--- author: - 'D. Hatzidimitriou, G. E. Addison, A. J. Drake, R. P. Fisher, S. P. Helden' title: 'A Search for CO in Planetary Nebulae with ALMA' --- [We present an ALMA 12-m Band 7 continuum and H$_2$O megamaser search of a sample of 12 planetary nebulae (PNe). Our data aim to place the first observational limits on the abundance of CO in the circumstellar ejecta of PNe and set limits on the H$_2$O surface abundance relative to H$_2$ and compare these abundances with theoretical predictions. ]{} [We observed all 12 targets with ALMA and obtained upper limits on the millimeter continuum emission from the ionized regions of the PNe, while simultaneously observing in the H$_2$O 6$_{16}$–5$_{23}$ line. Continuum visibilities and line visibilities were combined using an imaging method. All sources were detected in continuum emission at $\ge3\sigma$. We present upper limits on the CO luminosity and CO abundance relative to H$_2$. The H$_2$O lines are detected in one source (NGC 7027).]{} Introduction {#sec:intro} ============ Planetary nebulae (PNe) are formed when low-mass stars, either in the post-Asymptotic Giant Branch (AGB) phase or post-main sequence, eject their outer stellar envelopes. Material at the end of the AGB phase is ionized by shocks in a fast wind launched from the star. After the ejection of the envelope, these central stars evolve rapidly, and the post-AGB stellar evolution timescale is extremely short: a few 100-1000 yr [@kwok93]. The morphology and kinematics of PNe therefore reflect the properties of the circumstellar gas as it evolves during the recombination phase. The interaction of the fast wind with the circumstellar envelope is likely to produce shocks. @sugerman05 [@sugerman06] showed that H$_2$ emission can be found in a wide range of morphologies, from the well known cometary and hourglass structures to extended filaments or even more diffuse emission. They also showed that H$_2$ emission is common at levels of 0.1–1% of the H$\alpha$ intensity and that a good correlation is found between H$_2$ and H$\alpha$ fluxes in nearby PNe. The detection of molecular hydrogen (H$_2$) in most PNe indicates that H$_2$ must be present in these nebulae at some level. In PNe, as in molecular clouds, H$_2$ can be seen at large distances from the central star if there is a sufficient density of molecules. @kwok09 has proposed that the H$_2$ in PNe is present in a thin layer on the surface of the neutral shell. The fact that the H$_2$ and H$\alpha$ emission correlates suggests that a portion of the H$_2$ emission is associated with the ionized material [@henney04]. Hydrogen molecules are probably hydrogenated, and the molecules with the largest column densities of all the molecules formed in the recombination layers are CO, whose rotational transition lines are the most prominent molecular lines observed in PNe [@schoenfeld14]. The first detection of CO emission was reported in NGC 7027 by @dickman86. Since then, detections of CO lines and H$_2$O emission have been reported in both high-mass and low-mass PNe [@zuckerman92; @girardello97; @aaltostrom00; @aaltostrom12; @decin03; @dors03; @vanwinckel00; @boonman03; @yamauchi04]. These observations suggest that, after recombination of the gas, both carbon and oxygen are locked in molecules. It is generally accepted that in PNe the molecular formation depends on the availability of C and O atoms in the neutral atomic gas. It has been suggested that, due to their location in the shell of the nebula, molecular gas can be detected at different distances from the central star. There is little doubt that both the observed molecules have formed in the cold neutral material which is exposed to the ultraviolet photons and high temperatures of the hot-CSPN in a PNe. Many efforts have been carried out to study the role of UV radiation in the gas heating as well as chemistry of the gas. Theoretical predictions have included sputtering and grain sublimation, gas-phase chemistry of the most abundant elements, including that of CO [@stevens98], high-temperature chemistry of C, O and N [@willacy98] and UV-induced photodissociation of the most abundant molecules [@jura75; @vanD88; @lee07; @aaltostrom07]. The main factor controlling the fate of the ejected gas is the high-energy UV flux, which heats the gas to ionizing energies. These calculations consistently predict that the abundance of CO decreases with decreasing temperature as a result of photo-recombination to form C$^{+}$ and O$^{+}$ ions in the high temperature region. The lower limit for the CO abundance is $\sim10^{-6}$ to 10$^{-7}$ relative to H$_2$. Models also predict a steep rise of the CO abundance with temperature in a relatively narrow range of about 5000–35000 K [@aaltostrom07; @willacy98]. Such an abundance distribution predicts the possible presence of CO at distances from the central star $>$ 20–30 arcsec for $T_{\rm e}$ $\sim$10000 K. On the other hand, a higher temperature would also produce a larger radial extent of the carbon chain molecules. There are many chemical models developed to predict the formation of CO in PNe [e.g., @josselin08; @vand98; @pety05; @chia03; @robitaille10; @lee07; @tielens93; @henning04]. Most of these models predict the abundance of CO in PNe to be larger than about $10^{-4}$. These predictions were confirmed by interferometric observations of CO in a few PNe: BD+30$^\circ$3639 [@leurini15], Hen 2-428 [@kami98], NGC 6543 [@mats04] and NGC 7009 [@mookerjea09]. On the other hand, the theoretical CO abundance has been found to be too low by @schoenfeld14 for a wide range of PNe. On the other hand, the theoretical abundances of CO and H$_2$O are in agreement with observationally derived abundances [@schoenfeld14; @aaltostrom12]. The formation and stability of CO and CO molecules has been well studied in the last couple of decades [@chia03; @lee07; @aaltostrom07; @lee00; @vanD88]. As a result, it is now accepted that CO molecules are chemically and physically stable in PNe. Recent models indicate that the detection of carbon-bearing molecules is possible in PNe whose temperature and UV flux is sufficient to produce such molecules, and the emission of molecular lines becomes more prominent as the source is at larger distances from the central star [@fujii13]. Other molecules can be produced in PNe, but very few detections have been made for such molecules. Recently, @debeck14 detected H$_2$ emission from the A0Ib-type star IRC+10420, which is embedded in the well known PN K 3-35. This star is believed to be the precursor of a PN and, in fact, is believed to be an evolutionary progenitor of the Sun. This detection revealed the physical conditions of the early stages of star formation. Recently, @latter2014 have shown that H$_2$ emission is detected from the bipolar outflow from the PN AFGL 2688 [@jones13], a well known PPN [@weidmann96], while they also found H$_2$ in absorption in the direction of the very compact object HBC 722 [@bauer14], a young and compact PN [@napiwotzki93]. The detection of gas-phase molecular line emission in PNe indicates that this phenomenon is common and may be related to the presence of a large reservoir of molecular gas surrounding young PN central stars. @sahai98 proposed a model for the PN phase in which C$^{+}$ and O$^{+}$ are produced in the surface of the central star or in the gas close to the central star, which subsequently forms carbon-chain molecules (carbon-chain chemistry). @schilke97 suggested that, in addition to CH$^+$, C$_2$H$^+$, C$_3$H$^+$, C$_4$H$^+$ and C$_5$H$^+$ ions are the products of the ionization of the surface of the star, forming a carbon forest in the innermost part of the nebula. These ions would then react with C and O atoms, leading to carbon-chain molecules. Other ions formed from the destruction of CO molecules, such as C$_3$ and CO$_2^+$, can be produced via this mechanism. In this model, the abundance of carbon-chain molecules is controlled by the strength of UV field. However, in this model, the abundance of CO is not related to the abundance of other carbon-