A Comparison of Young Star Properties with Local Galactic Environment for LEGUS/LITTLE THINGS Dwarf Irregular Galaxies

There are five dIrr galaxies in common between the Hubble Space Telescope (HST) Legacy Extragalactic UV Survey²³ (LEGUS; Calzetti et al. 2015) and LITTLE THINGS²⁴ (Local Irregulars That Trace Luminosity Extremes, The H i Nearby Galaxy Survey; Hunter et al. 2012). LEGUS is an HST Cycle 21 Treasury survey aimed at exploring star formation from scales of individual stars to kiloparsec-size structures with multiband imaging of 50 galaxies within 16 Mpc. The galaxies span the range of star-forming disk galaxies, including dIrrs. The LITTLE THINGS survey is a multiwavelength survey from the far-ultraviolet (FUV) to 21 cm H i emission of 37 dIrr galaxies and 4 BCDs. LITTLE THINGS is aimed at understanding what drives star formation in tiny systems. The LITTLE THINGS galaxies were chosen to be nearby (≤10.3 Mpc), contain gas so they could form stars, and cover a large range in dwarf galactic properties. The galaxies in common between these two surveys—DDO 50, DDO 53, DDO 63, NGC 3738, and Haro 29—are the focus of this study. Some basic properties of the galaxies are given in Table 1. Haro 29 is classified as a BCD, and NGC 3738 has similar characteristics; both are more extreme in their star-forming properties compared to the other three systems, and NGC 3738 is more extreme than Haro 29.

Table 1.  The Galaxy Sample

		D		MV	RDc	log ${\mathrm{SFR}}_{D}^{{\rm{H}}\alpha }$ d	log ${\mathrm{SFR}}_{D}^{\mathrm{FUV}}$ d
Galaxy	Other Namesa	(Mpc)	Referencesb	(mag)	(kpc)	(M⊙ yr−1 kpc−2)	(M⊙ yr−1 kpc−2)	$E{(B-V)}_{f}$ e
DDO 50	UGC 4305, Holmberg II	3.05	1	−16.4	0.99 ± 0.05	−1.67 ± 0.01	−1.55 ± 0.01	0.028
DDO 53	UGC 4459	3.66	2	−13.9	0.73 ± 0.06	−2.42 ± 0.01	−2.41 ± 0.01	0.034
DDO 63	UGC 5139, Holmberg I	3.98	2	−14.8	0.69 ± 0.01	−2.32 ± 0.01	−1.95 ± 0.00	0.045
NGC 3738	UGC 6565	4.90	3	−17.1	0.78 ± 0.01	−1.66 ± 0.01	−1.53 ± 0.01	0.009
Haro 29	UGCA 281	5.90	4	−14.7	0.30 ± 0.01	−0.77 ± 0.01	−1.07 ± 0.01	0.013

Notes.

^aSelected alternate identifications obtained from NED. ^bReference for the distance to the galaxy. ^cR_D is the disk scale length measured from V-band images. From Hunter & Elmegreen (2006) revised to the distance adopted here. ^d ${\mathrm{SFR}}_{D}^{{\rm{H}}\alpha }$ is the star formation rate, measured from Hα, normalized to the area $\pi {R}_{D}^{2}$, where R_D is the disk scale length (Hunter & Elmegreen 2004). ${\mathrm{SFR}}_{D}^{\mathrm{FUV}}$ is the star formation rate determined from GALEX FUV fluxes (Hunter et al. 2010, with an update of the GALEX FUV photometry to the GR4/GR5 pipeline reduction). ^eForeground Milky Way extinction from Schlafly & Finkbeiner (2011).

References. (1) Hoessel et al. 1998; (2) Jacobs et al. 2009; (3) Karachentsev et al. 2003; (4) Schulte-Ladbeck et al. 2001.

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Table 1 also lists the distances adopted for this study and the references from which they came. These distances are used in order to be consistent with the rest of the LEGUS studies (see Calzetti et al. 2015). We note, however, that recent photometry of stars in the LEGUS galaxies has also yielded distance measurements from the apparent brightness of the tip of the red giant branch (Sabbi et al. 2018). A significant difference exists between the new LEGUS distances and the referenced distances for NGC 3738 (5.3 ± 0.3 Mpc versus 4.9 Mpc) and Haro 29 (3.4 ± 0.3 Mpc versus 5.9 Mpc). Tully et al. (2013) also give a distance of 5.3 Mpc for NGC 3738, while for Haro 29 they give a distance of 5.7 Mpc, which is close to the distance we adopt here. Furthermore, Jacobs et al. (2009) give a distance of 3.42 Mpc for DDO 50, compared to the 3.05 Mpc that we adopt from Hoessel et al. (1998). If these distances were used here instead of those given in Table 1, the masses and brightnesses of objects in NGC 3738 would be 1.2× higher, in Haro 29 they would be 0.3× lower, and in DDO 50 they would be 2.0× higher. However, the relative comparison of objects would stay the same.

The sample galaxies were observed with HST's WFC3 imager with filters F275W, F336W, and F438W and the ACS imager with filter F814W. In addition, DDO 50, DDO 53, and DDO 63 were observed with ACS with filter F555W, and NGC 3738 and Haro 29 were observed with ACS with filter F606W. The LEGUS team developed an exhaustive procedure for identifying and checking resolved compact stellar clusters on the images, and details of the catalog preparation are given by Calzetti et al. (2015) and Adamo et al. (2017). The first step is an automatic identification using the algorithm SExtractor (Bertin & Arnouts 1996). The second step involves the imposition of science-driven criteria aimed at reducing false detections and a visual inspection of selected clusters. This step imposes an absolute magnitude limit, and therefore the compact cluster sample misses low-mass objects, especially at older ages. Cluster catalogs for the LEGUS dwarf galaxies are presented by D. O. Cook et al. (2018a, in preparation).

Photometry of the clusters was performed in all available passbands. The clusters were characterized by their concentration index (CI), the integrated light within the central 1 pixel relative to that within a 3 pixel radius (pixel scale is 00396). Aperture corrections, as a function of filter, were made to the cluster photometry using two different methods: (1) taking an average of measurements of isolated clusters over an image and (2) as a function of the CI of the cluster. Here we used both catalogs in the beginning, but we found that it made little difference to the results and subsequently adopted the CI-based aperture corrections. Differences resulting from the two types of aperture corrections are discussed by D. O. Cook et al. (2018a, in preparation). The photometry was corrected for Galactic extinction using Schlafly & Finkbeiner (2011) with the $E(B-V)$ listed in Table 1. Spectral energy distribution (SED) fits were performed for those clusters with photometry in at least four filters in order to determine the age, mass, and reddening of the cluster within the host galaxy. The fit for one cluster from each galaxy is shown as an example in Figure 1. Several internal reddening curves were used, and here we adopted the catalogs in which the photometry was fit for internal extinction using the curve of Calzetti et al. (2000). The SED fitting used two methods: (1) the Yggdrasil single stellar population models (Zackrisson et al. 2011), and (2) the stochastically sampled cluster evolutionary models of Krumholz et al. (2015). A Kroupa (2001) stellar initial mass function (IMF) from 0.1 to 120 M_⊙ was assumed. The spread between stochastically based and deterministic derived cluster properties are within the age and mass uncertainties (D. O. Cook et al. 2018a, in preparation), but the differences are particularly noticeable for clusters with masses below 1000 M_⊙ (Krumholz et al. 2015). More details on the production of the cluster catalogs are given by Adamo et al. (2017).

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In using these catalogs, we eliminated clusters with masses less than 1000 M_⊙ in order to ensure completeness, those observed in fewer than four filters (class 0), and those having a classification indicating that it is likely a foreground or background source, single star, or artifact (class 4). We included cluster classes 1, 2, and 3, where classes 1 and 2 are compact clusters and class 3 is more likely compact stellar associations (Grasha et al. 2015, 2017; Adamo et al. 2017). We also imposed an age cutoff. We carried age cutoffs of 10, 50, and 100 Myr through the analysis, but differences were small, so we present the results for 100 Myr below, except in the first comparison of cluster properties against environmental properties, where we will also show the result for 10 Myr. An age of 100 Myr minimizes losses due to dissolution of clusters (Lamers 2009; Baumgardt et al. 2013; but see Chandar et al. 2017). without decimating the statistics of what are very small cluster samples.

The clusters found automatically were visually inspected in each galaxy down to a cluster absolute magnitude M_F555W of −6, or for NGC 3738 and Haro 29 an M_F606W of −6. We take the peak of the luminosity function of the clusters in a given galaxy as the 90% cluster completeness limit. In all but one LEGUS galaxy, the peak of the luminosity function is fainter than the limit for visual inspection of the clusters, so a cluster absolute magnitude limit of −6 is a conservative indication of completeness. In Figure 2 we show the luminosity functions for the clusters in our galaxies, and in Figure 3 we plot age versus mass for the clusters in our five galaxies before applying the mass and age cuts that we use in the analysis. The cluster absolute magnitude limit of −6 is translated here into age and mass and shown as a slanting dashed line from young, low-mass clusters up to old, high-mass clusters. We see that our −6 absolute magnitude limit shows potential incompleteness of clusters at the low-mass, older-age corner of our selection box represented by our cutoffs in mass and age. Thus, in the analysis that follows, one should keep in mind that the clusters with masses <2000 M_⊙ and ages >35 Myr may be somewhat more incomplete in this galaxy sample.

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The numbers of clusters are given in Table 2, including the number of clusters before the cutoff for mass is applied and the number of clusters with ages ≤10 Myr. There are relatively few clusters in DDO 50, DDO 53, and DDO 63 and even fewer with very young ages. In fact, DDO 63 has no clusters with masses ≥1000 M_⊙, although it has 12 clusters with smaller masses. DDO 63 does contain O stars.

We also used LEGUS catalogs of candidate O stars in the dwarf galaxies (J. C. Lee et al. 2018, in preparation). These stars were selected to have magnitudes in NUV, U, B, and V passbands; have been flagged in the original stellar catalogs as having a point-source profile; have an accurate F275W magnitude brighter than 25.5 (corresponding to a 3σ detection); and have a reddening-free Q value greater than 1.6 with an uncertainty less than 0.075. Q is defined by $Q\,=({M}_{F275W}-{M}_{U})\,-K({M}_{U}-{M}_{B})$, where K is a constant that is computed using $E(\mathrm{NUV}-U)/E(U-B)$ with a Milky Way dust type (R_V = 3.1). Such a value of Q selects for O stars, in particular stars with masses ≥17 M_⊙. Lower-mass stars, having redder colors, have Q values lower than this cutoff. However, O stars within H ii regions could be missed owing to higher differential extinction. Details on the LEGUS stellar photometry can be found in Sabbi et al. (2018).

The magnitude cutoff of 25.5 mag in F275W is near the magnitude at which incompleteness starts to become severe in these nearby galaxies. However, in practice the faintest F275W magnitudes in the catalogs are significantly brighter than this: 23.5, 22.6, 23.2, 22.7, and 22.5 in DDO 50, DDO 53, DDO 63, NGC 3738, and Haro 29, respectively. Thus, the populations of stars we are working with are at least 2 mag brighter than the typical limiting magnitude of 25.5 in F275W. Hence, we are not likely to be significantly affected by incompleteness issues that might also bias the sample toward more massive stars in more distant galaxies.

The photometry is only corrected for foreground extinction according to Schlafly & Finkbeiner (2011). In our analysis where we use the F275W magnitudes of the stars, we apply an additional correction for internal extinction using an $E(B-V)=0.05$ mag with the attenuation curve of Calzetti et al. (2000). Actual extinctions are not known for our sample of galaxies, and so 0.05 mag is used as a typical extinction for stars not buried in H ii regions. This value is half of the average E(B − V) derived from H ii region Balmer decrements for typical dwarfs (Hunter & Elmegreen 2006), but E(B − V) could be larger in some dwarfs (Cignoni et al. 2018). The numbers of candidate O stars are given in Table 2.

When we discuss the properties of star clusters and O stars below, one issue will be our ability to distinguish compact clusters from stars. Our galaxy sample is relatively nearby, and dIrr galaxies have lower stellar densities than spirals, but we have approached this distinction carefully and systematically for the LEGUS sample as a whole. The process is described in detail by Adamo et al. (2017), but the key step in distinguishing clusters from stars is summarized here. The CI is determined for a "training sample" of objects that are clearly stars and those that are clearly clusters, and a histogram of the CI is plotted. There is a clear gap between the CI of stars and the CI of compact clusters, and this is used to determine the CI cut for clusters and stars. Figure 4 shows a plot of the CI for all sources extracted from our sample of galaxies, and the red vertical line indicates the CI value used to distinguish compact clusters from stars in each galaxy. One can see that even in the more distant galaxies in our sample (NGC 3738 and Haro 29) there is a fairly clear drop to higher CI index. One can also see extended tails to higher CI values in each galaxy because the clusters have a broader distribution of CI values than stars.

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Not all star-forming units are clusters or compact associations, and there are larger groups of O stars in all five galaxies. Guided by the distribution of O stars and emission in the F275W images, we have, by eye, outlined apparent OB associations. These are objects that appear as obvious density enhancements in the number of O stars per area. The size of an OB association is taken to be the radius of the circle that encompasses the O stars and F275W emission.

The northwestern part of NGC 3738 is problematic in regard to OB association identification; there are so many O stars and clumps that it was difficult to decide whether it was a very large single association or a close grouping of many individual clumps. Whichever way it is described, it is an extraordinary region in terms of its size and density of O stars (and compact clusters), and here we chose to emphasize that by considering it as a single region with a radius of 260 pc. In addition, most of the star formation in NGC 3738 is concentrated to this region, and we discuss the morphology of star formation in NGC 3738 and a similar galaxy DDO 187 in Hunter et al. (2018). If we had described that region instead as many smaller associations, what would we have found? It is likely that most of the smaller associations in the center of the region, while having smaller radii and stellar masses, would have similar stellar mass densities and be associated with similar galactic environmental properties (see Figure 11 below). However, some of the smaller associations along the edges of the region in this scenario would have lower mass densities and be described as having less extreme environmental properties as well. It is unlikely that taking this alternate definition of the region in NGC 3738 would alter the results of the analysis presented here.

We measured photometry in the circles encompassing the OB associations, chosen by eye to include the O stars and F275W emission, on the HST images. We subtracted any clusters within the boundary of the OB association and subtracted background measured in an annulus around the association. The photometry is on the Vega system for an infinite aperture size, and it was corrected for foreground extinction E(B − V)_f according to Schlafly & Finkbeiner (2011). We performed SED fitting to the photometry, using the Yggdrasil single stellar population models as for the star clusters, to determine the mass, age, and E(B − V)_i internal to the host galaxy. Two examples of the SED fitting are shown in Figure 5. The OB associations are identified in Table 3, and the mass, the mass divided by the area of the encompassing circle, the age, and E(B − V)_i are given there. For absolute F275W magnitudes, we applied the additional extinction correction for internal reddening, as listed in Table 3, using an A_F275W/E(B − V) of 7.43 (Calzetti et al. 2000). The goodness of the fit (probability that the chi-square exceeds a particular value χ² by chance; Press et al. 2007) is also given in Table 3, where a value of 1 denotes a good fit and a value near 0 means that the fit is not well constrained. Uncertainties in age and mass come from the maximum values and minimum values allowed by the fits. The ages of the OB associations range from 1 to 50 Myr, and radii of the encompassing circles range from 20 to 300 pc.

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Table 3.  OB Associations

		R.A. (2000)	Decl. (2000)	R		log Mass	log Age	log Mass/Area	Goodness
Galaxy	ID	(hh mm ss.s)	(dd mm ss)	(pc)	MF275W,0	(M⊙)	(years)	(M⊙ pc−2)	of Fit	$E(B-V)$
DDO 50	1	8 19 17.4	+70 43 42	43.4	−11.65 ± 0.002	${3.90}_{-0.28}^{-.07}$	${6.48}_{-0.48}^{+0.12}$	0.128	0.8	${0.22}_{-0.07}^{+0.04}$
	2	8 19 29.1	+70 43 3	56.8	−12.19 ± 0.001	${4.25}_{-0.28}^{-.08}$	${6.30}_{-0.30}^{+0.30}$	0.243	0.9	${0.11}_{-0.05}^{+0.03}$
	3	8 19 29.1	+70 42 51	53.9	−11.76 ± 0.001	${3.97}_{-0.30}^{-.10}$	${6.48}_{-0.18}^{+0.12}$	0.009	0.9	${0.09}_{-0.08}^{+0.03}$
	4	8 19 30.2	+70 42 41	65.1	−11.54 ± 0.001	${4.05}_{-0.28}^{-.10}$	${6.00}_{-0.00}^{+0.60}$	−0.074	0.8	${0.07}_{-0.04}^{+0.04}$
	5	8 19 26.5	+70 42 48	60.4	−11.42 ± 0.002	${3.82}_{-0.26}^{-.08}$	${6.48}_{-0.18}^{+0.12}$	−0.239	0.9	${0.14}_{-0.06}^{+0.04}$
	6	8 19 27.9	+70 42 19	105.5	−12.62 ± 0.001	${4.38}_{-0.22}^{-.03}$	${6.60}_{-0.60}^{+0.00}$	−0.164	0.9	${0.04}_{-0.03}^{+0.07}$
	7	8 19 29.3	+70 42 29	45.7	−11.08 ± 0.004	${4.06}_{-0.23}^{+0.00}$	${7.00}_{-0.00}^{+0.00}$	0.243	0.0	${0.23}_{-0.05}^{+0.06}$
	8	8 19 12.2	+70 43 8	94.9	−13.58 ± 0.001	${4.86}_{-0.25}^{-.08}$	${6.00}_{-0.00}^{+0.30}$	0.408	1.0	${0.11}_{-0.03}^{+0.05}$
	9	8 19 27.4	+70 41 58	59.8	−12.34 ± 0.001	${4.34}_{-0.25}^{-.10}$	${6.00}_{-0.00}^{+0.30}$	0.290	0.9	${0.14}_{-0.04}^{+0.05}$
	10	8 19 25.9	+70 41 53	59.2	−10.89 ± 0.002	${3.73}_{-0.18}^{-.08}$	${6.70}_{-0.00}^{+0.00}$	−0.312	0.8	${0.02}_{-0.02}^{+0.03}$
	11	8 19 23.5	+70 41 53	93.8	−11.25 ± 0.001	${4.39}_{-0.19}^{-.03}$	${7.18}_{-0.03}^{+0.00}$	−0.051	0.4	${0.03}_{-0.03}^{+0.04}$
	12	8 19 23.0	+70 42 3	64.5	−9.66 ± 0.003	${3.41}_{-0.13}^{+0.36}$	${6.85}_{-0.24}^{+0.27}$	−0.706	0.5	${0.00}_{-0.00}^{+0.23}$
	13	8 19 23.1	+70 42 58	90.3	−12.02 ± 0.002	${4.02}_{-0.25}^{+0.18}$	${6.48}_{-0.00}^{+0.70}$	−0.388	0.1	${0.16}_{-0.16}^{+0.04}$
	14	8 19 30.5	+70 42 56	55.1	−10.19 ± 0.002	${3.95}_{-0.35}^{+0.02}$	${7.15}_{-0.45}^{+0.03}$	−0.029	0.9	${0.02}_{-0.02}^{+0.16}$
	15	8 19 10.1	+70 43 17	82.6	−11.86 ± 0.001	${4.48}_{-0.25}^{+0.39}$	${7.00}_{-0.05}^{+0.30}$	0.148	0.6	${0.09}_{-0.04}^{+0.13}$
	16	8 19 17.0	+70 42 40	34.0	−10.72 ± 0.004	${3.50}_{-0.26}^{-.08}$	${6.48}_{-0.00}^{+0.12}$	−0.060	0.4	${0.26}_{-0.06}^{+0.04}$
	17	8 19 23.8	+70 42 8	34.6	−9.64 ± 0.003	${3.22}_{-0.30}^{-.10}$	${6.30}_{-0.30}^{+0.30}$	−0.355	0.9	${0.05}_{-0.04}^{+0.06}$
DDO 53	1	8 34 6.9	+66 10 56	86.5	−12.61 ± 0.001	${4.21}_{-0.26}^{-.08}$	${6.48}_{-0.18}^{+0.12}$	−0.161	1.0	${0.13}_{-0.06}^{+0.04}$
	2	8 34 9.8	+66 10 44	42.9	−9.44 ± 0.004	${3.55}_{-0.15}^{-.07}$	${7.18}_{-0.03}^{+0.00}$	−0.212	0.6	${0.00}_{-0.00}^{+0.02}$
	3	8 34 7.8	+66 10 51	37.3	−10.39 ± 0.003	${3.50}_{-0.26}^{-.10}$	${6.00}_{-0.00}^{+0.60}$	−0.140	0.9	${0.10}_{-0.04}^{+0.05}$
	4	8 34 8.7	+66 10 52	19.7	−9.70 ± 0.003	${3.17}_{-0.28}^{-.08}$	${6.30}_{-0.30}^{+0.30}$	0.084	0.9	${0.03}_{-0.03}^{+0.05}$
	5	8 34 8.4	+66 10 49	22.5	−9.74 ± 0.004	${3.07}_{-0.26}^{-.08}$	${6.48}_{-0.00}^{+0.12}$	−0.132	1.0	${0.08}_{-0.06}^{+0.04}$
	6	8 34 8.7	+66 10 38	30.2	−8.69 ± 0.006	${2.72}_{-0.27}^{-.06}$	${6.70}_{-0.22}^{+0.00}$	−0.738	0.2	${0.01}_{-0.01}^{+0.04}$
	7	8 34 3.8	+66 10 37	31.6	−10.03 ± 0.003	${3.28}_{-0.25}^{-.06}$	${6.70}_{-0.22}^{+0.00}$	−0.218	0.6	${0.07}_{-0.04}^{+0.04}$
	8	8 34 8.6	+66 10 47	23.2	−7.42 ± 0.011	${2.74}_{-0.15}^{-.03}$	${7.18}_{-0.03}^{+0.00}$	−0.489	0.3	${0.00}_{-0.00}^{+0.04}$
	9	8 34 3.4	+66 10 41	42.2	−10.52 ± 0.003	${3.47}_{-0.30}^{+0.16}$	${6.70}_{-0.22}^{+0.48}$	−0.278	0.5	${0.11}_{-0.11}^{+0.04}$
	10	8 34 9.7	+66 10 38	33.8	−10.50 ± 0.004	${3.77}_{-0.22}^{-.01}$	${7.00}_{-0.00}^{+0.04}$	0.216	0.1	${0.18}_{-0.05}^{+0.04}$
	11	8 34 6.0	+66 10 21	33.8	−9.34 ± 0.004	${3.01}_{-0.21}^{-.06}$	${6.70}_{-0.00}^{+0.00}$	−0.544	0.8	${0.03}_{-0.03}^{+0.04}$
DDO 63	1	9 40 45.1	+71 11 0	237.9	−12.05 ± 0.002	${4.42}_{-0.16}^{+0.37}$	${7.00}_{-0.00}^{+0.30}$	−0.830	0.4	${0.02}_{-0.02}^{+0.12}$
	2	9 40 34.0	+71 09 58	304.4	−12.46 ± 0.001	${4.59}_{-0.12}^{+0.37}$	${7.00}_{-0.52}^{+0.30}$	−0.874	0.2	${0.00}_{-0.00}^{+0.24}$
	3	9 40 39.5	+71 10 13	109.4	−11.86 ± 0.003	${4.05}_{-0.25}^{-.08}$	${6.00}_{-0.00}^{+0.30}$	−0.525	1.0	${0.14}_{-0.04}^{+0.05}$
	4	9 40 24.7	+71 10 25	131.5	−11.76 ± 0.003	${4.22}_{-0.22}^{-.03}$	${7.00}_{-0.00}^{+0.04}$	−0.515	0.0	${0.15}_{-0.05}^{+0.04}$
	5	9 40 18.2	+71 11 22	129.2	−11.53 ± 0.001	${4.38}_{-0.11}^{-.07}$	${7.18}_{-0.00}^{+0.00}$	−0.340	0.0	${0.00}_{-0.00}^{+0.02}$
	6	9 40 35.5	+71 10 44	156.0	−12.03 ± 0.004	${4.29}_{-0.21}^{+0.03}$	${7.00}_{-0.05}^{+0.04}$	−0.594	0.0	${0.20}_{-0.04}^{+0.05}$
NGC 3738	1	11 35 47.4	+54 31 33	260.8	−15.44 ± 0.000	${6.23}_{-0.21}^{+0.46}$	${6.95}_{-0.26}^{+0.74}$	0.900	0.9	${0.01}_{--.15}^{+0.39}$
	2	11 35 48.4	+54 31 18	138.4	−13.77 ± 0.001	${6.12}_{-0.71}^{+0.06}$	${7.70}_{-0.92}^{+0.30}$	1.341	1.0	${0.05}_{--.11}^{+0.36}$
	3	11 35 48.8	+54 31 26	66.8	−12.48 ± 0.001	${5.65}_{-0.71}^{+0.07}$	${7.70}_{-0.92}^{+0.30}$	1.503	1.0	${0.04}_{--.12}^{+0.37}$
Haro 29	1	12 26 15.7	+48 29 38	56.7	−14.51 ± 0.001	${5.13}_{-0.25}^{-.10}$	${6.00}_{-0.00}^{+0.30}$	1.126	0.3	${0.12}_{-0.04}^{+0.03}$
	2	12 26 16.0	+48 29 37	45.3	−13.49 ± 0.001	${4.76}_{-0.23}^{-.10}$	${6.00}_{-0.00}^{+0.30}$	0.950	0.0	${0.16}_{-0.03}^{+0.03}$
	3	12 26 16.5	+48 29 37	45.3	−12.49 ± 0.003	${4.33}_{-0.25}^{-.10}$	${6.00}_{-0.00}^{+0.30}$	0.520	0.8	${0.18}_{-0.03}^{+0.04}$
	4	12 26 16.3	+48 29 40	57.8	−12.57 ± 0.002	${4.37}_{-0.25}^{-.10}$	${6.00}_{-0.00}^{+0.30}$	0.349	0.6	${0.16}_{-0.04}^{+0.04}$
	5	12 26 16.2	+48 29 35	36.3	−12.11 ± 0.004	${4.19}_{-0.25}^{-.11}$	${6.00}_{-0.00}^{+0.30}$	0.574	0.1	${0.24}_{-0.04}^{+0.03}$
	6	12 26 17.2	+48 29 39	54.4	−12.48 ± 0.002	${4.20}_{-0.22}^{-.05}$	${6.60}_{-0.12}^{+0.00}$	0.231	0.7	${0.14}_{-0.03}^{+0.07}$
	7	12 26 16.9	+48 29 38	23.8	−10.81 ± 0.007	${3.54}_{-0.24}^{-.05}$	${6.60}_{-0.30}^{+0.00}$	0.289	0.9	${0.24}_{-0.04}^{+0.07}$

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We also make use of SFR surface density maps produced by D. Thilker et al. (2018, in preparation). The maps we used were made at 0.25 kpc resolution and use GALEX FUV images to determine the SFR. Wide-field Infrared Survey Explorer (WISE) HiRes W4 22 μm maps, if the galaxy was detected, were used to correct for extinction. For DDO 53 the "unWISE" images (unofficial, unblurred co-adds of the WISE images) were used instead (Lang 2014; Meisner et al. 2017). We followed the method of T. H. Jarrett (2018, private communication; see also Jarrett et al. 2012) and the prescription by Boquien et al. (2016), attempting to allow for the spatially variable contribution of old stellar populations to the dust heating, with the scaling as a function of local FUV–W1 color. This method scales the IR bands by a factor of 6.0, appropriate for local scales. If instead we used a scaling appropriate for global measurements of galaxies, such as the value of 3.89 determined by Hao et al. (2011), we find that the SFR density in spots in the centers of the galaxies would be lower by as much as a factor of two.

The FUV was corrected for foreground extinction following Peek & Schiminovich (2013). The maps use a Kroupa IMF from 0.1 to 100 M_⊙ with an SFR timescale ≥100 Myr (Kroupa 2001). The units of the maps are M_⊙ yr⁻¹ kpc⁻². We note, however, that SFRs determined over regions, especially small regions, within dwarf galaxies can be highly affected by the stochastic sampling of a universal IMF and time-dependent fluctuations in the SFR (Fumagalli et al. 2011; da Silva et al. 2014).

We have integrated the SFR in DDO 50 over all pressure regions in order to compare to the SFR determined from the GALEX FUV based on a calibration from resolved stellar populations by McQuinn et al. (2015). Their value, converted to our distance, is log SFR = −1.21 ± 0.17. This is 1.4 times larger than our value from the SFR map described here, but they are the same within 1σ. The integrated SFR from GALEX FUV given in Table 1 from Hunter et al. (2012) is 50% lower than the McQuinn et al. (2015) value.

The LITTLE THINGS data sets include H i line maps obtained with the Very Large Array (VLA) interferometer.²⁵ The H i maps are characterized by high sensitivity (≤1.1 Jy beam⁻¹ per channel), high spectral resolution (≤2.6 km s⁻¹), and high angular resolution (∼6''). To obtain maps of gas surface density, we converted the naturally weighted integrated (moment 0) H i maps to units of column density (atoms cm⁻²) and multiplied by 1.36 to account for helium. In addition, we use B and V images obtained at Lowell Observatory to determine the stellar mass density in each pixel. We used the B − V color to determine the mass-to-light ratio using a formula determined from SED fitting to the LITTLE THINGS photometry (Herrmann et al. 2016), and with L_V we determined the stellar mass in each pixel. (Note that we do not use WISE near-IR images to determine the stellar mass because the dIrrs are not generally detected by WISE. We also do not use Spitzer 3.6 μm images for S/N issues. See Zhang & Puzia (2017) for a discussion on the effect of lack of red colors on stellar mass estimates). From Zhang & Puzia (2017) we can expect that these stellar masses are good to a factor of two, and we adopt an uncertainty of 0.3 dex in the stellar mass surface densities. The stellar mass densities were converted from a Chabrier (2003) stellar IMF to the Kroupa (2001) IMF used in the cluster and OB association masses as indicated by Herrmann et al. (2016). The integrated H i maps and stellar mass maps are shown in Figure 6.

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The H i and stellar surface density maps were combined at their native resolutions to produce maps of the hydrostatic midplane pressure in each galaxy:

$$\begin{eqnarray*}&&P=2.934\times {10}^{-55}\times {{\rm{\Sigma }}}_{\mathrm{gas}}({{\rm{\Sigma }}}_{\mathrm{gas}}+({\sigma }_{g}/{\sigma }_{* }){{\rm{\Sigma }}}_{* })\,\,[{\rm{g}}/({{\rm{s}}}^{2}\,\mathrm{cm})],\end{eqnarray*}$$

where Σ is a surface density and σ is a velocity dispersion (Elmegreen 1989). Here Σ_gas is determined solely from H i+He since the molecular H₂ content is unknown. Although the molecular gas is more closely tied to star formation than the atomic gas, the H i+He is the material that is available to become molecular on a larger spatial scale. Molecular gas is most likely to be found within the denser H i clouds in low-metallicity environments, so if molecular content were known and included, it would probably increase the pressure in the higher-pressure regions rather than increasing the pressure in low H i density regions. The gas velocity dispersion was derived from the H i moment 2 maps. The stellar velocity dispersion was estimated using log σ_* = −0.15M_B − 1.27 from Swaters (1999), where M_B is the integrated absolute B magnitude of the galaxy. Because dIrrs are gas dominated and since the gas surface density enters as ${{\rm{\Sigma }}}_{\mathrm{gas}}^{2}$, the pressure maps are dominated by the H i.

We estimate the uncertainties in Σ_{H i} in the integrated H i moment 0 map from the H i data cube channel rms (Hunter et al. 2012) and assume that the number of channels contributing to each pixel in the integrated moment zero map is the typical velocity profile FWHM divided by the channel width, about six channels. We take a typical pressure region of radius 200 pc and determine the number of H i pixels N summed in such a region for the galaxy's distance, and the uncertainty in Σ_{H i} goes as $\sqrt{N}$. The uncertainty in log Σ_{H i} is 0.02 (units M_⊙ pc⁻²) for Haro 29, 0.04 for NGC 3738, 0.07 for DDO 63, 0.06 for DDO 53, and 0.09 for DDO 50. For a typical H i surface density of 10 M_⊙ pc⁻², the uncertainty in Σ_{H i} is from 5% for Haro 29 up to 20% for DDO 50. The uncertainty in the pressure is determined from the fact that the pressure goes as ${{\rm{\Sigma }}}_{{\rm{H}}\,{\rm{I}}}^{2}$, so the uncertainty of log P is 2× the uncertainty of log Σ_{H i}.

For an idea of what to expect related to pressure, Figure 2 of Elmegreen & Parravano (1994) shows the minimum pressure expected for star formation to take place as a function of metallicity and stellar radiation field. This predicts that most dIrr galaxies have pressures at or below the minimum. In the sections that follow we divide the observed pressures into bins with bin 1 pressures below 4 × 10⁻¹³ g s⁻² cm⁻¹, bin 2 pressures up to 4 × 10⁻¹² g s⁻² cm⁻¹, and bin 3 pressures above that. For context, the typical total midplane pressure in the solar neighborhood is of order 3 × 10⁻¹² g s⁻² cm⁻¹, near the boundary between bins 2 and 3 (Cox 2005). The pressure in typical H ii regions in dIrrs is also relatively high and would fall between bins 2 and 3, but the typical disk of a dIrr is lower pressure by a factor of ∼10 (Elmegreen & Hunter 2000), putting the typical dIrr disk at the boundary between the lower-pressure bins 1 and 2. By contrast, typical GMCs have much higher internal pressures, of order 4 × 10⁻¹¹ g s⁻² cm⁻¹ (Blitz & Rosolowsky 2004), solidly in bin 3.

Therefore, we have maps of the pressure, gas mass surface density, and stellar mass surface density with which to characterize the environment in which a stellar object has formed. In order to associate a particular environment with a cluster, OB association, or O star, we divided the pressure maps into regions that sampled the different pressure environments of each galaxy. This was done by eye from the pressure maps, and each circle is meant to roughly select a region of similar pressure (i.e., brightness on the pressure map). The purpose of averaging over regions is to increase the signal-to-noise ratio and isolate high- and low-pressure areas. The pressure maps with the regions encircled are shown in Figure 7. All regions are shown even though many of them ended up not having clusters or O stars in them. F275W images of all of the galaxies are shown in Figures 8–12, with the clusters, OB associations, and O stars marked along with the pressure regions. We then measured the average pressure, gas mass surface density, and stellar mass surface density within each of these circles. The average values associated with a given circle are assigned to the clusters, OB associations, and O stars that fall within that circle. For those objects falling between circles, the closest circle is used.

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From these figures, we note, first, that there are far more O stars than clusters in each galaxy. Second, clusters are not always found where the O stars are located. Third, O stars are often clustered, and these clusterings are what we have identified as OB associations.

3.1.1. Characteristics as a Function of Galactic Properties

In Figure 13 we plot the cluster CI and mass against their galactic environmental properties of pressure, stellar mass density, and H i surface mass density. Each galaxy is plotted with a different symbol, but note that DDO 63 has no clusters and is included in the legend as a reminder that it is a part of this sample. We see that clusters are found at a wide range of pressures and H i surface densities. However, the clusters in NGC 3738 and Haro 29 are generally found at higher pressures, stellar mass densities, and H i surface densities than the clusters in the other two galaxies. Haro 29 is likely an advanced dwarf–dwarf merger (Ashley et al. 2013), and NGC 3738 may be too (Ashley et al. 2017). Perhaps such external events are necessary to produce large numbers of clusters or extraordinary star-forming regions in dwarfs. The other three systems are more typical, likely internally driven dIrrs (Hunter et al. 2012; but see Bernard et al. 2012; Egorov et al. 2017, concerning DDO 50). We find only one compact cluster (NGC 3738's) in the lowest pressure range. In the pressure range where these dwarfs form compact and likely bound stellar systems, it does not show a trend of characteristics with increasing pressure.

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To check whether a correlation between cluster characteristics and galactic environmental properties was being lost in noisy cluster data, we produced Figure 13 for only cluster class 1 objects. These are clusters that are compact and bright and less ambiguous in their classification as a compact cluster than other objects. The numbers of clusters drops, but there is no trend with this subset of clusters.

Figure 13 is for all compact clusters with ages up to 100 Myr. In Figure 14 we plot the same quantities but only for clusters with ages up to 10 Myr. There are fewer clusters (see Table 2), but again, no trend of cluster properties with environmental properties is seen.

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Within the statistical uncertainties, the clusters cover the same range of properties independent of the galaxy or part of the galaxy in which they are found. This could imply that larger-scale effects are more important in determining the cluster characteristics, as proposed by the model of Whitmore et al. (2007; see also Whitemore 2017). Another possibility is that once the conditions for clustered star formation are reached, the gravitational collapse and the fragmentation properties of the interstellar medium drive the final star formation efficiency within the regions, thus making cluster formation a local and stochastic process (e.g., Longmore et al. 2014). Current studies of the ICMF show that it is described by a power-law function with slope close to −2, consistent with the hierarchical fragmentation caused by the scale-free action of turbulence. Star formation in dIrr galaxies and BCDs is more sporadic than it is in spiral systems. Thus, the lack of a correlation may be caused by small number statistics in sampling the cluster mass function. The lack of dependence of cluster size on the midplane pressure could be explained if dynamical stellar processes, within the gravitationally bound regions where clusters formed, operate on very short timescales (e.g., Grudić et al. 2017), canceling any memory of the initial conditions. This fast dynamical evolution, which includes stellar feedback, merging of subclumps in the young cluster, and tidal stripping by the host galaxy, would explain why cluster sizes and surface brightness profiles do not depend on galactic environment, cluster age, and galaxy type (e.g., Grudić et al. 2017; Ryon et al. 2017).

One issue in comparing cluster characteristics with the cluster's environment is determining the true environment in which the cluster formed. We restrict ourselves to clusters with ages less than 100 Myr in order to minimize to some extent the amount by which the environment has changed since cluster formation, although the formation of the cluster itself modifies the natal environment. In addition, we minimize the degree to which the clusters have dissolved (Lamers 2009; Baumgardt et al. 2013).

Above we chose to capture the environmental characteristics in regions defined by sampling of pressure maps. For comparison, we also determine the environment in annuli centered on each cluster with increasing distance from the cluster. We want to see whether there is any scale at which a correlation becomes apparent. We define a region around each cluster to be eliminated from the environmental measurements as a circle with a radius of 25 pc so that we are not including the cluster or OB association itself. We then measure the average pressure, gas mass surface density, and stellar mass surface density in circles of radii 25–150 pc in steps of 25 pc, 150–300 pc in steps of 50 pc, and 300 pc–1 kpc in steps of 100 pc, for a total of 15 circles. Annuli were constructed as the area between two successive circles.

We made plots like Figure 13 for each environmental annulus and constructed an animated ensemble of the plots in order to easily see the changes with radius. The movie is available in the online materials associated with this paper. In Figure 15 we show the same panels as in Figure 13, but for the smallest annulus, ∼38 pc radius. This explores the environment immediately around the clusters, which can contain other star-forming units. In Figure 16 we also plot the cluster characteristics against pressure for annuli 1, 7, and 15 (radii of 38, 225, and 950 pc, respectively) as an illustration of the entire range of radii. We find that the environmental characteristics change with annulus, steadily becoming lower in value with increasing radius. Not only is each annulus further from the cluster with increasing radius, but the area over which the galactic characteristics are measured increases with radius. From the first annulus to the last there is a factor of 100 increase in area. Thus, the lower values of the larger radii annuli are likely due to averaging over a larger area, essentially smoothing out peaks and valleys. Nevertheless, there is no radius at which a trend of cluster characteristics with environment develops.

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In Figure 17 we also compare for each cluster the environmental characteristics measured in the regions shown in Figure 7 with the environmental characteristics measured in the annulus immediately around the cluster. There is a one-to-one relationship with scatter. Since we are after the environmental parameters in which the cloud formed that made the clusters, we prefer the regional characteristics that provide a reasonable average over conditions rather than characteristics determined in the close-in annulus that is subject to local variations and crowding of other recent star formation.

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3.1.2. Characteristics by Pressure Region

To look at the role of pressure in another way, we examine the clusters of the pressure regions of Figure 7 in three bins; bin 1 is log pressure <−12.4, bin 2 is log pressure between −12.4 and −11.4, and bin 3 is log pressure >−11.4, where units of pressure are g (s² cm)⁻¹. These bins were chosen by eye based on groupings of clusters and are marked with vertical dashed lines in Figures 13–16. Note that we are only including the regions outlined in Figure 7. These regions were chosen primarily to cover the parts of the galaxies where the stars and clusters are located, mostly the central regions, and they do not include all of the gas associated with each galaxy, particularly extended low-density gas. Furthermore, the pressure by which the region is binned is the average within each region. The purpose here is to describe and compare the identified pressure regions.

In the top panels of Figure 18 we plot the fraction of the total area covered by each pressure bin (panel (a)) and the fraction of the H i gas contained in each pressure bin (panel (d)). We see, for example, that although the clusters in NGC 3738 and Haro 29 are found mostly in pressure bin 3, the fraction of area occupied by these pressure regions is not high, 15%–18%. On the other hand, in NGC 3738 bin 3 contains the majority of the gas, in contrast to what is seen in the rest of the systems. For the three typical dIrrs (DDO 50, DDO 53, DDO 63) the majority of the gas is in pressure bin 2, and none to very little is in bin 3. Haro 29 is opposite to both of these trends, with the majority of its gas in bin 1, the lowest pressure. In terms of cluster characteristics, the number of clusters (panels (b) and (e)) and total mass in clusters (panels (c) and (f)) per unit area and per unit gas mass generally increase from pressure bin 2 to pressure bin 3 for the two galaxies with clusters in both bins 2 and 3—NGC 3738 and Haro 29. (DDO 63 has no clusters, and DDO 50 and DDO 53 only have clusters in bin 2.) We examine pressure bin 3 further by plotting, just for that pressure bin, the ratio of the cluster mass to H i mass against the fraction of the H i mass in pressure bin 3 in Figure 19. We see that the ratio of cluster mass to H i mass is independent of the fraction of the H i mass in pressure bin 3, although only two galaxies have clusters in bin 3.

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We were curious what the pressure distribution was among the larger sample of LITTLE THINGS dIrrs, and to look at that, we binned the pressure and integrated H i maps on a pixel-by-pixel basis for 29 of the LITTLE THINGS galaxies. Thus, here we include all of the gas, including low-density gas in the outer parts. Looking at the pressures on a pixel-by-pixel basis, we can investigate the full range of pressure environments in our galaxies and without averaging out the highs and lows as is a consequence of our analysis of selected regions. We found that 30% (12) of the galaxies have no gas in pressure bin 3, while another 30% have >3% of their gas in this bin. Of the 40 LITTLE THINGS galaxies, NGC 3738 has the highest percentage of all of its gas in bin 3, 26%. The starburst galaxies NGC 1569 and IC 10 have 14% and 10% of their gas in bin 3, respectively. The other galaxies in this study—DDO 50, DDO 53, DDO 63, and Haro 29—have 0.8%, 1.9%, 0%, and 2%, respectively. We examined the LITTLE THINGS sample for any correlation between the integrated SFR and percentage of gas in pressure bin 3 and found none.

In Figure 20 we compare the identified clusters to the SFR measured from the SFR maps by pressure bin. First, panel (a) compares the total SFR per unit area in the three pressure bins, while panel (b) compares the unnormalized SFR in the different bins. Even though DDO 63 has no clusters, it does have FUV emission, and so it has a measured SFR in bins 1 and 2. We see that generally the higher-pressure bins have a higher SFR surface brightness. In panel (c) we compare the total mass in clusters divided by the SFR in the three pressure bins. There are two galaxies with clusters in all three pressure bins: NGC 3738 and Haro 29. In Haro 29 the mass formed in clusters divided by the SFR is approximately a constant with pressure. For NGC 3738 the ratio is lower at intermediate pressures (bin 2) than at higher pressures (bin 3), and at low pressure (bin 1) there is only one cluster, so statistics are poor there. The other two galaxies with clusters only in bin 2 have ratios that are comparable to NGC 3738's value in that bin. However, this suggests that the increase in the mass formed in clusters as a function of pressure shown in Figure 18(c), is mainly a reflection of the fact that both the mass formed in clusters and the SFR are higher in higher-pressure regions (see also Blitz & Rosolowsky 2006). Figure 20(c) is also consistent with the finding by Chandar et al. (2015) that global cluster mass functions correlate with SFRs. In other words, the sampling of the cluster mass function is a stochastic process driven by size-of-sample effects, and higher SFR enables sampling the cluster mass function at the high-mass end (e.g., Adamo & Bastian 2015).

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3.1.3. Cluster Formation Rate

We have estimated Γ, the ratio of cluster formation rate to integrated SFR, for clusters in each of the three pressure bins. This is not the individual circular pressure regions of Figure 7, but the sum of the clusters whose environmental pressures fall into the three pressure bins defined in Section 3.1.2. We have included only clusters from the team catalogs that have classes of 1 or 2 since these are compact clusters and more likely than multiple-peaked class 3 objects to be bound. We also include clusters with masses greater than or equal to 1000 M_⊙ and ages less than or equal to 100 Myr. We extrapolate the mass in clusters with mass between 100 and 1000 M_⊙ assuming that the cluster mass function is described by a power-law function with slope −2. We do not exclude very young clusters, as the tracer used to derive the SFR is sensitive to star formation between 1 and 100 Myr. In bins with at least two clusters, we estimate the cluster formation rate as the total observed stellar mass divided by the age interval of 100 Myr. The uncertainty in Γ takes into account the Poisson statistics of the numbers of clusters and the uncertainties associated with the cluster mass and age (e.g., see Adamo et al. 2015, for a complete description of the method). For pressure bins that contain less than two clusters, Γ is not calculated. Issues related to the inconsistency in the timescale over which Γ and Σ_SFR are determined are discussed by D. O. Cook et al. (2018b, in preparation), particularly in relation to dwarf galaxies.

In Figure 21 we plot Γ as a function of pressure bin (left panel) and as a function of the SFR density (right panel) in the pressure bin where Γ was calculated. Γ varies from 0.9% to 33% in bin 2 and from 4% to 24% in bin 3. NGC 3738 in pressure bin 2 has a Γ that is significantly higher for that pressure than for DDO 50. For NGC 3738, with clusters in both pressure bins 2 and 3, Γ does not change significantly between the two pressure bins. Furthermore, Γ does not show a correlation with the total SFR density measured by pressure bin, as shown in Figure 20(c). However, our dIrrs do scatter around the sequence of Γ versus SFR density found in other galaxies (e.g., Goddard et al. 2010; Adamo et al. 2011, 2015; Annibali et al. 2011; Ryon et al. 2014; Lim & Lee 2015; Johnson et al. 2016): for the intermediate-pressure bin (green squares) one galaxy lies above the black curve and one lies near the curve. In the highest-pressure bin (number 3, red squares in Figure 21, right panel) NGC 3738 lies near the black curve and Haro 29 lies well below. In the same plot, we also include the measured SFR densities (arrows) of the regions of galaxies that do not have any estimate of Γ, color-coded according to pressure bin. The range of SFR densities for low-pressure bins (blue arrows) reaches 1 mag lower than the SFR density values where clusters are formed. The SFR density range of intermediate- and high-pressure bins that form or do not form clusters (green and red arrows and squares) spans about two orders of magnitude, suggesting that cluster formation may still be highly stochastic, probably because of the episodic nature of star formation in dwarf galaxies. There are other suggestions that Γ measured globally for galaxies is constant (see, e.g., Chandar et al. 2015, 2017). In that context, DDO 50 and Haro 29 are significantly different from NGC 3738 in this sample. In D. O. Cook et al. (2018b, in preparation) we will present global values of Γ calculated for these dwarfs and discuss the effects of using averaged SFR densities derived with calibrated flux conversions and SFR densities derived using stellar counts and resolved star formation histories. While the Γ used in this work are estimated using an age range sensitive to the SFR tracer adopted, resolved recent star formation histories will enable us to estimate Γ within smaller age ranges (D. O. Cook et al. 2018b, in preparation).

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For many of the LITTLE THINGS galaxies, including four of the galaxies in this paper, we also have catalogs of H ii regions to a completeness limit of about 2 × 10³² erg s⁻¹ pc⁻² (Youngblood & Hunter 1999). These represent very young star-forming units, where the surrounding galaxy has not had much time to change since the formation of the stars in the H ii region. Therefore, we made the equivalent of Figure 13 for the H ii regions, which we present in Figure 22. We characterize the H ii regions by the Hα surface brightness: the integrated Hα luminosity divided by the area covered by the H ii region (see Youngblood & Hunter 1999, for details). The diameters of the H ii regions range from 10 to 500 pc. In Figure 22 the bottom panels show the Hα surface brightness plotted against galactic properties for the galaxies in this study. The galactic properties in this figure were those measured in the regions defined on the pressure maps. The top panel contains these four galaxies plus 25 more from the LITTLE THINGS sample plotted against galactic pressure. In the top panel the pressure was measured in an annulus 200 pc wide located just beyond the H ii region. With the larger sample, we do see a correlation: as galactic pressure increases, the H ii region Hα surface brightness also increases. There is no correlation between diameter of the H ii region and pressure. We would expect the Hα surface brightness to be determined by the concentration of massive stars and gas. Hence, this suggests that higher concentrations of massive stars and gas are preferentially found in regions with higher pressure.

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The OB associations are outlined in Figures 8–12, and their properties are given in Table 3. These objects are large and loose associations of O stars, which are distinct from the cluster catalogs' class 3 objects that are compact associations. One can see from the summary of total numbers given in Table 2 that DDO 50, DDO 53, and DDO 63 have more OB associations than clusters. Even DDO 63, which has no clusters, has six OB associations. Hence, for these galaxies, OB associations appear to be a better descriptor of the mode of star formation in these systems. NGC 3738 and Haro 29 are different, perhaps because they are more extreme in SFR over all. Haro 29 has a comparable number of clusters and OB associations, 9 and 7, respectively, and NGC 3738 has 138 clusters and three OB associations. In addition, the OB associations in NGC 3738 and four of those in Haro 29 have a higher stellar mass density than those in the other three galaxies. OB association #3 in NGC 3738 has a density that is 12 times higher than the highest-density region in DDO 50, DDO 53, or DDO 63. OB association #1 in NGC 3738 is very large, encompassing half of the optical galaxy within 0.5 disk scale length radius (Hunter et al. 2018).

The equivalent of Figure 13 is shown for the OB associations in Figure 23. The OB association characteristics of stellar mass and mass surface density are plotted against environmental characteristics of pressure and H i surface density. We see, again, that OB associations in NGC 3738 and Haro 29 are more massive and have a higher mass surface density than those found in the other three galaxies. This is unlikely to be a consequence of their further distances since the OB associations are all highly resolved. The associations in NGC 3738 and Haro 29 are also found at higher pressure and mostly at higher H i surface density. The OB associations in DDO 50, DDO 53, and DDO 63 have similar masses and mass densities and are all found in the intermediate-pressure bin. The OB associations of DDO 53 and DDO 63 tend to be found at lower H i densities.

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Here we turn our attention from star clusters and OB associations to individual O stars. The distributions of the candidate O stars are shown in Figures 8–12. Not all stars are captured in the selected OB associations. This does not necessarily imply that some O stars have formed in isolation, although that is possible, but could imply that our recognition of OB associations, especially small or older associations, may be inadequate. The stellar characteristics that we have to work with are absolute F275W magnitude M_F275W and number of stars.

3.4.1. Characteristics as a Function of Galactic Characteristics

In Figure 24 we plot the O star equivalent of Figure 13: stellar M_F275W against the three environmental characteristics pressure, stellar mass density, and H i mass density. First, we see that O stars are found at a wide range of pressures, including the lowest-pressure bin 1 where no clusters are found, as we saw for the OB associations that contain most of the O stars. Furthermore, the O stars are not coincident with the clusters. This suggests that O stars in these dwarfs are preferentially formed in less compact units that are perhaps not bound.

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Second, we see that, like the clusters and OB associations, O stars at high pressure are found exclusively in NGC 3738 and Haro 29, and O stars at high stellar mass density and gas mass density are mostly found in NGC 3738 and Haro 29. Furthermore, most of the O stars in NGC 3738 and Haro 29 are found in regions with high densities.

Third, like the properties of clusters and OB associations, generally O star magnitudes cover a large range regardless of pressure or density. One exception is that O stars in all galaxies do not extend to the same faintness level. However, the lower limits correlate with the distance to the galaxy: DDO 50 (3.1 Mpc) stars extend to M_F275W of ∼−5, DDO 53 (3.7 Mpc) stars extend to ∼−5.5, DDO 63 (4.0 Mpc) stars extend to ∼−6, NGC 3738 (4.9 Mpc) stars extend to ∼−6, and Haro 29 (5.9 Mpc) stars extend to ∼−6.5. Therefore, the change in the lower limits is to some extent a distance effect, with the more distant galaxies having brighter absolute magnitude limits. In addition, incompleteness due to higher backgrounds in the higher SFR galaxies may also play a role. The horizontal dashed line in Figure 24 marks a stellar absolute magnitude in F275W, M_F275W, of −6.5. To see the effect of making an absolute magnitude lower limit cutoff to the stellar catalogs, look only at the stars above this line. Doing this, one can see that the stars in pressure bins 2 and 3 extend to more or less the same upper magnitude. However, the brightest stars are found in NGC 3738 and Haro 29 in pressure bin 3, but there are only a few of these, and they could be due to blending at the further distances of these galaxies. Also, at the low-pressure side of the figure, bin 1, there are no stars brighter than about −7.5, although there are also fewer stars in this pressure bin. Both of these effects could be due to size-of-sample effects in that the SFR is also a function of the pressure with the higher-SFR galaxies having many more O stars than the lower-SFR galaxies or regions (see Whitemore 2017).

To correct the F275W photometry of the O stars for extinction, we applied a modest constant correction for internal extinction of $E(B-V)=0.05$ mag per galaxy. This corresponds to an A_V of 0.16 mag. This value is also fairly consistent with E(B − V) of OB associations determined from SED fitting and given in Table 3. Additional extinction evenly distributed across a galaxy would only cause us to underestimate the luminosity of all O stars in that galaxy by the same factor. However, differential extinction across the galaxy would affect the intercomparison of stars. Kahre et al. (2018) have developed a method of mapping the extinction in LEGUS galaxies by determining the reddening for each object from its photometry in the galaxy's stellar catalog (see Sabbi et al. 2018). We have looked at the extinction map and stellar extinction histogram for NGC 3738 as likely the worst case in our sample of galaxies. NGC 3738 has dust lanes that are clearly visible in color images in a small region to the north of the center of the galaxy, at an R.A. and decl. centered around 11^h35^m490, 54°31'34''. The extinction map indeed shows that this region has the highest extinction, up to A_V ∼ 1.2, and this region contains of order 10 clusters and O stars used in this study. However, a histogram of stellar extinctions shows that most stars have A_V near zero with a tail to higher A_V that involves a relatively small number of stars. Thus, while we have underestimated the absolute F275W magnitude of some of the stars in NGC 3738 by up to 2 mag, the numbers that are affected are small. Furthermore, since the region of heaviest extinction is also at the highest pressure, these very luminous stars would only accentuate the trends that we see in that galaxy (see Section 3.4.2).

3.4.2. Characteristics by Pressure Region

In Figure 25 we examine the O star characteristics by pressure bin, including the third-brightest M_F275W, number of O stars, and M_F275W integrated over all of the O stars in the pressure bin. We choose to plot the third-brightest star rather than the brightest in order to reduce statistical scatter from using the single brightest star. We see that the third-brightest M_F275W and integrated M_F275W are generally higher at higher pressure, but only in NGC 3738 is the number of O stars significantly higher in the highest-pressure bin.

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In Figure 26 we plot the O star characteristics per unit area and per unit H i gas mass by pressure bin, similar to Figure 18. We see that the number of O stars and integrated F275W flux per unit area and per unit H i gas mass increase with pressure.

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Figure 27 is similar to Figure 20, but for O stars. Here we plot the integrated F275W flux relative to the SFR by pressure bin. We see that generally the higher the pressure, the higher the O star F275W flux per unit SFR. Similarly, Figure 25 showed that the maximum absolute F275W magnitude of the O stars increases with pressure bin. By contrast, in Figure 20 Haro 29 has flat values of integrated cluster mass divided by SFR with pressure bin. The O star cluster difference may imply that the mass of the most massive star increases with pressure or that the ratio between ongoing star formation and star formation averaged over the past 100 Myr increases with pressure.

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In the left panels of Figure 28, we examine the relative number of clusters and O stars. The top two panels show a histogram of each separately. The bottom panel shows the ratio of clusters to O stars. Here we have summed in 0.5 log pressure bins. The large black crosses are the ratios of the sums of clusters and O stars in all five galaxies. We see that the ratio increases with pressure.

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Here the clusters are small compact clusters or tiny associations that may be bound, while the O stars are primarily grouped into physically larger associations. For a given stellar IMF, the number of O stars formed in the clusters is just a scaling factor times the cluster mass. Therefore, the ratio of number of clusters to number of O star candidates is related to the ratio of the number of O stars formed in clusters to the number formed in larger OB associations. This relationship is messy because the clusters are not all the same mass and the number of O stars in a particular association declines with time. Nevertheless, the rise of the ratio of number of clusters to number of O star candidates with pressure could indicate that the number of O stars formed in clusters compared to the number formed in associations increases with pressure. This is in spite of the fact that the relationship is dominated at the high end by NGC 3738, where half of the central part of the galaxy is one giant OB association.

On the right side of Figure 28 we plot the sum of the mass in clusters divided by the sum of the mass in OB associations by pressure for each galaxy (for pressures that have at least one OB association). This may be related to the amount of star formation taking place in bound systems relative to that taking place in unbound systems. We find that the ratio of cluster mass to OB association mass is fairly low and fairly flat. When masses are summed over all galaxies (the large black crosses in Figure 28), the high values at log pressure −11.25 and −10.75 are also driven by NGC 3738, which has one very large OB association that is assigned to log pressure −10.4.