In planetary nebulae, heavy-element abundances derived from faint optical recombination lines (ORLs) exceed those derived from collisionally excited lines (CELs) by a factor of about two on average, and by more than an order of magnitude in a growing subclass of nebulae that — as established by Corradi et al. (2015) from deep spectroscopy of three post-common-envelope systems and confirmed statistically by Wesson et al. (2018) — almost exclusively host close binary central stars with orbital periods of roughly a day or less. All the observations require a second nebular gas phase — cold, dense, and metal-rich — embedded in the warm, normal-composition plasma, yet a decade of integral-field mapping, deep echelle spectroscopy, and photoionization modelling has not identified the ejection or enrichment event that produced this phase, nor produced any evolutionary scenario quantitatively consistent with the observed low ionized masses, planetary-nebula-like expansion velocities, dynamical ages of order 10,000 years, the empirical binary-period threshold near 1.15 days, and the anticorrelation between the abundance discrepancy and electron density. The problem is to identify this mechanism and establish it quantitatively, including the systematically selected joint sample of deep ORL/CEL spectroscopy and binary characterization needed to fix the prevalence and statistics of the binarity–discrepancy connection, and to clarify whether related mechanisms operate in other ionized nebulae such as H II regions.

Background

A planetary nebula (PN) is the ionized envelope expelled by a low- or intermediate-mass star at the end of its asymptotic-giant-branch evolution, photoionized by the hot stellar core it exposes. Chemical abundances in PNe and other ionized nebulae are measured in two independent ways. Collisionally excited lines (CELs) are forbidden transitions (e.g. [O III] λ5007) excited by electron impacts; their emissivity is extremely sensitive to electron temperature (TeT_e), so abundances derived from them are biased toward the hot gas. Optical recombination lines (ORLs) are faint permitted transitions (e.g. the O II lines near λ4649) produced when free electrons recombine with ions; they are nearly temperature-insensitive. The two methods disagree: the ratio of the oxygen abundance from ORLs to that from CELs, called the abundance discrepancy factor (adfadf), is typically about 2 across ionized nebulae, but a minority of PNe reach adfadf values of tens to hundreds. The standard interpretation of these extreme cases is a two-phase nebula: a hot component of roughly solar-composition gas at Te∼10,000T_e\sim10,000 K that emits the CELs, and cold (Te∼1,000T_e\sim1,000 K), dense inclusions highly enriched in heavy elements (hydrogen-poor) that dominate the ORLs.

A common envelope (CE) is a binary interaction in which a companion star spirals into the envelope of a giant; the orbital energy ejects the envelope, leaving a very close binary (periods of hours to days) containing the stripped stellar core — a post-CE system. Corradi, García-Rojas, Jones & Rodríguez-Gil (2015) obtained deep spectroscopy of three PNe with post-CE binary central stars (Abell 46, Ou5, Abell 63), found adfadf values of about 10 to above 50 (reaching ~300 in the inner regions of Abell 46), and argued for an intimate connection between close-binary evolution and extreme abundance discrepancies. The same nebulae have strikingly low ionized masses, between 0.001 and 0.1 solar masses depending on the adopted electron densities and temperatures, suggesting the observed nebulae were produced after the CE ejection, once the massive red-giant envelope had dispersed.

Corradi et al. (2015) examined candidate explanations, none consistent with all observations: a very late thermal pulse (a reignition of nuclear burning in a post-asymptotic-giant-branch star that can eject hydrogen-poor, carbon-rich material — disfavored by the low C/O ratios they measured); high-metallicity nova ejecta (thermonuclear runaways on an accreting white dwarf, whose ejecta are metal-enriched but are light, fast, and short-lived); fallback of common-envelope material onto the binary; and the tidal destruction of Jupiter-like planets. Follow-up work has since strengthened the empirical picture: Wesson et al. (2018) found adfadf values of 5–95 in seven more post-CE nebulae and showed statistically that all PNe with binary periods under about 1.15 days have adf>10adf>10 and low electron densities, while nebulae with longer-period binaries have normal values; integral-field-unit spectroscopy (MUSE on the Very Large Telescope, which yields a spectrum per image pixel) has directly mapped centrally concentrated, cold ORL-emitting gas in several extreme objects; and low-frequency radio observations report independent evidence for cold plasma in PNe. Nevertheless, current reviews still list the abundance discrepancy among the unsolved problems of PN research: the nature and location of the cold, hydrogen-poor component, and how common-envelope evolution could produce it, remain unidentified.

Problem Statement

Identify the physical origin of the cold, metal-rich, recombination-line-emitting gas phase in planetary nebulae with extreme abundance discrepancies, and the evolutionary mechanism by which close-binary (post-common-envelope) central stars produce it, establishing the answer quantitatively. The target requires (i) specification of the enrichment/ejection event and its timing relative to the common-envelope episode; (ii) quantitative consistency with the full set of observed constraints — ionized masses of order 10−310^{-3}–10−1 M⊙10^{-1}\,M_\odot, heavy-element enrichment of the cold phase while the warm phase retains normal composition, recombination contamination of auroral collisionally excited lines, the central concentration and distinct kinematics of the recombination-line gas with expansion velocities typical of planetary nebulae rather than novae, dynamical ages of order 10410^4 years, the empirical binary-period threshold near 1.15 days, and the anticorrelation between the abundance discrepancy factor and electron density; (iii) a quantitative account of the physical channel that produces the cold phase and of its behaviour across the relevant parameter space; and (iv) observational anchoring by a systematically selected sample of planetary nebulae with deep optical recombination-line and collisionally excited line spectroscopy combined with binary characterization of their central stars, drawn from the cited literature with its selection function stated, sufficient to establish the prevalence and statistical strength of the binarity–high-discrepancy connection and to test the prediction that extreme-discrepancy nebulae without a confirmed binary, such as NGC 6153 and M 1-42, host as-yet undetected close companions. Determining whether the mechanisms operating in planetary nebulae are relevant to the milder abundance discrepancies in other ionized environments such as H II regions — where temperature inhomogeneities have been shown to play a role — is part of the source question and turns on whether the identified mechanism extends to those milder discrepancies.

References

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