The Molecular Exoskeleton of the Ring-like Planetary Nebula NGC 3132

We present Submillimeter Array (SMA) mapping of $^{12}$CO $J=2\rightarrow 1$, $^{13}$CO $J=2\rightarrow 1$, and CN $N=2\rightarrow 1$ emission from the Ring-like planetary nebula (PN) NGC 3132, one of the subjects of JWST Early Release Observation (ERO) near-infrared imaging. The $\sim$5$''$ resolution SMA data demonstrate that the Southern Ring's main, bright, molecule-rich ring is indeed an expanding ring, as opposed to a limb-brightened shell, in terms of its intrinsic (physical) structure. This suggests that NGC 3132 is a bipolar nebula viewed more or less pole-on (inclination $\sim$15--30$^\circ$). The SMA data furthermore reveal that the nebula harbors a second expanding molecular ring that is aligned almost orthogonally to the main, bright molecular ring. We propose that this two-ring structure is the remnant of an ellipsoidal molecular envelope of ejecta that terminated the progenitor star's asymptotic giant branch evolution and was subsequently disrupted by a series of misaligned fast, collimated outflows or jets resulting from interactions between the progenitor and one or more companions.


INTRODUCTION
Planetary nebulae (PNe) are the near-endpoints of stellar evolution for intermediate-mass (∼1-8 M ⊙ ) stars.Each PN provides a snapshot of the brief (∼10 4 yr) stage in which the outflowing, dusty circumstellar envelope of an asymptotic giant branch (AGB) star is ionized by its newly unveiled core, itself a future white dwarf.The resulting ∼10 4 K circumstellar plasma is a rich source of optical emission lines, forming a classical PN.However, certain PNe retain cold (< 100 K), dense (∼10 4 -10 6 cm −3 ), massive envelopes of molecular gas and dust.These PN molecular envelopes are shaped and displaced by fast winds from their exceedingly hot (∼100-200 kK), rapidly evolving central stars, which are also sources of intense UV irradiation of the molecular gas.
The molecule-rich zones of PNe have been detected via IR imaging of H 2 rovibrational emission, which reveals shockheated and/or UV-irradiated molecular gas (e.g., Webster et al. 1988;Zuckerman & Gatley 1988;Kastner et al. 1994Kastner et al. , 1996)), and by mm-wave spectroscopy of CO rotational emission from far colder and more massive molecular reservoirs within PNe (e.g., Huggins et al. 1996Huggins et al. , 2005)).The vast majority of such molecule-rich PNe, most of which are detected in both near-IR H 2 and mm-wave CO, are Ring-like or bipolar in structure; these objects likely constitute a PN class descended from relatively massive progenitor stars (Kastner et al. 1996, and references therein).Interferometric observations of such molecule-rich planetary nebulae in the mm-wave regime afford unparalleled opportunities to study their density structures, kinematics, and compositions.The resulting high-resolution molecular line maps of PNe can provide -among other things -stringent tests of models of the shaping of such nebulae by collimated outflows from central binary systems as well as insight into the enrichment of the ISM in the products of intermediate-mass stellar nucleosynthesis (e.g., Kastner et al. 2018).
Corresponding author: Joel Kastner jhk@cis.rit.eduHere, we present Submillimeter Array (SMA) mapping of molecular emission from the PN NGC 3132.NGC 3132 is a nearby (D = 754 pc), "Ring-like" PN that harbors a wide visual binary comprising the central (progenitor) star and an A star companion (Ciardullo et al. 1999).The inner, ionized cavity of NGC 3132 is elliptical in shape, with a major axis of ∼40 arcsec (0.15 pc) and an electron density of n ∼ 10 3 cm −3 .The PN's ionization structure and abundances were the subject of a recent optical (VLT/MUSE) spectroscopic mapping study (Monreal-Ibero & Walsh 2020).
Like other PNe in its (Ring-like) class (Kastner et al. 1994), NGC 3132 has long been known to harbor a significant mass of molecular gas, as revealed by H 2 and CO emission (Storey 1984;Sahai et al. 1990;Zuckerman et al. 1990;Kastner et al. 1996).JWST Early Release Observation (ERO) imaging of NGC 3132 has now revealed the structure of its H 2 emission region in unprecedented detail (De Marco et al. 2022).The JWST H 2 images reveal a complex ring system surrounding the central ionized region, as well as a system of arcs within the nebula's extended halo.De Marco et al. (2022) assert that these structures were most likely sculpted by an unseen companion or companions orbiting within ∼60 au of the PN progenitor.Furthermore, the mid-IR JWST (MIRI) images demonstrate the ultra-hot central star has a significant IR excess that most likely emanates from a dusty disk that formed as the result of a close binary interaction, albeit not necessarily with the same companion that generated the H 2 ring and arc systems (De Marco et al. 2022;Sahai et al. 2023).
The H 2 emission imaged by JWST only traces the hot (∼1000 K), UV-illuminated and/or shock-excited molecular gas in the nebula, and such hot H 2 likely constitutes a small fraction of the total reservoir of molecular gas in NGC 3132.Furthermore, JWST imaging does not provide any information concerning the molecular gas kinematics, such as can be obtained via mm-wave molecular line mapping.However, the only previous such molecular line mapping of NGC 3132 consists of a single-dish 12 CO map obtained with the late SEST facility (beamwidth ∼20 ′′ ) well over 30 yr ago (Sahai et al. 1990).These SEST observations revealed strong CO emission from the PN's central ring system that is characterized by expansion at ∼15 km s −1 , with hints of faster (>20 km s −1 ) outflows.The only other molecule that has been detected in NGC 3132 thus far (apart from CO and H 2 ) is HCO + (Sahai et al. 1993).
To establish the distribution, mass, and velocity structure of the molecular gas in NGC 3132, and to probe its molecular gas composition, we have used the SMA to map the nebula in 12 CO(2-1), as well as the 2-1 rotational transitions of CN and CO isotopologues.In this paper, we present the SMA observations of NGC 3132, and describe how these observations yield new insight into the PN's three-dimensional structure and molecular chemistry.

OBSERVATIONS
We observed NGC 3132 with the Submillimeter Array (SMA) on 2023 May 16.The six operating antennas were in a compact configuration that provided baseline lengths from 6 to 68 meters.NGC 3132 is a challenging target for the SMA due to its southern declination (−40 • ) and consequent low elevations when observed from Maunakea, requiring favorable weather conditions.For these observations, the 225 GHz atmospheric opacity was 0.06 with very stable phase throughout.The two dual-sideband receivers were tuned to LO frequencies of 225.538 and 235.538GHz.With each receiver providing an IF range of 4-16 GHz, this setup provided continuous spectral coverage from 209.5 to 251.5 GHz.The SWARM digital backend provided 140 kHz channel spacing over the full bandwidth, which corresponds to 0.18 km s −1 at the frequency of the 12 CO J = 2 → 1 line (230.538GHz).The SMA primary beam size is 55 ′′ (FWHM) at this frequency.With baselines down to 6 meters, these SMA observations have a maximum recoverable scale of ∼27 ′′ .
We observed NGC 3132 in a small hexagonal mosaic of 7 pointings with 30 ′′ spacing to span the full extent of 12 CO J = 2 → 1 emission previously imaged with the SEST telescope (Sahai et al. 1990).The observing sequence consisted of 2 minutes on each of the 7 mosaic pointings, bracketed by the two calibrators J1037-295 and J1001-446.The target was observed over the hour angle range −2.1 to 2.8.We used the MIR software package to calibrate the visibilities following standard procedures for SMA data.The visibilities were initially inspected manually to flag a small number of channels that showed evidence for interference.The bandpass response was determined from observations of the strong source 3C 279, the absolute flux scale was set from a short observation of the asteroid Ceres (with ∼ 10% estimated systematic uncertainty), and time dependent complex gains were derived and applied from observations of J1037−295 (the stronger of the two gain calibrators, 1.31 Jy).
We used the MIRIAD software package to make images, using the mosaic option in the invert task followed by clean deconvolution with the mossdi task.We imaged the 12 CO J = 2 → 1, 13 CO J = 2 → 1, C 18 O J = 2 → 1, and CN N = 2 → 1 (226.875GHz hyperfine complex) lines by generating image cubes over velocity bins of 1.5 km s −1 width, chosen as a compromise between resolving kinematic structure and signal-to-noise ratio.frequency, beam size and position angle (PA) as obtained with robust=0 weighting, rms channel-to-channel noise, and integrated line intensity for each of the lines imaged.For the 12 CO J = 2 → 1 beam size (6.49′′ ×2.51 ′′ ), the flux density to brightness temperature conversion is 0.71 Jy K −1 .The SMA-measured line 12 CO J = 2 → 1 emission morphology and line fluxes (see §3) are overall consistent with those measured with the single-dish SEST (see Sahai et al. 1990, their Fig. 2), indicating that the SMA data do not suffer from significant interferometric flux losses.We also generated a continuum image using all of the bandwidth free of strong spectral lines, with an effective frequency of 228.7 GHz.This image has an rms noise of 4.2 mJy beam −1 and shows no significant features in the central region of uniform noise.

RESULTS
Channel maps obtained from the 12 CO J = 2 → 1 image cube are presented Fig. 1; channel maps for 13 CO J = 2 → 1 and CN N = 2 → 1 are presented in Appendix A. In Fig. 2, we display velocity-integrated (moment 0) images of 12 CO J = 2 → 1, 13 CO J = 2 → 1, and CN N = 2 → 1 line emission.The corresponding respective emission line profiles, obtained by spatially integrating the SMA image cubes within a ∼33 ′′ radius region centered on and encompassing the bright central molecular ring, are presented in Fig. 3.The spectra indicate that the nebular systemic velocity is ∼−25 km s −1 , consistent with the single-dish SEST results (Sahai et al. 1990).Table 1 lists the integrated line intensities obtained from the spectra.The CN radical is here detected for the first time in NGC 3132.Neither C 18 O nor continuum emission were detected.
It is immediately apparent from Fig. 1 and Fig. 2 that the brightest mm-wave molecular emission arises from the main ring of the nebula, as previously established by the SEST 12 CO(2-1) mapping (Sahai et al. 1990).However, as we describe in detail below, the ∼5' ′′ resolution SMA interferometric mapping elucidates various fundamental aspects of the structure of 12 CO(2-1) emission that could not have been ascertained from those previous (∼22 ′′ resolution) single-dish SEST mapping observations.
The 12 CO channel maps (Fig. 1) furthermore demonstrate that the more highly blueshifted and redshifted features, centered at −50 km s −1 and 0 km s −1 , respectively (and appearing as weak "satellite peaks" in the 12 CO(2-1) spectrum; Fig. 3), appear to arise from compact regions within this main ring rather than from exterior jets or ansae.The CN emission (Fig. 2, right) displays the same basic (ring) emission morphology, but the signal-to-noise ratio is relatively poor and hence the detected emission is limited to velocities between roughly −40 km s −1 and −12 km s −1 , while the (still weaker) 13 CO emission is restricted to a still smaller velocity range (Fig. 3).From left to right, velocity-integrated (moment 0) images of 12 CO(2-1), 13 CO(2-1) and CN(2-1) emission, respectively, from NGC 3132 obtained from the SMA image cubes.The 13 CO(2-1) and CN(2-1) moment 0 images were generated by rejecting image cube spaxels with values less than the rms noise in the data cube (see Table 1).

Comparison with archival JWST H 2 imaging
In the upper panels of Fig. 4, we compare the archival ERO JWST/NIRCam 2.12 µm H 2 image of NGC 3132 and the SMA 12 CO(2-1) moment 0 image.It is apparent that there is a close morphological correspondence between the two images, despite their sharply contrasting spatial resolution (∼0.2 ′′ and ∼5 ′′ , respectively); the brightest near-IR H 2 and mm-wave 12 CO are spatially coincident, and the main, bright ring appears bifurcated in the E-W direction in both images.In the lower panels of Fig. 4, we display spectrally integrated velocity slices through the 12 CO(2-1) image cube, overlaid on the SMA moment 0 image (lower left) and JWST H 2 image (lower right).These overlays reveal that the E-W spatial bifurcation of the bright ring has a corresponding velocity bifurcation, wherein the blueshifted (approaching) ring component is spatially offset to the west of the redshifted (receding) ring component.This resolution of the central ring into distinct spatial and velocity components suggests the ring possesses an overall cylindrical structure, and is viewed at low inclination and slightly tilted along the E-W direction with respect to the line of sight.
Fig. 4 further demonstrates that the most highly blueshifted and redshifted features (knots) detected in the 12 CO(2-1) mapping correspond to distinct H 2 filaments that are projected within the main ring, and appear to cut across the nebula to the northwest and southeast of the central (visual binary) star.The northwest H 2 filament is evidently somewhat more spatially extended and coherent than the southeast H 2 filament and, correspondingly, the blueshifted 12 CO knot is brighter and more extended than the redshifted 12 CO knot.

Position-velocity images
In Fig. 5, we display three views of the SMA 12 CO(2-1) data cube, as integrated (collapsed) along each of the three cube axes.The velocity-integrated (moment 0) image is displayed in the top frame, while position-velocity (P-V) images collapsed (integrated) along the RA and declination axes are displayed in the two panels below the moment 0 image.In Fig. 6 (top row), we present P-V images obtained by spatially integrating slices of width 20 ′′ through the SMA 12 CO(2-1) data cube along position angles (PAs) of 60 • and 150 • , corresponding to the minor and major axes of the main ring of NGC 3132, respectively.
These P-V images reveal the three-dimensional structure of the NGC 3132 molecular emission.Specifically, the RA-collapsed P-V image (Fig. 5, middle panel) demonstrates that the main, bright ring seen in the near-IR H 2 (JWST) and mm-wave 12 CO(2-1) (SMA moment 0) imaging -hereafter Ring 1 -indeed has a P-V morphology consistent with an expanding ring.The decl.-collapsed P-V image (Fig. 5, bottom panel) shows that its eastern edge is approaching, hence, tilted toward the observer, and its western edge is receding, hence, tilted away from the observer.This P-V image and that obtained from the cut through the data cube along along PA 60 • (Fig. 6, right panel) furthermore demonstrate that the minor axis of Ring 1 is tilted in velocity space by ∼10 km s −1 , i.e., that the line-of-sight blueshifted and redshifted (approaching and receding) velocities of the limbs of the ring are ∼5 km s −1 .In contrast, the P-V image obtained from the major-axis cut through Ring 1 shows essentially no velocity tilt (Fig. 6, middle panel), indicating that this line through the ring major axis, along PA 150 • , represents the intersection of the plane of Ring 1 with the plane of the sky.
The P-V images in Fig. 5 and Fig. 6 (top row) also reveal the velocity coherence of the clumpy molecular emission structures that are seen projected within Ring 1.In particular, the declination-collapsed P-V image (Fig. 5, bottom panel) and minor-axis P-V image in Fig. 6 (top right panel) show that the high-velocity clumps seen in Fig. 4 (lower panels) are in fact the brightest portions of what appears to be a continuous ring structure in P-V space.This second, expanding ring of molecular gas within NGC 3132 is hereafter referred to as Ring 2.
The SMA 12 CO moment 0 images and P-V diagrams (Fig. 6) furthermore demonstrate that Ring 1 and Ring 2 have very different inclinations with respect to the line of sight.The symmetry axis of (bright) Ring 1 is evidently viewed at low to intermediate inclination; specifically, its inclination is constrained to lie between ∼15 • and ∼45 • .The lower limit on Ring 1's inclination is obtained from its ∼10 km s −1 tilt in velocity space (i.e., the ∼5 km s −1 blueshift/redshift of the ring limbs; see above) under the assumption that its expansion velocity is identical to that of Ring 2 (∼25 km s −1 ), while the upper limit is obtained from Ring 1's observed (projected) major/minor axis ratio (∼1.4).

CO column densities and molecular gas mass
To obtain 12 CO column densities and (hence) estimate the total molecular gas mass of NGC 3132 from the SMA 12 CO(2-1) data, we use the publicly available RADEX radiative transfer code1 (van der Tak et al. 2007).For an assumed molecular gas kinetic temperature of T k = 30 K (see, e.g., Bachiller et al. 1997) and H 2 number density of n H2 = 10 6 cm −3 , RADEX calculations indicate that the measured SMA antenna temperatures -which range from ∼0.6 Jy beam −1 (∼1.0 K) to ∼6.5 Jy beam −1 (∼10 K) across the individual channel maps (Fig. 1) -correspond to a range in 12 CO column densities from N CO ∼7 × 10 14 cm −2 to ∼7 × 10 15 cm −2 .The 12 CO emission is predicted to be optically thin (τ 12CO < 0.5) over this domain of N CO for the foregoing assumptions for T k and n H2 .For significantly smaller assumed values of T k and n H2 , RADEX predicts that the emission would become marginally to very optically thick, which would be inconsistent with the relatively large measured value of 12 CO(2-1)/ 13 CO(2-1) ≈ 48 ( § 4.1).
The approximate mean of the velocity-integrated (moment 0 image) 12 CO line intensities is ∼30 K km s −1 .Given the foregoing, we hence infer that the mean integrated 12 CO column density along a line of sight through the CO-emitting regions of the nebula is ∼ 2 × 10 16 cm −2 .For purposes of a rough estimate of the total molecular mass of NGC 3132, we adopt this mean value of N CO .Approximating the 12 CO emitting region of NGC 3132 as an annulus of radius 20 ′′ (15,000 au) and thickness 3 ′′ (2250 au), we find that total number of CO molecules is N (CO) ∼10 51 .This estimate for N (CO) is very similar to (within ∼30% of) that obtained by Sahai et al. (1990).To convert N (CO) to an H 2 mass then requires an assumption for the CO abundance relative to H 2 , [CO]/[H 2 ], which is a notoriously uncertain quantity (e.g., Bolatto et al. 2013;Bisbas et al. 2015;Yu et al. 2017, and references therein).Adopting a plausible range of [CO]/[H 2 ] that is appropriate for evolved star envelopes -i.e., between 10 −4 and 10 −5 (see discussion in Sahai et al. 1990) -we obtain an estimated total molecular gas mass of between ∼0.015 M ⊙ and ∼0.15 M ⊙ for NGC 3132.

The structure of NGC 3132's molecular exoskeleton
The SMA data indicate that the Southern Ring's main, bright, molecule-rich ring (Ring 1) is indeed a ring that is viewed at low to intermediate inclination, as opposed to a limb-brightened shell, in terms of its intrinsic (physical) structure ( § 3).This conclusion, which is consistent with the results of the previous single-dish (SEST) CO mapping (as interpreted by Sahai et al. 1990), is supported by our empirical modeling of the 12 CO data (Appendix B and Fig. 6).Evidently, the main, CO-bright reservoir of molecular gas in NGC 3132 is largely confined to the equatorial and lower-latitude regions of the nebula.The SMA 12 CO(2-1) mapping results are hence consistent with those of previous surveys of H 2 and CO emission from PNe.As noted earlier, such molecular emission-line surveys have established that the vast majority of molecule-rich PNe are intrinsically bipolar in structure, with the bulk of the molecular gas residing in equatorial tori (Kastner et al. 1996;Huggins et al. 1996Huggins et al. , 2005)).The geometries of these toroidal or ring structures are conducive to self-shielding and dust-shielding of the molecules against the PN central star's intense, dissociating UV irradiation (Zuckerman & Gatley 1988).Our confirmation that the nebula's main, bright ring is intrinsically ring-like in structure, as opposed to a limb-brightened shell, therefore strongly supports the hypothesis of Sahai et al. (1990) that NGC 3132 is (or at least was) in fact a bipolar nebula with polar axis viewed at low to intermediate inclination with respect to the line of sight.
Indeed, the SMA data resolve Ring 1 into distinct spatial and velocity components, with indications of pointsymmetric structure (Fig. 4), suggesting that this 12 CO(2-1) emission arises from both an equatorial torus and the bases of polar lobes.The empirical model presented in Appendix B, in which Ring 1 is modeled as a simple cylindrical structure, does not account for these features (see, e.g., the right-hand column of Fig. 6).Ring 1 hence may constitute the low-latitude portions of the twin-cone ("Diabolo") geometry that has been proposed to explain the nebula's ionized gas morphology and kinematics (Monteiro et al. 2000;Monreal-Ibero & Walsh 2020).The polar lobes have presumably expanded far enough into the ISM over the ≳3000 yr (dynamical) lifetime of NGC 3132's ring system (see below) that any residual lobe molecular gas is now difficult to detect.However, it is possible that some of the extended (halo) H 2 emission seen both within and outside of the main bright molecular ring in JWST imaging arises from such polar lobe material.If so, then this polar lobe H 2 emission morphology would appear to be in conflict with the Diabolo model, as the brightest "halo" H 2 emission in the JWST images is more or less aligned with the major axis of Ring 1 (Fig. 4, top right panel), whereas the Diabolo model requires the projected lobe emission to be aligned with the ring's minor axis (see, e.g., Fig. 5 of Monteiro et al. 2000).We note that the SMA data also reveal weak 12 CO(2-1) emission exterior to Ring 1, in the form of a faint arc extending toward the ESE that has an even fainter potential counterpart to the WNW (see, e.g., Fig. 4, top left panel).These faint molecular halo structures warrant confirmation and followup via deeper, wider-field CO mapping.
Surprisingly, the data further reveal that the nebula also appears to harbor a second, dust-rich molecular ring (Ring 2) -detected in (dust) absorption, in low-excitation emission lines (Monteiro et al. 2000;Monreal-Ibero & Walsh 2020;De Marco et al. 2022), in H 2 (De Marco et al. 2022), and (now) in 12 CO(2-1) -that appears to lie nearly perpendicular to Ring 1, at least as seen in projection in the SMA 12 CO(2-1) moment 0 image.Under the assumption that Ring 2's radius is similar to the semimajor axis of Ring 1 (18,500 au; §3), the measured expansion velocity of Ring 2 (25 km s −1 ; §3.2) implies that the dynamical age of Ring 2 is ∼3700 yr.
Motivated by these results, we describe in Appendix B a simple geometrical model for the structure of NGC 3132's 12 CO(2-1) emission regions consisting of two rings with sharply contrasting inclinations with respect to the line of sight.This simple two-ring model of NGC 3132's molecular exoskeleton greatly oversimplifies aspects that are readily apparent in the SMA observations of NGC 3132, such as the line-of-sight velocity extent and structure of its main, bright 12 CO(2-1) ring (Ring 1) and the highly uneven (knotty) 12 CO(2-1) brightness distributions of both rings.Notwithstanding its simplicity, this empirical model can reproduce the apparent two-ring structure of the 12 CO(2-1) emission that is seen in velocity-integrated and P-V images obtained from the SMA data (Fig. 6 and Fig. 10) and in volumetric views of the data cube itself (Fig. 11), as well as the main features and basic shape of the SMA 12 CO(2-1) line profile (Fig. 12).
Based on the analysis presented in Appendix B, we furthermore conclude that Ring 1 either is intrinsically elliptical and is viewed only ∼20 • from pole-on (Model A); or, if Ring 1 is perfectly circular and viewed more obliquelyspecifically, at inclination ∼45 • , as indicated by its ellipticity -that its expansion velocity is ∼2.5 times smaller than that of Ring 2 (Model B).The parameters of these two alternative models (i.e., ring inclinations, expansion velocities, dynamical ages, and major/minor axis ratios) are listed in Table 2. Synthetic moment 0 and P-V images, where the latter have been extracted from cuts through the Model A and Model B along PAs of 60 • and 150 • , are presented in the middle and bottom rows of panels in Fig. 6, respectively.
As in the comparisons between SMA 12 CO data and models presented in Appendix B, Fig. 6 demonstrates that Models A and B both well reproduce the essential aspects of the basic morphologies of the SMA moment 0 and P-V images (top row of Fig. 6), despite the fundamental differences between the two models.In particular, Model B requires the dynamical ages of the two rings to be very different -i.e., ∼3700 yr (Ring 2) vs. ∼9000 yr (Ring 1) -whereas Model A relies on the assumption that their dynamical ages are identical.Furthermore, in Model A, the symmetry axes of the two rings are nearly orthoginal to one another, whereas in Model B, their inclinations differ by ∼60 • .The striking similarity of the moment 0 and P-V projections of these two fundamentally different two-ring model realizations hence emphasizes the degeneracy of the model parameters (ring inclinations, ellipticities, and dynamical ages).
The degeneracy between Models A and B can be broken via direct measurement of the expansion proper motion of Ring 1 from multi-epoch HST or JWST images, once available; such a measurement of its projected expansion velocity will firmly establish Ring 1's dynamical age.Meanwhile, for purposes of the following discussion of the potential shaping processes that have generated the present-day NGC 3132, we adopt Model A, on the basis of its relative simplicity and the various independent lines of evidence that favor a dynamical age significantly less than ∼9000 yr for the ionized nebula (see, e.g., De Marco et al. 2022).We stress, however, that we cannot yet rule out Model B based on the data at hand.

Implications for the shaping of NGC 3132 by its central star system
The main, bright molecular ring or torus structure that dominates the 12 CO(2-1) emission from NGC 3132 (Ring 1) would appear to closely resemble the molecular tori associated with "classical" pinched-waist bipolar nebulae, with perhaps the best example being NGC 6302 (Santander-García et al. 2017).That nebula, like NGC 3132, harbors a CO-bright equatorial torus with some CO emission extending into the polar lobes.There is broad consensus that the shaping of PNe characterized by such profound bipolar (pinched-waist plus lobe) structures requires a close (interacting) binary companion to the central star (see, e.g., De Marco 2009;Jones & Boffin 2017;Kastner et al. 2022, and references therein).
However, the apparent presence of a second, fainter, nearly pole-on molecular ring in NGC 3132 (Ring 2) would appear to complicate this (relatively simple) interpretation.That is, the formation and apparent near-simultaneous ejection of two nearly orthogonal molecular rings implied by Model A appears difficult to reconcile with a model of NGC 3132 as a nearly pole-on bipolar nebula shaped by a central, interacting binary star system.While a definitive explanation for the formation of such a two-ring structure is beyond the scope of this paper, we offer a general scenario here.
If the rings indeed have very similar dynamical ages then -given their similar, AGB-like expansion velocitieswe would conclude that Ring 2 is the remnant of the same massive ejection of molecular gas from the AGB progenitor that generated Ring 1.It is possible that this rapid mass loss event terminated the progenitor star's AGB evolution.The bulk of the AGB envelope ejection was evidently focused along the equatorial plane, forming Ring 1, but the rapid (and perhaps terminal) ejection of the AGB star's molecule-rich envelope -as traced in 12 CO(2-1) in the form of Ring 2 -appears to have been overall quasi-spherical or ellipsoidal in geometry.This would be consistent with recent 3D morpho-kinematic modeling of long-slit spectroscopy of [N ii] emission, which indicates that the central ionized gas cavity within NGC 3132 has a prolate ellipsoidal shell structure with its major axis oriented at ∼30 • with respect to the line of sight (De Marco et al. 2022).
It would then remain to explain the double-ring -as opposed to closed ellipsoidal -structure of the residual molecular gas that is apparent in the SMA 12 CO(2-1) data cube.One possibility is that, after its ejection, the initially ellipsoidal molecular shell was quickly disrupted by a rapid-fire series of misaligned jet pairs emanating from the central multiple star system.This process might leave only a narrow (quasi-circular or elliptical) region of the polar lobes "untouched," and this region could take the form of Ring 2, i.e., a second molecular ring oriented nearly perpendicular to the nebula's equatorial (molecular) torus.
Such a scenario, though highly speculative, would be consistent with the evidence for multiple, misaligned (possibly precessing) jet pairs imprinted in the inferred structure of NGC 3132's central ionized cavity and halo (Monreal-Ibero & Walsh 2020;De Marco et al. 2022).The presence of such intermittent, wobbling (possibly precessing) jets would strongly suggest that the mass-losing progenitor was a member of an interacting triple (as opposed to double) star system (De Marco et al. 2022, and references therein).As detailed in De Marco et al. (2022), the likelihood that the mass-losing AGB progenitor was a member of a hierarchical multiple system2 is further supported by JWST's detection of both a thermal IR excess from a dust disk at the central star (see also Sahai et al. 2023) and a ring or spiral pattern in the nebula's extensive H 2 halo.
The foregoing general scenario, wherein the AGB and post-AGB mass loss leading to PN formation rapidly progresses from quasi-spherical to highly collimated and perhaps somewhat chaotic, is of course not new; such a model has long been invoked to explain the ongoing, rapid structural metamorphosis of young bipolar and multipolar PNe (e.g., Sahai & Trauger 1998;Rechy-García et al. 2020).We further note that the superimposed structures observed in the young PN NGC 7027 -a halo ring system and equatorial molecular torus surrounding an inner elliptical shell that has recently been punctured by a set of (three) misaligned jet pairs (Moraga Baez et al. 2023) -would appear to make this object a particularly close analog to NGC 3132.Indeed, NGC 3132 may offer a glimpse into the future of the disruptive processes now underway in very young PNe such as NGC 7027.

CONCLUSIONS
We have obtained Submillimeter Array (SMA) mapping of 12 CO J = 2 → 1, 13 CO J = 2 → 1, and CN N = 2 → 1 emission from the Ring-like planetary nebula (PN) NGC 3132.Recent JWST (Early Release Observation) infrared imaging of NGC 3132 has revealed the structure of its H 2 emission region in unprecedented detail (De Marco et al. 2022), but provided no information concerning its molecular gas kinematics.The velocity-resolved SMA observations presented here, which constitute the first mm-wave interferometric mapping of molecular line emission from the nebula, provide additional insight into the structure of NGC 3132's molecular envelope.Our main results and conclusions are as follows.
• The bulk of the mm-wave 12 CO(2-1) emission from NGC 3132 arises from the PN's bright central ring system, with a velocity-integrated morphology closely resembling that of the brightest regions of H 2 emission imaged in the IR regime by JWST.The CN radical, a sensitive probe of N chemistry and photodissociation processes in PNe (e.g., Bachiller et al. 1997), is here detected for the first time in NGC 3132.The velocity-integrated CN(2-1) image displays a morphology very similar to that of 12 CO(2-1).
• We infer 12 CO(2-1)/ 13 CO(2-1) and 12 CO(2-1)/CN(2-1) abundance ratios of ∼50 and ∼10, respectively, from the measured integrated intensity ratios.These abundance ratios would appear to be consistent with the initial mass inferred for the progenitor star (i.e., ∼2.9 M ⊙ ; De Marco et al. 2022), given the predictions of models of surface AGB isotope yields.The mean integrated 12 CO column density across the emitting region is found to be ∼2 × 10 16 cm −2 , leading to an estimate for total nebular molecular (H 2 ) mass of between ∼0.015 M ⊙ and ∼0.15 M ⊙ .
• The SMA data demonstrate that the Southern Ring's main, bright, molecule-rich ring (designated Ring 1) is indeed a ring that is viewed at low to intermediate inclination, as opposed to a limb-brightened shell, in terms of its intrinsic (physical) structure.It therefore appears that the main (CO-bright) reservoir of molecular gas in NGC 3132 is confined to the low-latitude regions of the nebula.This in turn strongly suggests that the Southern Ring is, or at least was, in fact a bipolar nebula whose polar axis is inclined by ∼15-45 • with respect to our line of sight.
• The data further reveal that the nebula also harbors a second molecular (CO-emitting) ring (designated Ring 2) that is seen projected almost orthogonally to Ring 1.We show that a simplified geometrical model consisting of two expanding molecular rings can reproduce the basic, two-ring structure of the 12 CO(2-1) emission that is seen in velocity-integrated and P-V images obtained from the SMA data, as well as the general morphology of the spatially integrated 12 CO(2-1) line profile.This empirical modeling exercise demonstrates that if Ring 1 and Ring 2 have identical expansion velocities (∼25 km s −1 ) and dynamical ages (∼3700 yr), then Ring 1 is intrinsically elliptical and is viewed only ∼20 • from pole-on.Alternatively, if Ring 1 is perfectly circular, such that its apparent ellipticity is entirely the result of viewing angle (inclination ∼45 • ), then its expansion velocity must be ∼2.5 times smaller than -hence, its dynamical age ∼2.5 times larger than -that of Ring 2.
• The apparent presence of a second, fainter, nearly edge-on "twin" to the main, bright, nearly pole-on Ring 1 would appear to complicate the (relatively simple) interpretation of the structure of NGC 3132 as a nearly poleon bipolar nebula shaped by the gravitational influence of a single close companion to the progenitor star.We suggest that this apparent two-ring structure may be the remnant of an ellipsoidal molecular envelope of AGB ejecta that has been mostly dispersed by a series of rapid-fire but misaligned collimated outflows or jets.Such a scenario would be consistent with the hypothesis that the mass-losing AGB progenitor of NGC 3132 was a member of an interacting triple star system (De Marco et al. 2022).Detailed simulations of the dynamical effects of such multiple-star "toppling jets" systems on AGB molecular envelopes are required to test this speculative scenario for the shaping of the molecular exoskeleton of NGC 3132.
Additional (sub)mm-wave (ALMA) interferometric observations of molecular emission from NGC 3132 at higher resolution and sensitivity are necessary.Such ALMA molecular line observations are needed both to confirm and further elucidate the two-ring structure that is apparent in the SMA data and, more generally, to attempt to detect and map any cold (∼30-100 K) molecular gas that lies within the myriad faint knots and filamentary structures imaged in near-IR (hot, ∼1000-3000 K) H 2 by JWST.Meanwhile, a second epoch of HST and/or JWST imaging would enable measurement of the projected expansion speed of the main, bright ring of the nebula (Ring 1), so as to ascertain its dynamical age and thereby test the hypothesis that the two rings mapped in CO by SMA were ejected nearly simultaneously in an AGB-terminating mass loss episode.

APPENDIX B: A SIMPLE GEOMETRIC MODEL
To interpret the 12 CO emission morphology in P-V space as revealed by the SMA data ( § 3.2), we construct a simple model of the main molecular gas structures within NGC 3132.We make no attempt to model the 12 CO (rotational ladder) excitation or 12 CO(2-1) photon radiative transfer; rather, the model constructed here is purely a geometrical representation of the 12 CO(2-1) emission region within NGC 3132.Motivated and constrained by the SMA 12 CO(2-1) mapping results described in § 3.2, the model we consider consists of two expanding rings of molecular gas that are viewed at significantly different orientations: a bright Ring 1, whose symmetry axis is viewed at relatively low inclination with respect to the line of sight, and a fainter Ring 2, which is viewed nearly edge-on and appears to be oriented such that its major axis (along position angle ∼60 • , measured E from N) is nearly orthogonal to that of Ring 1 (position angle of roughly 330 • ).Both rings are modeled in 3D cartesian coordinates (x, y, z) as ellipses whose minor and major axes lie along x and y, respectively, and whose z dimension is scaled according to the ring's expansion velocity.Ring 1 can be rotated around the y axis, while Ring 2 can be rotated around the x axis.These orthogonal rotations result in ellipse dimensions along x and z (Ring 1) or y and z (Ring 2) that are foreshortened and modulated, respectively, by the projection effects resulting from the rings' inclinations.
To roughly reproduce the azimuthal asymmetry of the brighter, lower-inclination Ring 1 as seen in the SMA moment 0 CO image (Fig. 2, left), the (x, y, z) coordinates of Ring 1 are assigned intensity values ranging from 0 to 1.0, with a cos (2ϕ + ϕ 0 ) dependence on azimuthal angle ϕ and a rotation of ϕ 0 = 30 • .The (fainter) Ring 2 is assigned uniform intensity values of 0.125, so as to roughly match the contribution of Ring 2 to the integrated 12 CO(2-1) spectrum (see below).Off-ring positions are assigned values of 0.
To facilitate the comparison with observations, we convolve the resulting two-ring structure with Gaussian functions approximating the asymmetric (6.5 ′′ ×2.5 ′′ ) SMA beam and line spread function (3 km s −1 , i.e., two image cube channels).To roughly approximate the wide velocity range over which portions of Ring 1 appear to be detected (from ∼−40 km s −1 to ∼−5 km s −1 ; Fig. 1), the z (velocity) dimension of Ring 1 is further convolved with a boxcar convolution kernel of width 7.5 km s −1 .This velocity "smearing" is an attempt to model the line-of-sight extent of Ring 1, and is hence distinct from the blueshifts/redshifts due to the projected expansion velocity of Ring 1. Finally, we reproject the model cube spaxels from (x, y, z) into the equivalent SMA data cube (RA, decl., velocity) coordinate space and rotate the entire resulting image cube through a position angle of 330 • , to approximate the observed (projected) rotation of Ring 1 on the sky ( § 3).
To illustrate the output of the resulting two-ring model and the comparison with the SMA 12 CO mapping data, we first consider two model realizations, both invoking a pair of perfectly circular rings with identical radii (18,500 au) and expansion velocities (25 km s −1 ), hence identical dynamical ages (3700 yr).In the first realization, the inclinations of both Rings 1 and 2 are given by their major/minor axis ratios, as deduced from the SMA moment 0 12 CO image.These ratios are ∼1.4 and ∼4.5 for Rings 1 and 2, respectively (see § 3.2), so we set their respective model inclinations to ∼45 • and ∼78 • .
The resulting structural model data cube is illustrated in the center column panels of Fig. 9 in the form of a synthetic moment 0 image and synthetic P-V images obtained by "collapsing" the model image cube along the RA and declination axes.These images are presented, alongside their observational (SMA 12 CO data cube) counterparts, in the center and left columns of Fig. 9, respectively.It is readily apparent that the synthetic moment 0 image provides a good match to the data, as expected given that the ∼45 • inclination of Ring 1 in the model has been set by the degree of ellipticity of this Ring in the SMA moment 0 image.However, in the RA-and decl-collapsed P-V images, the full projected velocity extent of the model Ring 1 (∼40 km s −1 ) is much larger than that observed (∼20 km s −1 ).
In the second model realization, we attempt to qualitatively account for this discrepancy in the velocity extent of Ring 1, by moderating its inclination.We are guided by the observation that if the expansion velocity of Ring 1 is identical to that measured for Ring 2, ∼25 km s −1 , then the ∼10-12 km s −1 tilt of Ring 1 in P-V space (Fig. 6, top right panel) would indeed imply that Ring 1's inclination is only ∼15 • .We hence reduce Ring 1's inclination accordingly, in the second model realization.The resulting structural model data cube is illustrated in the right-hand panels of Fig. 9.As expected, this model provides an improved match to the observed RA-and decl-collapsed P-V images, but the synthetic moment 0 image (top right-hand column panel) fails to match the observed ellipticity of Ring 1 in the SMA moment 0 image (top right-hand column panel).
The data-model comparisons in Fig. 9 lead us to conclude that Ring 1 is either intrinsically elliptical in structure, or that its expansion velocity is significantly smaller -and hence its dynamical age significantly larger -than that of Ring 2. Thus, in an attempt to generate structural model data cubes that might more accuractely reproduce Ring 1's morphology in all three SMA data cube renderings -i.e., the observed moment 0 image as well as the P-V imageswe generate two additional, revised models corresponding to these two possibilities.In the first revised model (Model A), Ring 1 is elliptical, with major/minor axis ratio of 1.25 and semimajor axis of 18,500 au along the y direction, and is viewed at low inclination (20 • ).The expansion velocity of Ring 1 is modulated, from a maximum of 25 km s −1 along the major axis to 20 km s −1 along the minor axis, so as to maintain a uniform dynamical age of 3700 yr around the ring.In the second revised model (Model B), Ring 1 remains circular, with assumed radius of 18,500 au, but its expansion velocity is reduced to 10 km s −1 , corresponding to an increased dynamical age of 9250 yr.The values of the fundamental parameters of Models A and B -ring inclination, expansion velocity, dynamical age, and major/minor axis ratio -are listed in Table 2.For simplicity, the parameters of Ring 2 are held constant for the two models.
The resulting structural model data cubes are illustrated in the center and right-hand columns of Fig. 10.It is immediately apparent that both models more closely match the data than either of the models presented in Fig. 9. Comparison of volume renderings of the SMA 12 CO(2−1) data cube further support the general viability of both models; one such set of comparisons is presented in Fig. 11, where we show three example oblique views of SMA and model data cubes generated via the Glue software3 .In both Fig. 10 and Fig. 11, Models A and B are nearly indistinguishable.Evidently, the family of 2-ring models is degenerate in terms of their possible combinations of inclination, eccentricity, and expansion velocity (or, equivalently, assumed dynamical age).
Despite the simplicity of the foregoing double-ring model -and the complexities (knots, filaments) evident in the data that are not represented in such a simple model -the side-by-side comparisons in Fig. 10 and Fig. 11 demonstrate that the two-ring model can reproduce the fundamental morphologies apparent in the data.That is, in each of the views presented in these Figures, the 12 CO(2-1) emission appears as two intersecting elliptical rings whose ellipticity (eccentricity) and points of intersection are essentially functions of data cube "viewing angle."Because the model does not account for opacity effects -thereby implicitly representing optically thin emission -the integrated-intensity renderings of the model in Fig. 10 exhibit brightness peaks at specific locations along the two rings where each ring lies more nearly along the axis of integration (i.e., limb brightening), or where the two rings intersect.The 12 CO(2-1) data display brightness peaks in some of these same locations -compare, e.g., the bottom row of panels in Fig. 10 despite the fact that the model does not account for local density enhancements (knots) along the rings.This supports the notion that the 12 CO(2-1) emission in Ring-like PNe like NGC 3132 is optically thin (Bachiller et al. 1997).
In Fig. 12, we present a comparison of observed vs. model line profiles for Models A and B. As in the case of the moment 0 and P-V images and data cube renderings presented in Fig. 10 and Fig. 11, the model line profiles for the two models (shown in cyan in Fig. 12) are nearly indistinguishable.This Figure demonstrates that, in both cases, the simple 2-ring model described here can well reproduce the observed width and double-peaked profile of the bright line core, which is dominated by Ring 1.Both models also well reproduce the blueshifted "satellite peak" at ∼50 km s −1 generated by Ring 2. However, the model fails to reproduce the detailed shapes of the line wings and the redshifted satellite peak at ∼0 km s −1 ; the latter mismatch can be attributed to the patchy/knotty nature of the rearward (redshifted) side of Ring 2 (see Fig. 4, bottom frames).

Figure 5 .
Figure 5. Three views of the SMA 12 CO(2-1) data cube.Top: the noise-clipped moment 0 image.Middle and bottom: position-velocity (P-V) images obtained by "collapsing" the data cube along the RA and declination axes, respectively.The position-integrated P-V images have been constructed so as to exclude P-V frames lying outside of the spectral extraction region used for Fig. 3.

Figure 6 .
Figure 6.Top row: Position-velocity (P-V) images of 12 CO(2-1) emission for directions along the minor and major axes of the main ring of NGC 3132 (middle and right panels), respectively, obtained by spatially integrating slices of width 20 ′′ along position angles 60 • and 150 • .These positions of these cuts are shown in the left panel as magenta and yellow lines, respectively, overlaid on the 12 CO(2-1 moment 0 image).Middle row: The corresponding moment 0 and P-V images for the Model A, the 2-ring model structural invoking an elliptical Ring 1 that is viewed at an inclination of 20 • .Bottom row: The corresponding moment 0 and P-V images for Model B, the 2-ring structural model wherein Ring 1's dynamical age is 2.5× that of Ring 2 and is viewed at an inclination of 45 • .Note the similarity of the two models, which demonstrates the degeneracy of the model paramters.See Appendix B.
CO isotopologue and 12 CO/CN line ratios: implications for progenitor mass

Figure 9 .Figure 11 .
Figure 9. Left panels: The three views of the SMA 12 CO(2-1) data cube presented in Fig. 5. Top to bottom: velocity-integrated (moment 0) image; RA-collapsed P-V image; decl.-collapsedP-V image.Middle panels: the corresponding views of the simple geometrical model of CO emission for the case of two circular rings with identical radii and expansion velocities and inclinations of 45 • for Ring 1 and 78 • for Ring 2. Right panels: the corresponding views of the same model, but with the inclination set to 15 • for Ring 1.

Figure 12 .
Figure 12.Comparisons of the spatially integrated SMA 12 CO(2-1) line profile of NGC 3132 (blue) with line profiles extracted from the data cubes constructed for Model A (left) and Model B (right), the simple geometrical models illustrated in Fig. 10 (cyan), using the same (∼33 ′′ radius) extraction region.
Table 1 lists the transition

Table 1 .
SMA Molecular Emission Line Observations of NGC 3132

Table 2 .
Two-ring CO Emission Models: Parameters