The Distribution of Dense Cores near HII Regions
DDraft version August 16, 2019
Typeset using L A TEX manuscript style in AASTeX62
The Distribution of Dense Cores near HII Regions
George Bobotsis and Michel Fich Department of Physics & AstronomyUniversity of Waterloo200 University Ave. WestWaterloo, Ontario, Canada (Received Oct 28, 2018; Accepted Aug 1, 2019)
Submitted to ApJABSTRACTAn investigation of dust emission associated with a large sample of HII regions hasbeen carried out. Stacked results from this sample suggest that each HII region is at ornear the center of a cluster of dense cores, that extends far beyond the HII region, andhas volume density that decreases as r − . The data also shows evidence for enhancednumbers of cores near the boundary of the HII regions. At the same time, a significantdecrease in the number of cores, consistent with no cores, is observed in the interior ofthese HII regions. Neither these HII regions, nor their associated massive OB stars werefound to have a significant heating effect on their associated dusty clumps. “Clouds”, orthe outermost layers of the clumps in which the cores are embedded, are found to exerta strong shielding effect to external heating sources. Despite this, a large portion of theidentified cores was found to be warmer than their surrounding cloud and consequentlymay be in the initial stages of star formation. The star formation efficiency of the 7HII region systems with the most reliable mass budgets ranged between 1% and 9%. a r X i v : . [ a s t r o - ph . GA ] A ug Bobotsis and Fich
Keywords:
Star Formation, Collect-Collapse, HII Region, Molecular Clump, Dust, Gas,SCUBA-2, VLA INTRODUCTIONMuch of the study of the formation of stars focusses on the process of how a denser part of the “In-terstellar Medium” (ISM) evolves into a pre-main sequence star. However few stars form in isolation.There have been a number of studies in the past investigating the feedback of individual HII regionsincluding some that find evidence for feedback and other studies that have found no or very limitedsigns of feedback. In this paper, we use submillimeter wavelength observations of dust emissionto look at the relationship between HII regions and the dense interstellar material associated withthem. We measure the physical properties of this material, determine how it is distributed aroundthe HII regions, and look for signs of interactions taking place. Overall, we were able to amass alarge number of observations of many HII regions in order to set some constraints on their feedbackin general as well as to understand how important feedback is on average.An HII region is the product of one or more massive, OB stars embedded in a molecular cloud.The ionizing radiation provided by the parent OB star(s) not only drives the outward expansion ofthe HII region, but can also heat nearby clumps while progressively eroding them away by graduallyionizing them. Sandford et al. (1982) have suggested that dusty clumps bombarded by ionizingradiation can be lead to collapse due to the large radiation pressure exerted on their outer layers, butalso, the large extinction of the dusty content delays the ionization of gas in their interior regions.These claims have been followed up with analytic models (Kovalenko & Shchekinov 1992) as well assimulations (Motoyama, Umemoto, & Shang 2007), (Bisbas et al. 2011). This process of formingstars is now commonly referred to as “Radiative Driven Implosion” (RDI).Furthermore, older (post-Str¨omgren-sphere) HII regions have slowly-expanding, shockwave-ionization-front structures, whose propagation can have dramatic effects on the local ISM. More specifically, the
II Regions and SCUBA-2 Cores
Bobotsis and Fich total of 53 HII regions. Many of these results are only accessible through the use of such a largesample, which, to the best of our knowledge, has never been available before. The HII regionscomprising this sample are all larger, more evolved, mature objects, in which the effects of feedbackare expected to be most pronounced. OBSERVATIONSThe sample of HII region systems analyzed is comprised exclusively of mature, galactic HII re-gions taken from the “Sharpless” (Sh-2) (Sharpless 1959) and “Blitz-Fich-Stark” (BFS) (Blitz, Fich,& Stark 1982) catalogues. These catalogues select HII regions from the Palomar Sky Survey, aset of optical large (6 degree) images of the sky. This results in a sample of objects that haveevolved beyond the compact stage where they are still deeply embedded in, and obscured by, denseclouds. The smallest HII regions visible on these images are approximately half an arcminute inangular size but the largest may cover several degrees. Our sample is drawn from those that haveVLA observations available. This in practice limits the sample to objects less than ≈ (cid:48) in diameter.The properties of these HII regions are determined using 1.46 GHz and 4.89 GHz VLA data (Fich1986, 1993). This data was only available for 48 of the 53 HII regions located on these SCUBA-2images. The position and size of the HII regions is determined using the 10% flux contour of theirradio-continuum emission, which is subsequently fitted to a circle. Number densities are determinedusing the simplified expression from Mezger & Henderson (1967) along with small corrections forthe radio observing band and the use of a cylindrical approximation, and an electron temperature of ≈ × K , equal to the average electron temperatures of all HII regions analyzed in the work ofRudolph et al. (2006). To determine the physical radii used in this expression, radial distances pro-vided by Foster & Brunt (2015) are used, and when those aren’t available, older estimates compiledby Chan & Fich (1995) are used instead. The masses are determined by incorporating the overallnumber density, and assuming an abundance ratio He ++ /H + ≈ He + /H + = He/H ≈ . II Regions and SCUBA-2 Cores µ mand 850 µ m SCUBA-2 data was used, which was collected from various projects from the “CanadianAstronomical Data Center” (CADC) archives and reduced using a standard data reduction pipelineprocedure (Holly & Currie 2014). The resolution of the SCUBA-2 instrument allowed the separationof these clumps into a warm outer layer “cloud” and one or more inner, dense condensations “cores”.Photometry of the clumps was obtained using a scripted routine in Python. The routine treatsthe cloud and embedded cores individually, with the cloud flux always removed from that of theembedded cores. In addition, negative bowl artifacts persisting after the application of a mask duringdata reduction are treated on a clump-by-clump basis. This is done by approximating the residualnegative bowl as a step function, whose value is estimated using small, circular apertures that areemployed along the periphery of the source with the goal of finding the most negative mean fluxper pixel value occurring there. Once found, this value is used to characterize the negative bowl,and allows its removal from the source flux. Finally, the contamination in the 850 µ m band from themolecular CO(3-2) transition is treated using a correction factor of 10%. The choice for this valuecomes from consideration of SCUBA-2 surveys of NGC 1333, NGC 2071 and NGC 2024 by Drabeket al. (2012) in which the majority of SCUBA-2 sources experienced contamination levels less than20%, but also, a survey of the Taurus star-forming region by Buckle et al. (2015) within which allSCUBA-2 sources experienced a contamination level less than 15%, with a large number of sourcesnot exceeding a contamination level of 5%.The opacity model used is the one originally proposed by Ossenkopf & Henning (1994) foruse with protostellar cores. Due to the limitations from the consideration of only two submillimeterbands (450 µ m and 850 µ m), a prescribed value of β = 1 . H by-mass are also assumed throughoutthese calculations. Bobotsis and Fich (a) Sh-2 168 (b) Sh-2 201(c) Sh-2 242 (d) Sh-2 305
Figure 1.
A collection of 4 HII regions representing the variety of SCUBA-2 condensation morphologiesencountered in this work. The images consist of SCUBA-2 850 µ m emission overlaid with VLA 1.46 GHzcontours. The contours are color-coded based on confidence level multiples (blue/cyan/green/orange/red → σ ,2 σ , 3 σ , 4 σ , 5 σ ). The yellow ”x” ticks indicate the location of identified cores. A comprehensive list of properties was made for all identified cores and clouds of this sample.This included measured properties such as positions, size and 450 µ m/850 µ m flux, but also severalderived properties, such as average temperature, total mass, average column density and average II Regions and SCUBA-2 Cores µ m and 850 µ m systems investigated, 31 (82%) had one ormore dusty clumps identified in the vicinity of an HII region from the considered sample. A total of185 clumps and 333 cores were identified, and after discarding a few of these objects on the premisethat they were too far from the nearest HII region for an association to exist, 176 clumps (95%) and315 embedded cores (95%) continued to analysis.We portray the variety of structures we encountered with a set of 4 representative cases in Fig-ure 1. The most commonly seen structure (58% of our fields) have 4 or fewer dense cores embeddedin a few clumps as seen in the object Sh-2 201 in this Figure. 81% of our image fields have 20 orfewer dense cores, with a few cases where most or all of the cores are embedded in one massive clumpas in Sh-2 242 in Figure 1. Only six of our fields (the remaining 19%) show large numbers of cores(28 to 49 cores) as seen in Sh-2 168 and Sh-2 305 in Figure 1. However these six fields contain 69%of the dense cores in our sample. Many of the dense cores are found far beyond the boundary of theHII region: we examine the radial distribution of the positions of these cores below. RESULTS3.1.
Summarized Properties
Our sample was selected to include virtually all of the HII regions with data in the SCUBA-2archives. Nonetheless, we excluded a handful of more extreme HII regions, such as very nearbyand/or large in angular extent (e.g. the Orion HII region). Also, our sample was not selected byprioritizing similarity, such that it covered a small range in distance, angular size or brightness.Despite this, the measured and calculated properties for this sample were remarkably uniform. Table1 summarizes the properties of the sample, including median values, the “central population” (i.ethe range of each property when outliers are not considered) and finally, the full range.
Bobotsis and Fich
Table 1.
Table of summarized properties for all HII regions and their associated clouds and cores.
Property Median Range (Excluding Outliers) Sample Fraction Full Range
Distance (kpc) 3 . ≤ d ≤ . ≤ d ≤ . (cid:48)(cid:48) ) 100 30 ≤ R ≤
300 90% 24 ≤ R ≤ .
20 0 . ≤ R ≤ . ≤ R ≤ . n e ( cm − ) 40 . ≤ n e ≤
100 79% 7 . ≤ n e ≤ M (cid:12) ) 36 . ≤ M ≤
300 84% 0 . ≤ M ≤ (cid:48)(cid:48) ) 36 20 ≤ R ≤
90 96% 18 ≤ R ≤ .
64 0 . ≤ R ≤ . ≤ R ≤ . µ m Integrated Flux (Jy) 7 .
27 1 ≤ F ≤
40 83% 0 . ≤ F ≤ µ m Integrated Flux (Jy) 0 .
826 0 . ≤ F ≤ . ≤ F ≤ ≤ T ≤
30 82% 7 . ≤ T ≤ M (cid:12) ) 106 . ≤ M ≤ . ≤ M ≤ N H (10 cm − ) 2 .
36 0 . ≤ N H ≤ . ≤ N H ≤ n H ( cm − ) 727 150 ≤ n H ≤ . ≤ n H ≤ (cid:48)(cid:48) ) 12 10 ≤ R ≤
20 85% 4 ≤ R ≤ .
26 0 . ≤ R ≤ . . ≤ R ≤ . µ m Integrated Flux (Jy) 1 .
41 0 . ≤ F ≤ . ≤ F ≤ µ m Integrated Flux (Jy) 0 .
196 0 . ≤ F ≤ . . ≤ F ≤ . . ≤ T ≤
40 83% 6 . ≤ T ≤ M (cid:12) ) 22 . ≤ M ≤
150 84% 0 . ≤ M ≤ N H (10 cm − ) 3 . . ≤ N H ≤
15 80% 0 . ≤ N H ≤ n H ( cm − ) 2990 1000 ≤ n H ≤ ≤ n H ≤ The measured quantities in Table 1 (angular sizes, fluxes) have uncertainties that are typically ≤ ≤ II Regions and SCUBA-2 Cores µ m integrated flux measurement; all clouds and 312 (99%)cores had an 850 µ m integrated flux measurement; 136 (77%) clouds and 206 (65%) cores had anaverage temperature estimate; 129 (73%) clouds and 192 (61%) cores had a total mass estimate; 1330 Bobotsis and Fich (76%) clouds and 203 cores (64%) had an average H column density estimate; and finally 134 (76%)clouds and 203 (64%) cores had an average H number density estimate.A detailed listing of all HII regions and associated clouds and cores along with their individualproperties and their accompanying SCUBA-2 450 µ m and 850 µ m images can be found in the unpub-lished MSc thesis of Bobotsis (2018). A detailed discussion of all sources of uncertainty can also befound there. 3.2. Core Number Counts
As discussed earlier, the systems analyzed in this paper contained a large range of numbers ofcores, with only 19% of the sample containing more than 28 cores. Even the most populated of thesesystems do not have enough cores for a radial distribution profile to be fitted with any significantdegree of certainty.To further elaborate on this problem, we present the unscaled radial core distribution histogramof the 4 representative cases of Figure 1 in Figure 2. In the first 3 panels we have Sh-2 168 with19 cores, Sh-2 201 with 4 cores and Sh-2 242 with 10 cores. It is evident that no meaningful radialdistribution profile can be fitted due to the small number of cores available. For Sh-2 305, eventhough it contains 31 cores, the extended condensation along the HII region boundary is marginallydistinguishable, while the large span of unpopulated bins at intermediate distances from the HIIregion give rise to diverging Poisson counting errors, rendering these locations unusable for the radialprofile fitting procedure.To circumvent this issue, we stacked the counts from all the objects in our entire sample, seek-ing an average radial distribution fit rather than fitting on a case-by-case basis. Furthermore, toachieve a distance-independent result, we scaled the stacked data by the associated HII region radius;the new distance abbreviated simply as “scaled separation distance” from here onwards. It shouldbe noted that in the case of multiple HII regions in the vicinity of a core, the associated HII region
II Regions and SCUBA-2 Cores (a) Sh-2 168 (b) Sh-2 201(c) Sh-2 242 (d) Sh-2 305 Figure 2.
The core unscaled radial distribution profiles of the systems presented in Figure 1, with 30equally spaced bins used for each. The dashed red line indicates the boundary of each HII region. was selected to be the one that shared the smallest scaled separation distance with the core of interest.A cutoff was placed at Θ
SCALED = 12 to segregate cores that were less likely to be associatedwith their nearest HII region. This cutoff corresponds to an angular separation distance anywherebetween 6 (cid:48) and 150 (cid:48) (or 5 . pc and 313 pc ), with the most likely being 25 (cid:48) (or 33 pc ), although thespecific value strictly depended on the radius of the HII region at hand. These distant cores (18 intotal) were not considered in further data analysis. Furthermore, the clouds that ended up with nocores associated to an HII region because of this segregation (9 in total) were also not considered infurther data analysis.2 Bobotsis and Fich
Figure 3.
Two Histograms of core-to-HII Region, center-to-center, separation distances, scaled against theradius of each core’s associated HII region. The power-law of best-fit is displayed in red while the black-dashed line indicates the boundary of our HII regions. The top histogram includes the entire core sample,while the bottom histogram excludes the cores from the two “shell-like” HII regions Sh-2 104 and Sh-2 305.
II Regions and SCUBA-2 Cores
13A scaled separation distance histogram was made for the cores that were within Θ
SCALED ≤ N = c Θ n . Different binning options were tested and allcores existing at bins Θ SCALED ≥ SCALED values, something that is unphysical. Also,the HII regions have almost certainly affected the counts of cores at values Θ
SCALED ≤ N = (31 . ± .
3) Θ ( − . ± . SCALED cores per 12/40 binsize in Θ
SCALED , consistent with a volume number density power-law index of -3.This result is robust to variations of the binning used and the minimum Θ
SCALED bin to be includedin the fit. The other tested fits were within the error limits quoted with power-law indices n thatvaried between -1.3 and -0.8. Note that bins with only 1 counted core did not contribute at all tothe fitting procedure, as their Poisson counting uncertainty is ± +0 . −∞ . Integration of this fit suggests that out of the 315 identifiedcores, 70 ± ≤ Θ SCALED ≤
2, while the actual count was 90 (29%),which is significantly more than the expected amount. Fitting only the region Θ
SCALED ≥ ≈ − N = N π Θ was fitted between 20 ≤ Θ SCALED ≤ N were 4 × − and 1 . × − depending on which of theconsidered bins were assigned a higher weight. This value of N translated to a total of 2 to 6 cores4 Bobotsis and Fich expected to be part of the foreground/background in the entire core sample, and a probability of0.2% to 0.6% for encountering a background/foreground core within 20 (cid:48) from the center of any HIIregion from this sample, two results that rendered the issue of background/foreground contaminationinsignificant.Even though we did not fit for Θ
SCALED ≤
1, we can see that the behavior there is very dif-ferent than Θ
SCALED ≥ SCALED ≤
1, while an excess isseen near Θ
SCALED ≈ SCALED ≤
2, were all re-moved from the core counts and the resulting histogram is presented at the bottom plot of Figure3. A separate power-law fit was made for this histogram for the cores lying outside their associatedHII region (Θ
SCALED ≥ N = (25 . ± .
8) Θ ( − . ± . SCALED with power-law indices n that varied between -1.3 and -0.4; a result less robust than when considering the full sample.Integration of this fit made for the cores at Θ SCALED ≥ ± ≤ Θ SCALED ≤
2, while the actual count was 75 (31%), which is greater than the expectedamount by a larger and more significant amount than in the complete data set calculation above.It is evident that the observation of a large excess in the number of cores near the boundary of theHII regions (Θ
SCALED ≈
1) was unaffected by this experiment, suggesting that the two shell-like HIIregions do not introduce any significant bias in the interpretation of the earlier result.3.3.
Cloud and Core Temperatures
To investigate any heating effect taking place either due to the HII region, or the HII region’sparent star(s), the average temperature of each core and cloud is compared against the physicaldistance between them and their associated HII region, as well as their nearest OB star. The resultsfrom these comparisons are presented in Figure 4. There is no significant heating effect indicated
II Regions and SCUBA-2 Cores Figure 4.
Average temperature against physical separation distance. In order of appearance, the HIIRegion - Cloud (Top-Left), HII Region - Core (Top-Right), nearest OB star - Cloud (Bottom-Left) andnearest OB star - Core (Bottom-Right) comparisons are displayed.
Figure 5.
Average temperature against average H column density for clouds (Left) and cores (Right). Bobotsis and Fich in any of the relationships plotted in this figure. There is a slight trend apparent to the eye for alarger number of high temperature points at physical separation distances ≤ pc , but the statisticalsignificance of this trend is quite low.However, a comparison between cloud and core average temperature against average H col-umn density shown in Figure 5 does show a dependency of high significance for the clouds.The clouds surrounding these dense cores are generally found to be warmer when they havesmaller H column densities. A power-law fit was made for the clouds and the result was N H = (7 . × ± . × ) T ( − . ± . . This is not surprising, since a lower column densitycorresponds to a lower extinction, which in turn means a greater penetration for incoming photonsfrom nearby stars. This observation is consistent with various cooling models for molecular cloudswhich suggest a negative power-law dependency to both column and number density (Juvela, Padoan,& Nordlund 2001). On the other hand, the equivalent comparison for the cores does not show anyconvincing correlation between average temperature and average H column density.We compared the average temperature of all cores to the clouds surrounding them and presentthe result of this comparison in Figure 6. Out of the 315 cores considered, we were able to measure atemperature for 199 (63%) of these cores and their surrounding cloud. Of these 199 cores, 147 (74%)were found to be warmer than their surrounding cloud. No significant correlation between core andcloud average temperature was found. II Regions and SCUBA-2 Cores Figure 6.
Average cloud temperature against average embedded core temperature. A black, dashed line isused to display cloud-core temperature equivalence.
Star Formation Efficiency
The dust emission measured by the SCUBA-2 instrument provides a sensitive measure of the totalmass of material around the young stars near the HII regions considered in this sample. Conse-quently, it is possible to use the masses derived from SCUBA-2 measurements to determine the “StarFormation Efficiency” (SFE) for these systems. The SCUBA-2 measurements provide a separatemeasure from that of spectral line observations of molecules, such as CO.The SFE ( (cid:15) ) was determined for HII region systems with a complete, or almost-complete massbudget by simply comparing their gaseous and stellar mass budgets in the following manner: (cid:15) = 100 × (cid:18) M ST AR M ST AR + M GAS (cid:19) (1)8
Bobotsis and Fich
For the gaseous component, the mass of the ionized gas plus the masses of all clouds and cores aresummed together. The ionized gas mass is generally less uncertain than the cloud and core massesbecause the estimates of the latter are derived from dust mass which can sometimes suffer excessivelyfrom noisy 450 µ m photometry.For the stellar component, the mass of the massive OB stars is summed separately from that ofthe low and intermediate-mass stars, which is estimated using a Kroupa (2001) “Initial Mass Func-tion” (IMF). A maximum stellar mass must be set to use the Kroupa IMF. For each object wehave determined the OB stars associated with the HII region. We only calculate the SFE for thoseobjects where we find such OB stars located within or near enough the HII region to be the excitingstars. We use the least massive OB star in each HII region as the upper limit for the Kroupa IMFdetermination of the mass of the stars with lower masses.This assumes that all HII region systems have a complete account of their associated, massiveOB stars, and consequently the mass contributed from these. Identifying the OB stars associatedwith each HII region is likely the largest uncertainty contributor in the stellar mass budget. Thecalculated SFE values are presented in Table 2, with detailed descriptions of each system, includingimage diameters and 450 µ m/850 µ m noise-per-pixel values.Of the 31 HII region systems in our sample, only 16 (52%) had a sufficiently complete gas andstar mass budget for an SFE estimate to be made. Of these, a majority of 9 systems displayed SFEvalues below 10%, while 5 systems consisted of large-value outliers, and another 2 systems had veryincomplete gas mass budgets, leading to only an upper limit estimate for their SFE (indicated in redin Table 2). The first of these 2 systems was G173B which had an SFE value of 72.6%. This systemis comprised of 2 HII regions (Sh-2 234 and Sh-2 237), 4 submillimeter-emitting clumps, of whichonly 1 had a determined total mass, and an unusually large list of 15 potentially associated OB stars,of which several may not be associated with the 2 HII regions of the system. The second of the two II Regions and SCUBA-2 Cores Table 2.
Table of HII region systems whose SFE was obtainable from our data. Columns in order ofappearance indicate (1) System ID (2) Contained HII regions (3) SFE, and (4) a short description of eachsystem justifying assigned uncertainty. Systems in red are of very high uncertainty.
System HII Regions SFE (%) Description
G70 Sh-2 99,100 1 . ± . (cid:48)(cid:48) , [ N , N ] = [5 , .
3] mJy/beamG74 Sh-2 104 7 . ± . (cid:48)(cid:48) , [ N , N ] = [5 . , .
3] mJy/beamG97 Sh-2 128 2 . ± . (cid:48)(cid:48) , [ N , N ] = [5 . , .
3] mJy/beamG108 Sh-2 152 7 . ± (cid:48)(cid:48) , [ N , N ] = [81 . , .
4] mJy/beamG115 Sh-2 168 29 . +2 − (cid:48)(cid:48) , [ N , N ] = [4 . , .
4] mJy/beamG120 Sh-2 175 26 . +2 − (cid:48)(cid:48) , [ N , N ] = [25 . , .
2] mJy/beamG173 Sh-2 231,232233,235 19 . ± (cid:48)(cid:48) , [ N , N ] = [138 , .
4] mJy/beamG173B Sh-2 234,237 72 . +2 − (cid:48)(cid:48) , [ N , N ] = [187 , .
3] mJy/beamG182 Sh-2 242 9 . ± (cid:48)(cid:48) , [ N , N ] = [8 . , ,
7] mJy/beamG188 Sh-2 247 8 . ± (cid:48)(cid:48) , [ N , N ] = [16 . , .
8] mJy/beamG192 Sh-2 254,255,256,257,258 6 . +4 − (cid:48)(cid:48) , [ N , N ] = [11 . , .
0] mJy/beamG192B Sh-2 255B,259 3 . ± (cid:48)(cid:48) , [ N , N ] = [11 . , .
0] mJy/beamG210 Sh-2 283 29 . +3 − (cid:48)(cid:48) , [ N , N ] = [95 . , .
5] mJy/beamG219 Sh-2 288 69 . +5 − (cid:48)(cid:48) , [ N , N ] = [106 , .
6] mJy/beamG221 BFS 64 37 . +5 − (cid:48)(cid:48) , [ N , N ] = [141 , .
5] mJy/beamG233 Sh-2 305 3 . ± . (cid:48)(cid:48) , [ N , N ] = [5 . , .
2] mJy/beam Bobotsis and Fich systems was G219 which had an SFE value of 69.1%. This system is comprised of 1 HII region (Sh-2288), 1 submillimeter-emitting clump and 1 associated OB star. The mass of the single clump isexpected to be very underestimated. This is mostly due to poor atmospheric conditions at the timeof observation, but also, due to the short integration time per pixel used in the scan itself, somethingthat would most certainly render any low-mass clumps in the system practically undetectable. DISCUSSIONIn our analysis, even the 6 most populated HII regions did not have enough cores to produce astatistically significant radial profile fit. However, the entire sample of cores, brought together ina scaled fashion as was done in this work clearly shows an extended core population. Attempts toanalyze this population using un-binned statistics have so far been unsuccessful, in part due to thepresence of a (small) background of cores affecting the large scales and a divergence in the expectednumber of cores at the smallest scales (e.g one needs to also account for the sizes of the cores,especially at the center of the radial distribution).The results of this analysis of the distribution are (1) cores well beyond the HII region are dis-tributed around it such that their number is consistent with a spherical population; (2) there is anexcess number of dense cores just outside the HII regions, even when the obvious shell-like objectsare removed from the sample; (3) the number of dense cores at small distances is consistent with nodense cores existing inside the HII region; (4) the amount of background core contamination is veryinsignificant.Regarding our first result, our number counts are given in number of cores within equally spacedcircular rings. At larger distances from the HII region, far beyond the ionized gas boundary, thenumber of cores decreases approximately as r − ; therefore the surface density of the cores decreasesas r − . We consider two opposite extremes for the large scale distribution of these dense cores: (i) aspherical distribution against a (ii) filamentary structure. II Regions and SCUBA-2 Cores L max ), then the number of dense cores in each ring ( N (Θ scaled ))would follow a functional form proportional to ( L max - Θ scaled ) / , which is very different from theobserved number counts, even having the opposite curvature in the plot. However by using morecomplex filamentary structures, such as a distribution of the lengths of the filaments and/or a non-uniform distribution of the dense cores along the filaments, it is possible to fit these number counts.However, with this level of freedom to choose parameters one could fit almost any number countdistribution.Alternatively if the dense cores are in a spherical distribution at large distances from the HIIregion, then the determination of the distribution function is simple: the volume density of the densecores follows a r − distribution. There would likely be significant dynamical differences betweenthese two extremes (i.e filament versus spherical distribution). This suggests that a kinematic inves-tigation of these cores (e.g. radial velocity observations) would be very useful in making progresson this question. Furthermore, the spherical distribution model would appear to contradict modelsin which massive stars are formed near the edges of GMCs, where an external trigger has beenapplied to start the star formation process. Kirk et al. (2016) have examined clusters of densecores in Orion B and found that the most massive of these cores is near the center of each “densecore cluster”. They suggest that mass segregation has already occurred before the first star forms,and that the most massive star will then form in the center of this cluster. This is consistent withour result, where the massive OB star forming an HII region is at the center of a cluster of dense cores.Our second result that there are additional cores in a shell around the outer edge of the HIIregion, seems to be true in general, not only for the few obvious, generally well-studied, shell-like HIIregions. This may suggest that collect and collapse models are useful to describe most HII regions.Perhaps the lack of obvious shells around many HII regions is simply the result of lower densities of2 Bobotsis and Fich surrounding material.The idea that these HII regions have shells of dense cores around and immediately outside theionized region does not contradict the selection criteria that these HII regions are all very obvious invisible light. In theory these shells are expected to be far from uniform in density with strong insta-bilities causing the production of denser regions with these shells. This is observed. Many, perhapsmost, visible HII regions show patches at a few positions where the emission from recombinationis completely absorbed. However, when averaged over much of their surface area, the extinction tothese HII regions is typically only a few magnitudes as seen in many studies including from measure-ments of the Blamer decrement over large apertures (Fich and Silkey, 1991). Even deeply embedded,presumably younger HII regions show the neutral material in very clumpy structures with sphericalshells in 3D (Topchieva et al., 2018,2019).This is further complicated by the observation that many HII regions that are seen in the visi-ble are on the near side of large molecular clouds and emerging towards the observer, with much lessneutral material on the near side than on the far side. However, even these HII regions will still showstrong enhancements in the numbers of dense cores along the edges of the visible region when seen inprojection on the sky, with smaller numbers, from the far side, seen at smaller projected distances.Our third result from the core radial distribution is that the number of dense cores within theHII region boundary is small, and not of great surprise. There will be a significant number of coresseen in projection through the HII regions from the large scale distribution and from a shell aroundthe boundary of the HII regions. The number seen from the boundary shell, through or in front ofthe ionized gas, depends on the thickness of the shell, and the number in this shell is always less thatthe number seen around the projected edges of the HII region. There is no need to match the numbercounts for there to be any dense cores within the ionized gas region. This does not mean that suchobjects (dense neutral cores) will never be seen within HII regions but the numbers strongly suggest
II Regions and SCUBA-2 Cores T and N H correlation also suggests that a “shielding” effect is in-place, where essen-tially the outer cloud layer allows progressively less external radiation from reaching the inner corecondensations by virtue of its extinction, which in-turn prevents the interior cores from being heatedto any significant extent by external radiation.Our last temperature result was that most cores ( ≈ Bobotsis and Fich that the presence of the HII region has caused most of the nearby cores to begin collapse, becomingwarmer in the process. An alternative is that the cores are all on similar schedules, beginning toform into stars at the same time, but the most massive core has evolved faster, producing an OBstar and consequently an HII region which attracts our attention to investigate that part of the sky.Our final result involves the calculation of the “Star Formation Efficiency” (SFE). This requireda determination of the mass in stars compared to the total mass of the system (i.e stars + gas). Themeasurements described here are amongst the few to use the dust emission to measure the gas mass.The dust traces both the atomic and molecular material, an advantage over molecular spectral linestudies. However, on larger scales the submillimeter emission is faint and larger uncertainties ariseas a result. Identifying all of the stellar mass is also problematic, as the parent stars for some HIIregions are not seen, while for some others several candidates exist. Because of these difficulties wewere only able to reliably estimate the SFE for a small fraction of our HII region systems.About half (9) of these HII region systems had very reliable mass budgets and collectively sug-gested SFE values lower than 10%. On the other hand a very small portion (2) of these systems hadunreasonably high SFE estimates, likely due to the much lower reliability of their gas mass budgetas compared to the rest of the sample. Nonetheless, a considerable fraction (5) of these HII regionsystems with modestly reliable mass budgets suggested larger-than-typical SFE values (19.2, 26.2,29.5, 29.7 and 37.5 %). It may be important that for these 5 systems most of the identified ionizingstars are B-type, with only 3 consisting of earlier type, more luminous stars (O9V or O9.5V). Itshould be noted that the lowest SFE estimates were generally made in systems with earlier typestars (O5V, O7V).In order to validate the use of a Kroupa IMF in the determination of SFE values in the vicinity ofionized gas, we focus on the Sh-2 254 complex, which is the only system investigated sufficiently byother authors to allow for direct comparisons to be made. In our present work, we establish the mass
II Regions and SCUBA-2 Cores ≈ M (cid:12) using VLA 1.46 GHz data (Bobotsis, 2018). Inaddition, a lower limit of 3600 M (cid:12) is placed on the total H mass by summing the H mass presentwithin our identified SCUBA-2 clumps (Bobotsis, 2018). These two values together provide a lowerlimit of 3727 M (cid:12) to the total gas mass of the complex. A total star mass of ≈ M (cid:12) is obtainedby extrapolating the Kroupa IMF backwards from the least massive star associated with the region,assuming sample completeness for all mass ranges above that. This results in an upper limit of 6.6%to the average SFE of the complex.In Chavarria et al. (2008) the total gas mass of the complex was found to be ≈ M (cid:12) us-ing CO and CO data. The total star mass was found by converting total star counts to massusing the median YSO mass (0.5 M (cid:12) ). The obtained SFE values vary between 4% and 54% acrossdifferent components of the complex with an uncertainty up to a factor of 2. In order to make theseSFE estimates comparable to our result, we determine the mass-weighted average of the various SFEvalues from Chavarria to be ≈ ≤ M/M (cid:12) ≤ M (cid:12) is made for thetotal star mass contained in the complex. This is also in good agreement with our 265 M (cid:12) estimate.Finally, in Mucciarelli (Mucciarelli, Preibisch, & Zinnecker 2011), an extended Chandra X-raysurvey of the Sh-2 254 complex shows a population of young stars very similar to that expected fromextrapolating Kroupa’s IMF from the lower mass limit of the completely determined star sampledown to star masses of 0.5 M (cid:12) . In summary, the use of a Kroupa IMF to determine the totalstellar mass gives a result that is consistent with that found by others working in this field and using6 Bobotsis and Fich somewhat different assumptions. However, caution should be exercised regarding its use as many HIIregion systems such as the Sh-2 254 complex tend to favor low-mass star production (Lim et al 2015).Regarding our uncertainty for the SFE values presented in table 2, the strong, non-linear depen-dency of our gas mass calculations to the SCUBA-2 450 and 850 µ m flux is expected to significantlydominate. Rigorous calculation of this uncertainty is a complicated statistical problem, due to theinvolvement of non-Gaussian variables as is discussed in Bobotsis (2018). However, we do have agood understanding of this uncertainty level. SFE values prone to high levels of uncertainty arisefrom systems that: • Were detected in one of the JCMT Legacy Surveys • Have an incomplete accounting of massive OB stars • Contain multiple HII regions • Contain a lot of filamentary gas structureSystems that are part of a JCMT Legacy Survey are prone to much higher gas mass uncertainties ascompared to those that were specifically targeted as part of a project simply due to lower integrationtimes and consequently much higher noise per pixel levels across an image, a natural consequence ofbeing part of wide-field survey image.An incomplete budget of massive OB stars influences star mass estimates two-fold. Clearly, anunaccounted massive star would yield a significant change in the total star mass budget. In conjunc-tion to this however, missing such information can interfere with the choice of the upper mass limitused in the IMF for determining the mass of intermediate and low-mass stars in the system.In addition, the interaction between multiple HII region fronts in a particular system clearly in-fluences clump formation and consequently, star formation in their immediate vicinity. Contrary toisolated HII region fronts, these tend to drive SFEs up due to the enhancement of the collect-collapse
II Regions and SCUBA-2 Cores
Bobotsis and Fich ination from molecules such as CH OH and SO , as well as radio-continuum contamination fromthe HII regions themselves would provide even more reliable photometry. Finally, incorporation ofmultiple submillimeter wavelengths would allow the construction of an individual β fit tailored toeach source, as well as the usage of the band couple with the lowest uncertainty when performingflux ratios to determine temperature and subsequent derivative properties, lowering the uncertaintyof the obtained properties overall.Nonetheless, we have measured the properties of the material around a large sample of HII re-gions, all of them at a late stage in their evolution. Our sample was moderately uniform in mostmeasured properties. However our sample does not contain any of the very large and luminousHII regions that are traditionally used as star formation tracers on galactic scales. The clouds ofinterstellar material surrounding the HII regions in our sample are not the Giant Molecular Cloudswhich receive much attention in such studies. The typical masses in this sample are only ≈
1% of atypical GMC mass. However our sample is probably representative of most HII regions. It remainsto be seen how these contribute to overall star formation budgets as compared to the contributionsof the small number of very large HII regions associated with the largest GMCs. ACKNOWLEDGMENTSThe James Clerk Maxwell Telescope has historically been operated by the Joint Astronomy Centreon behalf of the Science and Technology Facilities Council of the United Kingdom, the NationalResearch Council of Canada and the Netherlands Organization for Scientific Research. Additionalfunds for the construction of SCUBA-2 were provided by the Canada Foundation for Innovation.
II Regions and SCUBA-2 Cores