Volume 575, March 2015
|Number of page(s)||22|
|Section||Interstellar and circumstellar matter|
|Published online||02 March 2015|
The population diagram method is a common tool for deriving physical gas conditions from molecular line observations (see Goldsmith & Langer, 1999, for a classic reference). It relies on two major assumptions: i) optically thin emission and ii) LTE conditions. The latter assumption (LTE) implies that the populations of all levels are described by the Boltzmann distribution with a unique rotational temperature, Trot6, which is equal to the kinetic temperature of the gas (Tkin = Trot). In this case, for a given molecule and a series of transitions u → l, a plot of the natural logarithm of the upper state column density per statistical weight (Nu/gu) versus the energy above the ground (Eu), the so-called population diagram, will yield a straight line with a slope 1/Trot.
Goldsmith & Langer (1999) have numerically investigated how the optical depth and deviations from LTE affect the temperature and column density derived using the population diagram technique for two molecules: HC3N and CH3OH. In this appendix, we perform a similar analysis for HNCO, HNCS, HC3N, and NO, but in this case, we focus on non-LTE excitation effects since the lines detected in OH 231.8+4.2 are optically thin. (For HC3N we compared our results, analysing both optical depth and non-LTE excitation effects, with those by Goldsmith & Langer 1999 and found an excellent agreement.)
In low-density regions7, LTE may not be a valid approximation, and therefore, the level populations, which may not longer be described well by the Boltzmann distribution, have to be numerically computed by solving the statistical equilibrium and radiation transport equations. The excitation analysis presented in this Appendix has been done using MADEX (Molecular and Atomic Database and EXcitation code, Cernicharo, 2012). This is a code that solves the molecular excitation (including collisional and radiative excitation mechanisms) and radiation transfer problem under the large velocity gradient (LVG) formalism. It contains up-to-date spectroscopy (rest frequencies, level energies, line strength/Einstein coefficients, etc.) and collisional rates available from the literature for more than 5000 different molecular and atomic entries including isotopologues and vibrationally excited states. MADEX computes molecule-H2 collisional rates from those available in the literature by adopting other collision partners, such as He or para-H2. MADEX also evaluates the partition function of the molecule (using a large enough number of levels to obtain accurate values of the partition function even at high temperatures) and predicts the emergent spectra.
To examine what happens if some or all of the transitions of HNCO, HNCS, HC3N, and NO are not thermalized, we computed the level populations for a range of densities, nH2, and a given input value of Tkin and Ntot for each molecule. The adopted values of Tkin and Ntot are similar to those obtained from the LTE analysis (Sect. 4.1). We assumed a linear velocity gradient d(lnV)/d(lnr) = 1 and typical line widths of FWHM = 20–40 km s-1, as observed towards OH 231.8+4.2 (Sects. 1 and 3). The resulting population diagrams based on our non-LTE excitation calculations, including the LTE theoretical points, are shown in Fig. A.1.
For HNCO we used collisional rates from Green (1986)8, computed for the lowest 164 levels at temperatures from 30 to 350 K. For the non-LTE analysis, we considered rotational levels in the ground vibrational state (v = 0) up to Jmax = 18 for both the Ka = 0 and Ka = 1 ladder transitions (and also up to Ka = 4, which has been included in the calculations). This implies a maximum upper state energy of 830 K. As shown in Fig. A.1 (top left box), for the lowest density models (nH2 = 105cm-3), there is a notable separation between the Ka = 0 and Ka = 1 ladders, which follow two straight lines with different slopes. The slope of the Ka = 0 ladder implies a rotational temperature of Trot~ 16 K, which is lower than the real input kinetic temperature (sub-thermal excitation), while the slope of the Ka = 1 ladder implies a rotational temperature of Trot~ 30 K. The y-offset between the two Ka ladders decreases as the density increases, until they merge in a single line at densities nH2≳ 108cm-3, with Trot = Tkin.
Population diagrams of HNCO, HNCS, HC3N, and NO for a range of molecular hydrogen densities (nH2, bottom left corner) and a given input value for the kinetic temperature and total column density (Tkin and Ntot; top right corner); the dotted line connects the LTE points. Only the transitions detected in this work are represented in this diagram (Table 3). For HNCO, the transitions within the Ka = 0 and Ka = 1 ladders are indicated by empty and filled symbols, respectively. For NO, we plot the three hyperfine components with the highest values of the Einstein coefficient (Aul) for each of the Π− and Π+ doublets at 250 and 350 GHz (i.e. at Eu = 19.2 and 36.1 K), the three hyperfine components with the largest Aul of the Π+ band at 150 GHz (i.e. at Eu = 7.2 K) and the Π−(3/2,3/2)–(1/2,1/2) line, which is spectrally isolated in our data, at 150 GHz (Eu = 7.2 K). These calculations have been done with a LVG radiative transfer code (MADEX) – see text in this appendix.
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Collisional rates are not available for HNCS, therefore we used those of HNCO after applying the standard reduced mass correction. As for HNCO, we included rotational levels of up to Jmax = 18 (within the Ka = 0, 1, and 2 ladders), which implies maximum upper state energies of Eu~ 355 K. As expected, deviations from LTE affect the population diagram of HNCS similarly to HNCO. In the case of HNCS, only the Ka = 0 ladder has been plotted since these are the only ones detected. For the lowest density model, nH2 = 104 cm-3, the inferred values of Trot~ 10–12 K deviate significantly from the real input values (Tkin = 25 K).
Collisional rates for HC3N are from Wernli et al. (2007), which include 51 levels and are computed for temperatures between 5 K and 100 K. Collisional rates for NO are adopted from Kłos et al. (2008), computed for 98 rotational levels and temperatures between 10 and 500 K. The highest rotational levels included in our non-LTE excitation calculations for HC3N an NO are Jmax = 30 (Eumax ~ 200 K) and Jmax = 13 / 2 (Eumax ~ 300 K), respectively. The resulting non-LTE models for HC3N and NO (Fig. A.1), as for the other species, clearly show steeper slopes (Trot<Tkin) for the lowest density models. Another effect of non-LTE excitation is that the different level populations cannot be described by a unique rotational temperature, which translates into a different slope for the low-J and high-J levels in the population diagram. This effect is most notable for HC3N: the temperatures implied are Trot~ 5 K for the three lowest-J levels and Trot~ 7 K for the four highest-J levels. The HC3N column densities that one would derive using low-J or high-J levels are also different, in particular, Ntot(low-J) = 3.3 × 1013 cm-3>Ntot = 3.0 × 1013 cm-3>Ntot(high-J) = 7.2 × 1012 cm-3. In the lowest density model of NO, the implied Trot (<Tkin = 26 K) does not vary appreciably across the different levels (less than 6%).
For all molecules, at the highest densities considered, the populations of the levels considered are thermalized or very close to thermalization, and the non-LTE and LTE predictions converge. In both cases, the data points in the population diagram can be satisfactorily fit by a straight line with Trot = Tkin. We consider of interest to provide a summary with the range of critical densities for the transitions analysed in this work. These are for a representative temperature of 25 K, which is common in the dominant emitting components of AGB CSEs and PPNs (Bujarrabal et al., 2001). For HNCO the critical densities are in the range of ncrit = [4 × 105–1 × 107] cm-3 for the Ka = 0 transitions, and ncrit = [1 × 106–1 × 107] cm-3 for the Ka = 1 transitions. For HNCS, HC3N, and NO, the critical densities are ncrit = [5 × 105–2 × 106] cm-3, ncrit = [1 × 106–3 × 106] cm-3, and ncrit = [2 × 104–2 × 106], respectively. In all these cases, the lowest value of ncrit in the ranges given above corresponds to the lowest-J and/or lowest-Eu transition.
Finally, we briefly comment on the possible effect of the pumping of the rotational levels of HNCO by the infrared (IR) photons emitted by the star and the central dust region (see e.g. Kuan & Snyder, 1996). This IR emission would cause the radiative pumping of levels inside the ground vibrational state and the vibrationally excited states of HNCO. The latter would eventually produce a fluorescence effect between the ground state and the six vibrational modes of HNCO. The radiative pumping inside the rotational levels of the ground state alone was found to be dominant in the HNCO excitation in Sgr B2 (Churchwell et al., 1986). In this region, the typical densities are relatively low, n(H2) ~ 104 cm-3, but the central source is optically thick at 100 μm and extended. The IR pumping through vibrationally excited states, has also noticeable effects in the emerging intensities of some rotational lines for certain molecules like H2O in IRC+10216 (Agúndez & Cernicharo, 2006). Recently, it has been pointed out that the time variability of the IR pumping can produce intensity variations in the high rotational lines of abundant molecules in the envelopes of Mira-type stars, such as CCH towards IRC+10216 (Cernicharo et al., 2014). Thus, to summarize, transitions with high upper level energies or those that are severely underexcited by collisions could be more sensitive to IR pumping. When HNCO levels were populated mainly by IR radiation, the column density implied by the rotational diagram method could be different than the true value; the rotational temperature would also be different than the gas kinetic temperature (but see next paragraph).
Our previous discussion of the excitation state of the observed lines of HNCO shows that they are practically thermalized to the temperatures expected in the studied nebula. The population diagram of HNCO (Fig. 9) covers a wide range of upper energies, and it clearly shows a single slope for both the Ka = 0 and Ka = 1 transitions. This should imply that the line intensities are described well by one rotational temperaure, so that the column density and the derived abundance should be close to the true value. Also, the range of derived kinetic temperatures is consistent with previous estimations of the rotational temperatures and the kinetic temperature in the CO flow (see e.g. Guilloteau et al., 1986; Morris et al., 1987; Alcolea et al., 2001). Finally, the bulk of the emission of HNCO (Sect. 3) arises from the central dense region of the CSE (I3) and the base of the southern lobe (I4). These regions are characterized by densities of n(H2) ≥ 106–107 cm-3 in the central region and n(H2) ≥ 105 cm-3 in the lobes (Alcolea et al., 2001; Bujarrabal et al., 2002). This leads to densities close or higher than the critical densities for HNCO Ka = 0 and Ka = 1 transitions. Therefore, the effects of vibrational cascades should be minor in our case, but we cannot rule out uncertainties in the abundance of HNCO less than a factor 2–5. On the other hand, we have seen that the excitation via the various vibrational states is extremely complex for these relatively heavy molecules. A detailed study of these intricate phenomena is obviously beyond the scope of this paper.
Isocyanic acid has been detected in different environments with a variety of physical conditions, including SgrB2 (Snyder & Buhl, 1972), the Taurus Molecular Cloud TMC-1 (Brown, 1981), external galaxies (Nguyen-Q-Rieu et al., 1991), the shocked-outflow of the young stellar object L1157 (Rodríguez-Fernández et al., 2010), hot cores (Churchwell et al., 1986; Martín et al., 2008), translucent clouds (Turner et al., 1999), etc. Nevertheless, prior to this work, HNCO was not detected in any CSE around evolved stars, either oxygen or carbon rich.
Formation of HNCO through gas-phase and grain surface chemistry from different chemical pathways has been studied by several authors (Iglesias, 1977; Turner et al., 1999; Zinchenko et al., 2000; Garrod et al., 2008; Marcelino et al., 2010; Quan et al., 2010). This molecule was first proposed as a high density tracer (Jackson et al., 1984) and, more recently, a shock tracer (Rodríguez-Fernández et al., 2010, and references therein).
The fractional abundance of HNCO varies somewhat in different sources, typically within the range ≈10-10–10-9. The highest fractional abundance (relative to H2) of HNCO has been measured towards the shocked region of the L1157 outflow, L1157-B2, where X(HNCO) ~9.6 × 10-8 (Rodríguez-Fernández et al., 2010). Interestingly, this value of the abundance is comparable to what is estimated towards OH 231.8+4.2.
Isothiocyanic acid was first detected in SgrB2 (Frerking et al., 1979) and has been recently observed in TMC-1 (Adande et al., 2010). Detection of HNCS in a CSE has not been reported previously to this work.
The formation of HNCS in the cold core TMC-1 and the hot core in SgrB2 has been studied theoretically through gas-phase, ion-molecule chemistry and grain surface reactions (Adande et al., 2010). Prior to this work, the highest abundance of HNCS had been found towards SgrB2 and TMC-1, with a value of ≈10-11. In OH 231.8+4.2 we derive a fractional abundance of HNCS that is about 1000 times higher.
Cyanoacetylene is detected in assorted environments, including SgrB2 (Turner, 1971), H II regions, dark clouds (Morris et al., 1976), the Orion molecular cloud (Goldsmith et al., 1982), the Perseus globules (Bachiller & Cernicharo, 1986), in the Taurus molecular clouds (Cernicharo et al., 1984), protoplanetary disks (Chapillon et al., 2012), etc. HC3N is also detected in several C-rich CSEs, including the well-known AGB star IRC+10216 and the protoplanetary nebula CRL 618 (e.g. Morris et al., 1975; Bujarrabal et al., 1994; Audinos et al., 1994; Cernicharo et al., 2000; Pardo et al., 2004); however, this molecule has not been identified before in an O-rich CSE.
HC3N is considered to be a high density tracer (Morris et al., 1976) and in CSEs, particularly in IRC+10216, it is distributed in a hollow spherical shell around the central star, which is a major product of photodissociation in the outer parts of the envelope (Audinos et al., 1994). The observed abundance in IRC+10216 is X(HC3N) ~1 × 10-6 agrees with theoretical predictions in C-rich CSEs (Agúndez et al., 2010). We infer X(HC3N) ~7 × 10-9 towards OH 231.8+4.2. This value is much lower than in IRC+10216 by virtue of the O-rich vs. C-rich nature of both sources.
Nitric oxide has been previously detected in several astrophysical environments, including molecular clouds (Gerin et al., 1992), SgrB2 (Halfen et al., 2001), and pre-protostellar cores (Akyilmaz et al., 2007). Recently, NO has been detected for the first time in the CSE around the yellow hypergiant (YHG) IRC+10420, which is a massive (~50 M⊙) evolved star with a N-rich chemistry (Quintana-Lacaci et al., 2013), with a fractional abundance of X(NO) ≈ 10-5.
Chemical models presented by Quintana-Lacaci et al. (2013) in IRC+10420 predict that indeed NO forms very efficiently by photochemistry (mainly through the reaction N + OH −→ NO + H) in the outer circumstellar layers, where it reaches a maximum abundance of ≈10-6. In the case of IRC+10240, nitrogen enrichment due to hot bottom burning has been proposed to explain the NO abundance observed, which is larger by a factor 10 than predicted by these models adopting the solar nitrogen abundance.
The sources of ionization and dissociation adopted in our model are cosmic rays and the interstellar ultraviolet radiation field. The cosmic-ray ionization rate adopted is 1.2 × 10-17 s-1 (Dalgarno, 2006). The intensity of the UV field assumed is the Draine field (X) or Go = 1.7 in units of the Habing field (Go = 1.6 × 103 erg s-1 cm-2; Habing 1968; Draine & Salpeter 1978). The ISM UV field illuminates the nebula externally.
We also evaluated two possible additional sources of internal ionization and dissociation in OH 231.8+4.2: 1) the UV radiation by the A0 main sequence companion of the primary AGB star (QX Pup) at the nucleus of the nebula; and 2) the high-energy radiation generated by the cooling of hot gas behind the fast shock fronts ahead of the lobe tips (Sect. 1). In both cases, the effect on the chemistry is not expected to be predominant and has not been considered in our model.
First, the UV radiation field emitted by the ~10 000 K main-sequence companion cannot penetrate very deep through the dense dusty wind of the AGB mass-losing star except, maybe, along the direction of the lobes owing to the lower extinction by dust along the outflow cavities (of the order of AV ~ 1 mag; Sánchez Contreras et al., 2004). However, there is observational evidence against the presence of a substantial amount of ionized or atomic gas in the stellar vicinity, hence against the existence of an intense stellar UV field that could have a noticeable effect on the chemistry in the inner regions of the lobes: (i) the lack of Hα emission (or any other recombination or forbidden lines in the optical) from the nucleus of OH 231.8+4.2 rules out an emergent ionized region around the star (Cohen et al., 1985; Reipurth, 1987; Sánchez Contreras et al., 2000a, 2004); and (ii) the lack of low-excitation atomic emission lines in the far-infrared, e.g. [O i] emission at 63.2 and 145.5 μm (unpublished Herschel archive data) indicates the absence of a photodissociation region (PDR) in the nebula centre. Moreover, considering the temperature and luminosity of the warm companion
(~10 000 K and ~5–30 L⊙; Sánchez Contreras et al., 2004), it can be demonstrated that the stellar UV flux that reaches to a point located at the inner edges of the lobes (~4′′ from the star) with a visual extinction of AV = 1.0 mag, would be smaller than, or at most comparable to, the ISM UV field. Therefore, including the stellar UV radiation as a source of internal illumination of the lobe walls in the model will yield very similar results (and even smaller molecular abundances for “daughter” species) to those obtained assuming external illumination by the ISM UV field.
Second, the shocks that are currently active in OH 231.8+4.2 are those traced by Hα emission, which arises in two bubble-like structures of shock-excited gas surrounding the molecular outflow (Reipurth, 1987; Sánchez Contreras et al., 2000a; Bujarrabal et al., 2002). These fast shocks may have been generated by interaction between the dense, fast molecular outflow and the tenuous ambient material. The characteristics of the exciting shocks have been studied in detail by Sánchez Contreras et al. (2000a). In particular, these authors compare the relative intensities of the different optical lines observed with the diagnostic diagrams by Dopita & Sutherland (1995), which can distinguish between shocks with or without a photoionized preshock region. These diagrams not only confirm the shock nature of the emission but also indicate that the emission from a photoionized precursor region is either weak or absent. We note, moreover, that even in the improbable case that sufficiently intense UV radiation from the current shocks is produced, its effect on the chemistry will be almost exclusively limited to the outflow regions immediately behind the shock fronts, that is, the molecular clumps at the very end of the lobes of OH 231.8+4.2. However, given the beam size of our observations (Fig. 1), the contribution of these molecular clumps to the total emission by the N-bearing molecules reported in this work is insignificant.
© ESO, 2015
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