Stellar feedback -the injection of energy and momentum by stars into the interstellar medium (ISM) -originates at the small scales of individual stars and star clusters ( 1 pc), yet it shapes the ISM on large scales ( 1 kpc). Stellar feedback is responsible for the low observed star formation efficiencies in Milky Way giant molecular clouds (GMCs; e.g., Zuckerman & Evans 1974; Krumholz & Tan 2007; Evans et al. 2009; Heiderman et al. 2010; Murray 2011; Evans et al. 2014; Lee et al. 2016 ; Barnes et al. 2017; Vutisalchavakul et al. olivier.15@osu.edu 2016) and across GMCs in nearby galaxies (e.g., Longmore et al. 2013; Kruijssen et al. 2014; Usero et al. 2015; Bigiel et al. 2016; Leroy et al. 2017; Gallagher et al. 2018; Utomo et al. 2018 ). This inefficiency arises from feedback processes that dissolve star clusters (e.g., see review by Krumholz et al. 2019 ) and ultimately destroy their host clouds (e.g., Whitworth 1979; Matzner 2002; Krumholz et al. 2006; Dale et al. 2013) .
Stars have several feedback mechanisms: e.g., radiation, photoionization, stellar winds, supernovae (SNe), protostellar jets, and cosmic rays (see reviews by Krumholz et al. 2019 and , and references therein). Extensive recent efforts have aimed to incorporate many feedback modes in simulations of arXiv:2009.10079v1 [astro-ph.GA] 21 Sep 2020 star-forming cores and GMCs (e.g., Dale et al. 2014; Rosen et al. 2014 Rosen et al. , 2016 Dale 2017; Tanaka et al. 2017 Tanaka et al. , 2018 Rosen & Krumholz 2020) , and in galaxy formation models (e.g. Stinson et al. 2013; Agertz & Kravtsov 2016; Hopkins et al. 2018) . While SNe may be the dominant mechanism in shaping galaxies on large scales (e.g., Hopkins et al. 2018) , pre-SN feedback from the other mechanisms is crucial to reproduce observed GMC properties (e.g., Grisdale et al. 2018; Fujimoto et al. 2019) .
Observational studies are crucial to anchor and test simulations. Individual feedback modes have been assessed for large samples of sources (e.g., Rosero et al. 2019) , and measurements of the relative role of multiple feedback modes have been done for particular starforming regions (e.g. Lopez et al. 2011; Pellegrini et al. 2011; Ginsburg et al. 2017; Lee et al. 2019; Xu et al. 2019 ) and across many regions (e.g. Lopez et al. 2014; Chevance et al. 2019; Kruijssen et al. 2019; McLeod et al. 2019 ; Barnes et al. 2020; McLeod et al. 2020 ). Among these latter works, Lopez et al. (2014, hereafter L14) analyzed multiwavelength data of 32 H ii regions in the Large (LMC) and Small Magellanic Clouds (SMC) to calculate the pressures associated with direct radiation, dust-processed radiation, photoionization heating, and shock-heating from stellar winds and SNe. They found that the warm (10 4 K) gas pressure is the dominant feedback mechanism at the H ii region shells. McLeod et al. (2019) also examined two LMC star-forming complexes using integral-field data from MUSE, characterizing the stellar content, the gas properties, and the kinematics. Consistent with the L14 results, McLeod et al. (2019) determined that photoionization heating drives the dynamics in their sample.
The studies published to date have focused on relatively large (R few pc) and evolved (t few Myr) H ii regions (except the recent work by Barnes et al. 2020) . However, theoretical models (e.g., Krumholz & Matzner 2009; Geen et al. 2020) suggest that mechanisms other than photoionization may be comparatively more important early in the evolution of H ii regions, when they are significantly smaller and younger than the range probed by L14 and other works. To assess this possibility, in this paper we aim to explore how feedback properties differ at earlier stages in massive star formation and how the driving feedback mechanisms evolve with time. We therefore carry out an analysis similar to that of L14 but targeting a radio/IR-selected sample of much smaller, younger H ii regions.
In Section 2, we describe our sample and data used in our analysis. In Section 3, we review our methods for measuring each form of feedback. In Section 4, we present our results, and in Section 5, we discuss the im-plications regarding young H ii region dynamics, their evolution, and how our results can inform stellar feedback modeling in numerical simulations. We summarize our conclusions in Section 6.
To evaluate the role of feedback mechanisms at the earliest stages of massive star formation, we consider 128 young H ii regions: 49 UCH ii regions (defined as those with radii R 0.05 pc), 67 compact H ii regions (with radii 0.05 R 0.25 pc), and 12 small H ii regions (with radii 0.25 R 0.5 pc) from the AT-LASGAL survey . Out of the 128 sources, 106 were resolved in the CORNISH survey (Purcell et al. 2013) , so we measure the feedback pressures in this sample and set limits on these terms for the 22 unresolved sources. The ATLASGAL survey covered a portion of the Milky Way Galactic plane, from longitude 10 • ≤ l ≤ 60 • and latitude −1 • ≤ b ≤ 1 • . These H ii regions were detected in the 5-GHz band by the CORNISH survey (Purcell et al. 2013 ) and in the 870 µm band by the ATLASGAL survey and then confirmed as H ii regions using mid-infrared colors from the GLIMPSE survey (Benjamin et al. 2003; Churchwell et al. 2009 ). The H ii regions have well-defined radii from the 5-GHz measurements and kinematic distances derived by Urquhart et al. (2013) . We require that the regions in our sample have bolometric luminosities measured by Mottram et al. (2011) and reported in Urquhart et al. (2013) . To illustrate the sample, in Figure 1 , we show a three-color image of the massive star-forming region W49A, which contains nearly twenty of the regions considered in this work.
To evaluate the pressures associated with the different feedback modes, we employ radio, infrared (IR), and Xray observations, as detailed in Section 3. Specifically, to measure the warm (∼10 4 K) gas pressure (P HII ) associated with photoionization, we use the 5-GHz detections from the CORNISH survey (Purcell et al. 2013 ). To constrain the dust-processed radiation pressure (P IR ), we utilize 2MASS J, H, and, K-band photometry (Skrutskie et al. 2006), 8, 12, 14, and 21 .3-µm data from the RMS catalog (Lumsden et al. 2013) , 70-µm data from Spitzer MIPS (Carey et al. 2009 ), 60-and 100-µm data from IRAS (Helou & Walker 1988) , and 870 µm data from ATLASGAL . We require that our sample has 21.3-µm data in order to constrain the peak of the spectral energy distribution (SED). To assess the hot (∼10 7 K) gas pressure attributed to shock-heating by stellar winds (P X ), we analyze 0.5-7 keV archival data from the Chandra X-ray Observatory. The scale is 1 in length, ≈3.5 pc for a distance of 11.9 kpc to W49A (Quireza et al. 2006 ).
To measure the pressures associated with each feedback mode, we adopt methods similar to those of Lopez et al. (2011) and L14, with some differences described in the following sections. As the sources in our sample are not highly resolved, we measure integrated pressures averaged within the H ii region shells. We adopt H ii region radii R from Urquhart et al. (2013) using distances measured with galactic kinematics and maser parallaxes. The regions have R = 0.01 − 0.4 pc (angular radii of R ang = 0.5 − 11.7 ) and are at distances of D = 1.1 − 18.8 kpc.
Following L14, we define the direct radiation pressure as the momentum available to drive motion in the H ii region shells at a radius R from the central stars:
where L bol is the bolometric luminosity of the central stars 1 . Mottram et al. (2011) derived L bol for a subsample of the H ii regions by fitting SED models of young stellar objects (YSOs) to their SEDs (Robitaille et al. 2007 ). As noted by Mottram et al. (2011) , these 1 Note that the factor of 3 in the numerator of equation 1 arises because we are computing the volume-averaged radiation pressure within the H ii region rather than simply the pressure at the surface. The reason for computing the volume-averaged pressure is that P dir dV is the quantity that appears in the virial theorem describing the overall dynamics of the region (McKee & Zweibel 1992) . For more discussion of why it is important to include this factor, see L14.
L bol are consistent with the ionizing fluxes measured by Urquhart et al. (2013) . Thus, we adopt the L bol reported by Mottram et al. (2011) for our H ii regions.
The stellar radiation is absorbed by dust and thermally re-radiated at longer wavelengths in the IR, thereby enhancing radiation pressure in young starforming regions. Measuring the dust-processed radiation pressure, P IR , for our sources is significantly more challenging than for the larger H ii regions examined in L14 and similar studies. For evolved sources, the column of material inside and in front of the H ii region is small enough to be optically thin at far-IR and longer wavelengths, and thus one can use dust re-radiation at these wavelengths as a diagnostic of the radiation field seen by the grains. We have intentionally selected much more embedded sources, which may be optically thick in the far-IR regime. Consequently, we estimate the volume-averaged radiation pressure by modelling the complete near-IR to sub-mm SED and then deriving the pressure from the model.
For this purpose, we fit the IR data using synthetic SEDs from models of young stellar objects (YSOs) computed by Robitaille (2017) to find a geometry that produces the IR SED from each region. In an effort to recreate the models adopted by Mottram et al. (2011) from Robitaille et al. (2007) , we use the most similar model set from Robitaille (2017) , the spubsmi model set. The spubsmi models include a central star, a passive disk, an accreting, rotationally flattened envelope (Ulrich 1976 ), a cavity around the star within the dust sublimation radius, an ambient medium, and bipolar cavities produced by protostellar outflows. We chose these models as highmass YSOs have observed accretion disks (Patel et al. 2005; Kraus et al. 2010 ); however we note that Robitaille (2017) does not model accreting disks, arguing that the difference between a passive and an accreting disk would not noticeably change the SED. We fit the synthetic SEDs produced by these models to the IR data using the SEDfitter from Robitaille et al. (2007) . We used the same extinction law as Forbrich et al. (2010) which has R V = 5.5 based on the larger grains anticipated in dense star-forming regions. When fitting the data, we limited the distances to within 2 kpc of the values reported by Urquhart et al. (2013) . Once we determined the best-fit SED, we took the parameters from the best-fit model and recreated the geometry in HYPERION to get the dust temperature distribution (Robitaille 2011) .
We fit the Robitaille (2017) models to an SED consisting of measurements at J, H, and K-band (from 2MASS), 8, 12, 14, and 21 µm (from MSX), 60 and Figure 2 . Examples of measured SEDs (circles with error bars represent detections, downward triangles are upper limits), together with the SEDfitter output of the ten best-fit models for three sample H iiregions. The black lines are the best-fit models, and the gray lines are the nine next bestfit models. The best-fit χ 2 and τ of the three regions are reported in the plot.
100 µm (from IRAS), 70 µm (from Spitzer /MIPS), and 870 µm from ATLASGAL, as described in Section 2. For the J, H, K, and 70-µm measurements, we compare to the filter-convolved fluxes that are available in the Robitaille (2017) models for the surveys from which the data came, while for the other wavelengths, we use the flux at the central wavelength of the filter. We treat the measurements at 100 and 870 µm as upper limits, since the beam sizes for these measurements are much larger than the ≈ 5 sizes of our sample H ii regions. We set the apertures for the data shorter than 21 µm, at 60 µm, at 70 and 100 µm, and at 870 µm to 3 , 10 , 20 , and 55 , respectively. This set of measurements ensures good coverage on both sides of the peak of the SED, enabling strong constraints on the model fits. We show some example fits produced by this procedure in Figure 2 .
From the HYPERION model, we calculate P IR for each source by integrating over the two-dimensional axisymmetric grid of dust temperatures, T d :
where a is the radiation constant a = 7.56 × 10 −15 erg cm −3 K −4 and V is the H ii region volume. Note that this expression implicitly assumes that the IR radiation temperature is equal to the dust temperature; this is a reasonable approximation in the highly-opaque regions with which we are concerned. We integrate out to R to include the dusty shell surrounding the H ii region. We set the dust temperature within the dust sublimation radius to T d = T sub , the dust sublimation temperature, to account for the energy contained in that radius. In our analysis, we include only the regions where the reduced chi-squared from the fit is χ 2 red < 30 which limits our sample to 81 sources. Nayak et al. (2016) used a χ 2 red cut of 10 to ensure that only YSOs were included in their sample. We use a less stringent cut on χ 2 red because Urquhart et al. (2013) already confirmed these objects are H ii regions.
The photoionization heating from massive stars creates warm, ≈10 4 K gas, the classical driver of H ii regions. We measure the pressure from this warm gas by using the ideal gas law:
We adopt a warm-gas temperature of T HII = 10 4 K, and we estimate the density, n HII , to calculate P HII . n HII is the number density of free particles and depends on the ionization state of the gas; if hydrogen is fully ionized and helium is singly ionized, then n HII = n e +n H +n He ≈ 2n e . We use Equation 5.14b from Rybicki & Lightman (1979) for free-free emission to calculate n e :
where D is the distance to the region, F ν is the flux density at frequency ν, and V is the volume of the region.
In this study, we use the measurements from CORNISH at 5 GHz, where free-free dominates. We adopt a Gaunt factor of 5.1 based on Draine (2011a) and van Hoof et al.
.
The stars powering the young H ii regions have radiatively-driven stellar winds that shock-heat gas to 10 6 K (Rosen et al. 2014 ). This hot gas creates pressure within the region according to the ideal gas law:
where n X is the electron density in the hot gas, and the factor of 1.9 assumes that He is doubly ionized and the He mass fraction is 0.25. Based on searches of the Chandra Data Archive, 26 out of 128 have archival observations. Among the 26 sources, only 6 have detections with >10 net counts in the 0.5-7.0 keV band. In these cases, the regions are not resolved 2 , and the limited number of counts precludes reliable spectral modeling. However, the high median energies of the counts (≈3-6 keV) and the elevated hardness ratios 3 (≈0.5-1.0) of the targets suggest that the spectra are quite hard. Previous X-ray studies of young H ii regions have also found that hard X-rays dominate their emission (e.g., Tsujimoto et al. 2006; Anderson et al. 2011) , which may indicate very hot plasma temperatures (with kT X 6 keV) and/or extreme column densities (of N H 10 23 cm −2 ) that attenuate the soft X-rays.
In young H ii regions, the origin of the X-ray emission is uncertain: it may be from unresolved point sources, interacting/colliding stellar winds, or wind-blown bubbles (see Tsujimoto et al. 2006) . However, the available data have insufficient counts to distinguish between these scenarios. Thus, given that the X-rays may arise from these other channels and not just the shock-heated gas from individual stellar winds, we treat all of the hotgas measurements as upper limits. We calculate the upper-limits on n X for each region by simulating an optically-thin thermal plasma with metallicity of Z = Z and temperature kT X =0.4 keV. We assume a Galactic column density N H toward each region using the values from HI4PI Collaboration et al. (2016) . We use WebPIMMS 4 to derive the emission measure EM X given these inputs, and then find n X using the relation n X = EM X /V , where V is the volume of the region.
To assess uncertainty in our pressure measurements, we examine the largest source of error in each calculation. For P HII , P dir , and P IR , the greatest uncertainty arises from the ∼10% error in the H ii region radii reported by . Thus, to ascertain the confidence range in the pressure terms, we adopt radii of R ± 0.1R and compute the associated pressures. For the 22 unresolved regions, we set 0.75 as the sources' angular diameter. These upper limits yield lower limits on the pressures derived for these objects.
From our 128 region sample, 106 sources were resolved in the CORNISH survey (Purcell et al. 2013) , and 81 meet our requirements for the IR SED fits. We find that 68 of the 81 regions are P IR -dominated, and 3 regions are P dir -dominated. Additionally, 4 regions have P HII ∼ P IR (within the uncertainties), and 6 others have P dir ∼ P IR (within the uncertainties). Overall, the median P dir (P HII ) is 17% (11%) of the median P IR in our sample.
We plot the distribution of L bol , radius R, and central star mass M * for all of the regions in Figure 3 . We derive M * using L bol and the empirical measurements of O stars from Martins et al. (2005) and of B stars from Schmidt-Kaler (1982) . We report the parameter ranges covered by the four groups of H ii regions (with P HII ∼ P IR , P dir ∼ P IR , P dir -dominated, and P IRdominated regions) in Table 1 . For the 81 region sample, the median log L bol /L is 4.9, the median R is 0.08 pc, and the median M * is 18.8 M .
In Figure 4 , we plot the pressures derived for the sample, and in Figure 5 , we compare our results with those of the evolved H ii regions in the LMC and SMC from L14 5 . The pressure terms decrease with radius, as expected given the increasing volume as the shell expands. L14 found that P HII dominated for the evolved H ii regions, while P IR is nearly an order of magnitude lower in their sample, contrasting the results from the young H ii regions in our sample. Our results, in combination with those found in L14, can probe the transition from radiation pressure dominated to warm gas pressure dominated H ii regions. Radiation pressure P rad and P HII have different radial dependences in a single region: P rad ∝ R −2 , whereas P HII ∝ R −3/2 . Consequently, a region transitions from being radiation-pressure driven to gas-pressure driven at a characteristic radius r ch (Krumholz & Matzner 2009 
which can be derived by setting the total radiation pressure (P dir +P IR ) equal to P HII . In the above equation, 0 = 13.6 eV, α B is the case-B recombination coefficient, and φ is the dimensionless quantity that accounts for dust absorption of ionizing photons and for free electrons from elements besides hydrogen. As in L14, we adopt (1997) . S is the ionizing photon power of the star, and the quantity ψ is the ratio of bolometric to ionizing power. We set ψ = 3.2 based on measurements by Murray & Rahman (2010) . The factor f trap represents the amount that radiation pressure is enhanced by trapping energy within the shell from stellar winds (f trap,w ), infrared photons (f trap,IR ), or Lyα photons (f trap,Lyα ):
where the 1 represents absorption of the direct radiation.
We are unable to constrain f trap,w without X-ray detections of the diffuse gas in the sources, and f trap,Lyα ≈ 0 since Lyα trapping is limited by the presence of dust (Henney & Arthur 1998) . Therefore, we assume that f trap ≈ 1 + f trap,IR ≡ 1 + P IR /P dir .
The distributions of f trap , r ch , and R/r ch are shown in Figure 6 . The median values of these parameters are f trap = 8.1, r ch = 0.42 pc, and R/r ch = 0.24.
As shown in Figure 5 , P HII and P dir are of similar magnitude for the young H ii regions, but P IR dominates statistically significantly in 68 out of the 81 source sample. By contrast, in the evolved L14 sources, P IR is roughly an order of magnitude lower than P HII , and almost all are P HII -dominated.
Moreover, the young H ii region pressures are orders of magnitude larger than those measured for the evolved sample from L14. This result suggests radial dependence of the pressures. For an individual H ii region, P HII ∝ R −3/2 (Equation 4), while P dir ∝ R −2 (Equation 1). However, we note the heterogeneity of our sample and the L14 sample. For example, based on their luminosities (see Table 1 ), the young H ii regions considered here are powered by individual O-and B-stars or small star clusters, whereas the L14 sample is driven by star clusters of mass M ≈ 300-3×10 4 M . Furthermore, the L14 sample is comprised of H ii regions in the LMC and SMC, where the metallicity is lower (with Z ≈ 0.5Z and 0.2Z , respectively; Russell & Dopita 1992; Kurt & Dufour 1998) .
To assess the radial dependence, we measure the power-law slopes with respect to radius for each pressure term for only the young H ii sample. We use all 106 resolved regions to measure the slopes for P HII and P dir , but we use only the 81 regions with P IR measurements to fit the P IR slope. We find P dir ∝ R −1.36±0.16 , P IR ∝ R −1.43±0.15 , and P HII ∝ R −0.74±0.07 . We note that P IR was measured differently in this work compared to L14: L14 used the Draine & Li (2007) dust models, which did not apply to the embedded H ii regions analyzed here because they are optically thick. Consequently, the best-fit power-law does not reflect the P IR measurements of the evolved H ii regions.
Given the different radial trends between P IR and P HII , we estimate the radius where the sources transition from P IR -dominated to P HII -dominated: ∼3 pc. This assumes that the dust remains optically thick around the H ii regions out to these large radii, which may not be physically probable. If instead they become optically thin, then this transition would occur at smaller radii. In the future, observations of ∼ 0.5 − 3 pc radius H ii regions are necessary to evaluate this transition.
P HII was the dominant form of feedback in the evolved H ii region sample of L14, whereas P X and P IR were factors of several weaker. The change in the pressure terms between the two H ii region populations demonstrates that the dynamical impact of feedback evolves and that direct and dust-processed radiation can be significant Recently, Barnes et al. (2020) conducted a similar analysis as our work, measuring feedback pressures in H ii regions with effective radii R eff ∼ 10 −3 − 10 pc in the Milky Way Central Molecular Zone. They found that P dir is the dominant feedback term for sources with R eff <0.1 pc, whereas P HII takes over the energy budget in larger regions. Although Barnes et al. (2020) measured P IR for their regions with R eff 0.5 pc, they did not extend down to smaller radii to estimate P IR because of spatial resolution limitations. However, we note that their estimates of P dir and P HII for sources with R eff 0.5 pc agree within an order-of-magnitude of our results, and their best-fit power-law slopes (of P HII ∝ R −1.0 eff and P dir ∝ R −1.5 eff ) are consistent with our findings (shown in Figure 4 ) given the uncertainties.
From the 81 regions discussed in Section 4, we find that 68 sources have P IR as the dominant pressure term. Three regions are P dir -dominated, four regions have comparable P HII and P IR , and six regions have comparable P dir and P IR . We report the range of properties for these four groups of sources (with P HII ∼ P IR , P dir ∼ P IR , dominant P dir , and dominant P IR ) in Table 1. We note that the L bol of the sources with P HII ∼ P IR are in the lower-luminosity end of the sample, whereas the P dir -dominated and P dir ∼ P IR regions have higher luminosities. The f trap values for the P dir -dominated and P dir ∼ P IR regions are among the lowest in the sample, while the measurements for the P IR -dominated and P HII ∼ P IR regions are systematically greater. The range of R/r ch for the regions with P HII ∼ P IR is 3.3-11.66, consistent with expectations that regions with R/r ch > 1 are gas-pressure dominated. As predicted, the vast majority (60 out of 68) of the P IRdominated regions have R/r ch < 1, though seven have R/r ch = 1 − 2 and one has R/r ch = 5.5. We note that the latter source has a relatively low f trap = 2.9 and log L bol /L = 4.5, leading to a small r ch of 0.01 pc.
Our results, where 84% of the young regions are P IR -dominated, indicate that radiation pressure can be significant at early times in H ii regions. This finding is consistent with the conclusions of Geen et al. (2020) who employed analytical models of H ii regions and showed that P rad and P X are most important when the shells are small (with radii <0.1 pc) and at high surface densities. However, our results contrast those from other theoretical studies that evaluated the impact of dust-processed radiation. Rahner et al. (2017) constructed semi-analytic, one-dimensional models of isolated 10 5 -10 8 M clouds with radiation (direct and dust-processed), stellar winds, and SNe. They found that P IR is negligible in their low-mass clouds (∼10 5 M ) and is only significant in the early phases of the massive GMCs or during recollapse following the initial starburst. Reissl et al. (2018) noted that photons absorbed and re-emitted by dust deposit little momentum in GMCs because they escape promptly, thus limiting the role of P IR in GMC disruption. However, in agreement with our results in combination with those of L14, they find that radiation pressure decreases as star clusters become more extended and evolved. Our observational results reflect H ii regions powered by individual stars or lower-mass clusters at earlier times than considered by Rahner et al. (2017) and at smaller scales than Reissl et al. (2018) . Our findings suggest that sub-pc H ii regions may have significant indirect radiation pressure, even if it does not lead to GMC disruption. P IR -dominated sources have distinct structure and dynamics (e.g. Mathews 1967 Mathews , 1969 Petrosian et al. 1972; Gail & Sedlmayr 1979) from classical H ii regions which are dominated by P HII (e.g., Strömgren 1939; Savedoff & Greene 1955) . In particular, P IR -dominated H ii regions are thought to have density gradients in the gas within the regions (e.g. Dopita et al. 2003 Dopita et al. , 2006 Draine 2011b) and have swept-up shells of gas and dust (e.g. Draine 2011b; Rodríguez-Ramírez & Raga 2016). Dynamically, radiation pressure leads to faster expansion at early times (e.g. Krumholz & Matzner 2009; Martínez-González et al. 2014; Geen et al. 2020) . Given the differences relative to classical H ii regions, our results underscore the importance of including dust and radiative feedback in small-scale massive star formation simulations and high-resolution GMC scale simulations.
Galaxy-and Star Cluster-Scale Simulations
As discussed above, one of the primary takeaways from our results is that dust and radiative feedback should not be neglected in small-scale, high-mass star formation and high-resolution, GMC-scale simulations. Quite often, due to the large computational expense of radiative transfer in numerical simulations (e.g., see Rosen et al. 2017) , the dust-processed radiation pressure is neglected. However, our results indicate that during the early evolution of massive star formation P IR is the dominant feedback mechanism regulating H ii region dynamics, at least up to a R ∼ 0.5 pc, corresponding to the median r ch value found in our sample.
In the future, simulations can incorporate our observationally-inferred results to model the energy and momentum injection by massive stars into the ISM at these scales by adopting the following sub-grid prescription. Within a radius R 0.5 pc, the rate of energy (E rad ) and momentum (p rad ) injection in nearby gas and dust by massive stars iṡ
where L bol = L + L acc is the sum of the stellar luminosity and accretion luminosity. Here, f trap takes into account both the direct radiation and indirect radiation pressure enhancement due to reprocessing by dust. We suggest using a value of f trap ∼ 8 following the median value obtained in our sample. Given that we do not find a correlation between H ii region size and f trap (as shown in Figure 7 ), we conclude that using a constant value for f trap is a reasonable approximation. However, we note that this f trap does likely depend on other physical parameters, e.g. the dust-to-gas ratio, metallicity, and the optical depth per unit dust mass.
Since these regions are compact they may be actively accreting material and gravitationally collapsing. We test this hypothesis by calculating the gravitational pressure (P grav ) to compare to our feedback pressures as calculated above. From our models discussed in Section 3, we estimate the gravitational pressure as
where G is the gravitational constant, M is the total mass within radius R (including the star and gas), and V = 4πR 3 /3 is the volume of the H ii region. We compare P grav to the total pressure from feedback, P tot = P HII + P dir + P IR , in Figure 8 by plotting their ratio as a function of R. The regions with P tot > P grav represent those dominated by feedback, while those with P tot < P grav (in the shaded region of Figure 8 ) are collapsing due to gravity. The figure shows that for all but the most compact of our H ii regions, feedback dominates over gravity, and thus is capable of ejecting gas.
In this work, we used radio, IR, and X-ray data to assess the dynamical impact of stellar feedback mecha- nisms in a sample of 106 resolved, young H ii regions with radii <0.5 pc. We measured the pressures associated with direct radiation (P dir ), dust-processed radiation (P IR ), photoionization heating (P HII ), and stellar winds (P X ). We found that P IR is statistically significantly dominant for 84% (68 out of 81) of the regions, and by comparison, the median P dir (P HII ) is 17% (11%) of the median P IR in our sample. We set upper limits on P X due to the lack of X-ray detections, and these limits are comparable to the measured P IR values. Our young H ii region results contrast with those of L14, who analyzed evolved sources in the LMC and SMC that were mostly P HII -dominated. Our sample yielded radial pressure dependences of P HII ∝ R −0.74±0.07 , P dir ∝ R −1.36±0.16 , and P IR ∝ R −1.43±0.15 . Using these relations, the transition radius from P IR -dominated and P HII -dominated regions would be at ∼3 pc. We found a median f trap of ∼8 without any radial dependence for regions 0.5 pc in size, suggesting this value can be adopted in sub-grid feedback models in galaxy-and star cluster-scale simulations. We compared the total pressure P tot to the gravitational pressure P grav in our sources, and we showed that only the smallest H ii regions are dominated by P grav . This result indicates that for the majority of our sources, the feedback pressure is sufficient to expel gas from the regions.
In the future, observations of H ii regions with radii of ∼0.5-3 pc can fill the gap between the young sources considered here and the evolved sample analyzed by L14. That work will enable stronger constraints on the scale where H ii regions transition from P rad -dominated to P HII -dominated.
G.M.O. would like to thank James W. Johnson, Adam Leroy, Todd Thompson, and the OSU Galaxy/ISM Group Meeting for useful discussions during the preparation of this work. G.M.O. and L.A.L. are supported by a Cottrell Scholar Award from the Research Corporation of Science Advancement. A.L.R. acknowledges support from NASA through Einstein Postdoctoral Fellowship grant number PF7-180166 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. M.R.K. acknowledges support from the Australian Research Council through its Future Fellowship and Discovery Projects schemes (awards FT180100375 and DP190101258. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This paper made use of information from the Red MSX Source survey database at http://rms.leeds.ac.uk/cgibin/public/RMS DATABASE.cgi which was constructed with support from the Science and Technology Facilities Council of the UK. L.A.L. and A.L.R. would also like to thank their coworkers, Slinky, Kerfuffle, and Nova for "insightful conversations" and unwavering support at home while this paper was being written during the coronavirus pandemic of 2020. Their contributions were not sufficient to warrant co-authorship due to excessive napping. 6 Facilities: Chandra, Spitzer Software: CIAO(v4.7; Fruscioneetal.2006) ,HYPER-ION (v0.9.10; Robitaille 2011), SEDfitter (Robitaille et al. 2007 ),