© ESO, 2015

1. Introduction

High-mass stars are characterized by luminosities in excess of ~10³L_⊙ and powerful Lyman continuum emission. The latter is bound to create an ionized region around the star, which is detected through its free-free emission. Such an Hii region expands and eventually disperses, although the details of this process and the corresponding time scale are still matters of debate as they also depend on the density distribution and velocity field of the dense gas enshrouding the newly born star. The early evolution of an Hii region is closely related to the formation process of an OB-type star, and is hence of great interest for studies of massive star formation. As a matter of fact, Hii regions are conventionally classified as hypercompact, ultracompact (UC), compact, and extended, in order of increasing size and, presumably, age. The last class is clearly associated with more evolved objects and possibly multiple OB stars, while sources belonging to the first class are very small and faint, especially below 5 GHz owing to their spectra rising with frequency. This explains why they are difficult to detect and resolve, even with sensitive radio interferometers (see Kurtz 2005 for a review on hypercompact Hii regions). Consequently, much attention has been devoted to UC and compact Hii regions.

One of the problems in the study of Hii regions is stellar multiplicity. The ideal template of a single star ionizing a spherical Hii region is inadequate to describe the real world where massive stars form in rich stellar clusters. A viable way to shed light on this issue is to compare the radio luminosity to the bolometric luminosity of these objects. The former is sensitive only to the most massive star(s), whereas all cluster members contribute to the latter. However, a problem with measuring the bolometric luminosity is that the major contribution comes from reprocessed radiation from dust emitted at far-IR wavelengths, heavily absorbed by the Earth’s atmosphere and thus impossible to observe from the ground. Moreover, the comparison between radio and far-IR emission was hindered by the dramatic difference in angular resolution between surveys conducted in the two wavelength regimes. While radio interferometers have been able to attain subarcsecond resolutions for many decades, until recently the best data available for a large number of Hii regions at ~100 μm were those of the IRAS mission with an angular resolution of only ~2′. As a consequence, the luminosity measurements based mostly on IRAS data were to be taken as upper limits, as unrelated objects falling in the large beam could contribute to the estimate.

This situation has now dramatically changed and pioneering studies such as that by Wood & Churchwell (1989) can be significantly improved on. On one hand, the ESA Herschel Space Observatory (Pilbratt et al. 2010) provides us with a tool to improve the angular resolution in the far-IR by a factor of ~10 with respect to IRAS. On the other hand, the completion of the CORNISH survey (Hoare et al. 2012; Purcell et al. 2013) of a large portion of the Galactic plane at 5 GHz with ~1.̋5 resolution has made it possible to obtain an unbiased census of UC and compact Hii regions. These radio maps are perfectly complementary to the far-IR images obtained in the context of the Hi-GAL project (Molinari et al. 2010), which covers a stripe 2° wide in latitude and 360° in longitude, following the warp of the Galactic plane, at five far-IR continuum bands. We thus decided to take advantage of the Hi-GAL and CORNISH databases to perform a systematic study of the radio and IR emission of young Hii regions located in the Galactic longitude range 10°–65°.

The present article is organized as follows. In Sects. 2 and 3.1 we describe the sample of Hii regions selected from the CORNISH catalogue and illustrate the method adopted to identify the corresponding Hi-GAL counterparts. In Sects. 3.2 to 3.4 source parameters such as the distance, luminosity, and mass are estimated, while in Sect. 4 we discuss the main results obtained. Finally, in Sect. 5 the conclusions are drawn.

2. The sample

Since the main scope of our study is to investigate the IR and radio properties of young massive stars, we have selected the sources classified as “ultracompact” and “compact” Hii regions in the CORNISH catalogue. This a classification was obtained after visual inspection also using the Spitzer IRAC and MIPSGAL images (more details on the method are given in Purcell et al. 2013 and will not be repeated here). Since the distinction between these two types was based on the angular size and as such does not necessarily mirror an intrinsic physical and evolutionary difference, for the sake of simplicity in the following we will refer to all of our sources simply as “Hii regions”.

Our sample consists of 281 bona fide Hii regions. In order to further characterize them, we searched for possible counterparts at 1.4 GHz in the MAGPIS survey by White et al. (2005), whose angular resolution is ~6′′. Although this resolution is ~4 times worse than the resolution of the CORNISH survey (~1.̋5), a comparison between the two surveys is feasible. For this purpose we selected the closest MAGPIS source within a conservative circle with 20′′ radius, taking into account that 99% of the Hii regions in the CORNISH catalogue have sizes below this value. We find 170 targets detected at both frequencies. In Fig. 1, we plot the spectral index (defined as α = log ₁₀(S_{5 GHz}/S_{1.4 GHz})/log ₁₀(5/1.4)) as a function of the ratio between the angular diameters, Θ, at the two frequencies. Although most Hii regions have a spectral index between –0.1 and +2, as expected for free-free emission, ~1/4 of the objects have α< −0.1, which appears inconsistent with thermal emission. However, one sees that basically all of these points have a size ratio below unity and it is therefore very likely that the steep negative spectral index is the result of part of the flux at the highest frequency being filtered out by the interferometer. We conclude that the comparison between the 5 GHz and 1.4 GHz continuum confirms the nature of our Hii region sample.

3. Analysis

3.1. IR and (sub)mm counterparts of the HII regions

Our first goal is to identify the IR counterparts of the Hii regions in the Hi-GAL images at five different bands (70, 160, 250, 350, and 500 μm). The angular resolution of Herschel (≥9′′) does not permit us to resolve some of the CORNISH Hii regions that lie too close to each other. We thus decided to consider as distinct objects only those targets whose separation from any other target is greater than the Herschel half-power beam width (HPBW) at 160 μm (i.e., >11.̋5). The Hii regions below this limit were artificially merged into a single target whose flux density is the sum of the individual flux densities and whose size is the largest of the sizes. In this way, we reduced the sample to 244 objects. For each of these, we searched for compact IR emission in the five Hi-GAL images, inside a circle of 15′′ radius, centered on the Hii region itself. To identify the IR source(s) and measure their flux densities, we used the CuTEx algorithm described in Molinari et al. (2011). This may result in multiple counterparts and we decided to choose the closest of these that is detected in the largest number of Hi-GAL bands. In the few cases where the emission was saturated, the flagged pixels were assigned the maximum flux of the closest pixels to the saturated region. Consequently, the corresponding luminosity is to be taken as a lower limit. However, one must keep in mind that saturation usually occurs at 250 μm or 350 μm, while the peak of the continuum emission lies at 70 μm (see Sect. 3.1), which implies that saturation should not affect our luminosity estimates significantly.

With the previous method we were able to identify 230 Hi-GAL counterparts out of 244 targets. In practice, in order to obtain a reliable estimate of the luminosity, from our analysis we excluded all sources that were detected in less than three Hi-GAL bands. This reduces the usable targets to 217. Finally, we rejected all counterparts whose separation from the CORNISH Hii region was >11.̋5 (the Herschel HPBW at 160 μm – see above). The final number of targets with a Hi-GAL counterpart is 204. The corresponding Hi-GAL images are shown in Figs. A.2–A.5 where we split the sources into four groups depending on their Lyman continuum properties (as discussed in Sect. 4.1), and in Fig. A.6 where we show the four sources without distance estimates (see Sect. 3.2). The selection process is summarized in Table 1.

Since Hii regions are known to be prominent mid-IR emitters, we also included the MSX (Price et al. 1999) 21 μm and WISE (Wright et al. 2010) 22 μm fluxes from the corresponding point-source catalogues, which will provide us with better sampled spectral energy distributions (SEDs) and thus more reliable luminosity estimates. We note that the MSX and WISE fluxes were obtained by summing the fluxes of all the point sources falling inside the full width at half power of the Hi-GAL 250 μm source. We decided not to consider the MIPSGAL 24 μm fluxes because in most of our objects these happen to be heavily saturated. For the sake of completeness, we also included the ATLASGAL¹ (Schuller et al. 2009; Contreras et al. 2013) 870 μm and BGPS v2 (Ginsburg et al. 2013) 1.1 mm fluxes. The resulting SEDs from 21 μm to 1.1 mm are shown in Fig. A.1. In Table A.1 we give the names and positions of the CORNISH Hii regions, the corresponding integrated flux density at 5 GHz (S_{5 GHz}) from the CORNISH catalogue, the coordinates of the Hi-GAL counterpart, and the values of the flux densities from 21 μm to 1.1 mm.

While a limited number of the SEDs may look questionable, possibly owing to faint emission and/or confusion with nearby sources, most of them appear very reasonable. In the following the SEDs will be used to obtain an estimate of both the source luminosity and mass of the associated molecular clump.

3.2. Distance estimates

A crucial parameter for our purposes is the source distance. A kinematical distance estimate can be obtained if a velocity measurement is available. Since the Hi-GAL data convey information only on the continuum emission, we investigated the literature to search for molecular or recombination line observations of the 204 usable targets. In particular, we refer to the following articles: Urquhart et al. (2013b; hereafter URQ13), Anderson et al. (2009; 2012), Beuther et al. (2002), Shirley et al. (2013), Bronfman et al. (1996), Jones et al. (2012), Kolpak et al. (2003), Pandian et al. (2008), Sewilo et al. (2004), Watson et al. (2003), Wienen et al. (2012), and the red MSX source (RMS) database² (Lumsden et al. 2013). We were able to assign an LSR velocity to all but four (G011.9786-00.0973, G026.0083+00.1369, G026.8304-00.2067, and G065.2462+00.3505) of the 204 sources.

The kinematic distance was computed for our final sample of 200 objects using the Galaxy rotation curve by Brand & Blitz (1993), which resulted in 17 cases without kinematic distance ambiguity (KDA), 172 with KDA, and 11 with velocity inconsistent with the assumed rotation curve. In the last case we assumed the distance to the tangent point. Only for source G10.62–0.38 did we replace our estimate with 4.2 kpc (Urquhart, pers. comm.). To solve the KDA we searched the literature for studies where different methods were employed to discriminate the near from the far distance, and we eventually used the following references: URQ13, Anderson & Bania (2009), Anderson et al. (2012), Jones & Dickey (2012), Kolpak et al. (2003), Pandian et al. (2008), Sewilo et al. (2004), and Watson et al. (2003). In this way, we assigned the near distance to 50 targets and the far to 107, while four targets were close to the tangent point. We note that the larger number of sources at the far distance is not surprising as the area of the Galactic plane sampled by CORNISH beyond the tangent point is >3.4 times that inside the tangent point³. For the remaining 11 targets we were unable to solve the KDA and we decided to adopt the far distance. This is a conservative approach that will be justified in Sect. 4.1; in all cases, an incorrect choice for these 11 objects is bound to have negligible effects on the results obtained in the present study. The distance estimates are given in Table A.2.

3.3. Luminosity estimates

The simplest way to obtain an estimate of the luminosity of our sources is to integrate the corresponding continuum spectra by linearly interpolating between the fluxes of the SEDs in Fig. A.1. We prefer this approach to fitting a modified blackbody because the SED of Hii regions is known to be made of at least two components, a relatively cold one peaking in the far-IR and a hot one peaking at shorter wavelengths. Therefore, a single fit from 21 μm to 1.1 mm is unlikely to give reliable results. More complex models such as the one developed by Robitaille et al. (2007) can provide us with satisfactory fits, but the results may significantly depend on the source geometry and orientation, which are difficult to establish. For example, the correction to the luminosity due to the flash-light effect may be important in these models, but it is unclear whether such an effect is indeed at work in our sources.

We obtained the value of the luminosity (listed in Table A.2) for all of the 200 sources with a distance estimate. In Fig. 2 the distribution of these luminosities is shown. The dotted histogram shows how the distribution would change if we chose the near distance for the 11 sources for which the KDA could not be solved (our choice is the far distance, see above). Clearly the near/far ambiguity has little impact on the global sample. One can conclude that most of our objects are characterized by luminosities above 10⁴L_⊙, with a handful of sources as weak as ≳10³L_⊙. This finding is in good agreement with the nature of our sample consisting of stars earlier than B3. In the same figure we also plot the luminosity distribution obtained by Mottram et al. (2011; see their Fig. 1) for the rms sample. This distribution appears to be consistent with our sources at high luminosities, while the rms Hii regions outnumber our CORNISH sample at lower luminosities. This is likely due to the CORNISH survey being less sensitive than the radio data acquired for the rms sample, part of which has been observed at 8.6 GHz, and is thus more complete.

3.4. Mass estimates

It is also interesting to estimate the mass of the parental clump where the Hii region is embedded. For this purpose, we use the flux density at 500 μm or, if this is not detected, at the longest available wavelength. In practice, the 500 μm flux was used in 92% (188 out of 204) of the cases. Following URQ13, whose sample is very similar to ours, we assumed the same temperature of 20 K for all of the objects. We prefer this choice rather than deriving a temperature estimate from the SED for two reasons: we believe that the temperature obtained from the ammonia data (see URQ13) is more reliable than a value estimated from a model-dependent fit to the SED, and because the variation of temperature across the sample of URQ13 is quite limited, with most values in the range 15–30 K, which implies a maximum uncertainty of ~50% on our mass estimates. The dust absorption coefficient at 500 μm (5 cm² g^-1) was taken from Col. 6 of Table 1 in Ossenkopf & Henning (1994). The dust absorption coefficient was assumed to vary as ν^1.9, obtained by fitting the values quoted in the same table. The derived masses are given in Table A.2.

Figure 3 shows a comparison between our mass estimates and those by URQ13, for the 158 sources in common between the two studies. We note that, for the sake of consistency, URQ13’s masses were scaled to our distances when necessary. While the two masses appear quite consistent, the estimate of URQ13 is systematically greater (on average by a factor 1.7) than ours. This is due to the way the sub-mm flux density has been computed: in our case, the CuTEx algorithm basically performs a Gaussian fit to the image, whereas URQ13 integrated the flux inside a suitable polygon. It is clear that the latter method is bound to measure more flux than the former as it also takes into account extended emission lying above the wings of the Gaussian fit. While any choice has its shortcomings, in our approach we have arbitrarily decided to consider the compact emission because we believe it to be more tightly related to the embedded Hii region.

The distribution of the clump masses, shown in Fig. 4, demonstrates that the vast majority of the clumps are above several 100M_⊙, as expected for high-mass star forming regions. It is thus very likely that our measurements refer to rich stellar clusters, tightly associated with the early-type stars ionizing the CORNISH Hii regions.

4. Discussion

4.1. Lyman continuum excess

The large luminosities and masses of the objects under study are strongly suggestive of the presence of multiple stars. In order to establish the contribution of low-mass stars and investigate the properties of the early-type stars, we have estimated their Lyman continuum emission, N_Ly, assuming the free-free emission to be optically thin. We used the expression ${\mathit{N}}_{\mathrm{Ly}}\mathrm{\left(}{\mathrm{s}}^{-1}\mathrm{\right)}\mathrm{=}\mathrm{9.9}\mathrm{\times }{\mathrm{10}}^{\mathrm{43}}\hspace{0.17em}{\mathit{S}}_{\mathrm{5}\mathrm{GHz}}\mathrm{\left(}\mathrm{mJy}\mathrm{\right)}\hspace{0.17em}{\mathit{d}}^{\mathrm{2}}\mathrm{\left(}\mathrm{kpc}\mathrm{\right)}\mathit{,}$(1)where S_5GHz is the integrated flux density at 5 GHz, d is the source distance, and the electron temperature has been taken equal to 8000 K (a mean value for Galactic Hii regions; see, e.g., Quireza et al. 2006). In Fig. 5 we compare N_Ly to the bolometric luminosity, L, of the 200 Hii regions for which a distance estimate was possible. When considering this plot, one should keep in mind that the Lyman continuum fluxes might be underestimated for three reasons: (i) the free-free emission could be optically thick; (ii) part of the ionizing photons could be absorbed by dust inside the Hii region or leaking out of it; or (iii) the radio emission could be partly resolved out by the interferometer. The last problem indeed seems to occur for a limited number of cases, as discussed in Sect. 2, while the other two are difficult to quantify. Therefore, a conservative approach is to consider the values of N_Ly as lower limits.

For the sake of comparison, in the figure we also plot the expected relationship between N_Ly and L for a single zero-age main-sequence (ZAMS) star (solid curve) as well as the Lyman continuum emission of a blackbody with the same radius and effective temperature as the ZAMS star (dashed curve). The properties of ZAMS stars have been obtained from Panagia (1973), Thompson (1984), Smith et al. (2002), and Martins et al. (2005). The solid curve is to be seen as an upper limit to the number of Lyman continuum photons per unit time that can be emitted by a ZAMS star of a given luminosity. As previously mentioned, it is very likely that the regions we studied are associated with stellar clusters rather than single early-type stars. In this case, the expected N_Ly must be less than that of a single star with the same luminosity and the hatched area in Fig. 5 is where 90% of the clusters should fall. This has been obtained by simulating a large number of clusters, up to a maximum stellar mass of 120 M_⊙, adopting the initial mass function of Kroupa et al. (2009), as explained in Sánchez-Monge et al. (2013).

Although many sources (44.5%) lie in the cluster area, a significant fraction falls below (22%) and above it (33.5%). To some extent, a deficit in N_Ly is not surprising because of the various effects that may lead to its underestimation (see above). In addition, the sources that most suffer from such a deficit have been assigned the far kinematic distance; if this is replaced by the near distance, the corresponding points below the hatched region move toward the bottom left, parallel to the arrow in the figure, thus approaching the hatched area. A more physical explanation might be that the stars ionizing the Hii regions are larger and cooler than on the ZAMS, possibly because of residual accretion onto the stellar surface (see Hosokawa & Omukai 2009), which implies a significant decrease of the Lyman continuum photon rate. Finally, it is also possible that we are dealing with clusters overabundant in low-mass stars, which would cause a smaller N_Ly/L ratio than for a normal cluster.

To find an explanation for the 67 objects falling above the cluster region, is instead non-trivial (see the discussion by Sánchez-Monge et al. 2013). In the following we will refer to the region above the solid curve in Fig. 5 as the “forbidden” region. We note that we have adopted the far distance for the sources for which the KDA could not be solved; this is a conservative choice, because assuming the near distance for these objects would increase the number of points falling in the forbidden region from 67 to 72. For the other points, mistaking the near with the far distance may indeed move some of them away from the forbidden region, but even assuming the far distance for all of the sources, only 17 out of 67 points would move to the right of the solid line in the figure. Moreover, one cannot appeal to an overestimate of the Lyman continuum flux, as previously explained. We have also verified the reliability of the N_Ly–L relationship that we adopted. For this purpose, we plot in Fig. 6 the same relationship based on the results of various studies available in the literature. As one can see, none of the N_Ly–L curves is consistent with all the points in the plot and some of them make the problem even worse.

Since it appears unlikely that we have overestimated the Lyman continuum flux, one may wonder whether we have underestimated the bolometric luminosity. An increase in L by a factor of 8 or less, would move all the points to the right out of the forbidden region. To test this possibility, we have re-computed the bolometric luminosity using the flux densities of the IRAS Point Source Catalogue counterparts of our sources. These counterparts have been selected by choosing the closest IRAS point source (if any) within 60′′ from the Hii region. Given the large IRAS HPBW at 100 μm (2 ′), the corresponding luminosity estimate is to be considered a conservative upper limit. However, ten sources still lie in the forbidden region, as demonstrated by Fig. 7. It is also worth noting that the number of points below the cluster region has dramatically increased with respect to Fig. 5, consistent with the idea that IRAS-based luminosities are by far too large. For these reasons, we consider Fig. 5 more reliable and will discuss this in the following.

Of course, we cannot rule out the possibility that a few objects in the forbidden zone are affected by an inappropriate estimate of L. In particular, some of the sources above the blackbody curve appear too extreme not to be misplaced. In Fig. 8 we compare the full width at half power (FWHP) at 70 μm of these sources with that of the other objects in the forbidden region lying below the blackbody curve. Clearly, the former are more extended than the latter and this could make it more difficult to estimate their integrated flux with CuTEx (see Sect. 3.1), which was conceived to identify compact sources. Consequently, it is plausible that the luminosity might have been underestimated for some of these sources.

In conclusion, we believe that Fig. 5 proves that the CORNISH sample of Hii regions contains a number of objects that really produce many more Lyman continuum photons than those emitted by a ZAMS star with the same bolometric luminosity. In the following, we will refer to this phenomenon as “Lyman excess”.

In Figs. 9 and 10, we compare the distributions in Galactic longitude and Galactocentric distance of the Hii regions with Lyman excess to those of sources without Lyman excess. No significant difference can be seen between the two types in Fig. 9, while Fig. 10 seems to suggest that Lyman-excess sources are perhaps more concentrated in the 5 kpc ring than the others, although the difference is only marginally significant.

4.2. Nature of the Lyman-excess sources

The existence of Hii regions with an excess of Lyman continuum emission was noted by Sánchez-Monge et al. (2013) and confirmed by Lumsden et al. (2013) and URQ13. These results, however, were obtained from low-resolution radio images and/or luminosity estimates based on IRAS data, whose limitations have already been discussed. Even when the 70 μm MIPSGAL fluxes were available, the angular resolution was still a factor of ~2 lower than in the Herschel images. The availability of the Hi-GAL and CORNISH unbiased surveys permits a more complete and systematic reconstruction of the SED of the Hii regions at far-IR wavelengths, which is crucial for an accurate estimate of the luminosity.

An important step towards a better understanding of the Lyman excess is to discover the nature of the sources with this peculiarity. In Fig. 11 we compare the distribution of L/M_gas of the Lyman-excess sources with that of the others. This comparison suggests that the Lyman-excess sources are less luminous than the rest of the sample for the same mass of the associated clumps. The Kolmogorov-Smirnov (hereafter K-S) statistical test gives a null probability (7.4 × 10^-5) that the two subsamples in the figure have the same distribution, confirming the existence of a substantial difference between them. A possible interpretation is that the Lyman-excess sources are on average more deeply embedded and younger. Alternatively, the clumps might contain less massive stars, which – for the same star formation efficiency – would produce less luminosity. However, the second explanation seems inconsistent with the fact that the Lyman-excess sources are also those with the largest N_Ly/L ratio, as shown in Fig. 12, where according to the K-S test the probability that the two distributions are equivalent is basically zero (1.1 × 10^-8).

The possibility that these peculiar objects could be in an early, embedded evolutionary phase is also supported by other findings. In Fig. 13 we plot the [250–70] color⁴ versus a quantity representing the amount of Lyman excess. The latter is defined by the expression ${\mathrm{\Delta }}_{\mathrm{ex}}\mathrm{=}\mathrm{\Delta }\mathrm{\left(}\log \mathrm{10}{\mathit{N}}_{\mathrm{Ly}}\mathrm{\right)}\frac{\mathrm{\left|}\mathrm{\Delta }\mathrm{\right(}\log \mathrm{10}\mathit{L}\mathrm{\left)}\mathrm{\right|}}{\sqrt{\mathrm{\left[}\mathrm{\Delta }\mathrm{\right(}\log \mathrm{10}{\mathit{N}}_{\mathrm{Ly}}\mathrm{)}{\mathrm{]}}^{\mathrm{2}}\mathrm{+}\mathrm{[}\mathrm{\Delta }\mathrm{\left(}\log \mathrm{10}\mathit{L}\mathrm{\right)}{\mathrm{]}}^{\mathrm{2}}}}\mathit{,}$(2)where Δ(log ₁₀N_Ly) and Δ(log ₁₀L) are, respectively, the separations measured along the log ₁₀N_Ly and log ₁₀L axes between a given point in Fig. 5 and the solid curve delimiting the forbidden region. In practice this expression gives the approximate distance of the point from that curve, assumed negative to the right of the curve.

The line in Fig. 13 is obtained after rebinning the points on a number of intervals and shows some increase with increasing Lyman excess. This means that the Lyman-excess sources may have lower color temperatures than the rest of the sample, consistent with the hypothesis that these sources are younger and more deeply embedded inside cold dusty envelopes. This result is confirmed by the distributions of the color indices of the two samples, with and without Lyman excess (see Fig. 14), which have a probability of 2.9 × 10^-4 of being intrinsically identical according to the K-S statistical test. Clearly, the sources with Lyman excess are on average “colder”, in terms of [250–70], than those without, in agreement with the finding by Sánchez-Monge et al. (2013) that most of the sources with Lyman excess belong to their “type 2” class, consisting of embedded young massive stars still undergoing accretion.

Based on all of the above, we can speculate that the Hii regions with Lyman excess could be ionized by young, mostly B-type stars still undergoing accretion. As discussed by Lumsden et al. (2013), our knowledge of early-type stars is based on visible stars, namely main-sequence stars that have dispersed their parental cocoons, but their properties might significantly differ from those of the young high-mass stars that we are considering in our study. Moreover, one cannot exclude that a significant fraction of the Lyman continuum luminosity could originate from the accretion shock onto a circumstellar disk. Indeed, the model calculations by Hosokawa & Omukai (2009) appear to predict Lyman continuum fluxes comparable to or even greater than those of the star itself (Hosokawa, pers. comm.), possibly sufficient to explain the observed excess.

Also the model by Smith (2014) provides us with a possible explanation of the Lyman excess. In this model the protostar predominantly accumulates low entropy material via cold accretion, but then accretes onto hot spots covering a small fraction of the protostellar surface. The cold accretion assures that the young star is relatively compact, which generates high free-fall speeds, while the free-fall onto the limited area significantly raises the temperature and hence the Lyman flux. In fact, a comparison between Figs. 15 and 16 of Smith (2014) and our Fig. 5 demonstrates the ability of the model to explain most of the Lyman-excess sources.

More detailed numerical calculations are needed in order to come to a firm conclusion on this issue, since a substantial improvement is necessary to predict the exact amount of Lyman continuum photons emitted in the accretion process.

4.3. Star formation efficiency

Our objects are bona fide young Hii regions (see Sect. 2), and it is thus reasonable to assume that all sources are in a similar evolutionary phase, with the caveat that those with Lyman-excess might be slightly younger than the others (see Sect. 4.2). That our sample of Hii regions spans a small range of ages can be verified by studying the size of the Hii region as a function of stellar mass, which should depend on the mass of the star ionizing it. In this case one should find a correlation between Hii region size and stellar mass. If, instead, the Hii regions are in different evolutionary stages, no correlation should be found because the size of the Hii region would depend not only on the stellar mass but also on the phase of expansion. In Fig. 15, we plot the ratio between the angular size of the Hii region (Θ_HII, provided by the CORNISH catalogue; see Purcell et al. 2013) and the FWHP at 500 μm of the Hi-GAL counterpart as a function of the ratio N_Ly/L. We prefer to use ratios to get rid of any error related to the distance estimates. The ratio N_Ly/L increases with stellar mass, while Θ_HII/FWHP_{500 μm} basically depends only on Θ_HII because the clump radius is only weakly dependent on the clump mass. Figure 15 shows a correlation between the two quantities (Spearman correlation coefficient 0.72), although with some spread, and confirms that all the regions are roughly coeval.

If our sample is indeed homogeneous, the observed distributions of mass, luminosity, and Lyman continuum emission should mirror the variation of the stellar cluster characteristics rather than a large spread in age. This can be verified by studying the ratios L/M_gas and N_Ly/L. Both should increase with time during the process of high-mass star formation because stars gain mass to the detriment of the surrounding envelope and thus increase their luminosities and Lyman continuum fluxes. Consequently, if our sources spanned a large age interval, one should observe a correlation between N_Ly/L and L/M_gas.

In Fig. 16 we plot these two ratios against each other for all of the 204 objects of our sample. We note that we have also included the four sources without V_LSR information because the L/M_gas and N_Ly/L do not depend on the distance. This feature makes the plot totally unaffected by the error on the distance. One does not see any significant correlation, consistent with the homogeneity of the sample. This allows us to obtain an estimate of the star formation efficiency. Using the same cluster simulations as in Sect. 4.1, we show in Fig. 16 the area over which 90% of the clusters should distribute, under the assumption that only 5% of the clump mass is converted into stars. The match between this region and the data points is very satisfactory, with the only exception being a handful of sources with the highest values of N_Ly/L. In the light of Sect. 4.1, this anomaly is not surprising, since these objects are the Hii regions with the most prominent Lyman excess.

We note that a star formation efficiency of ~5% is in reasonable agreement with the value of 10% found by URQ13 for the same type of objects. These authors compared the clump mass with the luminosity and Lyman continuum emission, instead of their ratios (as we did in Fig. 16). Using the same approach (see Fig. 17), we confirm the existence of a correlation between L and M_gas, and N_Ly and M_gas. Following URQ13, we verified that such correlations were not due to the fact that all these quantities (L, N_Ly, and M_gas) scale like d². For this purpose we performed a partial Spearman correlation test (see also Urquhart et al. 2013a and references therein), which gives correlation coefficients of 0.72 for L, M_gas, and d, and 0.54 for N_Ly, M_gas, and d. For 197 degrees of freedom, these values correspond to a null probability that the correlations L vs. M_gas and N_Ly vs. M_gas are not significant. Comparison with cluster simulations (shaded blue region in Fig. 16) confirm a star formation efficiency of 5%, independent of mass and luminosity of the cluster. This is interpreted by URQ13 as evidence that more massive clumps form more massive stars.

4.4. Clump stability

We have also investigated whether the clumps associated with the selected Hii regions are in virial equilibrium. To compute the virial mass, M_vir, one needs an estimate of the velocity dispersion in the molecular clumps, namely of the FWHM of a molecular line. This information is obviously missing in our continuum data, but we were able to recover it from the literature. Many of our targets have also been studied by URQ13, who estimated the corresponding M_vir using both new line observations and data from the literature. For the sake of comparison with our clump mass estimates, we scaled URQ13 virial masses to the distances and radii that we adopted. Moreover, we took the ammonia line widths from Wienen et al. (2012) and Urquhart et al. (2011) to calculate M_vir for some of the sources not in URQ13. For the sake of consistency with these authors, we used their Eqs. (3) and (5) with the same assumptions.

In Fig. 18, we plot the virial ratio as a function of the ratio L/M_gas. If the clump stability changed during the evolution, one should find a correlation between the two quantities, as L/M_gas is expected to increase during star formation. No such trend is visible in the figure, and this is consistent with the previous conclusion that our sample spans a relatively narrow range of ages. The plot confirms the findings of URQ13, namely that almost all of the sources are supervirial. This is in agreement also with other studies (e.g., Fontani et al. 2002; Kauffmann et al. 2013) and supports the idea that clumps above ~10³M_⊙ in high-mass star forming regions are unstable against gravitational collapse.

In the same figure, we also make a distinction between sources with Lyman excess (red solid points) and those without (black empty points). Interestingly, the distribution of the former appears skewed to the bottom left of the plot. This is confirmed by the mean values of the logarithms of the two ratios, which are ⟨ log ₁₀(M_gas/M_vir) ⟩ = 0.26 for the Lyman-excess sources and 0.55 for the others, and ⟨ log ₁₀(L/M_gas) ⟩ = 1.2 for the Lyman-excess sources and 1.4 for the others. According to the K-S test, the probability that sources with and without Lyman-excess have the same distribution is 3 × 10^-4 for log ₁₀(L/M_gas) and 5 × 10^-5 for log ₁₀(M_gas/M_vir), which supports the existence of a real difference between the two samples. These findings hint at slightly different evolutionary phases for the two types of objects, with the Lyman-excess sources being embedded in clumps closer to virial equilibrium and thus at the beginning of the collapse phase. In particular, it is worth noting that only 42% of the Lyman-excess sources have M_gas/M_vir> 2 (the critical value for clumps in virial equilibrium assuming equipartition between kinetic and magnetic energy; see URQ13), as opposed to 83% of the other xxx sources.

5. Summary and conclusions

We have identified the Herschel/Hi-GAL IR counterparts of the young Hii regions detected in the CORNISH survey, with the aim of studying the properties of the associated early-type stars and possibly of drawing some conclusion on the star formation process. Out of 281 Hii regions, we were able to reconstruct the SED for 204 objects. We determined the bolometric and Lyman continuum luminosity for 200 of these because it was not possible to obtain a kinematic distance estimate for four Hii regions in the sample. We also estimated the masses of the associated molecular clumps from the (sub)millimeter flux densities.

We find that 67 objects present a “Lyman excess”, as the Lyman continuum emission exceeds the maximum value expected for the same bolometric luminosity. No definitive explanation can be identified for this effect. We propose that infall onto the star and/or an associated accretion disk might cause the shocked material to emit additional UV photons that add up to the normal Lyman continuum of the OB star. While some models appear to support this interpretation, significant progress in the numerical calculations is still needed to prove our hypothesis and demonstrate that Hii regions are undergoing accretion during a considerable fraction of their lives.

We construct a distance-independent plot of the ratio between the Lyman continuum and bolometric luminosity versus the ratio between the bolometric luminosity and corresponding clump mass, and use cluster simulations to fit the observed distribution in this plot. The result is that a good match is found if only 5% of the clump mass is converted into stars, consistent with previous estimates of the star formation efficiency in similar objects.

Finally, we find that the majority of clumps associated with all Hii regions of our sample are supervirial and hence unstable against gravitational collapse. However, those associated with Lyman-excess sources are on average closer to equilibrium, hinting at these objects being in a slightly earlier evolutionary phase.

Online material

Appendix A

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Acknowledgments

G.S.S. acknowledges support received through grants awarded by NASA. Herschel Hi-GAL data processing, maps production and source catalogue generation have been possible thanks to Contracts I/038/080/0 and I/0 29/12/0 from ASI, Agenzia Spaziale Italiana. This paper made use of information from the Red MSX Source survey database at http://rms.leeds.ac.uk/cgi-bin/public/RMS_DATABASE.cgi which was constructed with support from the Science and Technology Facilities Council of the UK. This publication also makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This research made use of data products from the Midcourse Space Experiment. Processing of the data was funded by the Ballistic Missile Defense Organization with additional support from NASA Office of Space Science. This research has also made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

References

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