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A&A
Volume 534, October 2011
Article Number A49
Number of page(s) 9
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/201117257
Published online 30 September 2011

© ESO, 2011

1. Introduction

Photo-dissociation region (PDR) models are used to understand the evolution of the far-UV illuminated matter both in our Galaxy and in external galaxies. The spectacular instrumental improvements, which happen in radioastronomy with the advent of Herschel, ALMA and NOEMA, call for matching progresses in PDR modeling. In particular, the physics and chemistry of the dust grains and of the gas-phase are intricately intertwined. It is well known that the formation of ice grain mantles leads to the removal of chemical reservoirs like CO, O, and other abundant species from the gas phase, enabling new chemical routes to be opened and others to be closed. Despite their low temperature, the mantles are chemically active. Hydrogenation/deuteration reactions are known to be efficient, because hydrogen (or deuterium atoms) can migrate on the surfaces, but reactions with O, N, and C must also be considered. Complex molecules may therefore be formed before they are released into the gas phase. Moreover, the release of the products into the gas phase happens either through thermal processes (evaporation) or non-thermal ones (cosmic ray or far-UV photon-induced desorption). Recent photo-desorption experiments on water and CO ices show that this mechanism is much more efficient than previously thought (Öberg et al. 2009b,a; Muñoz Caro et al. 2010). These results led various groups to include photo-desorption into PDR models (see the results on H2O and O2 by Hollenbach et al. 2009; Walsh et al. 2010; Hassel et al. 2010). The availability of well-defined observations is essential here to distinguish between chemical assumptions about the significant grain surface processes, i.e., adsorption, desorption, and diffusion. It is now confirmed that some interstellar species are mostly formed in the gas-phase (CO for instance), others on grains (CH3OH, Garrod et al. 2007), while the chemical routes for other complex species such as formaldehyde, are still debated because it is likely that solid and gas-phase processes are both needed.

Table 1

Observation parameters for the maps shown in Fig. 1.

Table 2

Observation parameters of the deep integrations of the o - H2CO and p - H2CO lines toward the PDR and the dense-core.

Formaldehyde (H2CO) was the first organic molecule discovered in the interstellar medium (Snyder et al. 1969). It is a relatively simple organic molecule that can be formed in the gas-phase and on the surface of dust grains. In the warm gas, H2CO can trigger the formation of more complex organic molecules (Charnley et al. 1992). It is one of the most popular molecules used for studying the physical conditions of the gas in astrophysical sources. Indeed, it is a good probe of the temperature and density of the gas (Mangum & Wootten 1993). Owing to its large dipole moment (2.3 Debye), its rotational lines are easy to detect from ground-based observations. It is present in a variety of environments, such as Galactic HII regions (e.g., Downes et al. 1980), proto-stellar cores (e.g., Young et al. 2004; Maret et al. 2004), young stellar objects (e.g., Araya et al. 2007), PDRs (e.g., Leurini et al. 2010), starburst galaxies (e.g., Mangum et al. 2008) and comets (e.g., Snyder et al. 1989; Milam et al. 2006).

The Horsehead PDR is particularly well-suited to investigate grain surface chemistry in a UV irradiated environment. It is viewed nearly edge-on (Habart et al. 2005) at a distance of 400 pc (implying that 10′′ correspond to 0.02 pc). Thus, it is possible to study the interaction of far-UV radiation with dense interstellar clouds and the transition from warm to cold gas in a PDR with a simple geometry, very close to the prototypical kind of source needed to serve as a reference to chemical models. Its relatively low UV illumination (χ = 60 in Draine units, Draine 1978) and high density (nH ~ 104 − 105   cm-3) implies low dust grain temperatures, from Tdust ~ 30 K in the PDR to Tdust ~ 20 K deeper inside the cloud (Goicoechea et al. 2009a). The release of the grain mantle products into the gas phase is consequently dominated by photo-desorption, while regions with warmer dust (the Orion bar or the star-forming cores) provide mixed information on the thermal and non-thermal processes (e.g., Bisschop et al. 2007).

In this paper we present deep observations of several formaldehyde lines toward two particular positions in the Horsehead nebula: the PDR, corresponding to the peak of the HCO emission (Gerin et al. 2009), where the gas is warm (Tkin ~ 60 K); and the dense-core, a cold (Tkin ≤ 20 K) condensation located less than 40′′ away from the PDR edge, where HCO+ is highly deuterated (Pety et al. 2007). We present the observations and data reduction in Sect. 2, while the results and abundances are given in Sect. 3. In Sect. 4 we present the H2CO chemistry and PDR modeling. A discussion is given in Sect. 5 and we conclude in Sect. 6.

thumbnail Fig. 1

Integrated intensity maps of the Horsehead edge. The intensities are expressed in the main-beam temperature scale. Maps were rotated by 14° counter-clockwise around the projection center, located at (δx,δy) = (20′′,0′′), to bring the exciting star direction in the horizontal direction and the horizontal zero was set at the PDR edge, delineated by the red vertical line. The crosses show the positions of the PDR (green) and the dense-core (blue), where deep integrations were performed at IRAM-30m (see Fig. 3). The spatial resolution is plotted in the bottom left corner. Values of contour levels are shown on each image lookup table. The emission of all lines is integrated between 10.1 and 11.1   km   s-1.

2. Observations and data reduction

Tables 1 and 2 summarize the observation parameters for the data obtained with the IRAM-30 m and PdBI telescopes. Figure 1 displays the p - H2CO, HCO, DCO +  and 1.2   mm continuum maps. The p - H2CO line was mapped during 3.3 h of good winter weather (~1   mm of water vapor) using the first polarization (i.e. nine of the eighteen available pixels) of the IRAM-30m/HERA single-sideband multi-beam receiver. We used the frequency-switched, on-the-fly observing mode. We observed along and perpendicular to the direction of the exciting star in zigzags (i.e.  ±  the lambda and beta scanning direction). The multi-beam system was rotated by 9.6° with respect to the scanning direction. This ensured Nyquist sampling between the rows except at the edges of the map. The fully sampled part of the map covered a 150′′ × 150′′ portion of the sky. A detailed description of the HCO, DCO +  and 1.2 mm continuum observations and data reductions can be found in Gerin et al. (2009),  Pety et al. (2007), and Hily-Blant et al. (2005).

We performed deep integrations of o - H2CO and p - H2CO low-energy rotational lines (see Figs. 2 and 3) centered on the PDR and the dense-core. To obtain these deep integration spectra, we used the position-switching observing mode. The on-off cycle duration was 1 min and the off-position offsets were (δ RA, δ Dec) = ( − 100′′, 0′′), i.e. the H ii region ionized by σOri and free of molecular emission. From our knowledge of the IRAM-30 m telescope we estimate the absolute position accuracy to be 3′′.

The data processing was made with the GILDAS1 softwares (Pety 2005). The IRAM-30m data were first calibrated to the scale using the chopper-wheel method (Penzias & Burrus 1973), and finally converted to main-beam temperatures (Tmb) using the forward and main-beam efficiencies (Feff and Beff) displayed in Table 2. The resulting amplitude accuracy is  ~10%. Frequency-switched spectra were folded using the standard shift-and-add method before baseline subtraction. The resulting spectra were finally gridded through convolution with a Gaussian to obtain the maps.

Table 3

Spectroscopic parameters of the observed lines obtained from the CDMS data base (Müller et al. 2001).

thumbnail Fig. 2

Lower energy rotational levels of para- (left) and ortho-H2CO (right). The energy above para ground-state is shown at the left of each level. The arrows indicate the transitions detected in the Horsehead.

thumbnail Fig. 3

Radiative transfer modeling of H2CO lines for two positions toward the Horsehead. Two left columns: the PDR position (Tkin = 60 K, n(H2)    =    6    ×    104   cm-3, N(o - H2CO) = 7.2    ×    1012   cm-2) and two right columns: the dense-core position (Tkin = 20 K, n(H2)    =    105   cm-3, N(o - H2CO) = 9.6    ×    1012   cm-2). The two top rows display the ortho lines, for which we varied the column density around the best match (red curve) by a factor of 1.5 (blue curve) and 1/1.5 (green curve). The two bottom rows display the para lines, for which we kept the column density of the best match for o - H2CO (red curves) constant and varied the ortho-to-para ratio of H2CO: o/p = 1.5 (dashed blue), o/p = 2 (dashed red) and o/p = 3 (dashed green).

3. Results

3.1. H2CO spatial distribution

The 218.2 GHz p - H2CO integrated line-intensity map is shown in Fig. 1 together with the 86.7 GHz HCO, 216.1 GHz DCO +  integrated line-intensity maps and the 1.2 mm continuum-emission map. Formaldehyde emission is extended throughout the Horsehead with a relatively constant intensity. The H2CO spatial distribution ressembles the 1.2 mm continuum emission: it follows the top of the famous Horsehead nebula from its front to its mane. It also delineates the throat of the Horsehead. The peak of the H2CO emission spatially coincides with the peak of the DCO +  emission, which arises from a cold dense-core. However, H2CO emission is also clearly present along the PDR, which is traced by the HCO emission. The PDR and dense-core, namely the peaks of the HCO and DCO +  emission are shown with green and blue crosses respectively. Gaussian fits of the H2CO lines at the HCO peak result in broader line widths than at the DCO +  peak. That the lines are broader in the PDR confirms that H2CO lines toward the DCO +  peak arise from the dense-core rather than from the illuminated surface of the cloud. There is a peak in the H2CO emission toward the north-west region

thumbnail Fig. 4

and deuterated H2CO lines detected toward the dense-core. Gaussian fits are shown with red lines. For HDCO and D2CO the line width was fixed to the width of the HDCO (211 − 110) line, because it has the best signal-to-noise ratio.

of the nebula, near the edge of the PDR, where two protostars have been identified (B33-1 and B33-28, Bowler et al. 2009). These protostars heat the dust around them, so it is likely that H2CO has been evaporated from the grain ice mantles.

3.2. H2CO column density

We computed the column densities of H2CO at the PDR and the dense-core positions. For this we first used the lines to estimate the optical depth of the H2CO lines. Then, we made a first estimate of the column densities and excitation temperatures using rotational diagrams. Finally, we used these first estimates as an input for a detailed nonlocal non-LTE excitation and radiative transfer analysis to compute the H2CO abundances. The spectroscopic parameters for the detected transitions (shown in Fig. 2) are given in Table 3. We assumed that the emission is extended and fills the 30 m beam, as shown by the map of the 303 − 202 transition (see Fig. 1).

3.2.1. Opacity of the H2CO lines

We detected two transitions of the formaldehyde isotopologue in the dense-core position (see upper panels in Fig. 4). By comparing the flux between H2CO and for the same transition it is possible to estimate the opacity of the H2CO line, assuming that the line is optically thin, as follows: (1)where β is the escape probability function, which in the case of a homogeneous slab of gas (de Jong et al. 1980) is equal to (2)The isotopic abundance ratio 12C/13C  ≃  60 (Langer & Penzias 1990; Savage et al. 2002) is almost twice the line intensity ratio between formaldehyde and its isotopologue, and therefore the H2CO lines have moderate opacities. From the observations we estimate τ212 − 211 ~ 1.6 and τ202 − 101 ~ 1.9 for H2CO in the dense-core.

3.2.2. Rotational diagram analysis

First-order estimates of the beam-averaged column densities and the rotational temperatures can be found by means of the widely used rotational diagram analysis (Goldsmith & Langer 1999). To do this, we assume that the gas is under LTE, and therefore all excitation temperatures are the same, and the energy levels are populated following Boltzmann’s law. We built rotational diagrams corrected for line-opacity effects through (3)where N is the total column density of the molecule, gu is the level degeneracy, Eu/k is the energy of the upper level in K, Z is the partition function at the rotational temperature Trot, is a line-opacity correction factor, where τ is the opacity of the line, and is the column density of the upper level for an optically thin line when the source fills the beam. This last parameter is given by (4)where k is the Boltzmann constant, ν is the line frequency, W is the integrated line intensity, h is the Planck constant, c is the speed of light and Aul is the Einstein coefficient for spontaneous emission.

Ortho- and para forms of H2CO are treated as different species because radiative transitions between them are forbidden. Resulting rotational diagrams are shown in Fig. 5 for three different o - H2CO   (212 − 111) and p - H2CO   (202 − 101) line-opacities (τ = 0,1 and 5). We find column densities of N ~ 1012 − 1013   cm-2, depending on the opacity. We infer very different rotational temperatures for o - H2CO (Trot ~ 4−8 K) and p - H2CO (Trot ~ 10−30 K), which are also lower than the well-known conditions in the PDR (Tkin ~ 60 K) and in the dense-core (Tkin ~ 20 K). This suggests that the gas is far from thermalization, and therefore we used these column densities and rotational temperatures as an input for a more complex analysis to derive the H2CO column densities.

thumbnail Fig. 5

H2CO rotational diagrams corrected for line-opacity effects at the PDR and dense-core position. Rotational temperatures are shown for each considered opacity.

Table 4

H2CO critical densities (cm-3) for three different colliding partners computed for Tkin = 60 K.

3.2.3. Radiative transfer models

The critical density of a given collisional partner corresponds to the density at which the sum of spontaneous radiative de-excitation rates is equal to the sum of collisional de-excitation rates (γ) of a given level (5)Formaldehyde lines have high critical densities (~106   cm-3, see Table 4) compared to the H2 density in the Horsehead (~104 − 105   cm-3). Because we expect subthermal emission (Tex    ≪    Tkin) for transitions with high critical densities compared to the H2 density, we used a nonlocal non-LTE radiative transfer code adapted to the Horsehead geometry to model the observed H2CO line intensities (Goicoechea et al. 2006). We used a nonlocal code to take into account the radiative coupling between different cloud positions that might affect the population of the energy levels. The code is able to predict the line profiles. It takes into account line trapping, collisional excitation and radiative excitation by absorption of cosmic microwave background and dust continuum photons. We included 40 rotational levels for o - H2CO and 41 rotational levels for p - H2CO, where the maximum energy level lies at  ~285 K for both species. We considered o - H2, p - H2 and He as collision partners with the following collisional excitation rates:

  • collisional rates of o - H2CO and p - H2CO with He are taken from Green (1991);

  • collisional rates of o - H2CO with o - H2 and p - H2 from Troscompt et al. (2009) for the first 10 energy levels, i.e. Eu ≤ 50 K. We complemented these data with He collision rates of Green (1991) scaled to H2. Following the new H2CO − H2 collisional rate calculations, we scaled the H2CO − He rates by a factor 2.5 instead of the usual  ~1.4 mass factor (A. Faure, priv. comm.);

    Table 5

    Column densities and abundances.

  • collisional rates of p - H2CO with o - H2 and p - H2 from Troscompt et al. (to be submitted).

Results are presented in Fig. 3 for three different column densities. Best matches (see Table 5) are for column densities of N(o - H2CO) = 7.2    ×    1012   cm-2 and N(p - H2CO) = 3.6    ×    1012   cm-2 in the PDR position, and N(o - H2CO) = 9.6    ×    1012   cm-2 and N(p - H2CO) = 3.2    ×    1012   cm-2 in the dense-core position. In the excitation- and radiative transfer models we adopt an H2 ortho-to-para ratio of 3 (high-temperature limit), although it is likely that the ortho-to-para ratio is lower in the Horsehead (e.g., Habart et al. 2011). Indeed, the H2CO column densities are not sensitive to the change of the H2 ortho-to-para ratio for the physical conditions of the Horsehead (see Appendix A).

3.3. H2CO ortho-to-para ratio

The ratio between the column densities of o - H2CO and p - H2CO provides information about the formation of the molecule, because the characteristic conversion time from one symmetry state to the other is longer than the H2CO lifetime (Tudorie et al. 2006). When the molecule forms in the gas-phase, a ratio of 3 is expected, which corresponds to the statistical weight ratio between the ground states of the ortho- and para species. A ratio lower than 3 is expected when the molecule is formed on the surface of cold (Tdust ≲ 20 K) dust grains (Kahane et al. 1984; Dickens & Irvine 1999). From the derived column densities we infer H2CO ortho-to-para ratios of  ~2 in the PDR and of  ~3 in the dense-core. This suggests that in the dense-core H2CO is mainly formed in the gas-phase, whereas in the PDR H2CO is formed on the surface of dust grains. Dickens & Irvine (1999) measured H2CO ortho-to-para ratios between 1.5 and 2 toward star-forming cores with outflows, and ratios near 3 toward three quiescent cores. Jørgensen et al. (2005) also found an ortho-to-para ratio of 1.6 in the envelopes around low-mass protostars.

3.4. HDCO and D2CO column densities

We detected HDCO and D2CO in the dense-core (see two bottom rows in Fig. 4), and we estimated their abundances assuming LTE. For Tex = 6 K we obtain N(HDCO) = 1.6 × 1012   cm-2, N(D2CO) = 5.1 × 1011   cm-2 and a D2CO ortho-to-para ratio of 1, which translates into relative abundances or fractionation levels [HDCO]/ [H2CO] = 0.11 and  [D2CO]/ [H2CO] = 0.04 for the inferred formaldehyde column densities in the dense-core.

Deuterium fractionation can occur in the gas-phase by means of ion-molecule reactions, where D is transferred from HD to other species. High abundances of deuterated molecules compared to the elemental D/H abundance (~1.5 × 10-5, Linsky et al. 2006) have been observed in different astrophysical environments, from cold dense cores and hot molecular cores even to PDRs. Pety et al. (2007) found high deuteration ([DCO + ]/[HCO + ] > 0.02) in the Horsehead dense-core. A pure gas-phase chemical model was able to reproduce the observed fractionation level of HCO+ for Tkin ≤ 20 K. Parise et al. (2009) found high fractionation levels for DCN and HDCO toward the Orion Bar PDR ([XD]/[XH]  ~ 0.01). They found that these ratios are consistent with pure gas-phase chemistry models where the gas is warm (>50 K), so the deuterium chemistry is driven mainly by CH2D+, as opposed to colder regions (≲20 K) like the Horsehead dense-core, where H2D+ is the main actor. Owing to the low temperature in the core it is likely that a non-negligible fraction of CO is frozen on the dust grains, enhancing the deuterium fractionation.

Another way to form deuterated molecules in cold environments is trough D addition or H-D substitution reactions on the surface of dust grains (Hidaka et al. 2009). In the Horsehead core though, desorption from the grain mantles is not efficient in releasing products into the gas-phase (see Sect. 4). It is then more likely that the gas-phase HDCO and D2CO molecules detected here are formed in the gas-phase. Nevertheless, there can still be a considerable amount of deuterated H2CO trapped in the ices around dust grains.

4. H2CO chemistry

We used a one-dimensional, steady-state photochemical model (Le Bourlot et al. 1993; Le Petit et al. 2006) to study the H2CO chemistry in the Horsehead. The physical conditions have already been constrained by our previous observational studies and we keep the same assumptions for the density profile (displayed in the upper panel of Fig. 6), radiation field (χ = 60 in Draine units), elemental gas-phase abundances (see Table 6 in Goicoechea et al. 2009b) and cosmic ray ionization rate (ζ = 5 × 10-17   s-1).

Unlike other organic molecules like methanol, which can only be efficiently formed on the surface of grains (Tielens & Whittet 1997; Woon 2002; Cuppen et al. 2009), formaldehyde can be formed in both the gas-phase and on the surface of grains. Next, we investigate these two different scenarios.

thumbnail Fig. 6

Photochemical model of the Horsehead PDR. Upper panel: PDR density profile (nH = n(H) + 2n(H2) in    cm-3). Middle panel: predicted abundance (relative to nH) of H2CO (blue) and HCO (red). Lower panel: predicted HCO/H2CO abundance ratio. In the two bottom panels, models shown as solid lines include pure gas-phase chemistry and models shown as dashed lines include gas-phase as well as grain surface chemistry. The horizontal bars show the measured H2CO abundances and abundance ratios.

4.1. Pure gas-phase chemistry models

We used the Ohio State University (osu) pure gas-phase chemical network upgraded to photochemical studies. We included the photo-dissociation of HCO and of H2CO (leading to CO and H2) with rates of 1.1 × 10-9exp( − 0.8AV) and 10-9exp( − 1.74AV)   s-1, respectively (van Dishoeck 1988). We also included the H2CO photo-dissociation channel that leads to HCO and H (see e.g., Yin et al. 2007; Troe 2007) with the same rate of the one that leads to CO and H2, and the atomic oxygen reaction with the methylene radical (CH2) to explain the high abundance of HCO in the PDR (Gerin et al. 2009).

The predicted HCO and H2CO abundance profiles and the HCO/H2CO abundance ratio are shown as solid lines in Fig. 6 (middle and lower panel, respectively). The formation of H2CO in the PDR and dense-core is dominated by reactions between oxygen atoms and the methyl radical (CH3). The destruction of H2CO in the PDR is dominated by photo-dissociation, while it is dominated by reactions with ions in the dense-core. The pure-gas phase model satisfactorily reproduces the observed H2CO abundance in the dense-core (δx ~ 35′′) but it predicts an abundance in the PDR (δx ~ 15′′) that is at least one order of magnitude lower than the observed value.

4.2. Grain chemistry models

We considered the surface chemistry reactions introduced by Stantcheva et al. (2002), which include the following sequence of hydrogen addition reactions on CO to form formaldehyde and methanol We also introduce water formation via hydrogenation reactions of O, OH until H2O.

Adsorption, desorption and diffusive reactions were introduced in the Meudon PDR code in the rate equations approach. The corresponding implementation will be described in a specific paper (Le Bourlot et al., to be submitted) and we simply mention the main processes included in the present study. We distinguish between mantle molecules, which may accumulate in several layers (e.g., H2O,H2CO,CH3OH), and light species (e.g., H, H2), which stay on the external layer. Photo-desorption can be an efficient mechanism to release molecules to the gas phase in regions exposed to strong radiation fields, as shown recently in laboratory studies (Öberg et al. 2009b,a; Muñoz Caro et al. 2010). Thermal desorption is also introduced. It critically depends on the desorption barrier values, which are somewhat uncertain. Diffusive reactions occur on grain surfaces and the diffusion barriers are assumed to be 1/3 of the desorption energy values. Photodesorption efficiencies have been measured in the laboratory for CO, CO2, H2O and CH3OH. These experiments have shown that all common ices have photodesorption yields of a few 10-3 molecules per incident UV photon (Öberg et al. 2007, 2009a,b,c). Therefore, we also take a photo-desorption efficiency of 10-3 for those species that have not been studied in the laboratory. We assume in addition that for formaldehyde the two branching ratios toward H2CO and HCO+H channels are identical, i.e. 5 × 10-4. Given the high density in the dense-core, the grains are assumed to be strongly coupled to the gas in the inner region, so that their temperatures become equal to 20 K in the dark region, whereas the illuminated dust grains reach temperature values of about 30 K.

The predicted HCO and H2CO abundances are shown as dashed lines in Fig. 6. This model reproduces the observed H2CO abundance in the dense-core and predicts a similar abundance as the pure gas-phase model. This way, formation on grain surfaces does not contribute significantly to the observed gas-phase H2CO abundance in the dense-core. This is because of the low photo-desorption rates in the core caused by the shielding from the external UV field. On the other hand, the H2CO abundance can increase by up to three orders of magnitude in the illuminated part of the cloud (AV ≲ 4) when including the grain surface reactions. The H2CO abundance now even peaks in the PDR, while it peaked in the dense-core in the pure gas-phase model. The model predicts a H2CO abundance peak in the PDR that is higher than the observed abundance averaged over the 30 m (~16′′). This limited resolution prevents us from resolving the predicted abundance peak. Interferometric observations are needed to prove the existence of this peak in the PDR.

5. Discussion

H2COhas been detected in a variety of different astrophysical environments, with a wide range of gas temperatures and densities. It has been detected in diffuse clouds with high abundances (~10-9), observed in absorption against bright HII regions (e.g., Liszt & Lucas 1995; Liszt et al. 2006). It is not well understood how H2CO can be formed and survive in such harsh environments, because gas-phase process cannot compete with the photo-dissociation and dust grain temperatures are too high for molecules to freeze on their surfaces. Roueff et al. (2006) detected absorption lines of H2CO at 3.6 μm toward the high-mass protostar W33A, and estimated an H2CO abundance of  ~10-7 where the gas has a temperature of  ~100 K. Recently, Bergman et al. (2011) found H2CO abundances  ~5 × 10-9 in the ρ Ophiuchi A cloud core. Abundances of H2CO and other more complex molecules toward hot cores and protostars are high. In these regions the gas is dense and hot, so the dust grains also have high temperatures (>100 K). Therefore, the ice mantles, formed in the cold pre-stellar phase, are completely evaporated. Once these molecules are in the gas-phase, they trigger an active chemistry in the hot gas, forming even more complex molecules (Charnley et al. 1992).

H2COhas also been observed in other PDRs. Leurini et al. (2010) detected H2CO in the Orion Bar PDR toward both the clump (nH ~ 106   cm-3) and the inter-clump (nH ~ 104   cm-3) gas components. They found higher H2CO abundances (~10-9 − 10-7) than the ones inferred in this work for the Horsehead (~10-10). Molecules trapped in the ice mantles can be thermally desorbed when the dust grains are warm enough. The dust temperature at which a significant amount of H2CO evaporates can be estimated by equating the flux of desorbing molecules from the ices to the flux of adsorbing molecules from the gas (see Eq. (5) in Hollenbach et al. 2009). Taking an H2CO desorption energy of 2050 K (Garrod & Herbst 2006), we obtain an evaporation temperature of  ~41 K. In the Orion Bar the dust grains have temperatures of Tdust > 55−70 K, so molecules can be desorbed from the icy mantles both thermally and non-thermally. But in the Horsehead PDR dust grains are colder (Tdust ~ 20−30 K), therefore molecules can only be desorbed non-thermally. Hence, the main desorption mechanism in the PDR is photo-desorption. In this respect, the Horsehead PDR offers a cleaner environment to isolate the role of FUV photo-desorption of ice mantles. In the Horsehead dense-core dust grains are also cold (~20 K), but photo-desorption is not efficient because the dust is shielded from the external UV field. Cosmic rays can desorb molecules from the ice mantles, but this contribution is not significant because the desorption rates are too low compared to the H2CO formation rates in the gas-phase. Both the measured H2CO abundance and ortho-to-para ratio agree with the scenario in which H2CO in the dense-core is formed in the gas phase with no significant contribution from grain surface chemistry.

We have shown that photo-desorption is an efficient mechanism to form gas-phase H2CO in the Horsehead PDR. But, to understand the importance of grain surface chemistry over gas-phase chemistry in the formation of complex organic molecules, a similar analysis of other molecules, such as CH3OH and CH2CO, is needed. In particular, CH3OH is one of final products in the CO hydrogenation pathway on grain surfaces. It can also form H2CO when it is photo-dissociated. Therefore, their gas-phase abundance ratios will help us to constrain their dominant formation mechanism and the relative contributions of gas-phase and grain surface chemistry. Similar studies in different environments will also bring additional information about the relative efficiencies of the different desorption mechanisms.

6. Summary and conclusions

We have presented deep observations of H2CO lines toward the Horsehead PDR and a shielded condensation less than 40′′ away from the PDR edge. We complemented these observations with a p - H2CO emission map. H2CO emission is extended throughout the Horsehead with a relatively constant intensity and resembles the 1.2 mm dust continuum emission. H2CO beam-averaged abundances are similar (≃2–3 × 10-10) in the PDR and dense-core positions. We infer an equilibrium H2CO ortho-to-para ratio of  ~3 in the dense-core, while in the PDR we find a non-equilibrium value of  ~2.

For the first time we investigated the role of grain surface chemistry in our PDR models of the Horsehead. Pure gas-phase and grain surface chemistry models give similar results of the H2CO abundance in the dense-core, both consistent with the observations. This way, the observed gas-phase H2CO in the core is formed mainly trough gas-phase reactions, with no significant contribution from surface process. In contrast, photo-desorption of H2CO ices from dust grains is needed to explain the observed H2CO gas-phase abundance in the PDR, because gas-phase chemistry alone does not produce enough H2CO. These different formation routes are consistent with the inferred H2CO ortho-to-para ratios. Thus, photo-desorption is an efficient mechanism to produce complex organic molecules in the PDR. Because the chemistries of H2CO and CH3OH are closely linked, we will continue this investigation in a next paper by studying the chemistry of CH3OH in detail.

1

See http://www.iram.fr/IRAMFR/GILDAS for more information about the GILDAS softwares.

Acknowledgments

We thank A. Faure and N. Troscompt for sending us the p - H2CO – o - H2 and p - H2CO – p - H2 collisional rates prior to publication. We thank the referee for a careful reading of the manuscript and interesting comments. V.G. thanks support from the Chilean Government through the Becas Chile scholarship program. This work was also funded by grant ANR-09-BLAN-0231-01 from the French Agence Nationale de la Recherche as part of the SCHISM project. J.R.G. thanks the Spanish MICINN for funding support through grants AYA2009-07304 and CSD2009-00038. J.R.G. is supported by a Ramón y Cajal research contract from the Spanish MICINN and co-financed by the European Social Fund.

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Appendix A: H2 ortho-to-para ratio

thumbnail Fig. A.1

Radiative-transfer modeling of H2CO lines for the core position in the Horsehead. The two top rows display the ortho lines and the bottom row displays the para lines. The best-match models are given in colors (Tkin = 20 K, n(H2)    =    105   cm-3, N(o - H2CO) = 9.6    ×    1012   cm-2, N(p - H2CO) = 3.2    ×    1012   cm-2), taking a H2 ortho-to-para ratio of 3 (red lines) and of 0 (green lines).

We investigated the influence of the H2 ortho-to-para ratio adopted in the excitation and radiative transfer models. In Fig. A.1 we show the best-match models for the H2CO lines toward the core position in the Horsehead assuming two different values for the H2 ortho-to-para ratio. We show models for an H2 ortho-to-para ratio of 3 in red (high temperature limit), and we show models for the extreme case where the H2 ortho-to-para ratio is 0 in green (low temperature limit). The difference between the models is less than 10%, which is within the observational uncertainties and therefore not significant.

All Tables

Table 1

Observation parameters for the maps shown in Fig. 1.

In the text
Table 2

Observation parameters of the deep integrations of the o - H2CO and p - H2CO lines toward the PDR and the dense-core.

In the text
Table 3

Spectroscopic parameters of the observed lines obtained from the CDMS data base (Müller et al. 2001).

In the text
Table 4

H2CO critical densities (cm-3) for three different colliding partners computed for Tkin = 60 K.

In the text
Table 5

Column densities and abundances.

In the text

All Figures

thumbnail Fig. 1

Integrated intensity maps of the Horsehead edge. The intensities are expressed in the main-beam temperature scale. Maps were rotated by 14° counter-clockwise around the projection center, located at (δx,δy) = (20′′,0′′), to bring the exciting star direction in the horizontal direction and the horizontal zero was set at the PDR edge, delineated by the red vertical line. The crosses show the positions of the PDR (green) and the dense-core (blue), where deep integrations were performed at IRAM-30m (see Fig. 3). The spatial resolution is plotted in the bottom left corner. Values of contour levels are shown on each image lookup table. The emission of all lines is integrated between 10.1 and 11.1   km   s-1.
In the text
thumbnail Fig. 2

Lower energy rotational levels of para- (left) and ortho-H2CO (right). The energy above para ground-state is shown at the left of each level. The arrows indicate the transitions detected in the Horsehead.
In the text
thumbnail Fig. 3

Radiative transfer modeling of H2CO lines for two positions toward the Horsehead. Two left columns: the PDR position (Tkin = 60 K, n(H2)    =    6    ×    104   cm-3, N(o - H2CO) = 7.2    ×    1012   cm-2) and two right columns: the dense-core position (Tkin = 20 K, n(H2)    =    105   cm-3, N(o - H2CO) = 9.6    ×    1012   cm-2). The two top rows display the ortho lines, for which we varied the column density around the best match (red curve) by a factor of 1.5 (blue curve) and 1/1.5 (green curve). The two bottom rows display the para lines, for which we kept the column density of the best match for o - H2CO (red curves) constant and varied the ortho-to-para ratio of H2CO: o/p = 1.5 (dashed blue), o/p = 2 (dashed red) and o/p = 3 (dashed green).
In the text
thumbnail Fig. 4

and deuterated H2CO lines detected toward the dense-core. Gaussian fits are shown with red lines. For HDCO and D2CO the line width was fixed to the width of the HDCO (211 − 110) line, because it has the best signal-to-noise ratio.

In the text
thumbnail Fig. 5

H2CO rotational diagrams corrected for line-opacity effects at the PDR and dense-core position. Rotational temperatures are shown for each considered opacity.
In the text
thumbnail Fig. 6

Photochemical model of the Horsehead PDR. Upper panel: PDR density profile (nH = n(H) + 2n(H2) in    cm-3). Middle panel: predicted abundance (relative to nH) of H2CO (blue) and HCO (red). Lower panel: predicted HCO/H2CO abundance ratio. In the two bottom panels, models shown as solid lines include pure gas-phase chemistry and models shown as dashed lines include gas-phase as well as grain surface chemistry. The horizontal bars show the measured H2CO abundances and abundance ratios.

In the text
thumbnail Fig. A.1

Radiative-transfer modeling of H2CO lines for the core position in the Horsehead. The two top rows display the ortho lines and the bottom row displays the para lines. The best-match models are given in colors (Tkin = 20 K, n(H2)    =    105   cm-3, N(o - H2CO) = 9.6    ×    1012   cm-2, N(p - H2CO) = 3.2    ×    1012   cm-2), taking a H2 ortho-to-para ratio of 3 (red lines) and of 0 (green lines).
In the text

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