The large radiation field directly produced from young stellar objects can exert a significant pressure on the surrounding material. This radiation pressure, Prad, at a given position within an H ii region, is related to the bolometric luminosity, Lbol, of the stellar population and the distance, r, from each star to that position within the region:
(3)$$\begin{eqnarray*}
P_\mathrm{rad} = \sum {\frac{L_\mathrm{bol}}{4 \pi r^{2} c}},
\end{eqnarray*}$$where the summation is over all stars within the region. The volume-averaged direct radiation pressure, Pdir, is then given as (Lopez et al. 2014),
(4)$$\begin{eqnarray*}
P_\mathrm{dir} = \frac{3 L_\mathrm{bol}}{4 \pi R^{2} c},
\end{eqnarray*}$$where R is the radius of the H ii region (or effective radius, Reff, that we define later and use throughout the rest of the paper), and Lbol is the bolometric luminosity from the population of massive stars within the H ii region. This form differs by a factor of three from McLeod et al. (2019, equation 4), as these authors calculate the radiation surface pressure rather than the volume average pressure. This expression is appropriate to compute the force balance at the surface of an empty shell. However, as this work aims at understanding the large-scale dynamics of the Galactic Centre H ii regions (e.g. the total energy and pressure budget for each source), the inclusion of a factor of three in the numerator of the above equation is required. We also note here that the higher metallicity within the Galactic Centre, or increasing the amount of dust, has no effect on the Pdir calculation. Direct radiation pressure is limited by the momentum supplied by the stellar radiation field, and, as long as there is enough dust around to absorb all the radiation, the momentum per unit time delivered is the same. Lopez et al. (2011) determine the bolometric luminosity of the H ii regions within the LMC and SMC from H $\alpha$ emission. However, this is not possible for the H ii regions investigated here, due to the high optical extinction towards the Galactic Centre (Av >20 mag), which completely obscures any H $\alpha$ emission. We, therefore, adopt two alternative methods of calculating the bolometric luminosity using radio and infrared observations (i.e. wavelengths where the emission is much less affected by dust extinction). First, we can make the assumption that the bolometric luminosity is proportional to the flux of ionizing photons, $\mathcal {N}_\mathrm{LyC}$, such that $L_\mathrm{bol} = \mathcal {N}_\mathrm{LyC} \left\langle h \nu \right\rangle$, where 〈hν〉 ∼ 15  eV is the mean photon energy (Pellegrini et al. 2007). We use the $\mathcal {N}_\mathrm{LyC}$ for each H ii region as determined from the radio observations outlined in Table  2 (i.e. Gaume & Claussen 1990; Mehringer et al. 1992; Schmiedeke et al. 2016), and solve for the direct radiation pressure using equation (4). The second method assumes that the luminosity integrated over infrared wavelengths approximately corresponds to the total bolometric luminosity. This is a common assumption made for embedded star-forming regions, where the luminosity from massive stars produced at ultraviolet wavelengths is absorbed and remitted by the dust in the infrared. Barnes et al. (2017) have produced maps of the total infrared luminosity across the Galactic Centre. These authors fit a two-component modified blackbody function to extinction corrected 5.8–24 $\mu $m (Carey et al. 2009; Churchwell et al. 2009) and 160 –500 $\mu $m (Molinari et al. 2010) emission maps (referred to as the warm and cool component of the bolometric luminosity; see fig. 2 of Barnes et al. 2017). These infrared (i.e. bolometric) luminosity maps are used with the two methods outlined below to also determine the direct radiation pressure within each of the Galactic Centre H ii regions. In comparison with the first method for calculating the direct radiation pressure from radio observations, we choose to identify individual sources within the infrared maps. These can be considered as discrete H ii regions each with a single value of the direct radiation pressure. We choose to identify these H ii regions in the map of the warm component of the bolometric luminosity using a dendrogram analysis (Rosolowsky et al. 2008). We choose to use a structure finding algorithm, as opposed to by-eye identification, to give reproducibility within regions with particularly complex morphology (the warm bolometric luminosity map is given in fig. 2 from Barnes et al. 2017).3 We make use of the ‘leaves’ identified from the dendrogram analysis, which are the highest level (i.e. smallest) structures in the analysis and here represent distinct H ii regions. We take the mask of each H ii regions (dendrogram leaf), and apply this to both the warm and cool bolometric luminosity component maps, which we sum to then get the total bolometric luminosity. This is used with equation (4) to get the direct radiation pressure (Pdir) within each H ii region. The effective radius (Reff) of each H ii region is defined as the radius for a circle with the corresponding area (A) of each structure (i.e. $R_{\rm eff}=\sqrt{A/\pi }$). In addition to the dendrogram analysis, we also calculate the direct radiation pressure within apertures of increasing radius from the centre of each H ii region complex. To do so, we place circular masks for each source on to both the warm and cool bolometric luminosity component maps, and sum the enclosed values to then get the total bolometric luminosity. The circle is then increased in radius, and the process repeated. We again use equation (4) to determine the direct radiation pressure within these increasing circular apertures. This method differs from the dendrogram analysis, as it returns a continuous radial distribution from the source centre, as opposed to a distribution of distinct H ii region with various sizes.
Citation: Mehringer et al. 1992
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