Free Access
Issue
A&A
Volume 550, February 2013
Article Number A25
Number of page(s) 23
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201220466
Published online 18 January 2013

© ESO, 2013

1. Introduction

Observations of O-bearing molecular ions are powerful probes of the oxygen chemistry and related physical processes in the interstellar medium. The formation of OH+, H2O+, and H3O+ can be initiated by cosmic ray and/or X-ray ionization of H and H2  (e.g. Herbst & Klemperer 1973; Maloney et al. 1996), and hence their abundances are sensitive to the cosmic ray and X-ray fluxes that permeate the observed environments. Significant amounts of molecular ions can also be formed in the surfaces of photodissociation regions (PDRs) (Sternberg & Dalgarno 1995). The OH+/H2O+ and OH+/H3O+ abundance ratios are sensitive to the molecular fraction and to the fractional ionization, as the destruction paths for the three species are dominated by dissociative recombination (H3O+) and reactions with H2 (OH+ and H2O+; Gerin et al. 2010; Neufeld et al. 2010). In environments with T < 250 K, these are the intermediate species for the main gas-phase production route of OH and H2O, which are abundant species in the nuclei of some (ultra)luminous infrared galaxies ((U)LIRGs).

The successful launch and operation of the Herschel Space Observatory and its instruments have allowed the observation of O-bearing molecular ions in both galactic and extragalactic sources. In the Milky Way, and following the first detection of OH+ towards Sgr B2 with APEX (Wyrowski et al. 2010), the ground-state lines of OH+ and H2O+ have been observed in absorption toward a number of star-forming regions with high submillimeter continua, mainly tracing intervining diffuse/translucent clouds with low H2 fraction (Ossenkopf et al. 2010; Gerin et al. 2010; Neufeld et al. 2010). The ground-state lines of both species have also been detected in the Orion BN/KL outflow, though still in absorption against the continuum (Gupta et al. 2010), and toward the high-mass star forming region AFGL 2591, also indicating low excitation for both hydrides (Bruderer et al. 2010b). Most of the Galactic OH+ and H2O+ detections essentially sample low-excitation gas and are thought to be generated by the cosmic ray field in our galaxy (Ossenkopf et al. 2010; Gerin et al. 2010; Neufeld et al. 2010; Hollenbach et al. 2012). The more stable H3O+ was first detected in the Sgr B2 molecular cloud complex near the Galactic center (Wootten et al. 1991), and further mapped with APEX in the same region (van der Tak et al. 2006) through the non-metastable submillimeter line at 365 GHz. Recently, high-lying lines of H3O+ from metastable levels have been detected in Sgr B2 by Lis et al. (2012), who suggested that the excitation could be due to formation pumping in X-ray irradiated gas.

The situation in luminous extragalactic sources is different in some aspects. While the ground-state transition of ortho-H2O+ has been detected in absorption in M82 (Weiß et al. 2010), the ground-state OH+ and H2O+ lines have been detected in emission in Mrk 231, probably indicating a combination of high excitation conditions and high ionization rates that are plausibly tracing X-ray dominated regions (XDRs) due to the active galactic nucleus (AGN; van der Werf et al. 2010) or the high cosmic ray intensities suggested to be present in ULIRGs (Papadopoulos 2010). From ISO observations, hints of OH+ absorption at ~153 μm from the first excited rotational level were previously reported in the ULIRGs Arp 220 (González-Alfonso et al. 2004, hereafter G-A04), and Mrk 231 (González-Alfonso et al. 2008), but the absorption in Arp 220 was mostly ascribed to NH. Recently, Rangwala et al. (2011, hereafter R11) have reported the detection of the ground-state OH+ and o-H2O+ fine-structure components in absorption toward Arp 220, as well as two emission lines of H2O+ with excited lower levels. On the other hand, the H3O+ submillimeter line has also been detected in Arp 220 (van der Tak et al. 2008, hereafter vdT08) and other nearby galaxies (Aalto et al. 2011).

We report in this work on the Herschel/PACS detection of excited OH+, H2O+, and H3O+ in both Arp 220 and NGC 4418. In a recent study (González-Alfonso et al. 2012, hereafter Paper I), we have reported on the Herschel/PACS observations of these two sources in H2O, HO, OH, 18OH, HCN, and NH3, together with a quantitative analysis in which a deconvolution of the continuum into several components enabled us to derive the column densities and abundances of these species associated with each of the components. A chemical dichotomy was found in Paper I: on the one hand, the nuclear regions of both galaxies have high H2O abundances (~10-5), and high HCN and NH3 column densities, indicating a chemistry characterized by high Tgas, Tdust , and high density, where the release of molecules from grain mantles to the gas phase has occurred (through evaporation in “hot core” chemistry and sputtering in shocks). On the other hand, the high OH abundance found in both sources, with OH/H2O ~ 0.5, appears to indicate the occurrence of photoprocesses due to X-rays and/or the effects of cosmic rays. This second aspect of the chemistry is further studied in this paper from the observed O-bearing molecular cations detected in the Herschel/PACS spectra of both sources. The paper is organized as follows: the observations are presented in Sect. 2; column densities and abundances are inferred in Sect. 3; chemical models are presented and compared with observations in Sect. 4; the inferred important processes are discussed in Sect. 5, and the main conclusions are listed in Sect. 6. As in Paper I, we adopt distances to Arp 220 and NGC 4418 of 72 and 29 Mpc, and redshifts of z = 0.0181 and 0.00705, respectively.

thumbnail Fig. 1

Energy level diagrams of OH+, H2O+, and H3O+, showing with arrows the transitions that lie within the PACS range; colored numbers indicate round-off wavelengths in μm. The fine-structure splitting of the OH+ and H2O+ levels is out of scale. Solid-red arrows mark the lines detected in NGC 4418 and/or Arp 220; dashed-red arrows indicate marginal detection in any of the sources; green arrows indicate blended lines, and black arrows show undetected lines.

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2. Observations and results

The full, high resolution, PACS spectra of NGC 4418 and Arp 220, were observed as part of the guaranteed-time key program SHINING on July 27th and February 27th (2010), respectively1. The data reduction was done using the standard PACS reduction and calibration pipeline (ipipe) included in HIPE 5.0 975. For the final calibration, the spectrum was normalized to the telescope flux and recalibrated with a reference telescope spectrum obtained from Neptune observations. Further details of the data reduction are given in Graciá-Carpio et al. (2011), Sturm et al. (2011), and Paper I.

The PACS spectrum of Arp 220 in Paper I was corrected in both flux and wavelength calibration due to the effects of sub-spaxel pointing errors. Following newly made software corrections to the Herschel pointing star catalogue and the star-tracker x and y focal lengths, a second full spectrum of Arp 220 was taken by the Observatory to assess the improvement to Herschel’s pointing. Although the baseline of the new spectrum is of higher quality, general agreement with our corrected original spectrum was found in both flux and wavelength calibration. The data shown here are mostly an average of the two observations, except for some ranges where the new data set yields a more reliable baseline.

Spectroscopic parameters of OH+, H2O+, and H3O+ used for line identification and radiative transfer modeling were mostly taken from the spectral line catalogs of the CDMS (Müller et al. 2001, 2005) and JPL (Pickett et al. 1998), and are included in Table 1, together with the equivalent widths (Weq) and fluxes of the detected lines. The wavelength uncertainties tabulated in the catalogs are significantly lower than the PACS spectral resolution. Energy level diagrams for the three cations are shown in Fig. 1, where the solid red arrows indicate the detected transitions in at least one of the sources.

2.1. OH+

Owing to the electronic spin S = 1, all rotational levels of OH+ except the ground N = 0 state are split into 3 fine-structure levels with total angular momentum J = N − 1,N,N + 1 (Fig. 1)2. Of the six allowed fine-structure transitions between excited rotational levels, the three with ΔJ = ΔN are the strongest. Line spectroscopic parameters of OH+ were taken from the CDMS, and were derived by Müller et al. (2005). In that work, the N = 1−0 transition frequencies from Bekooy et al. (1985) were fit together with additional infrared data. A dipole moment of 2.256 D was taken from an ab initio study (Werner et al. 1983).

thumbnail Fig. 2

Continuum-normalized spectra around the OH+ lines in NGC 4418 (upper histograms) and Arp 220 (lower histograms). The dotted vertical lines indicate the rest wavelengths of the transitions for the nominal redshifts of z = 0.00705 (NGC 4418) and 0.0181 (Arp 220). The spectra in panels b) and c) have been scaled by a factor 2. (Potential) contamination by other species (NH in panel a) and H2O in d)) is also indicated. The marginal 5J − 4J lines in f) correspond to NGC 4418; this part of the spectrum is not available in Arp 220. Blue lines show model fits for OH+ in the nuclear components of both NGC 4418 and Arp 220, the green lines show the model fit for OH+ in the extended components of both sources, and the light-blue lines in a) are model fits for NH; red is total.

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Figure 2 shows the observed spectra around the OH+ lines in NGC 4418 (upper histograms) and Arp 220 (lower histograms). The spectra around the positions of the 2J ← 1J lines, with Elower ≈ 50 K, are displayed in panels a-c. The strongest 23 ← 12 at ≈ 153 μm is partially blended with NH, but the 22 ← 11 is free from contamination and clearly detected in both sources. In Arp 220, the 153 μm absorption appears to be dominated by OH+ rather than by NH, in contrast with the initial estimate by González-Alfonso et al. (2004) based on ISO data. The 21 ← 10 at ≈ 148.7 μm is also well detected, and the intrinsically weaker 21 ← 11 (158.4 μm) and 22 ← 12 (147.8 μm) lines are (marginally) detected in NGC 4418 but still very strong in Arp 220. There is in addition an apparent red-shifted wing in the NH 23 ← 12 spectrum of Arp 220, detected in both data sets, which coincides with the position of the intrinsically weak OH+ 21 ← 12 transition. As shown below (Sect. 2.3), however, this wing feature is most probably due to the very excited line of H3O+.

Table 1

Line equivalent widths and absorption fluxes.

Most 3J ← 2J lines at ~ 100 μm lie within the gap between the green (λ < 100 μm) and red (λ > 100 μm) bands of PACS and are not observable, except for the 32 ← 22 transition at 103.9 μm shown in Fig. 2d. The line in NGC 4418 is close to the edge of the red band where the spectral noise is high, but in Arp 220 a clear spectral feature is detected at the expected wavelength. The line, however, is blended with the H2O 615 ← 606 transition (Paper I), which may account for some of the observed absorption.

The three strongest 4J ← 3J lines at 76−76.5 μm are clearly detected in both sources (Fig. 2e), indicating a high-excitation component in the transient OH+. It is worth noting that while the 2J ← 1J lines are stronger in Arp 220, the more excited 4J ← 3J lines are slightly deeper in NGC 4418, resembling the behavior found for other species like H2O, OH, HCN, and NH3 (Paper I). The 4J ← 3J lines still have slightly higher equivalent widths in Arp 220 (Table 1) owing to the broader line profiles in this source. The line opacities of the fine-structure components are τ ∝ λ3guAul if the lower levels are populated according to their degeneracies, and then τ45 − 34:τ44 − 33:τ43 − 32 = 1:0.77:0.58. These are expected to be the ratios of the line equivalent widths (Weq) if the three components are optically thin. In Arp 220, the observed Weq ratios are 1:(0.69 ± 0.11):(0.53 ± 0.10) (Table 1), consistent with optically thin absorption. In NGC 4418 they are 1:(1.2 ± 0.6):(1.0 ± 0.5), compatible within the uncertainties with both optically thin and saturated absorption.

In NGC 4418, some marginal features around 61 μm roughly coincide with the positions of the OH+ 5J ← 4J lines (Fig. 2f). However, the feature associated with the intrinsically strongest 56 ← 45 component is relatively weak and shifted in wavelength by 0.015 μm, shedding doubt on this tantalizing identification. In Arp 220, this part of the spectrum was affected by instrumental problems and is not shown.

2.2. H2O+

thumbnail Fig. 3

Continuum-normalized spectra around the H2O+ lines in NGC 4418 (upper histograms) and Arp 220 (lower histograms). The dotted vertical lines indicate the rest wavelengths of the transitions for the nominal redshifts of z = 0.00705 (NGC 4418) and 0.0181 (Arp 220). The spectra in panels b) and c) have been scaled by a factor 2. Close features due to other species and potential contaminations are indicated. Dark blue and light blue lines show model fits; red is total.

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thumbnail Fig. 4

Continuum-normalized spectra around the H3O+ lines in NGC 4418 (upper histograms) and Arp 220 (lower histograms). The dotted vertical lines indicate the rest wavelengths of the transitions for the nominal redshifts of z = 0.00705 (NGC 4418) and 0.0181 (Arp 220). Panels a) − i) show the pure inversion, metastable lines of H3O+, while panels j) − p) show the rotation-inversion lines at λ < 100 μm. The spectra in panels h) and j) − p) have been scaled by a factor 2 and 3, respectively. The and lines at ≈ 181 μm are strongly contaminated by lines of CH and HO, and are not shown. Close features due to other species and potential contaminations are indicated. In panels f) and i), the contamination by NH2, HCN, and OH+ is expected to be small (see text). The blue lines show the best-fit model for H3O+; the green lines in panels g) and i) show model fits for NH3 and NH lines; red is the total.

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The asymmetric H2O+ also has fine-structure splitting of the rotational levels producing doublets (S = 1/2) and yielding a very rich spectrum in the far-infrared domain (Fig. 1). Predictions of the rotational spectrum were taken from the CDMS. The CDMS data were based on extrapolated zero-field frequencies in Mürtz et al. (1998), the derived N = 1 − 0 transition frequencies based on Strahan et al. (1986), and additional rovibrational (infrared) transitions and ground state data from electronic spectra. HIFI observations of the N = 110 − 101 transition frequencies above 600 GHz toward Sgr B2(M) reported by Schilke et al. (2010) are compatible with the transition frequencies in the CDMS, although these lines lie outside our accessible frequency range. A ground state dipole moment of 2.398 D was calculated ab initio by Weis et al. (1989).

As shown in Fig. 1, most low-lying lines of H2O+ are blended with lines of other species, but some of them lie in free windows (Fig. 3). Very prominent is the ground-state p-H2O+ 212 ← 101 transition at 183 − 184 μm in Arp 220, with the three fine-structure components clearly identified in the spectrum. This transition is not detected in NGC 4418. In Arp 220, the observed line strengths strongly decrease with increasing Elower, indicating that the ground-state p-H2O+ lines arise in low excitation gas. The opacity ratios of these components are τ5/2−3/2:τ3/2−1/2:τ3/2 − 3/2 = 1:0.55:0.12, so the observed Weq ratios of 1:(0.65 ± 0.07):(0.30 ± 0.05) (Table 1) suggest line saturation effects in at least the strongest 5/2 − 3/2 component. For σv = 60 kms-1, this component attains an optical depth of unity with a column of N(p − H2O+) ≈ 5 × 1014 cm-2. The line absorbs only ≈ 15% of the continuum, likely indicating some spectral dilution and a low covering factor of the continuum.

The two prominent features at 104.7 − 105 μm in both NGC 4418 and Arp 220 are most probably due to NH2. The feature at 143.8 μm may be contaminated by C3. In Arp 220, the excited 221 ← 110 , 313 ← 202 , 322 ← 211 , and 404 ← 313 lines of H2O+, with Elower up to 190 K, are clearly detected, but in NGC 4418 only the high-lying 322 ← 211 transition shows measurable absorption. Detection of the 404 ← 313 transition in NGC 4418 is questionable, as the spectral features associated with the 9/2 − 7/2 and 7/2 − 5/2 components are either too narrow or shifted (Fig. 3e).

2.3. H3O+

H3O+ and NH3 are isoelectronic and spectroscopically similar: both are oblate symmetric top rotors, have a double-minimum potential such that inversion takes place between the two equivalent minima, and have ortho (K = 3n) and para (K ≠ 3n) modifications. Figure 1 shows the energy level diagram for H3O+. Owing to the Δ K = 0 selection rule for all radiative transitions, the J = K levels in the lower tunneling state cannot be radiatively pumped and hence are metastable. They therefore will be “thermally” populated at a rotational temperature, Trot , which reflects either Tgas or, if the formation-destruction rates are faster than the rate for collisional relaxation, the formation process characteristics (e.g. Bruderer et al. 2010a; Lis et al. 2012, see also Appendix B).

Spectroscopic data for H3O+ were taken from the JPL catalogue (Pickett et al. 1998). The entry was based on the recent analysis by Yu et al. (2009), who also presented some improved transition frequencies. The majority of the pure tunneling transition frequencies were reported by Verhoeve et al. (1989). A ground state dipole moment of 1.44 D was calculated ab initio by Botschwina et al. (1985). The antisymmetric3 state is higher in energy by 1659 GHz (Yu et al. 2009) because of the low barrier to linearity, and thus the pure inversion transitions of H3O+ lie in the far-IR domain (150 − 185 μm)4.

The solid-red arrows in Fig. 1 indicate the H3O+ lines detected in Arp 220, and Fig. 4 presents the observed H3O+ spectra of NGC 4418 and Arp 220. In Arp 220, spectral features at the wavelengths of the H3O+ pure-inversion, metastable (hereafter PIMS) lines (panels a − i) are detected up to a lower level energy of ≈ 1400 K above the ground state (), while none of these lines is detected in NGC 4418. The rotation-inversion (hereafter RI) lines lie at shorter wavelengths (λ < 100 μm) and are shown in Fig. 4j − p. Four of them arise from non-metastable levels (Fig. 1), three of them from metastable levels (hereafter RIMS lines), and are detected within the lowest K ≤ 4 ladders up to an energy of ~ 200 K in both galaxies.

The , , and PIMS lines are contaminated by strong lines of CH, HO, and [C ii], and are not shown. All features in Arp 220 are detected in both datasets. Close lines due to other species, as well as potential contaminations (panels f and i), are also indicated in Fig. 4. Based on the weakness of the HCN 19 − 18 line (Paper I), the HCN 20 − 19 line at 169.39 μm is not expected to strongly contaminate the H3O+ line, though some contribution from HCN is not ruled out (see below). Likewise, the nearby NH2 330 ← 321 4 − 3 line is intrinsically weak, and NH2 modeling that accounts for other detected NH2 lines does not produce significant absorption at 169.38 μm. A broad feature is detected at 165.7 μm (panel g), which cannot be explained by only the NH3 and  lines (Paper I); thus strong absorption by ortho-H3O+ is inferred. The relatively weak H3O+ line is affected by an uncertain baseline, though the line is detected in both data sets. On the other hand, a line wing feature close to the NH 23 ← 12 153.35 μm line is detected, coinciding with both the ortho-H3O+ and the OH+ 21 ← 12 lines (153.47 μm, see also Fig. 2a). As mentioned earlier, the latter is also intrinsically weak, and modeling of the other OH+ 2J ← 1J lines (Sect. 3.4) yields negligible absorption in that component. Upon inspection of the CDMS and JPL catalogs, we have not found any other reliable candidate for the NH wing, which we tentatively ascribe to the very high-lying H3O+ line.

No potential contamination has been found for the RI lines. Contrary to the PIMS lines, some of these RI lines are detected in NGC 4418. The non-metastable levels are populated through absorption of far-IR photons, and trace the local far-IR radiation density.

The PIMS and RIMS lines are observed in absorption against the strong far-IR continuum source of Arp 220, and their relative strengths probe Trot . The population diagram of H3O+ is shown in Fig. 5, where the level columns have been calculated in the optically thin limit and by assuming that the H3O+ covers the whole continuum from Arp 220. Since the degeneracy of the ortho levels is twice that of the para levels, we expect a nearly continuous distribution for an ortho-to-para ratio of 1, as observed in the high-lying levels (crosses in Fig. 5). The distribution is roughly described with two values of Trot , ~ 180 K up to the  level, and ~ 550 K for higher-lying levels. This is strikingly similar to that found by Lis et al. (2012) towards Sgr B2. The column of the level (El ≈ 660 K) appears to be higher than expected, suggesting some contamination by HCN at 169.4 μm (Fig. 4f). On the other hand, there are two metastable levels, the and the , for which both PIMS and RIMS lines are available. In both levels, the columns derived from the RIMS lines are higher by a factor of ≈ 1.8 than those derived from the PIMS lines. Two main reasons can account for this: first, the level columns are calculated, as mentioned above, by assuming that the H3O+ covers the whole far-IR continuum, which is relatively cold (i.e. S180/S60 = 0.43). If the H3O+ is absorbing a warmer continuum that is diluted within the observed SED (i.e. filled in by a cooler continuum source), the intrinsic equivalent width and column of the PIMS lines will be increased relative to those of the RIMS line, and both columns will be in better agreement. Therefore, the discrepancy probably indicates that the highly excited H3O+ covers only a fraction of the observed continuum, and that the level columns are lower limits. Second, the columns in Fig. 5 are not corrected for stimulated emission, which will mainly increase the columns of the PIMS lines at long wavelengths.

thumbnail Fig. 5

Population diagram of H3O+ (metastable levels) in Arp 220. Red and blue symbols correspond to ortho and para levels, respectively. Columns derived from pure-inversion and rotation-inversion lines are shown with triangles and squares, respectively. The crosses indicate the expected population distribution for Trot = 550 K and a fixed ortho-to-para ratio of 1.

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2.4. Velocity shifts in Arp 220

Having confirmed the velocity calibration (or “corrections”) applied to the Arp 220 spectrum (Paper I) with the second Arp 220 dataset, we now compare the line profiles and velocity shifts presented in Paper I to the velocity profiles and centroids of the molecular ions. The average profiles of several H2O, OH+, H2O+, H3O+, HCN and NH3 lines detected in Arp 220 are compared in Fig. 6. In all panels, HE and LE mean high-excitation and low-excitation, respectively, qualitatively indicating whether the selected lines are high-lying or low-lying lines. Thus H2O HE is the average profile of two representative high-excitation lines of H2O, the 616 ← 505 and 322 ← 211 lines (Paper I); H2O LE is the average profile of the two low-lying 212 ← 101 and 221 ← 110 lines, and similarly for other species/excitation. The H3O+ PIMS spectrum is the average of the unblended high-lying, pure-inversion metastable lines of H3O+, and the NH3 RIMS one is the average of the relatively uncontaminated rotation-inversion metastable and lines. The averages were generating by resampling the individual spectra to a common velocity resolution, and adopting equal weights for all them. Figure 7 displays the velocity centroids of these generated line profiles.

Figures 6 and 7 indicate that there are systematic velocity shifts associated with line excitation, irrespective of the considered species. The averaged H2O HE profile, peaking at − 20 kms-1, has a shape very similar to the averaged OH+ HE (panel a), H2O+ HE (b), and NH3 HE (d) profiles, though the latter is somewhat narrower (and relatively uncertain due to line blending). The HCN 18 ← 17 line (panel a) could be even more blueshifted, though the signal-to-noise ratio is relatively low. On the other hand, there is a clear velocity shift in the peak absorption of the H2O HE and LE averages, with the latter peaking at a velocity of + 50 kms-1. The LE averages of OH+ and H2O+ also tend to peak at more positive velocities, though the OH+ LE lines are not ground-state lines (Elower ≈ 50 K) and thus may represent an intermediate situation.

The velocity centroids of the H3O+ PIMS lines, however, which are characterized by high Elower, peak at the velocity of the LE lines and thus present an exception to the finding discussed above. A velocity shift of ≈ 70 kms-1 is shown in Fig. 6c between the average H2O HE and H3O+ PIMS spectra, with the latter peaking at the velocity of the LE lines of H2O and H2O+. This shift is much lower than the line widths of ~300 kms-1, but larger than our spectral calibration accuracy. The average velocity of all H2O lines (excluding the lowest-lying LE lines) is − 20 ± 35 kms-1, whereas that of the metastable H3O+ lines is 50 ± 25 kms-1. The latter corresponds to vLSR = 5480 kms-1, in rough agreement with the velocity centroid of the line (vdT08) and close to the central velocity of CO 2 − 1 in the western nucleus (Downes & Eckart 2007). Excluding the low signal-to-noise H3O+ line, the other three non-metastable lines have an average velocity of 20 ± 15 kms-1. The low-lying line (Fig. 4k) is even more redshifted ( ≈ 100 kms-1), with the two data sets giving very similar line shapes. With the same lower level, the pure-inversion line (Fig. 4a) also shows hints of redshifted absorption at >100 kms-1.

thumbnail Fig. 6

Comparison between averaged line shapes of several lines in Arp 220. HE, LE, PIMS and RIMS mean high-excitation, low-excitation, pure-inversion metastable, and rotation-inversion metastable, respectively. H2O HE is the average of the 616 ← 505 and 322 ← 211 lines of H2O (Paper I); HCN HE is the 18 − 17 line of HCN; OH+ HE is the average of the 43 − 32 and 45 − 34 lines of OH+; H2O+ HE is the average of the 322 ← 211 7/2−5/2, 313 ← 202 5/2 − 3/2, and 404 ← 313 7/2 − 5/2 lines of H2O+; H3O+ PIMS is the average of the pure-inversion, metastable , , , and lines of H3O+; NH3 RIMS is the average of the rotation-inversion metastable and lines of NH3; H2O LE is the average of the 212 ← 101 and 221 ← 110 lines of H2O; OH+ LE is the average of the 22 − 12, 21 − 10, 22 − 11, and 21 − 11 lines of OH+; H2O+ LE is the average of the 212 ← 101 5/2−3/2 and 3/2−1/2 lines of H2O+; H3O+ 70.8 is the line of H3O+ at 70.8 μm. The dotted and dashed vertical lines indicate the velocity centroids of the averaged HE and LE spectra, respectively.

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At the very least, the velocity shift between the peak absorption of the H3O+ PIMS and the HE lines of other species indicates a spatial shift between the regions responsible for the strongest absorption in both sets of lines. On the one hand, this may not be surprising from excitation arguments. The H2O HE levels are excited through radiative pumping by dust (Paper I), and thus the corresponding lines trace the region of highest far-IR radiation density (and thus of highest Tdust ). On the other hand, the H3O+ metastable levels cannot be radiatively pumped, but are either excited through collisions indicating high Tgas , or reflect H3O+ formation in high-lying levels; thus the physical conditions that favor strong absorption in each set of lines are different and do not necessarily coincide spatially. On the other hand, the NH3 RIMS lines, with Elower = 300 − 400 K, are collisionally pumped but better match the H2O HE profile (Fig. 6d), suggesting either chemical differences between the two velocity components, or the dominance of chemical pumping on the formation of the PIMS lines of H3O+.

Given the velocity coincidence between the peak absorption of the H3O+ PIMS lines and the H2O LE lines, the question is whether the H3O+ PIMS lines arise from foreground gas in the direction of, but detached from the nuclear region, or the lines arise on the contrary from gas physically associated with the nuclei. The PACS spectrum of Arp 220 shows RI lines of H3O+ arising from non-metastable levels (Figs. 4m, l, n, p) that are radiatively pumped through dust emission. Of the above lines, the H3O+ at 70.8 μm is most sensitive to Tdust , requiring relatively high far-IR radiation densities. Figure 6h indicates a good match between the shape of the H3O+ 70.8 μm line and of the PIMS average, and thus it is likely that both sets of lines arise from essentially the same region. We thus expect that the H3O+ PIMS lines are of primarily nuclear origin though, as argued in Sect. 3.4.3, probably more extended than the region where the NH3 lines are formed.

The simplest scenario that can account for the observed velocity pattern in Arp 220 consists of the H3O+ PIMS lines and the LE lines of other species peaking at the “rest” velocity of the western nucleus, and thus primarily tracing rotating gas together with more foreground gas, while the HE lines of H2O, OH, NH3, and also OH+ and H2O+, mainly tracing an outflowing component with a line of sight velocity of ~75 kms-1, similar to that observed in HCO+ (Sakamoto et al. 2009)5. Besides grain mantle evaporation and neutral-neutral reactions at high Tgas (Paper I), sputtering in shocks could also remove the mantles and contribute to enhance the gas-phase abundances of H2O and NH3. Alternatively, both components may be tracing different sections of the nuclear rotating disk(s), which shows steep velocity gradients as seen in the (sub)millimeter lines of CO (Downes & Eckart 2007; Sakamoto et al. 2008).

thumbnail Fig. 7

Velocity centroids of the averaged line shapes in Arp 220 displayed in Fig. 6, derived from Gaussian fits. Velocities are calculated relative to z = 0.0181. Blue and red symbols correspond to HE and LE averages, respectively; for H3O+ the green symbols indicate the PIMS and RI averages. Errorbars are 1σ uncertainties.

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3. Environments, column densities and abundances

3.1. The excitation of the molecular ions

Derivation of the column densities implied by the observations require calculations of excitation appropiate for the environments where OH+, H2O+, and H3O+ reside. The rates for collisional excitation of these molecular ions are not known, but both Arp 220 and NGC 4418 have luminous-compact nuclear far-IR continuum sources that excite H2O, OH, and other species to level energies of > 500 K (Paper I). Therefore, a natural mechanism for exciting OH+, H2O+, and the non-metastable levels of H3O+ along a given K-ladder is via radiatively allowed transitions through absorption of dust-emitted photons.

Collisional excitation of the high-lying lines of OH+ and H2O+ is expected to be less efficient. The Aul-Einstein coefficients are high (Table 1), and thus the critical densities (ncr) are likely to be high as well. For the N = 1−0 transition of OH+, with Aul ≈ 0.02 s-1 and assuming a coefficient for collisional de-excitation with H and H2 of 10-9 cm3 s-1, ncr ≈ 2 × 107 cm-3, which is much higher than the expected densities (see Sect. 4.5 below), and also higher than the nuclear densities inferred from other tracers (Paper I). As a result, the expected excitation temperature of the N = 1−0 transition of OH+ from collisional excitation alone would be < 20 K, in contrast with the typical values of 35 − 70 K obtained from radiative excitation in the models shown below. On the other hand, excitation through collisions with electrons has rate coefficients that might be much higher than with H and H2, ~10-6 cm3 s-1 (Neufeld & Dalgarno 1989; Lim et al. 1999), and has been recently invoked by van der Tak et al. (2012) to explain the emission in the HF 1 − 0 line toward the Orion Bar. However, the expected electron density is several × 103 lower than the density of H (Fig. C.1), so that its effect on the excitation is not expected to be much higher than that of H. Finally, the detected lines are seen in absorption, and radiative pumping models generate the observed absorption features naturally, as we show below.

Another potential excitation mechanism is chemical formation in excited levels (Stäuber & Bruderer 2009), i.e. formation pumping. In environments with weak dust emission, a downward cascade after molecular formation in excited levels (e.g. Bruderer et al. 2010a) is expected to generate emission in non-metastable lines (i.e. chemoluminiscence). But again, in the specific case of NGC 4418 and Arp 220, all detected lines from molecular ions are seen in absorption, qualitatively matching the far-IR pumping scheme. Furthermore, ignoring excitation by dust emission, the equilibrium level populations of OH+ and H2O+ resulting from formation pumping (see Appendix B in Bruderer et al. 2010b) yield very low excitation even for very high formation rates (see Appendix A). This is due to the very high A-Einstein coefficients (Table 1) as compared with the expected formation/destruction rates (Sect. 4). Thus we do not expect that formation pumping has a measurable effect on the excitation of non-metastable transitions in these sources.

The case of the metastable lines of H3O+ is different. The K > 1 ladders cannot be populated from K = 0,1 through radiative pumping, but only through collisions or via molecular formation in high-lying levels. The latter process can be envisioned as follows: molecular formation in an excited (K,J) level will be followed by quick cascade down to the metastable J = K one, where no more paths for radiative decay are available. Then, the molecule will “freeze-out” in that metastable level (ignoring here radiative excitation for simplicity) until destruction through recombination or until a collisional thermalization event takes place. If the destruction rate dominates over collisional relaxation, the observed population distribution in the metastable levels (i.e., Trot ) will be governed by the formation process rather than by Tgas (Lis et al. 2012). Writing the rate of H3O+ formation per unit volume as ΓH3O+ = ϵH3O+nHζ, where ϵH3O+ is the efficiency with which ionizations are transfered to the production of H3O+ (see Neufeld et al. 2010, for OH+), the condition for formation pumping to dominate the observed excitation over collisions can be written as6(1)where kcol (in cm3 s-1) is the rate for collisional relaxation from a metastable level at Tgas , ζ is the ionization rate per H nucleus, χ denotes the abundance relative to H nuclei, and the reference value of ϵH3O+ = 0.4 is based on the chemical models of Sect. 4. Collisional rates for H3O+ excitation with H2 have been calculated by Offer & van Hemert (1992)7 for a temperature of 100 K and for the lowest H3O+ levels in the K = 0,1,2,3 ladders. Taking as a guide kcol ~ 2 × 10-10 cm3 s-1 at 100 K from the level (Offer & van Hemert 1992), formation pumping may have important effects at high ζ/nH, but collisional rates for higher levels and with H2 and H are required to check this point. Calculations for excitation of H3O+ through electron impact (Faure & Tennyson 2003) indicate that the ΔK > 0 transitions are negligible, so collisions with electrons are probably not important in populating the K > 1 metastable levels.

In our calculations for H3O+ below, we use the de-excitation rates by Offer & van Hemert (1992), and correct the excitation rates according to the value of Tgas in our models and the requirements of detailed balance. Since no collisional rates that connect the low- and high-K ladders are available, we simply force the metastable high-lying JJ+ levels to be populated according to the adopted Trot , which represents Tgas , the signature of the formation process, or a combination of both. This will be further discussed in Sect. 5. Additionally, we attempt to establish in Appendix B under which conditions the formation process can generate the observed high excitation in environments with moderate Tgas . Excitation of non-metastable levels is dominated by the far-IR field, and significant discrepancies between observations and model results would indicate the relevance of alternative excitation mechanism.

3.2. Source components

As shown in Paper I, the far-IR spectra of NGC 4418 and Arp 220 cannot be described by a single set of ISM parameters, but different lines have different excitation requirements and are thus formed in different regions of the galaxies associated with different far-IR continuum components that we summarize here (see also Figs. 1 and 16 and Tables 1 and 2 in Paper I). For NGC 4418, at far-IR wavelengths we require (i) a nuclear core (Ccore) with Tdust ≈ 130 − 150 K, that provides absorption in the high-lying lines of H2O, OH, HCN, and NH3; (ii) a warm component (Cwarm) with Tdust ≈ 110 − 85 K, that provides absorption in moderately excited lines of H2O and OH as well as a significant fraction of the far-IR continuum emission; and (iii) an extended, possibly infalling component (Cextended) with Tdust ≈ 90 − 40 K, which accounts for low-lying redshifted lines of OH and O0. For Arp 220, we require (i) the western and eastern nuclear components (Cwest and Ceast), where the high-lying molecular lines are formed; (ii) the extended component (Cextended), which provides a significant fraction of the far-IR continuum emission (though mostly reemission from the nuclei) and accounts for the absorption in moderate and low-excitation lines of H2O and OH; and (iii) an additional low-excitation, absorbing component or “halo” (Chalo), with no associated continuum that is required to fit the absorption in the ground-state lines of H2O, OH, and O0.

Calculations of excitation, line fluxes, and line profiles were first performed for the nuclear components in both sources to fit the high-lying lines, and then were done for the extended components to complete fitting of the absorption in the low-lying lines. Table 2 gives the inferred column densities, based on a “screen” approach for the nuclear components (i.e. the molecules are located in front of the nucleus) due to the high continuum opacities of these components in the far-IR; the “mixed” approach (i.e. the molecules and dust are mixed) would give columns highly exceeding the listed values (González-Alfonso et al. 2008). For the Cextended, the “mixed” approach is used owing to the much more moderate continuum opacities (Paper I).

3.3. NGC 4418

3.3.1. OH+

In NGC 4418 we first used the parameters of the Ccore and Cwarm components as given in Paper I to match the absorption in the high-lying 4J ← 3J lines of OH+, by assuming a covering factor of 1. The OH+ column densities were similar for both components, N(OH+) = (0.6−1) × 1016 cm-2, respectively. The model fits were also very similar for both components, so that we are not able to determine in which nuclear component the OH+ lines are (primarily) formed. By using the same normalization column as in Paper I, N(H) = 4 × 1023 cm-2, the OH+ abundance in the nuclear region of NGC 4418 is χ(OH+) = (1.5−2.5) × 10-8. Contrary to observed, the 45 ← 34 component in Fig. 2e is predicted to be the strongest, which could indicate significant departures of the fine-structure distribution of populations relative to the predicted one. The effective spatial extent (diameter) predicted by the Ccore and Cwarm models is ≈ 20 − 30 pc, respectively, and Tdust = 150−110 K.

Figure 2 shows (blue curves) the model fit for the nuclear component (similar for Ccore and Cwarm ), together with a model for NH in panel a (light-blue curve). The nuclear model that fits the 4J ← 3J lines underpredicts the 22 ← 11 line and the 153.0 μm feature (composed of the OH+ 23 ← 12 and the NH 22 ← 11 lines, see Fig. 2a). The OH+ 22 − 11 line has a redshifted excess, and the 153.0 μm feature cannot be fully reproduced at just the central wavelength of the feature, which is also redshifted relative to the OH+ line. This strongly suggests that the absorption that cannot be fit with the nuclear model is due to Cextended , a more extended, inflowing component proposed in Paper I in order to explain the redshifted absorption observed in the ground-state lines of OH and [O i]. Fitting the remaining OH+ absorption with the Cextended model in Paper I (green curves in Fig. 2a-upper), the fit shown with the red curve in Fig. 2a is obtained. We infer N(OH+) ~ 3 × 1015 cm-2, and roughly χ(OH+) ~ 2 × 10-8.

In summary, the OH+ lines are essentially formed in the nuclear Cwarm + Ccore components, with N(OH+) ≈ (6−10) × 1015 cm-2. Some contribution to the 22 ← 11 and 23 ← 12 lines due to inflowing gas in Cextended is also inferred, with N(OH+) ~ 3 × 1015 cm-2.

3.3.2. H2O+

H2O+ is weak in NGC 4418 (Sect. 2.2), though the 5/2 ← 3/2 component of the 322 ← 211 transition at 89 μm, and more tentatively the 7/2 ← 5/2 one, are detected in the source (Fig. 3d). We have carried out models for the Ccore and Cwarm components that fit the above lines. Both models give similar columns of N(H2O+) ≈ 3−4 × 1015 cm-2, but fail to account for the somewhat marginal 404 ← 313 components (Fig. 3e). The Ccore model prediction better matches these features but, as shown with blue curves in Fig. 3c, may (marginally) overestimate the 313 ← 202 components. The H2O+ 331 ← 220 7/2 ← 5/2 at 65.6 μm (panel f) is blended with NH2 and 18OH lines and affected by an uncertain baseline (Paper I). We conclude that the OH+/H2O+ column density ratio in the nuclear region of NGC 4418 is in the range 1.5−2.5. The ground-state H2O+ lines are not detected, indicating that H2O+ has a low abundance in the Cextended component of NGC 4418.

3.3.3. H3O+

Only the RI lines of H3O+ were detected in NGC 4418. They were fitted with the Ccore and Cwarm components, with an assumed ortho-to-para ratio of 1. Both components give similar column densities of N(H3O+) ≈ 5−8 × 1015 cm-2, similar to that inferred by Aalto et al. (2011) from observations of the line. The Ccore model is shown with blue curves in Fig. 4. The main drawback of both models is that the absorption in the transition (panel p) is significantly overpredicted; the line is not detected, possibly due to cancellation between absorption toward the continuum source and reemission from a more extended region. The OH+/H3O+ column density ratio in the nuclear region of NGC 4418 is ≈ 1.

The PIMS lines of H3O+ are not detected in NGC 4418, but the model for Ccore in Fig. 4 uses the same Trot = 500 K as in Arp 220, and the predicted faint PIMS lines are nevertheless quite compatible with the observed spectrum. The model predicts wing-like features at the wavelengths of the and ortho PIMS lines, which could be present in the spectrum at very low (but not significant) signal-to-noise. Therefore, the non-detection of the PIMS lines does not imply that Trot is low in NGC 4418, but according to our model can also be due to moderate continuum opacity and dilution of the nuclear continuum emission at long far-IR wavelengths.

Table 2

Inferred column densities, OH+ abundances, and OH+/H2O+ and OH+/H3O+ column density ratios.

3.4. Arp 220

3.4.1. OH+

In Arp 220, the high-lying OH+ 4J ← 3J lines shown in Fig. 2e are tentatively associated with the luminous western nucleus, Cwest, but they can be generally interpreted as the joint emission from the two nuclei (Paper I). In our model for Cwest, we include a velocity gradient through the absorbing shell of 130 kms-1, to reproduce the observed line broadening. We use two approaches to bracket the parameters inferred in Paper I for Cwest . For a compact/warm region, with Tdust = 110 K and d = 93 pc, the high-lying OH+ 4J ← 3J lines are well fitted with a column of N(OH+) = 1.1 × 1016 cm-2, similar to the value found in NGC 4418. The predicted spectrum is shown with blue curves in Fig. 2. The OH+ absorption in the 4J ← 3J lines, however, does not require such high Tdust. For a colder and more extended region, with Tdust = 90 K and d = 160 pc, the column density is N(OH+) = 4.5 × 1015 cm-2. These models, however, do not reproduce the strong 2J ← 1J and 32 ← 22 lines (Fig. 2a−d), so another component is required in addition. We identify this additional component as Cextended (Paper I), which has moderate excitation in H2O and OH. The Cextended component can be identified with the (inner region of) the external disk traced by CO (Downes & Eckart 2007). In Paper I we estimated d ~ 650 pc, though this is uncertain by at least a factor of 2. The additional OH+ absorption could indeed be produced in a relatively small region (d ≲ 300 pc) around the nuclei; our results are relatively uncertain for this component. Assuming that the extended OH+ mainly absorbs the continuum of the Cextended component (Fig. 1 in Paper I), it most probably has a column of N(OH+) ≈ (2−4) × 1016 cm-2. This reflects the widespread presence of OH+ in the regions surrounding the nuclei.

The joint contribution of Cwest and Cextended to the OH+ absorption, shown with a red curve in Fig. 2, yields a reasonable fit to most OH+ lines in Arp 220, though the 32 ← 22 line at 104 μm remains underpredicted (and blended with an H2O line). The wing-like spectral feature at 153.45 μm is not reproduced, though it is probably due to H3O+ (Sect. 3.4.3).

3.4.2. H2O+

The above models for Cwest were applied to H2O+. Using the parameters for the compact/warm approach, Tdust = 110 K and d = 93 pc, we derive a H2O+ column density similar to that found for OH+, N(H2O+) ≈ 0.9 × 1016 cm-2. The model result is shown in Fig. 3 (blue curves). In this model the 322 ← 211 5/2 ← 3/2 and possibly the 331 ← 220 7/2 ← 5/2 lines are overpredicted, but the other ortho-H2O+ lines are well reproduced. Using the more extended, colder approach, with Tdust = 90 K and d = 160 pc, the column density is N(H2O+) = 2.5 × 1015 cm-2. In the nuclear region of Arp 220, the most likely OH+-to-H2O+ ratio is 1−2.

Apart from the para-H2O+ ground transition, there is only one excited, non-contaminated para-H2O+ line detected in the spectrum of Arp 220, the 221 ← 110 5/2−3/2 at 105.7 μm. As can be seen in Fig. 3b, the absorbing flux in this line is well reproduced with our models, which use an ortho-to-para ratio of 3, the high-temperature limit. This provides a slightly better fit than the one obtained with an ortho-to-para ratio of ≈ 4.8, the value derived by Schilke et al. (2010) toward Sgr B2, which underestimates the absorbing line flux in Arp 220 by 35%.

The ground-state p-H2O+ 212 ← 101 lines at 183−184 μm cannot be reproduced with the Cwest component (Fig. 3a). Models for the Cextended were also unsuccessful in reproducing these spectral features, as the required high (1.6 × 1016 cm-2) H2O+ columns have also the effect of predicting too strong absorption in other lines, specifically in the 322 ← 211 components. The p-H2O+ 183−184 μm lines peak at a velocity different from the H2O+ HE lines (Fig. 6), and are thus likely generated in a low excitation region that generates faint absorption in other lines. This component is likely to be the same as that producing strong absorption in the ground-state lines of H2O and OH, i.e. the Chalo component (Paper I). The spatial extent of this component is not constrained, and can be interpreted as foreground gas located along the line of sight to the nuclei absorbing their nuclear far-IR emission. As shown below (Sect. 3.4.3), however, it probably includes gas within a few hundreds pc from the nuclei; the Cextended and Chalo components are hard to separate physically8. The derived H2O+ column in this component is N(H2O+) ≈ 3 × 1015 cm-2, and the fit is shown with a light blue curve in Fig. 3a.

thumbnail Fig. 8

Predicted SPIRE spectrum of H2O+ in Arp 220 between 600 and 1200 GHz. The contributions by the Cwest , Cextended , and Chalo are shown with blue, green, and light-blue curves (vertically shifted for clarity), respectively, and the red curve shows the total absorption/emission.

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The amount of H2O+ in Cextended is better traced with the excited H2O+ detected in emission with Herschel/SPIRE by R11. In Fig. 8 we show the predicted SPIRE spectrum of H2O+ in Arp 220 between 600 and 1200 GHz. The contributions by the Cwest , Cextended , and Chalo are shown with blue, green, and light-blue curves (vertically shifted for clarity), respectively, and the red curve shows the total absorption/emission. At these frequencies, the contribution by the nuclear region (Cwest) is not expected to be dominant. The absorption in the ground-state 111 ← 000J = 3/2 ← 1/2 and 1/2 ← 1/2 o-H2O+ lines at 1100−1150 GHz is expected to be dominated by the Chalo component, also responsible for the absorption in the ground-state p-H2O+ lines at 183−184 μm. Most relevant is the predicted emission in some H2O+ lines at 700−800 GHz, which are expected to arise from the Cextended component. The strongest H2O+ emission lines are the 202 → 111 5/2 → 3/2 at 742.1 GHz and the 211 → 202 5/2 → 5/2 at 746.5 GHz, in agreement with the emission features reported by R119. Two other transitions with significant predicted emission above the continuum are the 202 → 111 3/2 → 1/2 at 721.8 GHz and the 211 → 202 3/2 → 3/2 at 761.9 GHz. It is worth noting that the modeled emission features are generated through radiative pumping and not through collisions−collisional excitation is not included in our calculations. With a column density in Cextended of N(H2O+) ≈ 5 × 1015 cm-2, the lines fluxes at 700−800 GHz reported by R11 are nearly reproduced. Our models thus favor an OH+/H2O+ column density ratio of ≳ 5 for Cextended , significantly higher than in the nuclear region (Table 2). In the Chalo , the OH+/H2O+ is uncertain as the OH+ ground-state lines are certainly saturated (R11).

3.4.3. H3O+

The H3O+ lines in Arp 220 show an intriguing behavior: on the one hand, non-metastable RI lines are detected (Figs. 4l, m, n, p); on the other hand, although they are radiatively pumped by far-IR photons to moderate excitation, these lines peak at roughly the same velocity as the LE lines of H2O and H2O+ transitions (Fig. 6), i.e. they are redshifted relative to the HE lines of other species.

From the population diagram in Fig. 5, we have used two values for Trot : 180 K up to the K = 5 ladder, and 500 K for higher-lying metastable levels. The blue lines in Fig. 4 show the model results with Tdust = 90 K, d = 160 pc, and N(H3O+) = 9 × 1015 cm-2. The model for H3O+ nearly accounts for the pure-inversion metastable lines (panels a−i), which have moderate opacities (τ ~ 0.3−1), though the line is slightly underpredicted. The rotation-inversion lines (panels j−p) are more optically thin.

thumbnail Fig. 9

Model results for H3O+ and NH3 in Arp 220. a) Ratios of pure inversion metastable lines of H3O+ versus Trot : K = 6/K = 4 (red), K = 8/K = 4 (blue), K = 9/K = 4 (green), and K = 10/K = 4 (black). b) For NH3, the fluxes of the (red), (green), and (blue) are normalized to the flux of the 124.9 μm feature (composed of the 40−30 and NH3 lines, Paper I). c) Ratios of rotation-inversion lines of H3O+ as a function of Tdust . Dashed lines in all panels indicate the measured values, with typical uncertainties of 20%.

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Figure 9a shows the flux ratios of the pure inversion, metastable , , , and lines to the line (solid lines) as a function of Trot , and compares them with the measured values (dashed lines). The flux measured for the line has been estimated from the total flux of the broad 165.8 μm feature by subtracting the modeled contribution due to NH3 (Fig. 4g). The K = 8/K = 4 (blue) and K = 9/K = 4 (green) ratios indicate Trot ~ 600−800 K, while the K = 6/K = 4 (red) and K = 10/K = 4 (black) favor ~ 450 K. The high Trot inferred from the H3O+ lines is in striking contrast with that inferred from NH3 (Fig. 9b): the NH3 line ratios indicate Trot ~ 150 K, in general agreement with the value inferred by Ott et al. (2011) from the pure inversion lines, and with the HCN excitation (Paper I). Either the two species are sampling different regions, and/or Trot as derived from H3O+ better reflects the formation process rather than Tgas .

The strength of the non-metastable rotation-inversion lines is sensitive to Tdust , and in Fig. 9c we compare the fluxes of some of these lines relative to that of the metastable line. We focus in this analysis on those lines that have similar line shapes, i.e. the , , and transitions. Comparison with the measured values favors Tdust ~ 90−110 K. The most reliable comparison is between the and the , as they belong to the same K-ladder, favoring Tdust ~ 90 K. Furthermore, due to the warmer SED, Tdust = 110 K generally underestimates the PIMS lines relative to the RI lines. In contrast, the H2O HE lines are compatible with higher Tdust (Paper I), and detection of the NH3 and lines at 83.85 μm (Paper I and confirmed with the new data set), with Elow ~ 400 K and pumped through radiation, better supports Tdust = 110−130 K for NH3.

The value of N(H3O+) depends on the size of the far-IR continuum source. To produce the observed H3O+ absorptions, the models strongly favor optically thick far-IR continuum emission up to at least 180 μm. An upper limit to the size would then be 230 pc, as the continuum source with Tdust = 90 K would produce the entire bolometric luminosity of the galaxy, 1.5 × 1012 L. This upper limit is, however, unreliable, as Cextended is expected to generate some far-IR emission, and there is also an important fraction of the luminosity associated with dust warmer than 90 K. Sizes smaller than 100 pc are also unlikely, as the H3O+ PIMS lines would become optically thick, and the fit to the whole H3O+ SLED would get worse (specifically the line would be underpredicted due to saturation). We estimate d = 105−160 pc, overlapping with, but at the high end of our derived size range for the nuclear OH+ and H2O+ (93−160 pc) and significantly smaller than our estimate for the extended region as derived from the continuum emission (~650 pc, Paper I). This size range implies a column density range of N(H3O+) = (2.7−0.9) × 1016 cm-2. These columns are a factor of 2 higher than those of OH+ for the same source sizes. However, the H3O+ transitions do not have the same line shapes as the OH+ lines (Fig. 6h). There is, nevertheless, a good match between the OH+ HE and H3O+ 70.8 μm profiles on the blueshifted side, suggesting some spatial overlap between both components. On these grounds, we favor a column density ratio OH+/H3O+ ~ 1 in the nuclear region of Arp 220, with an uncertainty of ± 50%. The relatively large size found for the H3O+ absorption, the shift of the peak of the H3O+ velocity profile towards those of the low excitation lines, and the moderate Tdust found for the H3O+ lines, suggest that the H3O+ lines, while nuclear, trace a transition region between the high-excitation (HE) component and the extended component.

The model in Fig. 4 predicts a flux for the 365 GHz line of 1.1 × 10-23 W cm-2, a factor of 1.5 lower than measured by vdT08. The modeled line is slightly inverted but with negligible amplification, and thus behaves as optically thin with the flux proportional to the column. Either it is sampling in addition deep regions that are extincted in the far-IR, or it is sampling a larger region (vdT08), because the 365 GHz emission line does not require far-IR optically thick continuum emission behind.

3.5. Summary

The analysis of the O-bearing molecular ions in NGC 4418 and Arp 220 reveal (i) high nuclear OH+ column densities of (0.5−1) × 1016 cm-2 in both sources, with estimated abundances relative to H nuclei of (1−3) × 10-8; (ii) OH+/H2O+ column density ratios of ~1−2.5, with NGC 4418 at the high end of the range; (iii) high OH+ columns of ~(2.5−4) × 1016 cm-2 in the Cextended component of Arp 220, with an estimated abundance of ~4 × 10-8, as well as a high OH+/H2O+ ratio of ~5−10; (iv) H3O+ column densities of ~(0.5−0.8) × 1016 cm-2 in NGC 4418 and ~(0.9−2.7) × 1016 cm-2 in Arp 220, the latter essentially nuclear but likely tracing a region slightly more extended than that traced by OH+. In the nuclear region where the OH+ lines are formed, OH+/H3O+ ~ 1 is estimated.

4. Chemistry

4.1. Framework

The O-bearing molecular ions are expected to be formed in gas irradiated by cosmic rays or X-rays (Maloney et al. 1996; Gerin et al. 2010; Neufeld et al. 2010; Meijerink et al. 2011). The sequence is initiated by the ionization of H atoms and H2 molecules; OH+ and H2O+ are subsequently produced by ion-neutral chemistry, and their abundances are sensitive to the gas ionization rate ζ and the molecular fraction fH2. In regions with a significant atomic fraction, H+ transfers its charge to atomic oxygen, and the O+ reacts with H2 to form OH+; H2O+ is then formed from OH+ + H2, and similarly H3O+ from H2O+ + H2 (Gerin et al. 2010; Neufeld et al. 2010). In regions with high molecular fraction, OH+ and H2O+ can also be formed via (e.g. Herbst & Klemperer 1973; Gerin et al. 2010; Hollenbach et al. 2012). Furthermore, in environments with high reservoirs of OH and H2O, OH+ and H2O+ can be produced from the charge exchange reactions OH + H+ and H2O + H+, as well as from photoionization of OH and H2O (Gupta et al. 2010), while H3O+ may also be formed from . Finally, H+ can also be produced through C+ + OH and CO+ + H, and this FUV/chemical route does not require X/cosmic ray irradiation (Sternberg & Dalgarno 1995; Hollenbach et al. 2012).

In order to discriminate between the above paths of OH+, H2O+, and H3O+ production, and to infer the physical conditions implied by the observations, we have run a grid of chemical models with the code described by Bruderer et al. (2009), based on previous works by Stäuber et al. (2005) and Doty et al. (2002). The chemical models calculate the steady state abundances of all relevant species based on the UMIST06 reaction rates (Woodall et al. 2007). In our simple models, the gas with H nuclei density nH and molecular fraction fH2 is directly exposed to a cosmic ray and/or X-ray flux that produces a total ionization rate per H nucleus ζ (including secondary ionizations). We ignore any other external agent (e.g. dissociating UV radiation) in the calculations, though internally generated UV radiation is included.

In their models for the production of the O-bearing molecular ions in interstellar clouds, Hollenbach et al. (2012) found that PAHs have important effects on their expected abundances. Specifically, a fraction of H+ ions produced by cosmic rays was found to be neutralized mostly by PAH, truncating the path for the production of OH+, and thus reducing the efficiency ϵOH+ of OH+ formation relative to previous calculations (Neufeld et al. 2010). Recent observations of both OH+ and H toward the Galactic W51 by Indriolo et al. (2012) have indeed indicated a relatively low value of ϵOH+. In NGC 4418, however, PAH emission is very weak (Spoon et al. 2007), and it is also weak in Arp 220 relative to the submillimeter continuum (Haas et al. 2001). Although this may be due to extinction of nuclear far-UV photons or foreground mid-IR extinction, rather than low PAH abundance, we conservatively switch-off the charge exchange between gas and dust grains in our calculations. In this respect, the ionization rate ζ we derive below (Sect. 4.5) should be viewed as a lower limit.

Under our simplified assumptions, and as shown by previous studies (e.g. Maloney et al. 1996; Neufeld et al. 2010; Hollenbach et al. 2012), the relevant input parameters are ζ/nH, fH2, the gas temperature (Tgas), and the oxygen abundance in the gas phase (χO). For the latter parameters we adopt Tgas = 150 and 550 K, and solar metallicities with χO = 3 × 10-4. Freeze-out of atomic oxygen on grains surfaces is thus ignored owing to the high Tdust in the nuclear regions of these sources (e.g. Hollenbach et al. 2012).

thumbnail Fig. 10

Predicted a) OH+/H2O+ and b) OH+/H3O+ ratios as a function of χe × 103/fH2. Symbols show results for all generated chemical models, while the solid lines show the analytic curves by Gerin et al. (2010) and Neufeld et al. (2010). The inferred OH+/H2O+ ratios in the nuclear regions of NGC 4418 and Arp 220, and in the Cextended of Arp 220, are indicated with the shaded dark and light regions, respectively. Gas temperatures of 150 K (black) and 550 K (red) are assumed.

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In the calculations, we treat fH2 as an independent parameter, even though its value can in principle be obtained from the H2 formation and destruction rates. Treating fH2 as a free parameter has the advantage that it allows us to run simple single-point models without additional assumptions on the geometry or H2 formation efficiencies. Furthermore, fH2 also depends on other physical processes that are difficult to evaluate in the sources under study: photodissociation by UV radiation, and the evolutionary state of the cloud in low density (diffuse) clouds, where fH2 only attains steady state after ≳ 10 Myr (Liszt 2007). Concerning the latter point, the ground-state lines of OH+ and H2O+ have been detected in Galactic diffuse clouds indicating a very low fH2 (Gerin et al. 2010; Neufeld et al. 2010), probably reflecting regions that are evolving in fH2. Our calculations are intended to describe the observations of both the nuclear regions and the extended component in Arp 220; in the latter case similar conditions to those found in Galactic diffuse clouds may be present. For a given ζ/nH, the maximum value that fH2 can attain is described as10: (2)where we have adopted for the rate coefficient of H2 formation on grain surfaces the reference value with RG = 3 × 10-18 cm3 s-1 and Tgas = 150 K, and applied this constant value to all cases (i.e. regardless of Tgas and Tdust ) for simplicity (see discussion in Kaufman et al. 1999). For the ζ/nH values considered in the following sections, 5 × 10-19, 5 × 10-18, 2 × 10-17, 5 × 10-17, and 5 × 10-16 cm3 s-1, is estimated as 0.99, 0.88, 0.65, 0.43, and 0.07, respectively. Values of fH2 below are obtained in our models by manually increasing the H2 destruction rate. Equation (2) appears to be roughly consistent with the models by Bayet et al. (2011), who obtain fH2 ≈ 0.7 at high AV for ζ/nH = 10-17 cm3 s-1 and solar metallicities. However, the actual values could be lower, owing to the decreasing H2 recombination efficiency in warm grains ( ≳ 100 K; Cazaux & Tielens 2004; Cuppen et al. 2010). The grid of models cover the ζ/nH − fH2 plane, with fH2 varying from 0.02 to , and ζ/nH up to 5 × 10-16 cm3 s-1.

thumbnail Fig. 11

Predicted OH+, H2O+, and H3O+ abundances (left panels) and OH+/H2O+ and OH+/H3O+ abundance ratios (right panels) as a function of ζ/nH. In all these models, the molecular fraction is given by the maximum value in Eq. (2). Gas temperatures of 150 K (black) and 550 K (red) are assumed. The ranges derived from the observations and models for the nuclear regions of NGC 4418 and Arp 220 are indicated by the shaded regions.

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4.2. The OH+/H2O+ and OH+/H3O+ ratios

Figure 10 shows with squares, for all generated models, the predicted R1 ≡ OH+/H2O+ and R2 ≡ OH+/H3O+ ratios as a function of χe × 103/fH2, where χe is the electron abundance relative to H nuclei. As shown by Gerin et al. (2010) and Neufeld et al. (2010), if the H2O+ is exclusively formed by reaction of OH+ with H2, R1 only depends on χe/fH2 and Tgas , regardless of the formation mechanism of OH+, according to: (3)where T300 = Tgas/300  K. If in addition H3O+ is exclusively formed from H2O+ + H2, R2 is given by (4)These analytical dependences are shown with solid curves for Tgas = 150 and 550 K in Fig. 10. Equation (3) shows that a lower limit of R = 0.63 is expected when recombination of H2O+ is ignorable and the unique route of H2O+ destruction is reaction with H2 yielding H3O+. For χe/fH2 ≳ 10-3, recombination of H2O+ becomes increasingly important and R1 rises linearly with χe/fH2. This analytic approach to R1 is appropiate for regions where the formation of H2O+ is dominated by H2 + OH+. However, at low χe/fH2 values, i.e. in shielded/high density regions with low electron fraction and high molecular fraction, R1 deviates from the analytic curve because there are competing paths for H2O+ formation (mostly H+ + H2O and ) that do not involve formation of OH+, thus decreasing the OH+/H2O+ ratio below 0.63 (squares in Fig. 10a). On the other hand, R2 varies strongly with χe/fH2, and significant departures from the analytical approach in Eq. (4) are also obtained for low χe/fH2, and high Tgas .

Even in the nuclear regions of NGC 4418 and Arp 220 where densities are high and high concentration of molecular species are observed (Paper I), we do find relatively high values of R1 and R2, though significantly lower than in Galactic diffuse clouds. R1 is found ~1−2 and could be even higher in NGC 4418, and R2 ~ 1 (Table 2). Thus the inferred ratios appear to indicate that the primary route for H2O+ and H3O+ formation in the nuclear regions of NGC 4418 and Arp 220 is the same as in Galactic translucent clouds, H2 + OH+ and H2 + H2O+, respectively, additional routes for H2O+ and H3O+ formation being less important. We still expect, however, fH2 to be significantly higher than in translucent clouds. Adopting conservatively fH2 ≳ 0.5, we obtain χe ≳ 2 × 10-4. This value is higher than that expected from complete ionization of carbon, 1.4 × 10-4, pointing to a significant, additional source of free electrons arising from H and H2 ionization. In the more extended and diffuse Cextended of Arp 220, the high value of R1 probably reflects a relatively low value of fH2, resembling the situation found in Galactic translucent clouds.

The full chemical results for OH+, H2O+, and H3O+, together with the corresponding abundances of electrons and H+, are shown in Appendix C, where some analytical approaches to the abundance of OH+ are also derived. We find that the most likely path for OH+ formation is O+ + H2, with the contribution from the charge exchange reaction H+ + OH and from direct OH ionization being of secondary importance even in the nuclear regions, where high OH abundances are inferred (Paper I). Therefore, the sequence H+ → O+ → OH+ → H2O+ → H3O+ is favored as the production of the O-bearing cations. In Appendix C we also favor deep penetration of X-cosmic rays as the main source of H+ production, with the contribution due to the C+ + OH → CO+ + H → CO + H+ FUV/chemical route (Sternberg & Dalgarno 1995; Hollenbach et al. 2012) being presumably important only in small volumes around O stars.

4.3. The value of ζ/nH in the extended region of Arp 220

In the Cextended component of Arp 220, where high OH+ column and R1 values are found, our best fit values for ζ/nH and fH2 are (0.5−2) × 10-17 cm3 s-1 and 0.05−0.25, respectively (Fig. C.1). With this low molecular fraction, however, χOH+ is not far from saturation (see Appendix C), which occurs at χOH+ ≳ 10-7 and thus may be reached in some regions of Cextended . The low value of fH2 indicates that either the H2  abundance has not fully evolved to steady state, or H2 photodissociation keeps a large hydrogen fraction in atomic form. The electron abundance is expected to be in the range χe ~ (3−10) × 10-4.

These physical conditions are derived from the apparently high OH+ column in Cextended , and from the relatively low H2O+ column with the following caveat. The columns are derived from far-IR OH+ absorption and submillimeter H2O+ emission lines, which may probe different regions. The lowest-lying absorption lines of H2O+ at 183−184 μm, observed in absorption toward the nuclei (Chalo), indicate a foreground H2O+ column of ~ 3 × 1015 cm-2. A fraction of the H3O+ observed toward the nuclei is expected to arise also from foreground gas, with a column of also several × 1015 cm-2, though detailed models for PDRs irradiated by cosmic rays show that H3O+ attains significant columns deeper into the cloud than OH+ (Hollenbach et al. 2012). The extended gas in Arp 220 likely harbors regions with a diversity of physical conditions.

4.4. The value of ζ/nH in the nuclear regions

In the nuclear regions of NGC 4418 and Arp 220, where χOH+ ~ 2 × 10-8 and R1 = 1−2.5 (Table 2), χOH+ is unsaturated (see Appendix C), i.e. results are sensitive to ζ/nH. However, the inferred ζ/nH depends on the assumed fH2. In these regions, we may expect steady state for H2, and we adopt fH2 as given by Eq. (2) (i.e. we assume that cosmic/X rays are the only source of gas dissociation/ionization). Figure 11 shows the corresponding modeled cation abundances and ratios. Model results can be summarized as follows (see also Neufeld et al. 2010; Gerin et al. 2010; Gupta et al. 2010; Hollenbach et al. 2012). For very high ζ/nH, OH+ can still attain high abundances even with low fH2 < 10%, but H2O+ is primarily destroyed through recombination and the abundances of H2O+ and H3O+ are low. For low ζ/nH, low abundances of OH+ and H2O+ are obtained, but the H3O+ abundance for Tgas = 550 K remains high as H3O+ is formed through reaction of highly abundant H2O with and H+. Abundances of OH+ and H2O+ around 10-8 are obtained at typical ζ/nH ~ 10-17 cm3 s-1. The abundance of H3O+ is very sensitive to Tgas , and R2 is very sensitive to both Tgas and ζ/nH.

The inferred abundances and ratios, marked by shaded regions in Fig. 11, are consistent with ζ/nH in the range (1−2) × 10-17 cm3 s-1. The electron abundance is expected to be in the range χe ~ (1.5−5) × 10-4. These results are sensitive to the assumed H2 fraction, with higher (lower) fH2 implying higher (lower) ζ/nH. Decreasing γH2 in Eq. (2) to 10-17 cm3 s-1, the observed abundances and ratios can be explained with ζ/nH ~ 5 × 10-18 cm3 s-1. Further study of the H2 reformation on warm dust grains in these regions is required to refine our estimates.

4.5. The total ionization rate per H nucleus (ζ)

Estimation of the total ionization rate per H nucleus ζ requires knowledge of the gas density. In the Cextended of Arp 220, an average density of nH ~ 103 cm-3 is expected from the continuum emission and estimated size (Paper I). Therefore ζ ~ 10-14 s-1, about 100 times higher than in Galactic diffuse clouds. This value is however uncertain, as the absorption in the OH+ lines may be selectively produced in regions with densities much lower than the estimated average, and thus ζ significantly lower than our above estimate is not ruled out.

In the nuclear regions of NGC 4418 and Arp 220, very high densities are expected. In the Ccore of NGC 4418, densities of 3 × 106 cm-3 are derived from the faint OH absorption in the ground-state lines at central velocities, from the pattern of H2O absorption, and from the high excitation of HCN (Paper I). If the observed OH+ were formed in this region, this would imply an extreme, very unlikely value of ζ ~ 10-10 s-1. However, it is plausible that the OH+ lines are formed in a more tenous, nuclear region. There are several observations indicating that the molecular ions are formed in a component different from that responsible for the emission/absorption observed in neutral molecular species. Gupta et al. (2010) have detected broad blueshifted absorption in the ground-state lines of OH+ and H2O+ with HIFI toward the Orion KL, and their preliminary models appear to point toward a component of the low-velocity Orion outflow that has a density (~103 cm-3) far below the densities inferred from other species. In diffuse gas, Neufeld et al. (2010) show that the velocity distribution of the OH+ and H2O+ absorption is dissimilar from that of H2O; the absorption in the molecular ions (and atomic H) being more broadly distributed in velocity space. Theoretically, the models by Bayet et al. (2011) and Meijerink et al. (2011) indicate that the OH+ abundance is anticorrelated with the abundance of NH3 and HCN. Furthermore, the models by Meijerink et al. (2011) indicate that the H2O abundance is anticorrelated with ζ/nH, and thus with the abundances of OH+ and H2O+ as well.

We thus conservatively propose that the absorption observed in the high-lying lines of OH+ and H2O+ are formed in a relatively low-density region different from the dense component that accounts for the absorption in the high-lying lines of H2O, HCN, and NH3 (Paper I). This low density component could be interpreted in terms of a nuclear interclump medium, or a shell surrounding the high density nuclear gas. However, this component cannot be very extended as otherwise the far-IR radiation density could not excite the molecular ions up to the observed rotational levels (Elower ≈ 285 K). The width of the OH+ shell should be small in comparison with the radius of the far-IR source, which provides a lower limit on the density. Our models favor densities of at least ~104 cm-3 in Arp 220, and ~2 × 104 cm-3 in NGC 4418. For a density threshold of 104 cm-3, ζ ≳ (1−2) × 10-13 s-1. In NGC 4418, where high densities were inferred in Paper I, this is a strong lower limit, and yet still ζ ≳ several × 102 times the highest values currently estimated in the Milky Way (several × 10-16 s-1; e.g. Indriolo et al. 2007, 2012; Neufeld et al. 2010; Hollenbach et al. 2012).

5. Discussion

5.1. The O-bearing cations and the neutral species

Under the simple assumptions used in our schematic chemical models, predictions for the abundances of the neutral species OH, H2O, NH3, and HCN analyzed in Paper I are also obtained. The main results for the neutral species are: (i) OH attains abundances >10-6 even for the lowest ζ/nH = 5 × 10-19 cm3 s-1 and a wide range in fH2, in rough agreement with the derived values. (ii) H2O only attains the inferred high abundances of ~10-5 for high Tgas and ζ/nH < 2 × 10-17 cm3 s-1; otherwise gas-grain chemistry (not included in our simple chemical calculations) is required to account for the high H2O abundance (Paper I). (iii) HCN only approaches abundances as high as ~10-6 for the lowest ζ/nH = 5 × 10-19 cm3 s-1 and high Tgas , suggesting that indeed it is formed in regions with densities higher, and probably more protected from the ionization source, than those responsible for the molecular ions. (iv) NH3 attains abundances of only 10-8, far below the inferred ones, further indicating the importance of gas-grain chemistry. In general, clumpy regions with high contrast in nH, fH2, and ζ, and gas-grain chemistry, are most likely required to account for the full molecular absorption detected in the nuclear regions of both galaxies. The neutral/ion connection will be further analyzed in a future study.

5.2. X-rays or cosmic rays?

In the starburst galaxies NGC 253 and M82, detection of γ-rays (Acero et al. 2009; Acciari et al. 2009; Abdo et al. 2010) indicate a high CR energy density of ~200−300 times the value (~1 eV/cm3) in the Milky Way (Abramowski et al. 2012; Persic & Rephaeli 2012). Since the γ − rays are thought to be the result of cosmic rays accelerated by supernova remnant shocks that interact with high density target material, a high rate of cosmic-ray ionization indicates a high rate of supernovae in the central region of starburst galaxies (νSN ~ 0.03 yr-1 in NGC 253, Engelbracht et al. 1998), which would be expected to be accompanied by observable galactic outflows. These are indeed seen in both NGC 253 and M82 (e.g. Sugai et al. 2003; Strickland & Heckman 2007; Veilleux et al. 2009).

The cosmic-ray energy density inferred in Arp 220 from both the supernova rate (~4 yr-1, Lonsdale et al. 2006) and synchrotron radio emission is ~500−1000 times the Galactic value (Persic & Rephaeli 2012), in good agreement with our lower limit of several × 102 times the Galactic value for ζ. The blueshifted component in Arp 220 traced by the high-excitation lines of H2O, OH, NH3, and HCN may indicate outflowing gas with a line of sight velocity of ~75 kms-1 (Sect. 2.4). With an extent of ~80 pc, this would imply a (local) very high mass outflow rate of ~900 × (nH/105  cm-3) M yr-1. However, the outflowing gas is difficult to distinguish from the rotating gas for the relatively low outflow velocities in Arp 220 (Sect. 2.4), in stark contrast with the ~1000 kms-1 outflow velocities traced by OH in other ULIRGs (Fischer et al. 2010; Sturm et al. 2011). Nevertheless, clear indication of outflowing gas is seen in the P-Cygni HCO+ profiles observed at submillimeter wavelengths (Sakamoto et al. 2009), and is also suggested at redshifted velocities in the [O i] 145 μm line and in the low-lying OH and H2O emission component profiles (Paper I).

The above independent estimates of the CR energy densities in Arp 220, and the signatures of outflowing molecular gas with low-moderate velocities, appear to be compatible with the scenario of a high density of cosmic rays producing the observed molecular ions. Papadopoulos (2010) has proposed that very high cosmic ray energy densities, of the order of those we derive here, can turn the bulk of the nuclear molecular gas in ULIRGs into giant CR-dominated Regions (CRDRs) rather than ensembles of Photon-dominated Regions (PDRs). In this framework, the O-bearing cations can be considered excellent tracers of these regions.

The case of NGC 4418 is unclear. This highly buried (Spoon et al. 2001, 2007) and highly excited (Paper I) source, where the bulk of the luminosity arises from a very small volume, is deficient in synchrotron emission with respect to the far-infrared emission (Roussel et al. 2003). Furthermore, we did not find spectroscopic signatures of outflowing gas; on the contrary the far-IR lines observed with PACS are narrow (Paper I). Therefore, cosmic rays may only be of secondary importance. An explanation of the synchrotron deficit based on a nascent starburst (Roussel et al. 2003) can hardly account for the excited OH+ detected in the source, though observations of excited OH+ in Galactic and other extragalactic sources are needed to check this point. Preliminarily, NGC 4418 is better interpreted as a buried AGN, and the molecular ions as produced in a XDR. But given that Arp 220 can be considered as a scaled-up version of NGC 4418, and that the columns of the cations are found similar in the nuclear regions of both sources, the possible XDR nature of Arp 220 is not ruled out.

While both NGC 4418 and Arp 220 are underluminous in hard (2−10 keV) X-rays for their computed SFRs (Maiolino et al. 2003; Iwasawa et al. 2005), the X-ray absolute fluxes may suffice to produce the inferred ionization rate. The distance-corrected X-ray fluxes of 0.1 and 0.5 erg s-1 cm-2 estimated at the surface of the nuclear regions in NGC 4418 and Arp 220 (Paper I), respectively, are lower limits due to foreground absorption in both galaxies (with NH ~ 1023 cm-2, Paper I) and by the molecular shell itself where the ions reside. Depending on the X-ray spectrum, local (i.e. unattenuated) X-ray fluxes of ≳ 0.5 erg s-1 cm-2 may well produce ζ in excess of 10-13 s-1.

The strong high-ionization Fe K line in Arp 220 (Iwasawa et al. 2005) appears to indicate that the faint X-ray emission is not primarily due to high-mass X-ray binaries (as in starburst galaxies), but could arise either from an internally shocked hot bubble of starburst origin (the pressure of which would produce the observed molecular outflow), or from a deeply embedded supermassive black hole (Iwasawa et al. 2009). In the latter case, the molecular ions would then be formed in (somewhat extended) regions that are illuminated by X-rays from the AGN that can escape to the outer (nuclear) regions primarily through inhomogeneities in the nuclear media. The drawback of this alternative is that the far-IR molecular lines are observed in absorption against dust emission that is optically thick even at far-IR wavelengths, and thus the X-ray emission from a putative buried AGN would then be strongly attenuated in arriving at such nuclear, but “surface” regions unless some special geometry is invoked11. Further theoretical and observational studies are required to discriminate between CRDRs and XDRs.

5.3. H3O+: formation pumping or hot gas?

We show in Appendix B that the H3O+ population diagram for the PIMS lines in Arp 220 can be understood in terms of formation pumping described by Tform ~ 1000 K, but that plausible collisional relaxation and the lack of knowledge of collisional rates make the case uncertain. Interestingly, detailed chemical models of PDRs (Hollenbach et al. 2012) predict that H3O+ is primarily formed in fully molecular regions, while both OH+ and H2O+ peak closer to the PDR surface where fH2 is significantly lower than unity. On the contrary, in Arp 220, the H3O+ PIMS lines peak at the redshifted velocity (LE) component (Fig. 6), which is expected to be more widespread and less dense than the blueshifted velocity (HE) component.

Nevertheless, it is worth noting that Rangwala et al. (2011) have detected high-J rotational lines of CO, which the authors interpreted as arising from hot (~103 K), low density (~103 cm-3) gas that is mechanically heated. If the H3O+ lines are formed in the same region as the CO lines, the presence of such a hot molecular gas layer in Arp 220 may indeed suggest that both formation pumping and high Tgas are responsible for the observed PIMS absorption. Due to the low gas density associated with the redshifted (LE) component, inefficient cooling may keep the gas at high Tgas , which has the additional effect of boosting the H3O+ abundance (Fig. 11). On the other hand, the nuclear gas associated with the blueshifted velocity (HE) component is dense, and gas-grain thermal coupling (Goldsmith 2001) may be efficient in cooling the gas to the inferred 150−200 K (based on NH3 lines, Fig. 9b). Collisional relaxation of the H3O+ metastable populations may proceed efficiently at this Tgas (Fig. B.1).

For a density of 104 cm-3 and ζ = 10-13 s-1, the expected Tgas is ~ 300 K and rises very steeply with increasing ζ (Bayet et al. 2011); this result suggests X/cosmic ray heating may be important, together with mechanical heating, in explaining Tgas in the nuclear regions of NGC 4418 and Arp 220.

6. Conclusions

The observational results on OH+, H2O+, and H3O+ in NGC 4418 and Arp 220 are:

  • Absorption lines from excited levels of OH+ with Elower up to 285 K are detected in NGC 4418 and Arp 220. While the highest-lying lines have similar strengths in both sources, the low-lying lines are more prominent in Arp 220.

  • Lines of H2O+ are also well detected in absorption in Arp 220 up to a lower level energy of ~ 200 K, with strong absorption in the ground-state p-H2O+ transition at 183−184 μm. In contrast, in NGC 4418 the ground-state line is not detected and only several of the excited lines are detected with relatively low signal-to-noise.

  • The pure-inversion, metastable lines of H3O+ are detected in Arp 220 up to a lower level of ~ 1400 K, indicating a rotational temperature of ~ 550 K. These lines are not detected in NGC 4418. However, the rotation-inversion lines, some of them arising from non-metastable levels, are detected in both sources.

  • We identify two main velocity components in Arp 220 separated by ≈ 75 kms-1. The high-lying lines of all neutral (H2O, OH, NH3, HCN) and ionized (OH+, H2O+) molecular species peak at the blueshifted component, while the lowest-lying lines peak at the redshifted one. The exception corresponds to the pure-inversion metastable lines of H3O+, which also peak at the velocity of the redshifted component. The blueshifted line components may be tracing the outflow shown in the millimeter lines of HCO+ by Sakamoto et al. (2009), and grain mantle evaporation, sputtering, and neutral-neutral reactions at high Tgas may all be contributing to enhance the gas-phase abundances of H2O and NH3.

The observations are analyzed with radiative transfer modeling. The conclusions stemming from the analysis are:

  • The excited lines of OH+ and H2O+, and therotation-inversion lines of H3O+ are pumpedthrough absorption of far-IR radiation emitted by dust, but thepure-inversion metastable lines of H3O+ are eitherchemically and/or collisionally pumped.

  • OH+ column densities of (0.5−1.1) × 1016 cm-2 are derived toward the nuclear region of both sources for spatial extents of 20−30 pc in NGC 4418, and 90−160 pc in Arp 220. The estimated abundance is (1−3) × 10-8 in both sources. In addition, in Arp 220, absorption from an extended region is required to match the low-lying OH+ lines, with an estimated column of a few × 1016 cm-2 and an abundance of several × 10-8.

  • The nuclear columns of H2O+ are (0.3−0.9) × 1016 cm-2 in Arp 220, and (0.3−0.4) × 1016 cm-2 in NGC 4418, indicating OH+/H2O+ ratios of 1−2.5 (the lower value applies to Arp 220). In Arp 220, the emission lines detected with SPIRE indicate an additional extended region with columns of several × 1015, similar to the column derived from the ground-state p-H2O+ lines, indicating a OH+/H2O+ ratio of 5−10 in the extended region.

  • The H3O+ lines indicate columns of (0.5−0.8) × 1016 cm-2 in NGC 4418, and (1−2) × 1016 cm-2 in Arp 220. In Arp 220, the observed high excitation of the pure-inversion metastable lines may be due to both formation pumping and high Tgas , and the H3O+ lines are likely tracing a nuclear transition region into the more extended, low excitation gas. It is suggested that collisional relaxation of the H3O+ metastable populations is important in the dense nuclear gas of Arp 220. The H3O+ lines are redshifted relative to the high-lying lines of OH+ with uncertain velocity overlap, and we estimate a OH+/H3O+ ratio of ~ 1 in the nuclear region of both sources.

Simple chemical models are used to interpret the results of radiative transfer modeling. Our main conclusions are:

  • The sequence H+ → O+ → OH+ → H2O+ → H3O+ is favored as the primary route to explain the high columns of the O-bearing molecular ions toward the nuclear region of both sources.

  • The production of H+ is most probably dominated by X/cosmic ray ionization, rather than by FUV/chemical means (Appendix C). An ionization rate per hydrogen nuclei density of ζ/nH ~ (1−2) × 10-17 cm3 s-1 is estimated in the nuclei of both galaxies.

  • The full set of observations and models lead us to propose that the molecular ions arise in a relatively low-density interclump medium but with density of at least 104 cm-3, in which case the ionization rate is ζ > 10-13 s-1, a lower limit that is over two orders of magnitude greater than the highest current rate estimates of several × 10-16 s-1 for Galactic regions.

  • The cosmic-ray energy density inferred in Arp 220 from both the supernova rate and synchrotron radio emission is ~ 103 times the Galactic value (Persic & Rephaeli 2012), which is compatible with the lower limit found for ζ from the present observations and analysis. Nevertheless, an important contribution due to X-ray ionization in Arp 220 is also plausible. In NGC 4418, an XDR is favored. Further theoretical and observational studies are required to discriminate between X-ray and cosmic ray ionization.


1

The observation identification numbers (OBSIDs) are 1342202107−1342202116 for NGC 4418, and 134191304– 1342191313 and 1342238928−1342238937 for Arp 220.

2

The hyperfine structure of both OH+ and H2O+ is ignored in this work as the line splitting is much lower than both the PACS spectral resolution and the linewidths.

3

The symmetric and antisymmetric states are here denoted with +  and −, respectively.

4

For NH3, the antisymmetric state is higher in energy by 23.7 GHz and the pure-inversion transitions lie at centimeter wavelengths.

5

In Fig. 12 of Paper I, the HCO+ lines should be shifted 100 kms-1 to the red, as the original spectrum (Sakamoto et al. 2009) uses the radio convention for the velocities; thus the HCO+ absorption toward the western nucleus better matches the blueshifted absorption in the H2O HE lines.

6

In steady state, this condition can also be expressed as kcol < 10-10 × (Tgas/100)-0.5 × (χ(e)/1.4 × 10-4) cm3 s-1, suggesting possible significant formation pumping effects in high-AV translucent clouds (see Appendix B).

8

The difference between the Cextended and Chalo components in our models for Arp 220 arises from radiative transfer effects. The Cextended is characterized by optically thin, extended far-IR emission, where the molecules are still significantly excited via absorption of locally-emitted far-IR photons. The Chalo , however, describes foreground, low-excitation gas with strong, optically thick emission behind arising from the nuclei. The main difference may simply be the location of the molecules relative to the far-IR optically thick nuclei and the observer, thus basically describing the same spatially extended gas.

9

R11 assigned the 746.5 GHz feature to the 202 → 111 3/2 → 3/2 at nearly the same frequency, but this transition has an Einstein coefficient 5.4 lower than the main 5/2 → 3/2 component and is expected to give weak emission.

10

It is assumed that each H2 ionization gives rise to one net H2 destruction due to the expected dominant paths and .

11

The extinction in the X-ray regime for EX < 10 keV is higher than at 200 μm for a gas-to-dust ratio of 100 by mass (e.g. Montmerle 2001).

Acknowledgments

We thank the referee, David A. Neufeld, for useful indications that improved the manuscript. PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM (France); MPIA (Germany); INAFIFSI/OAA/OAP/OAT, LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI/INAF (Italy), and CICYT/MCYT (Spain). E.G.-A. is a Research Associate at the Harvard-Smithsonian Center for Astrophysics, and thanks the support by the Spanish Ministerio de Ciencia e Innovación under project AYA2010-21697-C05-01. Basic research in IR astronomy at NRL is funded by the US ONR; J.F. also acknowledges support from the NHSC. H.S.P.M. acknowledges support by the Bundesministerium für Bildung und Forschung (BMBF) through project FKZ 50OF0901 (ICC HIFI Herschel). S.V. thanks NASA for partial support of this research via Research Support Agreement RSA 1427277, support from a Senior NPP Award from NASA, and his host institution, the Goddard Space Flight Center. This research has made use of NASA’s Astrophysics Data System (ADS) and of GILDAS software (http://www.iram.fr/IRAMFR/GILDAS).

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Appendix A: Excitation of OH+ and H2O+ through formation pumping

Here we show that formation pumping is not important for the OH+ and H2O+ level population distribution or absorption line fluxes in Arp 220 and NGC 4418. The effect of formation pumping on the excitation of OH+ can be estimated from the statistical equilibrium equations by Bruderer et al. (2010b) (Eqs. (B1)−(B3) in their Appendix B), by ignoring the collisional and induced emission terms: (A.1)where AN,J;N′,J is the Einstein coefficient for spontaneous emission from level (N,J) to level (N′,J′), and ΓN,J (cm-3 s-1) and ΛN,J (s-1) are the chemical formation and destruction rates. The total OH+ formation rate is (A.2)where ζ is the ionization rate and ϵOH+ is the efficiency with which ionizations are transfered to OH+ production. The destruction rate ΛN,J is assumed to be independent of the considered level (Bruderer et al. 2010b), and for OH+ is given by (A.3)In steady state, ΛOH+ = ΓOH+/(nHχOH+), which is expected to be < 10-5 s-1. Since this value is much lower than the AN,J;N′,J values ( ≳ 0.05 s-1, Table 1), the OH+ molecules are destroyed once they are in the ground (N,J) = (0,1) level, and Eq. (A.1) yields for excited N > 0 levels (A.4)For the ground (N,J) = (0,1) level we can write: (A.5)Equations (A.4) and (A.5) are easily solved iteratively by starting from a high N-level down to the N = 0 state. Results show that for χOH+ ≳ 10-8, ζ < 10-12 s-1, and ϵOH+ ~ 0.5, the three N = 1 → 0 components have an excitation temperature Tex < 7 K, implying that less than 0.3% of OH+ molecules are in excited levels. Therefore, excitation by dust emission is much more efficient than formation pumping in these sources. A similar analysis was done for H2O+, with also similar results: Tex ≲ 7 K for the ground state transitions, and less than 1.5% of H2O+ molecules in excited levels.

The flux predicted in the OH+N → N − 1 transition as derived from formation pumping alone can also be easily estimated. By summing over all J-levels in Eq. (A.4), one obtains (A.6)thus the number of N → N − 1 line photons emitted per unit volume and time is equal in steady state to the accumulated formation rate in all N′ ≥ N levels, and is independent of the Aul − values. Writing the volume of the emitting region as V = πR2NH/nH, where NH and nH are the column and density of H nuclei, respectively, and R is the effective radius of the region, the flux in the N → N − 1 fine-structure lines due to formation pumping is given by (A.7)where D is the distance to the source. The double sum in Eq. (A.7) is evidently lower than the total OH+ formation rate (ΓOH+), and then (A.8)and using Eq. (A.2), (A.9)The reference value is ~ 500 times lower than the absorbing flux of the N = 2 ← 1 transition in Arp 220 (Table 1), indicating that formation pumping has a negligible effect on the observed line fluxes. For NGC 4418, the upper limit is 3 × 10-23  W  cm-2 for R = 20 pc, also much lower than observed.

Appendix B: Excitation of H3O+ through formation pumping

thumbnail Fig. B.1

a) The H3O+ rotation diagram (triangles), calculated in the optically thin limit. The colored squares (red: ortho, blue: para) show the expected column density distribution for a formation temperature of Tform = 1000 K, and neglecting collisional relaxation. The two solid lines correspond to rotational temperatures of Trot = 250 and 600 K. b) The rotational temperature of the metastable level of H3O+ relative to the one as a function of the electron abundance χ(e) for two adopted values of Tgas (50 and 200 K) and four assumed values of (curves 1), 1 × 10-10 (2), 3 × 10-10 (3), and 1 × 10-9 cm3 s-1 (4).

Open with DEXTER

As discussed in Sect. 3.1, the rates for H3O+ excitation through collisions are unknown and therefore the excitation mechanism of the high metastable levels cannot currently be determined. Nevertheless, here we attempt to constrain under what conditions formation pumping can account for the observed excitation. By assuming a range of reasonable collisional excitation rates and some simplifying but illustrative assumptions, we show here that formation pumping can play an important role in populating the highly excited metastable levels from which absorption is observed in Arp 220.

We assume that the formation distribution can be described by a formation temperature, Tform, so that the formation rate Γi in level i is (Bruderer et al. 2010b): (B.1)where ΓH3O+ is the total H3O+ formation rate, gi and Ei are the degeneracy and energy of level i, respectively, and Q is the partition function. H3O+ is expected to be formed through H2O+ + H2 → H3O+ + H, with an exothermicity of 1.7 eV. Imposing equal momentum of the products in the rest frame, and assuming energy equipartition of H3O+ between rotational, vibrational, and translational energy, we roughly estimate that ~0.08 eV per formed H3O+ molecule will go into rotational energy, implying Tform ~ 800 K. We adopt in the following Tform = 1000 K.

After a molecule is formed in a level, it will cascade down very quickly to the metastable one, where it will remain until a collisional event induces a transition to another level, or until the molecule is destroyed through recombination with an electron. If the latter process dominates, the population in the metastable levels will be determined by the formation process. However, the rotational temperature Trot of the metastable levels will be lower than Tform , because the former is determined by the J-accumulated formation rates in the different K-ladders. In Fig. B.1a, the colored symbols show the expected population diagram obtained by ignoring collisional relaxation. While there is not a unique Trot , there is a tendency for it to increase with El, and the expected distribution can be roughly fitted with Trot ~ 250 and ~600 K for El ≲ 300 K and El > 300 K, respectively. This resembles the double distribution found by Lis et al. (2012) toward Sgr B2. The triangles in Fig. B.1a show the columns obtained toward Arp 220 by assuming that the observed lines are optically thin (Sect. 2.3).

In order to check under which conditions the formation process can generate the observed high excitation of the metastable H3O+ levels in environments with moderate Tgas , we have made calculations for the equilibrium populations nK of the metastable levels by solving the rate equations (B.2)where ΓK denotes the accumulated formation rate in all levels of the K-ladder. The rate coefficient for H3O+ destruction through recombination is taken from the UMIST06 database (Woodall et al. 2007): (B.3)We treat the collisional relaxation in a rather simplistic, but still illustrative way: only collisions between a given metastable level and the neighboring upper and lower (ortho or para) metastable levels are considered, with an effective rate of collisional de-excitation from level K to level K′ given by , assumed independent of K. The excitation rate is fixed by the requirement of detailed balance at the adopted Tgas .

We solved Eqs. (B.2) for all metastable levels by assuming an H3O+ ortho-to-para abundance ratio of 1, and for four adopted values of : 3 × 10-11, 1 × 10-10, 3 × 10-10, and 1 × 10-9 cm3 s-1. In steady state, ΓK ∝ nH and under our simple assumptions the Trot values are independent of nH. As an example of this approach, Fig. B.1b shows the Trot value between the K = 10 and K = 5 metastable levels as a function of χe. We adopt here Tgas = 50 and 200 K, much lower than 500 K. Since both the recombination rate increases, and is expected to decrease with decreasing Tgas , we may expect the effect of formation pumping and Trot to be the highest for the lowestTgas . For Tgas = 50 K, Trot is much higher than Tgas even for relatively low χe ~ 10-6. Trot ~ 500 K is then obtained for χe ~ 10-4, typical of translucent clouds, provided that  cm3 s-1. Higher Tgas = 200 K implies a lower recombination rate and a presumably higher , with the consequence that Trot decreases for the same χe. From the excitation point of view, we thus roughly expect two opposite solutions to explain Trot ≳ 500 K as observed in Arp 220: low Tgas ( ≲ 100 K) and, of course, high Tgas ≳ 500 K.

Appendix C: The formation and abundance of OH+

thumbnail Fig. C.1

Predicted OH+ abundance (upper panel), OH+/H2O+ and OH+/H3O+ ratios (mid panels), and H+ and e abundances (lower panel), as a function of the molecular fraction fH2 (up to approximately , see Eq. (2)). Each curve corresponds to a value of ζ/nH, indicated in the upper panel in units of cm3 s-1. Solid and dashed curves correspond to Tgas = 150 and 550 K, respectively. The inferred values of χOH+, R1, and R2, in the nuclear regions of NGC 4418 and Arp 220, and in the Cextended of Arp 220, are indicated with the shaded dark and light regions, respectively. In the lower panel, squares and triangles show the predicted χH+ and χe.

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Here we present the full set of calculated abundances of OH+, H2O+, and H3O+, together with the corresponding abundances of electrons and H+, based on the methods discussed in Sect. 4. Some analytical expressions for OH+ production rates are compared, showing that the most likely path for OH+ formation is O+ + H2, with the contribution from the charge exchange reaction H+ + OH and from direct OH ionization being of secondary importance even in the nuclear regions, where high OH abundances are inferred (Paper I). We also show that H+ is most likely formed through X/cosmic ray ionization, rather than via the C+ + OH → CO+ + H → CO + H+ FUV/chemical path.

The predicted OH+ abundance relative to H nuclei, χOH+, and both R1 and R2 are shown in Fig. C.1 as a function of fH2 for several values of ζ/nH, together with the values inferred in the nuclear regions of NGC 4418 and Arp 220 (shaded dark regions) and in the Cextended of Arp 220 (shaded light regions). The abundances of H+ and e are also shown in the lower panel.

The values relevant to the nuclear regions, χOH+ = (1−3) × 10-8, R1 ~ 1−2.5, and R2 ~ 1, can be obtained for very different values of ζ/nH, provided that fH2 attains the appropriate regime. For example, values compatible with observations are found for ζ/nH ≈ 5 × 10-19 cm3 s-1, fH2 ≈ 0.1, and high Tgas . For low values of ζ/nH, however, the range of fH2 compatible with observations is very narrow. This range broadens for higher ζ/nH and fH2, which we favor owing to the inferred high column densities.

According to the equilibrium χH+ and χe, we can compare the OH+ volume formation rates due to O+ + H2, ΓOH+;O+ | H2, and due to , , at high fH2 (see Liszt 2007, for diffuse clouds). In what follows, kX | Y is the rate coefficient for the X + Y reaction. On the one hand, , where χO+ ≈ kH+ | OχO0χH+(0.5fH2kO+ | H2 + (1 − fH2)kO+ | H)-1. Using the UMIST06 reactions rates given in Table C.1 at Tg = 150 K, (C.1)On the other hand, , where . Therefore, (C.2)Taking the limit fH2 ≈ 1 in Eq. (C.1), one obtains (C.3)The reference values in Eqs. (C.1)−(C.3) are based on ζ/nH = 2 × 10-17 cm3 s-1 at Tg = 150 K, and indicate ; increasing ζ/nH would increase both χH+ and χe, thus further increasing the above ratio. The mechanism only becomes competitive for low ζ/nH ≲ 5 × 10-19 cm3 s-1 and fH2 ≈ 1, but the resulting OH+ abundance is then much lower than the inferred one (Fig. C.1) and the OH+/H2O+ ratio becomes lower than 1 (Hollenbach et al. 2012).

Table C.1

Relevant reaction rates involved in the OH+, H2O+, and H3O+ formation and destruction.

In the nuclear regions of both NGC 4418 and Arp 220, high reservoirs of OH and H2O are found, with estimated abundances χH2O ~ (0.5−1) × 10-5 and OH/H2O ~ 0.5 (Paper I). The OH+ volume formation rate due to H+ + OH is given by , and so (C.4)which is significantly lower than ΓOH+;O+ | H2 in Eq. (C.1) if there is enough free oxygen. However, a significant fraction of O0 in these high density regions is expected to be locked into CO, H2O, OH and O2. Depletion of free O0 into molecules in regions dominated by hot core chemistry (Paper I) would thus reduce the OH+ formation rate in Eq. (C.1), thus increasing the potential relative importance of ΓOH+;H+ | OH. There is, however, an observational drawback for the potential importance of H+ + OH. The rate of H2O+ formation due to H+ + H2O is higher than ΓOH+;H+ | OH, because both χH2O > χOH (Paper I) and kH+ | H2O > kH+ | OH (Table C.1). Thus, if the OH+ were formed via H+ + OH, one would also expect an additional, important contribution to H2O+ formation due to H+ + H2O, and then R1 would fall below the inferred value of 1−2.5. Likewise, direct ionization of OH due to UV photons is expected to be of secondary importance, because H2O has a higher cross-section for ionization. As we argue in Sect. 4.5, the observed lines of molecular ions are most probably formed in regions where the formation rate is enhanced due to the presence of high quantities of atomic oxygen, and where the ions survive sufficiently long due to the presence of moderate densities.

According to the above discussion, model results for χOH+ and R1 relevant for the current observations can be basically understood in terms of the H+ → O+ → OH+ → H2O+ → H3O+ sequence, but how is the H+ produced? We have been assuming in the analysis that the H+ ionization is caused by X/cosmic rays, but the possibility of enhanced H+ production by chemical routes, as discussed by Sternberg & Dalgarno (1995) and Hollenbach et al. (2012), is worth considering. According to their models for high density PDRs illuminated by strong FUV fields, in the hot transition region between the H i and H2 zones, a major source of H+ formation is given by OH + C+ → CO+ + H followed by CO+ + H → CO + H+. OH would be produced via the endothermic O + H2 → OH + H, that is enhanced provided that a fraction of H2 is vibrationally excited. The volume rate of H+ production is given by , where α stands for the chance that CO+ reacts with H2 rather than with H i. In the limit α = 0, and using the value for kOH | C+ given by Hollenbach et al. (2012), (C.5)for Tgas = 300 K; the reference value for χOH is taken from Paper I. This is equivalent to a cosmic ray ionization per unit density of ζ/nH ~ 2 × 10-18 cm3 s-1, and predicts a peak of OH+ abundance of ~10-8 as well as R1 and R2 values of ~1 (Sternberg & Dalgarno 1995; Hollenbach et al. 2012), as roughly inferred in both NGC 4418 and Arp 220. This FUV/chemical route for the production of H+ has in the present case, however, one main drawback: the nuclear OH+ is observed over a range in visual extinction of ΔAV ~ 200 mag, while theoretical predictions indicate a peak thickness in the OH+ abundance of ΔAV < 1 mag where C+ is still abundant and Tgas remains high. It seems very unlikely that FUV radiation maintains basically all carbon ionized, and a relatively low H2 fraction, over columns of ΔAV ~ 200 mag along the line of sight and over spatial scales of 20−30 and 80−150 pc in NGC 4418 and Arp 220, respectively (see also models by Abel et al. 2009). Even if 106 O stars were packed into a region of ~10 pc radius (NGC 4418), the column density between neighboring stars would be ~1023 cm-2, and the quickly absorbed FUV radiation would only affect relatively compact regions around the stars. In summary, the inferred columns of O-bearing cations favor a source of ionization that can penetrate through large columns of gas, indicating the importance of X and cosmic rays.

The dependence of χOH+ on both fH2 and ζ/nH in Fig. C.1 can be understood as follows. For given fH2, χOH+ scales linearly with ζ/nH for relatively low values of ζ/nH, but saturates for sufficiently high values of ζ/nH. Saturation occurs when the destruction of OH+ is dominated by recombination, rather than by reaction with H2 (producing H2O+). In the saturated regime, further increase of ζ/nH increases by the same factor the OH+ formation rate and the OH+ destruction rate per unit of OH+ molecule, leaving χOH+ unchanged. The condition for saturation is given by χekOH+ | e ≫ 0.5fH2kOH+ | H2, where kOH+ | e ≈ 5 × 10-8 cm3 s-1 at 150 K, and kOH+ | H2 = 10-9 cm3 s-1. The above condition yields χe ≫ 10-2 × fH2. Once saturated, χOH+ can be approximated analytically by (C.6)giving, for Tgas = 150 K, and 3.4 × 10-7 for fH2 = 0.02 and 0.3, respectively, in rough agreement with the values in Fig. C.1.

The dependence of χOH+ on fH2 is different in the saturated and unsaturated regimes. According to Eq. (C.6), χOH+ increases with fH2 in the saturated regime, because the O+ + H2 reaction producing OH+ is increasingly favored relative to O+ + H, which transfers the charge back to atomic hydrogen. However, in the unsaturated regime χOH+decreases with increasing fH2 (Fig. C.1). In this case, OH+ destruction is dominated by OH+ + H2 and χOH+ is thus analitically aproximated as (C.7)Therefore, decreases with increasing fH2. For given ζ/nH (i.e. for each curve in Fig. C.1), a maximum of OH+ is reached between the saturated regime (low fH2) and the unsaturated one (high fH2).

All Tables

Table 1

Line equivalent widths and absorption fluxes.

Table 2

Inferred column densities, OH+ abundances, and OH+/H2O+ and OH+/H3O+ column density ratios.

Table C.1

Relevant reaction rates involved in the OH+, H2O+, and H3O+ formation and destruction.

All Figures

thumbnail Fig. 1

Energy level diagrams of OH+, H2O+, and H3O+, showing with arrows the transitions that lie within the PACS range; colored numbers indicate round-off wavelengths in μm. The fine-structure splitting of the OH+ and H2O+ levels is out of scale. Solid-red arrows mark the lines detected in NGC 4418 and/or Arp 220; dashed-red arrows indicate marginal detection in any of the sources; green arrows indicate blended lines, and black arrows show undetected lines.

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In the text
thumbnail Fig. 2

Continuum-normalized spectra around the OH+ lines in NGC 4418 (upper histograms) and Arp 220 (lower histograms). The dotted vertical lines indicate the rest wavelengths of the transitions for the nominal redshifts of z = 0.00705 (NGC 4418) and 0.0181 (Arp 220). The spectra in panels b) and c) have been scaled by a factor 2. (Potential) contamination by other species (NH in panel a) and H2O in d)) is also indicated. The marginal 5J − 4J lines in f) correspond to NGC 4418; this part of the spectrum is not available in Arp 220. Blue lines show model fits for OH+ in the nuclear components of both NGC 4418 and Arp 220, the green lines show the model fit for OH+ in the extended components of both sources, and the light-blue lines in a) are model fits for NH; red is total.

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In the text
thumbnail Fig. 3

Continuum-normalized spectra around the H2O+ lines in NGC 4418 (upper histograms) and Arp 220 (lower histograms). The dotted vertical lines indicate the rest wavelengths of the transitions for the nominal redshifts of z = 0.00705 (NGC 4418) and 0.0181 (Arp 220). The spectra in panels b) and c) have been scaled by a factor 2. Close features due to other species and potential contaminations are indicated. Dark blue and light blue lines show model fits; red is total.

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In the text
thumbnail Fig. 4

Continuum-normalized spectra around the H3O+ lines in NGC 4418 (upper histograms) and Arp 220 (lower histograms). The dotted vertical lines indicate the rest wavelengths of the transitions for the nominal redshifts of z = 0.00705 (NGC 4418) and 0.0181 (Arp 220). Panels a) − i) show the pure inversion, metastable lines of H3O+, while panels j) − p) show the rotation-inversion lines at λ < 100 μm. The spectra in panels h) and j) − p) have been scaled by a factor 2 and 3, respectively. The and lines at ≈ 181 μm are strongly contaminated by lines of CH and HO, and are not shown. Close features due to other species and potential contaminations are indicated. In panels f) and i), the contamination by NH2, HCN, and OH+ is expected to be small (see text). The blue lines show the best-fit model for H3O+; the green lines in panels g) and i) show model fits for NH3 and NH lines; red is the total.

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In the text
thumbnail Fig. 5

Population diagram of H3O+ (metastable levels) in Arp 220. Red and blue symbols correspond to ortho and para levels, respectively. Columns derived from pure-inversion and rotation-inversion lines are shown with triangles and squares, respectively. The crosses indicate the expected population distribution for Trot = 550 K and a fixed ortho-to-para ratio of 1.

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In the text
thumbnail Fig. 6

Comparison between averaged line shapes of several lines in Arp 220. HE, LE, PIMS and RIMS mean high-excitation, low-excitation, pure-inversion metastable, and rotation-inversion metastable, respectively. H2O HE is the average of the 616 ← 505 and 322 ← 211 lines of H2O (Paper I); HCN HE is the 18 − 17 line of HCN; OH+ HE is the average of the 43 − 32 and 45 − 34 lines of OH+; H2O+ HE is the average of the 322 ← 211 7/2−5/2, 313 ← 202 5/2 − 3/2, and 404 ← 313 7/2 − 5/2 lines of H2O+; H3O+ PIMS is the average of the pure-inversion, metastable , , , and lines of H3O+; NH3 RIMS is the average of the rotation-inversion metastable and lines of NH3; H2O LE is the average of the 212 ← 101 and 221 ← 110 lines of H2O; OH+ LE is the average of the 22 − 12, 21 − 10, 22 − 11, and 21 − 11 lines of OH+; H2O+ LE is the average of the 212 ← 101 5/2−3/2 and 3/2−1/2 lines of H2O+; H3O+ 70.8 is the line of H3O+ at 70.8 μm. The dotted and dashed vertical lines indicate the velocity centroids of the averaged HE and LE spectra, respectively.

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In the text
thumbnail Fig. 7

Velocity centroids of the averaged line shapes in Arp 220 displayed in Fig. 6, derived from Gaussian fits. Velocities are calculated relative to z = 0.0181. Blue and red symbols correspond to HE and LE averages, respectively; for H3O+ the green symbols indicate the PIMS and RI averages. Errorbars are 1σ uncertainties.

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In the text
thumbnail Fig. 8

Predicted SPIRE spectrum of H2O+ in Arp 220 between 600 and 1200 GHz. The contributions by the Cwest , Cextended , and Chalo are shown with blue, green, and light-blue curves (vertically shifted for clarity), respectively, and the red curve shows the total absorption/emission.

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In the text
thumbnail Fig. 9

Model results for H3O+ and NH3 in Arp 220. a) Ratios of pure inversion metastable lines of H3O+ versus Trot : K = 6/K = 4 (red), K = 8/K = 4 (blue), K = 9/K = 4 (green), and K = 10/K = 4 (black). b) For NH3, the fluxes of the (red), (green), and (blue) are normalized to the flux of the 124.9 μm feature (composed of the 40−30 and NH3 lines, Paper I). c) Ratios of rotation-inversion lines of H3O+ as a function of Tdust . Dashed lines in all panels indicate the measured values, with typical uncertainties of 20%.

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In the text
thumbnail Fig. 10

Predicted a) OH+/H2O+ and b) OH+/H3O+ ratios as a function of χe × 103/fH2. Symbols show results for all generated chemical models, while the solid lines show the analytic curves by Gerin et al. (2010) and Neufeld et al. (2010). The inferred OH+/H2O+ ratios in the nuclear regions of NGC 4418 and Arp 220, and in the Cextended of Arp 220, are indicated with the shaded dark and light regions, respectively. Gas temperatures of 150 K (black) and 550 K (red) are assumed.

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In the text
thumbnail Fig. 11

Predicted OH+, H2O+, and H3O+ abundances (left panels) and OH+/H2O+ and OH+/H3O+ abundance ratios (right panels) as a function of ζ/nH. In all these models, the molecular fraction is given by the maximum value in Eq. (2). Gas temperatures of 150 K (black) and 550 K (red) are assumed. The ranges derived from the observations and models for the nuclear regions of NGC 4418 and Arp 220 are indicated by the shaded regions.

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In the text
thumbnail Fig. B.1

a) The H3O+ rotation diagram (triangles), calculated in the optically thin limit. The colored squares (red: ortho, blue: para) show the expected column density distribution for a formation temperature of Tform = 1000 K, and neglecting collisional relaxation. The two solid lines correspond to rotational temperatures of Trot = 250 and 600 K. b) The rotational temperature of the metastable level of H3O+ relative to the one as a function of the electron abundance χ(e) for two adopted values of Tgas (50 and 200 K) and four assumed values of (curves 1), 1 × 10-10 (2), 3 × 10-10 (3), and 1 × 10-9 cm3 s-1 (4).

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In the text
thumbnail Fig. C.1

Predicted OH+ abundance (upper panel), OH+/H2O+ and OH+/H3O+ ratios (mid panels), and H+ and e abundances (lower panel), as a function of the molecular fraction fH2 (up to approximately , see Eq. (2)). Each curve corresponds to a value of ζ/nH, indicated in the upper panel in units of cm3 s-1. Solid and dashed curves correspond to Tgas = 150 and 550 K, respectively. The inferred values of χOH+, R1, and R2, in the nuclear regions of NGC 4418 and Arp 220, and in the Cextended of Arp 220, are indicated with the shaded dark and light regions, respectively. In the lower panel, squares and triangles show the predicted χH+ and χe.

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In the text

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