© ESO, 2013

1. Introduction

Oxygen is the most abundant element in the interstellar medium apart from hydrogen and helium. Many oxygen-bearing species, most importantly water and its precursors, have a very limited observability from the ground because of atmospheric constraints. The Herschel Space Observatory (Pilbratt et al. 2010) outperforms previous space-borne facilities in sensitivity as well as spatial and spectral resolution. It is thus well suited to study the water chemistry in young stellar objects (YSOs) in more detail. Because water undergoes large gas-phase abundance variations with varying temperature or radiation field, it is an excellent probe of the physical conditions and dynamics in star-forming regions (Kristensen et al. 2012; van Dishoeck et al. 2011).

A key connecting piece between atomic oxygen and water is the hydroxyl radical (OH). In the high-temperature gas-phase chemistry regime (T > 230  K), all available gas-phase oxygen is first driven into OH and then into water by the O + H₂ → OH + H and subsequent OH + H₂ → H₂O + H reactions. The importance of the backward reaction H₂O + H → OH + H₂ depends on the atomic to molecular hydrogen ratio and therefore on the local UV field or shock velocity. H₂ is dissociated in J-type shocks when the velocity exceeds ∼25  km  s^-1 (e.g. Hollenbach & McKee 1980). OH is also a byproduct of the H₂O photo-dissociation process. Thus, OH is most abundant in regions with physical conditions different from those favoring the formation and existence of water and it therefore provides a complementary view of oxygen in the gas phase. In addition to its importance in the oxygen and water chemistry, OH also contributes to the FIR cooling budget of warm gas in embedded YSOs (e.g., Neufeld & Dalgarno 1989b; Kaufman & Neufeld 1996; Nisini et al. 2002; Karska et al. 2013). The goal of the “Water In Star-forming regions with Herschel” (WISH, van Dishoeck et al. 2011) Herschel key program is to study the H₂O and associated OH chemistry for a comprehensive picture of H₂O during protostellar evolution.

Detections of OH far-infrared (FIR) transitions from star-forming regions were made previously with the Kuiper Airborne Observatory (e.g. Melnick et al. 1987; Betz & Boreiko 1989), the Infrared Space Observatory (e.g. Ceccarelli et al. 1998; Giannini et al. 2001; Larsson et al. 2002; Goicoechea & Cernicharo 2002; Goicoechea et al. 2004, 2006), Herschel (e.g. van Kempen et al. 2010a; Wampfler et al. 2010, 2011; Goicoechea et al. 2011), and recently SOFIA (Csengeri et al. 2012; Wiesemeyer et al. 2012). Masers of OH hyperfine transitions are also commonly observed toward high-mass star-forming regions at cm wavelengths, but are not detected from low- and intermediate-mass protostars. Because this work focuses on low- and intermediate-mass YSOs, we will not discuss OH maser emission (a detailed overview can be found in e.g. Elitzur 1992).

From first Herschel results using the Photodetector Array Camera and Spectrometer (PACS, Poglitsch et al. 2010), van Kempen et al. (2010b) found that the OH emission from the low-mass class I YSO HH 46 is not spatially extended, in contrast to the H₂O and high-J CO emission from the same source. They speculated that at least parts of the OH emission could stem from a dissociative shock caused by the impact of the wind or jet on the dense inner envelope. Spectrally resolved Herschel observations of OH with the Heterodyne Instrument for the Far-Infrared (HIFI, de Graauw et al. 2010) support an outflow scenario based on the inferred broad line widths of more than 10  km  s^-1 (Wampfler et al. 2010, 2011). Furthermore, analysis of OH PACS lines from a set of six low- and intermediate-mass protostars yielded similar excitation conditions of OH in all these sources (Wampfler et al. 2010). A tentative correlation of the OH line luminosities with the [OI] luminosities as well as the bolometric luminosities of the protostars were found, indicating that the observed OH emission might originate from a dissociative shock.

In this paper we present Herschel-PACS observations of OH in an extended sample of 23 low-and intermediate-mass YSOs. Our first goal is to test whether the tentative correlations from earlier work can be confirmed and to determine the influence of different source properties on the strength of the emission. The second goal is to study the OH excitation and the spatial extent of the OH emission in the target sources. A detailed analysis of the OH excitation and spatial extent is important to determine the origin of the OH emission and whether this is consistent with the picture from H₂O observations.

The paper is organized as follows: Section 2 describes the source sample, the observations, and the data reduction methods. In Sect. 3 we present the observational results. Section 4 contains a discussion of spherically symmetric envelope models for OH (Sect. 4.1), the description and results of slab radiative transfer models to study the OH excitation in the outflow (Sect. 4.2), as well as the discussion and data interpretation (Sect. 4.3). Finally, the conclusions are summarized in Sect. 5.

2. Observations and data reduction

Observations of 23 low- and intermediate-mass YSOs were carried out with the Photodetector Array Camera and Spectrometer (PACS, Poglitsch et al. 2010) on the Herschel Space Observatory. All observations were obtained within WISH (van Dishoeck et al. 2011) except for IRAS 12496-7650 (DK Cha, van Kempen et al. 2010a), which was observed in the “Dust, Ice and Gas In Time” key program (DIGIT, PI N. Evans). The coordinates and properties of the targets can be found in Table 1 and the data identity numbers (obsids), observing modes, and the pipeline versions are given in Table A.1 in the appendix.

Two different observing modes are available for the PACS spectrometer, line and range spectroscopy. The “range spectroscopy” mode provides a full scan of the 50−220  μm wavelength regime. The “line spectroscopy” mode covers only small windows around selected target lines, but generally at higher spectral sampling and sensitivity than range spectroscopy. The majority of the sources in our sample have been observed with the PACS line spectroscopy mode, targeting four main OH rotational doublets: at 79  μm, at 84  μm, at 119  μm, and at 163  μm. The integration time and the noise level for all sources observed in line spectroscopy mode is similar. NGC 1333 IRAS 4A and NGC 1333 IRAS 4B have been observed in both line and full range spectroscopy. Range spectroscopy only was used for NGC 1333 IRAS 2A, Ser SMM 1, and DK Cha. An illustration of the OH pure rotational transitions that are accessible with PACS on-board Herschel is provided in Fig. 1. An overview on the molecular data used in this work can be found in Table 2.

The full spectral scan of DK Cha was presented previously in van Kempen et al. (2010a) and the line spectroscopy of HH 46 and NGC 7129 FIRS 2 in van Kempen et al. (2010b) and Fich et al. (2010), respectively. These three spectra plus IRAS 15398, TMR 1, and NGC 1333 IRAS 2A were part of the sample analyzed in our previous work (Wampfler et al. 2010). We have now re-reduced all spectra with a newer version of the PACS pipeline and calibration files. The full spectral scans of NGC 1333 IRAS 4B and Ser SMM1 are discussed in great detail in Herczeg et al. (2012) and Goicoechea et al. (2012), respectively.

The PACS spectrometer is an integral field spectrometer and operates simultaneously in a blue and a red channel. The detector consist of 5 by 5 square spatial pixels (“spaxels”) with a pixel size of 94. The Herschel half power beam width is smaller than a spaxel in the blue wavelength regime, but exceeds the spaxel size on the sky in the red part of the spectrum. The spatial resolution is therefore limited by the pixel size for short wavelengths and by the diffraction beam pattern at longer wavelengths. The spectral resolution depends on the grating order and varies from R = 3000−4000 at wavelengths λ < 100  μm to R = 1000−2000 for λ > 100  μm. All individual OH lines are therefore unresolved and at the lower resolutions, even blending of the OH doublets occurs, mostly at 79  μm and 119  μm. When doublet components are blended, they were assumed to be of equal strength in the analysis.

The spectra were reduced with the Herschel interactive processing environment (HIPE, Ott 2010), versions 8 (for line scans) and 6 (for range scans). The wavelength grid was rebinned to four pixels per resolution element for line scans and two pixels per resolution element for range scans. The spectra were flat-fielded to improve the signal-to-noise ratio. The fluxes were normalized to the telescopic background and then calibrated using measurements of Neptune as a reference. The relative calibration uncertainty on the fluxes is currently estimated to be below 20%. The PACS spectrometer suffers from spectral leakage in the wavelength ranges 70−73  μm, 98−105  μm, and 190−220  μm where the next higher grating order ranges 52.5−54.5  μm, 65−70  μm, and 95−110  μm are superimposed on the spectrum. The fluxes from lines in these wavelength bands might therefore be less reliable than in parts of the spectra that are not affected by spectral leakage. This applies to the OH 71  μm and 98  μm doublets.

The lines were then subsequently analyzed in IDL using first or, if required, second order polynomials as baselines and the flux was measured by integrating over the line. The fraction of the point-spread function (PSF) seen by the central spaxel is wavelength-dependent, reaching from around 0.7 for a perfectly centered point source at 60−80  μm down to about 0.4 at 200  μm. A significant fraction of the flux might therefore fall onto neighboring spaxels and even more so if the source is off-centered on the central spaxel. It is therefore important to investigate the flux distribution on the detector, which can be caused by spatially extended emission, the telescope PSF, or a combination of both. Extracting the flux from all 25 spaxels is not an optimal solution, because of contamination from nearby sources and because the signal-to-noise ratio drops if many spaxels without line emission but extra noise are added. This is particularly problematic for weak lines or lines with little spatial extent. For a subset of our targets, where contamination from nearby sources occurs, we chose a set of spaxels that excludes the contribution from close-by sources. This applies to NGC 1333 IRAS 4A, NGC 1333 IRAS 4B, Ser SMM3, and DK Cha. Spaxels excluded in the flux measurements of the WISH sources are marked in gray in the maps in the online appendix B. For DK Cha, a 3 by 4 set around the on-source spaxel was used. For all other sources, we used either the on-source spaxel, corrected for the spillover (L 1527, Ced 110 IRS 4, L 723, L 1489, RNO 91), 3 by 3 spaxels centered on the on-source spaxel (IRAS 15398, L 483, TMR 1, TMC 1A, TMC 1, HH 46, and Ser SMM1), or the full array (all intermediate-mass sources).

3. Results and analysis

3.1. Detected lines and spatial extent

We detected at least one OH doublet in all 23 sources. The fluxes integrated over the emitting area, obtained as described in Sect. 2, can be found in Table 3. The doublet that is most often detected, in 21 out of 23 sources, is the doublet at 84  μm, thanks to a combination of intrinsic strength and higher spectral resolution of the instrument at the shorter wavelengths. The component at 84.42  μm is however blended with CO(31–30) at 84.41  μm because the spectral resolution is around 0.037  μm. The sources in which the 84  μm lines were not detected are NGC 1333 IRAS 2A and AFGL 490. Figures 2 and 3 present the OH spectra of the low-mass class 0 and class I sources, Fig. 4 the spectra of the intermediate-mass sources. In 22 out of 23 sources at least one line was in emission, with the exception being NGC 1333 IRAS 2A, where the only detection is the 119  μm doublet feature in absorption (Wampfler et al. 2010). We mainly detected emission lines, but absorption is also found toward higher envelope masses. In the subsequent analysis, we only considered the fluxes of lines that are purely in emission. Absorption in the 119  μm OH intra-ladder doublet transitions is observed from NGC 1333 IRAS 2A and in some spaxels of AFGL 490, Vela IRS 17, and Vela IRS 19, but there are also spaxels with emission from these targets. For even higher envelope masses like AFGL 490, the 79  μm OH cross-ladder transitions are also in absorption. This behavior can be explained by the fact that both lines are directly coupled to the ground rotational state of OH: because the first excited state is at E_up ≈ 120  K, almost only the ground state is populated at temperatures below ∼100  K. The 119  μm transitions couple the ground state to the first excited state and have a large Einstein A coefficient (∼1.4 × 10^-1  s^-1). The 79  μm lines are cross-ladder transitions between the ground states of both rotational ladders. Cross-ladder transitions generally have much smaller Einstein A coefficients (∼3.6 × 10^-2  s^-1 for the 79  μm lines) than the intra-ladder transitions. Therefore, absorption at 79  μm does not occur as easily as for the 119  μm doublet.

Several sources show OH emission that is extended beyond what would be expected from a point source folded with the PSF of the telescope or leakage onto neighboring spaxels. The line emission is usually extended along the outflow direction (see Karska et al. 2013) and strongly correlated with the spatial extent of the atomic oxygen transitions, as illustrated in Fig. 5 and further discussed in Karska et al. (2013).

Maps of the OH 79, 84, 119, and 163  μm transitions for all WISH sources can be found in Appendix. An example of compact OH emission at 84  μm from the low-mass class I YSO L 1489 is shown in Fig. 6. Despite their location at further distances than the low-mass objects, all six intermediate-mass sources show signatures of extended OH emission. The largest spatial extent is seen in the 119  μm ground state lines, which can be excited most easily. Figure 7 presents the spaxel map of the 119  μm line from AFGL 490. The absorption is strongest toward the YSO and extended over an area of ∼25″ (25 000 AU) around the central position in the direction perpendicular to the outflow. The spatial extent of the emission is comparable to the 20 000 AU by 6000 AU envelope structure discussed in Schreyer et al. (2006). The OH absorption changes into weak emission along the outflow direction. For the full sample we provide an overview whether the flux observed outside the on-source spaxel is consistent or inconsistent with the spillover factor in Table 4.

3.2. OH emission line flux ratios

Comparison of the OH 84  μm line luminosities (flux corrected for the source distance) between the different source types shows that the intermediate-mass sources in our sample have higher OH luminosities than the low-mass sources by about two orders of magnitude on average. Among the low-mass sources, the class 0 sources are on average about a factor of two more luminous in OH than the class I sources.

In earlier work (Wampfler et al. 2010), we found that the line flux ratios among the sources in the sample were relatively constant. We have therefore also calculated the 79  μm / 84  μm, 79  μm / 119  μm, 79  μm / 163  μm, 84  μm / 119  μm, 84  μm / 163  μm, and 119  μm / 163  μm line flux ratios for the extended sample, i.e. the sources in Table 1 from which emission was detected. The fluxes of doublets are added except for the 84  μm doublet, because the 84.42  μm is blended with CO(31–30). Instead we use twice the flux of the 84.60  μm component assuming that both components are of similar strength. Cases where only one doublet component was clearly detected were not considered. The results are listed in Table 5.

Again we find that the line ratios remain relatively constant within less than a factor of four around their mean values over the whole luminosity, mass, and age range of several orders of magnitude spanned by the sample. The excitation of OH is therefore likely to be similar in all sources, indicating that either the OH emission stems from gas at similar physical conditions or that the ratios remain stable over a spread of parameter values. The latter possibility is supported by the models (cf. Sect. 4), but does not exclude the first option.

3.3. OH rotational temperature

The full spectral scans cover the OH transitions from about 55−200  μm (E_up ≈ 120−875  K) and therefore allow us to study the excitation conditions by means of rotational diagrams. Figure 8 presents the diagram for Ser SMM1. The derived rotational temperature is T_rot ≈ 72 ± 8  K if all the transitions shown on the plot except the 119  μm (optically thick), 84.42  μm (blended with CO), and 98  μm (in leaking region) are included. The rotational diagram for NGC 1333 IRAS 4B can be found in Herczeg et al. (2012), giving T_rot ≈ 60 ± 15  K. No emission lines were detected in the full spectral scan of NGC 1333 IRAS 2A and only very few line detections are available for NGC 1333 IRAS 4A and DK Cha (see also van Kempen et al. 2010a), so that the rotational diagram for these sources is very sparsely populated and a fit of the rotational temperature is therefore not feasible. For Ser SMM1, the corresponding OH column density would be N_OH = 1.0 × 10¹⁴  cm^-2 assuming a source size of 20″ and using an interpolated value for the partition function Q from the JPL catalog¹ (Pickett et al. 1998). However, the points fall below the fit, suggesting that these transitions are either optically thick, which is well possible because the ladder contains the ground rotational state, or that the two rotational ladders might have a different rotational temperature.

3.4. Dependence of OH luminosity on source properties

Understanding which source parameters influence or even determine the strength of the OH emission and the excitation of the different transitions is important to constrain the origin of the emission. We therefore test whether the OH line luminosity correlates with various envelope parameters and the emission from other molecular and atomic species. Because the different OH transitions are fairly well correlated (Sect. 3.2), we restrict the analysis to the 84  μm luminosity, where we have most detections.

In Figs. 9 and 10 the dependence of the OH line luminosity on the bolometric source luminosity and the envelope mass are shown, respectively. We use new values for L_bol that were derived by Kristensen et al. (2012) based on additional continuum values from PACS observations, which are presented in Karska et al. (2013). The envelope masses for the low-mass sources are calculated from spherical models based on continuum radiative transfer and include all material at temperatures above 10  K. For the intermediate-mass sources, we use literature values and the method that was used to determine the envelope mass may therefore be different.

The Pearson correlation coefficient, defined as ρ_X,Y = cov(X,Y) /  [σ(X) × σ(Y)], i.e. the covariance of two random variables X and Y divided by their standard deviations, for L_OH with L_bol is 0.93, including all 21 sources where the OH 84  μm line was detected. An overview on all obtained correlation coefficients and their corresponding significance levels is given in Table 6. Values of ρ close to 1 and − 1 describe a tight correlation or anticorrelation of the parameters X and Y, respectively, while values close to 0 indicate that X and Y are uncorrelated. At what level of ρ a correlation is considered to be significant, depends on the number of data points. The significance of ρ can be expressed as a probability value, the significance level p, and tells how likely the actual observed or a more extreme value of ρ is found under the assumption that the null hypothesis is true, i.e. that there is no relationship between the parameters. Another option is to express the significance in terms of number of standard deviations σ, calculated from , where N is the number of sources.

The correlation coefficient for L_OH with M_env is smaller (ρ = 0.84). As illustrated by Fig. 11, the bolometric luminosity and the envelope mass are not independent properties of the sources. This is consistent with Bontemps et al. (1996, Fig. 1) and André et al. (2000, Fig. 6b), who found that L_bol and M_env are strongly correlated for the class 0 sources and that class I sources move down in the diagram with time along the evolutionary tracks. From an L_OH − M_env correlation one would also expect L_OH to be correlated with T_bol (Fig. 8 of Jørgensen et al. 2002). Such a correlation is however not found for our low-mass source sample, as illustrated by Fig. 12, indicating that the underlying L_bol − M_env correlation might create the observed L_OH − M_env trend. A correlation between two variables can be caused by an underlying correlation of the two variables with a third one. A method to measure such effects is the concept of the partial correlation coefficient, defined as (see also Appendix A from Marseille et al. 2010). The resulting value for the partial correlation coefficient of L_OH with M_env under the influence of L_bol is 0.56, i.e. significantly reduced, thus indicating that the trend might indeed be based on an underlying relation between mass and luminosity. Class I YSOs that lie above the L_OH − M_env correlation in Fig. 10 are also the ones that do not follow the L_bol − M_env relation (Fig. 10), in particular DK Cha. These sources have a higher L_OH than what would be expected from their mass and a lower value than what would be expected from their bolometric luminosity. They are found in the region of more evolved class I sources (see Fig. 6 in André et al. 2000), i.e. they have a significantly lower envelope mass at a given bolometric luminosity than less evolved sources like e.g. HH 46, and are in the transitional stage to class II where disk emission may contribute as well.

We find that L_OH (the luminosity of the OH 84  μm transitions) seems to be well correlated with luminosity for both evolutionary stages and that class 0 and I sources lie on the same straight line. In contrast, Nisini et al. (2002) found from ISO data that class I sources fall systematically below class 0 sources in their plot of the total FIR luminosity L_FIR = L_[OI] + L_CO + L_H2O + L_OH versus L_bol. Furthermore, they concluded that class 0 and I sources fall onto the same straight line in the L_FIR − M_env plot, but in Fig. 6 of Nisini et al. (2002), class I sources with M_env ≲ 10^-1  L_⊙ tend to branch off as well.

A correlation of L_OH with the outflow momentum flux (“outflow force”, Bontemps et al. 1996) F_CO is not significant from our Fig. 13. The values for F_CO are taken from the literature and were not derived in a consistent way. New estimates of F_CO are currently work in progress (Yıldız et al., in prep.).

Furthermore, L_OH seems to decrease with evolution for class 0 sources, but not for class I, as can be seen from Fig. 14 showing L_OH plotted against , a quantity that was proposed as an evolutionary tracer by Bontemps et al. (1996).

The different behavior of the class 0 and I sources could be caused by their different geometry. If the OH was radiatively pumped, then the location of the warm dust would be an important parameter. Warm dust at 100  K (cf. Sect. 3.3) is expected from two physical components in YSOs, the inner envelope and the outflow walls. Class 0 and class I sources differ in the geometrical alignment of their warm dust components: in class 0 sources, high-energetic radiation from the protostar and accretion processes is reprocessed to a FIR field by the dust in the inner envelope, which represents a small solid angle. Thus the OH luminosity for sources where this component dominates should be mass dependent. In class I sources, the warm dust from the outflow walls can directly irradiate the local OH molecules and therefore the OH luminosity for these sources should depend on the bolometric luminosity. We extracted the radius at which the temperature reaches 100  K from the spherically symmetric envelope models to test this hypothesis. Figure 15 shows the OH luminosity plotted against the 100  K radius from the spherically symmetric envelope models (Kristensen et al. 2012) and there seems to be a trend of increasing OH luminosity when the size of the inner hot envelope T ≥ 100  K is larger. The OH luminosity does not seem to depend significantly on the density at 1000 AU as shown in Fig. 16. A correlation with density would not necessarily imply that collisions are the dominant excitation mechanism anyway as the dust mass also increases with density.

3.5. Correlation of the OH flux with other species

OH is tightly related to the formation and destruction processes of H₂O and a connecting piece between H₂O and atomic oxygen in the chemistry. We therefore test whether the OH emission is correlated with the [OI] and H₂O emission. The [OI] and H₂O fluxes for the low-mass protostars are tabulated in Karska et al. (2013) and those of the intermediate-mass protostars in Table A.2 in the appendix. Figure 17 shows the OH 84  μm flux plotted versus the [OI] PP₂ and PP₁ fluxes at 63  μm (left panel) and 145  μm (right panel), respectively. The Pearson correlation coefficients for OH 84  μm vs. [OI] 63  μm and 145  μm are 0.72 and 0.79, respectively, corresponding to a three sigma result. The [OI] 63  μm could be optically thick or more affected by contamination than the 145  μm, which would explain the slightly lower correlation coefficient for OH 84  μm vs. [OI] 63  μm compared to [OI] 145  μm. The OH and [OI] emission thus seem to be correlated both spatially and in total flux, hinting at a common origin, most likely from gas associated with the outflow, because in the cases of noncompact emission it is usually found to be extended along the outflow direction.

The correlation of the OH 84  μm flux with p-H₂O 3_{2, 2} − 2_{1, 1} (λ ≈ 89.99  μm, E_up = 296.8  K) is shown in Fig. 18. The p–H₂O 3_{2, 2} − 2_{1, 1} was chosen because it has a very similar upper level energy to the OH 84  μm transition (E_up = 290.5  K) and a similar wavelength, which strongly reduces the influence of instrumental effects, as the PSF is very similar. The fluxes were measured on the same spaxel sets. The correlation of the OH 84  μm flux with p–H₂O 3_{2, 2} − 2_{1, 1} is significant at more than 3σ with ρ = 0.85. The same plot for o–H₂O 2_{1, 2} − 1_{0, 1} (λ ≈ 179.53  μm, E_up = 114.4  K) can be found in Karska et al. (2013). The o–H₂O 2_{1, 2} − 1_{0, 1} line has a lower upper level energy and was observed in a larger beam, but was detected in more sources. Again, there is a statistical correlation between the fluxes of the OH and H₂O lines at similar energy, but the H₂O and OH spatial extents can differ (Karska et al. 2013).

The ratio of the two fluxes versus the bolometric luminosity is shown in Fig. 19. The low-mass class I sources lie in the upper part of the plot as they have OH 84  μm to H₂O 89  μm ratios above 2–3, whereas the class 0 sources have a slightly lower ratio on average. On the other hand, there is no significant trend with bolometric luminosity (ρ = −0.36). The ratio seems to decrease with envelope mass, as illustrated by Fig. 20, and to increase with bolometric temperature (Fig. 21), but there is a large spread. Figure 22 shows that an increase in the OH 84  μm to H₂O 89  μm ratio could be an evolutionary effect. The increase in OH compared to H₂O could for instance be caused by the envelope becoming more tenuous in the more evolved stages, allowing high-energy photons from the protostar to penetrate further and dissociate the H₂O. The intermediate-mass sources are missing in Fig. 21, because a consistent set of bolometric temperatures is not available.

Goicoechea et al. (2011) find that the OH 84  μm emission is not spatially correlated with o–H₂O 3_{0, 3} − 2_{1, 2} in the Orion Bar PDR, but with high-J CO and CH⁺. We cannot test such a spatial correlation here because the fluxes drop rapidly outside the on-source spaxels in our low-mass source sample.

4. Excitation and origin of OH

Where does the OH emission arise? The environment of low-mass protostars is known to consist of different physical components, including the collapsing envelope, shocks, outflow cavities heated by UV radiation, and entrained outflow gas, all of which are contained in the Herschel beams (see Visser et al. 2012, for an overview). To derive physical properties like the density and temperature of the emitting gas, the observed fluxes and line ratios are compared to the results from radiative transfer models. The obtained physical conditions can help in constraining the origin of the emission in combination with information about the spatial distribution of the emission. Furthermore, radiative transfer models permit to study what mechanism dominates the excitation under given physical conditions.

The lowest rotational transitions of OH lie in the FIR and therefore significantly interact with the dust continuum field, which peaks in the same wavelength regime for dust temperatures typical of embedded YSOs. Moreover, the properties of OH such as the large dipole moment and large rotational constant make radiative pumping an important excitation process. Therefore, the excitation of OH should be modeled using a code that includes radiative effects.

Before describing the models, we recall the clues on the origin of the OH emission that come from spectrally resolved OH line profiles. Wampfler et al. (2010) present upper limits on the OH 163  μm (1837 GHz) line intensities using HIFI for two low-mass sources which, when combined with measured PACS fluxes for the same lines, imply FWHM line widths of at least 10  km  s^-1. For a third low-mass source, Ser SMM1, a recent unpublished HIFI spectrum shows a detection of the broad (FWHM ≈ 20  km  s^-1) component, but no sign of a narrow component (Wampfler et al., in prep.). In contrast, Wampfler et al. (2011) found a narrow component (FWHM ≈ 4−5  km  s^-1) in the OH 1837 GHz spectrum from the high-mass protostar W3 IRS 5, which can be attributed to the quiescent envelope, on top of a broad outflow component with FWHM ≈ 20  km  s^-1. Therefore, the OH line profiles from low-mass YSOs seem to be dominated by the outflow contribution, whereas those of high-mass sources can contain both an outflow and envelope component.

4.1. Spherical envelope models

To further quantify any contribution from the protostellar envelope, spherically symmetric source models such as derived by Kristensen et al. (2012) are commonly used in combination with a nonLTE line radiative transfer code like RATRAN (Hogerheijde & van der Tak 2000) or LIME (Brinch & Hogerheijde 2010) to model the line emission.

We ran RATRAN calculations in spherical symmetry for a few low-mass sources, including Ser SMM1, using the same RATRAN code as for W3 IRS 5 (see Sect. 4.2.1 for molecular data input). The OH fractional abundances considered range from x_OH = 10^-9 to 10^-7. Note that the source structure on small scales is often not well constrained by the single-dish continuum observations and that the spherical symmetry starts to break down inside about 500 AU (e.g. Jørgensen et al. 2005). Thus this type of model is not ideally suited for lines with a high critical density, where the bulk of the emission usually arises from the innermost parts of low-mass protostellar envelopes. The inner envelope is also the area where the excited states of OH are mainly populated, and thus the model results should only be regarded as a rough order of magnitude estimate.

It is clear that these spherically symmetric source models cannot reproduce the observed OH emission in low-mass sources for a variety of reasons. First, the synthetic spectra from the model fail to reproduce the observed broad lines (FWHM of ∼20  km  s^-1). The model lines are typically much narrower (FWHM of a few km  s^-1) for any reasonable Doppler− b parameter that fits emission from other molecules. Therefore, the line width measured from the HIFI spectra is inconsistent with an envelope-only or envelope-dominated scenario for the low-mass sources observed with HIFI. Moreover, the 79, 84, and 119  μm lines from the RATRAN models are always in absorption, while the detected PACS lines from the low-mass sources are in emission, providing another indication that the bulk of the emission does not arise from the envelope. Although a minor envelope contribution to the 163  μm lines cannot be excluded, the bulk of the emission is likely associated with the outflow. For the intermediate-mass sources, absorption is observed at 119  μm in at least one spaxel (except for NGC 7129 FIRS 2), suggesting that a potential envelope contribution to the spectra of intermediate-mass sources cannot be excluded, in particular in the lowest rotational transitions.

4.2. Outflow model

4.2.1. Slab model description

To model OH emission from outflows or shocks, a simple slab geometry is appropriate. We use a radiative transfer code based on the escape probability formalism as described in Takahashi et al. (1983), which includes radiative pumping. The physical conditions such as density and temperature and the excitation of the molecule are assumed to be constant throughout the region. The free parameters of the model are the kinetic temperature of the gas T_gas, the temperature of the dust T_dust, the density of the collision partner n, the molecular column density of OH N_OH, and the dust column density N_dust. The line profile function has a rectangular shape with a width of where Δv is the full width at half maximum (FWHM) of a Gaussian line. Here, Δv is assumed to be 10  km  s^-1 for all models. As discussed above, this FWHM is motivated by the nondetection of OH from low-mass sources with HIFI (Wampfler et al. 2010) that lead to the conclusion that the line width must be broader than 10  km  s^-1.

Our slab code is similar to the “RADEX” code (van der Tak et al. 2007), but includes an active dust continuum, which is capable of both absorbing and emitting radiation. Results from our code in the limiting case where no dust is present agree very well with the RADEX results. An earlier OH excitation study by Offer & van Dishoeck (1992) included a dust continuum radiation field for the radiative excitation but not the absorption of line photons by dust grains. Furthermore, different dust properties were used in their calculations. Therefore, the comparability of the two models is limited.

We use the molecular data file from the Leiden atomic and molecular database (LAMDA, Schöier et al. 2005) for OH without hyperfine structure, because the resolution of PACS does not allow one to resolve the hyperfine components. The file contains frequencies, energy levels, and Einstein A coefficients from the JPL catalog (Pickett et al. 1998) and collision rates with ortho- and para-H₂ for temperatures in the range of 15−300  K from Offer et al. (1994). The highest excited state contained in the file has an energy of 875  K. The ortho-to-para-H₂ ratio in the model is temperature dependent according to (1)The dust opacities for dust grains with thin ice mantles in the wavelength range of 1−1300  μm are taken from Ossenkopf & Henning (1994,Table 1, Col. 5).

The parameter space explored in the slab models covers the full range of physical conditions expected in the protostellar environment, i.e., temperature range T = 50−800  K, densities of n = 10⁴−10¹²  cm^-3, dust column densities of N_OH = 10¹⁸−10²³  cm^-2, and OH molecular column densities of 10¹⁴−10¹⁸  cm^-2. Temperatures above 800  K are problematic because the highest rotational level included in the molecular data file is 875  K and the collision rates are only available up to 300  K. The collisional de-excitation rates are kept constant above 300  K, and the excitation rates are calculated from the de-excitation rates from the detailed balance relations and thus depend on the kinetic temperature through a factor exp[−ΔE / k_BT_kin].

4.2.2. Slab model results

A useful quantity to describe the excitation of a molecule is the excitation temperature, defined as (2)where g_l and g_u are the statistical weights of the lower and upper level, respectively, and n_l and n_u their normalized populations. The energy of the transition is ΔE = hν and k_B denotes Boltzmann’s constant.

Figure 23 shows the excitation temperature of the OH transitions at 79.18  μm, 84.60  μm, 119.44  μm, and 163.12  μm as a function of n_H2 and N_dust for a model of fixed gas and dust temperatures (T_gas = 200  K, T_dust = 100  K) and three values of N_OH. The N_OH = 10¹⁴  cm^-2 model largely represents the optically thin case, the N_OH = 10¹⁸  cm^-2 model the optically thick regime, and N_OH = 10¹⁶  cm^-2 is an intermediate case. The adopted parameters are representative for the OH emitting region.

We notice from Fig. 23 that all transitions behave relatively similar with respect to their excitation. Furthermore, this behavior is also comparable for all considered gas temperatures (50, 100, 200, 500, and 800  K). For densities above the critical density (∼10⁸  cm^-3), the excitation temperature approaches the kinetic temperature of the gas, as expected, irrespective of the dust column density. The populations are thermalized at the kinetic temperature. Collisions must therefore be the dominant excitation mechanism in this regime. For densities below the critical density, dust pumping dominates the excitation for dust column densities above ∼10²¹  cm^-2. This is illustrated by the fact that T_ex approaches T_dust, i.e. the populations are thermalized at the temperature of the dust radiation field. Below N_dust ≈ 10²¹  cm^-2, both mechanisms contribute to the excitation, whereby one order of magnitude increase in n_H2 and N_dust have similar effects on T_ex. If the OH column density is enhanced, the gas becomes optically thick and line photons are trapped. Then, the level populations thermalize at the gas temperature already at lower densities because the critical density is reduced with an effective critical density of n_cr(τ_line) ≈ n_cr(0) / τ_line.

In models of equal dust and gas temperature, we find that the 79  μm cross-ladder transition even experiences supra-thermal excitation for low densities (n_H2 ≲ 10⁸  cm^-3), temperatures above 50  K, OH column densities 10¹⁴−10¹⁶  cm^-2, and dust column densities in the range of 2 × 10²⁰−1 × 10²²  cm^-2.

As for line optical depths, the models show that the 119  μm transition reaches the highest optical depth as expected from the fact that this transition is connected to the ground state. It is followed by the 84  μm transition, originating from the same rotational ladder, just above the 119  μm. The 79  μm line is a cross-ladder transition with a much smaller Einstein A coefficient and does therefore not become optically thick as easily as the two afore mentioned intra ladder transitions.

Figure 24 presents the line flux ratios for the six possible combinations of the observed four transitions. We decided to use line ratios instead of fluxes because the ratios are less dependent on the source size. The black contours represent the minimum and maximum value of the observed ratios and the shaded area indicates where the models match the observed values, given in Table 5. White areas at high dust column densities indicate regions where at least one line is in absorption. The observed line ratios can be modeled with a wide range of parameters, but the observed line ratios still allow us to exclude parts of the parameter space. The very optically thin model (N_OH = 10¹⁴  cm^-2) fails to reproduce the observed 79  μm / 119  μm line flux ratio for temperatures below 200−500  K and can also hardly match the 119  μm / 163  μm ratio. Similar difficulties occur for the very optically thick case (N_OH = 10¹⁸  cm^-2), where the observed 79  μm / 163  μm ratio can only be found in a very narrow range of dust column densities. A direct comparison of the column density with observations is however difficult because the model does not include any geometrical effects.

There are basically two main regimes in the intermediate case (N_OH = 10¹⁶  cm^-2) that are able to reproduce to the observed values. First, there is the radiatively dominated regime at low densities (10⁴−10⁸  cm^-3) for dust column densities in the range of N_dust ≈ 1 × 10¹⁹−3 × 10²¹  cm^-2, slightly depending on temperature (lower N_dust for higher temperature and vice versa). In the regime where collisions start to become important (n ≳ 10⁶  cm^-3) and at low dust column densities (N_dust ≲ 10²⁰  cm^-2), it is harder to find a set of parameters that is able to reproduce all line ratios simultaneously, in particular the 79  μm / 84  μm, 79  μm / 163  μm, and 84  μm / 163  μm ratios. For densities of 10⁶−10⁸  cm^-3, small ranges can however be found, especially given the uncertainties of our line ratios. At temperatures below ∼100  K, a collision dominated solution exists toward higher densities (n ≳ 10⁸  cm^-3) and dust column densities above ∼3 × 10²⁰  cm^-2. So given the degeneracies in the models, we cannot well distinguish between collisional excitation and radiative pumping unless we have additional constraints on the density of the emitting gas and the dust column density.

To constrain which of the two scenarios is more likely, we ran additional RADEX slab models (van der Tak et al. 2007) that allow us to include the actual continuum field of a source at a given distance. The line width is chosen to be 10  km  s^-1 and the density and temperature at a given distance are taken from the continuum model of the source presented in Kristensen et al. (2012). The OH column density is a free parameter. The continuum field is only included in the excitation of the OH molecules, but not in the line formation, thus assuming a geometry in which the OH is not right in front of the line of sight to the continuum. Models which include the source continuum in both the excitation and the line formation yield several lines in absorption and cannot reproduce the observations. To study the importance of the continuum, models without the continuum field were calculated as well. The model fluxes were scaled such that the 84.60  μm flux is equal to the observed value.

Figure 25 shows the results for Ser SMM1 (n = 8 × 10⁷  cm^-3 and T = 90.3  K at a distance of 100 AU) and N_OH = 10¹⁶  cm^-2. While the modeled fluxes are fairly similar for the transitions with an upper level energy less than 300  K, the model including the continuum field matches the observed values better than that without a source continuum for the higher excited lines (98  μm, 65  μm, and 71  μm).

Another indication that the continuum may be important is illustrated by Fig. 26 showing the correlation of the OH 84  μm flux with the continuum at 63  μm and 84  μm as measured from the PACS data. A continuum field with a temperature similar to the observed rotational temperature of OH, i.e. T_rad ≈ 100  K, would peak at around 30  μm, which cannot be observed with Herschel. Therefore, we use the continuum at 63  μm and 84  μm instead.

For the Orion bar, Goicoechea et al. (2011) found line ratios that differ from the values derived for our source sample, except for the 79  μm / 119  μm and 79  μm / 163  μm ratios. The 79  μm / 84  μm ratio of almost four is higher than in our sample, as is the 119  μm / 163  μm ratio. On the other hand, the 84  μm / 119  μm and 84  μm / 163  μm ratios are lower. The temperature, density, and the column density of the dust grains are lower in the Orion bar, therefore both collisional excitation and pumping by the FIR field are likely lower.

4.3. Discussion

From the PACS observations we find that the excitation of the OH emission in our sample of 17 low- and 6 intermediate-mass protostars is similar in all sources, as indicated by the relatively constant line ratios among the target sample. This could either mean that the OH emission from all sources arises from gas at very similar physical conditions or that the observed line ratios can be realized by a broad range of gas properties. Comparison of the ratios to the modeling results (cf. Sect. 4.2.2) shows that the observed values can indeed be reproduced by a wide parameter range, which may explain why similar ratios are observed in sources that span a large range in luminosity, envelope mass, and evolutionary stage.

From the full range scans of the two class 0 YSOs Ser SMM1 and NGC 1333 IRAS 4B we find that the rotational temperature of OH in these sources is around 70  K. From the fact that the points can be relatively well fitted with a straight line in the rotational diagram, we conclude that the level population of OH can be represented by a Boltzmann distribution at T ≈ 70  K. The constant line ratios found in the sample may be an indication that other sources could have similar rotational temperatures. However, the models demonstrate that different physical conditions are able to reproduce the observed line ratios and thus full range scan data, which includes more than four OH transitions, of additional sources is needed to test how the OH rotational temperatures vary from source to source and whether there is any difference between evolutionary stages. If the rotational temperature were equal to the ambient kinetic temperature, the population would be in LTE. However, because of the very high critical densities of most OH transitions (around 10⁸  cm^-3), this scenario seems to be rather unlikely, as a significant amount of the emission stems from the outflow (Wampfler et al. 2010, 2011). Compression factors of a hundred are needed to obtain a post-shock density of 10⁸  cm^-3 for a pre-shock density of 10⁶  cm^-3 (Neufeld & Dalgarno 1989a). Alternatively, the OH excitation may be in equilibrium with the temperature of the FIR dust continuum field, that can strongly pump OH.

The models show that the degeneracy in the parameter space is large, allowing different combinations of parameters for the realization of the observational results. Therefore, it is only possible to distinguish between the collision-dominated and radiative pumping controlled scenarios described in Sect. 4.2.2 when additional constraints on the density and dust column density of gas emitting or absorbing in OH FIR lines are available. The similar line ratios could be a hint that the excitation is not controlled by a combination of both collisions and radiative pumping but rather by one dominant mechanism, because it would be much harder to match the same or a similar combination in all targets. The RADEX results point toward radiative pumping as the main excitation process, at least in Ser SMM1, as models including a FIR continuum field fit the observations better, in particular the high excited lines (65  μm and 71  μm). Another indication that the radiation field is important in the excitation is provided by the strong correlation of the OH 84  μm luminosity with the bolometric luminosity of the sources regardless of their evolutionary stage and type, and a tentative trend with the continuum measurements.

An envelope-only or strongly envelope-dominated scenario can be excluded for the low-mass sources from the fact that spherically symmetric radiative transfer models yield the 79, 84, and 119  μm transitions in absorption, in conflict with the observed emission lines. Furthermore, the FWHM of the modeled 163  μm line is at least a factor of two narrower than the observed value, pointing also at an outflow origin of the emission. Several physical regimes have been identified in the outflow from Herschel H₂O and CO observations (e.g. Nisini et al. 2010; Yıldız et al. 2010; van Kempen et al. 2010a; Lefloch et al. 2010; Kristensen et al. 2012; Herczeg et al. 2012; Vasta et al. 2012): the cold entrained outflow material, with typical densities around 10⁵  cm^-1 and temperatures around 100 K, an intermediate warm region (T ∼ 300  K, n ∼ 10⁶−10⁷  cm^-1), and the shock front, where temperatures reach T ∼ 800  K and densities are found up to n ∼ 10⁸  cm^-1. The OH rotational temperature of T ∼ 70  K is low compared to the values found for H₂O and CO and favors the intermediate warm regime over a shock front origin (Goicoechea et al. 2012). The entrained material however has a density that is significantly lower than the critical density, which would require the presence of a strong radiation field to excite the OH molecules, for instance close to the protostar.

5. Conclusions

We analyze Herschel-PACS spectroscopy of the OH lines at 79, 84, 119, and 163  μm in a set of 23 low- and intermediate-mass protostars. In addition, we use slab radiative transfer models to study the OH excitation. Our main results are:

• 1.

  At least one OH line is detected in all 23 sources. ForNGC 1333 IRAS 2A,only the 119  μm doublet is detected in absorption against the continuum. Most sources show only emission lines. Absorption occurs toward higher envelope masses.

• 2.

  The derived rotational temperatures for Ser SMM1 and NGC 1333 IRAS 4B, where additional OH lines are available from a full spectral scan, are similar and around 70  K.

• 3.

  The ratios between the fluxes of different OH emission lines are relatively constant among the source sample, i.e. the fluxes in the different transitions are well correlated.

• 4.

  There is a strong correlation (Pearson correlation coefficient of ρ = 0.93) between the OH line luminosity and the bolometric luminosity of the sources. The correlation with envelope mass is less tight (ρ = 0.84) and could even be introduced by an underlying correlation of the bolometric luminosity and the envelope mass. We do not find evidence for an evolutionary effect, i.e. a strong correlation with the bolometric temperature or the evolutionary tracer .

• 5.

  There are also trends of an increasing OH flux with increasing [OI] and H₂O fluxes.

• 6.

  The OH 84 μm/H₂O 89 μm ratio is slightly higher in the low-mass class I YSOs than in the class 0 sources in our sample. The ratio seems to increase with increasing bolometric temperature and to decrease toward higher envelope masses, indicating that a change in the ratio could be an evolutionary effect.

• 7.

  Spherically symmetric protostellar envelope models do not fit the observed OH line widths and produce 79, 84, and 119  μm lines in absorption rather than emission.

• 8.

  Slab radiative transfer models representative of an outflow show that the observed line ratios can be reproduced by a range of parameters. The degeneracy in the parameter space of the models and the currently available data make it challenging to clearly distinguish whether the excitation of OH is dominated by collisions or by radiative pumping or even a combination of both. Fluxes of transitions with E_up ≳ 300  K are clearly better reproduced by RADEX models with radiative pumping compared to those without a source continuum. The OH cannot be right along the line of sight to the continuum, however, since this would yield several lines in absorption.

• 9.

  Both the excitation and spatial extent observed by Herschel, combined with independent information on broad line widths, provide strong evidence that the OH emission from low-mass protostars is dominated by shocks impacting on the dense envelope close to the protostar.

---

Acknowledgments

We thank the referee for constructive comments that helped to improve the paper. The work on star formation at ETH Zurich is partially funded by the Swiss National Science Foundation (grant nr. 200020-113556). This program is made possible thanks to the Swiss HIFI guaranteed time program. WISH research in Leiden is supported by the Netherlands Research School for Astronomy (NOVA), by grant 614.001.008 from the Netherlands Organization for Scientific Research (NWO) and by EU-FP7 grant 238258 (LASSIE). HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada and the United States under the leadership of SRON Netherlands Institute for Space Research, Groningen, The Netherlands and with major contributions from Germany, France and the US. Consortium members are: Canada: CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS; Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri – INAF; Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astronómico Nacional (IGN), Centro de Astrobiología (CSIC-INTA). Sweden: Chalmers University of Technology – MC2, RSS & GARD; Onsala Space Observatory; Swedish National Space Board, Stockholm University – Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA: Caltech, JPL, NHSC.

References

Online material

Appendix A: Observational details

Appendix B: OH maps

All Tables

All Figures