HOT WATER IN THE INNER 100 AU OF THE CLASS 0 PROTOSTAR NGC 1333 IRAS2A^*

The full HIFI spectrum as recorded with the WBS back end is shown in Figures 6 and 7 in the Appendix. The strongest feature is the 3₁₂–3₀₃ line of H$_2^{16}$O, peaking at 230 mK. The 3₁₂–3₀₃ spectrum for each water isotopolog is plotted in Figure 1. Thanks to the excellent signal-to-noise ratio from the long integration (8 mK rms in 0.5 km s⁻¹ bins), the H$_2^{16}$O spectrum now shows a distinct narrow emission feature on top of the medium and broad features detected by Kristensen et al. (2010). The three components have full widths at half-maximum (FWHMs) of 42.5 ± 0.8, 10.7 ± 0.4, and 3.6 ± 0.3 km s⁻¹. Table 1 lists the integrated intensities. The broad and medium FWHMs are the same as those reported by Kristensen et al. for lower-excitation water lines. These components arise in shocked gas and are not considered here any further.

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The H$_2^{18}$O spectrum shows a weak emission feature (7σ) in both polarization filters, with the same intensity in the WBS and HRS recordings. The JPL and CDMS spectral line databases (Pickett et al. 1998; Müller et al. 2001) show no other plausible features at this position in either the upper or the lower sideband. Figure 1 shows a Gaussian fit with an FWHM fixed at 3.6 km s⁻¹ (taken from the H$_2^{16}$O decomposition), because the feature is too weak for a reliable independent measurement of its width. The constrained fit has a peak intensity of 20 ± 4 mK and an integrated intensity of 78 ± 11 mK km s⁻¹ (Table 1).

The H$_2^{17}$O spectrum in Figure 1 shows an apparent emission feature blueshifted by 2 km s⁻¹ from the source velocity, along with four features of similar strength at larger offsets. Three of them could represent lines of CH₂DOH (E_u/k = 229–294 K), which has been detected before in single-dish spectra of IRAS2A (Parise et al. 2006; see also Figures 6 and 7). The JPL and CDMS databases offer no plausible identification for the fourth feature. We consider the 3₁₂–3₀₃ line undetected in H$_2^{17}$O, but our analysis in Section 4 is unaffected by the question of whether it is real or not. The potential CH₂DOH lines are not considered any further.

The only other confirmed feature in the entire spectral setting is the C¹⁸O 10–9 line at 1097.163 GHz. It appears to be a blend of a narrow and a medium component, but the detection is too weak for an accurate decomposition. The intensity integrated over the full profile is 300 ± 30 mK km s⁻¹, split roughly halfway between the two components. Narrow and medium features have been detected previously in various low- and high-J CO isotopolog lines (Yıldız et al. 2010). The C¹⁸O 10–9 line is analyzed as part of a larger sample of lines and sources by San Jose-Garcia et al. (2013) and Yıldız et al. (2013).

The full spectrum in Figures 6 and 7 appears to contain a few more lines, but their nature is uncertain and not of interest to this paper. We merely mention two possible identifications: H₂CO at 1094.590 GHz (E_u/k = 526 K) and CH₃OH at 1095.063 GHz (E_u/k = 498 K). Both species have been detected previously in single-dish and interferometric studies of IRAS2A (Maret et al. 2005; Parise et al. 2006; Jørgensen et al. 2007).

IRAS2A has been targeted in various other water lines with Herschel. Visser et al. (2012) detected about a dozen spectrally unresolved lines with the PACS instrument (60–180 micron; E_u/k up to 1750 K), attributed to shocked gas on 100–1000 AU scales and unrelated to the narrow emission analyzed here. No narrow emission has been detected in any of the water lines previously observed with HIFI (Kristensen et al. 2010). Upper limits on such emission may be useful and are reported in Table 1. Another HIFI upper limit is available for H$_2^{16}$O 3₃₁–4₀₄ at 1894 GHz, observed alongside C^{+ 2}P_3/2–²P_1/2 (A. O. Benz et al., in preparation). In most cases, the upper limit in Table 1 is the 3σ limit computed from the rms noise in 0.5 km s⁻¹ bins. This method does not work for the H$_2^{16}$O 2₀₂–1₁₁ and 2₁₁–2₀₂ lines, where the broad and medium emission features can hide a narrow feature stronger than three times the noise. Instead, we forced a three-Gaussian fit on these spectra, with the position and width of the narrow feature fixed at the values found for the 3₁₂–3₀₃ line. The adopted upper limit is twice the integrated intensity of the force-fitted narrow component. In doing so, we assume the broad and medium components do not shield any narrow emission. The 1₁₀–1₀₁, 1₁₁–0₀₀, and 2₁₂–1₀₁ lines show narrow absorption due to cold water vapor in the outer envelope (Kristensen et al. 2010) and are excluded from our analysis.

Ground-based observations exist for two H$_2^{18}$O lines: 3₁₃–2₂₀ at 203 GHz (E_u/k = 204 K) and 4₁₄–3₂₁ at 391 GHz (E_u/k = 322 K). The latter was undetected with APEX in a 16'' beam, with a 3σ upper limit of 410 mK km s⁻¹ (Table 1; F. Wyrowski 2012, private communication). Persson et al. (2012) detected spatially resolved compact and extended emission in the 3₁₃–2₂₀ line with the Plateau de Bure Interferometer (PdBI). The extended component is associated with the outflow and is ignored here. The compact component has an FWHM of 4.0 ± 0.1 km s⁻¹, comparable to the narrow component in the H$_2^{16}$O 3₁₂–3₀₃ spectrum in Figure 1. The compact PdBI component has an integrated intensity of 0.98 Jy km s⁻¹ or 42 K km s⁻¹. Its spatial extent was marginally resolved to a diameter of 083, probing material out to a radius of 100 AU. Persson et al. attributed the compact emission to a flattened inner envelope or pseudo-disk dominated by infall rather than rotation.

The HIFI 3₁₂–3₀₃ lines have upper-level energies of 249 K. The bulk of the water in IRAS2A is present at temperatures below 100 K, where it generally exists as ice rather than vapor. The low gas-phase abundance in the cold envelope (∼10⁻⁸; Kristensen et al. 2010; Liu et al. 2011), coupled with the low excitation temperatures, falls orders of magnitude shy of reproducing the observed narrow intensities (van Kempen et al. 2008).

That leaves two options for the narrow 3₁₂–3₀₃ emission: a maser or the hot core. Furuya et al. (2003) observed maser emission toward IRAS2A at 22 GHz, with intensities varying by an order of magnitude on timescales of about a year. The maser lines were seen sometimes at the source velocity and sometimes blueshifted by a few km s⁻¹, with FWHMs from 1.2 to 2.3 km s⁻¹. The HIFI 3₁₂–3₀₃ and PdBI 3₁₃–2₂₀ spectra show no such blueshifted emission and the emission at the source velocity is 2–3 times as broad as the 22 GHz maser lines. Furthermore, our two epochs of HIFI data (Figure 1 and Kristensen et al. 2010) show no signs of variability on a one-year baseline. Hence, we conclude that the narrow 3₁₂–3₀₃ emission is not associated with maser activity. Persson et al. (2012) employed similar arguments to reach the same conclusion for their PdBI data.

Instead, the narrow HIFI and PdBI lines are thermal and likely originate in the inner 100 AU of IRAS2A, in quiescent gas above 100 K. If the circumstellar material in IRAS2A is approximated as a spherical envelope with a power-law density profile, the 100 K radius lies at 94 AU (Kristensen et al. 2012). While this matches the size of the emitting region seen with the PdBI, continuum interferometry of IRAS2A has shown that the assumptions of spherical symmetry and a single power-law density profile break down inside a radius of 15 or 350 AU (Jørgensen et al. 2004, 2005).

A simple test reveals that the spherical model also fails to reproduce the HIFI and PdBI data simultaneously. The test consists of synthesizing the 3₁₂–3₀₃ and 3₁₃–2₂₀ spectra from a step abundance profile, as described in detail by van Kempen et al. (2008). Kristensen et al. (2012) constructed a source model for IRAS2A to fit the spectral energy distribution and submillimeter brightness profiles. The model envelope has a total mass of 5.1 M_☉, distributed along an r^−1.7 power law. The temperatures of the gas and dust are coupled and decrease from 250 K at the inner edge (36 AU) to 10 K at the outer edge (17,000 AU). The step abundance profile consists of a high abundance X_in above 100 K (at 94 AU) and a lower abundance X_out below 100 K. The HIFI and PdBI emission originate above 100 K, so the question we want to answer is whether the spherical envelope model can reproduce both data sets with a single X_in.

The molecular excitation and line emission are computed with the one-dimensional radiative transfer code RATRAN (Hogerheijde & van der Tak 2000). This is a standard approach for interpreting molecular line spectra; see, e.g., Yıldız et al. (2010), Liu et al. (2011), and Coutens et al. (2012) for recent examples of C¹⁸O, HDO, and H₂O. We set the gas-to-dust ratio to 100 and use OH5 opacities (Ossenkopf & Henning 1994), appropriate for dust grains with thin ice mantles. The ortho/para ratio of H₂ is thermalized and that of water is fixed at 3. Collision rates are taken from Dubernet et al. (2006, 2009) and Daniel et al. (2010, 2011) as compiled in the LAMDA database (Schöier et al. 2005). The outer H$_2^{18}$O abundance does not affect the 3₁₂–3₀₃ and 3₁₃–2₂₀ lines and is fixed at 2 × 10⁻¹¹, derived from absorption seen with HIFI in lower rotational lines of water (Kristensen et al. 2010; Liu et al. 2011). The inner H$_2^{18}$O abundance is varied from 3 × 10⁻¹⁰ to 3 × 10⁻⁷ (2 × 10⁻⁷ to 2 × 10⁻⁴ for H$_2^{16}$O) to cover the full range from a "dry" to a "wet" hot core. Finally, the synthetic spectra are convolved to the appropriate beam size and compared to the available observations.

Figure 2 shows the convolved intensities for the H$_2^{18}$O 3₁₂–3₀₃ and 3₁₃–2₂₀ lines as function of the inner abundance. The horizontal dotted lines and bars mark the observed intensities and 1σ uncertainties: red for 3₁₂–3₀₃ and black for 3₁₃–2₂₀. The abundances required to fit each line individually are marked by the vertical dotted lines and bars. Within the confines of the spherical envelope model, the H$_2^{18}$O 3₁₂–3₀₃ spectrum from Figure 1 requires an inner H$_2^{18}$O abundance of 1.2 × 10⁻⁹. However, this underproduces the observed PdBI line intensity by a factor of 200. Matching the PdBI line requires a much higher inner H$_2^{18}$O abundance of 2.1 × 10⁻⁷, but then the 3₁₂–3₀₃ line comes out a factor of six too strong. The estimated uncertainty on the 3₁₂–3₀₃ intensity for H$_2^{18}$O is 17% (10% calibration, 14% statistical; Sections 2 and 3.1), so a factor of six is 35σ away. The RATRAN test clearly fails: a spherical envelope model with a single power-law density profile, such as used in previous attempts to derive hot core water abundances, cannot reproduce the single-dish and interferometric hot water observations simultaneously.

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The mismatch of best-fit abundances to single-dish and interferometric data has also been seen for methanol in IRAS2A (Jørgensen et al. 2005) and for deuterated water in the Class 0 protostar IRAS 16293−2422 (Coutens et al. 2012; Persson et al. 2013). We thus have several pieces of evidence that simple spherical models break down on the spatial scales of the hot core. Until more appropriate source models can be generated—for example from sub-arcsecond PdBI and ALMA observations of protostellar dust and gas—it is better to take a step back and see what we can learn about hot water in IRAS2A irrespective of the underlying density and temperature structure.

4.2.1. PdBI Emission: Optically Thin

In analyzing the PdBI data, Persson et al. (2012) assumed optically thin emission in local thermodynamic equilibrium (LTE) and considered gas temperatures between 50 and 250 K. The 3₁₃–2₂₀ line has a critical density of a few 10⁵ cm⁻³. The critical density of the HIFI 3₁₂–3₀₃ line is about a factor of 1000 higher, but with densities in the inner envelope easily exceeding 10⁹ cm⁻³ (Visser et al. 2009), the assumption of LTE is probably justified and we adopt it here as well.

The dust and gas temperatures are likely coupled at these high densities, so temperatures below 100 K can be excluded because of freeze-out. This also means that the 083 emitting region resolved with the PdBI represents the entire reservoir of quiescent (i.e., non-shocked) hot gas in IRAS2A. The PdBI observations have a field of view of 25'', a little larger than the HIFI beam of 19'' at 1097 GHz. Hence, if any other hot gas had been present within the HIFI beam but outside the central 083, it would have been detected with the PdBI.

Following Goldsmith & Langer (1999), the optical depth of a molecular line is

$$\begin{equation} \tau _\nu = \frac{N_{\rm u}}{\Delta v} \frac{A_{\rm ul}c^3}{8\pi \nu ^3}({e}^{h\nu /kT}-1)\,, \end{equation} \tag{ 1 }$$

with ν the frequency of the transition, A_ul the Einstein A coefficient, and Δv the observed FWHM. In LTE, the upper-level column density N_u is

$$\begin{equation} N_{\rm u} = \frac{N g_{\rm u}}{Q(T)} {e}^{-E_{\rm u}/kT}\,, \end{equation} \tag{ 2 }$$

with N the total column density, g_u the degeneracy, and Q the partition function. The PdBI line is optically thin with τ_ν ≈ 0.1. For a water ortho/para ratio of 3, the observed PdBI intensity requires $N({\rm H}_2^{18}{\rm O})\approx 3\times 10^{16}$ cm⁻² regardless of the exact temperature between 100 and 250 K (Persson et al. 2012). The 3₁₂–3₀₃ lines have Einstein A coefficients a few thousand times faster than the 3₁₃–2₂₀ line (Table 1) and are optically thick for all three isotopologs. For example, at 100 K, τ_ν = 9.7 for H$_2^{17}$O, 34 for H$_2^{18}$O, and 19,000 for H$_2^{16}$O. The optical depths decrease by about 50% if the temperature is increased to 250 K.

4.2.2. HIFI Emission: Optically Thick

If the HIFI emission in all three isotopologs is indeed optically thick and characterized by the same temperature, the 3₁₂–3₀₃ lines would have had the same intensities. This is clearly inconsistent with the data (Figure 1). However, the size of the optically thick region (approximately the τ_ν = 1 surface) may be different for each isotopolog, leading to different beam-filling factors. As argued below, this can explain the factor of 4.4 difference in observed intensities for H$_2^{16}$O and H$_2^{18}$O as well as the non-detection of H$_2^{17}$O.

Figure 3 shows a sketch of the flattened inner envelope of IRAS2A with the different emitting areas for the optically thick 3₁₂–3₀₃ lines. The H$_2^{18}$O 3₁₃–2₂₀ line observed with the PdBI is optically thin and traces the entire hot core to its outer radius of 100 AU. The extreme optical depth of 19,000 for H$_2^{16}$O 3₁₂–3₀₃ means that its τ_ν = 1 surface, measured from the outside, essentially lies right at the hot core's outer edge. H$_2^{16}$O therefore emits at close to 100 K. This is somewhat lower than the excitation temperature of 170 K assumed by Persson et al. (2012), but the difference has no substantial effect on our analysis. The temperature structure on these small scales is unknown, so we assume for simplicity that H$_2^{18}$O and H$_2^{17}$O also emit at 100 K. The radius of the H$_2^{18}$O τ_ν = 1 surface then has to be a factor of $\sqrt{4.4}=2.1$ smaller (r ≈ 47 AU) than that of H$_2^{16}$O (Figure 3). The size difference would be smaller if we take a higher temperature for H$_2^{18}$O, but the available data do not allow for a more precise estimate.

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4.2.3. Water Distribution

For an H$_2^{18}$O column density of 3 × 10¹⁶ cm⁻², the optical depth in the H$_2^{18}$O 3₁₂–3₀₃ line is 34 at 100 K (Equation (1)). If the water is distributed uniformly throughout the hot core, the τ_ν = 1 surface for H$_2^{18}$O would lie at 1/34th of the way in from the outer edge at 100 AU, i.e., at r ≈ 97 AU. The surface has to be at r ≈ 47 AU to explain the observed H$_2^{16}$O/H$_2^{18}$O intensity ratio from Figure 1, so the water cannot be distributed uniformly with radius.

A power-law distribution, n(H₂O)∝r^−p, offers a simple solution. This does not necessarily imply an abundance gradient, because it can be the total gas density itself that increases toward smaller radii (Visser et al. 2009). We need to know the inner radius of the water reservoir in order to compute the power-law exponent p, but the inner radius cannot be measured from the PdBI data. A rough estimate would be 0.1 AU, the typical inner edge of accretion disks around T Tauri stars (Akeson et al. 2005). The requirement that only 1/34th (3%) of the H$_2^{18}$O column lie at r > 47 AU then yields p = 1.2. The slope steepens to 1.4 if the inner radius is placed at 1 AU instead.

Figure 4 shows the resulting optical depth profiles (τ_ν as function of r) for H$_2^{18}$O and H$_2^{17}$O. The τ_ν = 1 surface for H$_2^{16}$O (not plotted) lies at 100 AU, consistent with Figure 3. H$_2^{18}$O reaches τ_ν = 1 at 47 AU, as needed to fit the 3₁₂–3₀₃ observations. The τ_ν = 1 surface for the least abundant isotopolog, H$_2^{17}$O, ends up at 9.4 AU, providing 110 times more beam dilution than experienced by H$_2^{16}$O. This places the observable H$_2^{17}$O 3₁₂–3₀₃ intensity about a factor of 10 below the 3σ upper limit from Figure 1 and Table 1.

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4.2.4. Summary of LTE Analysis

The scenario from the previous section matches the line intensity ratios for the HIFI 3₁₂–3₀₃ isotopolog lines, but what about the absolute intensities of those and other lines? For optically thick emission in LTE, the intrinsic line intensity is the intensity of a blackbody at the gas temperature:

$$\begin{equation} T_{\rm R}^{\rm thick} = \frac{c^2}{2 k \nu ^2} B_\nu (T)\,. \end{equation} \tag{ 3 }$$

The optically thin equation is taken from Goldsmith & Langer (1999):

$$\begin{equation} T_{\rm R}^{\rm thin} = \frac{h c^3 N_{\rm u} A_{\rm ul}}{8 \pi k \nu ^2 \Delta v} \left(\frac{1 - {e}^{-\tau _\nu }}{\tau _\nu } \right)\,, \end{equation} \tag{ 4 }$$

with all symbols as defined in Equation (1). The observable intensity T_mb is the intrinsic intensity T_R divided by the relevant beam-filling factor.

For a gas temperature of 100 K, the optically thick H$_2^{16}$O 3₁₂–3₀₃ emission has an integrated intensity of 320 K km s⁻¹ before applying beam dilution. The beam dilution factor is (19.3/0.83)² = 540, reducing the intensity to 590 mK km s⁻¹. This is still a factor of 1.7 stronger than observed (Table 1), which we attribute to extinction by dust. The implied optical depth of the dust is τ_d = ln 1.7 = 0.55 at 1097 GHz.

Single-dish and interferometric continuum data of IRAS2A provide a lower and upper bound to the observed dust optical depth. The single-dish data, processed through the spherical model of Kristensen et al. (2012), give a pencil-beam H₂ column density of 3.7 × 10²³ cm⁻² and τ_d = 0.26 at 1097 GHz. The interferometric data reveal an embedded pseudo-disk with a gas mass of 0.056 M_☉ within ∼100 AU (Jørgensen et al. 2009), which translates to τ_d = 2.3. The actual optical depth encountered by molecular line emission from the hot core has to lie between these two limits, so a value of 0.55 is quite reasonable.

The final test is to check whether our hot core scenario also matches the upper limits on narrow emission in other water lines. Again assuming a gas temperature of 100 K, we repeat the above exercise to estimate intrinsic line intensities. Most lines are optically thick, so the location of their τ_ν = 1 surfaces is calculated for the same r^−1.2 power-law water distribution as in Figure 4. The observable line fluxes, corrected for beam dilution and dust extinction (based on OH5 opacities; Ossenkopf & Henning 1994), are listed in Table 1. The predicted intensity of the H$_2^{16}$O 2₀₂–1₁₁ line at 988 GHz is right at the upper limit of how much narrow emission can be hidden in the observed broad and medium components. All other predictions fall below the upper limits. Our scenario of a 100 AU hot core with a power-law distribution of water (Figures 3 and 4) is therefore consistent with the combined PdBI, APEX, and Herschel data sets.

The high optical depths for the water isotopolog lines accessible with HIFI are not unique to IRAS2A. For example, spatially resolved data from the Atacama Large Millimeter/submillimeter Array (ALMA) show that the column density of hot water in IRAS 16293−2422 is a factor of 30 higher than in IRAS2A (Persson et al. 2013). The HIFI water lines observed in this source (Coutens et al. 2012) therefore likely suffer from the same problem. A combined analysis of the ALMA and HIFI data is recommended for the best overall understanding.

The conclusions from this paper can be tested with ALMA, in particular regarding the excitation and spatial distribution of hot water. The 5₃₂–4₄₁ line of H$_2^{18}$O at 692 GHz (E_u = 728 K) is accessible in band 9 and has been observed in the hot core of IRAS 16293−2422 (Persson et al. 2013). Within a few years, receivers in band 8 (385–500 GHz) will be able to access the 4₁₄–3₂₁ and 4₂₃–3₃₀ lines of H$_2^{18}$O at 391 and 489 GHz (E_u/k = 322 and 430 K). All three lines are predicted to be optically thin in IRAS2A and strong enough to be observable (Table 1). ALMA's spatial resolution of 01 or better in bands 8 and 9 will enable an investigation of the hot water in IRAS2A at an unprecedented level of detail.

Persson et al. (2012) derived an H$_2^{16}$O abundance of 4 × 10⁻⁶ in the inner 100 AU of IRAS2A by comparing their H$_2^{18}$O column density from the PdBI to the dust mass measured in a similar beam by Jørgensen et al. (2009). However, this is not the same as the hot core abundance: the simple picture painted in Figure 3 belies a more complicated three-dimensional structure, in which much of the gas and dust may be below 100 K. We present here an alternative approach to derive the real hot core water abundance, i.e., relative to only the gas above 100 K.

H₂ cannot be observed directly, so CO is used as a proxy for the hot core mass. The best available tracers of the hot CO column are the optically thin 9–8 and 10–9 lines of C¹⁸O (E_u = 237 and 290 K), observed with HIFI in IRAS2A. There are two caveats, however: the hot CO abundance itself is uncertain by a factor of a few and some fraction of the 9–8 and 10–9 line intensities originates at temperature below 100 K (Yıldız et al. 2010, 2013). We address the latter issue first.

The 9–8 and 10–9 lines have critical densities of about 10⁶ cm⁻³, so the assumption of LTE is justified. Invoking again an excitation temperature of 100 K, Equation (4) is used to predict the C¹⁸O column density required to match a certain line intensity. In the hypothetical case that all of the observed 9–8 and 10–9 emission arises in the hot core (about 150 mK km s⁻¹ for each line; Table 1), we get N(C¹⁸O) ≈ 2 × 10¹⁷ cm⁻² (corrected for beam dilution and dust extinction) or an H₂O/CO abundance ratio of ∼0.2. Figure 5 shows how the derived H₂O/CO ratio changes if only a certain fraction of the 9–8 and 10–9 emission arises in the hot core. For example, the H₂O/CO ratio is 0.5 for a fraction of 50%.

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Full radiative transfer calculations on the spherical envelope model of IRAS2A show that about 10%–30% of the observed C¹⁸O 9–8 and 10–9 emission originates above 100 K (Yıldız et al. 2010, 2013). This range is marked by the shaded area in Figure 5 and implies an H₂O/CO abundance between 0.8 and 3.6. However, as noted in Section 4.1, the spherical model is reliable only for radii larger than about 350 AU, where the dust temperature is ∼45 K (Kristensen et al. 2012). This can be used for a firm limit: the real fraction of 9–8 and 10–9 emission arising above 100 K cannot be larger than the fraction arising above 45 K in the spherical radiative transfer models. That latter fraction is ∼65%–80% for the 9–8 line and ∼90% for the 10–9 line (Yıldız et al. 2010, 2013). According to Figure 5, the lower limit on the hot core H₂O/CO abundance ratio is then 0.25.

Yıldız et al. (2010) derived a C¹⁸O abundance of 1.5 × 10⁻⁷ (8 × 10⁻⁵ for CO) for all gas above 25 K, a factor of three below the carbon and oxygen elemental abundances. This value is well constrained for the bulk of the gas between 25 and 100 K, but remains somewhat uncertain for the hot core above 100 K: the hot core represents only a small mass fraction and contributes little emission even to the C¹⁸O 9–8 and 10–9 lines (Yıldız et al. 2010, 2013), so varying the hot core CO abundance by a factor of a few would not affect the overall line intensities significantly.

Taking the CO abundance of 8 × 10⁻⁵ in IRAS2A at face value, the results from Figure 5 yield a lower limit to the hot core water abundance of 2 × 10⁻⁵. This is a conservative estimate, as the actual fraction of C¹⁸O 9–8 and 10–9 emission arising above 100 K is likely to be smaller than the fraction of 90% derived from the 45 K cutoff above. The available PdBI and HIFI observations are entirely consistent with a water abundance of (1–2) × 10⁻⁴ in the hot core, as expected for the evaporation of water ice above 100 K (Rodgers & Charnley 2003) and as typically found in high-mass protostars (van der Tak et al. 2006; Chavarría et al. 2010; Herpin et al. 2012). The uncertainties in the H₂O/CO ratio and the hot core CO abundance also allow for water abundances down to about 10⁻⁵. Hot water abundances of less than 10⁻⁵, as derived previously for IRAS2A (Kristensen et al. 2010; Liu et al. 2011) or reported for other low-mass sources (Ceccarelli et al. 2000; Maret et al. 2002; Coutens et al. 2012), are possible only if the inner CO abundance is significantly overpredicted by spherical models.

Lastly, we revisit the question of deuterium fractionation in the hot core of IRAS2A. Liu et al. (2011) presented five rotational lines of HDO measured with single-dish facilities. The best tracer of hot HDO is the 3₁₂–2₂₁ line at 226 GHz with an upper-level energy of 168 K. Once more invoking LTE at 100 K, the observed intensity of 0.50 K km s⁻¹ translates to an HDO column density of 2 × 10¹⁶ cm⁻² (Equation (4)). Liu et al. derived a hot HDO/H₂O ratio of ⩾0.01 based on a preliminary water abundance of ⩽10⁻⁵, which is now known to be too low. A more reliable deuterium fraction can be computed directly from the water column density of Persson et al. (2012), bypassing the uncertainties in the H₂O/CO ratio and the CO abundance. With $N({\rm H}_2^{16}{\rm O})=2\times 10^{19}$, the new HDO/H₂O abundance ratio in the hot core of IRAS2A is 1 × 10⁻³. This is the same level of deuterium fractionation as in IRAS 16293−2422 (Persson et al. 2013) and a factor of two higher than the upper limit for NGC 1333 IRAS4B (Jørgensen & van Dishoeck 2010a), both of which are based on interferometric data alone.

Continuum interferometry of IRAS2A and other low-mass embedded protostars has revealed the presence of a compact density enhancement, typically on ∼100 AU scales, that is not accounted for by simple spherical envelope models (Jørgensen et al. 2004, 2005, 2007; Chiang et al. 2008). For a given column density of hot water, correcting for the higher density would lead to a lower water abundance than what is found from the spherical models. Our conclusion in the previous section is exactly opposite: the new hot water abundance, based on the combined PdBI and HIFI data for H$_2^{18}$O and C¹⁸O, is higher than that obtained previously from single-dish data only.

The reason for this apparent discrepancy is the temperature structure in the inner 100 AU of IRAS2A. With an H$_2^{18}$O column density of 3 × 10¹⁶ cm⁻² and an H$_2^{16}$O abundance of 2 × 10⁻⁵ or higher, the column density of hot H₂ is 8 × 10²³ cm⁻² or lower. The total gas column within 100 AU, based on continuum interferometry, is 4 × 10²⁴ cm⁻² (Jørgensen et al. 2009). From this we reach the same conclusion as Persson et al. (2012): only a limited fraction of all quiescent material inside of 100 AU is hotter than 100 K. Persson et al. derived a hot fraction of 4% for an assumed water abundance of 1 × 10⁻⁴. Given the uncertainty in the water abundance, the actual hot fraction can be anything from 2% to 20%.

The corresponding physical picture is not that of a spherical hot core, because in such a geometry it would be difficult to have the bulk of the material at temperatures below 100 K, while still keeping some hotter gas out to 100 AU. An embedded disk or pseudo-disk is more likely, with a few percent of its mass heated to above the evaporation temperature of water. This scenario is qualitatively consistent with predictions from evolutionary models (Brinch et al. 2008; Visser et al. 2009; Ilee et al. 2011; Harsono et al. 2013). Specifically, it suggests that the bulk of the disk starts cold, with little water ice evaporating as material accretes from the larger-scale envelope (Visser et al. 2009).

Regarding the chemistry, the lower limit on the hot core water abundance is consistent with the value of ∼10⁻⁴ expected from the evaporation of water ice above 100 K. Stäuber et al. (2006) presented models of hot and cold envelope chemistry in the presence of UV and X-ray fields. For an X-ray flux of 10⁻³ erg s⁻¹ cm⁻² (equivalent to an isotropic X-ray luminosity of 3 × 10²⁸ erg s⁻¹ at 100 AU), the hot water abundance is reduced from 10⁻⁴ to 10⁻⁶ on a timescale of 10⁴ yr. However, the gas above 100 K is essentially in free fall, leading to a dynamical timescale of perhaps only 100 yr (Schöier et al. 2002; Visser et al. 2009). That is still long enough for water to evaporate from the grains, but not for it to be destroyed by X-rays. Our relatively high hot water abundance can be sustained by continuous replenishment of icy grains from further out in the envelope.

Several complex organic species have been observed in IRAS2A, including CH₃OH, CH₃CN, and CH₃OCH₃ (Maret et al. 2005; Parise et al. 2006; Bottinelli et al. 2007; Jørgensen et al. 2007; Persson et al. 2012). The line widths of a few km s⁻¹ and the excitation temperatures of about 100 K mark IRAS2A as a prototypical hot core or hot corino. This is in contrast to other protostars such as NGC 1333 IRAS4A and 4B, where the observed complex organics appear to be associated with outflow-induced shocks (Jørgensen et al. 2007). The aforementioned dynamical timescale of 100 yr in the hot core of IRAS2A is too short for the formation of complex organics in the gas phase after evaporation of the icy grain mantles. Instead, the organics observed in IRAS2A are likely to be so-called first-generation species (Herbst & van Dishoeck 2009), formed via grain-surface chemistry in the cold outer envelope and released into the gas phase in the hot core.