it gives the H$_2$ column density of 6 $\times$ 10$^{23}$ cm$^{-2}$ which would have been easy to detect through the infrared absorption spectrum \citep{lac94} even if the cloud has a high velocity dispersion. From their negative attempt at such observation, Usuda and Goto (manuscript in preparation) set an upper limit of the H$_2$ column density of 7.5 $\times$ 10$^{21}$ cm$^{-2}$ toward GCS 3-2. \citet{rod01} report ``a few 10$^{22}$ cm$^{-2}$" toward 16 sources. While it is possible that the sightline toward GCS 3-2 and the 7 other stars studied in this paper (and those stars used for other references cited above) happen to have low density of statistical fluctuation, it is more likely that the combination of the high density of $\geq$ 10$^4$ cm$^{-3}$ and the large volume filling factor of $f$ $\geq$ 0.1 is a gross overestimate. This gives mass of the gas in the CMZ which is much higher than 5 - 10 $\times$ 10$^7$ $M_{\bigodot}$ estimated from radio observations of molecules (see many references quoted in \citet{mor96}). More recent papers of \citet{oka98b} and \citet{tsu99}, using $J$ = 2 - 1 of CO and $J$ = 1 - 0 of CS, respectively, give even lower mass values. Also the large dense cloud path length of 20 pc would give a visual extinction which is more than an order of magnitude higher than $A_V$ = 25 - 40 reported by \citet{cot00} for four large regions within 40 pc of the Galactic center. Out of many molecular emissions used to study the CMZ, the 1 - 0 emission of CO and inversion spectrum of NH$_3$ cannot provide evidence of dense clouds since their critical densities are lower than 10$^4$ cm$^{-3}$ by more than an order of magnitude. The CO emission of 2 - 1 \citep{oka98b} and higher \citep{har85}, and the 1 - 0 emission of CS \citep{tsu99, saw01}, HCN, HCO$^+$ \citep{lin81, wri01} etc. provide definitive information of high density clouds but their filling factor is probably much lower than 0.1 and more likely 0.01 or even less. The high fraction of $\sim$ 10 \% which is quoted as a ratio of gas in the CMZ to the total gas content of the Galaxy (see for example \citet{dah98}) must also be a gross overestimate. \section{Summary} We have detected high column densities of H$_3^+$ indicating huge hot and diffuse clouds with high velocity dispersion toward the Galactic center which are likely all in the CMZ. The observed high column densities of H$_3^+$ in the ($J$, $K$) = (3, 3) metastable rotational level, which is 361 K above the (1,1) ground level, provides definitive evidence for the high temperature, and the observed absence or small quantity in the (2, 2) level, which is 210 K lower than the (3, 3) level, provides evidence for the low density. This remarkable non-thermal rotational distribution caused by the fast spontaneous emission from the (2, 2) to (1, 1) level is observed toward several infrared sources in the CMZ indicating the ubiquity of such clouds. The hot and diffuse gas toward the brightest infrared source GCS 3-2 in the Quintuplet Cluster has been quantitatively studied. The total H$_3^+$ column density toward the star, 4.3 $\times$ 10$^{15}$ cm$^{-2}$ are separated into that of the cold H$_3^+$ mostly in the intervening spiral arms, 1.2 $\times$ 10$^{15}$ cm$^{-2}$, and that of hotter gas, mostly in the CMZ, 3.1 $\times$ 10$^{15}$ cm$^{-2}$. The latter is grouped into three classes. The biggest cloud with velocity $-$ 100 km s$^{-1}$ and the large H$_3^+$ column density of (15.7 $\pm$ 1.7) $\times$ 10$^{14}$ cm$^{-2}$, high temperature of $T$ $\sim$ 270 K, and low density $n$ $\leq$ 50 cm$^{-3}$ is most likely associated with the EMR. In order to make the radial dimension of this cloud within a reasonable number of, say 20 pc, we need to assume a very high ionization rate approaching $\zeta$ = 10$^{-14}$ s$^{-1}$ if we take into account the higher metallicity in the CMZ. The observed two peaks at $-$ 123 km s$^{-1}$ and $-$ 97 km s$^{-1}$ indicate a structure of EMR. The $-$ 50 km s$^{-1}$ clouds whose signal is overlapped with sharp absorptions of cold H$_3^+$ in the 3 kpc spiral arms has total H$_3^+$ column density of (6.6 $\pm$ 1.3) $\times$ 10$^{14}$ cm$^{-2}$, the temperature of $\sim$ 250 K and density of $\sim$ 70 cm$^{-3}$. The radial distance of this cloud from the Galactic center is uncertain. Whether the agreement of the velocity of this cloud with that of the 3 kpc spiral arm is accidental or not remains to be seen. The 0 km s$^{-1}$ cloud is composed with several clouds in the CMZ and has a total H$_3^+$ column density of (8.4 $\pm$ 1.6) $\times$ 10$^{14}$ cm$^{-2}$ and lower average temperature of $\sim$ 120 K and higher density of $\leq$ 200 cm$^{-3}$. Almost all of H$_3^+$ in the CMZ exist in low density clouds. The volume filling factor of high density clouds, $f$ $\geq$ 0.1 must be a gross overestimate. We will further study H$_3^+$ and CO toward many more infrared stars in the CMZ including those at larger distances from the Galactic nuclei and this will enable us to study more clouds and provide a clearer overall picture. Questions abound on the hot and diffuse clouds: How are they related to dense clouds studied by neutral molecules and the HII regions studied by hydrogen recombination lines? What is their relation with the intense X-rays and strong magnetohydrodynamic effect? What is their heating mechanism? How is the pressure balanced? More H$_3^+$ observations may provide unique information for some of those questions. \acknowledgments We are grateful to Tetsuya Nagata for providing us information on the suitability of the NHS stars for the H$_3^+$ observations, and to Cornelia Lang for giving us the HI radio spectrum of the Sickle prior to publication. We are grateful to Harvey Liszt and Tomoharu Oka for critical reading of this paper and to, Mark Morris, Tetsuya Nagata, Giles Novak, Tomoharu Oka, Masato Tsuboi, and Farhad Yusef-Zadeh for helpful discussions on the Galactic center. T. O. acknowledges the NSF grant PHY-0354200. T. R. G.'s research is supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom and the United States of America. M. G. is supported by a Japan Society for Promotion of Science fellowship. \clearpage \begin{thebibliography}{} \bibitem[Adamson et al.(2004)]{ada04} Adamson, A., Mason, R., MacDonald, E., Wright, G., Chiar, J., Pendleton, Y., Kerr, T., Bowey, J., Whittet, D., \& Rawlings, M. 2004, \\\emph {Proceedings of the Galactic Center Workshop 2002, the Central 300 parsecs of the Milky Way} pp 211-215, ed. A. Cotera, S. Markoff, T. R. Geballe, and H. Falcke, Wiley-VCH \bibitem[Anderson et al.(1980)]{and80} Anderson, T. G., Gudeman, C. S., Dixon, T. A., \& Woods, R. C. 1980, J. Chem. Phys., 72, 1332 \bibitem[Arimoto, Sofue, \& Tsujimoto(1996)]{ari96} Arimoto, N., Sofue, Y., \& Tsujimoto, T. 1996, \pasj, 48, 275 \bibitem[Bally et al.(1987)]{bal87} Bally, J., Stark, A. A., Wilson, R. W., \& Henkel, C. 1987, \apjs, 65, 13 \bibitem[Bally et al.(1988)]{bal88} Bally, J., Stark, A. A., Wilson, R. W., \& Henkel, C. 1988, \apj, 324, 223 \bibitem[Becklin et al.(1978)]{bec78} Becklin, E. E., Matthews, K., Neugebauer, G., \& Willner, S. P. 1978, \apj, 219, 121 \bibitem[Binney \& Tremaine(1987)]{bin87} Binney, J., \& Tremaine S. 1987, $\emph{Galactic Dynamics}$, Princeton University Press, Princeton, New Jersey \bibitem[Binney et al.(1991)]{bin91} Binney, J., Gerhard, O. E., Stark, A. A., Bally, J., \& Uchida, K. I. 1991, \mnras, 252, 210 \bibitem[Binney(1994)]{bin94} Binney, J., 1994, \emph {The Nuclei of Normal Galaxies -- Lessons from the Galactic Center}, pp 75, ed R. Genzel, and A. I. Harris, Dordrecht: Kluwer. \bibitem[Blitz et al.(1993)]{bli93} Blitz, L., Binney, J., Lo, K. Y., Bally, J., \& Ho, P. T. P. 1993, Nature, 361, 417 \bibitem[Brittain et al.(2004)]{bri04} Brittain, S. D., Simon, T., Kulesa, C., \& Rettig, T. W. 2004, \apj, 606, 911 \bibitem[Brown \& Liszt(1984)]{bro84} Brown, R. L., \& Liszt, H. S. 1984, \araa, 22, 223 \bibitem[Butchart et al.(1986)]{but86} Butchart, I., McFadzean, A. D., Whittet, D. C. B., Geballe, T. R., \& Greenberg, J. M. 1986, \aap, 154, L5 \bibitem[Cordonnier et al.(2000)]{cor00} Cordonnier, M., Uy, D., Dickson, R. M., Kerr, K. E., Zhang, Y., \& Oka, T. 2000, J. Chem. Phys., 113, 3181 \bibitem[Cotera et al.(2000)]{cot00} Cotera, A. S., Simpson, J. P., Erickson, E. F., Colgan, S. W. J., Burton, M. G., \& Allen, D. A. 2000, \apjs, 129, 123 \bibitem[Dahmen et al.(1998)]{dah98} Dahmen, G., H\"{u}ttemeister, S., Wilson, T. L., \& Mauersberger, R. 1998, \aap, 331, 959 \bibitem[Geballe, Baas, \& Wade(1989)]{geb89} Geballe, T. R., Baas, F., \& Wade, R. 1989 \aap, 208, 255 \bibitem[Geballe \& Oka(1996)]{geb96} Geballe, T. R.,\& Oka, T. 1996, Nature, 384, 334 \bibitem[Geballe et al.(1999)]{geb99} Geballe, T. R., McCall, B. J., Hinkle, K. H., \& Oka, T. 1999, \apj, 510, 251 \bibitem[Genzel, Hollenbach, \& Townes(1994)]{gen94} Genzel, R., Hollenbach, D., \& Townes, C. H. 1994, Rep. Prog. Phys., 57, 417 \bibitem[Goto et al.(2002)]{got02} Goto, M., McCall, B. J., Geballe, T. R., Usuda, T., Kobayashi, N., Terada, H., \& Oka, T. 2002, \pasj, 54, 951 \bibitem[Green \& Chapman(1978)]{gre78} Green, S., \& Chapman, S. 1978, \apjs, 37, 169 \bibitem[G\"{u}sten, Walmsley, \& Pauls(1981)]{gus81} G\"{u}sten, R., Walmsley, C. M., \& Pauls, T. 1981, \aap, 103, 197 \bibitem[G\"{u}sten \& Henkel(1983)]{gus83} G\"{u}sten, R., \& Henkel, C. 1983, \aap, 125, 136 \bibitem[Harris et al.(1985)]{har85} Harris, A. I., Jaffe, D. T., Silber, M., \& Genzel, R. 1985, \apj, 294, L93 \bibitem[Herrnstein \& Ho(2002)]{her02} Herrnstein, R. M., \& Ho, P. T. P. 2002, \apj, 579, L 83 \bibitem[H\"{u}ttemeister et al.(1993)]{hut93} H\"{u}ttemeister, S., Wilson, T. L., Bania, T. M., \& Mart\'{\i}n-Pintado, J. 1993, \aap, 280, 255 \bibitem[Kaifu, Kato, \& Iguchi(1972)]{kai72} Kaifu, N., Kato, T., \& Iguchi, T. 1972, Nature, 238, 105 \bibitem[Kaifu, Iguchi, \& Kato(1974)]{kai74} Kaifu, N., Iguchi, T., \& Kato, T. 1974, PASJ, 26, 117 \bibitem[Kim et al.(2002)]{kim02} Kim, S., Martin, C. L., Stark, A. A., \& Lane, A. P. 2002, \apj, 580, 896 \bibitem[Kokoouline \& Greene(2003a)]{kok03a} Kokoouline, V., \& Greene, C. H. 2003a, Phys. Rev. Lett., 90, 133201-1 \bibitem[Kokoouline \& Greene(2003b)]{kok03b} Kokoouline, V., \& Greene, C. H. 2003b, Phys. Rev., A68, 012703 \bibitem[Koyama et al.(1989)]{koy89} Koyama, K., Awaki, H., Kunieda, H., Takano, S., Tawara, Y., Yamauchi, S., Hatsukade, \& I., Nagase, F. 1989, Nature, 339, 603 \bibitem[Koyama et al.(1996)]{koy96} Koyama, K., Maeda, Y., Sonobe, T., Takeshima, T., Tanaka, Y., \& Yamauchi, S. 1996, \pasj, 48, 249 \bibitem[Kreckel et al.(2004)]{kre04} Kreckel, H., Tennyson, J., Schwalm, D., Zajfman, D., \& Wolf, A. 2004, New J. Phys., 6, 151 \bibitem[Lacy et al.(1994)]{lac94} Lacy, J. H., Knacke, R., Geballe, T. R., \& Tokunaga, A. T. 1994, \apj, 428, L69 \bibitem[Lang, Goss, \& Morris(2002)]{lan02} Lang, C. C., Goss, W. M., \& Morris, M. 2002, \aj, 124, 2677 \bibitem[Lang et al.(2004)]{lan04} Lang, C. C., Cyganowski, C., Goss, W. M., \& Zhao, J. -H. 2004 \\\emph{Proceedings of the Galactic Center Workshop 2002, the Central 300 parsecs of the Milky Way} pp 1-7, ed. A. Cotera, S. Markoff, T. R. Geballe, and H. Falcke, Wiley-VCH \bibitem[LaRosa et al.(2000)]{lar00} LaRosa, T. N., Kassim, N. E., Lazio, T. J. W., \& Hyman, S. D. 2000, \aj, 119, 207 \bibitem[Liao \& Herbst(1996)]{lia96} Liao, Q., \& Herbst, E. 1996 J. Chem. Phys., 104, 3956 \bibitem[Linke, Stark, \& Frerking(1981)]{lin81} Linke, R. A., Stark, A. A., \& Frerking, M. A. 1981 \apj, 243, 147 \bibitem[Liszt(2003)]{lis03} Liszt, H. S. 2003 \aap, 398, 621 \bibitem[Liszt, Burton, \& van der Hulst(1985)]{lis85} Liszt, H. S., Burton, W. B., \& van der Hulst, J. M. 1985 \aap, 142, 237 \bibitem[Mauersberger et al.(1986)]{mau86} Mauersberger, R., Henkel, C., Wilson, T. L., \& Walmsley, C. M. 1986, \aap, 162, 199 \bibitem[McCall et al.(1998a)]{mcc98a} McCall, B. J., Geballe, T. R., Hinkle, K. H., \& Oka, T. 1998a, Sciene, 279, 1910 \bibitem[McCall et al.(1999)]{mcc99} McCall, B. J., Geballe, T. R., Hinkle, K. H., \& Oka, T. 1999, \apj, 522, 338 \bibitem[McCall et al.(1998b)]{mcc98b} McCall, B. J., Hinkle, K. H., Geballe, T. R., \& Oka, T. 1998b, Faraday Discuss., 109, 267 \bibitem[McCall et al.(2002)]{mcc02} McCall, B. J., Hinkle, K. H., Geballe, T. R., Moriarty-Schieven, G. H., Evans, N. J., II, Kawaguchi, K., Takano, S., Smith, V. V., \& Oka, T. 2002, \apj, 567, 391 \bibitem[McCall et al.(2003)]{mcc03} McCall, B. J., Huneycutt, A. J., Saykally, R. J., Geballe, T. R., Djuric, N., Dunn, G. H., Semaniak, J., Novotny, O., Al-Khalili, A., Ehlerding, A., Hellberg, F., Kalhori, S., Neau, A., Thomas, R. D., \"{O}sterdahl, F., \& Larsson, M. 2003, Nature, 422, 500 \bibitem[McCall et al.(2004)]{mcc04} McCall, B. J., Huneycutt, A. J., Saykally, R. J., Djuric, N., Dunn, G. H., Semaniak, J., Novotny, O., Al-Khalili, A., Ehlerding, A., Hellberg, F., Kalhori, S., Neau, A., Thomas, R. D., Paal, A., \"{O}sterdahl, F., \& Larsson, M. 2004, Phys. Rev., A70, 052716 \bibitem[Menon \& Ciotti(1970)]{men70} Menon, T, K., \& Ciotti, J. E. 1970, Nature, 227, 579 \bibitem[Mezger, Duschl \& Zylka(1996)]{mez96} Mezger, P, G., Duschl, W. J., \& Zylka, R. 1996, Astron. Astrophys. Rev., 7, 289 \bibitem[Morris \& Serabyn(1996)]{mor96} Morris, M., \& Serabyn, E. 1996, \araa, 34, 645 \bibitem[Nagata et al.(1993)]{nag93} Nagata, T., Hyland, A. R., Straw, S. M., Sato, S., \& Kawara, K. 1993, \apj, 406, 501 \bibitem[Nagata et al.(1990)]{nag90} Nagata, T., Woodward, C. E., Shure, M., Pipher, J. L., \& Okuda, H. 1990, \apj, 351, 83 \bibitem[Neale, Miller, \& Tennyson(1996)]{nea96} Neale, L., Miller, S., \& Tennyson, J. 1996, \apj, 464, 516 \bibitem[Odenwald \& Fazio (1984)]{ode84} Odenwald, S. F., \& Fazio, G. G. 1984, \apj, 283, 601 \bibitem[Oesterling et al.(2001)]{oes01} Oesterling, L. C., De Lucia, F. C. \& Herbst, E. 2001, Spectrochim. Acta A, 57, 705 \bibitem[Oka(1980)]{oka80} Oka, T. 1980, Phys. Rev. Lett. 45, 531 \bibitem[Oka(2004a)]{Oka04a} Oka, T. 2004a, J. Mol. Spectrosc. 228, 635 \bibitem[Oka(2004b)]{oka04b} Oka, T. 2004b, \emph{The Dense Interstellar Medium in Galaxies}, pp. 37-42, ed. S. Pfalzner, C. Kramer, C. Staubmeier, \& A. Heithausen, Springer-Verlag, Berlin, Heidelberg \bibitem[Oka \& Epp(2004)]{oke04} Oka, T., \& Epp, E. 2004, \apj, 613, 349 \bibitem[Oka et al.(1998b)]{oka98b} Oka, T., Hasegawa, T., Hayashi, M., Handa, T., \& Sakamoto, S. 1998b, \apj, 493, 730 \bibitem[Oka et al.(1998a)]{oka98a} Oka, T., Hasegawa, T., Sato, F., Tsuboi, M., \& Miyazaki, A. 1998a, \apjs, 118, 455 \bibitem[Oka et al.(2001)]{oka01} Oka, T., Hasegawa, T., Sato, F., Tsuboi, M., \& Miyazaki, A. 2001, \pasj, 53, 779 \bibitem[Oka et al.(1971)]{oka71} Oka, T., Shimizu, F. O., Shimizu, T., \& Watson, J. K. G. 1971, \apj, 165, L15 \bibitem[Okuda et al.(1990)]{oku90} Okuda, H., Shibai, H., Nakagawa, T., Matsuhara, H., Kobayashi, Y., Kaifu, N., Nagata, T., Getley, I., \& Geballe, T. R. 1990, \apj, 351, 89 \bibitem[Oort(1977)]{oor77} Oort, J. H. 1977, \araa, 15, 295 \bibitem[Pan \& Oka(1986)]{pan86} Pan, F.-S., \& Oka, T. 1986, \apj, 305, 518 \bibitem[Pearson et al.(1995)]{pea95} Pearson, J. C., Oesterling, L. C., Herbst, E., \& DeLucia, F. C. 1995, Phys. Rev. Lett. 75, 2940 \bibitem[Pendleton et al.(1994)]{pen94} Pendleton, Y. J., Sanford S. A., Allamandola, L. J., Tielens, A. G. G. M., \& Sellgren, K. 1994, \apj, 437, 683 \bibitem[Pierce-Price et al.(2000)]{pie00} Pierce-Price, D., Richer, J. S., Grieves, J. S., Holland, W. S., Jenness, T., Lasenby, A. N., White, G. J., Matthews, H. E., Ward-Thompson, D., Dent, W. R. F., Zylka, R., Mezger, P., Hasegawa, T., Oka, T., Omont, A., \& Gilmore, G. 2000, \apj, 545, L121 \bibitem[Ridge (2004)]{rid04} Ridge, D. P. 2004, \emph {The Encyclopedia of Mass Spectrometry, Vol. 1, Theory and Ion Chemistry} ed. P. B. Armentrout, pp 1 - 8, Elsevier, Amsterdam \bibitem[Rodr\'{\i}guez-Fern\'{a}ndez et al.(2001)]{rod01} Rodr\'{\i}guez-Fern\'{a}ndez, N. J., Mart\'{\i}n-Pintado, J., Fuente, A., de Vincente, P., Wilson, T. L., \& H\"{u}ttemeister, S. 2001, \aap, 365, 174 \bibitem[Rodr\'{\i}guez-Fern\'{a}ndez et al.(2004)]{rod04} Rodr\'{\i}guez-Fern\'{a}ndez, N. J., Mart\'{\i}n-Pintado, J., Fuente, A., \& Wilson, T. L. 2004, \aap, 427, 217 \bibitem[Rougoor \& Oort(1960)]{rou60} Rougoor, G. W., \& Oort, J. H. 1960, Proc. Natl. Acad. Sci. USA, 46, 1 \bibitem[Sawada et al.(2001)]{saw01} Sawada, T., Hasegawa, T., Handa, T., Morino, J., Oka, T., Booth, R., Bronfman, L., Hayashi, M., Castellanos, A. L., Nyman, L., Sakamoto, S., Seta, M., Shaver, P., Sorai, K., \& Usuda, K. S. 2001, \apjs, 136, 189 \bibitem[Scoville(1972)]{sco72} Scoville, N. Z. 1972, \apj, 175, L127 \bibitem[Sofue(1995)]{sof95} Sofue, Y. 1995, \pasj, 47, 551 \bibitem[Sodroski et al.(1995)]{sod95} Sodroski, T. J., Odegard, N., Dwek, E., Hauser, M. G., Franz, B. A., Freedman, I., Kelsall, T., Wall, W. F., Berriman, G. B., Odenwald, S. F., Bennett, C., Reach, W. T., \& Weiland, J. L. 1995, \apj, 452, 262 \bibitem[Tollestrup, Capps, \& Becklin(1989)]{tol89} Tollestrup, E. V., Capps, R. W., \& Becklin, E. E. 1989, \aj, 98, 204 \bibitem[Tsuboi, Ukita, \& Handa(1997)]{tsu97} Tsuboi, M., Ukita, N., \& Handa, T. 1997, \apj, 481, 263 \bibitem[Tsuboi, Handa, \& Ukita(1999)]{tsu99} Tsuboi, M., Handa, T., \& Ukita, N. 1999, \apjs, 120, 1 \bibitem[van Woerden, Rougoor, \& Oort(1957)]{van57} van Woerden, H., Rougoor, G. W., \& Oort, J. H. 1957, C. R. Acad. Sciences, Paris, 244, 1691 \bibitem[Wada et al.(1994)]{wad94} Wada, K., Taniguchi, Y., Habe, A., \& Hasegawa, T. 1994, \apj, 437, L 123 %\bibitem[Watson(1971)]{wat71} Watson, J. K. G. 1971, J. Mol. Spectrosc., 40, %536 \bibitem[Whiteoak \& Gardner(1979)]{whi79} Whiteoak, J. B., \& Gardener, F. F. 1979, \mnras, 188, 445 \bibitem[Whittet et al.(1997)]{whi97} Whittet, D. C. B., Boogert A. C. A., Gerakines, P. A., Schutte, W. , Tielens, A. G. G. M., de Graauw, Th., Prusti, T., van Dishoeck, E. F., Wesselius, P. R., \& Wright, C. M. 1997 \apj, 490, 729 \bibitem[Willner et al.(1979)]{wil79} Willner, S. P., Russell, R. W., Puetter, R. C., Soifer, B. T., \& Harvey, P. M. 1979 \apj, 229, L65 \bibitem[Wilson et al.(1982)]{wil82} Wilson, T. L., Ruf, K., Walmsley, C. M., Martin, R. N., Pauls, T. A., \& Batrla, W. 1982 \aap, 115, 185 \bibitem[Wright et al.(2001)]{wri01} Wright, M. C. H., Coil, A. L., McGray, R. S., Ho, P. T. P., \& Harris, A. I. 2001 \apj, 551, 254 \bibitem[Yusef-Zadeh, Law, \& Wardle(2002)]{yus02} Yusef-Zadeh, F., Law, C., \& Wardle, M. 2002, \apj, 568, L121 \bibitem[Yusef-Zadeh, Morris, \& Chance(1984)]{yus84} Yusef-Zadeh, F., Morris, M., \& Chance, D. 1984, Nature, 310, 557 \end{thebibliography} \clearpage \begin{figure} \epsscale{.80} \plotone{f1.eps} \caption{Observed H$_3^+$ (top three) and CO spectra toward GCS 3-2. The three H$_3^+$ spectra are (from the top) the $R$(1, 1)$^l$, $R$(3, 3)$^l$, and $R$(2, 2)$^l$ transitions, starting from the (1, 1) ground level, the (3, 3) metastable level, and the (2, 2) unstable level, respectively. The $R$(3, 3)$^l$ and $R$(2, 2)$^l$ spectra are multiplied by a factor of 2 and the CO spectrum is divided by 2 for clarity. The abundant H$_3^+$ in the (3, 3) level which is higher than (1, 1) by 361 K demonstrate high temperature of clouds, and the absence of H$_3^+$ in the (2, 2) level 210 K below the (3, 3) level clearly demonstrates the low density. The velocity of the two clouds $-$ 123 km s$^{-1}$ and $-$ 97 km s$^{-1}$ suggests that they are in the EMR.\label{fig1}} \end{figure} \clearpage \begin{figure} \epsscale{.50} \plotone{f2.eps} \caption{The $R$(1, 1)$^l$, $R$(3, 3)$^l$, and $R$(2, 2)$^l$ spectral lines observed by the IRCS of Subaru toward bright infrared sources in the CMZ, GC IRS 1W, GC IRS 3, GC IRS 21, NHS 21, NHS 22, NHS 42, NHS 25, and GCS 3-2. Note that all targets show the $R$(3, 3)$^l$ metastable spectrum indicating the high temperature and none of them show clear $R$(2, 2)$^l$ spectrum indicating the low density of clouds.} \end{figure} \clearpage \begin{figure} \epsscale{1} \plotone{f3.eps} \caption{Location of infrared stars toward which hot and diffuse clouds have been observed. The overlapped radio VLA 90 cm image is from \citet{lar00}. GC IRS 1W, GC IRS 3, and GC IRS 21 are close to Sgr A*. GCS 3-2 is one of the quituplet stars which are located close to NHS 25, the Pistol Star. Both of them are very close to the non-thermal Radio Arc \citep{yus84, cot00}. NHS 22 is located approximately 2' to the west of the quintuplet stars. NHS 42 and NHS 21 are located off the Radio Arc. \label{fig3}} \end{figure} \clearpage \begin{figure} \epsscale{1.5} \plotone{f4.eps} \caption{The H$_3^+$ $R$(1, 1)$^l$ spectrum toward GCS 3-2 (the top trace of Fig. 1) separated into sharp components that are caused by cold H$_3^+$ in intervening spiral arms and broad components that are caused by hot and diffuse clouds with high velocity dispersion that are most likely in the CMZ. \label{fig4}} \end{figure} %% This figure uses \includegraphics to scale and rotate the still frame %% for an mpeg animation. \clearpage \begin{deluxetable}{llllllrlllc} \tabletypesize{\scriptsize} \rotate \tablecaption{Log of observations} \tablewidth{0pt} \tablehead{ \colhead{UT date} & \colhead{Telescope} & \colhead{Instrument} & \colhead{Object} & \colhead{RA(2000)} & \colhead{D(2000) } & \colhead{$l$($^{\circ}$)} & \colhead{$b$($^{\circ}$)} & \colhead{Spectrum} & \colhead{$\lambda(\mu$m)} & \colhead{time(min)} } \startdata July 23, 03 & Gemini S & Phoenix & GCS 3-2 &17 46 14.9& -28 49 43& 0.16 & -0.06& H$_3^+$ $R$(1, 1)$^l$ & 3.7155 & 20 \\ July 24, 03 & Gemini S & Phoenix & GCS 3-2 &&&&& H$_3^+$ $R$(2, 2)$^l$ & 3.6205 & 30 \\ Apr. 2, 04 & Gemini S & Phoenix & GCS 3-2 &&&&& CO $R$(0)-$R$(3) & 2.342& 8 \\ July 7, 04 & Subaru & IRCS & GCS 3-2 &&&&& H$_3^+$ multiline & --- & 45 \\ & Subaru & IRCS & GC IRS 3 & 17 45 39.6 & -29 00 24 & -0.06& -0.04& H$_3^+$ multiline & --- & 52 \\ July 8, 04 & Subaru & IRCS & GC IRS 3 &&&&& H$_3^+$ multiline & --- & 40 \\ & Subaru & IRCS & NHS 21 & 17 46 04.3 & -28 52 49 & 0.10 & -0.06 & H$_3^+$ multiline & --- & 100 \\ July 27, 04 & Subaru & IRCS & GC IRS 1W & 17 45 40.2& -29 00 27& -0.06 & -0.05& H$_3^+$ multiline & --- & 85 \\ & Subaru & IRCS & NHS 42 & 17 46 08.3& -28 49 55& 0.15& -0.04 & H$_3^+$ multiline & --- & 80 \\ July 28, 04 & Subaru & IRCS & GC IRS 21 & 17 45 40.2& -29 00 30& -0.06& -0.05& H$_3^+$ multiline & --- & 30 \\ Aug. 30, 04 & UKIRT & CGS4 & GCS 3-2 &&&&& H$_3^+$ $R$(3, 3)$^l$ & 3.5337 & 8.2 \\ Sept. 1, 04 & UKIRT & CGS4 & GCS 3-2 &&&&& H$_3^+$ $R$(2, 2)$^l$ & 3.6205 & 45 \\ Sept. 2, 04 & Subaru & IRCS & GC IRS 21 &&&&& H$_3^+$ multiline & --- & 40 \\ Sept. 4, 04 & Subaru & IRCS & NHS 22 & 17 46 05.6& -28 51 32& 0.12& -0.05& H$_3^+$ multiline & --- & 40 \\ & Subaru & IRCS & NHS 25 & 17 46 15.3 & -28 50 04& 0.16& -0.07& H$_3^+$ multiline & --- & 40 \\ Sept. 25, 04 & Subaru & IRCS & GC IRS 3 &&&&& H$_3^+$ multiline & --- & 50 \\ Sept. 26, 04 & Subaru & IRCS & GC IRS 3 &&&&& H$_3^+$ multiline & --- & 32 \\ \enddata %% Text for table notes should follow after the \enddata but before %% the \end{deluxetable}. Make sure there is at least one \tablenotemark %% in the table for each \tablenotetext. \end{deluxetable} %% If you use the table environment, please indicate horizontal rules using %% \tableline, not \hline. %% Do not put multiple tabular environments within a single table. %% The optional \label should appear inside the \caption command. \clearpage %% If the table is more than one page long, the width of the table can vary %% from page to page when the default \tablewidth is used, as below. The %% individual table widths for each page will be written to the log file; a %% maximum tablewidth for the table can be computed from these values. %% The \tablewidth argument can then be reset and the file reprocessed, so %% that the table is of uniform width throughout. Try getting the widths %% from the log file and changing the \tablewidth parameter to see how %% adjusting this value affects table formatting. %% The \dataset macro has also been applied to a few of the objects to %% show how many observations can be tagged in a table. %\begin{table} %\begin{center} \begin{deluxetable}{ccrccrcc} \tabletypesize{\scriptsize} \rotate \tablecaption{Observed velocities, equivalent widths, and the H$_3^+$ column densities of clouds toward GCS 3-2} \tablewidth{0pt} \tablehead{ \colhead{$v_{LSR}$} & \colhead{Range}& & \colhead{$W_\lambda$ } &&& \colhead{$N$(H$_3^+$)$_{level}$} & } \startdata [km s$^{-1}$] & [km s$^{-1}$] & & [10$^{-5} \mu$m] & && [10$^{14}$ cm$^{-2}$]& \\ && $R$(1, 1)$^{l,a}$& $R$(3, 3)$^l$ & $R$(2, 2)$^l$ &(1, 1)$^b$ & (3, 3) & (2, 2)\\ \tableline - 123& - 140 $\rightarrow$ - 113 & 0.56 $\pm$ 0.10& 0.32 $\pm$ 0.14 & $\leq$ 0.07 & 2.6 $\pm$ 0.5 & 1.1 $\pm$ 0.5 & $\leq$ 0.3 \\ - 97& - 113 $\rightarrow$ - 74 & (0.04) 0.96 $\pm$ 0.14 & 0.93 $\pm$ 0.20 & $\leq$ 0.10 & (0.2) 4.4 $\pm$ 0.6 & 3.3 $\pm$ 0.7 & $\leq$ 0.4 \\ \tableline - 52& - 74 $\rightarrow$ - 40 & (0.63) 0.57 $\pm$ 0.12 & 0.46 $\pm$ 0.18 & 0.12 $\pm$ 0.11 & (2.9) 2.6 $\pm$ 0.5 & 1.6 $\pm$ 0.6 & 0.4 $\pm$ 0.4 \\ \tableline - 33& - 40 $\rightarrow$ - 26 & (0.30) 0.27 $\pm$ 0.05 & 0.08 $\pm$ 0.07 & $\leq$ 0.05 & (1.4) 1.2 $\pm$ 0.2 & 0.3 $\pm$ 0.3 & $\leq$ 0.2 \\ & - 26 $\rightarrow$ - 13 & 0.23 $\pm$ 0.05 & 0.08 $\pm$ 0.07 & $\leq$ 0.05 & 1.1 $\pm$ 0.2 & 0.3 $\pm$ 0.3 & $\leq$ 0.2 \\ - 5 & - 13 $\rightarrow$ +12 & (0.48) 0.40 $\pm$ 0.09 & 0.10 $\pm$ 0.13 & $\leq$ 0.05 & (2.2) 1.8 $\pm$ 0.4 & 0.4 $\pm$ 0.5 & $\leq$ 0.2 \\ +19 & +12 $\rightarrow$ +32 & (0.03) 0.17 $\pm$ 0.05 & $\leq$ 0.05 & $\leq$ 0.04 & (0.1) 0.8 $\pm$ 0.2 & $\leq$ 0.2 & $\leq$ 0.1 \\ \tableline & Total & 4.64 $\pm$ 0.24 & 1.97 $\pm$ 0.35 & 0.12 $\pm$ 0.11 & 21.3 $\pm$ 1.1 & 7.0 $\pm$ 1.2 & 0.4 $\pm$ 0.4 \\ \tableline\tableline & Transition & $\lambda$ ($\mu$m) & $\mid\mu\mid^{2}$ (D$^2$) &&&& \\ & $R$(1, 1)$^l$ & 3.7155 & 0.01407 &&&& \\ & $R$(3, 3)$^l$ & 3.5227 & 0.01914 &&&& \\ & $R$(2, 2)$^l$ & 3.6205 & 0.01772 &&&& \\ \enddata %\end{tabular} %% Any table notes must follow the \end{tabular} command. \tablenotetext{a}{The equivalent widths of the $R$(1, 1) spectrum are separated into those of sharp features in the parantheses and broad features. No sharp features exists in the $R$(3, 3)$^l$ and $R$(2, 2)$^l$ spectra.} \tablenotetext{b}{The column densities of the (1, 1) level are separated into those of sharp features in the parentheses and broad features.} %\end{center} %\end{table} \end{deluxetable} \clearpage \begin{deluxetable}{ccccccccccc} \tabletypesize{\scriptsize} \rotate \tablecaption{The H$_3^+$ column densities, temperatures and densities of the three groups of clouds with high velocity dispersion toward GCS 3-2}\tablewidth{0pt} \tablehead{ \colhead{Clouds} & \colhead{$v_{LSR}$}& \colhead{Range } &&& \colhead{$N$(H$_3^+$)$_{level}$ } & \colhead{ } & & &\colhead{$T$} &\colhead{$n$} } \startdata & [km s$^{-1}$] & [km s$^{-1}$] & & & [10$^{14}$cm$^{-2}$] & & & & [K] & [cm$^{-3}$] \\ & & & (1, 1) & (3, 3) & (2, 2) & (1, 0)& HM$^a$ & Total && \\ \tableline ``$-$ 100 km s$^{-1}$" & $-$ 123, $-$ 97 & $-$ 140 $\rightarrow$ $-$74 & 7.0 $\pm$ 0.8 & 4.4 $\pm$ 0.9 & $\leq$ 0.7 & 2.9 $\pm$ 1.0 & 1.4 $\pm$ 0.7 & 15.7 $\pm$ 1.7 & 270 $\pm$ 70 & $\leq$ 50\\ ``$-$ 50 km s$^{-1}$" & $-$ 52 & $-$ 74 $\rightarrow$ $-$ 40 & 2.6 $\pm$ 0.5 & 1.6 $\pm$ 0.6 & 0.4 $\pm$ 0.4 & 1.6 $\pm$ 0.9 & 0.4 $\pm$ 0.2 & 6.6 $\pm$ 1.3 & 250 $\pm$ 100 & $\leq$ 100 \\ ``0 km s$^{-1}$" & $-$ 33, $-$ 5, +19 & $-$ 40 $\rightarrow$ +32 & 4.9 $\pm$ 0.5 & 1.0 $\pm$ 0.7 & $\leq$ 0.7 & 2.4 $\pm$ 1.3& 0.1 $\pm$ 0.1 & 8.4 $\pm$ 1.6 & 130 $\pm$ 100 & $\leq$ 200 \\ \tableline Total & & & 14.5 $\pm$ 1.1 & 7.0 $\pm$ 1.3 & 0.4 $\pm$ 0.4 & 6.9 $\pm$ 1.9 & 1.9 $\pm$ 0.7 & 30.7 $\pm$ 2.7 & & \\ \enddata \tablenotetext{a}{HM represents sum of the calculated H$_3^+$ column densities for high nmetastable levels (4, 4), (5, 5), and (6, 6).} %\vspace{5in} %\end{tabular} %% Any table notes must follow the \end{tabular} command. %\tablenotetext{a}{}\tablenotetext{b}{} %\end{center} %\end{table} \end{deluxetable} %% \input{table} \end{document}