Oversized Gas Clumps in an Extremely Metal-poor Molecular Cloud Revealed by ALMA's Parsec-scale Maps

To probe the internal structure of the star-forming region in DDO 70, we resolved the CO J = 2–1 emission using ALMA with a field of view of 264 (177 pc), as shown in Figure 1. The ALMA observations (PID: 2016.1.00359.S, PI: Y. Shi) were composed of two-array configurations of C40-4 and C40-7, which have an angular resolution of 011 and 039, respectively. The corresponding integration times are 1.1 hr and 0.6 hr, respectively. The observations were performed on 2016 November 11 and 2017 August 3, respectively. We calibrated the data individually with CASA, following the standard pipeline, then combined all visibility data together for cleaning. We selected Briggs weighting with a weighting of 1.5, to optimize the sensitivity and side lobe of the dirty beam response. A final datacube with a beam size of 021 × 019(1.47×1.27 pc) was produced. The 1σ sensitivity is about 0.9 mJy beam⁻¹ at a velocity resolution of 0.4 km s⁻¹. We list the calibrators in Table 1. The uncertainty of the absolute flux calibration is about 10%, according to a comparison with the monitored fluxes of the ALMA calibrators.

To search for CO clumps, we first identified pixels that have a signal-to-noise ratio (S/N) > 3.5 in two adjacent channels of ALMA data. The search was done over the velocity range of the IRAM 30 m CO spectrum (280–290 km s⁻¹). For regions with more than 10 detected pixels (>15% beam in area), we extracted their spectra and counted those with an integrated S/N > 4 as detections. A single Gaussian profile was used to fit the spectra. In total we identified five clumps, as shown in Figure 2 and listed in Table 2. To measure the size of each CO clump, we used CASA imfit() to fit a 2D Gaussian profile to the velocity-integrated flux (moment-zero) map of the clump within a circular region. As shown in Figure 2, each circle is defined to be slightly larger than the 1σ noise contour (2.3 mJy beam⁻¹•km s⁻¹) to include some background emission, but not so large that the enclosed pixels are dominated by noises. Note that the circle is not the size of the clump but encloses pixels over which the imfit() performed the fitting. We tested that, if the size of the circular region increases or decreases by 20%, the changes in the derived clump sizes are negligible. The imfit() also returns the associated uncertainties. The derived size dispersions (σ_ma, σ_mb) along major and minor axes were used to estimate the radius of the core: R = D×tan($\sqrt{{\sigma }_{\mathrm{ma}}{\sigma }_{\mathrm{mb}}}$)$\tfrac{3.4}{{\pi }^{0.5}}$ (Solomon et al. 1987), where D is the distance of DDO 70. The defined radius represents the square root of the area of a clump. The virial mass of each core was calculated using ${M}_{\mathrm{vir}}=1040\,R{\sigma }_{v}^{2}$ (Solomon et al. 1987), where σ_v is the line width dispersion from the spectral fitting.

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The multi-wavelength ancillary data of DDO 70 were available in the literature, as compiled in our previous work (Shi et al. 2016). The infrared data at 70, 160, 250, and 350 μm were retrieved from the archive of the Herschel Space Observatory and were reduced with unimap (Traficante et al. 2011). We refer readers to our previous work Shi et al. (2014, 2016) for details. The reduced Spitzer images at 3.6, 4.5, 5.8 and 24 μm are from the Local Volume Legacy program (Dale et al. 2009). The H i image is from the program of Local Irregulars That Trace Luminosity Extremes (Hunter et al. 2012) and the far-UV image is available in the Galaxy Evolution Explorer data archive (http://galex.stsci.edu/GalexView/).

In the Milky Way, ultraviolet photons with energies larger than 11.1 eV can photodissociate CO molecules such that CO emission only exists in dust-shielded regions with a visual extinction higher than 1.0-2.0 mag (Bergin & Tafalla 2007; Glover et al. 2010). Studies of metal-poor dwarf galaxies including the Large Magellanic (LMC) Cloud and Small Magellanic Cloud (SMC) confirm similar shielding conditions for CO emission. And the relationship between the CO intensity (I_CO) and the visual extinction (A_V) shows little dependence on the gas-phase metallicity (Leroy et al. 2009; Lee et al. 2015, 2018). Using the I_CO-A_V relationship of the SMC (Lee et al. 2018), our CO clumps are inferred to have A_V between 1 and 2.5 mag, supporting the above required shielding for the presence of CO emission in DDO70.

To quantitatively determine the extinction levels above which dust clumps have similar sizes to CO clumps, we used the dust and CO maps of the SMC, given that the galaxy has high-S/N maps, while hosting the metallicity as close as possible to our target galaxy. To produce the dust map of the SMC, the Herschel images were retrieved from the Herschel Inventory of the Agents of Galaxy Evolution (HERITAGE; Meixner et al. 2013) at 100, 160, 250, and 350 μm with angular resolutions of 7.7, 12, 18, and 25 arcsec, respectively. Following Lee et al. (2015), we used the single modified blackbody (MBB) model with a fixed dust emissivity of 1.5 to fit the Herschel spectral energy distribution (SED) to produce the dust temperature maps at 350 μm resolutions. We then interpolated this map to the 160 μm resolution and produced the extinction map using ${\tau }_{160\mu m}={I}_{160\mu {\rm{m}}}/{B}_{\nu }({T}_{\mathrm{dust}},160\mu {\rm{m}})$ and A_V = 2200τ_160μm (Lee et al. 2015). The CO J = 2–1 data with an angular resolution of 28 arcsec were retrieved from the archive of the APEX telescope and reduced in a standard way. The CO clump sizes were measured with the same approach used for the CO data in DDO 70. Sizes of dust clumps were measured above two A_V values of 1.0 and 1.5, respectively: we first subtracted constant A_V (1.0 or 1.5) from the extinction map of the SMC and convolved to the CO resolution, then measured the sizes with the same approach used for the CO data in DDO 70. Using spatially resolved clumps that are defined to have sizes larger than 1.2 times the FWHM, we calculated the ratio of the major-axis FWHM of CO and the FWHM of the dust emission. In total, we had 14 clumps with A_V > 1.5 and 20 clumps with A_V > 1.0, respectively. As shown in Figure 4, the median ratio with a standard deviation is 1.29 ± 0.24 for CO/dust(${A}_{{\rm{V}}}\gt 1.5$) and 1.05 ± 0.26 for CO/dust(A_V > 1.0). As a result, the dust clumps with A_V > 1.0 or τ_160μm > 1/2200 have sizes similar to those of CO clumps. Since τ_160μm is a direct measurement from the MBB fitting and thus suffers less systematic uncertainties compared to A_V, we will adopt the limiting τ_160μm = 1/2200 in the following analysis. Although the SMC maps have poorer spatial resolutions than the maps of our DDO 70, the relationship between I_CO and extinction has little dependence on the spatial resolution down to subparsecs, as done for the Milky Way (Lee et al. 2015, 2018), implying that the above result of the SMC likely holds at parsec scales for our maps. While the I_CO-A_V relationship shows little dependence on the metallicity from the Milky Way to the SMC at 20%Z_⊙, we assume that such an independence can extend to DDO 70 at 7%Z_⊙.

The required extinction for CO to exist in the Milky Way (${A}_{{\rm{V}}}=1.0$ mag) corresponds to a gas-mass surface density of 14 M_⊙ pc⁻², assuming ${N}_{{\rm{H}}}/{A}_{{\rm{v}}}=1.87\times {10}^{21}$ cm⁻² mag⁻¹ (Draine 2003). At lower metallicities, the required extinction corresponds to a higher gas surface density given the corresponding larger GDR, making CO suitable to trace the gas of a high surface density at low metallicity (Rubio et al. 2015; Schruba et al. 2017). Arguably, one of the most reliable methods to measure the GDR at extremely low metallicity is to use the ratio of the atomic gas and the dust mass in the diffuse region where the total cold gas is dominated by the atomic gas instead of the molecular gas (Israel 1997; Dame et al. 2001; Bolatto et al. 2011; Shi et al. 2014; Jameson et al. 2016).

Following the methods of our previous work (Shi et al. 2014), we first carried out the photometric measurements of a diffuse region as well as the whole disk of DDO 70 and the region within the ALMA aperture. These regions are illustrated in Figure 5 for far-UV, H i gas, and infrared bands at 70, 160, and 250 μm, respectively. The diffuse region was identified as extended emission at all Herschel wavelengths, not overlaid with star formation regions, and was used to infer the GDR of the galaxy. In these regions the total cold gas is dominated by atomic gas, so the ratio of atomic gas to dust mass can be treated as the GDR (Leroy et al. 2011; Sandstrom et al. 2013; Shi et al. 2014). The results of Herschel and Spitzer infrared photometry are presented in Table 3. Similar to what has been done for other extremely metal-poor galaxies (Fisher et al. 2014; Shi et al. 2014), we fitted the full infrared SEDs with the DL07 dust model (Draine & Li 2007) to estimate the dust masses, as shown in Figure 6 and listed in Table 4. The GDR of the galaxy is thus derived to be ${6078}_{-1600}^{+1000}$; we refer to this as the diffuse-region GDR. If adopting SMC or LMC dust grains, the derived ratio increases by about 10%–20%. This ratio roughly corresponds to the trend of the GDR $\propto \,{Z}^{-\alpha }$ with α = 1.6 given the Galactic GDR of 100. An α larger than unity is consistent with the fact that the dust-to-metal ratio decreases with decreasing metallicity, as measured in absorption-line systems (De Cia et al. 2013) as well as the global GDR of dwarf galaxies where the H i gas dominates the total cold gas at global galaxy scales (Rémy-Ruyer et al. 2014).

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Table 4.  Fitting Results of the Infrared SEDs

Region	Umin	Umax(fixed)	γ	χ2/dof	Mdust	MH i/Mdust
					(M⊙)
DDO70/disk	3.0	106	0.00	1.95	(${7.2}_{-1.5}^{+2.4}$) × 103	(${2.2}_{-0.7}^{+0.4})\times {10}^{3}$
DDO70/diff-1	7.0	106	0.00	3.06	(${2.1}_{-0.4}^{+0.6}$) × 102	(${6.1}_{-0.7}^{+0.4}$) × 103
DDO70/ALMA	5.0	106	0.00	1.08	(${5.3}_{-1.0}^{+1.3}$) × 102	($1{.}_{-0.7}^{+0.4}$) × 103

Note. In addition to the flux uncertainties in Table 3, absolute calibration errors (20%) are included when performing the fits.

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From the above measurements, we can infer other physical properties of the region within the ALMA FOV. It contains a dust mass of 530 M_⊙, a total gas mass of 3.2 × 10⁶ M_⊙ given the above diffuse-region GDR, and a molecular gas mass of 2.7 × 10⁶ M_⊙ after subtracting an H i mass of 0.53 × 10⁶ M_⊙. It has a stellar mass of 1.7 × 10⁶ M_⊙ and a star formation rate of 1.6 × 10⁻⁴ M_⊙ yr⁻¹ from the 3.6 μm and 24μm+far-UV photometry, respectively, as detailed in Shi et al. (2014).

As argued above, the size of the CO clump is set by the spatial extent above a threshold extinction (τ_160μm = 1/2200) for CO to survive. This can be converted to the required gas-mass surface density with τ_λ = κ_λΣ_dust and the corresponding GDR of DDO 70, where κ_λ is the mass absorption coefficient of dust and Σ_dust is the dust-mass surface density. We derived the required shielding gas density and its uncertainty with the following steps:

• (1)  
  The threshold τ_160μm above which the dust clump size represents the CO clump size: as discussed above, this limiting τ_160μm is 1/2200, and above this extinction the size of a dust clump is similar to the CO size within 26%. We thus adopted 26% as the error of the limiting τ_160μm.
• (2)  
  The diffuse-region GDR of DDO 70: the diffuse-region GDR of DDO 70 is derived to be ${6078}_{-1600}^{+1000}$, where the error reflects the photon noise plus 30% systematic flux uncertainties. An additional 15% uncertainty is included if adopting different dust models (SMC or LMC), as stated above. The GDR across a galaxy is roughly constant if removing the metallicity gradient, with variation up to 50% based on spatially resolved studies (Sandstrom et al. 2013; Draine et al. 2014; Shi et al. 2014). By adding the above three errors quadratically, we have a final uncertainty of 56%. Note that our derived GDR is near the lower bound at similar metallicities in the study of Rémy-Ruyer et al. (2014), if assuming the CO conversion factor increases with decreasing metallicity, implying an even larger shielding gas surface density.
• (3)  
  The difference in the MBB fitting versus DL07 dust modeling: the extinction map of the SMC used to derive the above limiting τ_160μm = 1/2200 is based on the MBB fitting to the Herschel SED. The GDR of DDO 70 is, however, derived from the fitting to the Spitzer+Herschel SED using the DL07 dust model. This could cause some systematic offset. As a result, we added Spitzer photometry to the SED of the SMC and carried out DL07 dust modeling. By adopting κ_160μm = 13.1 cm² g⁻¹ (Li & Draine 2001; Weingartner & Draine 2001), we obtained the DL08/MBB dust ratio of 1.89 ± 0.37. The above GDR of DDO 70 is thus corrected to be 11487 with a 1σ error of 59%.
• (4)  
  The drop in the GDR from the diffuse region to the dense region: the above diffuse-region GDR is derived from the diffuse region. Studies suggest a decrease in the GDR by a factor of 2–3 from the diffuse to the dense region in the Milky Way (Jenkins 2009; Planck Collaboration et al. 2011), SMC, and LMC (Bot et al. 2004; Roman-Duval et al. 2014). It seems that such a decrease is not a function of the galaxy metallicity. We thus adopted a factor of 2.5 ± 0.5 to correct the above GDR to be 4594 with a 1σ error of 62%. We are aware of the work by Roman-Duval et al. (2017) that claims a factor of 7 drop in the GDR of the SMC from the diffuse to the dense region. However, their diffuse region has a very low gas density mainly located on the outskirts of the SMC, resulting in a very high GDR of 1.5 × 10⁴ that is a factor of 10 larger than that of other works (Bouchet et al. 1985; Gordon et al. 2009; Leroy et al. 2011; Roman-Duval et al. 2014). Such a region is different from our diffuse region; which is still within the galaxy disk; also, our diffuse region has Σ_{H i} = 11.6 M_⊙ pc⁻² compared to that of the ALMA region, ~21 M_⊙ pc⁻². We further used their result to show that the adopted drop with a factor of 2.5 ± 0.5 is approximate for our study. In DDO 70, our defined diffuse region has a dust-mass surface density of 1.9 × 10⁻³ M_⊙ pc⁻², which is a factor of 10 lower than that of the ALMA region. Their Equations (13) and 14 give the relationships between dust-mass surface densities and total cold gas-mass surface densities for the LMC and SMC, respectively. These two equations indicate that the GDR drops by a factor of 2.1–3.2 if the dust-mass surface density increases by a factor of 10 over their observed dynamic ranges.

By adopting the above final GDR (4594 ± 2848), τ_160μm = 1/2200 and ${\kappa }_{160\mu {\rm{m}}}=13.1$ cm² g⁻¹, we derived the gas-mass surface densities of CO clumps in DDO 70 to be 756 ± 468 M_⊙ pc⁻².

In order to evaluate whether gas clumps at low metallicity show some systematic differences from those at solar metallicity, we compared clumps in DDO 70 to those in the Milky Way. We measured the clump sizes in the Milky Way using maps of gas-mass surface densities of four massive star-forming regions including Cygnus X (Cao et al. 2019), NGC 6344 (Russeil et al. 2013), RCW 79 (Liu et al. 2017), and NGC 7538 (Fallscheer et al. 2013) at distances of 1.4, 1.75, 4.3, and 2.7 kpc, respectively. Table 5 compares some global properties of these regions to our targeted region in DDO 70. The total cold gas mass is derived from the Herschel dust emission as shown below, and the star formation rate (SFR) is estimated from the WISE 22 μm by assuming f_22μm = f_24μm (Leroy et al. 2008). As listed in the table, these regions have global gas-mass surface densities similar to that of DDO 70. But their global SFR surface densities are significantly larger that that in DDO 70, consistent with our previous study that the SFR efficiency is eliminated at extremely low metallicities (Shi et al. 2014).

The gas maps in the Milky Way are based on the dust maps through the MBB fitting to the Herschel SED with β = 2, ${\kappa }_{300\mu {\rm{m}}}=10$ cm² g⁻¹, and GDR=100 (Beckwith et al. 1990). We further corrected these maps with two factors in order to have fair comparisons with DDO 70. The first factor is about the dust model. As shown in the above section, the dust model for DDO 70 and SMC is the silicate-graphite-PAHs interstellar one (Li & Draine 2001; Weingartner & Draine 2001), which gives ${\kappa }_{300\mu {\rm{m}}}$ of 4.81 cm² g⁻¹. As a result, we increased the original densities by a factor of 2.1. Another factor is the drop in the GDR from the diffuse region to the dense region (as also discussed in the above section), which makes the gas densities decrease by a factor of 2.5. We therefore corrected the map by multiplying with a final factor of 0.83. To remove the effects of different spatial resolutions and pixel sizes on the clump size measurements, we further rebinned these maps to the same physical pixel sizes as DDO 70's CO map and convolved with Gaussian functions to the same physical spatial resolutions as DDO 70's.

Similar to what has been done for the measurements of dust clump sizes in SMC, we first subtracted a series of given surface densities from the whole maps of the above regions, and only used pixels with positive values. We denoted these surface densities as ${{\rm{\Sigma }}}_{\mathrm{gas}}^{\mathrm{limit}}$, which represent the contour levels above which clumps are defined. We then used the same method as for DDO 70 to identify clumps and measured the deconvolved clump radii that were obtained by quadratically subtracting the beam size from the measured one. In the DDO 70's CO map, the 1σ noise is about 10% of the peak intensity of its whole map. To remove the effect of the noise in the derived clump sizes, when defining a circle for fitting a clump in the Milky Way, we make sure that the size of the circle is larger than the DDO 70's percentage noise level that is 10% of the peak intensity of the whole map. An example is shown in Figure 7 for four Milky Way's regions with ${{\rm{\Sigma }}}_{\mathrm{gas}}^{\ \mathrm{limit}}=700$ M_⊙ pc⁻², and the corresponding clump sizes are listed in Table 6. As shown in the figure, some clumps are below the DDO 70's percentage noise level, indicating that they would not have been detected in DDO 70. Such non-detection implies that the Milky Way should have on average smaller clump sizes. Since we have five detected clumps in DDO 70, we compare them to the five largest clumps in each region of the Milky Way, including those below the DDO 70's percentage noise level. If the derived size is smaller than the Herschel resolution of the map, we used it as the upper limit.

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In Figure 8, the sizes of our CO clumps in DDO 70 were compared to those in the Milky Way at different ${{\rm{\Sigma }}}_{\mathrm{gas}}^{\mathrm{limit}}$. Since we only detected five clumps in DDO 70, we thus only used the five largest ones in each Milky Way region for comparison. Note that ${{\rm{\Sigma }}}_{\mathrm{gas}}^{\mathrm{limit}}$ is not the average gas density of a clump within its size, but rather the contour level above which the region is defined. In the figure, we also overlay a modeled trend for a clump with a mass of 4000 M_⊙, a radius of 2.0 pc, and a density profile of ∝R^−1.8. This density profile is the mean of the star-forming clumps found in the Milky Way (Beuther et al. 2002; Mueller et al. 2002).

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As shown in the figure, for the same ${{\rm{\Sigma }}}_{\mathrm{gas}}^{\mathrm{limit}}$, the CO clumps in DDO70 show much larger sizes than those in the Milky Way. The mean radius of the former is 2.0 pc, while the latter has a mean of ∼0.5 pc, including upper limits. All clumps in DDO 70 are larger than 1.5 pc, while all clumps in the Milky Way at the same ${{\rm{\Sigma }}}_{\mathrm{gas}}^{\mathrm{limit}}$ are below 1.5 pc. Even at the gas density of 288 M_⊙ pc⁻² (1σ lower bound), DDO 70 has on average two times larger clump sizes than all four star-forming regions in the Milky Way. In the Herschel Infrared GALactic plane survey, a sample of ∼1.5 × 10⁴ dense clumps has been identified and all their radii are smaller than 1.3 pc (Veneziani et al. 2017). This further excludes the statistical outliers in the Milky Way as the cause of the large clumps in DDO 70. In principle, similar analyses can be carried out for other dwarf galaxies such as WLM at 13%Z_⊙ (Elmegreen et al. 2013; Rubio et al. 2015) and NGC 6822 at 20%Z_⊙ (Schruba et al. 2017). But their relatively smaller GDRs compared to DDO 70 will make the results inconclusive due to the large error bars of the final derived gas densities as shown in the Figure 8.

The existence of large CO clumps in DDO 70 is consistent with theoretical expectations of suppressed gas fragmentation at extremely low metallicities. The high gas temperature results in a high sound speed, low Mach number, and thus weak turbulence (Glover & Clark 2012). Therefore, large clumps cannot further fragment into small ones (Omukai et al. 2005). High gas temperature may also cause top-heavy stellar initial mass functions, as seen both in the metal-poor LMC and high-z starburst galaxies (Schneider et al. 2018; Zhang et al. 2018). The difficulty in gas fragmentation at extremely low metallicity suggests a small number of dense clumps in which stars can form. This offers a physical origin for inefficient star formation at low metallicity (Shi et al. 2014; Filho et al. 2016; Shi et al. 2018), implying the suppression of gas fragmentation and subsequent collapse in the early universe. Unfortunately, our result is not statistically important, given that our observation is only for one cloud. It is difficult to justify whether it is typical for all metal-poor clouds with the current data set.