The importance of radiative pumping on the emission of the H₂O submillimeter lines in galaxies

Soon after the launch of the Herschel Space Observatory (Pilbratt et al., 2010), spectroscopic observations with the SPIRE instrument (Griffin et al., 2010) revealed strong H₂O submillimeter (hereafter submm) emission from the ultraluminous infrared galaxy (ULIRG) Mrk 231, with strengths comparable to the those of the CO lines (van der Werf et al., 2010). The H₂O submm lines were subsequently detected in a variety of local galaxies with SPIRE (see Yang et al., 2013; Lu et al., 2017, and references therein) and also HIFI (Liu et al., 2017), as well as in high-redshift ULIRGs and Hyper-LIRGs from ground based facilities (e.g. Omont et al., 2011, 2013; van der Werf et al., 2011; Yang et al., 2016, 2019). Based on the H₂O line fluxes in galaxies at all redshifts, Omont et al. (2013) and Yang et al. (2013) found a strong correlation between the H₂O line luminosities and the infrared luminosities of the galaxies, $L_{\mathrm{H_{2}O-submm}}\propto L_{\mathrm{IR}}^{\alpha}$, with an index $\alpha$ slightly higher than unity. The extragalactic H₂O submm emission has been modeled in terms of radiative pumping (González-Alfonso et al., 2010, 2014, 2021; Pereira-Santaella et al., 2017), and the $L_{\mathrm{H_{2}O-submm}}-L_{\mathrm{IR}}$ correlations appeared to support this view (Omont et al., 2013; Yang et al., 2013; Lu et al., 2017).

In parallel, several H₂O submm lines have been observed in a large number of both low-mass and high-mass star-forming regions (LMSFR and HMSFRs) in our galaxy (e.g. van Dishoeck et al., 2021, and references therein) with the HIFI instrument (de Graauw et al., 2010). The lines were resolved with the high spectral resolution provided by HIFI, showing broad profiles characteristic of outflows and their associated dense shocked gas where the H₂O submm emission is collisionally excited. The H₂O line profiles also often showed a narrower spike at central velocities, which contributes negligibly (often in absorption) to the integrated emission in LMSFRs (e.g. Kristensen et al., 2012), but accounts for an average of $\sim 40$% in HMSFRs (San José-García et al., 2016) and is attributed to the warm, massive envelopes around the luminosity sources. Considering both galactic and extragalactic sources, San José-García et al. (2016) found a strong $L_{\mathrm{H_{2}O-submm}}-L_{\mathrm{IR}}$ correlation with an index $\alpha$ that was higher (and closer to unity) than when only the galactic sources were fitted.

Using Infrared Space Observatory (ISO, Kessler et al., 1996) data (with $80^{\prime\prime}$ aperture) and radiative transfer models, Cernicharo et al. (2006) found that much of the H₂O line excitation in the Orion KL outflow is driven by the dust continuum radiation. On the other hand, van Dishoeck et al. (2021) argued, based on the nearly linear ($\alpha=0.95\pm 0.02$) correlation they found between Herschel H₂O $2_{02}-1_{11}$ 988 GHz line luminosities of both galactic and extragalactic sources versus source luminosity, that the H₂O submm emission in galaxies may be a scaled-up version of galactic sources, where the $L_{\mathrm{H_{2}O-submm}}-L_{\mathrm{IR}}$ correlation is set by H₂O collisional excitation in dense shocks.

In this Letter we address this lack of consensus on the excitation mechanism of these lines in galaxies, and thus on the physical information that H₂O provides on the sources from which the H₂O emission lines arise. We propose both a qualitative and a quantitative diagnostic to distinguish between the two mechanisms, each involving the far-infrared (far-IR) H₂O $3_{21}-2_{12}$ 75 $\mu$m and $2_{20}-1_{11}$ 101 $\mu$m lines, and apply them to all extragalactic sources and a sample of HMSFRs where the H₂O 75 $\mu$m and 1163 GHz lines have been observed with Herschel/PACS (Poglitsch et al., 2010) and SPIRE, respectively. A flat $\Lambda$CDM cosmology with $H_{0}=70$ km s^-1 Mpc^-1 and $\Omega_{\mathrm{M}}=0.27$ is adopted, but for some nearby galaxies preferred distances are used.

The simplified energy level diagram of Fig. 2a illustrates the basic mechanism of radiative pumping: if a 75 $\mu$m photon emitted by dust pumps an ortho-H₂O molecule from the $2_{12}$ level to the $3_{21}$ one, it can relax via cascade down along the $3_{21}\rightarrow 3_{12}\rightarrow 3_{03}\rightarrow 2_{12}$ ladder through emission in the corresponding 1163, 1097, and 1717 GHz lines. Likewise, a pumping event in the para-H₂O $2_{20}\leftarrow 1_{11}$ 101 $\mu$m line followed by cascade down along the $2_{20}\rightarrow 2_{11}\rightarrow 2_{02}\rightarrow 1_{11}$ ladder generates H₂O emission in the 1229, 752, and 988 GHz lines. These can be denoted as “radiative pumping cycles”, and always involve the loss of a continuum photon in the 75 and 101 $\mu$m pumping lines. Assuming that the absorption is isotropic, the 75 and 101 $\mu$m pumping lines will be seen in absorption. On the other hand, if H₂O is collisionally excited (e.g. in dense shocks), the $3_{21}$ and $2_{20}$ levels will be populated accordingly and subsequent spontaneous emission in the $3_{21}\rightarrow 2_{12}$ and $2_{20}\rightarrow 1_{11}$ transitions will generate emission, rather than absorption, in both the 75 and 101 $\mu$m lines. We can then establish the first qualitative criterion to distinguish between radiative pumping and collisional excitation of the H₂O submm lines assuming isotropy: in the former case, the 75 and 101 $\mu$m lines are expected in absorption, while in the latter case they are expected in emission.

Caveats on the above diagnostic are related to geometry effects. Shock-excited gas could be in front of a strong continuum source that could ultimately generate line absorption at 75 and 101 $\mu$m in the direction of the observer. However, since $T_{\mathrm{gas}}$ and $n_{\mathrm{H2}}$, which determine the excitation in shocks, are fully decoupled from the properties of the continuum source behind (and specifically $T_{\mathrm{gas}}>T_{\mathrm{dust}}$), fine tuning of the shock model would be required to obtain the absorption/emission pattern. On the other hand, lack of absorption in the 75 and 101 $\mu$m lines does not fully preclude the radiative pumping mechanism because the responsible far-IR field could be external without impinging on the H₂O molecules from the back side (in the direction of the observer), and hence would not produce line absorption (Appendix A in González-Alfonso et al., 2014).

A quantitative criterion for radiative pumping arises from statistical equilibrium of the H₂O levels: since the populations of the $3_{21}$ and $2_{20}$ levels remain constant in time, and assuming that their populations are exclusively determined by the above pumping cycles, the net rate of absorption events in the $3_{21}\leftarrow 2_{12}$ 75 $\mu$m line (hereafter $R^{\mathrm{abs}}_{\mathrm{75\,\mu m}}$) should be equal to the net rate of emission events in the $3_{21}\rightarrow 3_{12}$ 1163 GHz line ($R^{\mathrm{ems}}_{\mathrm{1163\,GHz}}$). Likewise, the same equality holds for the para-H₂O pumping cycle, $R^{\mathrm{abs}}_{\mathrm{101\,\mu m}}=R^{\mathrm{ems}}_{\mathrm{1229\,GHz}}$. We calculate $R^{\mathrm{ems,abs}}_{\mathrm{line}}$ in the limit of optically thin continuum emission at 75(101) $\mu$m and isotropic line absorption/emission:

where $E_{\mathrm{line}}=h\nu_{0}$ is the energy of line photons, $D_{L}$ is the luminosity distance, $z$ is the redshift, $h$ is the Planck constant, $c$ is the speed of light, and $L_{\mathrm{line}}$ and $F_{\mathrm{line}}$ are the line luminosity in erg s^-1 and line flux in Jy km s^-1 above (emission, $+$ sign) or below (absorption, $-$ sign) the continuum ($D_{L}$, $h$, and $c$ are in cgs units).

Equation (1) holds if the H₂O 75(101) $\mu$m line is optically thick, provided that it remains effectively optically thin and repeated absorption/re-emission events in the line end with the photon either escaping from the source (with no contribution to $R^{\mathrm{ems,abs}}_{\mathrm{line}}$) or generating a submm cascade (contributing to both $R^{\mathrm{ems}}_{\mathrm{line}}$ and $R^{\mathrm{abs}}_{\mathrm{line}}$). However, if the far-IR continuum optical depth becomes significant, thermal continuum photons emitted at 75(101) $\mu$m will have a higher chance, after multiple line absorption/re-emission events, of being absorbed by dust grains before escaping from the source, generating absorption in the far-IR line with no submm line counterpart. In very optically thick regions (with continuum optical depths at 100 $\mu$m $\tau_{100}>>1$ as found in a number of (U)LIRGs) the emission in the submm lines will be partially extincted and could even be observed in absorption. As $\tau_{100}$ increases, additional radiative paths (de)populating the $3_{21}$ and $2_{20}$ levels come into play, but the overall general result is that the absorption fluxes of the 75 and 101 $\mu$m surface tracers are increased relative to the emission fluxes of the 1163 and 1229 GHz volume tracers. Therefore, in case of significant far-IR continuum optical depth effects, the $R^{\mathrm{ems,abs}}_{\mathrm{line}}$ rates calculated in Eq. (1) are only apparent, and we can more generally state that

are criteria for the radiative pumping mechanism in isotropic conditions. Anisotropy effects of the exciting radiation field could favor either $R^{\mathrm{abs}}_{\mathrm{75,101\,\mu m}}$ or $R^{\mathrm{ems}}_{\mathrm{1163,1229\,GHz}}$, and would spread their relative values for randomly oriented sources.

The “base levels” from which the radiative pumping cycles operate, $2_{12}$ and $1_{11}$, must still be populated in some way. They could be populated via absorption of dust-emitted photons in the $2_{12}\leftarrow 1_{01}$ 179 $\mu$m and $1_{11}\leftarrow 0_{00}$ 269 $\mu$m ground-state lines, but this mechanism may be inefficient in optically thin $\tau_{100}<1$ sources where the dust emission at these wavelengths is weak. At very high redshift, H₂O excitation from the ground-state can also be produced by the cosmic microwave background (Riechers et al., 2022). Alternatively, the “base levels” could be excited through collisions in warm and dense regions, so that collisional excitation of the low-excitation lines combined with the radiative pumping mechanism would be required to account for the submm emission (González-Alfonso et al., 2014).

The preponderance of H₂O 75 $\mu$m absorption is difficult to reconcile with collisional excitation in shock cavities devoid of significant amounts of warm dust. An alternative is to assume that the H₂O 1163 GHz line is generated in an ensemble of shock cavities, where the H₂O 75 $\mu$m line is also generated in emission, while a spatially separated and unrelated $\tau_{100}>>1$ component produces the 75 $\mu$m absorption (almost always stronger than the emission to generate net absorption in the line). However, this scenario does not explain the correlation between $R^{\mathrm{abs}}_{\mathrm{75\,\mu m}}$ and $R^{\mathrm{ems}}_{\mathrm{1163\,GHz}}$ as the two lines are generated in different regions and by different mechanisms. Even if $\dot{E}$ (mechanical) and $L_{\mathrm{IR}}$ are related, the specific lines respond in different ways to the far-IR and mechanical feedback. The case of Orion KL illustrates this point: large FoVs show emission in the 75 $\mu$m line far above the absorption towards the HC (lower insert in Fig. 2a).

The following interpretation of the $L_{\mathrm{H2O\,988\,GHz}}-L_{\mathrm{IR}}$ correlation stems from the present analysis. In Fig. 2c, we have increased the dynamic range of the correlation found by Yang et al. (2013) for extragalactic sources to the luminosities characteristic of galactic sources, assuming that the “radiative pumping slope” of 1.12 holds. Then, a number of HMSFRs and basically all LMSFRs, where H₂O is shock-excited, lie well above this line. Using the spectral decomposition of the H₂O 988 GHz spectra in HMSFRs carried out by van der Tak et al. (2013) and San José-García et al. (2016), we have plotted in Fig. 2c the H₂O 988 GHz luminosities due to only the massive envelopes of HMSFRs (light-blue symbols), finding a good match with the extended extragalactic correlation. We thus propose that these galactic massive envelopes play a role similar to the circumnuclear disks in galaxies (including the CND of the Milky Way), where the H₂O submm emission is radiatively pumped⁴⁴4In this framework, the slope of 1.1 could be due to the increasing linewidth $\Delta v$ with $L_{\mathrm{IR}}$, as for the optically thick 75 and 101 $\mu$m lines $R^{\mathrm{abs}}_{\mathrm{75-101\,\mu m}}\propto\Delta v$. If $\Delta v$ increases by a factor $\sim 5$ as $L_{\mathrm{IR}}$ increases by 7 dex, the index of the correlation will be $\sim 1+(\log_{10}5)/7=1.1$. -combined at least in some cases with collisional excitation of the low-energy levels. Galactic sources located significantly above the blue line in Fig. 2c would indicate dominance of excitation by shocks. The location of the galactic HMSFRs in Fig. 2a resemble the starburst galaxies NGC 253 and IRAS 13120-5453, lacking an obscured nucleus that in its prominent form is a unique feature of extragalactic sources.

While we expect that the para-H₂O 101 $\mu$m pumping cycle is as important as the ortho-H₂O 75 $\mu$m one, the low-excitation $1_{11}$ and $2_{02}$ levels will be more affected by collisions in warm/dense regions than the $3_{21}$ one; therefore the 988 GHz line has less ability than the 1163 GHz line to discriminate between the two mechanisms.