Free Access
Issue
A&A
Volume 568, August 2014
Article Number A122
Number of page(s) 16
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201322639
Published online 04 September 2014

© ESO, 2014

1. Introduction

Multiple rotational transitions of CO are a powerful tool to study the physical environment and the excitation conditions of molecular gas in galaxies. For galaxies harboring active galactic nuclei (AGN), the nuclear activity is often powered by the molecular gas surrounding the nuclear region, and the feedback – jets, winds, and radiation – may enhance or quench the star-forming (S-F) activity (e.g., Bundy et al. 2008; Sani et al. 2010). The excitation of molecular gas in the torus (~a few pc to tens of pc) and in the circumnuclear disk (CND; a few tens to hundreds of pc) reflects the activity invoked by the illumination from the central supermassive black hole (SMBH; e.g., Schinnerer et al. 2000; Pérez-Beaupuits et al. 2011; Harada et al. 2013). Because of its symmetry, molecular hydrogen (H2) has no permanent dipole moment and its infrared transitions require high excitation conditions, thus the H2 emission is not able to trace molecular clouds (e.g., Kennicutt & Evans 2012). Carbon monoxide (CO), the second most abundant molecule, has a dipole moment of 1.122 Debye and is heavy enough for a rotational spectrum accessible at submillimeter (submm) wavelengths, tracing both cold and warm gas. CO lines are therefore regarded as the best tracers to the probe the physical properties and the excitation conditions of the entire molecular gas reservoir (e.g., Mao et al. 2000; van der Werf et al. 2010; Papadopoulos et al. 2012b).

So far, in nearby galaxies most studies of the molecular gas emission focus on the J = 1 → 0, 2 → 1, and 3 → 2transitions of CO (e.g., Braine et al. 1993; Dumke et al. 2001; Israel & Baas 2003; Wilson et al. 2011). At high redshifts mid-J (4 ≤ J ≤ 8) CO transitions are almost exclusively measured (e.g., Omont et al. 1996; Carilli et al. 2010; Wang et al. 2010). Therefore, observations of the mid-J transitions in some nearby galaxies are essential to investigate the gas excitation, as reference of the high-redshift galaxies. Such studies have been focused on nearby S-F galaxies such as NGC 253, IC 342, and NGC 4038, (e.g., Güsten et al. 2006; Hailey-Dunsheath et al. 2008; Bayet et al. 2009), but only a few nearby galaxies with prominent AGNs have been studied so far in these mid-J CO lines (e.g., NGC 1068; Israel 2009a; Spinoglio et al. 2012).

The Circinus galaxy is a prototypical Seyfert-2 galaxy located in the southern sky, at a small distance of D ~ 4Mpc (e.g., Maiolino et al. 1998; Tully et al. 2009). Although it has a large angular size (80) at optical wavelengths and in atomic gas (Hi), Circinus was not discovered until the 1970s (Freeman et al. 1977; Jones et al. 1999), because it is located only ~4° above the Galactic plane with a Galactic visual extinction of 4.8 mag (e.g., Schlegel et al. 1998). H2O mega-masers at both mm and submm wavelengths were found in the center of Circinus (e.g., Greenhill et al. 2003; Hagiwara et al. 2013), indicating a molecular torus around the central SMBH. The mass of the SMBH is estimated to be 1.7 ± 0.3 × 106M (e.g., Greenhill et al. 2003), and the torus accretion rate is as high as ~20% of the Eddington luminosity (e.g., Tristram et al. 2007).

A large amount of molecular gas in Circinus was detected through the 12COJ = 1 → 0 and 13COJ = 1 → 0 observations by Aalto et al. (1991), with the Swedish-ESO 15m Submillimeter Telescope (SEST). Besides the isotopologues of CO lines (i.e., 13CO, C18O), Curran et al. (2001) contained rich molecular spectra, including lines from HCN, HNC, and HCO+, which indicate the presence of highly excited dense gas in the central region of Circinus. Furthermore, Circinus was also mapped in the J = 1 → 0, 2 → 1, and 3 → 2 transitions of CO (Curran et al. 2001, 2008). With the deconvolved 12COJ = 2 → 1 map, Johansson et al. (1991) found a face-on molecular ring structure, which seems to be associated with the S-F ring shown in Hα (Marconi et al. 1994). Curran et al. (1998, 1999) found that the gas kinematics could be modeled with a highly inclined molecular ring and two outflows using the 12COJ = 2 → 1 data.

Hitschfeld et al. (2008) observed the 12COJ = 4 → 3 and Ci3PP0 (hereafter Ci 10) lines in the center of Circinus with the NANTEN-2 4 m telescope. They studied the molecular gas excitation and predicted that the global CO cooling curve peaks at the J = 4 → 3 transition, however, higher-J CO transitions are still needed to test their model and to compare the results with other nearby galaxies at similar scales. The turnover of the global CO line ladders is also very important for comparisons with molecular line surveys of gas-rich S-F objects (e.g., Blain et al. 2000; Combes et al. 1999; Geach & Papadopoulos 2012; Carilli & Walter 2013). With the large beam sizes of the single dish telescopes in the published low-J observations, it is in any case difficult to explore the excitation conditions in the very central region of Circinus. For these reasons, we have performed high-resolution mapping observations of mid-J CO lines and the Ci 1 → 0 transition in the central region of Circinus.

This article is organized as follows. Section2 describes the observational methods and data reduction procedure. Section3 presents the spectra and maps. In Sect.4, the CO lines are analyzed using large velocity gradient (LVG) modeling. The discussion of the data and our modeling results are also presented. In Sect.5, our findings and conclusions are summarized. Throughout this paper, we adopt for the distance of Circinus a value of 4.2Mpc (Freeman et al. 1977). Thus 1′′ corresponds to ~20pc.

2. Observations and data reduction

2.1. CO and CI 10 spectral line observations

Table 1

Parameters of 13CO, 12CO, and Ci observations

The observations were performed with the 12-m Atacama Pathfinder EXperiment (APEX) telescope1 on the Chajnantor Plateau in Chile. Most observations were obtained in good (τ< 0.3 at 810 GHz) to median (τ ~ 0.6 − 1 at 345 GHz and 460 GHz) weather conditions during several runs between 2006 and 2010. The Ci 1 → 0 data and a part of the 12COJ = 3 → 2 data were taken simultaneously on 14 July, 2010, with the FLASH dual-frequency receiver. 12COJ = 6 → 5 and 7 → 6 maps were obtained simultaneously with the CHAMP+ 7-pixel receiver array (Kasemann et al. 2006), during June and August 2009. Single point 13COJ = 3 → 2 measurements were taken toward the central position of Circinus (α(J2000) = 14h13m10.0s, δ(J2000) = −65°20′21.″0) in July 2006 and October 2009. Fast Fourier Transform Spectrometer (FFTS) backends (Klein et al. 2006) were employed in all observations, with channel spacings of 1 or 2 MHz, which were then smoothed to suitable velocity resolutions in the data reduction.

We determined focus every four to five hours on Saturn and Jupiter. We calibrated pointing every one to two hours. This ensures 2 (rms) pointing uncertainties derived from G327.3–0.6 for 12COJ = 6 → 5 and 12COJ = 7 → 6. The angular resolution varies from 18′′ (for 12COJ = 3 → 2) to 8′′ (for 12COJ = 7 → 6), according to the observing frequencies. At the 345 GHz and 460 GHz bands, because there was no suitable strong nearby pointing calibrator at similar elevations, we made pointing calibrations with planets, NGC6334I (about 40° away from Circinus), and the strong 12COJ = 3 → 2 emission from Circinus itself. Here we estimate systematic position errors to be ~5′′ (rms).

We carried out the mapping observations in raster scan or on-the-fly (OTF) mode. We used a position of 10 to the east of the center of Circinus as the sky reference. Except for 13COJ = 3 → 2, which was only measured at the central position of Circinus, all CO lines are fully sampled in the innermost ~ 40″ × 40″ (~800 × 800 pc) with Nyquist sampling. The mapped sizes of 12COJ = 6 → 5 and 7 → 6 are about 80′′ × 60′′, but the inner 40′′ × 40′′ region has a better root mean square (rms) noise level than that in the outer region because the integration time was longer in the center. Ci 1 → 0 is mapped in a region of size ~15″ × 25″.

All observations were performed with frequencies corresponding to a velocity of νLSR ~ 420kms-1 (Local Standard of Rest). We list the observation date, instruments, typical rms. noise levels, system temperatures, telescope efficiencies, and map sizes for different epochs in Tables 1 and 2.

2.2. Spectral line data reduction

All spectral line data are reduced with the CLASS/GILDAS2 package. We inspect each spectrum by eye and classify the spectral quality from baseline flatness and system temperature levels. About 5% of the spectra are discarded, except for 13COJ = 3 → 2 and 12COJ = 7 → 6, for which 50% and 20% of the data have to be dropped respectively, because of unstable baselines. Linear baseline is subtracted for each individual spectrum. All spectra are then coadded and resampled to 5 kms-1 velocity resolution.

We find that the emission peaks and the intensity distributions of 12COJ = 3 → 2, 4 → 3, and Ci 10 observed during different epochs have offsets of ~3 − 5′′, which are likely caused by our limited pointing accuracy. These offsets are systematic for each observing epoch. Within the limits of pointing errors (<1/4 of the beam size), relative intensity distributions are the same for the observed maps. We assume that the central position of Circinus should show particularly strong CO emission with a symmetrical line profile, and this profile should also correspond to the peak position of the integrated intensity in an individual map. We fit the map distributions and shift the positions of 12COJ = 3 → 2, 4 → 3, and Ci 10 accordingly, and then coadd the maps to improve signal-to-noise ratios (S/N). From several measurement epochs, we estimate calibration uncertainties to be 10% for 12COJ = 3 → 2 and 4 → 3, and 15% for 12COJ = 6 → 5 and 7 → 6.

We convert the antenna temperature () to the main beam brightness temperature (Tmb) scale, using , where ηf and Beff are the forward hemisphere and beam efficiency of the telescope. We list them in Table 1. All spectra presented in this paper are in units of Tmb(K). In Table 2 we list frequencies, angular resolutions, and noise levels of the reduced data.

For each transition, we combine all the calibrated spectra and use the gridding routine XY_MAP in CLASS to construct datacubes, with weightings proportional to 1/σ2, where σ is the rms. noise level. This routine convolves the gridded data with a Gaussian kernel of full width to half maximum (FWHM) ~1/3 the telescope beam size, yielding a final angular resolution slightly coarser than the original beam size. For the analysis below, we further convolve the datacubes to several angular resolutions to facilitate comparisons with data from the literature.

Table 2

Parameters of the observed lines.

2.3. Other archival data

We obtained a 70 μm image observed with the Photoconductor Array Camera and Spectrometer (PACS) on board the Herschel space telescope3 through the Herschel Science Archive. We downloaded the post processed data of level 2.5. The observation ID is 1342203269, and it contains data observed on 20 August 2010. We also used an archival Hα image of the Hubble Space Telescope (HST; Wilson et al. 2000), downloaded from the NASA/IPAC Extragalactic Database (NED).

3. Results

3.1. Spatial distributions

3.1.1. Herschel 70 μm and HST maps of the Circinus galaxy

The left panel of Fig. 1 shows Herschel 70 μm contours overlaid on an HST Hα image (Wilson et al. 2000). The 70 μm emission has a concentration in the very central region, and an extended emission out to about 40′′ (in diameter). The Hα emission shows structures of both the S-F ring and the central nuclear region. Therefore, we separate the center of Circinus into three regions: the nuclear region (D< 18′′~ 360pc), the entire central 45′′ (D< 45′′ ~ 900pc) region, and the S-F ring region (18′′<D< 45′′). We define the Hα bright ring like structure as the S-F ring, rather than the ring structure modeled in Curran et al. (1999). The concentric circles show the nuclear region (white) and the entire central region (red) including both the nucleus and the S-F ring. The peak of the 70 μm emission is consistent with the center of the CO emission (e.g., Curran et al. 2001), and has a slight shift down to the south of the Hα peak, which is likely attenuated by the dust extinction. The central 18′′ region contributes ~20% of the 70 μm emission of the entire galaxy. These features are also consistent with the Spitzer mid-infrared images (For et al. 2012).

thumbnail Fig. 1

Left panel: Herschel 70 μm contours overlaid on an Hα image of the HST (Wilson et al. 2000). The contour levels are 500, 1000, 2000, 3000, and 4000 MJy/sr. The concentric circles show the beam sizes of 12COJ = 3 → 2 for APEX (18′′, white thick line) and 12COJ = 1 → 0 for SEST (45′′, red dashed line). Right panel: CO spectra observed in the central position. 12COJ = 6 → 5, 7 → 6, and Ci are multiplied by a factor of 2, and 13COJ = 3 → 2 is multiplied by a factor of 5. The (shaded) line emission ranges from ~200 to ~700kms-1.

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3.1.2. CO and Ci 10 spectra

The CO and Ci spectra from the central position (Fig. 1, right panel) are shown with their original angular resolutions (before the convolution in XY_MAP). Although the 12COJ = 7 → 6 and Ci lines have relatively low S/N, all of the line profiles look fairly similar, i.e., their intensity ratios are constant to within 30% as a function of velocity. This implies that overall, the gas components probed by the different lines follow the same kinematics.

We convolve Gaussian kernels with all datacubes to match the angular resolutions of the low-J CO data. Using the beam matched datacubes, we extract spectra in the central position and calculate the integrated line intensities in the velocity range from 200 kms-1 to 700 kms-1. Table3 summarizes the observed line properties at the angular resolutions of 18′′ and 45′′.

Figure 2 shows spectra of Ci and 12COJ = 3 → 2 from the central region of Circinus. We obtained these two lines simultaneously, free from pointing inaccuracy. We overlay their spectra in their original angular resolutions, ~12.5′′ for Ci and ~18′′ for 12COJ = 3 → 2. At most positions, there is no obvious discrepancy between the line profiles of 12COJ = 3 → 2 and Ci, neither in the central position nor at the edges of the mapped region.

thumbnail Fig. 2

Ci 10 and 12COJ = 3 → 2 spectra from the central region of the Circinus galaxy. The Ci spectra are relatively noisier and are presented in red, while the 12COJ = 3 → 2 profiles are plotted in black. To reach similar intensities, Ci is scaled up by a factor of three.

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Table 3

CO line intensities.

3.1.3. CO and Ci maps

Figure 3 presents the integrated intensity images (moment-zero maps) of all 12CO transitions mapped with the APEX telescope. The dotted thick (red) contour lines present half of the peak intensity level for each map. The CO emission of all transitions is well confined within the central 40′′ × 40′′ region. To increase the S/N level of 12COJ = 7 → 6, we convolved it to the angular resolution of the 12COJ = 3 → 2 map. The 12COJ = 6 → 5 and J = 7 → 6 distributions show elongations along the major axis, i.e., along the direction from the northeast to the southwest. The thin dotted contours (blue) in the 12COJ = 6 → 5 and J = 7 → 6 maps mark the regions with almost uniform scanning coverage in the OTF mappings, so these regions have lower noise levels than those outside. We mask the corners of the 12COJ = 7 → 6 image to avoid displaying regions farther out with high noise and poor baselines.

To explore the sizes of the emitting regions in different CO transitions, we deconvolve the moment-zero maps with circular Gaussian beams, and fit the source sizes using two-dimensional Gaussian models. For 12COJ = 3 → 2, 4 → 3, and 6 → 5, the beam sizes (FWHM) of 18′′, 14.0′′, and 9.4′′ (see Table 2) are adopted to deconvolve the images, respectively. The S/N of the 12COJ = 7 → 6 map is not high enough to provide reliable fitting results. We list the fitting parameters in Table 4. For 12COJ = 3 → 2 we get a position angle of 33.5°, which is adopted in the following analysis to define the major axis of molecular gas emission. This result is also close to the position angle of 34° derived from 12COJ = 1 → 0 and 2 → 1 maps (Curran et al. 2008). The fitted position angle of Ci 10 is 65.5°, which is much larger than those determined from the CO images. This is most likely a consequence of the small size of our Ci map. Because Ci emission follows CO in all studied cases (e.g., Ikeda et al. 2002; Zhang et al. 2007), a different distribution is highly unlikely.

Table 4

Fitting parameters of CO moment-zero maps.

thumbnail Fig. 3

Moment-zero images of multiple-J CO transitions. Big crosses mark the central position of Circinus; small crosses in the upper panels denote the sampled positions. Upper left: 12COJ = 3 → 2; upper right: 12COJ = 4 → 3; lower left: 12COJ = 6 → 5; lower right: 12CO J = 7 → 6. Circles in the lower left of each panel show the beam. The 12COJ = 7 → 6 map was convolved to an angular resolution of 18′′. Contour levels are 20, 60, ..., 180 Kkms-1in steps of 40 Kkms-1 for 12COJ = 3 → 2, J = 4 → 3, and J = 6 → 5, and 10, 20, 30 Kkms-1 for 12COJ = 7 → 6 (1σ = 1.9, 3, 10, and 3 Kkms-1 for 12COJ = 3 → 2, J = 4 → 3, J = 6 → 5, and J = 7 → 6). Red (thick dotted) contours present the half maximum level of all images. The thin dotted lines in the lower two panels denote the regions that have been scanned with higher S/N than other regions farther away from the centers (see Sects.2 and 3.1.3). The outer dotted lines in the 12COJ = 7 → 6 map are related to masking.

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In Fig. 4, we present the integrated intensity image of Ci 492 GHz emission. In spite of a smaller mapping area compared to CO, the thick dotted (red) line denoting the half maximum level of the emission peak is still mostly within the confines of the map. The detected structure covers an angular distance of ~20′′ from northeast to southwest, corresponding to 400pc on the linear scale. Both the nuclear region and the S-F ring seen in the 12COJ = 1 → 0 and 2 → 1 images (Curran et al. 1998) are covered by the Ci 10 map.

thumbnail Fig. 4

The 492 GHz Ci 1 → 0 integrated intensity image of the central part of the Circinus galaxy. Plotted contour levels are: 20 (6σ), 30, 40, 50, and 60 mKkms-1. The red contour presents the half maximum level of the Ci emission. The beam size (FWHM) is 13.5′′.

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thumbnail Fig. 5

CO channel maps of the central region of the Circinus galaxy. The velocity range is given at the top, and the nuclear position of the Circinus galaxy is labeled by white crosses. Beam sizes are shown in the panels at the left hand side. Upper panels: 12COJ = 6 → 5 channel maps. The contours are from 0.1 (2σ) to 0.5 K with a spacing of 0.1 K. Middle panels: 12COJ = 4 → 3 channel maps. The contours are –0.1 (dotted) and 0.1 to 1.0 Kkms-1, the latter with a spacing of 0.1K. The 3σ noise level corresponds to 0.1 K. Lower panels: 12COJ = 3 → 2 channel maps. The contours are the same as for 12COJ = 4 → 3. The 5σ noise level corresponds to 0.1 K.

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3.2. Gas kinematics

3.2.1. CO channel maps

In Fig. 5, we plot the channel maps of 12COJ = 3 → 2, 4 → 3, and 6 → 5. The northeastern side of Circinus is approaching and the southwestern side is receding. 12COJ = 6 → 5 is highly concentrated near the peaks of the 12COJ = 3 → 2 and 4 → 3, i.e., near the central position of Circinus. The systematic velocity variations of different CO transitions are apparent. The emission of all three lines is particularly strong at the velocity bins of 300400kms-1 and 450550kms-1, and the brightness temperature peaks even exceed those in the central velocity bin ranging from 400 to 450kms-1. The 12COJ = 4 → 3 and 6 → 5 emission drops faster than that of 12COJ = 3 → 2 when the velocity is higher than 550 kms-1 and lower than 300 kms-1.

3.2.2. CO P-V diagrams

Figure 6 shows the position-velocity (P-V) diagrams of 12COJ = 3 → 2, 4 → 3, and 6 → 5, along the major axis of Circinus. We make cuts with a position angle of 33.5°, which is from the fitting result of Sect. 3.1.3 (see also Table 4). In the P-V diagram of 12COJ = 3 → 2, the ridge of maximum intensity covers a velocity range of about 400kms-1, in accordance with the high inclination (i ~ 65 − 78°; Curran et al. 2008) of the galaxy, over a region of roughly ±10′′. The rotation field in this area is characterized by a velocity gradient of dν/ dθ = 400kms-1/20′′ (~20kms-1/arcsec), corresponding to dν/ dr ~ 1.0 kms-1 pc-1 in the plane of the galaxy, when an inclination angle of 65° is adopted (Freeman et al. 1977). The higher-J level and the higher the angular resolution, the steeper the rotation curve appears. The 12COJ = 4 → 3 distribution looks similar to that of 12COJ = 3 → 2, but appears to be slimmer because of the higher angular resolution. For 12COJ = 6 → 5, the ridge of maximum intensity covers a velocity range of ~350kms-1 in a small region encompassing offsets of ±5′′. We derive a velocity gradient of ~350 kms-1/10′′ (dν/dr~ 1.5 kms-1 pc-1), which corresponds to dν/dr~ 1.7 kms-1 pc-1 when an inclination angle of 65° is applied. Limited by the spatial resolution, these velocity gradients only provide lower limits for the actual rotational motions in the central region of Circinus.

We estimate the dynamical mass from Mdyn[M] = [kms-1] ×r [pc] (e.g., Schinnerer et al. 2000), where νrot is the inclination-corrected rotation speed in kms-1, and r is the radius in pc. We find a rotation velocity νrot = (340kms-1/2)/sin(65°± 5°) ~ 190 ± 10kms-1, and derive dynamic masses of Mdyn = 1.4 ± 0.1 × 109M within 180pc of the center, and 3.6 ± 0.4 × 109M within a galactocentric radius of 450pc. The latter is consistent with the dynamical mass of 3.3 ± 0.3 × 109M estimated for an outer radius of 560pc by Curran et al. (1998).

thumbnail Fig. 6

Position-velocity (P-V) maps of CO emission from the Circinus galaxy. From left to right: P-V diagrams of 12COJ = 3 → 2, 12COJ = 4 → 3, and 12COJ = 6 → 5. The slice is taken along the major axis obtained from 12COJ = 3 → 2 (position angle: 33.°5, see Table 4) and the direction is from northeast (bottom) to southwest (top). The contours are from 30% to 90% of the peak intensities with a spacing of 20%.

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Unlike the case of the moment-zero maps, where all CO emission peaks at the central position, the CO transitions in the P-V diagrams mainly peak at the edges of the velocity distributions on the major axis. This scenario indicates a central molecular void and a circumnuclear ring. The P-V diagram of 12COJ = 3 → 2 is, within the errors, symmetric for the lowest emission levels around the AGN, with respect to a radial velocity of 430 ± 20 kms-1. The earlier adopted central positions (Figs. 26) are consistent with the dynamical center of the galaxy and the velocity can be interpreted as the systemic velocity (νsys).

4. Excitation conditions and discussions

Including our new measurements, 12CO has been observed toward the nuclear region of Circinus in all transitions up to J = 7 → 6, except for J = 5 → 4 (e.g., Aalto et al. 1991; Israel 1992; Elmouttie et al. 1997; Curran et al. 1998, 2001; Hitschfeld et al. 2008). The rare isotopologue 13CO has been measured in transitions from J = 1 → 0 to J = 2 → 1 (e.g., Curran et al. 1998, 2001; Hitschfeld et al. 2008), and J = 3 → 2 (this paper). The low-J transitions were observed mostly with SEST 15m and Mopra 22 m (equivalent 15 m beam size at 115 GHz; Elmouttie et al. 1997), while the mid-J transitions were observed with the APEX 12 m and the NANTEN-2 4 m telescopes. Table 3 summarizes 12CO and 13CO observations collected from the literature.

The wide range of critical density4 (from ~3 × 102 cm-3 for CO J = 10 to ~4 × 105 cm-3 for CO J = 7 → 6) and Eupper/kB (from 5.5K to 155K) of CO lines from J = 1 → 0 up to J = 7 → 6 allows us to probe the molecular gas physical conditions ranging from the cold and low-density average states in giant molecular clouds all the way up to the state of the gas found only near their S-F regions (e.g., Yang et al. 2010; Bradford et al. 2005). Bright 12COJ = 6 → 5 and J = 7 → 6 emission in Circinus implies that there is a large amount of molecular gas in a highly excited phase, while the low-J CO transition lines are also sensitive to the colder and possibly more diffuse gas phase.

4.1. The large velocity gradient radiative transfer model

To estimate the physical parameters of the molecular gas, we employ a large velocity gradient (LVG) radiative transfer model (e.g., Scoville & Solomon 1974; Goldreich & Kwan 1974) to constrain the excitation conditions. We adopt an escape probability of β = (1 − eτ) /τ, which implies a spherical geometry and an isothermal environment. While multiple phases of physical conditions should exist in the molecular cloud complexes of Circinus, it is difficult to disentangle them (but see below). We thus adopt homogeneous clouds in the LVG modeling to constrain the average physical properties of molecular gas.

We proceed with a three-dimensional parameter grid with regularly spaced kinetic temperature (Tkin), H2 number density (nH2), and fractional abundance versus velocity gradient (xCO/ (dν/dr)) as input, where xCO is the abundance ratio of CO relative to H2. In the following analysis, is fixed to 8 × 10-5 (Frerking et al. 1982). The input parameter grid consists of Tkin from 101 to 103K, nH2 from 102 to 107 cm-3, and dν/dr from 100 to 103 kms-1 pc-1. We sample all these parameters with logarithmic steps of 0.1. We adopt RADEX (van der Tak et al. 2007) to generate the model grids. We excluded all solutions with τ> 100 and the solutions did not reach convergence.

We adopt the 12CO to 13CO abundance ratio (R1213) to be 40 in the following analysis. It is intermediate between the values measured near the Galactic center and the solar circle (e.g., Wilson & Matteucci 1992). This value is also consistent with the ratios derived in the active nuclear regions of nearby galaxies (e.g., NGC 1068, NGC 253, NGC 4945; Henkel & Mauersberger 1993; Langer & Penzias 1993; Wilson & Rood 1994; Henkel et al. 2014). We do not adopt R1213 = 60 − 80 given in Curran et al. (2001), because we obtained 25% higher 12COJ = 3 → 2 flux (confirmed with several redundant observations) than their results. If the new 12COJ = 3 → 2 measurement is adopted in their model, higher excitation conditions will be obtained, and less R1213 would be expected. We also tried R1213 = 80 and 20, which do not significantly change the final conclusions (see Table 7 and Sect. 4.7). The CO collisional rates are from Flower (2001), with an ortho/para H2 ratio of three. The output model grid includes excitation temperature, line brightness temperature, column density, and optical depth.

For each individual model, a χ2 value is calculated using differences in the ratios of line brightness temperatures obtained from the models and the observations. We derive χ2 with χ2 = Σi(1 /σi)2(Robs(i)Rmodel(i))2, where Robs is the ratio of the measured line brightness temperatures, σi the error of the measured line ratio, and Rmodel the ratio of the line brightness temperatures calculated by the LVG model.

4.2. Single-component LVG modeling

The comparatively small beam sizes of our new APEX data help us to probe the molecular gas properties in the innermost part of the galaxy. The beam size of the 12COJ = 3 → 2 data is 18′′, which is smaller than the diameter (~30 − 40′′) of the S-F ring in the HST Hα image (see Fig. 1). Therefore, as the first step, we analyze data exclusively taken with APEX to study the average physical conditions in the nuclear region. Because the published 12COJ = 1 → 0 and 12COJ = 2 → 1 data were measured with larger beams of 45′′, 38′′, and 22′′ (see Table 6), we only model CO emissions with J ≥ 3.

In our modeled grids, not all solutions have physical meaning. Therefore we set some priors to exclude solutions when they are either unphysical or contradictory to known information.

4.2.1. Parameter restrictions

We assume flat priors (P) for nH2, dν/dr, and Tkin with P = 1 inside the ranges given in Sect.4.1 and Table 5, and assign P = 0 for solutions that do not match these prior criteria. In the modeling of the parameter xCO/(dν/dr), we keepxCO constant (Sect. 4.1) and adjust the velocity gradient. Because of the degeneracy between the velocity gradient and the molecular abundance, modifications of dν/dr have the same effect as changingxCO for a given fixed dν/dr, which reflects the kinetic information of the modeled molecular gas. Varying dν/dr helps us to find the thickness of the gas layer coupling (rcoupling) in the radiative transfer via rcoupling = dνcell/ (dν/dr), where cell = [(dνthermal)2 + (dνmicroturb)2] 1/2 is the intrinsic local line width of the gas cell where radiative coupling occurs (e.g., White 1977). We list the prior restrictions in Table5 and discuss them below.

Table 5

Parameter restrictions for the LVG modeling.

Dynamical restriction – K vir , lower bound

For a molecular cloud in virial equilibrium, random motions inside the cloud are compensated by self-gravity. If these motions are below a certain level, collapse should set in, however, even in the case of free-fall motions, velocities should not strongly deviate from those in a bound but non-collapsing system (e.g., Bertoldi & McKee 1992; Krumholz & McKee 2005). In the opposite case, however, when the gas experiences violent motion, as it may be in the case of shocks and outflows, the cloud could reach a highly supervirial state. The ratio between the modeled velocity gradient and that in the virialized state (Kvir; Appendix A) reflects the gas motion against self-gravity. The virialized state Kvir is near unity in individual “normal” molecular clouds (e.g., Papadopoulos & Seaquist 1999).

Subvirialization (i.e., Kvir 1) is unphysical because gas motions inside GMCs can never be slower than what the cloud self-gravity dictates. The linear scales addressed here (several 100pc) are dynamically dominated by galactic rotation, so that subvirialization can be firmly excluded. We therefore constrain Kvir≥ 1 throughout this paper.

Dynamical restriction – dν/dr , upper bound

The H2O masers measured with the Australia Telescope Long Baseline Array (Greenhill et al. 2003) indicate a particularly large velocity gradient, defined by the rotation of the maser disk around the central SMBH of Circinus. The velocity of the H2O masers varies by ~400 kms-1 over a small warped disk of a diameter ~80mas, which corresponds to ~1.6 pc. We derive an effective velocity gradient of dν/dreff = 400/1.6 = 250 kms-1 pc-1. This yields a convenient upper limit of 360kms-1 pc-1 to the velocity gradient in the LVG modeling, assuming that the adopted fractional CO abundance is correct within ~50%.

Dynamical restriction – M dyn , upper bound

We also discard solutions that have a total gas mass (Mgas) higher than the dynamical mass (Mdyn). In Sect. 3.2.2, we have derived the dynamical mass within a galactocentric radius of 180pc to be 1.4 ± 0.1 × 109M, which is the upper limit of the interstellar gas mass. This mass limit corresponds to a limit of beam average H2 column density of 9 × 1023cm-2, for a CO abundance of xCO = 8 × 10-5.

Flux density limits – low-J CO

The single LVG component models are based on the CO emission from the central 18′′ of Circinus, while the published 12COJ = 1 → 0 and 12COJ = 2 → 1 data were measured with larger beams of 45′′, 38′′, and 22′′ (see Table 6). We set the constraint that the modeled flux densities of the 12COJ = 1 → 0, 2 1 and their isotopic 13CO lines cannot exceed the values observed with beam sizes >18′′.

thumbnail Fig. 7

Top: integrated flux densities of 12CO and 13CO transitions in the central region (18′′ in diameter) of Circinus. We plot the solution range of 12CO (dark gray) and 13CO (light gray) derived from single-component LVG modeling of CO and 13CO lines with J ≥ 3. The range is selected from all solutions satisfying < 1.5 (or Likelihood L> 0.6). We plot 12COJ = 2 → 1, 12COJ = 1 → 0, and their 13CO isotopic transitions for beam sizes >18′′ as upper limits (black boxes and circles) to our models. Bottom: integrated flux densities of 13CO, in a zoomed in view.

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Table 6

CO detections toward the central position of Circinus in the literature

4.2.2. The CO ladder in the central 18′′

In Fig. 7 we show the observed CO spectral line energy distribution (SLED; velocity integrated flux density versus rotational transition number J) and our modeled SLED for the central 18′′ region. We also plot the line fluxes of the lower CO transitions (12COJ = 1 → 0 and 2 1) and their 13C isotopic lines as upper limits. For all successful models, the 12CO SLEDs peak at 12CO J = 5 → 4, which cannot be observed with ground-based telescopes because of the very low atmospheric transmission at this frequency.

With five observational points and three fitting parameters, our modeling has two degrees of freedom (d.o.f.), so we discuss the general properties of the set of solutions satisfying = χ2/ (d.o.f. − 1) ≤ 1.5, where is the reduced χ2 . This corresponds to a likelihood limit of L> 0.6. L is defined by (1)where Lmax is the maximum likelihood for all solutions, which corresponds to the solution with the smallest value of χ2 . The best fitting result has a of 0.5, indicating that our adopted calibration error may be a bit conservative or that the number of degrees of freedom is not large enough to reach a lower limit of exactly unity (see Andrae et al. 2010).

The best fitting result (Table 7) indicates average physical conditions of nH2~ 103.2 cm-3, Tkin~ 200K, and dν/dr~ 3kms-1 pc-1. Various sets of degenerated parameter combinations satisfy < 1.5, and these solutions also provide reasonable fittings. The degeneracy not only affects Tkin and nH2, but also dν/dr. For example, the “dense solution” has nH2 = 103.7 cm-3, Tkin = 125K, and dν/dr = 20.0kms-1 pc-1, with a ~ 1.5. A “hot solution” with nH2 = 103.2 cm-3, Tkin = 250 K, and dν/dr = 5.0kms-1 pc-1 achieves a similar χ2 value. In summary, these solutions encompass a range of 102.7 cm-3<nH2<103.8cm-3, 80 K <Tkin< 400 K, 1kms-1 pc-1<dν/dr< 25kms-1 pc-1.

We calculate the area filling factors (φA) with the ratio of the observed and the modeled line intensities, by φA = ΣTobs(i)/ΣTLVG(i), where i is the upper level of the transitions. We find a narrow range of φA between 1.8% and 2.3%. We calculate the equivalent radius with: , where φA is the beam filling factor, and rbeam is the physical size covered by the telescope beam. The corresponding effective emission sizes are between 10 pc and 15 pc in diameter. A detailed likelihood analysis is presented in Appendix B.

Table 7

Physical parameters of single-component fitting in the central 18′′ region, with < 1.5.

4.3. Two-component modeling in the central 45′′ region

In this section, we explore the physical conditions in the central 45′′ (900pc) region with LVG modeling. We combine our mid-J CO measurements with the low-J CO data from the literature to perform a global fitting. We convolve all CO maps to the beam size of the SEST at the frequency of 12COJ = 1 → 0, i.e., FWHM = 45′′. The intensity and resolution of these lines are tabulated in Table 6. We convolve the 13COJ = 3 → 2 emission to a resolution of 45′′, assuming that the distribution of 13COJ = 3 → 2 is the same as that of 12COJ = 3 → 2.

We tried to fit CO ladders in the central 45′′ with a single LVG component first, however, it does not produce a good fit. This is not surprising since the modeling results in previous studies (e.g., Kamenetzky et al. 2012; Hailey-Dunsheath et al. 2012; Rigopoulou et al. 2013) have shown that the coexistence of multiple excitation gas components in nearby galaxies (also see Lu et al. 2014). Therefore, we use two LVG components to model the gas excitation in the central 45′′ region.

In the two-component LVG modeling, we assume that both components have the same chemical abundance:xCO= 8 × 10-5, and R1213 = 40. Each component has its own nH2, Tkin, dν/dr, and a relative contribution to the measured line intensities. We list the priors in the two-component models in Table 8.

We analyze with the same grids as in the single-component fitting (see Sect. 4.2) and model the line intensities for both components simultaneously. We assume that the two-components have independent excitation conditions. The sum of the two-components should match the observed SLED. To construct the contributions of the two-components, we assume that the LE and the higher-excitation (HE) components are diluted by the filling factors of φLE and φHE, respectively. The observed main beam temperature can be modeled with: Tobs = TLE × φLE + THE × φHE = C × [(1 − R) × TLE + R × THE], where C (=φLE + φHE) is a constant number for each model, and TLE and THE are the modeled line intensities for the low- and high-excitation components, respectively. The relative ratio R (=, and 0 <R< 1) reflects the contribution relative to the total line intensity, and R is calculated from 5% to 95% with a step size of 5%. The relative mass contributions of these phases can be expressed by: MH2(LE)/MH2(HE) = φLE/φHE × (TLE/TTE) × [XCO(LE)/XCO(HE)], where XCO(LE,HE) are the XCO factors for those phases (Papadopoulos et al. 2012a):

where α = 0.55 − 2.4, depending on the assumed cloud density profile, Tb(J = 1 → 0) is the brightness temperature of 12COJ = 1 → 0.

With nine measurements and seven fitting parameters, we discuss the general properties of the set of solutions satisfying likelihood L ≥ 0.7. In Fig. 8 we plot the line flux ranges of all the accepted solutions. For all good solutions, the 12COJ = 1 → 0 and 2 → 1 intensities of the LE component are much higher than those of the HE component. The 12COJ = 3 → 2 and 4 → 3 intensities profit by similar contributions from both components. The 12COJ = 6 → 5 and 7 → 6 emission are dominated by the HE component.

We find that in the solutions with the lowest χ2, the relative contribution ratio is R~ 0.15. Setting this ratio as the basis for the two-components, we probe the ranges of physical parameters in the following analysis. The best-fit model shows a HE component of Tkin~ 60 K, nH2~104.2 cm-3, and dν/dr~ 50 kms-1 pc-1, and a LE component of Tkin~ 30K, nH2~103.0 and dν/dr~ 6kms-1 pc-1(for details, see Appendix C). The best fit shows an equivalent emission radius of ~20pc for the HE component, which is larger than the effective emission radius of 10–15pc found in the previous single-component fitting.

The best solutions show that the HE component model has a velocity gradient about 10 times higher than the LE component. This indicates that more violent kinematics are associated with the HE component, and that the molecular gas in the inner 18′′ region (Sect. 4.2.2) is in a state of high excitation because a high dν/dr is expected in the center (e.g., Tan et al. 2011). We summarize the results of the two-component fittings in Table 9. Although we obtain a lower temperature, the best density solution of the LE component is also similar to the fitting results of the low-J transitions of CO in Curran et al. (2001), where they find Tkin = 50−80 K, nH2 = 2 × 103 cm-2, and dν/dr = 10 kms-1 pc-1.

thumbnail Fig. 8

Integrated flux densities of 12CO and 13CO in the central 45′′ region of the Circinus galaxy. The shadowed regions are the ranges of the best fitting results derived from the two-component LVG modeling. The high- and low-excitation components and the total integrated 12CO flux densities are plotted in red, blue, and green. The total integrated 13CO flux densities are plotted in gray.

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Table 8

Parameter restrictions for the two-component LVG modeling.

Table 9

Physical parameters of two-component fitting in the central 45′′ region.

4.4. Does the HE component arise from the 18′′ region?

Single LVG component fitting of the inner 18′′ region leads to an order of magnitude lower density and four times lower temperature than the corresponding parameters derived from the HE component in the 45′′ region. If the inner 18′′ dominates the HE component, why are there such large discrepancies? Does the HE component mainly arise from the 18′′ region? First, the HE component in the 45′′ region cannot entirely arise from the 18′′ nuclear region because the ring contributes about 35% and 45% fluxes of 12COJ = 6 → 5 and 7 6, respectively (see Sect. 4.5). Second, the single LVG component modeling only reflects the average physical conditions in this region, where the gas may not be dominated by the HE component. In the 18′′ region the mid-J transitions (especially 12COJ = 3 → 2 and 4 3) are also likely contaminated by the lower excitation component, which may provide a large amount of diffuse cold gas along the line of sight. Third, the degeneracies between temperature, density, and velocity gradient are responsible for the difference. A component with lower density and higher temperature can produce similar CO SLEDs to a component with higher density but lower temperature.

thumbnail Fig. 9

Integrated flux densities of 12CO and 13CO in the S-F ring region of the Circinus galaxy. The shadowed regions are the ranges of the fittings satisfying likelihood L> 0.8, derived from the two-component LVG modeling. The high- and low-excitation components and the total integrated 12CO flux densities are plotted in red, blue, and green. The total 13CO flux densities are plotted in gray.

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4.5. Gas excitation in the S-F ring

For the 12CO J = 6 → 5 and J = 7 → 6 transitions, we find that aboutwh 35% - 45% of the CO fluxes come from the S-F ring region (diameter = 18′′–45′′), and the rest comes from the center. This indicates that the HE component derived in the two-components decomposition is not likely from the nuclear region alone, and a large amount of highly excited gas seems to exist in the S-F ring.

Benefiting from the mapping observations, we derive CO emission in the S-F ring region by subtracting line fluxes, which were derived from the best model obtained in Sect. 4.2, in the central 18′′ region from those in the 45′′ region. We fit the CO residual with two LVG components, to model the gas excitation exclusively in the S-F ring region, as can be seen in Fig. 9. We fit the model with all transitions of 12CO and 13COJ = 1 → 0, 2 → 1. Because 13COJ = 3 → 2 was not measured in the S-F ring region, we cannot make any constraint on it. The J = 1 → 0 and 2 → 1 transitions are derived from the residual by subtracting the LVG model in the central 18′′ region from the fluxes in the 45′′ region. The best fit of the ring shows a HE component of nH2~ 104.1cm-3, Tkin~ 125K, and an LE component of nH2~ 102.9cm-3, Tkin~ 30K, as shown in Table 10.

Table 10

Physical parameters of two-component fitting of the S-F ring at diameter 18′′<D< 45′′, with Likelihood L> 0.8 (see Eq. (1)).

4.6. Comparison with NGC 1068

Circinus and NGC 1068 have many similarities. They are both nearby Seyfert galaxies, and contain gas-rich nuclei and molecular S-F rings. Although Circinus has a much smaller distance (~4 Mpc) than NGC 1068 (~14.4 Mpc Bland-Hawthorn et al. 1997), the angular sizes of the gas-rich region in these two galaxies are both about 40′′ (in diameter). Both of them have strong S-F activities in their centers, and are fed by large amounts of molecular material (e.g., Curran et al. 2001; Hailey-Dunsheath et al. 2012).

In NGC 1068, the inner ends of the S-F spiral arms lead to a large S-F ring of diameter ~2.3kpc (e.g., Schinnerer et al. 2000; Gallimore et al. 2001). Closer to the center there is a CND of diameter ~300pc, seen most prominently in line emission of dense gas tracers (e.g., Schinnerer et al. 2000; Krips et al. 2011). Between the S-F ring and the CND there is a gap region deficient in molecular gas (e.g., Helfer et al. 2003; Schinnerer et al. 2000; Tacconi et al. 1997; Tsai et al. 2012). Spinoglio et al. (2012) modeled the excitation conditions with the CO SLED deduced from the Herschel observations and found an LE component (Tkin= 120 K, nH2= 102.8 cm-3) associated with an extended source (the S-F ring), a medium excitation (ME) component (Tkin= 100 K, nH2=104.6 cm-3) associated with the CND, and a HE component (Tkin= 150 K, nH2=105.7 cm-3) possibly arises from the central few pc heated by the AGN (e.g., Hailey-Dunsheath et al. 2012).

Considering the whole inner 45′′ region of Circinus, the LE component has nH2~ 103.0 cm-3, similar to the LE component derived from the extended emission in NGC 1068 and the central region of the Milky Way (e.g., Spinoglio et al. 2012; Ott et al. 2014). The temperature of the LE component, however, is Tkin~ 30 K, which is much lower than the LE component in NGC 1068, indicating that Circinus may have lower excitation conditions.

On the other hand, the HE component in Circinus is also characterized by a similar density and a lower temperature compared to the ME component in NGC 1068, which is from the CND region, and is fitted using the high-J transitions (J = 98 to 1312) in a 17′′ region (i.e., Spinoglio et al. 2012). The velocity gradient of the HE component spans a large range and all solutions indicate that this gas component is in a highly supervirialized state.

In NGC 1068, the LVG modeling was made step by step from higher to lower excitation components. Each component was fitted individually, after subtracting the higher excitation components. In Circinus we fit the two-components simultaneously, which allows for a much larger parameter space. The different fitting methods could also introduce differences. High angular resolution observations of multiple-J CO transitions in Circinus are needed to fully resolve the gas phase distribution and fully test the above scenarios.

4.7. Molecular gas mass

We calculate molecular gas mass from the LVG models derived from previous sections. RADEX gives the column density NCO without beam dilution. We convert it to a beam-averaged 12CO column density NCO, which is then further converted to the column density of molecular hydrogen with the assumed CO abundance ofxCO= 8 × 10-5. The molecular gas mass is derived with (2)where mH2 is the mass of a single H2 molecule and the factor of 1.36 accounts for the mass of helium in the molecular clouds. The beam area , where r0 is radius of the beam. The velocity integrated line intensity W is calculated in the LVG models. The main beam temperature Tmb is obtained from the observations (Ward et al. 2003).

In the single-component modeling, the beam size corresponds to a region with radius r0 of (central) 180pc. From the best fitting results (see Sect. 4.2), a velocity gradient dν/dr~ 3 kms-1 pc-1, and a density nH2~ 103.2 cm-3are used. We derived a molecular gas mass of 1.3 × 107M, and an area filling factor of ~2%.

The two-component fitting refers to a region of 45′′ in radius, which corresponds to a radius of 450pc. The total molecular gas mass is derived to be 8.9 × 107M for the best-fit result, which contains a gas mass of 6.6 × 107M for the LE component, and 2.3 × 107M for the HE component.

The molecular gas mass in Circinus has been debated for a long time. Using the 1.3mm continuum, Siebenmorgen et al. (1997) derived a molecular gas mass of 1.6 × 108M within their 3′ × 4′ maps of the central region of Circinus. From the Galactic disk standard conversion factor (2 × 1020(Kkms-1)-1; Strong et al. 1988; Bolatto et al. 2013), the molecular gas mass derived from 12COJ = 1 → 0 reaches 1.6 × 109M in the central 560pc (e.g., Elmouttie et al. 1997; Curran et al. 1998). This would indicate that the molecular gas mass constitutes half of the dynamical mass in the central 560 pc region, which is more than the molecular gas mass fractions in most luminous galaxies and nuclear regions of normal S-F galaxies (e.g., Young & Scoville 1991; Sakamoto et al. 1999). Hitschfeld et al. (2008) performed both Local Thermal Equilibrium (LTE) and LVG analysis with the lowest four transitions of CO and the Ci transition. They found that the column density of CO is about 4 − 7 × 1017 cm-2in the central 560pc region, and this is ~1/10 of the column density (NCO = 3 × 1018 cm-2) derived from the standard conversion factor. This evidence implies that the standard conversion factor in Circinus is ten times lower than the Galactic disk value (e.g., Dahmen et al. 1998; Bell et al. 2007; Israel 2009a,b; Bolatto et al. 2013)

The best fitting in our two-component LVG modeling gives a total molecular gas mass of ~9 × 107M in the central 45′′ region, which corresponds to a standard conversion factor of N(H2) /ICOJ = 1 → 0 = 0.37 × 1020cm-2(K km s-1)-1 (forxCO = 8 × 10-5 used here). The molecular gas mass determined from LVG modeling is about 60% of the mass of 1.6 × 108M derived by the 1.3mm continuum obtained in a larger region (Siebenmorgen et al. 1997). Mauersberger et al. (1996), Downes & Solomon (1998), Papadopoulos & Seaquist (1999), Israel (2009a), and Bolatto et al. (2013) also derived conversion factors significantly lower than the Galactic value by analyzing the low-J CO emission in NGC 1068 and other galaxies with bright CO emission and high stellar surface density. This suggests that the lower conversion factor likely arises from gas being not virialized (e.g., Aalto et al. 1995; Dahmen et al. 1998; Narayanan et al. 2011).

4.8. Molecular gas mass estimates using CI

Atomic carbon (Ci) could help circumvent the problem of defining a proper conversion factor because its emission traces molecular gas independently. The critical density of Ci is 1 × 103 cm-3 (e.g., Tielens 2005), similar to that of 12COJ = 1 → 0, thus provides approximate thermalization at the densities reported here (see Tables 7, 9, and 10). Strong evidence shows that Ci and CO luminosities have a tight correlation in galaxies, independent of physical environment, IR luminosity, or redshift (e.g., Papadopoulos & Greve 2004; Zhang et al. 2007; Walter et al. 2011). This suggests that Ci emission arises from the same volume and shares similar excitation temperature as CO (e.g., Ikeda et al. 2002). Constant ratios between the column densities of Ci, 12CO, and H2 are expected over a large range of physical conditions (e.g., Papadopoulos & Greve 2004; Walter et al. 2011).

Constraining H2 column density with the optically thin Ci lines is an independent and robust way to probe the molecular gas mass in galaxies. We can calculate the mass of Ci following Weiß et al. (2005):

where Q(Tex) = 1 + 3eT1/Tex + 5eT2/Tex is the Ci partition function, and T1=23.6K and T2=62.5K are the energies above the ground state. The [Ci]/[H2] abundance chosen here is xCI = 5 × 10-5 (Weiß et al. 2005). We adopt an excitation temperature of 30K derived from the LE component in the two-component LVG fittings (Table 9). Assuming Tex = Tkin = 30 K, we derive a molecular gas mass of 8.3 × 107M. If Tex = 60 K from the HE component is adopted, the molecular gas mass is 8.9×107M. These masses are, within the errors, consistent with the result derived from our LVG solution, 9 × 107M (Sect. 4.7).

thumbnail Fig. 10

as a function of . The empty triangles show observed positions in Circinus. The empty circles show the galaxies at high redshift (Walter et al. 2011). The crosses represent results of nearby galaxies found in literature. NGC 6946 and M 83: (Israel & Baas 2001), M 51: (Israel et al. 2006), Hennize 210 and NGC 253: (Bayet et al. 2004), IC 342: (Israel & Baas 2003).

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4.9. Luminosities of CI and 3P13P0

In Fig. 2, we present the spectra of Ci and 12COJ = 3 → 2 observed in the central region of Circinus. The line profiles of the two species are similar. In the following, we calculate the line luminosities () of CO and Ci, and compare them with nearby galaxies and high-z systems. We determine the line luminosity following the definition in Solomon et al. (1992): (3)where L is the line luminosity in Kkms-1pc2, SlineΔν is the velocity integrated flux density in Jy kms-1, DL denotes the luminosity distance in Mpc, and νobs represents the observing frequency in GHz. The ratios stand for ratios of the intrinsic brightness temperatures.

In Fig. 10, we plot the Ci line luminosity as a function of 12COJ = 3 → 2 luminosity. We combined the Ci data from the literature, including the Ci detections in nearby and high-redshift galaxies (e.g., Walter et al. 2011). The luminosities of Ci and 12COJ = 3 → 2 match each other and the scatter of the ratios lies within an order of magnitude (the dashed diagonal lines). The correlation derived from multiple position in Circinus basically follows the same trend found in high-redshift galaxies.

We find that the Ci to 12COJ = 3 → 2 luminosity ratios RCI/CO32 in nearby galaxies (red crosses) are lower than those found in the high-redshift galaxies and the AGN hosting galaxies (i.e., Circinus and M 51). An average ratio of RCI/CO32 = 0.17 ± 0.03 is found in Circinus, and this is only about half of the average ratio found at highredshift (Walter et al. 2011, 0.32 ± 0.13). In the quiescent nearby galaxies, RCI/CO32 are mostly close to 0.1. In the central positions of M 51 and Circinus, the RCI/CO32 ratios are both ~0.2, about two times higher than those in quiescent galaxies. These high RCI/CO32 ratios are likely caused by the enhanced gas excitation due to the AGN activities.

5. Summary and conclusions

We present new APEX mapping observations of 12COJ = 3 → 2, 4 → 3, 6 → 5, 7 → 6 and Ci 10 in the central region of the Circinus galaxy. These data are to date the highest transitions published. All these lines reveal extended strong emission and similar kinematic structures. We find strong 12COJ = 6 → 5 and 7 → 6 emission not only in the nuclear region, but in the gas-rich, star-forming (S-F) ring region at galactocentric diameter of 18′′<D< 45′′ as well. The latter region contributes about 3545% of the measured high-J CO emission. With the CO maps we are able to decompose the gas excitation spatially.

By using radiation transfer analysis we find two distinct areas with different gas excitation conditions: the 18′′ nuclear region and the S-F ring within 18′′<R< 45′′. Our main results are as follows:

  • 1)

    With a single excitation component, we use APEX 12CO and 13CO detections (J ≥ 3) to perform a LVG modeling. We derive nH2~103.2 cm-3, Tkin~ 200 K, dν/dr~ 3.0 kms-1 pc-1, and MH2 ~ 1.3 × 107M in the central 18′′ region, which accounts for ~15% of the total molecular gas mass in the central gas-rich 45′′ region in Circinus.

  • 2)

    Combined with low-J CO data in the literature, we perform two-component LVG modeling in the central 45′′ diameter region, and in the S-F ring. We find two excitation components that can fit the measurements in the whole region, one with nH2~103.0 cm-3, Tkin~ 30 K, dν/dr~ 6 kms-1 pc-1, and MH2 ~ 6.6 × 107M, and the other with nH2~104.2 cm-3, Tkin~ 60 K, dν/dr~ 50 kms-1 pc-1, and MH2 ~ 2.3 × 107M. In the ring region, the high density component represents a smaller fraction (~13%) of the total gas mass. All these gas components are supervirialized.

  • 3)

    We find the molecular gas mass of Circinus is ~0.9 × 108M in the 45′′ region. This is consistent with the gas mass derived from Ci (~0.9 × 108M) and is ~60% of the gas mass obtained using submm continuum in a larger area (1.6 × 108M). A gas mass of about ~ 1.3 × 107M is found in the central 18′′ nuclear region, and ~7.5 × 107M is located in the surrounding ring. In the 45′′ region, we thus derive a conversion factor of N(H2) /ICOJ = 1 → 0 = 0.37 × 1020 cm-2(Kkms-1)-1, which is about 1/5 of the Galactic disk value.

  • 4)

    We find the average luminosity ratio between Ci (1 → 0) and 12COJ = 3 → 2 (RCI/CO32) in Circinus to be 0.2, about twice the average value found in nearby normal galaxies (Gerin & Phillips 2000, ~0.1). This is near the low end of what is observed in high-redshift systems (Walter et al. 2011, ~0.29).


1

This publication is based on data acquired with the Atacama Pathfinder Experiment (APEX). APEX is a collaboration between the Max-Planck-Institut für Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory.

3

Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

4

The critical densities are calculated with ncrit = Aul/ Σ(Cu ≠ l) as a function of kinetic temperature Tkin, under an optically thin assumption (Yang et al. 2010). Here A is the Einstein coefficient for spontaneous emission, and C is the collisional coefficient. Here we adopt Tkin = 20 K. All state-to-state cross sections and rate coefficients for quenching are available in the LAMDA web site (http://home.strw.leidenuniv.nl/~moldata/; Schöier et al. 2005).

Acknowledgments

We thank the anonymous referee for his/her very thorough reading of the draft, and the very detailed comments that have significantly improved the quality of the paper. We are grateful to the staff at the APEX Station of MPIfR for their assistance during the observations. Z.Z. thanks J. Z. Wang, L. J. Shao and K. J. Li for their constructive discussions. Z.Z. acknowledges support from the European Research Council (ERC) in the form of Advanced Grant, cosmicism. This work was partly supported by NSF China grants #11173059 and #11390373, and CAS No. XDB09000000. Y.A. acknowledges support from the grant 11003044/11373007 from the National Natural Science Foundation of China.

References

Online material

Appendix A: Virialized gas state

The gravitational potential of the densely packed stars and the nearby supermassive nuclear engine in the central region of a massive galaxy may cause significant velocity gradients along lines of sight, which can be well in excess of what would be found in a normal cloud near virial equilibrium. Therefore the velocity gradient expected in the virialized gas motion can be taken as a lower limit. The ratio between the measured velocity gradient and that calculated from virial equilibrium is defined by (A.1)The virialized velocity gradient is given by (A.2)where μ is the mean particle mass, G is the gravitational constant, n is the mean number density of the cloud, and α is a constant between 0.5 to 3 depending on the assumed density profile (Bryant & Scoville 1996). For a cloud with assumed density of 105 cm-3, and with the largest value of α = 3, the estimated (dv/dr) is about 10 kms-1 pc-1. For more diffuse gas with a density of 103 cm-3and α = 0.5, (dv/dr) is around 0.5kms-1 pc-1. Molecular gas close to the central massive black hole will be strongly influenced by gravity (e.g., Bonnell & Rice 2008), thus could be subvirialized (Kvir< 1). However such an effect is likely obvious only within a few tenths pc in the center. On the other hand, the tidal shear produced by the black hole would also increase the instability of molecular gas, where Kvir> 1.

Appendix B: Likelihood analysis of the single-component fitting

In the following, we analyze possible solution ranges for the central 18′′ of the Circinus galaxy and corresponding physical conditions satisfying maximum likelihood achievable in the set of all combinations parameters (see also Sect. 4.2.1). We caution, however, that these findings – in particular the numbers shown below – are rather uncertain, and will be only indicative.

Instead of the Bayesian probability, which is the integral of all probabilities in the parameter space (e.g., Weiß et al. 2005; Hailey-Dunsheath et al. 2012; Kamenetzky et al. 2011; Rangwala et al. 2011), we analyze the trend of the solutions with the highest likelihood. The maximum likelihood function of a given parameter (or given parameters) is based on the best fitting results in the whole parameter space.

Figure B.1 (upper panel) shows the maximum likelihood as a function of velocity gradient in a range of 1kms-1 pc-1dν/dr 103 kms-1 pc-1. We plot the corresponding values of nH2 and Tkin of the best fit for each given velocity gradient (lower panel). Over the modeled dν/dr range, Tkin and nH2 vary by about an order of magnitude. The likelihood drops below half of the peak value when dν/dr is beyond 101.8 kms-1 pc-1, where the solutions have relative high temperature and low density. This suggests that reasonable models are not likely to have a dν/dr higher than 60 kms-1 pc-1 because then even the best fitting result shows poor fits to the measurements.

thumbnail Fig. B.1

Upper panel: maximum likelihood as a function of the velocity gradient dν/dr for single-component LVG fitting. Lower panel: best-fit values of density (blue circles) and temperature (red squares) for a given velocity gradient as functions of velocity gradient, with error bars showing a 1σ range of the likelihood distribution. The gray regions have Kvir~ 1, 10, and 100.

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thumbnail Fig. B.2

Upper panel: maximum likelihood as a function density for single-component LVG fitting. Lower panel: best-fit velocity gradient for a given density as a function of density. The gray regions have Kvir~ 1, 10, and 100.

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thumbnail Fig. B.3

Upper panel: maximum likelihood as a function of temperature for single-component LVG fitting. Lower panel: best-fit density for a given temperature as a function of temperature. The dashed lines show thermal pressure, log (nH2×Tkin), in units of K cm-3.

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thumbnail Fig. B.4

The contours show the distributions of the maximum likelihood for a given density and temperature in the single-component LVG fitting. Contours are drawn from 0.1 to 0.9 by 0.2. Background gray scale levels show the velocity gradient associated with the best LVG fitting results, for each given temperature and density. The dashed lines indicate the thermal pressure log (nH2×Tkin) in units of K cm-3.

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Figure B.2 shows the maximum likelihood as a function of nH2 in a H2 density range from 102 cm-2to 106 cm-2. We plot the corresponding dν/dr of the best fits as a function of density. The solutions are found over a broad range of velocity gradients, which increase almost linearly as density increases. Solutions with high densities also have high velocity gradients. But the density is not likely to be higher than 104.5 cm-3where the likelihood is dropping below half of the peak value and Kvir exceeds ten. This implies that models with high density solutions are highly supervirialized and are not bound by self-gravity.

Figure B.3 shows the maximum likelihood as a function of Tkin from 10 K to 103 K. The thermal pressure P = nH2 × Tkin of the best fitting results is presented for given temperatures. The thermal pressure decreases by an order of magnitude when Tkin increases from a few tens of K to about 200 K. This indicates that the solutions of high temperature will have low thermal pressure because of the corresponding low density of these solutions.

In Fig. B.4, we show as contours the density-temperature likelihood distribution of the LVG modeling. The gray scale background displays the velocity gradient associated with the best fitting results, at given temperatures and densities. The contours present a banana-shaped likelihood distribution, which is mainly caused by the degeneracy between temperature and density. In the contour map, thermal pressure almost stays constant along the ridge of the distribution. Both density and temperature vary by two orders of magnitude within the 50% contour. The likelihood distribution covers a range of thermal pressure from 104.8 to 106.5 Kcm-3 and peaks at ~105.2 Kcm-3. From the map of the associated velocity gradients in the background, dν/dr increases with nH2, and decreases with Tkin. Most good solutions have small dν/dr between 1 kms-1 pc-1 and 10 kms-1 pc-1.

Appendix C: Likelihood analysis of the two-component fitting

thumbnail Fig. C.1

Background gray scale images show the maximum likelihood distributions of temperature and density, derived from the two-component LVG modelings. The gray levels are from 0.1 to 0.9 with a spacing of 0.2. The low- and high-excitation components are plotted in blue and red contours. The dashed lines indicate thermal pressure, log (nH2×Tkin), in units of K cm-3.

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thumbnail Fig. C.2

Upper panel: velocity gradients of the best fitting results as functions of density, derived from the two-component LVG modeling. The gray regions have Kvir~ 1 and 10. Lower panel: maximum likelihood as functions of the densities of both excitation components. The low- and high-excitation components are plotted in blue and red shadows, respectively.

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thumbnail Fig. C.3

Upper panel: thermal pressure (log (nH2×Tkin)) of the best fitting results as functions of density, derived from the two-component LVG modeling. Lower panel: maximum likelihood as functions of temperatures for both excitation components. The low- and high-excitation components are plotted in blue and red shadows, respectively.

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In Fig. C.1, we show the maximum likelihood distribution of both components in our modeling, with contours of the enclosed probability. Both distributions have banana shapes that are mainly caused by the degeneracy between Tkin and nH2. We find that both distributions are characterized by component specific thermal pressures. The thermal pressure of the HE component is about one order of magnitude higher than that of the LE component.

The HE component shows a steep slope in the high density and low temperature regime, and a flat slope at the high temperature side with a very broad range of Tkin solutions. This indicates that the density is not tightly constrained for the HE component. The HE component has a best-fit dν/dr of ~ 50kms-1 pc-1, which is about 10 times higher than that of the LE component, where ~6kms-1 pc-1 is the best fitting result. General fitting results of both excitation components are listed in Table 9.

FigureC.2 shows the density likelihood as functions of both excitation components (lower panel), and the corresponding velocity gradient of the best fittings for given densities (upper panel). The higher the density, the larger the velocity gradient for both components. Solutions with higher densities also have higher Kvir. Molecular gas in such conditions has very violent motions and high temperature. Unless the HE component adopt a low density solution of ~103.5 cm-3, Kvir is always higher than unity. The density range of the HE component is much wider than that of the LE component, which is due to the high degeneracy between nH2, Tkin, and dν/dr, and less constrained for the high-J transitions. In Fig. C.3, the temperatures of both components are not well constrained although the likelihood curve of the LE component looks narrower and peaks at lower temperature (~40 K) than that of the higher temperature (~50 K). The thermal pressure drops when the temperature increases, and stays nearly constant when the temperatures of both components are higher than 100 K.

All Tables

Table 1

Parameters of 13CO, 12CO, and Ci observations

Table 2

Parameters of the observed lines.

Table 3

CO line intensities.

Table 4

Fitting parameters of CO moment-zero maps.

Table 5

Parameter restrictions for the LVG modeling.

Table 6

CO detections toward the central position of Circinus in the literature

Table 7

Physical parameters of single-component fitting in the central 18′′ region, with < 1.5.

Table 8

Parameter restrictions for the two-component LVG modeling.

Table 9

Physical parameters of two-component fitting in the central 45′′ region.

Table 10

Physical parameters of two-component fitting of the S-F ring at diameter 18′′<D< 45′′, with Likelihood L> 0.8 (see Eq. (1)).

All Figures

thumbnail Fig. 1

Left panel: Herschel 70 μm contours overlaid on an Hα image of the HST (Wilson et al. 2000). The contour levels are 500, 1000, 2000, 3000, and 4000 MJy/sr. The concentric circles show the beam sizes of 12COJ = 3 → 2 for APEX (18′′, white thick line) and 12COJ = 1 → 0 for SEST (45′′, red dashed line). Right panel: CO spectra observed in the central position. 12COJ = 6 → 5, 7 → 6, and Ci are multiplied by a factor of 2, and 13COJ = 3 → 2 is multiplied by a factor of 5. The (shaded) line emission ranges from ~200 to ~700kms-1.

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In the text
thumbnail Fig. 2

Ci 10 and 12COJ = 3 → 2 spectra from the central region of the Circinus galaxy. The Ci spectra are relatively noisier and are presented in red, while the 12COJ = 3 → 2 profiles are plotted in black. To reach similar intensities, Ci is scaled up by a factor of three.

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In the text
thumbnail Fig. 3

Moment-zero images of multiple-J CO transitions. Big crosses mark the central position of Circinus; small crosses in the upper panels denote the sampled positions. Upper left: 12COJ = 3 → 2; upper right: 12COJ = 4 → 3; lower left: 12COJ = 6 → 5; lower right: 12CO J = 7 → 6. Circles in the lower left of each panel show the beam. The 12COJ = 7 → 6 map was convolved to an angular resolution of 18′′. Contour levels are 20, 60, ..., 180 Kkms-1in steps of 40 Kkms-1 for 12COJ = 3 → 2, J = 4 → 3, and J = 6 → 5, and 10, 20, 30 Kkms-1 for 12COJ = 7 → 6 (1σ = 1.9, 3, 10, and 3 Kkms-1 for 12COJ = 3 → 2, J = 4 → 3, J = 6 → 5, and J = 7 → 6). Red (thick dotted) contours present the half maximum level of all images. The thin dotted lines in the lower two panels denote the regions that have been scanned with higher S/N than other regions farther away from the centers (see Sects.2 and 3.1.3). The outer dotted lines in the 12COJ = 7 → 6 map are related to masking.

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In the text
thumbnail Fig. 4

The 492 GHz Ci 1 → 0 integrated intensity image of the central part of the Circinus galaxy. Plotted contour levels are: 20 (6σ), 30, 40, 50, and 60 mKkms-1. The red contour presents the half maximum level of the Ci emission. The beam size (FWHM) is 13.5′′.

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In the text
thumbnail Fig. 5

CO channel maps of the central region of the Circinus galaxy. The velocity range is given at the top, and the nuclear position of the Circinus galaxy is labeled by white crosses. Beam sizes are shown in the panels at the left hand side. Upper panels: 12COJ = 6 → 5 channel maps. The contours are from 0.1 (2σ) to 0.5 K with a spacing of 0.1 K. Middle panels: 12COJ = 4 → 3 channel maps. The contours are –0.1 (dotted) and 0.1 to 1.0 Kkms-1, the latter with a spacing of 0.1K. The 3σ noise level corresponds to 0.1 K. Lower panels: 12COJ = 3 → 2 channel maps. The contours are the same as for 12COJ = 4 → 3. The 5σ noise level corresponds to 0.1 K.

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In the text
thumbnail Fig. 6

Position-velocity (P-V) maps of CO emission from the Circinus galaxy. From left to right: P-V diagrams of 12COJ = 3 → 2, 12COJ = 4 → 3, and 12COJ = 6 → 5. The slice is taken along the major axis obtained from 12COJ = 3 → 2 (position angle: 33.°5, see Table 4) and the direction is from northeast (bottom) to southwest (top). The contours are from 30% to 90% of the peak intensities with a spacing of 20%.

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In the text
thumbnail Fig. 7

Top: integrated flux densities of 12CO and 13CO transitions in the central region (18′′ in diameter) of Circinus. We plot the solution range of 12CO (dark gray) and 13CO (light gray) derived from single-component LVG modeling of CO and 13CO lines with J ≥ 3. The range is selected from all solutions satisfying < 1.5 (or Likelihood L> 0.6). We plot 12COJ = 2 → 1, 12COJ = 1 → 0, and their 13CO isotopic transitions for beam sizes >18′′ as upper limits (black boxes and circles) to our models. Bottom: integrated flux densities of 13CO, in a zoomed in view.

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In the text
thumbnail Fig. 8

Integrated flux densities of 12CO and 13CO in the central 45′′ region of the Circinus galaxy. The shadowed regions are the ranges of the best fitting results derived from the two-component LVG modeling. The high- and low-excitation components and the total integrated 12CO flux densities are plotted in red, blue, and green. The total integrated 13CO flux densities are plotted in gray.

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In the text
thumbnail Fig. 9

Integrated flux densities of 12CO and 13CO in the S-F ring region of the Circinus galaxy. The shadowed regions are the ranges of the fittings satisfying likelihood L> 0.8, derived from the two-component LVG modeling. The high- and low-excitation components and the total integrated 12CO flux densities are plotted in red, blue, and green. The total 13CO flux densities are plotted in gray.

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In the text
thumbnail Fig. 10

as a function of . The empty triangles show observed positions in Circinus. The empty circles show the galaxies at high redshift (Walter et al. 2011). The crosses represent results of nearby galaxies found in literature. NGC 6946 and M 83: (Israel & Baas 2001), M 51: (Israel et al. 2006), Hennize 210 and NGC 253: (Bayet et al. 2004), IC 342: (Israel & Baas 2003).

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In the text
thumbnail Fig. B.1

Upper panel: maximum likelihood as a function of the velocity gradient dν/dr for single-component LVG fitting. Lower panel: best-fit values of density (blue circles) and temperature (red squares) for a given velocity gradient as functions of velocity gradient, with error bars showing a 1σ range of the likelihood distribution. The gray regions have Kvir~ 1, 10, and 100.

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In the text
thumbnail Fig. B.2

Upper panel: maximum likelihood as a function density for single-component LVG fitting. Lower panel: best-fit velocity gradient for a given density as a function of density. The gray regions have Kvir~ 1, 10, and 100.

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In the text
thumbnail Fig. B.3

Upper panel: maximum likelihood as a function of temperature for single-component LVG fitting. Lower panel: best-fit density for a given temperature as a function of temperature. The dashed lines show thermal pressure, log (nH2×Tkin), in units of K cm-3.

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In the text
thumbnail Fig. B.4

The contours show the distributions of the maximum likelihood for a given density and temperature in the single-component LVG fitting. Contours are drawn from 0.1 to 0.9 by 0.2. Background gray scale levels show the velocity gradient associated with the best LVG fitting results, for each given temperature and density. The dashed lines indicate the thermal pressure log (nH2×Tkin) in units of K cm-3.

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In the text
thumbnail Fig. C.1

Background gray scale images show the maximum likelihood distributions of temperature and density, derived from the two-component LVG modelings. The gray levels are from 0.1 to 0.9 with a spacing of 0.2. The low- and high-excitation components are plotted in blue and red contours. The dashed lines indicate thermal pressure, log (nH2×Tkin), in units of K cm-3.

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In the text
thumbnail Fig. C.2

Upper panel: velocity gradients of the best fitting results as functions of density, derived from the two-component LVG modeling. The gray regions have Kvir~ 1 and 10. Lower panel: maximum likelihood as functions of the densities of both excitation components. The low- and high-excitation components are plotted in blue and red shadows, respectively.

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In the text
thumbnail Fig. C.3

Upper panel: thermal pressure (log (nH2×Tkin)) of the best fitting results as functions of density, derived from the two-component LVG modeling. Lower panel: maximum likelihood as functions of temperatures for both excitation components. The low- and high-excitation components are plotted in blue and red shadows, respectively.

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In the text

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