Physical Properties of Molecular Clouds at 2 pc Resolution in the Low-metallicity Dwarf Galaxy NGC 6822 and the Milky Way

Table 1 summarizes the global properties of NGC 6822. In many ways NGC 6822 resembles a two times less massive version of the SMC (e.g., Jameson et al. 2016), except that the SMC is currently undergoing a strong interaction with the LMC and the Milky Way. The proximity ($D=474\pm 13\,\mathrm{kpc};$ Rich et al. 2014) makes NGC 6822 an ideal target to study cloud structure and star formation at high resolution; at this distance, $1^{\prime\prime} \approx 2.3$ pc, so that ALMA easily resolves cloud substructure. Like other comparatively isolated dwarf irregular galaxies, NGC 6822 is rich in gas with an atomic gas mass¹¹ of ${M}_{\mathrm{atom}}\approx 1.3\times {10}^{8}$ ${M}_{\odot }$ (Weldrake et al. 2003; de Blok & Walter 2006b). This is comparable to the galaxy's stellar mass, ${M}_{\mathrm{star}}\approx 1.5\times {10}^{8}$ ${M}_{\odot }$ (Madden et al. 2014), so that the gas mass fraction is $\sim 50 \%$. NGC 6822 is actively forming stars; the star formation rate (SFR) derived from various tracers is SFR ≈ 0.015 M_⊙ yr⁻¹ (Efremova et al. 2011, and references therein), giving it a specific star formation rate, $\mathrm{sSFR}\,\approx {10}^{-10}$ yr⁻¹, typical of a star-forming galaxy.

Table 1.  Global Properties of NGC 6822

Property	Value	Reference
Hubble type	IB(s)m (9.8)	NED/LEDA
R.A.a	19h44m5774	NED
Decl.a	−14d48m124	NED
Distance	474 ± 13 kpc	Rich et al. (2014)
Systemic vel.	−57 ± 2 km s−1	Koribalski et al. (2004)
Inclination	60 ± 15 deg	Weldrake et al. (2003)
Position angle	115 ± 15 deg	Weldrake et al. (2003)
E(B − V)foreground	0.21 mag	Schlafly & Finkbeiner (2011)
E(B − V)internal	0.0–0.3 mag	Efremova et al. (2011)
$12+\mathrm{log}\,{\rm{O}}/{\rm{H}}$	8.02 ± 0.05 dex	García-Rojas et al. (2016)
R25	8.69 arcmin	LEDA
${M}_{{\rm{V}}}$	−15.2 ± 0.2 mag	Dale et al. (2007)
${M}_{\mathrm{star}}$	$1.5\times {10}^{8}$ ${M}_{\odot }$	Madden et al. (2014)
${M}_{\mathrm{atom}}$	$1.3\times {10}^{8}$ ${M}_{\odot }$	Weldrake et al. (2003)
${M}_{\mathrm{mol}}$	$\lt 1\times {10}^{7}$ ${M}_{\odot }$	Gratier et al. (2010)
${M}_{\mathrm{dust}}$ b	${2.9}_{-0.8}^{+2.9}\times {10}^{5}$ ${M}_{\odot }$	Rémy-Ruyer et al. (2015)
GDRb	${480}_{-240}^{+170}$	for above values
SFR(mix)	0.015 M⊙ yr−1	Efremova et al. (2011)

Notes. All masses scaled according to our adopted distance.

^aOptical center; the Hi dynamical center is nearby. ^bDust mass derived for an amorphous carbonaceous component.

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Despite abundant atomic gas and signatures of high-mass star formation, NGC 6822 has a modest reservoir of molecular gas. The molecular gas mass is ${M}_{\mathrm{mol}}\lesssim 1.0\times {10}^{7}$ ${M}_{\odot }$ (based on IRAM 30 m observations by Gratier et al. 2010; but also see Sections 4.1 and 5.5 below). Like other low-mass galaxies, NGC 6822 is poor in metals, with metallicity $\sim 1/5$ the solar value¹² ($12+\mathrm{log}\,{\rm{O}}/{\rm{H}}=8.02\pm 0.05$; García-Rojas et al. 2016; Hernández-Martínez et al. 2009). It is also poor in dust, with dust mass¹³ ${M}_{\mathrm{dust}}\approx 3\times {10}^{5}$ ${M}_{\odot }$ (Rémy-Ruyer et al. 2015). The implied gas-to-dust ratio is $\mathrm{GDR}\approx 480$, which is $\sim 3$ times the solar neighborhood value of ${{GDR}}_{\odot }\,=162$ (Zubko et al. 2004; Rémy-Ruyer et al. 2014), but with a factor of $\sim 2$ uncertainty.

Figure 1 shows the morphology of NGC 6822 in atomic gas (gray scale) and recent star formation traced by Hα (orange color) with our ALMA survey fields marked (blue boxes). Star formation is concentrated in the inner part of the H i distribution, coincident with the main stellar disk. Our four inner ALMA fields target prominent star-forming (H ii) regions in this active area. Together, these harbor 63% of the global Hα flux and 65% of the global Spitzer $24\,\mu {\rm{m}}$ flux (a tracer of embedded star formation), so that with our ALMA survey we probe the cloud complexes responsible for $\sim 2/3$ of the current star formation activity in NGC 6822. Our fifth field targets a region in the northwest part of the H i disk, selected to search for cold gas associated with low-level star formation activity evidenced in optical, ultraviolet, and Hα imaging (de Blok & Walter 2003, 2006a).

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Table 2 summarizes the properties of our target regions. All four inner regions have been studied extensively, and two of them, Hubble V and X (our ALMA Fields 2 and 1), are classic targets for extragalactic studies of young stellar clusters. As a result, they have been studied via ground-based optical broadband (de Blok & Walter 2000; Bianchi et al. 2001) and narrowband (Hα) imaging (Hodge et al. 1989; de Blok & Walter 2006a), as well as space-based broadband (Bianchi & Efremova 2006; Efremova et al. 2011; Bianchi et al. 2012) and narrowband (various nebular lines) imaging (O'Dell et al. 1999). These studies show that all four inner regions are actively forming massive stars and have likely done so for the past $\sim 10\,\mathrm{Myr}$. They contain up to $\sim 100$ OB-type stars each and have Hα luminosities of a few times 10³⁸ erg s⁻¹, which would rank them among the brightest and most massive star-forming regions in our Galaxy. There is no clear evolutionary sequence established in the literature, but Hubble IV and V (our ALMA Fields 4 and 2) show more compact CO and SFR morphologies than Hubble I, III, and X (our ALMA Fields 3 and 1) and higher ratios of embedded to exposed SFR tracer luminosities ($8\,\mu {\rm{m}}$ or $24\,\mu {\rm{m}}$ versus Hα; Table 2). Based on this, we argue below that these two regions (Fields 4 and 2) may be currently more active (i.e., younger) than the others.

Table 2.  Properties of Target Regions

Property	Unit	Field 1	Field 2	Field 3	Field 4	Field 5
H ii region name	...	Hubble X	Hubble V	Hubble I and III	Hubble IV	...
Cluster name	...	OB 13	OB 8	OB 1 and 3	OB 5	...
Cluster mass	M⊙	$7\times {10}^{3}$	$4\times {10}^{3}$	...	...	...
No. O-type stars	...	35 O−B2V	$\gt 40$	...	...	...
No. OB-type stars	...	70 O−B5V	80 O−B5V	...	...	...
Hα luminosity	1038 erg s−1	3.362 (18%)	4.100 (22%)	3.409 (18%)	0.941 (5.0%)	0.010 (0.1%)
8 μm flux density	μJy	0.087 (2.3%)	0.211 (5.5%)	0.055 (1.5%)	0.150 (3.9%)	...
24 μm flux density	μJy	0.241 (9.4%)	0.931 (36%)	0.155 (6.0%)	0.332 (13%)	...
ALMA Cycle 1 CO(2–1) Data (Natural Weighting)
Beam major axis	arcsec	0.97	1.03	1.04	1.55	1.16
Beam minor axis	arcsec	0.71	0.69	0.69	0.68	0.74
Beam size	arcsec	0.83	0.85	0.85	1.03	0.92
	pc	1.90	1.94	1.96	2.36	2.13
rms noise	mJy	18.7	14.1	14.9	12.4	13.1
	K	0.63	0.45	0.47	0.27	0.35
Sensitivity	K km s−1	1.1	0.8	0.8	0.5	0.6
	M⊙ pc−2	4.9	3.5	3.7	2.1	2.7
	${M}_{\odot }$	17.5	13.3	14.0	11.7	12.3
Flux	103 K km s−1	15.1	117.6	24.3	123.5	...
Luminosity	103 K km s−1 pc2	1.8	14.0	2.9	14.7	...
Mass (for ${\alpha }_{\mathrm{CO},\mathrm{MW}}$)	103${M}_{\odot }$	7.8	60.8	12.6	63.8	...
ALMA Cycle 1 1.3 mm Continuum Data (Natural Weighting)
Beam size	arcsec	0.87	0.89	0.90	1.08	0.96
rms noise	mJy	0.19	0.16	0.17	0.14	0.13
Atomic–Molecular Complex Masses as Derived from Herschel Dust Modeling
H i mass	105 ${M}_{\odot }$	3.97 ± 0.04	3.50 ± 0.04	0.76 ± 0.04	6.34 ± 0.04	...
Dust mass	103 ${M}_{\odot }$	3.1 ± 2.2	5.5 ± 3.8	1.7 ± 1.1	4.0 ± 4.0	...
GDR	...	420 ± 345	275 ± 127	410 ± 215	420 ± 293	...
Inferred H i+H2 mass	105 ${M}_{\odot }$	13.1 ± 1.9	15.0 ± 4.2	6.8 ± 1.8	16.9 ± 1.9	...
Inferred H2 mass	105 ${M}_{\odot }$	9.1 ± 1.3	11.5 ± 4.2	6.0 ± 1.8	10.5 ± 2.8	...
Inferred ${\alpha }_{\mathrm{CO}}$	${M}_{\odot }$ pc ${}^{-2}$ (K km s−1)−1	572 ± 93	90 ± 33	235 ± 72	83 ± 22	...

Note. Adopted distance D = 474 kpc; CO brightness temperature ratio ${R}_{21}=1.0;$ and CO-to-H₂ conversion factor ${\alpha }_{\mathrm{CO}}=4.35$ M_⊙ pc⁻² (K km s⁻¹)⁻¹. Sensitivity ($1\sigma$) determined over 5.0 km s⁻¹. Percentages (given in parentheses) for Hα, $8\,\mu {\rm{m}}$, and $24\,\mu {\rm{m}}$ flux state fractions of NGC 6822's global fluxes.

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We compare the CO emission to Hα and dust emission. At low resolution, the Hα map (de Blok & Walter 2006a) traces the distribution of recent star formation. At the high ($0\buildrel{\prime\prime}\over{.} 9\approx 2$ pc) resolution of our ALMA data, Hα traces the structure of H ii regions. We compare CO to dust emission at $8\,\mu {\rm{m}}$ and $24\,\mu {\rm{m}}$, both from the Spitzer Infrared Nearby Galaxy Survey (Kennicutt et al. 2003) and first presented in Cannon et al. (2006). The $8\,\mu {\rm{m}}$ map is dominated by emission from polycyclic aromatic hydrocarbons (PAHs) and traces PDRs; the $24\,\mu {\rm{m}}$ map measures hot dust and traces embedded star formation.

We use H i and dust surface density maps to measure the large-scale structure of the star-forming complexes. The H i data are from the Very Large Array (VLA) taken as part of the LITTLE THINGS survey (Hunter et al. 2012). Due to calibration complications, these were not released with the rest of the survey; however, they will be presented in I. Bagetakos et al. (2017, in preparation) and have been kindly provided for use in this paper.

The distribution of dust mass surface density is inferred from infrared data from the Herschel Dwarf Galaxy Survey (Madden et al. 2013). We model the infrared spectral energy distribution (SED) between 70 and 500 μm using a modified blackbody, the Draine & Li (2007) model, and the Galliano et al. (2011) model with an amorphous carbonaceous component (see Galametz et al. 2010; Rémy-Ruyer et al. 2015 for details). The latter data set has been kindly provided by M. Galametz and S. Madden (private communication). The agreement between the three dust maps is generally poor. The Galactic cirrus toward NGC 6822 has similar brightness to NGC 6822 itself, which severely complicates the usability of the infrared data. We have tested several methods to remove the Galactic cirrus but failed to converge on robust results. In addition, we suspect problems in the Herschel PACS and SPIRE data products themselves (e.g., potentially related to the dynamic range or recovery of extended emission; see also Abreu-Vicente et al. 2016) as individual bands show inconsistencies in their intensities (by a factor of a few) with any reasonable infrared SEDs in either faint or bright regions. For that reason, we reverted to using SPIRE's $350\,\mu {\rm{m}}$ band as a dust proxy, but we note that results derived from more complex dust modeling (i.e., modified blackbody, Galliano et al., or Draine & Li model) agree within a factor of a few. This uncertainty dominates the error budget in our analysis of dust-inferred gas masses.

The H i and dust maps are evaluated at a common resolution of $25^{\prime\prime} \approx 57$ pc, set by the diffraction limit of SPIRE's $350\,\mu {\rm{m}}$ band. At this resolution, each of our fields has 5 × 5 almost independent 50 × 50 pc elements. The outer 50 pc wide ring lacks signatures of high-mass star formation and molecular gas; we use it to measure the local gas-to-dust ratio and to measure the amount of foreground and background emission from dust and H i.

In order to interpret our results, we use matched-resolution CO data from the Milky Way and WLM. Matched spatial resolution measurements of CO emission from Milky Way clouds offer a view on cloud structure at high (solar) metallicity, while WLM is the only other low-metallicity galaxy observed so far with data quality matching our own. The contrast of these clouds with our results in NGC 6822 illuminates how conditions in our target galaxy affect cloud structure and the degree to which conclusions about the impact of metallicity may be general (if they apply to both WLM and NGC 6822).

In the Milky Way, we use CO maps of Orion, Carina, and W3/W4. As Table 4 shows, these clouds have masses only a bit lower than the atomic–molecular complexes targeted in NGC 6822. They span a range of massive star formation activity, with Orion showing modest high-mass star formation and with Carina and W3/W4 being two of the most active star-forming regions in the Galaxy. The CO(1–0) data for Orion and Carina are part of the CfA 1.2 m Galactic Plane Survey¹⁴ and have been presented in Wilson et al. (2005) and Grabelsky et al. (1987). The CO(2–1) data for the molecular cloud complex W3/W4 have been obtained with the 10 m Heinrich Hertz Submillimeter Telescope (HHT) by Bieging & Peters (2011). For a rigorous comparison, we convolve the Orion and W3/W4 data to the same spatial (2 pc) and spectral (0.635 km s⁻¹) resolution as our NGC 6822 data. We do not match the sensitivities, which typically are a factor of a few better for the Galactic data. The Carina data from the CfA 1.2 m telescope have a native resolution of $5.6\,\mathrm{pc}\,\times 1.3$ km s⁻¹; we compare these with our data at their native resolution.

Table 4.  Properties of Milky Way Clouds

Property	Orion	W3/W4	Carina
Distance (kpc)	0.45	2.0	2.3
No. O-type stars	3	10	70
No. OB-type stars	43	105	135 (200)
Cloud mass (M⊙)	$2\times {10}^{5}$	$4\times {10}^{5}$	$6\times {10}^{5}$

References. Orion: Muench et al. (2008); Wilson et al. (2005); W3/W4: Kiminki et al. (2015); Polychroni et al. (2012); Carina: Smith & Brooks (2008); Roccatagliata et al. (2013).

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We compare the clump properties that we measure for NGC 6822 with those measured from the FCRAO Outer Galaxy Survey (Heyer et al. 2001). These data, as reprocessed by Brunt et al. (2003), have a resolution of $100^{\prime\prime} \times 0.98$ km s⁻¹. At the distance of the Perseus arm ($D\approx 2$ kpc), this corresponds to $\sim 1$ pc. They are thus closely matched to the resolution of our ALMA data and provide an ideal Galactic point of reference.

We also compare to the ALMA observations of WLM by Rubio et al. (2015). WLM is a Local Group dwarf galaxy with $\sim 1/8$ solar metallicity. Its stellar mass and current star formation activity are both $\sim 10$ times lower than NGC 6822. Rubio et al. have observed CO(1–0) at $6.2\,\mathrm{pc}\times 4.3\,\mathrm{pc}$ and 0.5 km s⁻¹ resolution in two atomic–molecular complexes and report the detection of 10 CO-emitting structures. In our analysis of the macroscopic properties of the CO-emitting structures in NGC 6822 (Section 4.5), we include their measurements for WLM as listed in their Table 1.

We identify discrete objects in our data set; measure their size, line width, and luminosity; and compare them with the properties of similarly sized objects in our comparison data sets. To do this, we use an updated version of the CPROPS algorithm¹⁵ (Rosolowsky & Leroy 2006; A. K. Leroy & E. Rosolowsky 2017, in preparation). For details on CPROPS, we refer the reader to Rosolowsky & Leroy (2006), Leroy et al. (2015), and A. Schruba et al. (2017, in preparation). Briefly, we consider only significant emission, identified by a signal-to-noise cut across several channels. Within this mask, we find all significant local maxima. For each maximum, we identify the nearby pixels that can be associated with only that peak (and no others) in an iso-intensity contour. For each region of emission, we measure its size, line width, and luminosity. We use several methods to do this: spatial and spectral moments, area measurements at half-peak value or some threshold, and ellipse fitting. Each measurement is corrected for the fact that it is made at finite sensitivity and resolution. The sensitivity calculations either assume a Gaussian profile or use a curve-of-growth method to account for the finite sensitivity of the data. The resolution corrections are made after the correction for sensitivity and use quadratic subtraction of the two-dimensional beam and channel width. The values reported here are the mean across all of these characterization methods. We adopt the scatter in results from different measurement approaches as our best estimate of the uncertainty of the size, line width, and luminosity, because this tends to be as large as any statistical or calibration uncertainty.

We observe CO(2–1) at high ($0\buildrel{\prime\prime}\over{.} 9\approx 2$ pc) spatial resolution. Similarly to CO(1–0), we find CO(2–1) emission to emerge from cold dense gas, especially gas with significant optical depth, though it can also be emitted under other conditions. However, the ratio of the brightness temperatures of the two lines, R₂₁, can vary. If CO(2–1) is subthermally excited or when the Rayleigh–Jeans approximation breaks down at low temperatures, then ${R}_{21}\leqslant 1$. On the other hand, gas of low opacity has ${R}_{21}\geqslant 1$. Observations in our Galaxy find ${R}_{21}=0.65\pm 0.1$ at a spatial scale of a few tens of parsecs; this is an average of diffuse emission from low-density gas and opaque emission from dense gas (Yoda et al. 2010, J. Mottram et al. 2017, in preparation). Observations of nearby disk galaxies suggest a very similar line ratio of ${R}_{21}=0.7$ measured on a roughly kiloparsec spatial scale (e.g., Leroy et al. 2009, 2013). On the other hand, values of ${R}_{21}=1.0\pm 0.3$ are found in molecular clouds at 20 pc resolution in the LMC and SMC (Israel et al. 2003; Bolatto et al. 2003) or on larger (∼100 pc) spatial scales in IC 10 (L. Bittle et al. 2017, in preparation). More detailed multi-transition studies of the CO emission from molecular clouds in the SMC indicate that the CO emission originates from two gas components: a more tenuous and not very dense (${n}_{{{\rm{H}}}_{2}}={10}^{2}\mbox{--}{10}^{3}$ cm⁻³) component of high temperature (${T}_{\mathrm{kin}}=100\mbox{--}300$ K) and a population of much denser clumps (${n}_{{{\rm{H}}}_{2}}={10}^{4}-{10}^{5}$ cm⁻³) of low temperature (${T}_{\mathrm{kin}}=10-60$ K) (Israel et al. 2003; Bolatto et al. 2005). As we will see in Section 4.5, we do not probe the very dense clumps with our ALMA data, and most of the admittedly scarce observations of low-metallicity star-forming galaxies seem to favor ${R}_{21}\approx 1;$ therefore, we adopt ${R}_{21}=1.0$ throughout the paper. This mainly affects comparisons to Galactic data, and we discuss possible variations when they become relevant.

We measure CO emission but are often interested in the distribution of H₂. The metallicity of NGC 6822 and the high spatial resolution of our data both complicate the translation of CO to H₂. The CO abundance strongly depends on shielding of the dissociating radiation field and thus is a strong function of metallicity (Wolfire et al. 2010). So far, the exact metallicity dependence of the CO-to-H₂ conversion factor, ${\alpha }_{\mathrm{CO}},$ remains poorly known, as does any secondary dependence on radiation field, cloud structure, and other quantities. We will derive our own estimates for ${\alpha }_{\mathrm{CO}(2-1)}$ for NGC 6822 using alternative ISM tracers (dust) and dynamical methods. Doing so, we reference the commonly adopted Milky Way value, ${\alpha }_{\mathrm{CO}(1-0)}=4.35$ M_⊙ pc⁻² (K km s⁻¹)⁻¹, which includes a factor of 1.36 to account for heavy elements (Bolatto et al. 2013).

Because of our high resolution, the scale dependence of ${\alpha }_{\mathrm{CO}}$ will also be relevant. The conventional extragalactic definition of ${\alpha }_{\mathrm{CO}}$ is the mass-to-light ratio of H₂ mass to CO emission over a large part of a galaxy. In this definition cloud substructure and even, to some degree, cloud populations are averaged over. Within an individual cloud, the relationship between CO and H₂ can be more complex, especially at low metallicity, where a large envelope of CO-poor H₂ may exist. We will consider three scales for ${\alpha }_{\mathrm{CO}}$: the scale of CO-bright clumps, the scale of whole individual complexes, and the whole galaxy. At the small scales of clumps we disregard the H₂-rich but CO-poor envelopes of molecular clouds. At the scale of individual atomic–molecular complexes we account for all gas (including CO-poor H₂), but results may reflect the local environment or evolutionary state of an individual region. At the scale of the whole galaxy we somewhat marginalize over these conditions.

Throughout the paper we work with the H i emission without opacity correction. Galaxy-wide studies conclude that local opacity corrections to the column density can exceed an order of magnitude and add globally 20%–30% to the atomic gas mass (see Braun et al. 2009; Kalberla & Kerp 2009; Bolatto et al. 2013, and references therein), but without providing clear quantitative prescriptions of how to correct observed 21 cm H i data sets for optical depth effects. Small-scale or pencil-beam studies within the Milky Way suggest the cold neutral medium (that causes the absorption) to be in compact clouds of parsec size or narrow filaments and sheets with up to $10\mbox{--}100$ pc length (Heiles & Troland 2003; Kalberla & Kerp 2009), but here it remains unknown how these findings extend to galactic scales. Recently, Bihr et al. (2015) presented work on the massive cloud complex W43 and advocated for opacity corrections as high as $\sim 2.4$ over $\sim 100$ pc scales, but the mass and surface density of W43 are a factor $\gtrsim 5$ higher than the cloud complexes studied in NGC 6822. Overall, these results highlight that optical depth effects are present in H i observations but also show that we lack a conclusive understanding how to correct 21 cm H i observations. Therefore, we adopt the standard assumption of optically thin H i emission and work without opacity correction.

The whole area of NGC 6822 has not yet been mapped in CO, but the galaxy-integrated CO luminosity is important to compare the galaxy to other systems. We estimate this quantity via an "aperture correction" from our observed fields to the whole galaxy. To do this, we consider several tracers of recent star formation, Hα, $24\,\mu {\rm{m}}$, and $70\,\mu {\rm{m}}$. These tracers should scale linearly with molecular gas, and hence CO emission, over large, roughly kiloparsec, spatial scales (e.g., Schruba et al. 2011; Leroy et al. 2013). We measure CO luminosity in our fields and then also measure the luminosity of these tracers of recent star formation both within our fields and over the whole galaxy. Our "aperture correction" is the ratio of total star formation tracer luminosity of the galaxy to the luminosity inside our fields. Applying this scale factor to the CO emission from our fields, we estimate the total CO luminosity of the galaxy.

The sum of CO(2–1) luminosities inside our four inner ALMA fields is $3.34\times {10}^{4}$ K km s⁻¹ pc², and these fields harbor 63% of the global Hα flux and 65% of the global Spitzer $24\,\mu {\rm{m}}$ flux. Scaling our observed CO luminosity by $1/0.64$, we estimate the global CO(2–1) luminosity to be $5.2\times {10}^{4}$ K km s⁻¹ pc². Because ALMA recovers only $(73\pm 20) \%$ of the total flux (see Section 2), we scale this further by $1/(0.7\pm 0.2)$ to arrive at a best-estimate global CO(2–1) luminosity of NGC 6822 of $\sim (6\mbox{--}10)\times {10}^{4}$ K km s⁻¹ pc². This value agrees within the uncertainty with a similarly derived estimate by Gratier et al. (2010), who scaled from their IRAM 30 m map to estimate a global CO(2–1) luminosity of $\sim (8\mbox{--}13)\times {10}^{4}$ K km s⁻¹ pc².

To calculate the CO(1–0) luminosity, we need to further scale by the ratio ${R}_{21}^{-1}$. We argue by analogy with other systems that ${R}_{21}\approx 0.7-1.0$ but uncertain. Our best estimate of the global CO(1–0) luminosity for NGC 6822 is thus $\sim (10\pm 5)\,\times {10}^{4}$ K km s⁻¹ pc².

This integrated luminosity is small, establishing that NGC 6822 resembles other star-forming, low-metallicity dwarf galaxies in showing a low amount of CO luminosity compared to its present-day SFR, stellar mass, and atomic gas mass. For comparison, our estimate for the total CO luminosity of NGC 6822 is comparable to the CO luminosity of one of our individual Galactic comparison clouds, which have CO luminosities of $\sim (5\mbox{--}20)\times {10}^{4}$ K km s⁻¹ pc².

Our four inner fields host $\sim 2/3$ of the star formation activity in NGC 6822. The Hα and dust morphology, visible in Figures 4 and 5, extends for many tens of parsecs in each region. Though measured at much lower resolution ($25^{\prime\prime} =57$ pc), the H i and dust maps show that our observed CO clumps exist inside larger structures of gas and dust. We expect optically thin dust emission to trace the distribution of gas and H i emission to show the dominant atomic gas reservoir, modulo optical depth effects. We use these to estimate the overall mass and atomic–molecular balance in the star-forming complexes.

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We use dust, combined with a gas-to-dust ratio ${\delta }_{\mathrm{GDR}}$, to trace the total gas reservoir,

$$\begin{eqnarray}&&{\delta }_{\mathrm{GDR}}{{\rm{\Sigma }}}_{\mathrm{dust}}={{\rm{\Sigma }}}_{\mathrm{atom}}+{{\rm{\Sigma }}}_{\mathrm{mol}}.\end{eqnarray} \tag{ 1 }$$

Because ${{\rm{\Sigma }}}_{\mathrm{atom}}$ can be measured directly, we estimate the GDR by comparing ${{\rm{\Sigma }}}_{\mathrm{atom}}$ and ${{\rm{\Sigma }}}_{\mathrm{dust}}$ in regions where atomic gas makes up most of the gas. We use the outer 50 pc wide ring in each of our regions, assuming based on the lack of CO emission and bright signatures of high-mass star formation that the gas in this ring is mostly atomic. Table 2 lists the GDR with scatter for each of our regions.

On average, we find ${\delta }_{\mathrm{GDR}}=380\pm 70$, with only moderate variation among the four fields. This is $\sim 2.5$ times higher than the Galactic value but only half the value expected for the $\sim 1/5$ solar metallicity of NGC 6822 when assuming an inverse linear scaling of GDR and metallicity (Rémy-Ruyer et al. 2014). However, the absolute normalization of dust masses estimated from IR SED modeling remains uncertain at a level that could resolve this discrepancy (see Section 3.2). Our application of the dust map is to trace gas. For that purpose we require only a linear scaling of dust and gas; any normalization issues are controlled by measuring GDR in the local control field.

Before calculating the mass of the complexes, we subtract a local background from the H i and the dust maps. To do this, we measure the mean surface density in the outer 50 pc ring and subtract this value from the whole H i and dust map for the complex. This isolates the star-forming complex as the excess emission over the diffuse ISM. This is a particular concern for dwarf galaxies whose (warm atomic) ISM has large spatial extent, large scale height, and high filling factor (e.g., Bagetakos et al. 2011). This also lets us assess whether the star-forming complexes have an atomic gas component in excess of the diffuse atomic gas. No similar subtraction appears necessary for the CO emission.

After background subtraction, we find for each region a large concentration of dust (and thus gas) coincident with the star-forming complex (Figure 5). Applying our measured GDR to the dust distribution, we derive total gas masses of ${M}_{\mathrm{gas}}=0.7\mbox{--}1.7\times {10}^{6}$ ${M}_{\odot }$ for each complex. We subtract from the dust-inferred total gas mass the local excess H i mass and find that about $30 \%$ of the mass in these complexes is atomic gas traced by the 21 cm line. The rest is visible in dust but not in 21 cm emission. This is either opaque H i, H₂, or the signature of small-scale variations in the gas-to-dust ratio with the sense of a $\sim 3$ times lower gas-to-dust ratio. We proceed by interpreting the signal as molecular gas, but we note the need for more work in this area (see discussions in Leroy et al. 2007, 2011; Sandstrom et al. 2013; Jameson et al. 2016). In this case, the gas structures hosting star formation in NGC 6822 are approximately the mass of the biggest Galactic high-mass star-forming clouds of order $\sim {10}^{6}$ ${M}_{\odot }$, with $\sim 70 \%$ of their mass in the molecular form and $\sim 30 \%$ of their mass in the atomic form.

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The impact of the background subtraction is to remove the diffuse atomic ISM from the excess gas that we associate with the star-forming complexes. This diffuse medium has ${{\rm{\Sigma }}}_{\mathrm{atom}}\,=15\mbox{--}25$ M_⊙ pc⁻² in our survey regions and makes $\sim 80 \%$ of the atomic gas columns along the lines of sight toward the star-forming complexes. If the reader prefers to associate this diffuse gas with the star-forming complexes, then their total gas masses increase by a factor of $\sim 1.6$ and the atomic and molecular gas phases contribute roughly equal amounts to the complexes' mass. We note that the mass of the molecular component of the star-forming complexes—and thus all results that consider only the molecular gas and its CO emission—remains unchanged (within $5 \%$) by (not) applying the background subtraction.

From the ratio of H₂ derived from dust to CO emission, this analysis implies a CO-to-H₂ conversion factor. If we carry out a joint solution for ${\alpha }_{\mathrm{CO}}$ and GDR across the galaxy (following Leroy et al. 2011; Sandstrom et al. 2013), we derive ${\delta }_{\mathrm{GDR}}=320\pm 80$ and ${\alpha }_{\mathrm{CO}}=110\pm 30$ M_⊙ pc⁻² (K km s⁻¹)⁻¹, about 2 times and 25 times the Galactic values, respectively. However, this obscures strong variations among our four fields. Figure 6 shows that ${\alpha }_{\mathrm{CO}}$ varies systematically with the CO, Hα, and $24\,\mu {\rm{m}}$ morphology and luminosity. For the two fields (Fields 2 and 4) with compact CO and Hα morphology, dominated by embedded star formation (i.e., low ${\rm{H}}\alpha /24\,\mu {\rm{m}}$ ratio), and bright CO emission, we determine ${\alpha }_{\mathrm{CO}}=85\pm 25$ M_⊙ pc⁻² (K km s⁻¹)⁻¹, $\sim 20$ times the Galactic value. In the other two fields (Fields 1 and 3), which have more extended and exposed SFR tracer emission (i.e., high ${\rm{H}}\alpha /24\,\mu {\rm{m}}$ ratio) and much lower CO luminosity, ${\alpha }_{\mathrm{CO}}$ appears much larger, though uncertain, ${\alpha }_{\mathrm{CO}}\approx 235\pm 72$ and $\approx 572\pm 93$ M_⊙ pc⁻² (K km s⁻¹)⁻¹, respectively. We stress that considerable uncertainties remain in this analysis, mainly due to the large uncertainty in the dust mass.

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We speculate that the large discrepancy in ${\alpha }_{\mathrm{CO}}$ between fields is linked to the evolutionary state of the star-forming complex. Early in the history of the complex, the gas is compact and dense. Such structures are good at forming CO and effective at shielding it from dissociating radiation. In this case ${\alpha }_{\mathrm{CO}}$ is relatively small (Fields 2 and 4). Later in a complex's life, the gas gets disrupted by stellar feedback, which is visible as an evolving H ii region. With lower density, the ability of gas to form and shield CO is suppressed, driving ${\alpha }_{\mathrm{CO}}$ to larger values as more and more H₂ survives without CO (Fields 1 and 3).

We targeted our survey toward regions of active star formation, traced by bright Hα and mid-IR emission. CO emission tracks these other wavelengths on much larger scales because stars form out of molecular gas. Figure 4 shows a more complicated relationship on smaller scales, reflecting the evolution of young stellar populations and the different emission mechanisms at play. In Table 5 we quantify how CO emission correlates with Hα and IR emission at resolutions of $2^{\prime\prime} \approx 4.6$ pc (Hα and $8\,\mu {\rm{m}}$) and $6^{\prime\prime} \approx 14$ pc (all three tracers).

Table 5.  Association of the Top 80% of CO and IR Emission

Data	Flux Cuta	Flux Fractionb	Area Fractionc	Rank Corr.
Resolution of $2^{\prime\prime} \approx 4.6$ pc
CO	1.6 ± 0.7	0.79 ± 0.09	1.0	1.0
Hα	0.003 ± 0.013	0.77 ± 0.27	23 ± 22	0.19 ± 0.19
8 μm	0.65 ± 0.21	0.78 ± 0.14	5.1 ± 4.6	0.41 ± 0.10
Resolution of $6^{\prime\prime} \approx 14$ pc
CO	0.5 ± 0.3	0.81 ± 0.13	1.0	1.0
Hα	0.005 ± 0.010	0.77 ± 0.25	6.9 ± 6.5	0.20 ± 0.34
8 μm	0.40 ± 0.24	0.82 ± 0.15	3.4 ± 2.3	0.54 ± 0.09
24 μm	1.1 ± 0.5	0.80 ± 0.09	3.4 ± 2.0	0.37 ± 0.16

Notes.

^aCommon flux threshold for CO [K km s⁻¹], or Hα or IR [MJy sr⁻¹] holding 80% of the CO flux within each region. ^bFraction of CO, Hα, and IR flux in each region above the common threshold. ^cFraction of area covered by Hα or IR common threshold versus area holding $80 \%$ of the CO emission.

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First, we determine the maximum intensity contour for each tracer that encompasses $80 \%$ of the total CO emission, that is, we ask what threshold in Hα or $8\,\mu {\rm{m}}$ is needed to capture most of the CO. This threshold usually also encompasses a large area with little or no CO emission. To quantify how large this area is, and hence the closeness of correspondence with CO, we report an "area fraction," which is the ratio of the area inside the 80% CO threshold for that tracer to the 80% threshold for CO. Finally, we report the Spearman rank correlation coefficient between each tracer and CO above this threshold.

We find the closest correspondence between CO and $8\,\mu {\rm{m}}$ emission and the weakest relationship between CO and Hα, with $24\,\mu {\rm{m}}$ intermediate. This reflects the different emission mechanisms at play. The $8\,\mu {\rm{m}}$ emission originates from PAH molecules and traces PDRs. Despite a few compact sources, most emission comes from extended, diffuse structures that coincide with the CO emission. Overall, the distribution of the two tracers matches well. Gratier et al. (2010) noted a similar good correspondence at larger scales.

The $24\,\mu {\rm{m}}$ emission traces warm dust heated by young, embedded stars. At this scale, $24\,\mu {\rm{m}}$ sources correspond to an early, embedded phase of star formation that takes place before feedback can disrupt the parent gas cloud. The distribution of $24\,\mu {\rm{m}}$ intensity is concentrated into a few ($\sim 1\mbox{--}2$) bright sources per survey field. Each $24\,\mu {\rm{m}}$ source is associated with a CO-bright structure, but the reverse is not true. Many CO peaks lack a corresponding $24\,\mu {\rm{m}}$ source.

Hα emission and photospheric UV emission are most visible after the embedded phase traced by $24\,\mu {\rm{m}}$ emission. At the scales that we probe, Hα emission is not cospatial with the CO emission, reflecting both the disruption of clouds and the finite extent of H ii regions. Instead, we see the neutral gas (including the CO-bright clumps) swept up at the boundary of the H ii region bubbles—a picture that is well known from Galactic star-forming clouds (e.g., the W3/W4 molecular cloud–H ii region complex; see images by Bieging & Peters 2011).

Thus, the $8\,\mu {\rm{m}}$ emission correlates most directly with CO emission. The areal extent of the $8\,\mu {\rm{m}}$ contour needed to capture 80% of the CO emission is the smallest of the tracers that we test, but the correspondence is not perfect. This $8\,\mu {\rm{m}}$ contour is still a factor of $\sim 4$ larger than the actual CO-bright regions. The $24\,\mu {\rm{m}}$ shows the second-best correlation over similar areal coverage, but the scaling between CO and $24\,\mu {\rm{m}}$ emission on these scales is strongly nonlinear. Hα shows only marginal correlation, and the encompassing Hα contour has large areal extent.

Figure 7 shows this result by plotting the cumulative distribution of CO integrated intensity as a function of the threshold intensity at $8\,\mu {\rm{m}}$ or $24\,\mu {\rm{m}}$ at 2 pc resolution. The curves for $8\,\mu {\rm{m}}$ are steep, and high CO fractions are reached over a small intensity range near ${I}_{8\mu {\rm{m}}}\approx 0.5$ MJy sr⁻¹. A contour with this intensity does a good job of predicting where bright CO emission may be found. Our results reinforce the idea from Sandstrom et al. (2010) and Gratier et al. (2010) that PAH emission can provide a predictor of the location, and perhaps strength, of CO emission in low-metallicity environments. We have used $8\,\mu {\rm{m}}$ here; given the full-sky coverage of the Wide-field Infrared Survey Explorer (WISE), it will be important to test whether the same conclusions would apply using the $12\,\mu {\rm{m}}$ PAH feature covered by WISE's band 3.

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The distribution of intensities in our survey provides a basic measure of the structure of the CO-emitting gas in NGC 6822. We show this in Figure 8, where we plot the fraction of total flux above a specified CO pixel intensity threshold (expressed as intensity times channel width, W_CO). For reference we also plot the distributions for our three Galactic comparison clouds after convolving them to the resolution of our data (2 pc × 0.635 km s⁻¹) and applying the same masking procedure that we use for NGC 6822.

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The distributions in NGC 6822 differ from those of the Milky Way clouds, with emission coming from a narrower range of intensities in the NGC 6822 data. Less flux and less pixels show either low or high intensities. The absence of low-intensity emission may be explained physically, corresponding to a suppression of CO abundance in regions that are weakly shielded. However, given uncertainties in flux recovery and the limited sensitivity of our data, this difference is not significant. The difference at higher intensity does appear significant but modest in strength: on average, the NGC 6822 cumulative distribution functions (cdfs) are shifted to $\sim 30 \%$ lower pixel intensities with less flux in the brightest regions than in the Orion or Carina molecular clouds.

Our survey recovers a number of compact CO structures. We identify and measure the properties of $\sim 150$ of these roughly parsec-scale "clumps," estimating a size, line width, and CO luminosity for each. We use combinations of these properties to assess the surface and volume density, strength of turbulence, and dynamical state of the clumps. Table 6 lists the inferred properties of each clump, while Table 7 lists their average values and dynamic range. We compare these with results for similarly sized structures in WLM (Rubio et al. 2015) and the outer Milky Way (Brunt et al. 2003); their average values and dynamic range¹⁶ are also listed in Table 7. Figure 9 shows these comparisons, with the WLM data shown as open black circles and the Galactic clumps shown as grayscale contours of data density. Black lines show power-law fits to the NGC 6822 clumps, which are useful for comparison to the Galactic distribution.

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Table 6.  Molecular Cloud Catalog

ID	R.A.	Decl.	${V}_{\mathrm{LSR}}$	${T}_{\mathrm{pk}}$	S/N	${R}_{\mathrm{maj}}$	${R}_{\min }$	P.A.	R	${\sigma }_{{\rm{v}}}$	${L}_{\mathrm{CO}}$	${M}_{\mathrm{vir}}$	${\alpha }_{\mathrm{vir}}$
	(hh:mm:ss.s)	(dd:mm:ss)	(km s−1)	(K)		(pc)	(pc)	(deg)	(pc)	(km s−1)	(caption)	(102 ${M}_{\odot }$)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
1	19:45:03.8	−14:43:36	−45.0	1.5	2.4	0.9	0.3	96	0.5 ± 0.1	0.19 ± 0.00	0.0 ± 0.0	0.2 ± 0.0	1.3 ± 0.2
2	19:45:03.6	−14:43:40	−44.0	3.3	5.2	3.3	2.5	62	2.9 ± 0.6	0.58 ± 0.12	0.5 ± 0.2	10.1 ± 3.8	5.0 ± 2.8
3	19:45:01.7	−14:43:21	−42.0	2.4	3.8	2.9	1.8	148	2.3 ± 0.9	0.46 ± 0.02	0.2 ± 0.0	5.1 ± 2.1	6.9 ± 2.9
4	19:45:03.8	−14:43:36	−40.0	4.2	6.6	3.6	2.7	131	3.1 ± 0.8	1.26 ± 0.02	1.2 ± 0.0	51.9 ± 13.9	9.6 ± 2.6
5	19:45:01.7	−14:43:20	−40.0	2.3	3.7	2.3	1.2	6	1.7 ± 0.4	0.39 ± 0.05	0.1 ± 0.0	2.6 ± 0.9	4.5 ± 1.7
6	19:45:03.6	−14:43:41	−39.0	5.4	8.5	3.7	1.9	144	2.6 ± 0.5	2.06 ± 0.28	1.8 ± 0.5	116.9 ± 30.9	14.5 ± 5.7
7	19:45:01.9	−14:43:21	−39.0	2.1	3.4	...	...	...	1.1 ± 0	0.36 ± 0.04	0.1 ± 0.0	1.5 ± 0.0	3.6 ± 0.0
8	19:45:01.7	−14:43:21	−37.0	4.6	7.4	4.4	1.1	2	2.2 ± 0.5	1.10 ± 0.11	1.4 ± 0.5	27.4 ± 7.4	4.3 ± 1.9
9	19:45:01.7	−14:43:19	−36.0	3.5	5.5	...	...	...	0.5 ± 0	0.53 ± 0.08	0.3 ± 0.1	1.4 ± 0.0	1.2 ± 0.0
10	19:45:05.1	−14:43:20	−35.0	2.1	3.3	5.8	1.2	176	2.6 ± 0.2	0.45 ± 0.01	0.2 ± 0.0	5.6 ± 0.6	8.3 ± 0.8
...	...	...	...	...	...	...	...	...	...	...	...	...	...
...	...	...	...	...	...	...	...	...	...	...	...	...	...
...	...	...	...	...	...	...	...	...	...	...	...	...	...
156	19:44:49.0	−14:52:55	−41.0	2.7	10.0	7.5	2.2	6	4.1 ± 0.3	1.63 ± 0.11	2.2 ± 0.0	113.4 ± 13.7	12.0 ± 1.5

Note. Columns: (1) cloud identification number (ID); (2) right ascension (R.A. (J2000)); (3) declination (decl. (J2000)); (4) velocity (${V}_{\mathrm{LSR}}$); (5) peak brightness temperature (${T}_{\mathrm{pk}}$); (6) peak signal-to-noise ratio (S/N); (7) semimajor-axis length (${R}_{\mathrm{maj}}$); (8) semiminor-axis length (${R}_{\min }$); (9) position angle of cloud major axis, measured from R.A. through decl. (P.A.); (10) radius (R); (11) velocity dispersion (${\sigma }_{{\rm{v}}}$); (12) CO luminosity (${L}_{\mathrm{CO}}$ [10² K km s⁻¹ pc²]); (13) virial mass (${M}_{\mathrm{vir}}$); (14) virial parameter (${\alpha }_{\mathrm{vir}}$).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 7.  Average Properties of Molecular Clouds

Target		WLM	NGC 6822					Outer Milky Way
Property	Unit	Median	Min	$25\mathrm{th}$	Median	$75\mathrm{th}$	Max	Min	$25\mathrm{th}$	Median	$75\mathrm{th}$	Max
R	pc	2.21	0.27	1.64	2.29	3.14	7.23	0.50	1.25	1.87	2.79	14.87
${\sigma }_{{\rm{v}}}$	km s−1	0.77	0.17	0.68	1.06	1.40	2.84	0.30	0.60	0.82	1.14	8.47
${\sigma }_{{\rm{v}}}^{2}/R$	km2 s−2 pc−1	0.35	0.01	0.26	0.45	0.82	2.62	0.03	0.21	0.36	0.65	12.16
LCO	102 K km s−1 pc2	0.69	0.02	0.40	1.13	2.42	8.05	0.04	0.41	0.90	2.34	180.05
Mlum	102 ${M}_{\odot }$	2.99	0.09	1.75	4.90	10.54	35.03	0.15	1.67	3.70	9.61	738.22
Mvir	102 ${M}_{\odot }$	13.91	0.18	8.52	27.41	63.13	530.69	0.57	5.40	12.90	31.83	2096.26
${\alpha }_{\mathrm{vir}}$	4.38		0.46	3.22	5.00	8.27	83.07	0.44	1.97	3.11	5.32	61.25
${ \mathcal M }$		3.92	0.89	3.48	5.39	7.14	14.46	1.54	3.07	4.20	5.80	43.13
${{\rm{\Sigma }}}_{\mathrm{FWHM}}$	${M}_{\odot }$ pc−2	17.59	1.02	11.46	22.97	40.95	302.62	4.69	18.81	27.27	42.28	382.70
${n}_{\mathrm{FWHM}}$	102 cm−3	1.47	0.12	1.40	3.63	7.46	156.09	0.18	1.56	2.79	5.04	44.01
${\tau }_{\mathrm{ff},\mathrm{FWHM}}$	Myr	2.83	0.35	1.61	2.31	3.73	12.75	0.38	1.39	1.87	2.50	9.51
${\tau }_{\mathrm{cross},\mathrm{FWHM}}$	Myr	2.22	0.41	1.15	1.64	2.21	4.61	0.21	1.07	1.57	2.31	12.29

Note.

All values are extrapolated to zero flux. Assuming ${R}_{21}=1.0$ and ${\alpha }_{\mathrm{CO}}=4.35$ M_⊙ pc⁻² (K km s⁻¹)⁻¹.

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The top left panel of Figure 9 shows the line width of a clump as a function of its size. For clumps in virial equilibrium, the amplitude of turbulence at fixed size reflects the surface density of the structure. Regardless of dynamical state, one might interpret a higher dispersion at fixed size as stronger turbulence—modulo temperature effects, this will correspond to a higher Mach number. Differences among the three populations are small in this parameter space, but there is some tendency for NGC 6822 clumps to have higher line width at $\sim 5$ pc sizes.

Beyond the scaling, the absolute values shown in the top left panel of Figure 9 bear comment. The bright CO-emitting structures in NGC 6822 are remarkably small, a few parsecs across, with typical rms line widths $\sim 1$ km s⁻¹. This highlights a fundamental result for CO in dwarf galaxies, seen by Rubio et al. (2015) and extended here to 150 objects: CO emission comes mostly from compact, narrow line width structures. This observation is only possible with the high resolution and sensitivity of ALMA, so that to our knowledge this is the first time that a large set of clump properties at 2 pc spatial scale have been measured for an external galaxy.

The top right panel shows the CO luminosity as a function of clump size. As shown in the previous section, clumps in NGC 6822 have average CO SB $\sim 30 \%$ lower than those in the Milky Way. This is within the systematic uncertainties on flux recovery and excitation, but could also indicate suppressed CO emission in NGC 6822 or that the clumps are not fully resolved. Again, agreement among clump properties for the three galaxies is more notable than differences given how underluminous NGC 6822 appears in its ratio of global CO luminosity to other quantities.

The bottom left panel shows the virial mass, the mass implied by the clump's size and line width when assuming a simple geometry and virial equilibrium (${M}_{\mathrm{vir}}\,[{M}_{\odot }]\,=1040R{\sigma }^{2}\,[\mathrm{pc}\,{\mathrm{km}}^{2}\,{{\rm{s}}}^{-2}]$), as a function of clump mass estimated from the CO luminosity using a fiducial Galactic CO-to-H₂ conversion factor ${\alpha }_{\mathrm{CO}}=4.35$ M_⊙ pc⁻² (K km s⁻¹)⁻¹ and ${R}_{21}=1$. There is a good correspondence between clump virial mass and clump luminosity within each sample, but the NGC 6822 clumps show higher virial masses at a given CO luminosity than Milky Way clumps. This offset is not large (less than a factor of $\sim 2$), but appears significant.

The bottom right panel shows similar information. We plot the virial parameter, the ratio of virial to luminous mass, as a function of the luminous mass. Assuming that the conversion factor adopted to estimate the luminous mass is correct, then clumps with virial ratio of $\sim 1$ are in virial equilibrium, while clumps with virial ratios of $\sim 2$ are marginally bound. Those with higher ratios are either pressure confined or gravitationally unbound. This plot shows clumps in the outer Galaxy to be marginally bound, with ${\alpha }_{\mathrm{vir}}\approx 2.5$, while clumps in NGC 6822 are offset by a factor of $\sim 2$ toward larger virial parameters. This has two natural interpretations. Either the use of a Galactic conversion factor leads us to underestimate the clump mass in NGC 6822, or the clumps in this galaxy are unbound or pressure confined.

The main result from Figure 9 is that the properties of clumps in the three galaxies are similar independently of their host galaxy's mass or metallicity. Differences are small, a factor of $\lesssim 2$, and comparable to what we might expect from differing methodologies, flux recovery issues, and assumptions about excitation. Still, there is evidence here for either a different, more pressure-confined dynamical state for the NGC 6822 clumps or a slightly higher CO-to-H₂ conversion factor on scales of a few parsecs. We return to the implications of these results in Sections 5.4 and 5.5.

We identify $\sim 150$ compact CO structures in our cubes. These CO-bright clumps have an average size of $R\approx 2.3$ pc, velocity dispersion of ${\sigma }_{{\rm{v}}}\approx 1.1$ km s⁻¹, and virial mass of ${M}_{\mathrm{vir}}\approx 2.7\times {10}^{3}$ ${M}_{\odot }$ (see Table 7). These sizes and masses are small compared to a whole giant molecular cloud, so we have referred to these as "clumps." The very small size of these clumps is a main observational result of this paper. It shows that many previous results regarding the faintness of CO in dwarf galaxies can be explained in terms of beam filling: bright CO is confined to small structures that occupy only a small portion of the available area. Observations with physical beams larger than our 2 pc will dilute this intensity and so will recover faint CO emission.

Following an analysis presented by Rubio et al. (2015) for WLM, we evaluate the dynamical state of the clumps in three ways: (1) Assuming approximate virialization, so that ${M}_{\mathrm{vir}}\approx {M}_{\mathrm{gas}}$, the clumps have a gas mass surface density of ${{\rm{\Sigma }}}_{\mathrm{gas}}=125$ M_⊙ pc⁻² and an H₂ volume density of ${n}_{{{\rm{H}}}_{2}}\,=1000$ cm⁻³. (2) We can consider pressure equilibrium between the internal turbulent pressure of the CO clumps and external pressure by the weight of the overlaying gas layers of the atomic–molecular complex and the diffuse atomic medium. The external pressure due to self-gravity on the CO clump is ${P}_{\mathrm{ext}}/{k}_{{\rm{B}}}=\pi /2G{{\rm{\Sigma }}}_{\mathrm{gas}}^{2}=5\times {10}^{5}$ K cm⁻³, where ${{\rm{\Sigma }}}_{\mathrm{gas}}=120$ M_⊙ pc⁻² is the sum of gas columns of the atomic–molecular complex and the diffuse ISM. This pressure has to be balanced by the internal pressure ${P}_{\mathrm{int}}/{k}_{{\rm{B}}}=\rho {\sigma }_{{\rm{v}}}^{2}$ due to turbulence, which, if turned around, requires an H₂ density of the clumps of ${n}_{{{\rm{H}}}_{2}}\approx 1200$ cm⁻³. (3) The volume density required for collisional excitation of CO rotational transitions is ${n}_{{{\rm{H}}}_{2}}\approx 1000$ cm⁻³ (Glover & Clark 2012b). Overall, we conclude that the virial density, excitation density, and pressure equilibrium density for the H₂ gas in the CO-bright clumps are quite similar around ${n}_{{{\rm{H}}}_{2}}\approx 1000$ cm⁻³, and therefore considering these gas structures to be in (quasi-)dynamical equilibrium seems justified.

Our analysis of the CO-bright clumps in NGC 6822 has shown that their macroscopic properties are very similar (with possible offsets less than a factor of two) to CO-bright structures within our Galaxy. For our adopted ${R}_{21}=1$ and ${\alpha }_{\mathrm{CO}}=4.35$ M_⊙ pc⁻² (K km s⁻¹)⁻¹, the clumps in NGC 6822 have $\sim 30 \%$ lower SB and a factor of $\lesssim 2$ higher virial masses or virial ratios for fixed (CO-inferred) luminous masses. There are three easy explanations that can explain the (apparent) small difference to the Galactic observations: (1) The CO excitation is subthermal, and R₂₁ is closer to the standard value (∼0.7) derived for Milky Way clouds or massive disk galaxies. This would directly remove the difference in SB but leave clumps in NGC 6822 to be slightly less bounded than in the Milky Way. (2) The CO-to-H₂ conversion factor is larger (by a factor of ∼2) than the standard value for Milky Way clouds or massive disk galaxies, which would be motivated by the lower SB (due to a lower beam filling factor) and results in identical virial ratios in NGC 6822 and the Milky Way. (3) The more massive shielding layers around the CO-bright clumps in NGC 6822 provide sufficient external pressure to bring the internal turbulent pressure and self-gravity into a dynamical balance. In the previous sections we have seen that the required changes listed here are all consistent with our measurements within the uncertainties, and thus one of the three cases or a combination of them provide a viable pathway to explain our observations.

We can therefore conclude that the structure of the atomic–molecular complexes and the CO-bright clumps in NGC 6822 seems normal in terms of density, pressure, and column density, and that they appear to be marginally gravitationally bound. The main effect of the lower CO abundance in NGC 6822 is to lower the brightness and extent of the CO-bright structures. This explains why the clumps in NGC 6822 and the Milky Way populate the same loci in plots of scaling relations of their macroscopic properties (see Section 4.5). Rubio et al. (2015) have arrived at the same set of conclusions in their analysis of 10 CO-bright clumps in WLM, which has only $\sim 1/8$ solar metallicity. Taking these results together, we conclude that clumps inside molecular clouds appear to be in virial equilibrium after the non-negligible contribution of surface pressure from the surrounding gas is accounted for. We find no dependence on gas-phase metallicity over ∼0.2–1 solar metallicity. The dynamical state of dense clumps—the location where stars form—is thus indistinguishable between clouds in the Milky Way and those in nearby low-metallicity dwarf galaxies.

We have determined the CO-to-H₂ conversion factor, ${\alpha }_{\mathrm{CO}}$, on several scales. On the largest scales, our result mirrors the discussion in Section 5.2: integrating over our dust-inferred molecular gas masses and dividing by the ALMA CO(2–1) luminosity, we find ${\alpha }_{\mathrm{CO}(2-1)}\approx 110$ M_⊙ pc⁻² (K km s⁻¹)⁻¹. Adjusting this to account for our expectation of $\sim 73 \%$ flux recovery lowers this number to $\sim 80$ M_⊙ pc⁻² (K km s⁻¹)⁻¹. For a CO(1–0) conversion factor, this should be modified by the appropriate line ratio; we argue that a value close to thermal ($\sim 1$ in K units) is likely appropriate for a dwarf irregular galaxy like NGC 6822. This large-scale ${\alpha }_{\mathrm{CO}}$ value is $\sim 20\mbox{--}25$ times larger than the Milky Way value of ${\alpha }_{\mathrm{CO}}=4.35$ M_⊙ pc⁻² (K km s⁻¹)⁻¹. Our ${\alpha }_{\mathrm{CO}}$ estimate is a factor of $\sim 4.7$ larger than the calculations by Leroy et al. (2011), who used Spitzer and IRAM 30 m data by Gratier et al. (2010) to derive ${\alpha }_{\mathrm{CO}(2-1)}=17$ M_⊙ pc⁻² (K km s⁻¹)⁻¹ with 0.3 dex uncertainty. These two results agree within $\sim 2\sigma$ of their uncertainties.

Motivated by the dust-inferred ${\alpha }_{\mathrm{CO}}$ values derived for Local Group galaxies by Leroy et al. (2011) and 27 nearby spiral galaxies by Sandstrom et al. (2013), Bolatto et al. (2013) proposed the formula ${\alpha }_{\mathrm{CO}}={\alpha }_{\mathrm{CO},\mathrm{MW}}{f}_{\mathrm{COF}}{f}_{\mathrm{SB}}$, in which ${\alpha }_{\mathrm{CO}}$ may deviate from the Galactic value ${\alpha }_{\mathrm{CO},\mathrm{MW}}$ for two reasons: the factor f_COF accounts for the H₂ mass in the outer complex CO-faint layers, where CO is dissociated; and f_SB accounts for changes in the CO SB due to temperature and velocity dispersion. The former term may scale as ${f}_{\mathrm{COF}}\approx 0.67\exp (+0.4/{Z}^{\prime }{{\rm{\Sigma }}}_{\mathrm{GMC}}^{100})$, as derived by Wolfire et al. (2010). For the cloud complexes in NGC 6822 (${Z}^{\prime }=0.2$ and ${{\rm{\Sigma }}}_{\mathrm{GMC}}^{100}=1.05$ M_⊙ pc⁻²) this results in ${f}_{\mathrm{COF}}\approx 5$ and thus a similar increase in ${\alpha }_{\mathrm{CO}}$ (assuming no change in f_SB given the similarity of the CO-bright clumps in NGC 6822 and the Milky Way). This prediction is $\sim 4\mbox{--}5$ times below our measurement of ${\alpha }_{\mathrm{CO}}$ for complexes in NGC 6822. This deviation does not come as a surprise, as Bolatto et al. (2013) empirically calibrated their formula against the ${\alpha }_{\mathrm{CO}}$ values derived by Leroy et al. (2011) and Sandstrom et al. (2013), and we already noted the difference between our and Leroy et al.'s results above. The underlying reason for this discrepancy remains unclear, but dust maps of higher fidelity seem necessary to resolve these questions.

As Figure 6 has shown, we find different ${\alpha }_{\mathrm{CO}}$ values for different complexes with a substantial difference between the two CO-bright Fields 2 and 4, where ${\alpha }_{\mathrm{CO}}\approx 85$ M_⊙ pc⁻² (K km s⁻¹)⁻¹, and the CO-faint Fields 1 and 3, where ${\alpha }_{\mathrm{CO}}\approx 235\mbox{--}570$ M_⊙ pc⁻² (K km s⁻¹)⁻¹. The difference may be linked to the evolutionary state of the complexes. The two CO-faint complexes (Fields 1 and 3) with high ${\alpha }_{\mathrm{CO}}$ also have prominent H ii regions with fewer signatures of compact embedded star formation at $24\,\mu {\rm{m}}$. This might also lead to more dissociating photons and weaker shielding because the gas has been dispersed by stellar feedback, in which case we might expect a larger component of H₂ without CO. By contrast, the other two complexes (Fields 2 and 4) may be in an earlier state, with embedded star formation and gas more concentrated and better shielded. This could lead to the overall brighter CO emission and the lower conversion factors. While this scenario does make sense "by eye," we might also expect this case to produce CO intensity distributions that differentiate the fields in this way. However, this does not appear to be the case for our four complexes and warrants further investigation with larger samples.

We also constrain the CO-to-H₂ conversion factor via dynamical measurements at small scales of individual dense clumps. If we assume that the dynamical state of the clumps in NGC 6822 and WLM is the same as for those in the Milky Way, then the difference in the apparent ratio of virial mass to luminosity reflects differences in ${\alpha }_{\mathrm{CO}}$ as small as a factor of $\lesssim 2$ despite metallicity variations of $\sim 1/8-1\,{Z}_{\odot }$ when measured for dense clumps on spatial scales of only a few parsecs.

In summary, this highlights the strong dependence of ${\alpha }_{\mathrm{CO}}$ on both metallicity and spatial scale. The CO-to-H₂ ratio can be very low in low-metallicity systems on spatial scales (few tens of parsecs to 1 kpc) of whole molecular clouds to the entire galaxy, while it can approach Galactic values inside small (∼parsec), dense, well-shielded gas clumps. Accounting for the scale dependence of ${\alpha }_{\mathrm{CO}}$ seems to bring previous, apparently differing estimates of the metallicity dependence of ${\alpha }_{\mathrm{CO}}\propto {Z}^{-\gamma }$ together (see also Bolatto et al. 2013; Schruba 2013). Using dust modeling to infer H₂ masses, Lee et al. (2015) derived $\gamma \approx 1\mbox{--}2$ on spatial scales of $\sim 10$ pc in the LMC and SMC, while Leroy et al. (2011) and Sandstrom et al. (2013) derived $\gamma \approx 1.5$ on ∼kiloparsec scales in local galaxies. Scaling the SFR by a depletion time to get H₂ masses, Genzel et al. (2012), Schruba et al. (2012), and Hunt et al. (2015) derived $\gamma \approx 2\mbox{--}3$ for entire galaxies in the local and distant universe. Furthermore, we find that ${\alpha }_{\mathrm{CO}}$ as measured for individual molecular clouds depends on the cloud's evolutionary state driven by particular dynamical, chemical, and feedback timescales (see Figure 6). Here we suggest that these ${\alpha }_{\mathrm{CO}}$ measurements can be brought together when considering the interlinked metallicity and spatial scale dependence of ${\alpha }_{\mathrm{CO}}$, but sensitive observations of CO and dust continuum at high resolution for a set of low-metallicity galaxies are critical for a definite answer.

We can use the derived properties (i.e., size, mass, surface and volume density) of the atomic–molecular complexes and the CO-bright clumps to analyze their "state of equilibrium" and determine whether they share the same properties as clouds in the Milky Way. The basic idea consists of (numerous) CO clumps residing in an atomic–molecular complex that have to be close to pressure and chemical equilibrium so that the entire gas cloud is in a (quasi-)static state. In Section 5.1 we have determined that the parsec-sized, CO-bright clumps have properties suggesting that these structures are in gravitational, excitation, and pressure equilibrium, and that their properties are similar to Galactic clumps. Here we extend this analysis to consider the equilibrium state of the $\sim 100$ times larger atomic–molecular complexes.

The atomic–molecular complexes have a (dust-inferred) typical diameter of D = 110 pc and gas mass of ${M}_{\mathrm{gas}}=1.3\times {10}^{6}$ ${M}_{\odot }$, the average surface density is ${{\rm{\Sigma }}}_{\mathrm{gas}}=105$ M_⊙ pc⁻², and about $30 \%$ of their mass is in atomic form and $70 \%$ in molecular form. These complexes are surrounded by a diffuse atomic medium with average surface density of ${{\rm{\Sigma }}}_{\mathrm{ISM}}=20$ M_⊙ pc⁻², as determined from the 21 cm observations.

In a static picture, the reservoir of H₂ and CO gas has to be in an equilibrium between formation and destruction processes. This requires that H₂ and CO are sufficiently shielded from dissociating radiation. In the Milky Way and Magellanic Clouds, H₂ molecules require an extinction of ${A}_{V}\approx 0.3$ mag and CO molecules require ${A}_{V}\approx 1.5$ mag (we note that these numbers are rough, first-order estimates; they reflect the good agreement among theoretical and observations studies on the magnitude of A_V but may neglect a minor, still-debated metallicity dependence; e.g., Krumholz et al. 2008; Pineda et al. 2008; Wolfire et al. 2010; Glover & Mac Low 2011; Sternberg et al. 2014; Lee et al. 2015; Lee et al. 2017). At solar metallicities, this corresponds to gas columns of ${{\rm{\Sigma }}}_{\mathrm{gas}}\approx 6$ M_⊙ pc⁻² and $\approx 30$ M_⊙ pc⁻², respectively. In NGC 6822, which has $\sim 1/5$ solar metallicity, the corresponding gas columns are expected to be ${{\rm{\Sigma }}}_{\mathrm{gas}}\approx 30$ and $\approx 150$ M_⊙ pc⁻², under the assumption that A_V is linearly proportional to metallicity. The former is satisfied by the atomic component of the atomic–molecular complexes with ${{\rm{\Sigma }}}_{\mathrm{atom}}\approx 0.3\times 105$ M_⊙ pc⁻² plus additional shielding from the diffuse atomic medium, and the latter by the total gas column of ${{\rm{\Sigma }}}_{\mathrm{atom}+\mathrm{mol}}\approx 105+125$ M_⊙ pc⁻² calculated from the atomic and molecular gas of the complex plus the molecular gas from the embedded CO-bright clumps. In regions of strong radiation fields—our ALMA survey specifically targets prominent H ii regions—the required shielding columns will need to be somewhat higher, which our derived numbers allow for. In summary, the atomic–molecular complexes have properties (i.e., column densities) conforming with chemical equilibrium. The dynamical state cannot be evaluated, as we lack information on the gas (turbulent) velocities of the entire complex.

We have estimated the global CO(1–0) luminosity and the H i and H₂ mass of the star-forming complexes hosting $\sim 2/3$ of the star formation activity in NGC 6822. Using these, we are in a position to discuss the relative abundance of gas, molecular gas, and star formation on large scales. NGC 6822 appears typical of dwarf galaxies in two respects: The timescale for the current star formation rate, SFR ≈ 0.015 M_⊙ yr⁻¹, to consume all (atomic and molecular) gas of the entire galaxy is long, ∼9 Gyr. Such a long timescale is typical of dwarf galaxies and the outer disks of spiral galaxies (e.g., Lee et al. 2009; Bigiel et al. 2010; Schruba et al. 2011; Huang et al. 2012; Roychowdhury et al. 2015). This is usually interpreted as reflecting the inability of dwarf galaxies to effectively convert their atomic material into dense, cold, star-forming clouds.

NGC 6822 also displays a small CO luminosity relative to its apparent rate of star formation. With a CO luminosity of ${L}_{\mathrm{CO}}\approx 6\mbox{--}10\times {10}^{4}$ K km s⁻¹ pc², the whole galaxy compares to only the CO luminosity of a single Milky Way high-mass star-forming cloud. In this sense it resembles the SMC (Mizuno et al. 2001), which also has L_CO of order $\sim {10}^{5}$ K km s⁻¹ pc² and an SFR of $\sim 0.05$ M_⊙ yr⁻¹. In its very high ratio of SFR to CO, $\sim 50\mbox{--}80$ times higher than in (massive) disk galaxies, it conforms to a broader population of dwarf galaxies (see Schruba et al. 2012). This low CO luminosity relative to SFR is usually interpreted as a selective destruction of CO molecules, as discussed in the introduction.

In detail, however, our mass budget for NGC 6822 holds a surprise. When focusing on our four star-forming complexes, at face value, the ratio of the recent SFR to the apparent gas reservoir—H₂, H i, or both—appears high. That mean that the apparent consumption time of the star-forming gas is quite short. We compare the integrated H₂ mass of our complexes (as inferred from dust modeling) to their SFR and find that present-day star formation will consume the molecular gas content of the complexes in $\sim 360\,\mathrm{Myr}$. This is much shorter than the typical 1–2 Gyr molecular gas depletion time seen for massive disk galaxies (e.g., Bigiel et al. 2011; Saintonge et al. 2011; Schruba et al. 2011; Leroy et al. 2013). Even including the atomic gas associated with the complexes, this consumption time appears short, with star formation being able to consume all of the complex's atomic and molecular gas (as inferred from dust) in $\sim 510\,\mathrm{Myr}$ (or $\sim 760\,\mathrm{Myr}$ if we add the diffuse atomic gas component that we had removed by our background subtraction). At first glance, these "short" depletion timescales seem to be in good agreement with estimates for other nearby low-mass (${M}_{\star }\approx {10}^{8}\mbox{--}{10}^{9}$ ${M}_{\odot }$), low-metallicity ($Z\approx 0.1-0.5{Z}_{\odot }$) galaxies (Gardan et al. 2007; Gratier et al. 2010; Bolatto et al. 2011; Bothwell et al. 2014; Cormier et al. 2014; Hunt et al. 2015; Jameson et al. 2016), but are in conflict with the very long depletion times ($\sim 60$ Gyr) found by Shi et al. (2014). All these studies (with the exception of Shi et al.) suggest that the molecular gas depletion time in low-mass, low-metallicity dwarf galaxies is a factor of $\sim 2\mbox{--}5$ shorter than that in massive disk galaxies.

Here we want to bring forward a line of thought on why the depletion time in NGC 6822 (and potentially other dwarf galaxies) may be considerably longer than the $\sim 0.5\,\mathrm{Gyr}$ repeatedly stated. Our survey of NGC 6822 has selectively targeted regions of current active star formation, a selection bias that frequently applies to observations of (dwarf) galaxies. However, when considering the time evolution of the gas-star cycle in galaxies, these actively star-forming regions may not be the regions that host most star-forming gas. Especially if the formation timescale of star-forming gas clouds is much longer than the star formation process itself, then a significant amount of the star-forming gas is in "quiescent" clouds that may have been missed by surveys that selectively targeted regions of active star formation. This caveat especially applies to studies of nearby galaxies with large angular extent on the sky.

The biasing in the gas depletion time for small apertures selectively targeting star-forming or gas-rich regions has been studied observationally by Schruba et al. (2010) and theoretically by Kruijssen & Longmore (2014). Here we utilize the Kruijssen & Longmore model to estimate the bias in the depletion time when focusing selectively on star-forming regions as compared to a complete survey of the entire galaxy. In detail, we use their Equation (16), which is

$$\begin{eqnarray}&&\displaystyle \frac{{t}_{\mathrm{dep},\mathrm{star}}}{{t}_{\mathrm{dep},\mathrm{gal}}}=\displaystyle \frac{\beta ({t}_{\mathrm{over}}/{t}_{\mathrm{gas}}){[1+(\beta -1)({t}_{\mathrm{over}}/{t}_{\mathrm{gas}})]}^{-1}+({t}_{\mathrm{star}}/{t}_{\mathrm{tot}}){({l}_{\mathrm{ap}}/\lambda )}^{2}}{1+({t}_{\mathrm{star}}/{t}_{\mathrm{tot}}){({l}_{\mathrm{ap}}/\lambda )}^{2}},\end{eqnarray} \tag{ 2 }$$

and adopt the following parameters: lifetime of the complexes ${t}_{\mathrm{gas}}=35\,\mathrm{Myr}$ (one dynamical timescale at the location of our survey fields; Weldrake et al. 2003), duration of star formation ${t}_{\mathrm{over}}=5\,\mathrm{Myr}$ (age spread of massive stars from HST; O'Dell et al. 1999), visibility timescale of (Hα) star formation tracer ${t}_{\mathrm{star}}\equiv {t}_{{\rm{H}}\alpha }+{t}_{\mathrm{over}}=10\,\mathrm{Myr}$ (with ${t}_{{\rm{H}}\alpha }=5\,\mathrm{Myr}$ from stellar synthesis modeling; Leroy et al. 2012; D. T. Haydon et al. 2017, in preparation), total time range ${t}_{\mathrm{tot}}\equiv {t}_{\mathrm{gas}}+{t}_{\mathrm{star}}-{t}_{\mathrm{over}}$, separation of star-forming regions $\lambda =400$ pc (estimated from the Hα map), fraction of gas decrease during star formation process $\beta =1$, and the aperture size l_ap as an independent variable. We note that these parameters are rough estimates; a detailed derivation and analysis of uncertainties are beyond the scope of this paper and will be presented in forthcoming papers.

Figure 10 quantifies the bias in the molecular gas depletion time as derived by the Kruijssen & Longmore (2014) model. It shows the molecular gas mass (as inferred from the dust) and SFR measurements for the four complexes (gray circles) and their mean average (red circle), as well as the model-predicted scale dependence of the bias (black curve) for the adopted parameters. In detail, the model predicts how M_mol and SFR scale with aperture size, l_ap,

$$\begin{eqnarray}&&{M}_{\mathrm{mol},\mathrm{model}}={{\rm{\Sigma }}}_{\mathrm{mol},\mathrm{gal}}\times \left({l}_{\mathrm{ap}}^{2}+\displaystyle \frac{{t}_{\mathrm{over}}}{{t}_{\mathrm{star}}}{\lambda }^{2}\right),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\mathrm{SFR}}_{\mathrm{model}}=\displaystyle \frac{{M}_{\mathrm{mol},\mathrm{model}}}{{t}_{\mathrm{dep},\mathrm{gal}}}\times {\left(\displaystyle \frac{{t}_{\mathrm{dep},\mathrm{star}}}{{t}_{\mathrm{dep},\mathrm{gal}}}\right)}^{-1}.\end{eqnarray} \tag{ 4 }$$

In Equation (3), the first term in parentheses reflects the "random" background population of clouds and star-forming regions, whereas the second term reflects the contribution of the region that the aperture is focused on, with the ratio ${t}_{\mathrm{over}}/{t}_{\mathrm{star}}$ indicating the probability that the region contains a representative gas reservoir. In Equation (4), the bias of the gas depletion time from Equation (2) is used to convert the molecular gas mass to an SFR. The model is constrained at small aperture size (${l}_{\mathrm{ap}}\approx 100$ pc) by the average M_mol and SFR for the star-forming complexes and at large aperture size (${l}_{\mathrm{ap}}\approx 1.6$ kpc) by the total SFR over the star-forming disk of NGC 6822 (a rectangle of $1.1\times 2.4$ kpc²). These boundary conditions fully constrain the galaxy's molecular gas depletion time and total molecular gas mass, which we estimate as ${t}_{\mathrm{dep},\mathrm{gal}}\approx 2\,\mathrm{Gyr}$ and ${M}_{\mathrm{mol}\mathrm{gal}}\approx 2\times {10}^{7}$ ${M}_{\odot }$, respectively. This implies a molecular gas fraction of $\sim 0.35$ over the star-forming disk or $\sim 0.15$ for all of NGC 6822, values that are in good agreement with estimates for other dwarf galaxies (Bothwell et al. 2014; Hunt et al. 2015).

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If all molecular gas is in massive complexes of $\sim {10}^{6}$ ${M}_{\odot }$ (as estimated for our four targeted complexes), then we expect $\sim 20$ such complexes in NGC 6822. It remains unclear, however, whether this expectation holds. Gratier et al. (2010) identified 15 CO-bright clouds in their IRAM 30 m CO map (covering about half the star-forming disk), but those typically have a lower mass of $\sim {10}^{5}$ ${M}_{\odot }$. Alternatively, (the dust component of) the predicted clouds should be visible in the Spitzer and Herschel infrared maps, but those do not provide a conclusive answer, due to confusion with Galactic foreground emission. On the other hand, our estimate of a long depletion time is in agreement with theoretical predictions that on large (≳1 kpc) scales, star formation and the amount of molecular gas may show a nearly constant ratio for metallicity $Z\gtrsim 0.1\,{Z}_{\odot }$ because star formation and H₂ formation have similar density and shielding requirements (e.g., Krumholz et al. 2011; Glover & Clark 2012a, 2012b).

The presence or absence of a large CO-faint H₂ component pivots on joint analysis of the dust and gas data. This process has a number of subtleties and uncertainties, which are discussed in detail in, e.g., Leroy et al. (2007, 2011) and Sandstrom et al. (2013). This analysis is not the focus of this paper; given the apparent discrepancy between our results and those of other recent analyses, we defer a detailed commentary until we are able to achieve a better determination of the dust content and analyze the whole set of Local Group galaxies in a self-consistent way. Furthermore, a large-scale survey of neutral or ionized carbon line emission could verify the existence of a large CO-faint H₂ component.

Another explanation leading to a short depletion time could be invoked in time rather than space: if NGC 6822 recently experienced a large burst of star formation, then we might observe this burst in star formation tracers, but the reservoir for the burst might have been dispersed by feedback. This scenario also does not appear viable. The SFR in NGC 6822 has been roughly constant over the past ∼400 Myr (with variations of a factor $\lesssim 2$ over durations of a few tens of megayears; Efremova et al. 2011), and the galaxy displays a typical specific SFR ($\mathrm{SFR}/{M}_{\star }$). There is no evidence that NGC 6822 has recently undergone a galaxy-wide starburst.