A comparison of young star properties with local galactic environment for LEGUS/LITTLE THINGS dwarf irregular galaxies
Deidre A. Hunter Angela Adamo Bruce G. Elmegreen Samavarti Gallardo Janice C. Lee David O. Cook David Thilker Bridget Kayitesi Hwihyun Kim Lauren Kahre Leonardo Ubeda Stacey N. Bright Jenna E. Ryon Daniela Calzetti Monica Tosi Kathryn Grasha Matteo Messa Michele Fumagalli Daniel A. Dale Elena Sabbi Michele Cignoni Linda J. Smith Dimitrios M. Gouliermis Eva K. Grebel Alessandra Aloisi Bradley C. Whitmore Rupali Chandar Kelsey E. Johnson






1Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, Arizona 86001 USA
2Department of Astronomy, The Oskar Klein Centre, Stockholm University, Stockholm, Sweden
3IBM Research Division, T. J. Watson Research Center, Yorktown Heights, New York 10598 USA
4Northern Arizona University, Flagstaff, Arizona 86011 USA
5Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, Maryland 21218 USA
6Department of Astronomy and Astrophysics, California Institute of Technology, Pasadena, California 91125 USA
7Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland USA
8Hamilton College, 198 College Hill Rd, Clinton, New York 13323 USA
9Gemini Observatory, Casilla 603, La Serena, Chile
10Department of Astronomy, New Mexico State University, Las Cruces, New Mexico USA
11Department of Astronomy, University of Massachusetts – Amherst, Amherst, Massachusets 01003 USA
12INAF – Osservatorio di Astrofisica e Scienza dello Spazio, Bologna, Italy
13Institute for Computational Cosmology and Centre for Extragalactic Astronomy, Durham University, Durham, United Kingdom
14Deptartment of Physics and Astronomy, University of Wyoming, Laramie, Wyoming USA
15Department of Physics, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy 
16INFN, Largo B. Pontecorvo 3, 56127, Pisa, Italy
17European Space Agency/Space Telescope Science Institute, Baltimore, Maryland 21218 USA
18Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
19Max Planck Institute for Astronomy,  Königstuhl 17, 69117 Heidelberg, Germany
20Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr. 12–14, 69120 Heidelberg, Germany
21Department of Physics and Astronomy, The University of Toledo, Toledo, Ohio 43606 USA
22Department of Astronomy, University of Virginia, Charlottesville, VA 22904 USA


We have explored the role environmental factors play in determining characteristics of young stellar objects in nearby
dwarf irregular and Blue Compact Dwarf galaxies.
Star clusters are characterized by concentrations, masses, and formation rates,
OB associations by mass and mass surface density,
O stars by their numbers and near-ultraviolet absolute magnitudes, and  regions by  surface brightnesses.
These characteristics are compared to surrounding galactic pressure, stellar mass density,
 surface density, and star formation rate surface density.
We find no trend of cluster characteristics with environmental properties,
implying that larger scale effects are more important in determining cluster characteristics
or that rapid dynamical evolution erases memory of the initial conditions.
On the other hand, the most massive OB associations are found at higher pressure and  surface density,
and there is a trend of higher  region  surface brightness with higher pressure, suggesting
that a higher concentration of massive stars and gas are found preferentially in regions of higher pressure.
At low pressures we find massive stars but not bound clusters and OB associations.

We do not find evidence for an increase of cluster formation efficiency as a function of star formation rate density.
However, there is an increase in the ratio of the number of clusters to number of O stars with pressure, perhaps
reflecting an increase in clustering properties with star formation rate.







§ INTRODUCTION
 

Age and mass distribution functions of compact star clusters are similar among different types of galaxies <cit.>.
Nevertheless, the products of star formation come with a wide range in numbers of stars and spatial concentration <cit.>.
There are massive, compact, bound clusters, such as the old globular clusters and young super star clusters
<cit.>.
Yet, spatially large or massive does not always mean spatially concentrated <cit.>, as shown by large loose associations of stars,
some of which occupy a large fraction of a dwarf galaxy
<cit.>.
At the small end in spatial size or mass, the star formation process also produces both small compact clusters and small associations
<cit.>.

The characteristics of natal clouds affect the products of the star formation process.
Simulations by <cit.>, for example, show that massive, dense, long-lived clouds produce massive clusters and that smaller clusters form
in short-lived clouds.
Furthermore, clustered star formation occurs in parts of clouds with enhanced turbulence and density while
isolated star formation is found in parts of clouds with subsonic turbulence <cit.>.
In addition, star formation proceeds faster in higher density gas, leading to a more narrow age distribution, while there are
longer star formation time scales and larger age spreads in low density regions <cit.>.

There is also evidence that the star formation rate (SFR) depends on pressure <cit.> and that
large-scale galactic conditions affect the star formation products <cit.>. We see this spectacularly in merging
galaxy systems that have produced large numbers of super star clusters <cit.>.
<cit.>, for example, suggests that triggering cloud formation through processes that increase the pressure, such as shocks,
could be significant in interacting galaxies and in early galaxy formation when globular clusters formed.
The old halo globular clusters presumably formed at very high pressures <cit.>.
In fact, in a study of a giant molecular cloud (GMC) in the Antennae system, <cit.> find that the pressure
in the region in which this GMC is embedded is 10^4 times higher than that in a typical galaxy.
<cit.> find that a massive starburst galaxy at z=2.3 has star-forming regions with luminosity densities
comparable to cores of GMCs but 100 times larger
and 10^7 times more luminous than what we see locally.
High pressure regions caused by collision of supershells within a galaxy and external ram pressure stripping
can also facilitate star formation <cit.>.
Furthermore, there is evidence that the fraction of star formation resulting in bound clusters, Γ, is higher
in regions of high SFR density, especially starburst systems <cit.>,
although this is not universally agreed on <cit.>.

Consequences of the environmental conditions on the star formation products may extend to more local regions within galaxies as well.
For example, <cit.> found that Γ decreases by factors of a few from the center of M83 to the outer disk and
varies from region to region within the galaxy with the local SFR density. In addition the initial cluster mass function (ICMF)
steepens in the outer disk as the upper cluster mass limit declines. Changes in Γ and the ICMF with radius are
consistent with a decrease in gas pressure <cit.> or, similarly, gas density <cit.>.
Streaming of gas around bar potentials and piling up at the ends can also be a local factor in creating giant star forming
regions <cit.>.
In Blue Compact Dwarfs (BCDs) the migration of gas to the central regions <cit.>
increases the SFR densities and the local pressure,
enhancing the ability to form massive, concentrated star clusters <cit.>.

<cit.> <cit.>
have suggested that the dominant factor in determining the kind of unit (bound super star cluster, open clusters, associations)
that is formed is pressure. A high pressure environment
facilitates the formation of massive, bound clusters, whether the high pressure is the result of high gas density or large-scale shocks such as in merging galaxies.
An equally massive cluster could be born at lower pressure but it would not be bound.
This is consistent with finding super star clusters in starbursts and merging galaxies and not finding them today in galaxies like the Milky Way where star formation is driven by internal processes.
<cit.>, on the other hand, argue that the formation of massive clusters is determined by gravitational instabilities and
surface density of gas, and so massive clusters represent the largest scale in galaxies not stabilized by rotation.
However, young and old super star clusters and the somewhat less massive populous clusters are found even in some nearby dwarf irregular (dIrr) galaxies
although dIrrs in general have gas densities too low for gravitational instabilities to drive star formation
<cit.>.
On the other hand, these are usually systems in which there is evidence that the formation of massive star clusters is an anomalous event;
the galaxies are too small to sample the cluster mass function to the extreme of super star clusters <cit.>.
In addition, super star clusters are also usually found in a setting of unusually high star formation activity overall, suggesting
that some external perturbation has produced large-scale flows <cit.>.



Given the evidence that the characteristics of the SF products relate to their local galactic environment,
we undertook a study of five dIrr galaxies for which we have catalogues of star clusters and O star candidates
as well as pressure, stellar mass, integrated , and  maps of the galaxies.
These data allow us to compare the concentrations and masses of young stellar objects 
with respect to the surrounding pressure,  surface density, and stellar mass surface density.
We use the term “cluster” here as defined by the LEGUS project <cit.>: compact and centrally-concentrated sources (class 1 or 2 objects)
which could be gravitationally bound systems, as well as objects
with asymmetric profiles and multiple peaks on top of diffuse underlying wings (class 3).
We also identify larger and looser OB associations in our sample of galaxies, defined by clumping of O stars.
Thus, here we are probing the realm of “normal” star formation products, that is, not super star clusters,
and examining all types of SF products, from small compact clusters to larger OB associations, to individual O stars.
And, we are examining the role local factors play in determining the characteristics of these objects.

In Section <ref> we describe the galaxy sample, the data that we worked with, and the way in which we have
defined the environment within the galaxies.
In Section <ref> we present the observational results for the  star clusters, in Section <ref> the results for  regions,
and in Section <ref> the results for the O stars, including
their characteristics as a function of galactic characteristics and characteristics of regions at different
pressures.
We also define clusterings of O stars and discuss the properties of these associations in Section <ref>

and we compare the numbers of clusters and of O stars by pressure.

In Section <ref> we summarize our findings.





§ DATA
 



 §.§ Galaxy sample


There are 5 dIrr galaxies in common between the Hubble Space Telescope (HST) Legacy Extragalactic UV Survey[Based on observations obtained with the NASA/ESA Hubble
Space Telescope, at the Space Telescope Science Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5-26555.]
<cit.>
and LITTLE THINGS[ Funded in part by the
National Science Foundation through grants AST-0707563, AST-0707426, AST-0707468, and
AST-0707835 to US-based LITTLE THINGS team members and with generous technical and logistical support from the
National Radio Astronomy Observatory.] <cit.>.
LEGUS is an HST Cycle 21 Treasury survey aimed at exploring star formation from scales of
individual stars to kpc-size structures with multi-band 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 multi-wavelength survey
from the far-ultraviolet to 21-cm  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 <ref>.
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 <ref> 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 <cit.>.
We note, however, that recent photometry of stars in the LEGUS galaxies have also yielded distance measurements from the apparent
brightness of the tip of the red giant branch <cit.>. A significant difference exists between the new LEGUS
distances and the referenced distances for NGC 3738 (5.3±0.3 Mpc vs. 4.9 Mpc)
and Haro 29 (3.4±0.3 Mpc vs. 5.9 Mpc).
<cit.>  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, <cit.> gives a distance of 3.42 Mpc for DDO 50 compared to the 3.05 Mpc that we adopt from <cit.>.
If these distances were used here instead of those given in Table <ref>, the masses and brightnesses
of objects in NGC 3738 would be 1.2× higher, in Haro 29 would be 0.3× lower, and in DDO 50 would be 2.0× higher.
However, the relative comparison of objects would stay the same.


lcccccccc




9
460pt
The Galaxy Sample  

          D          M_V
    R_Dc
    log SFR_D^Hαd     log SFR_D^FUVd 

Galaxy       Other namesa
    (Mpc)     Refb     (mag)
    (kpc)
    (M yr^-1 kpc^-2)     (M yr^-1 kpc^-2)
    E(B-V)_fe

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 

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 <cit.> revised to the distance adopted here.
dSFR_D^Hα is the star formation rate, measured from
Hα, normalized to the area π R_D^2, where R_D is the disk scale length <cit.>.
SFR_D^FUV is the star formation rate determined from GALEX FUV fluxes
<cit.>.
eForeground Milky Way extinction from <cit.>.

1 – <cit.>;
2 – <cit.>;
3 – <cit.>;
4 – <cit.>.






 §.§ Star cluster catalogues


lccccc
490pt

5
Numbers of  clusters, OB associations, and O star candidates 

       # clusters      # clusters      # clusters           

       (masses >10^3 M)      (masses >10^3 M)      (no mass cut)            

Galaxy       (ages≤10 Myrs)      (ages≤100 Myrs)      (ages≤100 Myrs)     # OB assoc     # O stars

DDO 50         7     11        56     17     404 

DDO 53         1      1        7     11     101 

DDO 63         0      0        12     6      105 

NGC 3738     51     138     172      3     281 

Haro 29         8     9         13      7     61 



The sample galaxies were observed
with HST's WFC3 imager and 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 and filter F555W,
and NGC 3738 and Haro 29 were observed with ACS and filter F606W.
The LEGUS team developed an exhaustive procedure for identifying and checking resolved compact stellar clusters on the images,
and details of the catalogue preparation are given by <cit.> and <cit.>.
The first step is an automatic identification using the algorithm SExtractor <cit.>.
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 catalogues for the LEGUS dwarf galaxies are presented by
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 0.0396).
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 catalogues in the beginning, but 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 
Cook et al. (2018a, in preparation).
The photometry was corrected for Galactic extinction using <cit.> with the E(B-V) listed in Table <ref>.
Spectral energy distribution (SED)
fits were performed for those clusters with photometry in at least 4 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 <ref>.
Several internal reddening curves were used, and here we adopted the catalogues
in which the photometry was fit for internal extinction using the curve of <cit.>.
The SED fitting used two methods: 1) the Yggdrasil single stellar population models <cit.>, and 2)
the stochastically sampled cluster evolutionary models of <cit.>.
A <cit.> stellar initial mass function (IMF) from 0.1-120 M was assumed.



The spread between stochastically based and deterministic derived cluster properties are within the age and mass uncertainties 
(Cook et al. 2018a, in preparation), but the differences are particularly noticeable for clusters with masses below 1000 M <cit.>.
More details on the production of the cluster catalogues are given by <cit.>.

In using these catalogues, we eliminated clusters with masses less than 1000 M in order to ensure completeness,
those observed in fewer than 4 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 are more likely compact stelllar associations
<cit.>.
We also imposed an age cut-off. We carried age cut-offs of 10 Myr, 50 Myr, 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
we will also show the result for 10 Myr.
An age of 100 Myr minimizes losses due to dissolution of clusters <cit.> <cit.>.
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 <ref> we show the luminosity functions for the clusters in our galaxies, and
in Figure <ref> we plot age versus mass for the clusters in our 5 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 cut offs 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.

The numbers of  clusters are given in Table <ref>, 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.



 §.§ O star catalogues


We also used LEGUS catalogues of candidate O stars in the dwarf galaxies 
(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 catalogues 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 parameter 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(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 cut off.
However, O stars within  regions could be missed due to higher differential extinction.
Details on the LEGUS stellar photometry can be found in <cit.>.

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 mag in the catalogues 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 mag of 25.5 in F275W.
Hence, we are not likely to be significantly affected by incompleteness issues that might also bias the sample towards
more massive stars in more distant galaxies.


The photometry is only corrected for foreground extinction according to <cit.>.
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 <cit.>.
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  regions. This value is half of the average E(B-V) derived from
 region Balmer decrements for typical dwarfs <cit.>, but
E(B-V) could be larger in some dwarfs <cit.>.
The numbers of candidate O stars are given in Table <ref>.




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 <cit.>, but the key step in distinguishing clusters from stars is
summarized here. The concentration index 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 <ref> 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.



 §.§ OB associations


Not all star-forming units are clusters or compact associations, and there are larger groups of O stars in all 5 galaxies.
Guided by the distribution of O stars as well as 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 <cit.>.
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 <ref> 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 <cit.>.
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 <ref>.
The OB associations are identified in Table <ref>, and the mass, the mass divided by the area of the encompassing circle,
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 <ref>, using an A_F275W/E(B-V) of 7.43 <cit.>.
The goodness of the fit <cit.>
is also given in Table <ref>, where a
value of 1 denotes a good fit and a value near 0 means 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 1-50 Myr and radii of the encompassing circles from 20 pc to 300 pc.


lccccrccccc
485pt


11
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)    
M_F275W,0     (M)     (yr)    
(Mpc^-2)     of fit     E(B-V)

DDO 50         1      8 19 17.4     +70 43 42      43.4     -11.65±0.002     3.90^-.07_-0.28     6.48^+0.12_-0.48      0.128     0.8     0.22^+0.04_-0.07 

               2      8 19 29.1     +70 43  3      56.8     -12.19±0.001     4.25^-.08_-0.28     6.30^+0.30_-0.30      0.243     0.9     0.11^+0.03_-0.05 

               3      8 19 29.1     +70 42 51      53.9     -11.76±0.001     3.97^-.10_-0.30     6.48^+0.12_-0.18      0.009     0.9     0.09^+0.03_-0.08 

               4      8 19 30.2     +70 42 41      65.1     -11.54±0.001     4.05^-.10_-0.28     6.00^+0.60_-0.00     -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^-.08_-0.26     6.48^+0.12_-0.18     -0.239     0.9     0.14^+0.04_-0.06 

               6      8 19 27.9     +70 42 19     105.5     -12.62±0.001     4.38^-.03_-0.22     6.60^+0.00_-0.60     -0.164     0.9     0.04^+0.07_-0.03 

               7      8 19 29.3     +70 42 29      45.7     -11.08±0.004     4.06^+0.00_-0.23     7.00^+0.00_-0.00      0.243     0.0     0.23^+0.06_-0.05 

               8      8 19 12.2     +70 43  8      94.9     -13.58±0.001     4.86^-.08_-0.25     6.00^+0.30_-0.00      0.408     1.0     0.11^+0.05_-0.03 

               9      8 19 27.4     +70 41 58      59.8     -12.34±0.001     4.34^-.10_-0.25     6.00^+0.30_-0.00      0.290     0.9     0.14^+0.05_-0.04 

              10      8 19 25.9     +70 41 53      59.2     -10.89±0.002     3.73^-.08_-0.18     6.70^+0.00_-0.00     -0.312     0.8     0.02^+0.03_-0.02 

              11      8 19 23.5     +70 41 53      93.8     -11.25±0.001     4.39^-.03_-0.19     7.18^+0.00_-0.03     -0.051     0.4     0.03^+0.04_-0.03 

              12      8 19 23.0     +70 42  3      64.5      -9.66±0.003     3.41^+0.36_-0.13     6.85^+0.27_-0.24     -0.706     0.5     0.00^+0.23_-0.00 

              13      8 19 23.1     +70 42 58      90.3     -12.02±0.002     4.02^+0.18_-0.25     6.48^+0.70_-0.00     -0.388     0.1     0.16^+0.04_-0.16 

              14      8 19 30.5     +70 42 56      55.1     -10.19±0.002     3.95^+0.02_-0.35     7.15^+0.03_-0.45     -0.029     0.9     0.02^+0.16_-0.02 

              15      8 19 10.1     +70 43 17      82.6     -11.86±0.001     4.48^+0.39_-0.25     7.00^+0.30_-0.05      0.148     0.6     0.09^+0.13_-0.04 

              16      8 19 17.0     +70 42 40      34.0     -10.72±0.004     3.50^-.08_-0.26     6.48^+0.12_-0.00     -0.060     0.4     0.26^+0.04_-0.06 

              17      8 19 23.8     +70 42  8      34.6      -9.64±0.003     3.22^-.10_-0.30     6.30^+0.30_-0.30     -0.355     0.9     0.05^+0.06_-0.04 

DDO 53         1      8 34  6.9     +66 10 56      86.5     -12.61±0.001     4.21^-.08_-0.26     6.48^+0.12_-0.18     -0.161     1.0     0.13^+0.04_-0.06 

               2      8 34  9.8     +66 10 44      42.9      -9.44±0.004     3.55^-.07_-0.15     7.18^+0.00_-0.03     -0.212     0.6     0.00^+0.02_-0.00 

               3      8 34  7.8     +66 10 51      37.3     -10.39±0.003     3.50^-.10_-0.26     6.00^+0.60_-0.00     -0.140     0.9     0.10^+0.05_-0.04 

               4      8 34  8.7     +66 10 52      19.7      -9.70±0.003     3.17^-.08_-0.28     6.30^+0.30_-0.30      0.084     0.9     0.03^+0.05_-0.03 

               5      8 34  8.4     +66 10 49      22.5      -9.74±0.004     3.07^-.08_-0.26     6.48^+0.12_-0.00     -0.132     1.0     0.08^+0.04_-0.06 

               6      8 34  8.7     +66 10 38      30.2      -8.69±0.006     2.72^-.06_-0.27     6.70^+0.00_-0.22     -0.738     0.2     0.01^+0.04_-0.01 

               7      8 34  3.8     +66 10 37      31.6     -10.03±0.003     3.28^-.06_-0.25     6.70^+0.00_-0.22     -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^-.03_-0.15     7.18^+0.00_-0.03     -0.489     0.3     0.00^+0.04_-0.00 

               9      8 34  3.4     +66 10 41      42.2     -10.52±0.003     3.47^+0.16_-0.30     6.70^+0.48_-0.22     -0.278     0.5     0.11^+0.04_-0.11 

              10      8 34  9.7     +66 10 38      33.8     -10.50±0.004     3.77^-.01_-0.22     7.00^+0.04_-0.00      0.216     0.1     0.18^+0.04_-0.05 

              11      8 34  6.0     +66 10 21      33.8      -9.34±0.004     3.01^-.06_-0.21     6.70^+0.00_-0.00     -0.544     0.8     0.03^+0.04_-0.03 

DDO 63         1      9 40 45.1     +71 11  0     237.9     -12.05±0.002     4.42^+0.37_-0.16     7.00^+0.30_-0.00     -0.830     0.4     0.02^+0.12_-0.02 

               2      9 40 34.0     +71 09 58     304.4     -12.46±0.001     4.59^+0.37_-0.12     7.00^+0.30_-0.52     -0.874     0.2     0.00^+0.24_-0.00 

               3      9 40 39.5     +71 10 13     109.4     -11.86±0.003     4.05^-.08_-0.25     6.00^+0.30_-0.00     -0.525     1.0     0.14^+0.05_-0.04 

               4      9 40 24.7     +71 10 25     131.5     -11.76±0.003     4.22^-.03_-0.22     7.00^+0.04_-0.00     -0.515     0.0     0.15^+0.04_-0.05 

               5      9 40 18.2     +71 11 22     129.2     -11.53±0.001     4.38^-.07_-0.11     7.18^+0.00_-0.00     -0.340     0.0     0.00^+0.02_-0.00 

               6      9 40 35.5     +71 10 44     156.0     -12.03±0.004     4.29^+0.03_-0.21     7.00^+0.04_-0.05     -0.594     0.0     0.20^+0.05_-0.04 

NGC 3738       1     11 35 47.4     +54 31 33     260.8     -15.44±0.000     6.23^+0.46_-0.21     6.95^+0.74_-0.26      0.900     0.9     0.01^+0.39_–.15 

               2     11 35 48.4     +54 31 18     138.4     -13.77±0.001     6.12^+0.06_-0.71     7.70^+0.30_-0.92      1.341     1.0     0.05^+0.36_–.11 

               3     11 35 48.8     +54 31 26      66.8     -12.48±0.001     5.65^+0.07_-0.71     7.70^+0.30_-0.92      1.503     1.0     0.04^+0.37_–.12 

Haro 29        1     12 26 15.7     +48 29 38      56.7     -14.51±0.001     5.13^-.10_-0.25     6.00^+0.30_-0.00      1.126     0.3     0.12^+0.03_-0.04 

               2     12 26 16.0     +48 29 37      45.3     -13.49±0.001     4.76^-.10_-0.23     6.00^+0.30_-0.00      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^-.10_-0.25     6.00^+0.30_-0.00      0.520     0.8     0.18^+0.04_-0.03 

               4     12 26 16.3     +48 29 40      57.8     -12.57±0.002     4.37^-.10_-0.25     6.00^+0.30_-0.00      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^-.11_-0.25     6.00^+0.30_-0.00      0.574     0.1     0.24^+0.03_-0.04 

               6     12 26 17.2     +48 29 39      54.4     -12.48±0.002     4.20^-.05_-0.22     6.60^+0.00_-0.12      0.231     0.7     0.14^+0.07_-0.03 

               7     12 26 16.9     +48 29 38      23.8     -10.81±0.007     3.54^-.05_-0.24     6.60^+0.00_-0.30      0.289     0.9     0.24^+0.07_-0.04 






 §.§ LEGUS star formation rate maps


We also make use of SFR surface density maps produced by 
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 <cit.>.
We followed the method of Jarrett <cit.>

and the prescription by <cit.>, 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 <cit.>,
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 <cit.>.
The maps use a Kroupa IMF from 0.1 to 100 M with a SFR timescale ≥100 Myr <cit.>.
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
<cit.>.

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 <cit.>.
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 one sigma. The integrated SFR from GALEX FUV
given in Table <ref> from <cit.> is 50% lower than the <cit.> value.



 §.§ Galactic environments


The LITTLE THINGS data sets include
-line maps obtained with the Very Large Array interferometer (VLA[
The VLA, now NSF's Karl G. Jansky Very Large Array (JVLA), is a facility of the National Radio Astronomy Observatory.
The National Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.]).
The  maps are characterized by high sensitivity (≤1.1 Jy beam^-1 per
channel), high spectral resolution (≤2.6 ), and high angular resolution (∼6).
To obtain maps of gas surface density, we
converted the naturally-weighted integrated (moment 0)  maps to units of column density ()
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 <cit.>, and with L_V we determined the
stellar mass in each pixel. (Note that we do not use WISE NIR 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 <cit.> for a discussion on the effect of lack of red colors on stellar mass estimates).
From <cit.>
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 <cit.> stellar initial mass function to the <cit.> function
used in the cluster and OB association masses as indicated by <cit.>.
The integrated  maps and stellar mass maps are shown in Figure <ref>.

The  and stellar surface density maps were combined at their native resolutions to produce maps of the hydrostatic mid-plane pressure in each galaxy:

    P = 2.934×10^-55×Σ_gas(Σ_gas + (σ_g/σ_*)Σ_*)     [g/(s^2 cm)],

where Σ is a surface density and σ is a velocity dispersion <cit.>.
Here, Σ_gas is determined solely from +He since the molecular H_2 content is unknown.
Although the molecular gas is more closely tied to star formation than the atomic, the +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  clouds in low metallicity environments,
so if molecular content was known and included, it would probably increase the pressure in the higher pressure regions
rather than increasing the pressure in low  density regions.
The gas velocity dispersion was derived from the  moment 2 maps.
The stellar velocity dispersion was estimated using logσ_* = -0.15M_B - 1.27 from <cit.>,
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 Σ_gas^2,
the pressure maps are dominated by the .

We estimate the uncertainties in Σ_HI in the integrated  moment 0 map
from the  data cube channel rms <cit.> and
assume 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 6 channels.
We take a typical pressure region of radius 200 pc and determine the number of  pixels N summed
in such a region for the galaxy's distance, and the uncertainty in Σ_HI goes as √(N).
The uncertainty in logΣ_HI 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  surface density of 10 M pc^-2, the uncertainty in Σ_HI is 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 Σ_HI^2, so the uncertainty of log P is 2× the uncertainty of logΣ_HI.

For an idea of what to expect related to pressure,
Figure 2 of <cit.> 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 mid-plane pressure in the solar neighborhood is of order 3×10^-12 g s^-2 cm^-1, near the
boundary between bins 2 and 3 <cit.>.
The pressure in typical  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 <cit.>, putting the typical dIrr disk at the boundary
between the lower pressure bins 1 and 2.
By contrast typical giant molecular clouds have much higher internal pressures, of order 4×10^-11 g s^-2 cm^-1 <cit.>,
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 and isolate high and low pressure areas.
The pressure maps with the regions encircled are shown in Figure <ref>.
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 <ref> through <ref> 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.

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.




§ RESULTS
 



 §.§ Cluster characteristics
 



  §.§.§ Characteristics as a function of galactic properties
 

In Figure <ref> we plot the cluster CI and mass against their
galactic environmental properties of pressure, stellar mass density, and  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  surface densities. However,
the clusters in NGC 3738 and Haro 29 are generally found at higher
pressures, stellar mass densities, and  surface densities than the clusters in the other two galaxies.
Haro 29 is likely an advanced dwarf-dwarf merger <cit.> and NGC 3738 may be, too <cit.>.
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 <cit.> <cit.>.



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.


To check whether a correlation between cluster characteristics with galactic environmental properties was being
lost in noisy cluster data, we produced Figure <ref> 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 <ref>  is for all compact clusters with ages up to 100 Myr. In
Figure <ref> we plot the same quantities but only for clusters with ages up to 10 Myr.
There are fewer clusters (see Table <ref>), but again, no trend of cluster properties
with environmental properties is seen.

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 <cit.> <cit.>.
Another possibility is that once the conditions for clustered star formation are reached,
the gravitational collapse and the fragmentation properties of the ISM drive the final star formation efficiency within the regions,
thus making cluster formation a local and stochastic process <cit.>.
Current studies of the initial cluster mass function 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 mid-plane pressure could be explained if dynamical stellar processes,
within the gravitationally bound regions where clusters formed, operate on very short time scales <cit.>,
canceling any memory of the initial conditions.
This fast dynamical evolution, which includes stellar feedback, merging of sub-clumps 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 <cit.>.

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 <cit.>.

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 if 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 pc to 150 pc in steps of 25 pc,
150 pc to 300 pc in steps of 50 pc, and 300 pc to 1 kpc in steps of 100 pc, for a total of 15 circles.


Annuli were constructed as the area between two successive circles.

We make plots like Figure <ref> 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 on-line materials associated with this paper.
In Figure <ref> we show the same panels as in Figure <ref>, 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 <ref> we also plot the cluster characteristics against pressure for annuli 1, 7, and 15 (radii of 38 pc, 225 pc, 950 pc)
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.

In Figure <ref> we also compare for each cluster the environmental characteristics measured in the regions
shown in Figure <ref> 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 formed 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.



  §.§.§ Characteristics by pressure region
 

To look at the role of pressure in another way, we examine the clusters of the pressure regions of Figure <ref>
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 (s^2 cm)^-1.
These bins were chosen by eye based on groupings of clusters and are marked with vertical dashed lines in Figures <ref>-<ref>.
Note that we are only including the regions outlined in Figure <ref>.
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 <ref> we plot the fraction of the total area covered by each pressure bin (panel a) and the
fraction of the  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  mass against the fraction of the   mass in pressure bin 3 in Figure <ref>.
We see that the ratio of cluster mass to  mass is independent of the fraction of the  mass in pressure bin 3 although only two
galaxies have clusters in bin 3.

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  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 <ref> 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 has a measured
SFR in bins 1 and 2.
We see that, generally the higher pressure bins have a higher SFR surface brightness.
In the right panel 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 middle 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 <ref>, panel (c),
is mainly a reflection of the fact that both the mass formed in clusters
and SFR are higher in higher pressure regions <cit.>.
Figure  <ref>, right panel, is also consistent with the finding by <cit.>
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,
higher SFR enables sampling the cluster mass function at the high mass end <cit.>.








  §.§.§ 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 <ref>, but the sum of the clusters whose environmental
pressures fall into the three pressure bins defined in Section <ref>.
We have included only clusters from the team catalogues that have classes of 1 or 2 since these are compact clusters
and more likely than multi-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 <cit.>.

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 
Cook et al. (2018b, in preparation) particularly in relation to dwarf galaxies.

In Figure <ref> 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 the second pressure bin 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 <ref>, panel (c).

However, our dIrrs do scatter around the sequence of Γ vs. SFR density found in other galaxies
<cit.>: for the middle 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 <ref>, 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 accordingly to pressure bin. The range of SFR densities for low pressure bins (blue arrows) reaches one magnitude 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 magnitudes, 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 <cit.>.

In that context, DDO 50 and Haro 29 are significantly different from NGC 3738 in this sample.
In 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 enables us to estimate Γ within smaller age ranges 
Cook et al. (2018b, in preparation).



 §.§  regions
 

For many of the LITTLE THINGS galaxies, including four of the galaxies in this paper, we also have catalogues of  regions to a completeness limit of about 2×10^32 ergs s^-1 pc^-2
<cit.>.
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  region.
Therefore, we made the equivalent of Figure <ref> for the  regions, which we present in Figure <ref>.
We characterize the  regions by the  surface brightness: the integrated  luminosity divided by the area covered by the  region
<cit.>.
The diameters of the  regions range from 10 pc to 500 pc.
In Figure <ref> the bottom panels show the  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  region.
With the larger sample, we do see a correlation: as galactic pressure increases, the  region  surface brightness also increases. There is no correlation between diameter of the  region and pressure.
We would expect the  surface brightness to be determined by the concentration of massive stars and gas.
So this suggests that higher concentrations of massive stars and gas are preferentially found in regions with higher pressure.




 §.§ OB associations
 

The OB associations are outlined in Figures <ref> to <ref>, and their properties are
given in Table <ref>.
These objects are large and loose associations of O stars, which are distinct from the cluster catalogues'
class 3 objects that are compact associations.
One can see from the summary of total numbers given in Table <ref> that DDO 50, DDO 53,
and DDO 63 have more OB associations than clusters. Even DDO 63 that has no clusters has six OB associations.
So 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 DDO63.
OB association #1 in NGC 3738 is very large, encompassing half of the optical galaxy within 0.5 disk scale length radius
<cit.>.

The equivalent of Figure <ref> is shown for the OB associations in Figure <ref>.
The OB association characteristics of stellar mass and mass surface density are plotted against
environmental characteristics of pressure and  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  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 middle pressure bin. The OB associations of DDO 53 and DDO 63 tend to be found at lower  densities.



 §.§ O star distributions
 

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 <ref> to <ref>.
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.



  §.§.§ Characteristics as a function of galactic characteristics
 

In Figure <ref> we plot the O star equivalent of Figure <ref>:
stellar M_F275W against the three environmental characteristics
pressure, stellar mass density, and  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.

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) extend to ∼ -5.5,
DDO 63 (4.0 Mpc) extend to ∼ -6,
NGC 3738 (4.9 Mpc) extend to ∼ -6,
and Haro 29 (5.9 Mpc) extend to ∼ -6.5.
Therefore, the change in the lower limits are 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 <ref> 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 catalogues, 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 <cit.>.

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 <ref>.
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
inter-comparison of stars.
<cit.> 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 <cit.>.
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 RA and Dec centered around 11^h 35^m 49.0^s,
54^o 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 magnitudes, 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 <ref>).



  §.§.§ Characteristics by pressure region
 

In Figure <ref> 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.

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

Figure <ref> is similar to Figure <ref> 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 <ref> showed that the maximum absolute F275W magnitude of the O stars
increases with pressure bin.
By contrast, in Figure <ref> 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.



In Figure <ref>, left, 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 Xs are the ratio of the sums of clusters and O stars in all 5 galaxies.
We see that the ratio increases with pressure.

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 initial mass function, 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 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 <ref> 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 Xs in Figure  <ref>), 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.




§ SUMMARY
 

In order to examine the role environmental factors play in determining characteristics of typical star-forming units,
we present a comparison of the concentrations, masses, and formation rates of young (≤100 Myr)  compact star clusters,
surface brightnesses of  regions, masses and mass surface densities of large and loose OB associations,
and distributions and F275W magnitudes of candidate O stars
with surrounding galactic pressure, stellar mass density,  surface density, and SFR surface density.
Our sample consists of three dIrr galaxies and two BCD-like galaxies within 5.9 Mpc. For  region characteristics
we include an additional 25 dIrrs and BCDs from the LITTLE THINGS sample.
We find the following:




  * The BCD galaxies are more extreme than the dIrrs: most  of  their clusters, OB associations,
and O star candidates are found at higher pressures, stellar mass
densities, and  mass densities. In addition NGC 3738 has an extraordinary OB association that
occupies half of the inner part of the galaxy <cit.>.
Both of these galaxies may be dwarf-dwarf mergers <cit.>, and perhaps such events
are necessary to produce large numbers of clusters or extraordinary regions in dwarfs.


  * There is no trend of cluster characteristics with environmental properties,
implying that larger scale effects are more important in determining cluster characteristics
<cit.> or that rapid dynamical evolution
(such as stellar feedback, merging of sub-clumps in the young cluster, tidal stripping by the host galaxy)
 is taking place in bound stellar systems that erases memory of the initial conditions.


  * The most massive OB associations are found at higher pressure and  surface densities,
and there is a trend of higher  region  surface brightness with higher pressure, suggesting
that a higher concentration of massive stars and gas are found preferentially in regions of higher pressure.
Furthermore, the SFR per unit area increases with pressure.


  * The number of  clusters and total mass in clusters per unit area and per unit gas mass generally increase
with pressure, while the mass formed in clusters divided by the SFR is approximately a constant with pressure.


  * Γ, the ratio of cluster formation rate to SFR, does not show a correlation with the total SFR density,
but the galaxies studied here do scatter in Γ around the sequence of Γ vs. SFR density found in other galaxies.


  * O star candidates are found at a wide range of pressures, including low pressures where bound clusters and
OB associations are not found. 


  * The number of candidate O stars and the integrated F275W flux per unit area and per unit  gas mass increase with pressure.
Furthermore, the total O star F275W flux per unit SFR and the third brightest absolute F275W magnitude of an O star
increase with pressure.
This 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.


  * The ratio of the number of  clusters to number of O star candidates increases with pressure, perhaps
reflecting an increase in clustering properties with star formation rate.



Results presented here are based on observations made with the NASA/ESA Hubble Space Telescope
under the LEGUS survey.
Support for HST Program number 13364 was provided by NASA through a
grant from the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Incorporated, under NASA
contract NAS5-26555.
A.A. acknowledges the support of the Swedish Research Council (Vetenskapsrdet) and the Swedish National Space Board (SNSB).
S.G. appreciates funding from the National Science Foundation grant AST-1461200 to Northern Arizona University for
Research Experiences for Undergraduates summer internships
and Drs. Kathy Eastwood and David Trilling for running the NAU REU program in 2016.
S.G. also appreciates the support of the 2016 CAMPARE Scholar program and Dr. Alexander Rudolph for directing that program.


Facilities: HST(ACS,WFC3), VLA, Lowell Observatory


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