Free Access
Issue
A&A
Volume 567, July 2014
Article Number A91
Number of page(s) 13
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201423980
Published online 17 July 2014

© ESO, 2014

1. Introduction

With its high dipolar moment, extremely rich spectrum, and high level spacing (in comparison to those of other molecules with low-lying transitions at millimeter wavelengths), H2O couples very well to the radiation field in warm regions that emit strongly in the far-IR. In extragalactic sources, excited lines of H2O at far-IR wavelengths (λ< 200 μm) were detected in absorption with the Infrared Space Telescope (ISO; Fischer et al. 1999; González-Alfonso et al. 2004, 2008), and with Herschel/PACS (Pilbratt et al. 2010; Poglitsch et al. 2010) in Mrk 231 (Fischer et al. 2010), Arp 220 and NGC 4418 (González-Alfonso et al. 2012, G-A12). Modeling and analysis have demonstrated the ability of H2O to be efficiently excited through absorption of far-IR dust-emitted photons, thus providing a powerful method for studying the strength of the far-IR field in compact/warm regions that are not spatially resolved at far-IR wavelengths with current (or foreseen) technology.

Herschel/SPIRE (Griffin et al. 2010) has enabled the observation of H2O at submillimeter (hereafter submm, λ > 200 μm) wavelengths in local sources, where the excited (i.e., non-ground-state) lines are invariably seen in emission. In Mrk 231, lines with Eupper up to 640 K were detected (van der Werf et al. 2010; González-Alfonso et al. 2010, hereafter G-A10), with strengths comparable to the CO lines. The H2O lines have been also detected in other local sources (Rangwala et al. 2011; Pereira-Santaella et al. 2013), including the Seyfert 2 galaxy NGC 1068 (Spinoglio et al. 2012, S12). Furthermore, submm lines of H2O have been detected in a dozen of high-z sources (Impellizzeri et al. 2008; Omont et al. 2011; Lis et al. 2011; van der Werf et al. 2011; Bradford et al. 2011; Combes et al. 2012; Lupu et al. 2012; Bothwell et al. 2013), even in a z = 6.34 galaxy (Riechers et al. 2013). Recently, a striking correlation has been found between the submm H2O luminosity (LH2O), taken from the 202−111 and 211−202 lines, and the IR luminosity (LIR), including both local and high-z ULIRGs (Omont et al. 2013, hereafter O13). Using SPIRE spectroscopy of local IR-bright galaxies and published data from high-z sources, the linear correlations between LH2O and LIR for five of the strongest lines, extending over more than three orders of magnitude in IR luminosity, has recently been confirmed (Yang et al. 2013, hereafter Y13). There are hints of an increase in LH2O that is slightly faster than linear with LIR in some lines (211−202 and 220−211 ) and in high-z ULIRGs (O13). HCN is another key species that also shows a tight correlation with the IR luminosity, even though the excitation of the 1−0 transition is dominated by collisions with dense H2 (Gao & Solomon 2004a,b).

The increasing wealth of observations of H2O at submm wavelengths in both local and high-z sources and the correlations discovered between LH2O and LIR require a more extended analysis in parameter space than the one given in G-A10 for Mrk 231. In this work, models are presented to constrain the physical and chemical conditions in the submm H2O emitting regions in warm (U)LIRGs and to propose a general framework for interpreting the H2O submm emission in extragalactic sources.

2. Excitation overview

At submm wavelengths, H2O responds to far-IR excitation by emitting photons through a cascade proccess. This is illustrated in Fig. 1, where four far-IR pumping lines (at 101, 75, 58, and 45 μm) account for the radiative excitation of the submm lines (G-A10). The line parameters are listed in Table 1, where we use the numerals 1−8 to denote the submm lines. Lines 2−4, 5−6, 7, and 8 are pumped through the 1011, 75, 58, and 45 μm far-IR transitions, respectively.

The ground-state line 1 has no analog pumping mechanism, so that the upper 111 level can only be excited through absorption of a photon in the same transition (at 269 μm) or through a collisional event. In the absence of significant collisional excitation, and if approximate spherical symmetry holds, line 1 will give negligible absorption or emission above the continuum (regardless of line opacity) if the continuum opacity at 269 μm is low or will be detected in absorption for significant 269 μm continuum opacities2. This is supported by the SPIRE spectrum of Arp 220, in which line 1 is observed in absorption (Rangwala et al. 2011) and high submm continuum opacities are inferred (González-Alfonso et al. 2004; Downes & Eckart 2007; Sakamoto et al. 2008). Collisional excitation and thus high densities and gas temperatures are then expected in sources where line 1 is detected in emission (10 sources among 176, Y13), as in NGC 1068 (S12; see also Appendix A). Line 1 can then be collisionally excited in regions where the other lines do not emit owing to weak far-IR continuum; this effect has recently been observed in the intergalactic filament in the Stephan’s Quintet (Appleton et al. 2013).

thumbnail Fig. 1

Energy level diagram of H2O, showing the relevant H2O lines at submillimeter wavelengths with blue arrows, and the far-IR H2O pumping (absorption) lines with dashed-magenta arrows. The lines are numbered as listed in Table 1. The o-H2O 312−221 transition is not considered due to blending with CO (10-9) (G-A10), and the far-IR 212−101 transition at 179.5 μm discussed in the text is also indicated in green for completeness.

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If collisional excitation of the 111 and 212 levels dominates over absorption of dust photons at 269 and 179 μm (i.e., in very optically thin and/or high density sources), the submm H2O lines 2−6 will be boosted because these 111 and 212 levels are the base levels from which the 101 and 75 μm radiative pumping cycles operate (Fig. 1). In addition, in regions of low continuum opacities but warm gas, collisional excitation of the para-H2O level 202 from the ground 000 state can significantly enhance the emission of line 2. Therefore, the H2O submm emission depends in general on both the far-IR radiation density in the emitting region and the possible collisional excitation of the low-lying levels (111, 212, and 202). Lines 7−8 require strong far-IR radiation density not only at 58−45 μm, but also at longer wavelengths, together with high H2O column densities (NH2O) in order to significantly populate the lower backbone 313 and 414 levels.

Table 1

H2O transitions at λ > 200 μm considered in this work.

Table 2

Model parameters.

3. Description of the models

The basic models for H2O were described in G-A10 (see also references therein). Summarizing, we assume a simple spherically symmetric source with uniform physical properties (Tdust, Tgas , gas and dust densities, H2O abundance), where gas and dust are assumed to be mixed. We only consider the far-IR radiation field generated within the modeled source, ignoring the effect of external fields (except for NGC 1068, Appendix A). The source is divided into a set of spherical shells where the statistical equilibrium level populations are calculated. The models are non-local, including line and continuum opacity effects. We assume an H2O ortho-to-para ratio of 3. Line broadening is simulated by including a microturbulent velocity (Vturb), for which the FWHM velocity dispersion is ΔV = 1.67Vturb. No systemic motions are included.

3.1. Mass absorption coefficient of dust

The black curve in Fig. 2 shows the dust mass opacity coefficient used in the current and our past models (González-Alfonso et al. 2008, 2010, 2012, 2013, 2014). Our values at 125 and 850 μm are κ125 = 30 cm2 g-1 and κ850 = 0.7 cm2 g-1, in good agreement with those derived by Dunne et al. (2003). Adopting a gas-to-dust ratio of X = 100 by mass, and using κ100 = 44.5 cm2 g-1, the column density of H nuclei is (1)where τ100 is the continuum optical depth at 100 μm.

For this adopted dust composition, the fit across the far-IR to submm (blue line in Fig. 2) indicates an emissivity index of β = 1.85, slightly steeper than the β = 1.5−1.6 values favored by Kóvacs et al. (2010) and Casey (2012). The H2O excitation is sensitive to the dust emission over a range of wavelengths (from 45 to 270 μm), but we find that our results on LH2O/LIR are insensitive to β for β values above 1.5 (Sect. 4.3.3).

thumbnail Fig. 2

Adopted mass absorption coefficient of dust as a function of wavelength. The dust emission is simulated by using a mixture of silicate and amorphous carbon grains with optical constants from Draine (1985) and Preibisch et al. (1993). As shown by the fitted blue line, the emissivity index from the far-IR to millimeter wavelengths is β = 1.85.

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3.2. Model parameters

As listed in Table 2, the model parameters we have chosen to characterize the physical conditions in the emitting regions are Tdust , the continuum optical depth at 100 μm along a radial path (τ100), the corresponding H2O column density per unit of velocity interval (NH2OV), the velocity dispersion ΔV, Tgas , and the H2 density (nH2). Fiducial numbers for some of these parameters are τ100 = 0.1, ΔV = 100 kms-1, Tgas = 150 K, and nH2 = 3 × 105 cm-3. Collisional rates with H2 were taken from Dubernet et al. (2009) and Daniel et al. (2011). Our relevant results are the line-flux ratios (Fi/Fj) and the luminosity ratios3LH2O/LIR. We also explore models where collisions are ignored, appropriate for low-density regions (nH2 ≲ 104 cm-3), for which Fi/Fj only depend on Tdust , τ100, and NH2OV, while LH2O/LIR depends in addition on ΔV.

Depending on the values of the above parameters, our models can be interpreted in terms of a single source or are better applied to each of an ensemble of clouds within a clumpy distribution. The radius of the modeled source is (2)where Eq. (1) has been applied. The corresponding IR luminosity can be written as , where γ(Tdust,τ100) ≤ 1 accounts for the departure from a blackbody emission due to finite optical depths, ranging from γ = 0.2 for Tdust = 50 K and τ100 = 0.1 to γ = 0.9 for Tdust = 95 K and τ100 = 1. In physical units, (3)in L , indicating that a model with τ100 ~ 0.1 and moderate Tdust should be considered as one of an ensemble of clumps to account for the typically observed IR luminosities of 1011L (Y13). For very warm (Tdust ~ 90 K) and optically thick (τ100 ~ 1) sources with low average densities (nH2 = 3 × 103 cm-3), Eq. (3) gives LIR ~ 5 × 1011L and the model can be applied to a significant fraction of the circumnuclear region of galaxies where the clouds may have partially lost their individuality (Downes & Solomon 1998).

The velocity dispersion ΔV in our models can be related to the velocity gradient used in escape probability methods as dV/ dr ~ ΔV/ (2R), and using Eq. (2) (4)Defining Kvir as the ratio of the velocity gradient relative to that expected in gravitational virial equilibrium, Kvir = (dV/ dr)/(dV/dr)vir, and using (dV/dr)vir ~ 10 × (nH2/105 cm-3)1 / 2km s-1 pc-1 (Bryant & Scoville 1996; Goldsmith 2001; Papadopoulos et al. 2007; Hailey-Dunsheath et al. 2012), we obtain (5)Values of Kvir significantly above 1 and up to ~20, indicating non-virialized phases, have been inferred in luminous IR galaxies from both low- and high-J CO lines (e.g., Papadopoulos & Seaquist 1999; Papadopoulos et al. 2007; Hailey-Dunsheath et al. 2012). For clarity, the velocity dispersion is rewritten in terms of Kvir as (6)which shows that, for compact and dense clumps (τ100 = 0.1, nH2 = 3 × 105 cm-3), ΔV ~ 25 × (Kvir/10) kms-1 and the typical observed linewidths (~300 kms-1) are caused by the galaxy rotation pattern and velocity dispersion of clumps. In contrast, for optically thick sources with low densities (τ100 = 1, nH2 ≲ 104 cm-3), ΔV ≳ 130 km s-1 is required for Kvir ≳ 1.

Instead of calculating ΔV for each model according to Eq. (6), which would involve a “universal” Kvir independent of the source characteristics4, we have used ΔV = 100 kms-1 for comparison purposes between models (in Sect. 4.3.5 we also consider models with constant Kvir). Nevertheless, results can be easily rescaled to any other value of ΔV as follows. For given Tdust and τ100, the relative level populations, the line opacities, and thus the H2O line-flux ratios (Fi/Fj) depend on NH2OV, while the luminosity ratios LH2O/LIR are proportional to ΔV. Therefore, for any ΔV, identical results for Fi/Fj are obtained with the substitution (7)while LH2O/LIR should be scaled as (8)Both the line-flux ratios (Fi/Fj) and the luminosity ratios LH2O/LIR are independent of the number of clumps (Ncl) if the model parameters (Tdust, τ100, Tgas , nH2, NH2OV, and ΔV) remain the same for the cloud average. With the effective source radius defined as , both the line and continuum luminosities scale as . Therefore, if the effective source size is changed and all other parameters are kept constant, a linear correlation between each LH2O and LIR is naturally generated, regardless of the excitation mechanism of H2O. (For reference, however, all absolute luminosities below are given for Reff = 100 pc.) The question, then, is what range of dust and gas parameters characterizes the sources for which the observed nearly linear correlations in lines 2−6 (O13, Y13) are observed. The detection rates of lines 1, 7, and 8 are relatively low, but the same trend is observed in the few sources where they are detected (Y13).

thumbnail Fig. 3

Relevant model results for the normalized H2O SLED (a1)f1)), and for the LH2O/LIR ratios (for ΔV = 100 kms-1) as a function of Tdust and LIR (assuming a source of Reff = 100 pc, a2)f2)). In panels a1)f1), model results for lines 1 to 8 (Table 1) are shown from left to right. Values for NH2OV and τ100 are indicated at the top of the figure. The different colors in panels a1)f1) indicate different Tdust , as labeled in b1), while they indicate different lines in panels a2)f2) (labeled in a2), see Table 1). Models with collisional excitation ignored (a)c)), and with collisions included for nH2 = 3 × 105 cm-3 and Tgas = 150 K (d)f)) are shown. The gray lines/symbols in panels d1)f1) show model results that ignore radiative pumping (i.e., only collisional excitation). Collisional excitation has the overall effect of enhancing the low-lying lines (1 and 2) relative to the others and of increasing the LH2O/LIR ratios of all lines (see text). The dashed lines in panels a2)f2) indicate the average LH2O/LIR ratios reported by Y13. When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities, because single temperature dust models are unable to reproduce the observed SEDs (Sect. 4.3.1); the H2O submm emission traces warm regions of luminous IR galaxies (see text).

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In the following sections, the general results of our models are presented, while specific fits to two extreme sources, Arp 220 and NGC 1068, are discussed in Appendix A.

4. Model results

4.1. General results

In Fig. 3, model results are shown in which Tdust is varied from 35 to 115 K, NH2OV from 5 × 1014 to 5 × 1015cm-2/ (km s-1), τ100 from 0.1 to 1.0, and where collisional excitation with nH2 = 3 × 105 cm-3 and Tgas = 150 K is excluded (ac) or included (df). Panels a1f1 (top) show the expected SLED normalized to line 2, and panels a2-f2 (bottom) plot the corresponding LH2O/LIR × (100 km s-1/ ΔV) ratios as a function of Tdust and LIR (for Reff = 100 pc; all points would move horizontally for different Reff). The effect of collisional excitation is also illustrated in Fig. 4, where the H2O submm fluxes of lines 2−6 relative to those obtained ignoring collisional excitation are plotted as a function of nH2 for Tgas = 150 K.

The first conclusion that we infer from Figs. 3a1-f1 is that the relative fluxes of lines 5−6 generally increase with increasing Tdust . These lines are pumped through the H2O transition at λ ~ 75 μm (Fig. 1), thus requiring warmer dust than lines 2−4, which are pumped through absorption of 100 μm photons. The SLEDs obtained with Tdust < 45 K yield F4 significantly above F6, and are thus unlike those observed in most (U)LIRGs (Y13). The two peaks in the H2O SLED (in lines 2 and 6) generally found in (U)LIRGs (Y13) indicate that the submm H2O emission essentially samples regions with Tdust ≳ 45 K. Significant collisional excitation enhances line 4 relative to line 6 (Figs. 3d1f1), thus aggravating the discrepancy between the Tdust < 45 K models and the observations.

Lines 7−8 provide stringent constraints on Tdust , τ100, and NH2OV. Since line 6 is still easily excited even with moderately warm Tdust ~ 55 K, the 8/6 and 7/6 ratios are good indicators of whether very warm dust ( > 80 K) is exciting H2O. Sources where lines 7−8 are detected (e.g., Mrk 231, Arp 220, and APM 08279) can be considered “very warm” on these grounds, with NH2O/ ΔV ≳ 3 × 1015cm-2/ (km s-1). Sources where lines 7−8 are not detected to a significant level, but where the SLED still shows a second peak in line 6, are considered “warm”, i.e. with Tdust varying between ~45 and 80 K, and NH2O/ ΔV ~ (5−20) × 1014cm-2/ (km s-1).

Sources in which lines 2−6 are not detected to a significant level, that do not show a second peak in line 6, or for which the H2O luminosities are well below the observed LH2OLIR correlation are considered “cold”. These sources are characterized by very optically thin and extended continuum emission, and/or with low NH2O (these properties likely go together). Such sources include starbursts like M82 (Y13), where the continuum is generated in PDRs and are physically very different from the properties of “very warm” sources like Mrk 231 (G-A10).

In the models that neglect collisional excitation (a1c1), line 1 is predicted to be in absorption, transitioning to emission in warm/dense regions where it is collisionally excited (d1f1), as previously argued. Its strength will also depend on the continuum opacity, which should be low enough to allow the line to emit above the continuum. Direct collisional excitation from the ground state in regions with warm gas but low τ100 efficiently populates level 202, so that the 2/3, 2/4, 2/5, and 2/6 ratios strongly increase with increasing nH2 (Fig. 4a). As advanced in Sect. 2, collisional excitation also boosts all other submm lines for moderate Tdust owing to efficient pumping of the base levels 212 and 111; radiative trapping of photons emitted in the ground-state transitions increases the chance of absorption of continuum photons in the 101 and 75 μm transitions. Nevertheless, collisional excitation is negligible for high τ100 and high Tdust (Fig. 4b).

thumbnail Fig. 4

Effect of collisional excitation on the H2O fluxes of the submm lines 2−6 as a function of nH2. The ordinates show the calculated line fluxes relative to the model that ignores collisional excitation. Tgas = 150 K is adopted in all models. a) In the case of moderate Tdust and low τ100, collisional excitation has a strong impact on the H2O fluxes at nH2 of a few × 104 cm-3, especially on line 2. b) Collisional excitation is negligible for high τ100 and very warm Tdust (note the difference in ordinate scales in a) and b)).

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4.2. Predicted line ratios

In sources where lines 7 and 8 are not detected, the 6/4 flux ratio is the most direct indication of the hardness of the far-IR radiation field seen by the H2O gas responsible for the observed emission. Since line 4 is pumped through absorption of 101 μm photons and line 6 by 75 μm photons (Fig. 1), one may expect a correlation between the 6/4 ratio and the 75-to-100 μm far-IR color, f75/f100. As shown in Fig. 5a, our models indeed show a steep increase in the 6/4 ratio with Tdust for fixed τ100 and NH2O. The averaged observed 6/4 ratio of 1.45−1.7 in strong-AGN and HII+mild-AGN sources (Y13) indicates, assuming an optically thin continuum (Fig. 5a), Tdust ≈ 55−75 K and f75/f100 = 1.5−1.8. For the case of high τ100 and NH2OV, the averaged 6/4 ratio is consistent with lower Tdust and f75/f100 = 1 −1.2. In general, the 6/4 ratio indicates Tdust ≈ 45−80 K5. Similarly, the 6/2 ratio is also sensitive to Tdust , as shown in Fig. 5b. The observed averaged 6/2 ratio of 1−1.2 is compatible with Tdust somewhat lower than estimated from the 6/4 ratio. This is attributable to the effects of collisional excitation of the 202 level (thus enhancing line 2 over line 6, see Fig. 4a and magenta symbols in Fig. 5b), or to the contribution to line 2 by an extended, low Tdust component.

There is, however, no observed correlation between the 6/4 ratio and f60/f100 (Y13), which should still show a correlation (though maybe less pronounced) than the expected correlation with f75/f100. As we argue in Sect. 4.3, this lack of correlation suggests that the observed far-IR f60/f100 colors, and in particular the observed f100 fluxes, are not dominated by the warm component responsible for the H2O emission. Indeed, current models for the continuum emission in (U)LIRGs indicate that the flux density at 100 μm is dominated by relatively cold dust components (Tdust ~ 30 K) (e.g. Dunne et al. 2003; Kóvacs et al. 2010; Casey 2012). The observed H2O emission thus arises in warm regions whose continuum is hidden within the observed far-IR emission, but may dominate the observed SED at λ ≲ 50 μm (e.g., Casey 2012, see also Sect. 4.3.1).

thumbnail Fig. 5

a)F6/F4 (oH2O 321−312-to-pH2O 220−211) and b) F6/F2 (oH2O 321−312-to-pH2O 202−111) line flux ratios as a function of the 75-to-100 μm far-IR color. Blue symbols: NH2OV = 1015cm-2/ (km s-1) and τ100 ≤ 0.1; black: NH2OV = 5 × 1015cm-2/ (km s-1) and τ100 ≤ 0.1; red: NH2OV = 5 × 1015cm-2/ (km s-1) and τ100 = 1.0; green: NH2OV = 1015cm-2/ (km s-1) and τ100 = 1.0; magenta: same as blue symbols but with collisional excitation included with Tgas = 150 K and nH2 = 3 × 105 cm-3. The small numbers close to the symbols indicate the value of Tdust . The observed averaged ratios for strong-AGN and HII+mild-AGN sources (Y13) are indicated with dashed horizontal lines, and indicate that the regions probed by the H2O submm emission are characterized by warm dust (Tdust ≳ 45 K).

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thumbnail Fig. 6

F6/F5 (oH2O 321−312-to-312−303) line flux ratio as a function of τ100. The small numbers on the right side of the curves indicate the values of Tdust for each curve. The H2O column density per unit of velocity interval is NH2OV = 1015cm-2/ (km s-1) (green, blue, and magenta curves) and NH2OV = 5 × 1015cm-2/ (km s-1) (red and black curves).

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The H2O lines 5 and 6 are both pumped through the 75 μm transition. Assuming that the lines are optically thin, statistical equilibrium of the level populations implies that every de-excitation in line 6 will be followed by a de-excitation in either line 5 or in the 312−221 transition (dotted arrow in Fig. 1), with relative probablities determined by the A-Einstein coefficients. In these optically thin conditions, we expect a 6/5 line flux ratio of F6/F5 = 1.16 (Fig. 6). This is a lower limit, because in case of high NH2O/ ΔV and/or high Tdust and τ100, absorption of line 5 emitted photons that can eventually be reemited through the 312−221 transition, or absorption of continuum photons in the H2O 423−312 transition, will decrease the strength of line 5 relative to line 6.

Although with significant dispersion, overall data for HII+mild AGN sources indicate F6/F5 ~ 1.2 (Y13)6, consistent with the optically thin limit; examples of this galaxy population are NGC 1068 and NGC 6240 (Spinoglio et al. 2012; Meijerink et al. 2013). There are, however, sources like Arp 220 and Mrk 231 with F6/F5 ≈ 1.6, favoring warm dust ( > 55 K) and substantial columns of H2O and dust. This indicates that sources in both the optically thin and optically thick regimes are H2O emitters.

In optically thin conditions and with moderate Tdust , lines 2−4, together with the pumping 220−111 101 μm transition, form a closed loop (Fig. 1) where statistical equilibrium of the level populations implies equal fluxes for the three submm lines (Figs. 3a1c1). The rise in Tdust and τ100, however, increases the chance of line absorption in the strong 322−211 transition at 90 μm, thus decreasing the flux of line 3 relative to both line 2 and 4. Consequently, the F2/F3 ratio is expected to increase from 1 (for low τ100) to 2 (for τ100 ~ 1 and NH2O/ ΔV ≳ 1017cm-2/ (km s-1)), consistent with the relatively high values found in the warm Mrk 231 and APM 08279 (Y13). If collisional excitation is important (Figs. 3df), F2/F3 is also expected to increase because collisions mainly boost the lower lying line 2 (Fig. 4a).

One interesting caveat is, however, the behavior of the 4/3 ratio, because increasing Tdust and/or NH2O is predicted to increase F2/F3 but maintains F4/F3 > 1 (Figs. 3a1c1). In Mrk 231, the high F2/F3 ratio and mostly the detection of lines 7−8 indicate very warm dust (G-A10), but the relatively low F4/F3 ≲ 1 observed in the source does not match this simple scheme. The problem is exacerbated with the 6/2 ratio, which is also expected to increase with increasing Tdust and τ100 to 1.5 (Fig. 5), but Mrk 231 shows F6/F2 ≈ 1. Nevertheless, the problem can be solved if source structure is invoked. A composite model where a very warm component accounts for the high-lying lines and a colder (dust) component enhances lines 2 −4 (with probable contribution from collisionally excited gas, as suggested by the high F2/F3 ratio), can give a good fit to the SLED (G-A10), although the characteristics of the “cold” component (density, extension, Tdust ) are relatively uncertain. A relatively low flux in line 4 can also be produced by absorption of continuum photons emanating from a very optically thick component, as in Arp 220 (see Appendix A).

4.3. The LH2O – LIR correlations

4.3.1. H2O and the observed SED

It has long been recognized that single-temperature graybody fits to galaxy SEDs at far-IR wavelengths often underpredict the observed emission at λ< 50 μm. Therefore, multicomponent fitting, based on, for example, a two-temperature approach, a power-law mass-temperature distribution, a power-law mass-intensity distribution, or a single cold dust temperature graybody with a mid-IR power law (Dunne et al. 2003; Kóvacs et al. 2010; Dale & Helou 2002; Casey 2012), is required to match the full SED from the mid-IR to millimeter wavelengths. Our single-temperature model results on the H2O SLED favors Tdust ≳ 45 K (Sect. 4.2), significantly warmer than the cold dust temperatures (<40 K) that account for most of the observed far-IR emission in luminous IR galaxies, indicating that the H2O submm emission primarily probes the warm region(s) of galaxies where the mid-IR (20−50 μm) emission is generated (see footnote 5).

Relative to the total IR emission of a galaxy, , the contribution to the luminosity by a given Tdust component i is , and the observed H2O-to-IR luminosity ratio is (9)where (LH2O/LIR)i are the values plotted in Figs. 3a2f2 (for ΔV = 100 kms-1), and the problem is grossly simplified by considering only two “warm” and “cold” components. From the comparison of the observed average SLED (Y13) with our models, we infer that the contribution by the cold component to is small, even though fcold may be high. Since our modeled LIR emission from the warm component is thus only a fraction, fwarm, of the total IR budget, the modeled LH2O/LIR ratios in Figs. 3a2–f2 should be considered upper limits. The value of fwarm can only be estimated by fitting the individual SEDs.

thumbnail Fig. 7

Model results showing the luminosity of the H2O line 6 (321−312) as a function of the product of the monochromatic luminosities at 75 and 179 μm. Luminosities are calculated for a source with Reff = 100 pc, NH2OV = 1015cm-2/(km s-1), and ΔV = 100 kms-1. Blue squares indicate models with τ100 = 0.1, resulting in optically thin or moderately thick H2O emission, without collisional excitation. Magenta squares show results for the same models but with collisional excitation included with Tgas = 150 K and nH2 = 3 × 105 cm-3. Green symbols indicate models with τ100 = 1.0, resulting in optically thick H2O emission. For optically thin H2O emission and without collisional excitation, the models indicate a linear correlation between LH2O and L75 × L179 (red line).

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4.3.2. H2O emission and monochromatic luminosities

The H2O submm emission of lines 2−6 essentially involves two excitation processes, that of the base level (212 for ortho and 111 for para-H2O) and absorption in the transitions at 75 μm (ortho) or 101 μm (para, Fig. 1). If collisional excitation is unimportant, the excitation of the base levels is also produced by absorption of dust-emitted photons in the corresponding transitions, i.e., in the 212−101 line at 179 μm (ortho) or 111−000 at 269 μm (para). In optically thin conditions and for fixed NH2O and ΔV, our models then show a linear correlation between the H2O luminosities LH2O and the product of the continuum monochromatic luminosities responsible for the excitation, L179 × L75 (ortho) or L269 × L101 (para). This linear correlation is illustrated in Fig. 7 for line 6. The linear correlation, however, breaks down when the line becomes optically thick or when collisional excitation becomes important (in which case, LH2O is independent of L179(269)).

4.3.3. The LH2O/LIR ratios and Tdust

The above considerations are relevant for our understanding of the behavior of the modeled LH2O/LIR values with variations in Tdust . In the optically thin case and with collisional excitation ignored, the double dependence of LH2O on two monochromatic luminosities implies that LH2O is (nearly) proportional to LIR. Our predicted SEDs indicate that, for small variations in Tdust around 55 K, and . Therefore, for the para-H2O lines 2−4, in optically thin conditions, slightly slower than linear. For the ortho lines, and , so that L5−6LIR. This explains why, in Figs. 3a2b2, the L2−4/LIR ratios show a slight decrease with increasing Tdust above 55 K, while L5−6/LIR versus Tdust attain a maximum at Tdust ≈ 55 K in optically thin models that omit collisional excitation. These results are robust against variations in the spectral index of dust down to β = 1.5 (Sect. 3.1).

thumbnail Fig. 8

Modeled LH2O/LIR × (100 km s-1/ ΔV) for lines 2 (upper), 4 (middle), and 6 (lower) as a function of the f25/f60 color. The dashed vertical lines indicate the lower and upper limits for f25/f60 measured by Y13. In the upper panel, the small numbers below the squares indicate the value of Tdust , and τ100 is also indicated. Blue squares: NH2O/ ΔV = 1015cm-2/ (km s-1) and τ100 = 0.1; magenta: same as blue symbols but with collisional excitation included with Tgas = 150 K and nH2 = 3 × 105 cm-3; green: NH2OV = 1015cm-2/ (km s-1) and τ100 = 1.0; black: same as green but with NH2OV = 5 × 1015cm-2/ (km s-1). Red squares show results for fixed Tdust = 55 and 65 K with NH2O/(ΔVτ100) = 5 × 1015cm-2/ (km s-1) and τ100 = 0.1−0.3. The starred symbols indicate the positions of Arp 220 (blue), NGC 6240 (green), Mrk 231 (red), and NGC 1068 (magenta), as reported by Rangwala et al. (2011), Meijerink et al. (2013), G-A10, and Y13, respectively. When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities (Sect. 4.3.1). If f60 is contaminated by cold dust, the points would move to the left.

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In Fig. 8 we show the LH2O/LIR ratios (with ΔV = 100 kms-1; LH2O/LIR ∝ ΔV) for lines 2, 4, and 6 as a function of the f25/f60 color. The observed f25/f60 was used by Y13 to characterize the H2O emission and is especially relevant given that the H2O submm emission arises in warm regions in which the mid-IR continuum emission is not severely contaminated by cold dust. However, the continuum at λ = 60 μm may still be contaminated to some extent, in which case the data points in Fig. 8 will move toward the left. We also recall that the LH2O/LIR values are upper limits.

The first conclusion inferred from Fig. 8 is that the range of f25/f60 colors measured by Y13 (between the dashed lines) matches Tdust in the ranges favored by the observed H2O line flux ratios, that is, 50−75 K and optically thin conditions (τ100 = 0.1) and also Tdust = 60−95 K and τ100 = 1.0. This indicates that the warm environments responsible for the H2O emission are best traced in the continuum in this wavelength range, but also that the f25/f60 color alone involves degeneracy in the dominant Tdust and τ100 responsible for the mid-IR continuum emission. As shown in Sect. 4.2, the first set of conditions can explain the line ratios 2−6 in warm sources (where lines 7−8 are not detected to a significant level), while the second set is required to explain the H2O emission in very warm sources (with detection of lines 7−8).

Second, it is also relevant that the LH2O/LIR values differ by a factor 2 between models with warm dust in the optically thin regime (Tdust = 55 K, τ100 = 0.1, NH2O/ ΔV = 1015cm-2/ (km s-1)) and those with very warm dust in the optically thick regime with high H2O columns (Tdust = 95 K, τ100 = 1, NH2O/ ΔV = 5 × 1015cm-2/ (km s-1)), potentially explaining why sources with different physical conditions show similar LH2O/LIR ratios (Y13).

Third, in optically thin conditions (τ100 ~ 0.1) and if collisional excitation is unimportant, the models with constant NH2O/ ΔV = 1015cm-2/ (km s-1) (blue symbols) predict a slow decrease in L2−4/LIR and a nearly constant L5−6/LIR with increasing f25/f60, as argued above. This behavior, however, fails to match the observed trends (Y13), as L2−4/LIR and L6/LIR decrease by factors of ~2 and ~3, respectively, when f25/f60 increases from 0.08 to 0.15. When collisional excitation is included (magenta symbols), the L2−4/LIR ratios show a stronger dependence on f25/f60, but L6/LIR still changes only slightly with f25/f60.

Therefore, optically thin models with varying Tdust but constant τ100, NH2O/ ΔV, and ΔV cannot account for the observed LH2O/LIRf25/f60 trend. This indicates that, in optically thin galaxies, parameters other than Tdust are systematically varied when f25/f60 is increased and that optically thick sources also contribute to the observed trend:

  • (i)

    Galaxies in the optically thin regime (with τ100 < 1) are predicted to show a very steep dependence of LH2O/LIR on τ100 for constant Tdust and NH2O/(ΔVτ100) (that is, for constant H2O abundance), with higher τ100 impling lower f25/f60. We illustrate this point in Fig. 8 with the red squares, corresponding to fix Tdust = 55 and 65 K and NH2O/(ΔVτ100) = 5 × 1015cm-2/ (km s-1), with τ100 ranging from 0.1 to 0.3. Therefore, we expect that the observed increase in f25/f60 is not only due to an increase in Tdust from source to source, but also to variations in τ100 in the optically thin regime. Examples of galaxies in this regime are the AGNs NGC 6240 and NGC 1068 (see also Appendix A).

  • (ii)

    In the optically thick regime (τ100 ≳ 1), galaxies are also predicted to show a relatively steep variation in LH2O/LIR with f25/f60 due to increasing Tdust (black symbols in Fig. 8) because the H2O lines saturate and their luminosities flatten with increasing monochromatic luminosities (Fig. 7). Extreme examples of this galaxy population are Arp 220 and Mrk 231. Line saturation also implies that the LH2O/LIR ratios are not much higher than in the optically thin case even if much higher NH2OV = 5 × 1015cm-2/ (km s-1) are present, and the corresponding ratios are consistent with the observed values to within the uncertainties in fwarm. The presence of even warmer dust ( > 100 K) with significant contribution to LIR will additionally decrease LH2O/LIR (Y13).

In summary, the steep decrease in LH2O/LIR at f25/f60 ≈ 0.1−0.15 measured by Y13 is consistent with both types of galaxies (with optically thin and optically thick continuum) populating the diagram and suggests that the observed variations in f25/f60 are not only due to variations in Tdust but also to variations in τ100 in the optically thin regime. At the other extreme, the optically thick (saturated) and very warm galaxies are also expected to show a decrease in LH2O/LIR with increasing Tdust (and f25/f60), as anticipated by Y13. To distinguish between both regimes for a given galaxy, the line ratios (specifically F6/F5, Sect. 4.2) and mostly the detection of lines 7−8 or the detection of high-lying H2O absorption lines at far-IR wavelengths are required. The observations reported by Y13 indicate that these optically thick and warm components (diagnosed by the detection of lines 7−8) are present in at least ten sources. At least in NGC 1068 the upper limits on lines 7−8 are stringent (S12), allowing us to infer optically thin conditions.

4.3.4. Line saturation and a theoretical upper limit to LH2O/LIR

thumbnail Fig. 9

Modeled LH2O/LIR × (100 km s-1/ ΔV) values for lines 2 (upper), 4 (middle), and 6 (lower) as a function of τ100. Collisional excitation is ignored except for the red dashed lines, where Tgas = 150 K and nH2 = 3 × 105 cm-3 are adopted. The small numbers on the right side of the upper panel indicate the value of Tdust in K, and those on the left side indicate NH2OV in cm-2/(km s-1). When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities (Sect. 4.3.1). For τ100 = 12 and Tdust = 95 K, line 4 is predicted to be in absorption. For fixed Tdust and τ100 ~ 1, the LH2O/LIR ratios are similar for very different NH2O, indicating line saturation.

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Saturation of the H2O submm lines in optically thick (τ100 ~ 1) sources implies that there is an upper limit on LH2O/LIR × (100 km s-1V) that, in the absence of significant collisional excitation, cannot be exceeded. In Fig. 9, the LH2O/LIR × (100 km s-1V) ratios for lines 2, 4, and 6 are plotted as a function of τ100 for the most favored Tdust range of 55−95 K and NH2OV = (1−5) × 1015cm-2/ (km s-1). In optically thin conditions (τ100 ≲ 0.1 for NH2OV = 1015cm-2/ (km s-1)) and without collisions, LH2O/LIR scales linearly (for fixed ΔV) with τ100 because while LIRτ100. The curves flatten as the H2O lines saturate and show a maximum at τ100 ≈ 0.5−1. Values of τ100 significantly higher than unity are predicted to decrease LH2O/LIR. In very optically thick components of very warm sources, the submm lines are predicted to be observed in weak emission or even in absorption, especially in line 4. Arp 220 is a case in point (Sakamoto et al. 2008), in which the H2O submm emission is expected to arise from a region that surrounds the optically thick nuclei (see Appendix A). For ΔV = 100 kms-1, the maximum attainable values of LH2O/LIR (red curves) are 3.5 × 10-5, 4 × 10-5, and 7 × 10-5 for lines 2, 4, and 6, respectively, comfortably higher than the values observed in any source by Y13. Recently, a value of L2/LIR = (4.3 ± 1.6) × 10-5 has been measured in the submillimeter galaxy SPT 0538-50, a gravitationally lensed dusty star-forming galaxy at z ≈ 2.8 (Bothwell et al. 2013). Although the authors do not exclude differential lensing effects, which could affect the line-to-luminosity ratios, this value is still consistent with our upper limit, suggesting strong saturation in this source. In HFLS3 at z = 6.34, Riechers et al. (2013) have measured F6/F2 = 2.2 ± 0.5 and F6/F5 = 2.6 ± 0.8; within the uncertainties, these values are consistent with warm or very warm Tdust ≳ 65 K and high NH2O (Figs. 5, 6). The H2O lines are most likely saturated in HFLS3 as is also indicated by the L6/LIR = (7.7 ± 1.3) × 10-5 ratio, which is still consistent with the strong saturation limit for warm Tdust given the very broad linewidth of the H2O line (~940 kms-1; see Sect 3.2). O13 reported L2/LIR = (0.5−2) × 10-5 in high-z ultra-luminous infrared galaxies, also consistent with the upper limit in Fig. 9 even for Tdust ~ 75 K when taking the broad line widths of the H2O lines into account. Line saturation and a relatively small contribution from cold dust to the infrared emission in these extreme galaxies are implied. With collisional excitation in optically thin environments with moderate Tdust but high NH2O, the above LH2O/LIR ratios (red dashed lines in Fig. 9) may even attain higher values, though the adopted ΔV = 100 kms-1 is too high for τ100 < 0.3 and nH2 = 3 × 105 cm-3 (Sect 3.2, Eq. (6)).

4.3.5. The correlation

thumbnail Fig. 10

Modeled L2/LIR ratio as a function of τ100. Squares and triangles indicate Tdust = 55 and 75 K, respectively. In all models, collisional excitation is included with Tgas = 150 K and nH2 = 3 × 104 cm-3. NH2O/τ100 = 1018 cm-2 is adopted, corresponding to a constant H2O abundance of 7.7 × 10-7 (Eq. (1)). Blue symbols indicate models with ΔV = 100 kms-1 and thus with variable Kvir (Eq. (5)) indicated with the numbers. Green symbols show results with ΔV = 100 × τ100 kms-1 simulating a constant value of Kvir = 1.3. When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities (Sect. 4.3.1), and thus the modeled L2/LIR values are upper limits.

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The broad range in observed LIR in luminous IR galaxies with H2O emission may be attributable to varying the effective size of the emitting region. As noted in Sect. 3.2, varying Reff (equivalent to varying the number of individual regions that contribute to LIR or to increasing LIR for a single source) is expected to generate linear LH2OLIR correlations if the other parameters (Tdust, τ100, Tgas , nH2, NH2OV, and ΔV) remain constant.

In Fig. 10 we show the L2/LIR ratio as a function of τ100 for models with Tdust = 55 K and Tdust = 75 K that assume a constant H2O-to-dust opacity ratio, that is, NH2O/τ100 = 1018 cm-2. According to Eq. (1), this corresponds to a constant H2O abundance of 7.7 × 10-7. Both models with ΔV = 100 kms-1 (independent of τ100), and ΔV/τ100 = 100 kms-1 (corresponding to a constant Kvir = 1.3) are shown. The figure illustrates that a supralinear correlation between LH2O and LIR can be expected if, on average, τ100 is an increasing function of LIR. If most sources with LIR ~ 5 × 1010L were optically thin (τ100 ~ 0.1), and the high-z sources with LIR ~ 1013L (O13) were mostly optically thick (τ100 ~ 1), one would then expect from Fig. 10, which can account for the observed supralinear correlation found by O13 and Y13. However, similar supralinear correlations would then be expected for the other submm lines 3−6.

5. Summary of the model results for optically classified starbursts and AGNs

Following the classification of sources by Y13 into optically classified star-formation-dominated galaxies with possible mild AGN contribution (HII+mild AGN sources) and optically identified strong-AGN sources, we now consider these two groups separately.

5.1. HII+mild AGN sources

We focus here on those HII+mild AGN sources where lines 2−6 are detected but lines 7−8 are undetected (that is, “warm” sources as defined in Sect. 4.1). The average H2O flux ratios reported by Y13 (their Table 2) indicate that (i)F6/F2 ~ 1.2, favoring Tdust = 55 K if there is no significant collisional excitation and Tdust = 75 K if the H2O emission arises in warm and dense gas (Fig. 5); (ii)F6/F5 ~ 1.2, consistent with the optically thin regime (Fig. 6). For these Tdust , Fig. 11a shows the values of NH2O for ΔV = 100 kms-1 required to explain the observed LH2O/LIR ratios, as a function of τ100. Models with included or excluded collisional excitation are considered. We recall that ΔV is the velocity dispersion of the dominant structure(s) that accounts for the H2O emission (Sect. 3.2), and for the case of low τ100 and relatively high densities, Eq. (6) suggests ΔV < 100 kms-1 with the consequent increase in NH2O (Fig. 10).

The decrease in τ100 implies the increase in NH2O in optically thin conditions and when collisional excitation is unimportant. Our best fit models for the average SLED (big solid symbols) favor optically thin far-IR emission (τ100 ≲ 0.3). In Figs. 11be, the detailed comparison between the τ100 = 0.1 models and the observations (Y13) is shown. Significant collisional excitation is not favored for Tdust = 55 K, since it would increase F2 relative to F6. In addition, these optically thin models have the drawback of overestimating F4/F2. Conversely, the Tdust = 75 K models favor significant collisional excitation in order to increase F2 relative to F6. The very optically thin models (τ100 ≲ 0.05) are also not favored given the very high amounts of H2O required to explain (with no collisional excitation) the LH2O/LIR ratios.

thumbnail Fig. 11

a) Values of NH2O for ΔV = 100 km s-1 as a function of τ100, for Tdust = 55 K (red) and 75 K (blue), required to account for the observed averaged LH2O/LIR ratios in HII-mild AGN sources (as given by Y13). Models both without (squares) and with (triangles) collisional excitation are shown. In the latter models, Tgas = 150 K, and nH2 = 5 × 104−3 × 105 cm-3 for Tdust = 55−75 K, respectively. The large filled symbols indicate the best fit models to the averaged SLED. Panels b) e) compare in detail the four models with τ100 = 0.1 (both with and without collisions) with the observed values (black circles) in HII-mild AGN sources (both the normalized flux ratios (SLED) and the LH2O/LIR ratios, Y13, for lines 26). In panels b) and d), the models indicate the values of LH2O/LIR for ΔV = 100 kms-1. Lines 1, 7, and 8 are excluded from the comparison because of their low detection rates (Y13).

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In summary, Tdust = 55−75 K, τ100 ~ 0.1, and NH2O ~ (0.5−2) × 1017 cm-2 can explain the bulk of the H2O submm emission in warm star-forming galaxies (Table 2). As shown in Fig. 8, Tdust = 55 K and τ100 = 0.1−0.2 predict 25-to-60 μm flux density ratios of f25/f60 = (8.5−6.0) × 10-2, in agreement with the observed values for the bulk of sources (Y13), while Tdust = 75 K and τ100 = 0.1−0.2 predict f25/f60 = 0.42−0.30 (close to the observed upper values). Assuming a gas-to-dust ratio of 100 by mass, τ100 ~ 0.1 corresponds to a column density of H nuclei of NH ≈ 1.3 × 1023 cm-2 (Eq. (1)), and thus an H2O abundance of XH2O ~ 10-6. To within a factor of 3 uncertainty due to the τ100NH calibration, the specific values used for τ100 and ΔV, and variations in the measurements for individual sources, this is the typical H2O abundance that we infer from the observed LH2OLIR correlation. Molecular shocks and hot core chemistry are very likely responsible for this XH2O, which is well above the volume-averaged values inferred in Galactic dark clouds and PDRs (e.g., Bergin et al. 2000; Snell et al. 2000; Melnick & Bergin 2005; van Dishoeck et al. 2011).

Finally, we note that Tdust = 55 K and τ100 = 0.1−0.2, and the assumption that most of the IR is powered by star formation in these sources of Y13, imply a star-formation-rate surface density7 of ΣSFR = 121−195M yr-1 kpc-2 and gas mass surface density of Σgas = 1430−2860M pc-2. The implied depletion or exhaustion time scale, tdep = Σgas/ ΣSFR, is ~12−15 Myr. These values lie close to the ΣSFR−Σdense star-formation correlation found by García-Burillo et al. (2012) from HCN emission in (U)LIRGs with their revised HCN-Mdense conversion factors. This agreement suggests that the submm H2O and the mm HCN emission in (U)LIRGs arise from the same regions. Sources with Tdust = 75 K would imply even shorter time scales and suggest high rates of ISM return from SNe and stellar winds. A follow-up study of the relationship between LH2O and LHCN is required to check this point. In addition, modeling the individual sources simultaneously in the continuum and the H2O emission will provide further constraints on the nature of these regions.

5.2. Strong optically classified AGN sources

The general finding that the H2O emission is similar in star-forming and strong-AGN sources (Y13) may simply indicate that the far-IR pumping of H2O occurs regardless of whether the dust is heated via star formation or an AGN. There are, however, some differences between the two source types. Strong AGNs show a higher detection rate in H2O 111−000 (Y13), indicating that the gas densities are higher in the circumnuclear regions of AGNs. Another difference is that the LH2O/LIR ratios are somewhat lower in strong AGN sources (Y13). While relatively low columns of dust and H2O in these sources could explain this observational result, it is also possible that high X-ray fluxes photodissociate H2O, reducing its abundance relative to star-forming galaxies. High abundances of H2O require effective shielding from UV and X-ray photons and thus high columns of dust and gas that, in AGN-dominated galaxies, may be effectively provided by an optically thick torus probably accompanied by starburst activity. In addition, warm dust further enhances XH2O through an undepleted chemistry and pumps the excited H2O levels, while warm gas will further boost XH2O through reactions of OH with H2. These appear to be the ideal conditions for the presence of large quantities of H2O in the (circum)nuclear regions of galaxies.


1

This line lies within the PACS 100 μm gap, but was detected in Arp 220 and Mrk 231 with ISO (González-Alfonso et al. 2004, 2008).

2

This is analogous to the behavior of the OH 119 μm doublet, see González-Alfonso et al. (2014).

3

We denote LH2O as the H2O luminosity of a given generic H2O submm line, while Li is the luminosity of the H2O line i (numbering in Table 1). The H2O line fluxes Fi are given in Jy km s-1. LIR is the 8−1000 μm luminosity.

4

We may expect Kvir > 1 for clouds in a clumpy distribution due to the gravitational potential of the galaxy and external pressure (Papadopoulos & Seaquist 1999), but Kvir ~ 1 may be more appropriate for sources where the clouds have coalesced and the resulting (modeled) structure can be considered more isolated. However, Kvir > 1 in case of prominent outflows.

5

Such high Tdust can be explained in the optically thin case as follows: first, the para-111 level is more easily populated through radiation than the ortho-212 level, because the Blu/Aul ratio for the 111−000 transition is a factor 6 higher than for the 212−101 one (Blu and Aul are the Einstein coefficients for photo absorption and spontaneous emission). Second, the Blu coefficient of the para-220−111 pumping transition is a factor of 2.3 higher than that of the ortho-321−212 pumping transition. Taking into account an ortho-to-para ratio of 3, a 6/4 ratio of 1 is obtained for J179J75/(J269J101) ≈ 4.5 (Jλ is the mean specific intensity at wavelength λ), which requires Tdust ≈ 45 K.

6

We infer this value from the (LH2O/LIR)2/(LH2O/LIR)i ratios listed in Table 2 by Y13, though F6/F5 ~ 1.4 as derived directly from (LH2O/LIR)5/(LH2O/LIR)6, indicating that the averaged F6/F5 depends on the details (weights) of the average computation.

7

ΣSFR is estimated as 10-10LIR/(πR2), where a Chabrier (2003) initial mass function is used, and Σgas is given by Mgas/(πR2) where with NH = 1.3 × 1024τ100 cm-2 (Eq. (1)).

Acknowledgments

We are very grateful to Chentao Yang for useful discussions on the data reported in Y13. E.G.-A. is a Research Associate at the Harvard-Smithsonian Center for Astrophysics, and thanks the Spanish Ministerio de Economía y Competitividad for support under projects AYA2010-21697-C05-0 and FIS2012-39162-C06-01. Basic research in IR astronomy at NRL is funded by the US ONR; J.F. also acknowledges support from the NHSC. This research has made use of NASA’s Astrophysics Data System (ADS) and of GILDAS software (http://www.iram.fr/IRAMFR/GILDAS).

References

Online material

Appendix A: Two opposite, extreme cases: Arp 220 and NGC 1068

Arp 220 and NGC 1068 are prototypical sources that have been observed at essentially all wavelengths. With regard to their H2O submm emission, these galaxies are extreme cases and deserve special consideration.

In the nearby ULIRG Arp 220, discrepancies between the observed SLED (Rangwala et al. 2011, Y13) and the single-component models of Figs. 3a1c1 are worth noting. The observed high L6/LIR ≈ 2.4 × 10-5 (Fig. 8), together with the high 6/2 ratio of 1.4 (Fig. A.1a), suggest Tdust ≳ 65 K and NH2O ≳ 1017 cm-2, consistent with detection of lines 7−8. However, high Tdust and NH2O are mostly compatible with F4/F3 > 1, while the observed ratio is 0.7 (Fig. A.1a). As in Mrk 231, a composite model is required to account for the H2O SLED in this galaxy.

In sources with very optically thick and very warm cores such as Arp 220 (G-A12), the increase in τ100 above 1 decreases the submm H2O fluxes due to the rise of submm extinction (Fig. 9). While higher Tdust generates warmer SEDs, but lowers the LH2O/LIR ratios for lines 2−6, the increase in τ100 further decreases LH2O/LIR. This behavior suggests that the optimal environments for efficient H2O submm line emission are regions with high far-IR radiation density but moderate extinction, i.e., those that surround the thick core(s) where the bulk of the continuum emission is generated. In contrast, the H2O absorption at shorter wavelengths is more efficiently produced in the near-side layers of the optically thick cores, primarily if high-lying lines are involved. Absorption and emission lines are thus complementary, providing information on the source structure.

thumbnail Fig. A.1

a) Proposed composite model for the H2O submm lines in Arp 220 (see G-A12), compared with the observed line fluxes (black squares, from Rangwala et al. 2011). Toward the far-IR optically thick nuclear region (blue symbols), the Eupper< 400 K lines are expected mostly in absorption. The H2O emission is generated around that nuclear region, in the Cextended (G-A12) component (green). Red is total. b) Resulting predicted composite PACS/SPIRE H2O continuum-subtracted spectrum of Arp 220, which is dominated by absorption of the continuum.

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We have taken the models in G-A12 for Arp 220 to predict its submm H2O emission. In Fig. A.1a, the blue symbols/line indicate the predicted H2O fluxes towards the optically thick, warm nuclear region (both Cwest and Ceast , see G-A12), indicating that most submm lines (with the exception of lines 3, 7, and 8) are predicted in absorption. The observed H2O submm line emission (Rangwala et al. 2011) must therefore arise in the surrounding, optically thinner region, i.e., the Cextended component, where the H2O abundance in the inner parts (R ≲ 150 pc, where Tdust = 70−90 K) is increased relative to G-A12 (so Cextended has NH2O = 1.3 × 1017 cm-2 in Fig. A.1a). According to our model, the relatively low flux in line 4 is due to line absorption towards the nuclei. The main drawback of the model in Fig. A.1a is that line 7 is underestimated by a factor 2. The submm H2O emission in Arp 220 traces a transition region between the compact optically thick cores and the extended kpc-scale disk (G-A12). The overall H2O spectrum is, however, dominated by absorption of the continuum (Fig. A.1b).

thumbnail Fig. A.2

a) Composite model for the H2O emission in NGC 1068 favored in this work. Blue/red indicate ortho/para lines, and the submm H2O 1−6 lines (Table 1) are indicated. Open squares and triangles show the contribution by a moderate-excitation (ME) and a low-excitation (LE) component, and filled symbols indicate the total emission (see text for details); in both cases the submm H2O lines 2−6 are pumped through far-IR photons emitted by dust. b) Comparison between the observed fluxes of the H2O submm lines (black squares, from Spinoglio et al. 2012) and those predicted with the composite model.

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Just the opposite set of conditions characterizes the nearby Seyfert 2 galaxy NGC 1068, since the nuclear continuum emission is optically thin and collisional excitation is important (S12). All detected H2O lines, including those in the far-IR (100−200 μm) are seen in emission, and most of them show fluxes (in erg/s/cm2) unrelated to wavelength, upper level energy (up to 300 K), or A-Einstein coefficient (S12). In particular, the H2O 221−110 (108 μm) and 221−212 (180 μm) lines share the same upper level and show similar fluxes but the A-Einstein coefficient of the 108 μm transition is a factor of 8.4 higher than that of the 180 μm transition. With pure collisional excitation, the only way to account for the observed line ratios is to invoke high densities and H2O column densities, but also a relatively low Tgas to avoid significantly populating the high-lying levels ( > 300 K). S12 found that Tgas ~ 40 K, and very high NH2O and nH2 can provide a reasonable fit to the SLED. However, these conditions are unrelated to the warmer gas conditions in the nuclear region of NGC 1068, as derived from the CO SLED (S12, Hailey-Dunsheath et al. 2012, hereafter H12). In addition, the observed H2O submm SLED (Fig. A.2) is fairly similar to the SLEDs obtained in optically thin models with significant collisional excitation of the low-lying levels.

We have explored an alternative composite solution for the H2O emission in NGC 1068 with lower densities and H2O columns and higher Tgas , based on the far-IR pumping of the lines by an external anisotropic radiation field. In this framework, we can account for the weakness of the 108 μm line by the absorption of continuum photons, and indeed we would have to explain why this line is not observed to be even weaker than it is or in absorption. The higher lying far-IR 322−313 emission line at 156.2 μm is in this scenario pumped through absorption of continuum photons in the 322−211 line at 90 μm.

For the first component, we closely follow H12 in modeling the moderate-excitation (ME) component as an ensemble of clumps, which are described by Tdust = 55 K, τ100 = 0.18, nH2 = 106 cm-3, Tgas = 150 K, and NH2O = 6.5 × 1016 cm-2, and Vturb = 15 kms-1 (giving Kvir ~ 10, see H12). With a mass of 7.5 × 106M, this component is unable to account for the H2O submm lines 2−6, but generates a significant fraction of the observed emission in line 1 and some far-IR lines (Fig. A.2a and panel b).

We then added another, low-excitation (LE) component, which is identified with the gas generating the low-J CO lines (Krips et al. 2011, S12) and is thus assigned a density of nH2 = 2 × 104 cm-3. For simplicity, we also assume Tdust = 55 K, τ100 = 0.18, and NH2O = 6.5 × 1016 cm-2 as for the ME, but adopt the higher Vturb of 60 kms-1 (giving Kvir ~ 7). For the LE component, and besides the internal far-IR field described by its Tdust and τ100, we also follow H12 in including an external field (associated with the emission from the whole region), which is described as a graybody with TBG = 55 K and . The resulting mean specific intensity at 100 μm of the external field, , matches the value estimated by H12 within a factor of 2 (their Eq. (1)). A crucial aspect of the present approach is that this external field is assumed to be anisotropic, that is, it does not impinge into the LE clumps on the back side (in the direction of the observer). As a result, the external field contributes to the H2O excitation without generating absorption in the pumping far-IR lines (though some absorption is nevertheless produced by the internal field). As shown in Fig. A.2a, the LE component is expected to dominate the emission of the submm lines 2−6, as well as the emission of the majority of the far-IR lines. The required mass of the LE component is 3.5 × 107M, consistent with the mass inferred from the CO lines for the CND (S12), and the IR luminosity is 2.6 × 1010L.

A key assumption of the present model is that the external radiation field does not produce absorption in the far-IR lines, as otherwise (that is, in a perfectly isotropic radiation field) the strengths of the far-IR lines would weaken, and in particular, the H2O 221−110 line at 108 μm line would be predicted to be observed in absorption. The proposed anisotropy could be associated with the heating by the central AGN, and it seems possible as long as the source is optically thin in the far-IR. Radiative transfer in 3D would be required to check this feature. On the other hand, the external field, while having an important effect on the far-IR lines, has a secondary effect on the submm lines, which are primarily pumped by the internal (isotropic) radiation field (that is, by the dust that is mixed with H2O). With the caveat of the assumed intrinsic radiation anisotropy in mind, we preliminary favor this model over the pure collisional one in predicting the H2O submm fluxes and conclude that radiative pumping most likely plays an important role in exciting the H2O in the CND of NGC 1068.

From the models for these two very different sources and the case of Mrk 231 studied previously (G-A10), we conclude that the excitation of the submm H2O lines other than the 111−000 one is dominated by radiative pumping, though the relatively low-lying 202−111 line may still have a significant “collisional” contribution in some very warm/dense nuclear regions, and the radiative pumping may be enhanced with collisional excitation of the low-lying 111 and 212 levels. These individual cases also show that composite models to account for the full H2O far-IR/submm spectrum in a given source may be a rather general requirement.

All Tables

Table 1

H2O transitions at λ > 200 μm considered in this work.

Table 2

Model parameters.

All Figures

thumbnail Fig. 1

Energy level diagram of H2O, showing the relevant H2O lines at submillimeter wavelengths with blue arrows, and the far-IR H2O pumping (absorption) lines with dashed-magenta arrows. The lines are numbered as listed in Table 1. The o-H2O 312−221 transition is not considered due to blending with CO (10-9) (G-A10), and the far-IR 212−101 transition at 179.5 μm discussed in the text is also indicated in green for completeness.

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In the text
thumbnail Fig. 2

Adopted mass absorption coefficient of dust as a function of wavelength. The dust emission is simulated by using a mixture of silicate and amorphous carbon grains with optical constants from Draine (1985) and Preibisch et al. (1993). As shown by the fitted blue line, the emissivity index from the far-IR to millimeter wavelengths is β = 1.85.

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In the text
thumbnail Fig. 3

Relevant model results for the normalized H2O SLED (a1)f1)), and for the LH2O/LIR ratios (for ΔV = 100 kms-1) as a function of Tdust and LIR (assuming a source of Reff = 100 pc, a2)f2)). In panels a1)f1), model results for lines 1 to 8 (Table 1) are shown from left to right. Values for NH2OV and τ100 are indicated at the top of the figure. The different colors in panels a1)f1) indicate different Tdust , as labeled in b1), while they indicate different lines in panels a2)f2) (labeled in a2), see Table 1). Models with collisional excitation ignored (a)c)), and with collisions included for nH2 = 3 × 105 cm-3 and Tgas = 150 K (d)f)) are shown. The gray lines/symbols in panels d1)f1) show model results that ignore radiative pumping (i.e., only collisional excitation). Collisional excitation has the overall effect of enhancing the low-lying lines (1 and 2) relative to the others and of increasing the LH2O/LIR ratios of all lines (see text). The dashed lines in panels a2)f2) indicate the average LH2O/LIR ratios reported by Y13. When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities, because single temperature dust models are unable to reproduce the observed SEDs (Sect. 4.3.1); the H2O submm emission traces warm regions of luminous IR galaxies (see text).

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In the text
thumbnail Fig. 4

Effect of collisional excitation on the H2O fluxes of the submm lines 2−6 as a function of nH2. The ordinates show the calculated line fluxes relative to the model that ignores collisional excitation. Tgas = 150 K is adopted in all models. a) In the case of moderate Tdust and low τ100, collisional excitation has a strong impact on the H2O fluxes at nH2 of a few × 104 cm-3, especially on line 2. b) Collisional excitation is negligible for high τ100 and very warm Tdust (note the difference in ordinate scales in a) and b)).

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In the text
thumbnail Fig. 5

a)F6/F4 (oH2O 321−312-to-pH2O 220−211) and b) F6/F2 (oH2O 321−312-to-pH2O 202−111) line flux ratios as a function of the 75-to-100 μm far-IR color. Blue symbols: NH2OV = 1015cm-2/ (km s-1) and τ100 ≤ 0.1; black: NH2OV = 5 × 1015cm-2/ (km s-1) and τ100 ≤ 0.1; red: NH2OV = 5 × 1015cm-2/ (km s-1) and τ100 = 1.0; green: NH2OV = 1015cm-2/ (km s-1) and τ100 = 1.0; magenta: same as blue symbols but with collisional excitation included with Tgas = 150 K and nH2 = 3 × 105 cm-3. The small numbers close to the symbols indicate the value of Tdust . The observed averaged ratios for strong-AGN and HII+mild-AGN sources (Y13) are indicated with dashed horizontal lines, and indicate that the regions probed by the H2O submm emission are characterized by warm dust (Tdust ≳ 45 K).

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In the text
thumbnail Fig. 6

F6/F5 (oH2O 321−312-to-312−303) line flux ratio as a function of τ100. The small numbers on the right side of the curves indicate the values of Tdust for each curve. The H2O column density per unit of velocity interval is NH2OV = 1015cm-2/ (km s-1) (green, blue, and magenta curves) and NH2OV = 5 × 1015cm-2/ (km s-1) (red and black curves).

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In the text
thumbnail Fig. 7

Model results showing the luminosity of the H2O line 6 (321−312) as a function of the product of the monochromatic luminosities at 75 and 179 μm. Luminosities are calculated for a source with Reff = 100 pc, NH2OV = 1015cm-2/(km s-1), and ΔV = 100 kms-1. Blue squares indicate models with τ100 = 0.1, resulting in optically thin or moderately thick H2O emission, without collisional excitation. Magenta squares show results for the same models but with collisional excitation included with Tgas = 150 K and nH2 = 3 × 105 cm-3. Green symbols indicate models with τ100 = 1.0, resulting in optically thick H2O emission. For optically thin H2O emission and without collisional excitation, the models indicate a linear correlation between LH2O and L75 × L179 (red line).

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In the text
thumbnail Fig. 8

Modeled LH2O/LIR × (100 km s-1/ ΔV) for lines 2 (upper), 4 (middle), and 6 (lower) as a function of the f25/f60 color. The dashed vertical lines indicate the lower and upper limits for f25/f60 measured by Y13. In the upper panel, the small numbers below the squares indicate the value of Tdust , and τ100 is also indicated. Blue squares: NH2O/ ΔV = 1015cm-2/ (km s-1) and τ100 = 0.1; magenta: same as blue symbols but with collisional excitation included with Tgas = 150 K and nH2 = 3 × 105 cm-3; green: NH2OV = 1015cm-2/ (km s-1) and τ100 = 1.0; black: same as green but with NH2OV = 5 × 1015cm-2/ (km s-1). Red squares show results for fixed Tdust = 55 and 65 K with NH2O/(ΔVτ100) = 5 × 1015cm-2/ (km s-1) and τ100 = 0.1−0.3. The starred symbols indicate the positions of Arp 220 (blue), NGC 6240 (green), Mrk 231 (red), and NGC 1068 (magenta), as reported by Rangwala et al. (2011), Meijerink et al. (2013), G-A10, and Y13, respectively. When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities (Sect. 4.3.1). If f60 is contaminated by cold dust, the points would move to the left.

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In the text
thumbnail Fig. 9

Modeled LH2O/LIR × (100 km s-1/ ΔV) values for lines 2 (upper), 4 (middle), and 6 (lower) as a function of τ100. Collisional excitation is ignored except for the red dashed lines, where Tgas = 150 K and nH2 = 3 × 105 cm-3 are adopted. The small numbers on the right side of the upper panel indicate the value of Tdust in K, and those on the left side indicate NH2OV in cm-2/(km s-1). When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities (Sect. 4.3.1). For τ100 = 12 and Tdust = 95 K, line 4 is predicted to be in absorption. For fixed Tdust and τ100 ~ 1, the LH2O/LIR ratios are similar for very different NH2O, indicating line saturation.

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In the text
thumbnail Fig. 10

Modeled L2/LIR ratio as a function of τ100. Squares and triangles indicate Tdust = 55 and 75 K, respectively. In all models, collisional excitation is included with Tgas = 150 K and nH2 = 3 × 104 cm-3. NH2O/τ100 = 1018 cm-2 is adopted, corresponding to a constant H2O abundance of 7.7 × 10-7 (Eq. (1)). Blue symbols indicate models with ΔV = 100 kms-1 and thus with variable Kvir (Eq. (5)) indicated with the numbers. Green symbols show results with ΔV = 100 × τ100 kms-1 simulating a constant value of Kvir = 1.3. When compared with observations, the modeled LIR values should be considered a fraction of the observed IR luminosities (Sect. 4.3.1), and thus the modeled L2/LIR values are upper limits.

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In the text
thumbnail Fig. 11

a) Values of NH2O for ΔV = 100 km s-1 as a function of τ100, for Tdust = 55 K (red) and 75 K (blue), required to account for the observed averaged LH2O/LIR ratios in HII-mild AGN sources (as given by Y13). Models both without (squares) and with (triangles) collisional excitation are shown. In the latter models, Tgas = 150 K, and nH2 = 5 × 104−3 × 105 cm-3 for Tdust = 55−75 K, respectively. The large filled symbols indicate the best fit models to the averaged SLED. Panels b) e) compare in detail the four models with τ100 = 0.1 (both with and without collisions) with the observed values (black circles) in HII-mild AGN sources (both the normalized flux ratios (SLED) and the LH2O/LIR ratios, Y13, for lines 26). In panels b) and d), the models indicate the values of LH2O/LIR for ΔV = 100 kms-1. Lines 1, 7, and 8 are excluded from the comparison because of their low detection rates (Y13).

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In the text
thumbnail Fig. A.1

a) Proposed composite model for the H2O submm lines in Arp 220 (see G-A12), compared with the observed line fluxes (black squares, from Rangwala et al. 2011). Toward the far-IR optically thick nuclear region (blue symbols), the Eupper< 400 K lines are expected mostly in absorption. The H2O emission is generated around that nuclear region, in the Cextended (G-A12) component (green). Red is total. b) Resulting predicted composite PACS/SPIRE H2O continuum-subtracted spectrum of Arp 220, which is dominated by absorption of the continuum.

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In the text
thumbnail Fig. A.2

a) Composite model for the H2O emission in NGC 1068 favored in this work. Blue/red indicate ortho/para lines, and the submm H2O 1−6 lines (Table 1) are indicated. Open squares and triangles show the contribution by a moderate-excitation (ME) and a low-excitation (LE) component, and filled symbols indicate the total emission (see text for details); in both cases the submm H2O lines 2−6 are pumped through far-IR photons emitted by dust. b) Comparison between the observed fluxes of the H2O submm lines (black squares, from Spinoglio et al. 2012) and those predicted with the composite model.

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In the text

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