ALMA Observation of NGC 5135: The Circumnuclear CO (6–5) and Dust Continuum Emission at 45 pc Resolution^*

The four panels in Figure 1 show the images of the total CO (6–5) emission integrated between the observed velocities of 3971 and 4157 $\mathrm{km}\,{{\rm{s}}}^{-1}$, the 435 μm continuum, the velocity field (i.e., moment 1), and velocity dispersion map (moment 2). Each image roughly covers the ALMA primary beam. The contours overlaid in Figures 1(a) and (b) refer to the same total CO (6–5) emission and start at signal-to-noise ratio (S/N) = 3.

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The CO (6–5) emission detected at S/N > 3 appears clumpy and is confined to a few discrete regions along two spiral-arm-like features corresponding spatially to the dust lanes seen in the UV and optical (e.g., Muñoz Marín et al. 2007). We mark four separate regions, namely, (a, b, c, d), which are compact and concentrated in the integrated CO (6–5) map. Region d appears more diffuse compared with the other three. The total CO (6–5) flux from the combined four regions in Figure 1(a) is 512 ± 24 Jy $\mathrm{km}\,{{\rm{s}}}^{-1}$. With a much larger beam of ∼31'', the Herschel/FTS observation gives a CO (6–5) flux of 1617 Jy $\mathrm{km}\,{{\rm{s}}}^{-1}$ (Lu et al. 2017). Therefore, the clump regions in Figure 1(a) together account for ∼32% of the total CO (6–5) flux of the galaxy. The "missing" line flux could be due to a combination of the line emission outside the ALMA field of view, or possible faint emission at peak surface brightness below our 3σ (i.e., 3.6 Jy beam⁻¹ $\mathrm{km}\,{{\rm{s}}}^{-1}$) detection limit, or resolved out on larger scales. We analyze individual clumps in more detail in Section 4.2.

We set the threshold at 4σ_ch, where σ_ch is the rms noise per frequency channel, to obtain the moment 1 and 2 maps. To reveal the kinematics better, the moment 1 and 2 maps, shown respectively in Figures 1(c) and (d), were based on the uv-taper image (the details about the uv-taper image are presented in the last paragraph of this subsection). The velocity scale in Figure 1(c) was calculated using the formula ν_obs = ν_rest(1 − V/c), where ν_obs is the observed CO (6–5) line frequency, c the speed of light, and V the velocity to calculate. The line velocity ranges from 3992 to 4140 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Figure 1(d) shows that the line-of-sight velocity dispersion ranges from 10 to 40 $\mathrm{km}\,{{\rm{s}}}^{-1}$, using only those pixels with S/N > 4σ_ch. The overall kinematic pattern can also be seen in the channel maps displayed in Figure 2, where the contours from an individual channel of width 13.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$ are overlaid on the grayscale image of the total CO (6–5) flux map shown in Figure 1(a). While regions a, c, and d are mainly confined within a velocity range of 3992–4073 $\mathrm{km}\,{{\rm{s}}}^{-1}$, region b has a range between 4046 and 4127 $\mathrm{km}\,{{\rm{s}}}^{-1}$. This suggests that the observed velocity pattern is not dominated by a simple rotation within the galaxy disk. In the channel maps, some CO (6–5) clumps break down into smaller clumps (or clouds) in some velocity channels, e.g., region a in the channel centered at V = 4073 $\mathrm{km}\,{{\rm{s}}}^{-1}$. These clouds have sizes <50 pc.

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In Figures 3(a) and (b), we reproduced the same images as in Figures 1(a) and (b), respectively, but with a larger effective beam of 04 × 04 (equivalent to 112 × 112 pc) by applying a uv-taper (with the parameter "outertaper" = 04) to our uv data before imaging. The peak signal of region d is higher than 4σ (σ = 8 Jy beam⁻¹ $\mathrm{km}\,{{\rm{s}}}^{-1}$). The total flux of the four regions combined, as defined in Figure 1, is 841 ± 45 Jy $\mathrm{km}\,{{\rm{s}}}^{-1}$. This flux equals 1.6 times the flux from the original ALMA image and is ∼52% of the total flux measured by Herschel, confirming that there exists some more diffuse or lower surface brightness CO (6–5) emission within the region of Figure 1(a).

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As shown in Figure 3(b), the continuum at 435 μm generally coincides with the CO (6–5) line emission in regions a and c at scales of 04 (equivalent to 112 pc), which corresponds to an angular size of 114 pc at the distance of NGC 5135. This is consistent with the findings in the other LIRGs we imaged in CO (6–5), i.e., NGC 34, NGC 1614, NGC 7130, and IC 5179 (Xu et al. 2014, 2015; Zhao et al. 2016, 2017), i.e., at scales ≳100 pc, there is a good spatial correspondence between the CO (6–5) line and its underlying continuum emissions.

However, at scales significantly smaller than 100 pc, there are apparent offsets between the local peaks of the line and continuum emissions in Figure 1(b). This small-scale offset between the line and continuum emissions is also seen in the LIRGs of moderately high nuclear gas surface densities, e.g., IC 5179 (at linear resolution ${R}_{\mathrm{linear}}\approx 34$ pc; Zhao et al. 2017) and NGC 7130 (R_linear ≈ 70 pc × 40 pc; Zhao et al. 2016). Furthermore, in both Figures 1(b) and 3(b), the dust continuum is unusually weak relative to the line emission in regions b and d. As argued in Zhao et al. (2016), these differences between the line and dust continuum emissions at small scales can only be understood if the gas and dust are heated by different mechanisms. We discuss this in more detail in Section 4.3.

By combining the four regions in Figure 1(b), we derived a total flux of 181 ± 25 mJy for the 435 μm continuum emission. This flux would be 1.6 times higher if we had derived it from the same regions in Figure 3(b).

The AGN position can be constrained by the peak of the [Si vi] line emission at 1.96 μm in a ground-based observation (Bedregal et al. 2009) and by the peak of the hard X-ray (4–8 keV) emission detected with Chandra (Levenson et al. 2004). The estimated astrometric uncertainty associated with either of these images is on the order of 05. The VLA 6 cm radio continuum image of Ulvestad & Wilson (1989) has a modest resolution of 091 × 060 and an astrometric accuracy of 03. We overlaid our CO (6–5) contours from Figure 1(a) on this radio continuum image in Figure 4(a). As already stated in Section 1, the main peak of the 6 cm emission is ∼3'' south of the galaxy nucleus, spatially coincident with the peak of the broad (FWHM ∼ 513 $\mathrm{km}\,{{\rm{s}}}^{-1}$) [Fe ii] emission (Bedregal et al. 2009). However, there is a minor radio emission peak (10σ) near the anticipated AGN position. We take the position of this radio peak (R.A. = 13^h25^m4402, decl. = −29°50'004; J2000) as the AGN location (i.e., marked by the black plus sign), with a positional uncertainty of 03–05. In Figure 4(b), we overlaid the same CO (6–5) contours on the hard X-ray emission.

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As shown in Figure 1(a), the CO (6–5) emission is undetected at the 4σ level at the AGN position (i.e., integrated over the velocity range of 186 $\mathrm{km}\,{{\rm{s}}}^{-1}$). This would hold true even if we had lowered the detection threshold to 3σ. We assume that the AGN-related CO (6–5) emission is confined to an area smaller than our ALMA beam size (∼48 × 40 pc), and then the 3σ flux upper limit is equal to 3 × (1.2 Jy $\mathrm{km}\,{{\rm{s}}}^{-1}$) = 3.6 Jy $\mathrm{km}\,{{\rm{s}}}^{-1}$ (σ = 1.2 Jy beam⁻¹ $\mathrm{km}\,{{\rm{s}}}^{-1}$).

However, an apparent narrow emission feature at the AGN location is seen at 3σ–4σ significance over only two velocity channels (i.e., V = 4019.0 and 4032.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$). The image summed over these two velocity channels is presented in Figure 5(a), which shows a peak surface brightness of 33 mJy beam⁻¹ (at 5σ significance). The spectrum in Figure 5(b) is extracted from a circular aperture of radius = 04 (=2.5 times the FWHM of the 3σ surface brightness of the emission in Figure 5(a)). Its narrow velocity width of ∼40 $\mathrm{km}\,{{\rm{s}}}^{-1}$ makes it unlikely that this signal is physically associated with the AGN. Nevertheless, considering that the CO (6–5) emission associated with the gas torus of the AGN in NGC 1068 is observed to have only a modest velocity width of ∼80 $\mathrm{km}\,{{\rm{s}}}^{-1}$ (García-Burillo et al. 2016), we defer to a future observation of higher angular resolution to firmly conclude the reality of this narrow CO (6–5) emission. Fluxwise, the narrow CO (6–5) emission in Figure 5(b) has a flux of 1.7 Jy $\mathrm{km}\,{{\rm{s}}}^{-1}$, which is smaller than the 3σ flux upper limit of 3.6 Jy $\mathrm{km}\,{{\rm{s}}}^{-1}$ derived above. Therefore, we conclude that the AGN in NGC 5135 contributes at most 1% of the CO (6–5) flux observed within the ALMA field of view. This is consistent with the Herschel finding that the mid-J CO line emission in LIRGs is mainly associated with SF regardless of whether there is an AGN or not (Lu et al. 2017). The fractional contribution of the AGN to the bolometric luminosity of NGC 5135 is about 24% ± 6% (Díaz-Santos et al. 2017). The AGN in NGC 5135 is heavily obscured; the surrounding gas could be heated to a very high temperature by the X-rays associated with the AGN, resulting in a CO spectral line distribution that peaks at J > 10 (Spaans & Meijerink 2008). Such a scenario seems to be the case in the Seyfert galaxy NGC 1068: While the high-resolution ALMA imaging shows that the vast majority of the nuclear CO (6–5) emission is associated with the compact circumnuclear ring of SF at a radius of ∼100 pc (García-Burillo et al. 2016), the total nuclear CO emission line spectrum has a distinct component that peaks at J ∼ 16 (Spinoglio et al. 2012). This hot spectral component of the CO emission is presumably due to the AGN in NGC 1068. The central AGN in NGC 5135 is bright in terms of the 1–0 S(1) 2.12 μm H₂ rovibrational line (Bedregal et al. 2009) associated with warm molecular gas. Although this line could be excited by different physical processes, including UV fluorescence (photons), shock fronts (collisions), and X-ray illumination, Bedregal et al. (2009) argued that the excited near-IR H₂ emission is mainly caused by X-ray illumination in the AGN region of NGC 5135. Such an X-ray-dominant scenario is also favored based on nondetection of the CO (6–5) emission here.

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The 435 μm dust continuum is also undetected at the AGN position, with the 3σ flux upper limit equal to 5.4 mJy (σ = 1.8 mJy beam⁻¹; the same method used for deriving the CO (6–5) flux upper limit). We compare this flux upper limit with the expected 435 μm continuum flux from an average infrared spectral energy distribution (SED) appropriate for the AGNs of X-ray luminosities comparable to that of NGC 5135: the intrinsic 2.0–10 keV X-ray luminosity of NGC 5135 is ∼1.8 × 10⁴³ erg s⁻¹ (Singh et al. 2012). We therefore used the infrared AGN SED for ${L}_{2.0-10\mathrm{keV}}\gt {10}^{42.9}$ erg s⁻¹ in Mullaney et al. (2011) and anchored it at the 12 μm luminosity of NGC 5135 estimated from the X-ray and mid-IR correlation given in Asmus et al. (2015). This derived SED is shown in Figure 6, along with two continuum flux upper limits (at 3σ) at 435 and 1300 μm based on the ALMA observation. The latter continuum flux upper limit was estimated from an archival ALMA Band 6 observation (Project 2013.1.00243.S; PI: L. Colina). This plot suggests that the ALMA data points are consistent with what is expected from the typical infrared SED for AGNs like NGC 5135.

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Several clumpy features are resolved in the CO (6–5) image shown in Figure 1(a). The resolved clump sizes of ∼100 pc are comparable to or larger than the beam size. For other (U)LIRGS, such clumpy features are traced more commonly by low-J CO or isotopologues, owing to the difficulty in observing dense tracers. However, it is more appropriate to analyze the properties of compact clumpy structures as seen in Figure 1(a) using denser gas tracers rather than the diffuse gas traced by low-J CO observation. Dense gas tracers, such as CS (2–1), HCN(1–0), and CO (6–5), usually trace embedded cloud clumps or cores within a more extended distribution of CO emission (Rosolowsky & Blitz 2005; Sakamoto et al. 2011; Leroy et al. 2015) and therefore are very useful for studying the dense, embedded star-forming structures within a much larger molecular region.

In Figure 1(a), the CO (6–5) emission peaks are resolved into separate clumps at S/N = 4, labeled as a1, a2, a3, a4, a5, b, c, and d. For each clump, we list in Table 2 a number of parameters derived from the image in Figure 1(a) for all the clumps except for clump d. At the resolution of Figure 1(a), clump d is detected only at S/N = 3 and appears to be quite diffuse. We therefore derived its parameters from the image in Figure 3(a), which has a coarser resolution of 112 × 112 pc.

Table 2.  Physical Properties of the Individual Clumps in Our CO (6–5) Image

No.	Size	PA	Radius	V0	ΔVFWHM	fpeak	${f}_{\mathrm{CO}(6-5)}$	${I}_{\mathrm{cont}}$	Mvir	Mmol	${M}_{\mathrm{mol}}^{* }$	R${}_{\mathrm{CO}/\mathrm{cont}}$
	(arcsec × arcsec)	(deg)	(pc)	(km s−1)	(km s−1)	(Jy beam−1)	(Jy km s−1)	(mJy)	(×107 M⊙)	(×108 M⊙)	(×108 M⊙)	(km s−1)
						$\mathrm{km}\,{{\rm{s}}}^{-1}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
a1	0.65 × 0.34	16.50	99.2	4062.9	88.0	13.3	91.1	81.8	37.0	10.5	12.6	1113.0
	±0.019 × 0.010		±2.2	±3.0	±7.6		±3.0	±8.4	±7.4	±2.9	±0.4	±119.0
a2	0.36 × 0.10	−0.45	44.1	4084.4	63.6	9.2	15.5	11.4	7.6	1.4	2.1	1362.0
	±0.025 × 0.012		±3.0	±3.7	±9.2		±3.1	±2.7	±2.7	±0.5	±0.4	±419.0
a3	0.40 × 0.25	0.74	62.6	4053.7	59.1	10.6	29.6	28.7	8.9	3.7	4.1	1032.0
	±0.023 × 0.014		±2.9	±4.0	±6.0		±2.1	±6.2	±2.3	±1.2	±0.3	±236.0
a4	0.64 × 0.19	0.13	54.1	4047.6	62.6	9.6	28.5	21.6	9.4	2.6	3.9	1321.0
	±0.054 × 0.011		±4.0	±2.4	±7.2		±1.8	±2.4	±2.7	±0.7	±0.2	±171.0
a5	0.72 × 0.44	3.38	123.9	4027.6	61.7	9.6	55.0	39.7	19.7	5.1	7.6	1850.0
	±0.023 × 0.022		±4.3	±1.2	±5.6		±1.5	±6.3	±4.5	±1.5	±0.2	±221.0
b	0.52 × 0.38	5.09	95.7	4089.6	76.7	8.9	55.3	13.5	25.9	1.7	7.6	4084.0
	±0.028 × 0.026		±4.4	±1.2	±4.4		±2.0	±1.9	±3.6	±0.5	±0.3	±598.0
c	0.72 × 0.21	−32.46	76.1	4027.8	69.1	9.4	41.8	48.3	16.0	6.2	5.7	866.0
	±0.025 × 0.007		±2.1	±1.9	±5.0		±2.8	±5.9	±2.8	±1.7	±0.4	±120.0
da	0.94 × 0.84	0.00	182.0	4067.3	87.3	30.2	69.4	13.0	66.6	1.7	9.6	5320.0
	±0.016 × 0.014		±2.4	±1.7	±4.8		±5.5	±3.8	±8.4	±0.7	±0.8	±1603.0

Note. The flux shown in this table is measured after the primary-beam correction. Table columns are as follows: Col. (1): clump number (as shown in Figure 1(a)). Col. (2): major and minor axes by 2D Gaussian fit. Col. (3): major-axis position angle (PA; N to E). Col. (4): effective clump radius after a deconvolution with the ALMA beam (R = $1.91\sqrt{({\sigma }_{x}\times {\sigma }_{y})}$, where σ = FWHM/2.3548; Solomon et al. 1987). Col. (5): line-center velocity from 1D Gaussian fit to the line profile within an elliptical aperture with radii of (major and minor axes (FWHM)). Col. (6): line velocity FWHM width from 1D Gaussian fit within an elliptical aperture with radii of (major and minor axes (FWHM)). Col. (7): clump peak surface brightness from the clump intensity map. Col. (8): CO (6–5) flux within an elliptical aperture with radii of (major and minor axes (FWHM)). Col. (9): continuum flux density within an elliptical aperture with radii of (major and minor axes (FWHM)). Col. (10): virial mass (see the text). Col. (11): molecular gas mass (estimated from the dust continuum; see the text). Col. (12): molecular gas mass (estimated from the CO flux; see the text). Col. (13): ratio of the total CO (6–5) flux to the 435 μm dust continuum flux density.

^aUsing the image in Figure 3(d), corresponding to a larger beam of 04 × 04.

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The size of a clump is specified by its FWHM major and minor axes plus the major-axis position angle (PA), which are given in Columns (2) and (3) of Table 2, respectively. These were derived from a 2D Gaussian fit to the clump intensity map. For the blended clumps (a4 and a5), we segmented the cloud into subclouds employing a variant of the CLUMPFIND algorithm (Williams et al. 1994). We divided the blended clumps by the half distance of two peaks and measured their parameters. We also calculated the effective clump radius R, following Solomon et al. (1987). After the deconvolution with the appropriate ALMA beam (using the CASA function "deconvolvefrombeam"), the radii range from 45 to 180 pc for the clumps (see Table 2, Column (4)).

We also extracted the 1D spectrum for each clump within an elliptical aperture with radii of (major and minor axes (FWHM)) as the oval areas marked in Figure 1(a). The resulting spectra are plotted for all the clumps in Figure 7. Using the same elliptical aperture, we derived the integrated CO (6–5) flux from the clump intensity map and the 435 μm continuum flux density from the continuum map. The line central velocity, the line velocity width ΔV_FWHM, the integrated CO (6–5) flux, and the 435 μm continuum flux density are given in Columns (5), (6), (8), and (9) of Table 2, respectively. The resulting ΔV_FWHM ranges from 60 to 88 $\mathrm{km}\,{{\rm{s}}}^{-1}$.

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We also estimated the virial and molecular gas masses for each clump. Following Larson (1981) and Heyer et al. (2009), the virial mass (M_vir) is estimated as

$$\begin{eqnarray}&&{M}_{\mathrm{vir}}/{M}_{\odot }=\displaystyle \frac{5{({\rm{\Delta }}{V}_{\mathrm{FWHM}}/\mathrm{km}{{\rm{s}}}^{-1})}^{2}\,R/\mathrm{pc}}{G},\end{eqnarray} \tag{ 1 }$$

where R is simply the effective clump radius and ΔV_FWHM refers to the value which has been deconvolved with channel width 13.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$, and a possible contribution of about 10 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from the disk rotation is further removed. (This correction amount was set to the mean velocity change over the size of one ALMA beam by examining the P–V plots of all the clumps. In the following, the ΔV_FWHM that we have used in Figures 8 and 9 are those corrected ones.) The derived virial masses, shown in Column (10) of Table 2, are in the range of ∼(7–60) × 10⁷ M_⊙.

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We estimated the molecular gas mass of a clump, M_mol, using the 850 μm continuum flux density based formula in Scoville et al. (2016) by converting the observed 435 μm flux density to that at 850 μm assuming a dust temperature of 25 K:

$$\begin{eqnarray}\begin{array}{rcl}{L}_{{\nu }_{850\mu {\rm{m}}}} & = & 1.19\times {10}^{27}\times {S}_{\nu }/\mathrm{Jy}\times \displaystyle \frac{{({\nu }_{850\mu {\rm{m}}})}^{3.8}}{{\nu }_{{obs}}(1+z)}\times \displaystyle \frac{{({d}_{L}/\mathrm{Mpc})}^{2}}{1+z}\\ & & \times \displaystyle \frac{{{\rm{\Gamma }}}_{\mathrm{RJ}}(25,{\nu }_{850\mu {\rm{m}}},0)}{{{\rm{\Gamma }}}_{\mathrm{RJ}}(25,{\nu }_{\mathrm{obs}},z)}/(\mathrm{erg}\,{{\rm{s}}}^{-1}{\mathrm{Hz}}^{-1})\end{array}\end{eqnarray} \tag{ 2 }$$

and

$$\begin{eqnarray}&&{\alpha }_{\nu }={L}_{{\nu }_{850\mu {\rm{m}}}}/{M}_{\mathrm{mol}}=6.7\pm 1.7\times {10}^{19}/(\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}\,{{\rm{M}}}_{\odot }^{-1}),\end{eqnarray} \tag{ 3 }$$

where ${{\rm{\Gamma }}}_{\mathrm{RJ}}({T}_{{\rm{d}}},\nu ,z)=\tfrac{h\nu /{{kT}}_{{\rm{d}}}}{{e}^{h\nu /{{kT}}_{{\rm{d}}}}-1}$ and the S_ν is the dust emission flux density. As the 435 μm flux density shown in Table 2 is measured within FWHM (diameter), it should only account for about 58% of the total flux. Thus, we multiply the flux density by 1.731 to estimate the total flux. For the gas clumps in the nuclear region of NGC 5135, T_d could be warmer. In this case, the calculated ${M}_{\mathrm{mol}}$ would be overestimated by roughly a factor of T_d/(25 K). The resulting M_mol, given in Column (11) of Table 2, is in the range of ∼(1–10) × 10⁸ M_⊙.

To check the molecular gas mass, we derived the molecular gas mass from the CO flux. We chose the conversion factor ${\alpha }_{\mathrm{CO}}=0.8$ M_⊙(K km s⁻¹ pc²)⁻¹ (Downes & Solomon 1998). The CO (6–5)/CO (1−0) ratio is about 2 (this will be explained in Section 4.3.1). The molecular gas mass derived this way is consistent with the one derived from the dust continuum as shown in Column (12) of Table 2.

Table 2 shows that all clumps have M_mol > M_vir except for clumps b and d. The clumps in the former category (hereafter referred to as Category (i)) are likely to be self-gravitationally bound or even undergoing initial collapse. On the other hand, clumps b and d in the other category (hereafter Category (ii)) would require external pressure to remain bound. Interestingly, the Category (ii) clumps are far away from ongoing SF activity and also show significantly higher CO (6–5)/dust continuum flux ratios (see Table 2, Column (13)) than the clumps in Category (i).

We can also compare the clumps in NGC 5135 with the molecular gas clouds in other galaxies. Figure 8 is a plot of the cloud (FWHM) velocity dispersion as a function of the cloud radius for the clumps in NGC 5135, as well as discrete clouds in the center of the Milky Way, nearby spiral galaxies, and two starburst galaxies NGC 253 and IC 5179. In comparison to the molecular clouds over the disks of nearby normal galaxies, the clouds in the Milky Way center observed by Oka et al. (2001) have a larger line width but a smaller size. In contrast, the clouds in the starburst galaxy NGC 253 (Leroy et al. 2015) and the LIRG IC 5179 (Zhao et al. 2017) show both larger sizes and broader line widths than clouds in the Milky Way center, but generally following the lines of equal gas surface density for the case of virialized clouds. The clouds in the nuclear region of NGC 5135 are characterized by still larger sizes and line widths.

Figure 9 is a plot of the parameter ${\rm{\Delta }}{V}_{\mathrm{FWHM}}^{2}/R$ as a function of molecular gas mass surface density Σ for the same data set as in Figure 8. The thick diagonal line shows the locus of virialized clouds. For bound clouds clearly lying above this line, the cloud velocity width is likely a manifestation of some external pressure. The dashed curves in Figure 9, taken from Field et al. (2011), indicate the relationship between ${\rm{\Delta }}{V}_{\mathrm{FWHM}}^{2}/R$ and Σ for a varying external pressure. The Category (i) gas clumps in NGC 5135 lie around the line tracing the virial equilibrium. In contrast, the two Category (ii) clumps are clearly located above the virial equilibrium and require external pressure of the order of 10⁸ cm⁻³ K in order to remain bound.

4.3.1. CO (6–5) Emission to Continuum Ratio

On galaxy scales, the ratio of the CO (6–5) line luminosity, ${L}_{\mathrm{CO}(6-5)}$, to L_IR varies only by up to 30% among local LIRGs and shows little dependence on L_IR or the FIR color (Lu et al. 2014, 2017). This strongly requires that the energy sources for both the CO (6–5) and the dust emissions are ultimately tied to the same SF process. This narrows down the candidate heating mechanisms for the CO (6–5) emission to fewer choices, including photon heating in the photon-dominant regions (PDRs) around young massive stars and SN-powered shock heating.

Our recent ALMA observations of nearby LIRGs show that, on scales of 100 pc or less, local peaks of the CO (6–5) emission do not always have corresponding peaks of the 435 μm dust continuum emission. Such examples include NGC 7130 (Zhao et al. 2016), IC 5179 (Zhao et al. 2017), and the case of NGC 5135 shown here. Under the assumption of a constant dust-to-gas abundance ratio, the spatial peaks of the two emissions should follow each other if both the dust and CO (6–5) emissions are related to the same photon heating. This finding therefore favors the SN-powered shock gas heating scenario for the CO (6–5) emission. Here we investigate further this subject in the case of NGC 5135.

As shown in Column (13) of Table 2, the CO (6–5) flux to the 435 μm continuum flux density ratio, R_CO/cont, varies among the CO (6–5) clumps. Furthermore, while the Category (i) clumps satisfy $600\,\mathrm{km}\,{{\rm{s}}}^{-1}\lesssim {R}_{\mathrm{CO}/\mathrm{cont}}\lesssim 1800$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, the two Category (ii) clumps have R_CO/cont > 4000 $\mathrm{km}\,{{\rm{s}}}^{-1}$. It is evident in Table 2 that the higher ${R}_{\mathrm{CO}/\mathrm{cont}}$ values associated with the Category (ii) clumps are mostly due to the unusually faint dust continuum emission at 435 μm. One can express

$$\begin{eqnarray}&&{R}_{\mathrm{CO}/\mathrm{cont}}\propto ({f}_{\mathrm{CO}(6-5)}/{f}_{\mathrm{CO}(1-0)})({M}_{\mathrm{gas}}/{M}_{\mathrm{dust}}){T}_{{\rm{d}}}^{-1},\end{eqnarray} \tag{ 4 }$$

where we have assumed that the CO (1–0) flux, ${f}_{\mathrm{CO}(1-0)}$, scales with the molecular gas mass M_gas. This shows that a higher ${R}_{\mathrm{CO}/\mathrm{cont}}$ can stem from either a hotter CO gas or/and a cooler dust temperature. In the nuclear region of NGC 5135, the variation of T_d is limited to, perhaps, a factor of 3 (i.e., from 15 to 50 K) at most. The observed variation of ${R}_{\mathrm{CO}/\mathrm{dust}}$ is a factor of ∼5 in Table 2, mainly between the two clump categories. A comparable variation is also seen in the case of IC 5179 (Zhao et al. 2017). Therefore, it requires a modest variation of a factor of 2 or so in ${f}_{\mathrm{CO}(6-5)}/{f}_{\mathrm{CO}(1-0)}$ in order to explain the observation. If the CO (6–5) emission is associated with SN shock heating, the ideal location for a higher ${R}_{\mathrm{CO}/\mathrm{cont}}$ ratio is where massive O star formation has ended while SN activity is still strong, a scenario we discussed in the case of NGC 7130 (Zhao et al. 2016). A necessary condition for the validity of this scenario is that some dense gas can survive the massive star formation, which might be possible in the dense and clumpy ISM.

4.3.2. CO (6–5) Emission and Current SF

In Figure 10, the black contours of the integrated CO (6–5) line emission are overlaid on a ground-based 8.7 μm image (Díaz-Santos et al. 2008) on the left side, and on an HST Paα image (Alonso-Herrero et al. 2006) on the right. In both plots, we also show the low-resolution Chandra 0.4–8 keV broadband X-ray emission (Levenson et al. 2004) in red contours. This X-ray emission is mostly associated with a hot, ionized gas powered by SNRs (Levenson et al. 2004; Colina et al. 2012).

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The 8.7 μm image is dominated by the mid-IR emission bands from the so-called polycyclic aromatic hydrocarbons (PAHs). The Paα emission is caused by the ionizing UV radiation from massive O stars and is regarded as a reasonable tracer of the ongoing SF activity (timescale ∼ 10 Myr). The PAH emission traces SF of 10 times longer timescale (∼100 Myr), as PAH molecules are mostly heated by nonionizing B stars (Díaz-Santos et al. 2008). As shown in Figure 10, the PAH and Paα emissions show similar surface brightness distributions. In contrast, the overall spatial morphology of the CO (6–5) emission appears to be different from that of either the PAH or the Paα emission. However, the Category (i) CO (6–5) clumps are all relatively close to local emission peaks of the PAH or Paα emission, whereas the Category (ii) CO (6–5) clumps are significantly farther away from any bright PAH or Paα peak. Therefore, it is reasonable to expect a much weaker far-UV radiation intensity at the location of each Category (ii) clump. This naturally explains why the dust emission is unusually faint at each of the Category (ii) clumps.

4.4.1. SN-powered Shock Heating Scenario

With an integral field spectrograph, Colina et al. (2012) measured the intensity and velocity fields of both the Brγ and the [Fe ii] 1.64 μm emission lines in the nuclear region of NGC 5135. While the Brγ traces the current star formation, the [Fe ii] line emission is regarded as a particularly good tracer of SNRs (Greenhouse et al. 1991). In Figure 11, we show a plot of the [Fe ii]-to-Brγ line ratio versus the CO (6–5)/continuum flux density ratio for all the clumps listed in Table 2, except for clump d, which is located outside the field of view of the [Fe ii] observation. We also indicated the typical [Fe ii]-to-Brγ line ratios for different astrophysical objects, taken from Falcón-Barroso et al. (2014). Note that the line ratio range shown for Seyferts is largely irrelevant here, as our molecular clouds are all located far away from the AGN.

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A number of studies have attempted to identify the physical causes behind the observed variations of the [Fe ii]-to-Brγ line ratio (e.g., Alonso-Herrero et al. 1997; Moorwood & Oliva 1988; Mouri et al. 1990, 1993; Greenhouse et al. 1991; Rodríguez-Ardila et al. 2004, 2005; Ramos Almeida et al. 2006, 2009; Riffel et al. 2013; Falcón-Barroso et al. 2014). From these studies, two main conditions for an enhanced [Fe ii] emission relative to a hydrogen recombination line emission emerge: (a) presence of shocked gas and (b) favorable environment for the gas-phase Fe to be abundant in the form of Fe⁺. Iron is normally depleted onto grains in the interstellar gas phase, so fast shocks, such as those associated with SNe, can cause grain destructions and therefore enrich gas-phase Fe abundance. Another important prerequisite for a strong [Fe ii] line is an ionization field in favor of Fe⁺. Given the low ionization potential of Fe⁺ (16.2 eV), most of Fe is in higher ionization states in H ii regions. In comparison, partially ionized gas in SNRs and Fe ⁺  is believed to be abundant (Moorwood & Oliva 1988). The collisional exitation with electrons could therefore make the [Fe ii] line much brighter in SNRs.

The [Fe ii]-to-Brγ line ratios for the Category (i) clumps in NGC 5135 are around 3, which is just outside the upper tip of the range for Galactic H II regions. These ratios are slightly higher than those seen in the nuclear star-forming regions in the Seyfert galaxy NGC 613 (Falcón-Barroso et al. 2014), suggesting some mild enhancement in the [Fe ii] line emission for the gas clouds in NGC 5135. In comparison, this line ratio for the Category (ii) clump b equals 6.5, implying a factor of 2 further enhancement in the relative [Fe ii] emission from the Category (i) clouds. It is not surprising for the observed line ratio of the Category (ii) cloud to be smaller than the typical values seen in Galactic SNRs because we are averaging over a much larger area than the typical size of Galactic SNRs and also because there is still low surface brightness star-forming activity near the cloud (see Figure 10). The observed trend in Figure 11 indicates that the same SN shocks are likely to play a positive role in the observed variations in both [Fe ii]/Brγ and CO (6–5)/dust ratios.

Additional evidence in favor of the SN shock heating scenario for the CO (6–5) emission in NGC 5135 includes (a) the prevailing X-ray emission from the hot, ionized gas excited via SN shocks (Colina et al. 2012) and (b) that there is a very good velocity field correspondence between the CO (6–5) clumps and that of the underlying [Fe ii] emission: the nominal CO (6–5) and [Fe ii] line velocity offset varies around the mean of −142 $\mathrm{km}\,{{\rm{s}}}^{-1}$ by only a few $\mathrm{km}\,{{\rm{s}}}^{-1}$ among the clumps. (Note that the mean velocity field difference is likely a result of the different velocity reference frames adopted.) This velocity correspondence suggests that the warm CO gas and the shocked/ionized gas are reasonably well mixed with each other in space and velocity field. Another independent evidence in favor of the SN shock heating scenario is the global tight correlation between the IR dust emission and the mid-J CO line emission shown by Lu et al. (2017), which requires that the gas heating ultimately derives the energy from the same SF process. The SN heating scenario would naturally fit this requirement.

4.4.2. Bar-Induced Shock Heating Scenario

Figure 12 displays the integrated CO (6–5) line emission contours overlaid on the HST F606W (0.606 μm) image (Malkan et al. 1998) and HST F160W (1.60 μm) image (Alonso-Herrero et al. 2006), respectively. The HST images aligned with our CO (6–5) data by matching our adopted AGN position with the brightest point in each optical image. As already mentioned before, the CO (6–5) emission has a good spatial correspondence with the dust lanes that can be seen in the optical and near-IR continuum images here. These roughly symmetrical dust lanes are induced by the inner stellar bar, both of which are more visible in a larger UV/optical image such as the one shown by Mulchaey & Regan (1997). This correspondence between the CO (6–5) emission and the bar-induced dust lanes in NGC 5135 is similar to that observed in NGC 7130, another LIRG with a strong stellar bar (Zhao et al. 2016). Indeed, NGC 5135 and NGC 7130 have many similarities: both are LIRGs with a strong circumnuclear star formation and a Seyfert 2 nucleus. Circumnuclear dust lanes have been found in many spiral galaxies, though strong two-arm dust lanes are found only in barred galaxies such as NGC 5135 and NGC 7130 (Martini et al. 2003).

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According to the model of Athanassoula (1992), the two-arm dust lanes are associated with the shock fronts triggered by the presence of a bar in a rotating gas disk. Thus, bar-induced shocks could be possible in the nuclear region of NGC 5135. Inside the dust lanes, the gas (and dust) density is significantly enhanced, but SF is suppressed by strong shears (Athanassoula 1992). This seems to imply that the warm dense gas traced by CO (6–5) and the SF regions traced by Paα are not related to each other.

In order to account for the tight correlation between the CO (6–5) emission and the total dust emission on galaxy scales for LIRGs, one has to relate the CO (6–5) emitting gas to the SF activity in this scenario. It is still possible that the warm dense gas and the SF regions are related to each other, albeit their positions are slightly offset. It is known that some galaxies with weak stellar bars (therefore weaker shears in dust lanes) have SF in their dust lanes (Comte & Duquennoy 1982; Martini et al. 2003). Hypothetically, one can envisage the following scenario: First, SF does occur in clouds of dense gas formed in the post-shock gas downstream from the bar-induced shock front (the dust lane). Then, these dense gas clouds will be rapidly consumed/destroyed by the SF and the associated feedback. In this scenario, under the assumption that the destruction timescale of the dense clouds is much shorter than the SF timescale associated with the Paα emission (a few Myr), the spatial offset is the product of the SF timescale times the downstream velocity of the post-shock gas, which is a few tens of kilometers per second (Athanassoula 1992). This indeed results in an estimate for the offset of ≲100 pc. It is worth noting that similar offsets between H II regions and dust lanes associated with spiral arms in grand-design galaxies such as M51 have been found in the literature, and Scoville et al. (2001) argued that it implies that the H II regions develop subsequent to the time of maximum concentration of the dust and molecular clouds.

However, it is unclear how this bar-induced shock heating scenario for the CO (6–5) emission can be made to explain the similar variation in the CO (6–5)/continuum flux ratio seen in IC 5179 (Zhao et al. 2017), which does not have a strong stellar bar.