The ¹⁷O/¹⁸O Ratio of Post-AGB Sources: Canonical and Non-Canonical Populations

Abstract

Stellar evolution models serve as tools to derive stellar parameters from elemental and isotopic abundance ratios. For low-to-intermediate mass evolved stars, C/O, ¹²C/¹³C, and ¹⁷O/¹⁸O ratios are proxies of the initial mass, a largely unknown parameter in post-AGB sources, yet fundamental to establish correlations with the main properties of their post-AGB envelopes, progressing in understanding their formation and evolution. In these sources, the C/O ratio can be constrained from the detection of C- or O-bearing species in addition to CO, while the ¹⁷O/¹⁸O ratio is straightforwardly determined from the C¹⁷O-to-C¹⁸O intensity ratio of rotational lines. However, the theory is at odds with the observations. We review the status of the question, including new accurate ¹⁷O/¹⁸O ratios for 11 targets (totaling 29). Comparing the results for the ¹⁷O/^$18$O ratios and C-rich/O-rich chemical composition, we find that ∼45% of the cases are canonical, i.e., the observations align with standard model predictions. O-rich non-canonical sources, with ^$17$O/^$18$O ratios above the expected, can be explained by a premature interruption of their AGB evolution as a consequence of a quasi-explosive ejection of a large fraction of the initial mass. For non-canonical C-rich sources, with ^$17$O/^$18$O ratios below predictions, we suggest the possibility they are extrinsic C-rich stars.

1. Elemental and Isotopic Ratios as Proxies of the Initial Stellar Mass in Post-AGB Sources

Low- to intermediate-mass stars (LIMS), with initial masses between 0.8 and 8 $M_{\odot }$, are responsible for the enrichment of carbon, nitrogen, and s- and i-process elements of the interstellar medium (ISM), as well as the major producers of cosmic dust. This recycling of matter mostly takes place at the end of LIMS’ lives, along the late asymptotic giant branch (late-AGB) and post-AGB phases, when more than one-half of the star’s initial mass is thrown back to the ISM via mass loss processes at copious rates [1,2,3,4]. During the AGB phase, stars experience gradual chemical changes due to the occurrence of several third dredge-up (TDU) events. All stars enter the AGB phase as O-rich (C/O < 1), but if the initial mass of the star is in the ∼1.5–4 $M_{\odot }$ range, the accumulated effect of the successive TDU events transform them into C-rich (C/O > 1) by the end of the AGB phase, while also increasing the ^$12$C/^$13$C ratio [1,3,5,6]. For masses above 4 $M_{\odot }$, the hot bottom burning (HBB) process transforms ^$12$C into ^$14$N, thus the stars remain O-rich, with a nitrogen increase in their composition. For masses below 1.5 $M_{\odot }$, the small number of TDU events along the AGB evolution of the star does not produce ^$12$C enrichment enough for the C-rich transformation to occur, the star remaining O-rich. The exact initial mass limits between O-rich, C-rich, and HBB stars depend on the metallicity (see [7] for a review on this topic). The initial mass boundaries between classes given before are valid for the solar metallicities expected in our targets [3,5,7,8]. Because of this ^$12$C enrichment, the ^$12$C/^$13$C ratio also increases along the AGB evolution, with final values of about 20 and lower for O-rich and HBB stars and larger values of 60 to more than 100 for stars in the C-rich range [5]. In principle, these elemental and isotopic ratios can be used to infer the initial mass of AGB stars; however, as these values change throughout the AGB evolution, this introduces a degree of uncertainty. For example, an O-rich target with a low ^$12$C/^$13$C may be a star below the transformation limit of 1.5 $M_{\odot }$ or a star destined to be C-rich but has not yet evolved far enough through the AGB phase for the ^$12$C-rich transformation to occur. Despite this, several authors have used these ratios to estimate masses for AGB stars [9,10,11,12]. Other abundance ratios do not present this problem as they do not vary during the AGB evolution and therefore can be more safely used to derive initial masses. This is the case of the ^$17$O/^$18$O ratio, which becomes fixed after the first dredge-up (FDU) during the previous red giant phase and remains practically constant along the AGB phase, except for HBB sources where it becomes very large very soon after the beginning of this phase with the occurrence of the second dredge up (SDU) and the destruction of ^$18$O via the ^$18$O(p,$\alpha$)^$15$N reaction [5,13]. Since the value of this isotopic ratio also depends on the initial mass, it can potentially be used to weigh LIMS [3,5,14,15,16]. According to these models, O-rich stars should show ^$17$O/^$18$O lower than one, while the opposite holds for C-rich sources, with HBB targets lacking ^$18$O [5,16,17,18].

This problem of not knowing the evolutionary status along the AGB of a target is sorted out if, instead of studying AGB stars, we focus our attention on post-AGB sources. Due to the intense mass loss that characterizes the AGB, LIMS gradually lose their fully convective stellar mantle, leaving the core exposed. At this point, the copious mass loss stops, signaling the end of the AGB phase. From here on, the stars rapidly evolve across the HR diagram, becoming extremely hot in several thousand years. At the same time, their surrounding nebulae, which resulted from the mass loss while on the AGB, also experience drastic changes, ultimately becoming planetary nebulae (PNe) when the central post-AGB source becomes hot enough to photo-dissociate and ionize the molecular gas. As a result of the strong UV radiation of their central stars (CSPNe), PNe are usually poor in molecular content. However, young-PNe (yPNe) and post-AGB nebulae whose central stars are not hot enough to efficiently emit UV photons, in-between objects termed pre-PNe (pPNe), are still rich in molecular gas and therefore are excellent targets to test the stellar mass proxies described before, with the advantage that we already know they have completed their AGB evolution. In these post-AGB sources, the composition of their surrounding nebulae should reflect that of the star at the end of the AGB phase, and in principle, we can safely use all three C/O, ^$12$C/^$13$C, and ^$17$O/^$18$O ratios to derive the initial mass of the progenitor star, test the consistency of all these three methods and the validity of the standard evolutionary models for these sources: see e.g., [19,20,21,22] for ^$12$C/^$13$C measurements in post-AGBs. Although the number of sources for which these ratios are available in the literature is small, it was soon realized that the theory is at odds with the observations. In addition to sources for which C/O and ^$17$O/^$18$O ratios suggest similar/compatible initial masses according to standard nucleosynthesis models, which we will denominate canonical hereafter, there is a significant number of sources with O-rich chemistry but with ^$17$O/^$18$O ratios larger than one that would correspond to C-rich stars: see the cases of the Water Fountains [23] and M 1–92 [24,25]. Similarly, we also find some chemically C-rich targets with low ^$17$O/^$18$O ratios typical of O-rich stars: see the case of 89 Her [19]. Given this puzzling situation, we decided to embark on a program to increase the number of targets with precise determination of these chemical and isotopic ratio proxies of the stellar mass, conclude the prevalence of non-canonical sources among the post-AGB population, and find out about their possible origin. Southern hemisphere targets are being observed with ALMA, while northern ones were observed with the IRAM 30 m MRT. Here, we present the results of our IRAM 30 m survey and summarize the status of the question after these and five new sources observed with ALMA [26].

2. Observations and Data Reduction

The new observations presented here were carried out at the 30-m diameter single-dish millimeter radio-telescope (30 m-MRT) operated by the Institut de Radioastronomie Millimétrique1. This facility is located on the Pico Veleta in Sierra Nevada (Spain) at an altitude of 2850 m. We used the Eight MIxer super-heterodyne Receiver (EMIR), which allows simultaneous observation over a bandwidth of up to 32 GHz. The observations were performed in the dual-band (E090 and E230 receivers at 3 mm and 1.3 mm respectively) single-sideband (LSB) dual-polarization mode (H + V), simultaneously covering two eight-Gigahertz wide frequency ranges, from 86.7 to 93.7 GHz (E090) and from 216.7 to 224.7 GHz (E230), in both polarizations (see Figure 1 and Figure 2). The E230 range covers the J = 2 − 1 lines of ^$13$CO, C^$17$O, and C^$18$O for determining the ^$17$O/^$18$O isotopic ratio. At the same time, the E090 frequencies were selected to cover several molecular lines of HCO⁺, HCN, HNC (and their ^$13$C substitutions), N_$2$H⁺, SO, and SO_$2$ to help in distinguishing the C-rich or O-rich nature of the target. The telescope provides a resolving power (HPWB) of 17′′ and 11′′ at 90 and 220 GHz, respectively. This resolution/beamwidth is enough for observing the whole molecular envelope of the targets with the single pointing we performed, except for the cases of NGC 7027, CRL 618, and CRL 2688, where the molecular emitting region is larger than the telescope beam. However, our results on the ^$17$O/^$18$O ratios and chemical types (C/O-richness) are not affected by the relative sizes of the telescope beam and the target, provided that we use the correct formula for deriving isotopic ratios from line intensity ratios (see Section 3, Equation(1)).

As a spectrometer, we used the fast Fourier transform (FFT) units covering the whole 32 GHz observed (8 GHz × 2 receivers × 2 polarizations) with a resolution of 200 kHz, equivalent to a velocity resolution of ∼0.67 and 0.27 km s⁻¹ at 90 and 220 GHz, respectively, though the data have been smoothed to a final velocity resolution of 3.25 km s⁻¹ for improving the S/N of the spectra. We follow the standard calibration procedure at Pico Veleta, observing hot and cold loads (at ambient and liquid nitrogen temperatures) and the blank sky approximately every 20 min. Hot and cold loads are used to scale spectrometer units into temperature units, while observing the sky brightness provides a measurement of the transmission properties of the local atmosphere via numerical modeling [27]. As a consequence, data from the spectrometer are delivered in (atmosphere-corrected) antenna temperature ($T_a^{*}$). The expected absolute calibration accuracy is about 10% for 3 mm data and 15% for 1.3 mm data. However, the relative calibration of the lines simultaneously observed within the same receiver, as in the case of ^$13$CO, C^$17$O, and C^$18$O, is nearly perfect.

The observations were performed by nodding the sub-reflector between the ON-source and OFF-source positions at a frequency of 0.5 Hz (wobbler switching mode, WSW). The OFF-position is acquired at a separation of ±60′′ in azimuth with respect to the target. This procedure ensures an optimal removal of the atmospheric and instrumental contribution to the signal, resulting in very flat baselines in the spectra. The ON–OFF subtractions are accumulated for 4.15 min. This process is repeated three times followed by a calibration of the data. Including overheads, this 3 × ON–OFF + Calibration cycle, which was the basic unit of our observing procedure, lasts for 17 min and results in a total effective ON–OFF integration time of 24.7 min (note that we are observing with two receivers, one for each polarization, simultaneously). The telescope’s pointing is good, with typical errors of about 2′′–4′′. Nevertheless, pointing was checked, and corrected if necessary, by observing strong continuum sources close in the sky to the science targets. This pointing check was performed when changing to a new target or every two hours, the corrections always being of the same order as the blind pointing accuracy. In any case, these errors have no impact on the relative calibration of the lines observed within the same band.

Data reduction has been performed using the Continuum and Line Analysis Single-dish Software (CLASS) program of the GILDAS2 astronomical software package (jul24b version). The process includes data inspection and flagging of bad scans/channels, averaging of valid data, averaging of H and V receivers, smoothing to 3.25 km s⁻¹ velocity resolution, removal of residual baselines, and recalibration into $T_{\mathrm{mb}}$ (main-beam temperature) scale. Only low-degree polynomials (usually of zero or first order) have been used for the baseline subtraction. For the conversion of the spectra from $T_a^{*}$ into $T_{\mathrm{mb}}$ scale, we have followed the directions in the EMIR for Astronomers user guide3. As an example of the results, in Figure 1 and Figure 2, we show the full H+V 8 GHz wide spectra for IRAS 21282+5050 after about one hour of telescope time (three basic observing procedure units plus pointing checks).

3. Results

As previously mentioned, we present in detail only the results obtained with the 30 m-MRT; our most recent ALMA results will be thoughtfully presented and discussed in a separate publication [26]. We have observed ten post-AGB sources without previously available C^$17$O/C^$18$O intensity ratios: the pPNe Frosty leo, IRAS 02229+6808, IRAS 17436+5005, IRAS 19475+3119, IRAS 19500–1709, IRAS 21282+5050, IRAS 22272+5435, IRAS 23304+6147, and IRAS 23321+ 6545, and the PN NGC 6781 (see

Table 1. Species other than ^$13$CO detected in our IRAM 30-m MRT survey of post-AGB sources.

Source Name	Species Detected	Chemical Type
Frosty Leo 1	C$17$O, C$18$O, SiO, $29$SiO, SO, SO$2$, H$2$S, HCN	O-rich
IRAS 02229+6808 1	C$17$O, C$18$O, SiO, $13$CS, SiS, SiC$2$, HCN, H$13$CN, HNC, HC$3$N, HC$5$N, $13$CN, C$3$N, CH$3$CN, C$2$H, C$4$H	C-rich
IRAS 17436+5005 1	C$17$O, C$18$O, SiO	O-rich
IRAS 19475+3119 1		unknown
IRAS 19500–1709 1	C$17$O, C$18$O, HCN	C-rich
IRAS 21282+5050 1	C$17$O, C$18$O, HCN, HCO+	C-rich
IRAS 22272+5435 1	C$17$O, C$18$O, $28$SiO, $13$CS, SiC$2$, HCN, H$13$CN, HNC, HC$3$N, HC$5$N, HN$13$C, HCO+, C$2$H, C$4$H, C$3$N	C-rich
IRAS 23304+6147 1	C$17$O, C$18$O, SiC$2$, HCN, H$13$CN, HNC, HC$3$N, HC$5$N, $13$CN, C$2$H, C$4$H, C$3$N	C-rich
IRAS 23321+6545 1	C$17$O, C$18$O, SiS, SiC$2$, HCN, H$13$CN, HNC, HC$3$N, CH$3$CN	C-rich
NGC 6781 2	HCN, HCO+, HNC	C-rich
CRL 618 1	C$17$O, C$18$O, SiS, SiC$2$, HCN, H$13$CN, HCO+, H$13$CO+, HNC, HN$13$C, $13$CN, HC$3$N, HC$5$N, HC$7$N, CH$3$CN, C$3$N, etc.	C-rich
CRL 2688 1	C$17$O, C$18$O, SiO, SiS, SiC$2$, HCN, H$13$CN, HCO+, HNC, HN$13$C, C$2$H, C$4$H, HC$3$N, HC$5$N, $13$CS, $13$CN, NaCN, c-C$3$H$2$	C-rich
NGC 7027 2	C$17$O, C$18$O, HCN, H$13$CN, HNC, c-C$3$H$2$, N$2$H+, HCO+, H$13$CO+, HC$17$O+, HC$18$O+, etc.	C-rich
CRL 2777 3	C$17$O, C$18$O, SiO, SiS, SiC$2$, $13$CS, HCN, H$13$CN, HNC, HN$13$C, C$2$H, C$4$H, HC$3$N, HC$5$N	C-rich
AFGL 2324 4	C$17$O, C$18$O, SiO, $29$SiO, HCN, SO, H$2$S	O-rich

¹ post-AGB: pPN. ² post-AGB: PN. ³ S-type AGB star: control target. ⁴ post-red super giant: control target.

). The sources were selected based on their relatively strong ^$13$CO and ^$12$CO emissions in the hope of securing their detection in C^$17$O and C^$18$O. We have also re-observed three strong C-rich post-AGB sources (CRL 618, CRL 2688, and NGC 7027) to obtain C^$17$O/C^$18$O intensity ratios consistently. Finally, we have also included two control targets, the S-type AGB star CRL 2477 and the post-red supergiant AFGL 2343. We have detected both C^$17$O and C^$18$O J = 2 − 1 in all targets but two: IRAS 19475+3119 and NGC 6781. Based on the detected species other than CO, we have also determined the C-rich or O-rich nature of our targets in all cases but IRAS 19475+3119, where only ^$13$CO was detected. Therefore, we provide for the first time or improve C^$17$O/C^$18$O for 11 post-AGB sources (about 1/3 of all sources for which this ratio has been determined), also including a chemical classification based on the molecular composition of their envelopes.

The C/O ratio is not determined but constrained to be higher or lower than one, i.e., whether the source is C-rich (C/O > 1) or O-rich (C/O < 1), based on the detected species other than CO. In addition to H_$2$, the molecular content of AGB and post-AGB envelopes is largely dominated by CO. This creates a clear dichotomy in the inventory of the other species detected, with a prevalence of C-bearing species in C-rich sources, such as CS, ${\mathrm{HC}}_{2n+1}$N, ${\mathrm{C}}_{2n}$H, SiC_$2$, and other complex organic molecules, and of O-bearing species in O-rich sources, such as SiO, SO, SO_$2$, H_$2$O, and OH ([28,29] and references therein). Some molecules are unique to each of the two chemical types like SO_$2$ and SiC_$2$, while in other cases, as for SiO, CS, HCN, etc., it is their relative strength that informs us about the chemical nature of the object. We summarize the non-CO detected species in each source and the assigned chemical type depending solely on these detections in Table 1. As can be seen, our sample comprises three O-rich sources and 11 C-rich sources (including the three targets re-observed and the control sources). In Figure 3, we show an example of some of the lines identified in the non-canonical C-rich pPN IRAS 22272+5435. Note the strong HCN line, that SiS is more intense than SiO, and that SO remains undetected. In addition, we have also identified lines of ^$13$CS, SiC_$2$, HC_$3$N, HC_$5$N, C_$2$H, C_$4$H, and C_$3$N, indicating that the object is C-rich. However, C^$18$O is notably stronger than C^$17$O, an unexpected result for a C-rich envelope.

In contrast, the ^$17$O/^$18$O ratio has been determined from the intensity ratio of the J = 2 − 1 rotational lines of the corresponding oxygen substitutions of CO. Assuming that these lines are optically thin, have similar excitation, and also identical extent, something that is very reasonable and has been confirmed where accurately measured [24,25], the C^$17$O/C^$18$O abundance ratio is given by the expression [16,23,26]

$${\displaystyle \frac{{\mathrm{C}}^{17}\mathrm{O}}{{\mathrm{C}}^{18}\mathrm{O}}}={\displaystyle \frac{I\left({\mathrm{C}}^{17}\mathrm{O}J=2-1\right)}{I\left({\mathrm{C}}^{18}\mathrm{O}J=2-1\right)}}\times {\displaystyle \frac{A_{ij}\left({\mathrm{C}}^{18}\mathrm{O}J=2-1\right)\nu \left({\mathrm{C}}^{18}\mathrm{O}J=2-1\right)}{A_{ij}\left({\mathrm{C}}^{17}\mathrm{O}J=2-1\right)\nu \left({\mathrm{C}}^{17}\mathrm{O}J=2-1\right)}}\times {\displaystyle \frac{\Omega \left({\mathrm{C}}^{18}\mathrm{O}J=2-1\right)}{\Omega \left({\mathrm{C}}^{17}\mathrm{O}J=2-1\right)}}.$$

(1)

In this expression, I, $A_{ij}$, and $\nu$ are the integrated intensity, Einstein-A coefficient, and frequency of the corresponding rotational line, respectively. The Einstein-A coefficient and line frequency ratios are 0.941 and 0.977, respectively. The factor $\Omega$(C^$18$O J = 2 − 1)/$\Omega$(C^$17$O J = 2 − 1) corrects for the different source-to-beam size ratios of the different lines. Its value is 1 in the case that the source is larger than the beam (as for CRL 618, CRL 2688, and NGC 7027), and $\nu$(C^$18$O J = 2 − 1)/$\nu$(C^$17$O J = 2 − 1) = 0.977 if the source is not resolved (the rest of the cases). Assuming that there is no chemical fractionation either, the ^$17$O/^$18$O ratio results in

$${\displaystyle \frac{{}^{17}\mathrm{O}}{{}^{18}\mathrm{O}}}\approx {\displaystyle \frac{\mathrm{C}^{17}\mathrm{O}}{\mathrm{C}^{18}\mathrm{O}}}={\displaystyle \frac{I\left(\mathrm{C}^{17}\mathrm{O}J=2-1\right)}{I\left(\mathrm{C}^{18}\mathrm{O}J=2-1\right)}}\times \Gamma ,$$

(2)

where $\Omega$ is the product of the Einstein-A coefficient, line frequency, and source-to-beam size ratios, with a value of 0.92 or 0.90 depending on whether the source is resolved or not. Note that the difference between the two values is rather small, only 2.3%, which is negligible in the unlikely event of using the value for an unresolved object for an extended source and vice versa.

Our new values for ^$17$O/^$18$O ratios are summarized in Figure 4. Here, we also plot 18 additional sources for which we know their chemical composition and ^$17$O/^$18$O ratios estimated following a similar procedure. Here, the y-position of each source reflects the actual value of the ^$17$O/^$18$O ratio, while the x-position just indicates whether the source is O-rich, C-rich, or an HBB source. The white line marks the expected value for the ^$17$O/^$18$O abundance ratio as a function of the initial stellar mass (x-axis) according to standard evolution models for solar metallicities ([3,16,30,31] and references therein). Note that the C/O ratio has not been numerically computed; we only know whether the star/envelope is C-rich or O-rich by the molecular species other than CO detected in the source.

4. Discussion: The Canonical and Non-Canonical Post-AGB Populations

The first result is that we do not find any source in the range of 4 to 8 $M_{\odot }$, whereas, as a result of the HBB process, the stars retain their O>C initial composition and ^$17$O/^$18$O become very large due to the destruction of ^$18$O. For O-rich sources, with initial masses between 1 and 1.5 $M_{\odot }$, we find six sources with ^$17$O/^$18$O ratios ≲ 1, that are compatible with model predictions (canonical sources). However, there are nine (non-canonical) sources for which their ^$17$O/^$18$O ratios are larger one, which corresponds to C-rich stars. For the C-rich sources, with expected masses between 1.5 and 4 $M_{\odot }$, a similar situation is observed: we have seven canonical sources with ^$17$O/^$18$O > 1 consistent with predictions, and an equal number of (non-canonical) sources with ^$17$O/^$18$O values < 1 expected for O-rich sources. In summary, we have fewer well-behaved sources (13 cases, which represents ∼45% of the whole sample) than oddballs (16, ∼55%).

Non-canonical O-rich sources, with ^$17$O/^$18$O > 1, are interpreted as a result of an interrupted AGB evolution of stars that were bound to be C-rich. Since for stars with initial masses between 1.5 and 4 $M_{\odot }$ the C/O ratio increases along the AGB evolution, it may happen that if this evolution is interrupted the star remains O-rich. This hypothesis is in line with the belief that some post-AGB nebulae are the result of a sudden ejection of mass (possibly as a consequence of merging with a companion, for example) that terminates the AGB evolution early [34,35]. This scenario has been proposed to explain the formation of the O-rich pPN M1–92, for which we obtain a ^$17$O/^$18$O ratio of 1.6 that corresponds to an initial mass of 1.7 $M_{\odot }$, and that should have been turned C-rich by the end of the AGB if the star had completed this phase [24,25]. This idea is further supported by our recent finding of a ^$12$C/^$13$C ratio ≈30 in M1–92, which lies in between those expected at the beginning (≈20) and end (≈70) of the AGB phase for a 1.7 $M_{\odot }$ star [24]. Most likely, the premature end of this phase resulted in a lower than expected ^$12$C enrichment and, as a consequence, a C/O < 1 along with a moderate value for the ^$12$C/^$13$C ratio. As for the non-canonical C-rich sources, there is no clear working hypothesis, but given the bipolar (and therefore probably binary) nature of the sources, we suggest that they could be the result of mass transfer phenomena such as those occurring in extrinsic carbon stars [36], but see also the work by [14].