To appear in the refereed proceedings of the 11th Pacific Rim Conference on Stellar Astrophysics held in Hong Kong, Dec.14-17, 2015, Sun Kwok (editor). 10 pages, 2 figures
Emission and absorption line observations of molecules in late-type stars are a vital component in our understanding of stellar evolution, dust formation and mass loss in these objects. The molecular composition of the gas in the circumstellar envelopes of AGB stars reflects chemical processes in gas whose properties are strong functions of radius with density and temperature varying by more than ten and two orders of magnitude, respectively. In addition, the interstellar UV field plays a critical role in determining not only molecular abundances but also their radial distributions. In this article, I shall briefly review some recent successful approaches to describing chemistry in both the inner and outer envelopes and outline areas of challenge for the future.
Chemical modelling of AGB outflows is typically focused on either non-thermodynamic equilibrium chemistry in the inner region or photon-driven chemistry in the outer region. We include, for the first time, a comprehensive dust-gas chemistry in our AGB outflow chemical kinetics model, including both dust-gas interactions and grain-surface chemistry. The dust is assumed to have formed in the inner region, and follows an interstellar-like dust-size distribution. Using radiative transfer modelling, we obtain dust temperature profiles for different dust types in an O-rich and a C-rich outflow. We c…
Recent high spatial resolution observations of gas and dust in the circumstellar envelopes (CSEs) of AGB stars indicate morphologies much more complex than the smooth density distributions generated by spherically symmetric, constant mass loss rates. In particular, the observation of spiral arcs and disks indicate the likely presence of a binary companion which in some cases give rise to the UV photons detected by GALEX. In this Article, we extend our recent model of the chemistry in a clumpy, porous CSE around an AGB star to include the influence of stellar blackbody photons on the CSE chemis…
The envelopes of AGB stars are irradiated externally by ultraviolet photons; hence, the chemistry is sensitive to the photodissociation of N$_2$ and CO, which are major reservoirs of nitrogen and carbon, respectively. The photodissociation of N$_2$ has recently been quantified by laboratory and theoretical studies. Improvements have also been made for CO photodissociation. For the first time, we use accurate N$_2$ and CO photodissociation rates and shielding functions in a model of the circumstellar envelope of the carbon-rich AGB star, IRC +10216. We use a state-of-the-art chemical model of a…
Chemical equilibrium has proven extremely useful to predict the chemical composition of AGB atmospheres. Here we use a recently developed code and an updated thermochemical database, including gaseous and condensed species involving 34 elements, to compute the chemical equilibrium composition of AGB atmospheres of M-, S-, and C-type stars. We include for the first time TixCy clusters, with x = 1-4 and y = 1-4, and selected larger clusters ranging up to Ti13C22, for which thermochemical data is obtained from quantum chemical calculations. We find that in general chemical equilibrium reproduces …
Context. There is a class of binary post-asymptotic giant branch (post-AGB) stars that exhibit remarkable near-infrared (NIR) excess. Such stars are surrounded by Keplerian or quasi-Keplerian disks, as well as extended outflows composed of gas escaping from the disk. This class can be subdivided into disk- and outflow-dominated sources, depending on whether it is the disk or the outflow that represents most of the nebular mass, respectively. The chemistry of this type of source has been practically unknown thus far. Methods. We focused our observations on the 1.3, 2, 3 mm bands of the 30 m IRA…
AGB stars are, together with supernovae, the main contributors of stellar dust to the interstellar medium (ISM). Dust grains formed by AGB stars are thought to be large. However, as dust nucleation and growth within their outflows are still not understood, the dust-grain size distribution (GSD) is unknown. This is an important uncertainty regarding our knowledge of the chemical and physical history of interstellar dust, as AGB dust forms $\sim$ 70% of the starting point of its evolution. We expand on our chemical kinetics model, which uniquely includes a comprehensive dust-gas chemistry. The G…
We investigate the formation of hydrogen cyanide (HCN) in the inner circumstellar envelopes of thermally pulsing asymptotic giant branch (TP-AGB) stars. A dynamic model for periodically shocked atmospheres, which includes an extended chemo-kinetic network, is for the first time coupled to detailed evolutionary tracks for the TP-AGB phase computed with the COLIBRI code. We carried out a calibration of the main shock parameters (the shock formation radius and the effective adiabatic index) using the circumstellar HCN abundances recently measured for a populous sample of pulsating TP-AGB stars. O…
We have observed a small sample of hot post-AGB stars with the InfraRed Array Camera (IRAC) and the InfraRed Spectrograph (IRS) on-board the Spitzer Space Telescope. The stars were selected from the literature on the basis of their far-Infrared excess (i.e., post-AGB candidates) and B spectral type (i.e., close to the ionization of the envelope). The combination of our IRAC observations with 2MASS and IRAS catalog data, along with previous radio observations in the cm range (where available) allowed us to model the SEDs of our targets and find that in almost all of them at least two shells of …
We present yields from stars of mass in the range Mo<M<8Mo of metallicities Z=0.0003 and Z=0.008, thus encompassing the chemistry of low- and high-Z Globular Clusters. The yields are based on full evolutionary computations, following the evolution of the stars from the pre-Main Sequence through the Asymptotic Giant Branch phase, until the external envelope is lost. Independently of metallicity, stars with M<3Mo are dominated by Third Dredge-Up, thus ejecting into their surroundings gas enriched in carbon and nitrogen. Conversely, Hot Bottom Burning is the main responsible for the modification …
We have monitored over a ten-year interval the light variations of five evolved stars with very large mid-infrared excesses. All five objects appear to have oxygen-rich or mixed oxygen-rich and carbon-rich chemistries. They all vary in light: four over a small range of $\sim$0.2 mag and the fifth over a larger range of $\sim$0.7 mag. Spectral types range from G2 to B0. Periodic pulsations are found for the first time in the three cooler ones, IRAS 18075$-$0924 (123 days), 19207$+$2023 (96 days), and 20136$+$1309 (142 days). No significant periodicity is found in the hotter ones, but they appea…
Asymptotic giant branch (AGB) stars are significant contributors to the chemical enrichment of the interstellar medium (ISM) of galaxies. It is therefore essential to constrain the AGB contribution to the dust budget in galaxies. Recent estimates of the total dust injection rate to the Large and Small Magellanic Clouds (LMC and SMC; Riebel et al. 2012, Boyer et al. 2012, Srinivasan et al. in prep) have used data from the Spitzer Space Telescope SAGE (Surveying the Agents of Galaxy Evolution; Meixner et al. 2006) and SAGE-SMC (Gordon et al. 2011) surveys. When sorted by dust chemistry, the data…
(abridged) In the inner regions of AGB outflows, several molecules have been detected with abundances much higher than those predicted from thermodynamic equilibrium (TE) chemical models. The presence of the majority of these species can be explained by shock-induced non-TE chemical models, where shocks caused by the pulsating star take the chemistry out of TE in the inner region. Moreover, a non-uniform density structure has been detected in several AGB outflows. A detailed parameter study on the quantitative effects of a non-homogeneous outflow has so far not been performed. We implement a p…
To explain the properties of dust in the interstellar medium (ISM), the presence of a refractory organic mantle is necessary. The outflows of AGB stars are among the main contributors of stellar dust to the ISM. We present the first study of the refractory organic contribution of AGB stars to the ISM. Based on laboratory experiments, we included a new reaction in our extended chemical kinetics model: the photoprocessing of volatile complex ices into inert refractory organic material. The refractory organic feedback of AGB outflows to the ISM is estimated using observationally motivated parent …
We report an unbiased radio line survey towards the circumstellar envelopes of evolved stars at the frequency range from 20 to 25 GHz, aiming to obtain a more complete unbiased picture of the chemical evolution in the final stages of stellar evolution. The observation sample includes the asymptotic giant branch (AGB) star IRC+10216, the proto-planetary nebulae (PPNs) CRL\,2688 and CRL\,618, and the young planetary nebula (PN) NGC\,7027, representing an evolutionary sequence spanning about 10,000 years. Rotational transitions from cyanopolyyne chains and inversion lines from ammonia are detecte…
Binaries with circumbinary disks are commonly found among optically bright post-AGB stars. Although clearly linked to binary interaction processes, the formation, evolution and fate of these disks are still badly understood. Due to their compactness, interferometric techniques are required to resolve them. Here, we discuss our high-quality multiwavelength interferometric data of two prototypical yet very different post-AGB binaries, AC and 89 Herculis, as well as the modeling thereof with radiative transfer models. A detailed account of the data and models of both objects is published in three…
We present AKARI/IRC and Spitzer/IRS observations of a selected sample of galactic IRAS sources considered to be heavily obscured AGB/post-AGB stars based on their characteristic IRAS colours. All of them are completely invisible in the optical range but extremely bright in the infrared. Based on AKARI and Spitzer spectroscopy and using DUSTY we are able to determine the dominant chemistry of their circumstellar shells as well as the properties of the dust grains contained in these shells. Most of the sources are found to be C-rich (being the reddest C-rich stars observed so far). We find only…
Spherical asymmetries are prevalent within the outflows of AGB stars. Since binary interaction with a stellar or planetary companion is thought to be the underlying mechanism behind large-scale structures, we included the effects of UV radiation originating from a stellar companion in our chemical kinetics model. The one-dimensional model provides a first approximation of its effects on the chemistry throughout the outflow. The presence of a close-by stellar companion can strongly influence the chemistry within the entire outflow. Its impact depends on the intensity of the radiation (set by th…
The circumstellar environments of objects on the asymptotic giant branch and beyond are rich in molecular species. Nevertheless, methanol has never been detected in such an object, and is therefore often taken as a clear signpost for a young stellar object. However, we report the first detection of CH3OH in a post-AGB object, HD101584, using ALMA. Its emission, together with emissions from CO, SiO, SO, CS, and H2CO, comes from two extreme velocity spots on either side of the object where a high-velocity outflow appears to interact with the surrounding medium. We have derived molecular abundanc…
We investigate the dual-dust chemistry (DDC) phenomenon in PNe and discuss reasons for its occurrence, by analyzing Spitzer/IRS spectra of a sample of 40 Galactic PNe among which 26 belong to the Galactic Bulge (GB). The mixed chemistry is derived from the simultaneous detection of PAH features in the 6-14 micron range and crystalline silicates (CS) beyond 20 microns in the Spitzer/IRS spectra. Out of the 26 PNe observed in the GB, 21 show signatures of DDC. Our observations reveal that the simultaneous presence of O- and C-rich dust features in the IR spectra of [WC]-type PNe is not restricte…
Chemistry in the High expansion-velocity C-rich evolved star AFGL2233. Isotopic ratios, peculiarities and evolutionary status
Instituto de Física Fundamental (IFF-CSIC)（基础物理研究所）；Observatorio Astronómico Nacional (IGN)（国家天文台）；Institut de Radioastronomie Millimetrique（毫米波射电天文学研究所）
We model the synthesis of molecules and dust in the inner wind of the oxygen-rich Mira-type star IK Tau, by considering the effects of periodic shocks induced by the stellar pulsation on the gas, and by following the non-equilibrium chemistry in the shocked gas layers between 1 and 10 Rstar. We consider a complete set of molecules and dust clusters, and combine the nucleation phase of dust formation with the condensation of these clusters into dust grains. Our derived molecular abundances and dust properties are compared to the most recent observational data. The chemistry is described by usin…
The AKARI and Spitzer satellites provided an unique opportunity to observe a variety of stars, which are considered as departing from the Asymptotic Giant Branch (AGB) and have started their post-AGB evolution recently. Most of these stars are absent optically and are bright in the mid-IR wavelength range. Spectra of close to 200 objects have been obtained. For all of them the 1-60 micron spectral energy distribution has been constructed using photometric data from various surveys. We report here on the results of Spitzer observations of 88 IRAS selected post-AGB candidates and discuss them in…
W Aql is an asymptotic giant branch (AGB) star with an atmospheric elemental abundance ratio C/O$\approx$0.98 and reported circumstellar molecular abundances intermediate between those of M-type (C/O$<$1) and C-type (C/O$>$1) AGB stars. This intermediate status is considered typical for S-type stars, although our understanding of the chemical content of their circumstellar envelopes (CSEs) is currently rather limited. We performed observations in the frequency range 159-268 GHz with the APEX telescope and make abundance estimates through comparison to available spectra towards some well-studie…
Among presolar materials recovered in meteorites, abundant SiC and Al$_{2}$O$_{3}$ grains of AGB origins were found. They showed records of C, N, O, $^{26}$Al and s-element isotopic ratios that proved invaluable in constraining the nucleosynthesis models for AGB stars \cite{zin,gal}. In particular, when these ratios are measured in SiC grains, they clearly reveal their prevalent origin in cool AGB circumstellar envelopes and provide information on both the local physics and the conditions at the nucleosynthesis site (the H- and He-burning layers deep inside the structure). Among the properties…
Using a revised version of the catalog of AGB stars by Suh & Kwon (2009), we present various infrared two-colour diagrams (2CDs) for 3003 O-rich, 1168 C-rich, 362 S-type and 35 silicate carbon stars in our Galaxy. For each object in the new catalog, we cross-identify the AKARI, MSX and 2MASS counterparts by finding the nearest one from the position information in the IRAS PSC. For the large sample of AGB stars, we present infrared two-colour diagrams using IRAS (PSC), AKARI (PSC and BSC), MSX (PSC) and near infrared (K and L bands; including 2MASS data at KS band) data for different classes of…
The detected variety in chemistry and circumstellar shell morphology of the limited sample of Galactic post-AGB stars is so large that there is no consensus yet on how the different objects are linked by evolutionary channels. The evaluation is complicated by the fact that their distances and hence luminosities remain largely unknown. Via cross-correlation of the Spitzer SAGE catalogue with optical catalogues we selected a sample of LMC post-AGB candidates based on their [8]-[24] colour index and estimated luminosity. We determined the fundamental properties of the central stars of 105 of thes…
Many complex organic molecules and inorganic solid-state compounds have been observed in the circumstellar shell of stars (both C-rich and O-rich) in the transition phase between Asymptotic Giant Branch (AGB) stars and Planetary Nebulae (PNe). This short (~100-10.000 years) phase of stellar evolution represents a wonderful laboratory for astrochemistry and provides severe constraints on any model of gas-phase and solid-state chemistry. One of the major challenges of present day astrophysics and astrochemistry is to understand the formation pathways of these complex organic molecules and inorga…
We study the asymptotic giant branch (AGB) evolution of stars with masses between $1~M_{\odot} - 8.5~M_{\odot}$. We focus on stars with a solar chemical composition, which allows us to interpret evolved stars in the Galaxy. We present a detailed comparison with models of the same chemistry, calculated with a different evolution code and based on a different set of physical assumptions. We find that stars of mass $\ge 3.5~M_{\odot}$ experience hot bottom burning at the base of the envelope. They have AGB lifetimes shorter than $\sim 3\times 10^5$ yr and eject into their surroundings gas contami…
We present new Spitzer/IRAC observations of 55 dusty Long Period Variables (LPVs, 48 AGB and 6 RSG stars) in the Galaxy that have different chemistry, variability type, and mass-loss rate. O-rich AGB stars (including intrinsic S-type) tend to have redder [3.6]-[8.0] colors than carbon stars for a given [3.6]-[4.5] color due to silicate features increasing the flux in the 8.0 μm IRAC band. For colors including the 5.8 μm band, carbon stars separate into two distinct sequences, likely due to a variable photospheric C$_3$ feature that is only visible in relatively unobscured, low mass-loss rate s…
We present nucleosynthesis predictions (HeCNOCl) from asymptotic giant branch (AGB) models, with diffusive overshooting from all the convective borders, in the metallicity range Z/4 < Z < 2Zsun. They are compared to recent precise nebular abundances in a sample of Galactic planetary nebulae (PNe) that is divided among double-dust chemistry (DC) and oxygen-dust chemistry (OC) according to the infrared dust features. Unlike the similar subsample of Galactic carbon-dust chemistry PNe recently analysed by us, here the individual abundance errors, the higher metallicity spread, and the uncertain du…
Context: Stars evolving through the asymptotic giant branch (AGB) phase provide significant feedback to their host system, in form of both gas enriched in nuclear-burning products and dust formed in their winds, which they eject into the interstellar medium. Therefore AGB stars are an essential ingredient for the chemical evolution of the Milky Way and other galaxies. Aims: We study AGB models with super-solar metallicity, to complete our large database, so far extending from metal-poor to solar chemical compositions. We provide chemical yields for masses in the range 1-8 Msun and metallicitie…
To measure the mass loss from dusty oxygen-rich (O-rich) evolved stars in the Large Magellanic Cloud (LMC), we have constructed a grid of models of spherically-symmetric dust shells around stars with constant mass-loss rates using 2Dust. These models will constitute the O-rich model part of the "Grid of Red supergiant and Asymptotic giant branch star ModelS" (GRAMS). This model grid explores 4 parameters - stellar effective temperature from 2100 K - 4700 K; luminosity from 10^3-10^6 L_Sun; dust shell inner radii of 3, 7, 11, and 15 R_Star; and 10.0 micron optical depth from 10^-4 to 26. From a…
Stars are bad neighbors: they often disturb their surroundings. They sometimes travel very fast through the interstellar medium (ISM). They frequently undergo violent ejection events which leave an imprint on their neighborhood (jets, winds, supernovae). These supersonic flows generate shocks both in the ejected material (bow shock) and in the stellar environment (termination shock). The global purpose of this thesis is to link the properties of stars and the ISM by studying these shocks. We model them with the Paris-Durham planar shock code, which incorporates a wealth of micro-physics and ch…
The main aim is to derive reliable mass-loss rates and circumstellar SiO abundances for a sample of 40 S-type AGB stars based on new multi-transitional CO and SiO radio line observations. In addition, the results are compared to previous results for M-type AGB stars and carbon stars to look for trends with chemical type. The circumstellar envelopes are assumed to be spherically symmetric and formed by a constant mass-loss rate. The mass-loss rates are estimated from fitting the CO observations using a non-local, non-LTE radiative transfer code. Once the physical properties of the circumstellar…
The production of the elements heavier than iron via slow neutron captures (the s process) is a main feature of the contribution of asymptotic giant branch (AGB) stars of low mass (< 5 Msun) to the chemistry of the cosmos. However, our understanding of the main neutron source, the 13C(alpha,n)16O reaction, is still incomplete. It is commonly assumed that in AGB stars mixing beyond convective borders drives the formation of 13C pockets. However, there is no agreement on the nature of such mixing and free parameters are present. By means of a parametric model we investigate the impact of differe…
We combine variability information from the MAssive Compact Halo Objects (MACHO) survey of the Large Magellanic Cloud (LMC) with infrared photometry from the Spitzer Space Telescope Surveying the Agents of a Galaxy's Evolution (SAGE) survey to create a dataset of ~30 000 variable red sources. We photometrically classify these sources as being on the first ascent of the Red Giant Branch (RGB), or as being in one of three stages along the Asymptotic Giant Branch (AGB): oxygen-rich, carbon-rich, or highly reddened with indeterminate chemistry ("extreme" AGB candidates). We present linear period-l…
The first high-resolution (R~50,000) optical spectrum of the B-type star, LS III +52 24, identified as the optical counterpart of the hot post-AGB candidate IRAS 22023+5249 (I22023) is presented. We report the detailed identifications of the observed absorption and emission features in the full wavelength range (4290-9015 A) as well as the atmospheric parameters and photospheric abundances (under the Local Thermodinamic Equilibrium approximation) for the first time. The nebular parameters (Te, Ne) are also derived. We estimate Teff=24,000 K, log g=3.0, xi=7 kms-1 and the derived abundances ind…
The studies focused on the Thermally-Pulsing Asymptotic Giant Branch phase experienced by low- and intermediate-mass stars are extremely important in many astrophysical contexts. In particular, a detailed computation of their chemical yields is essential for several issues, ranging from the chemical evolution of galaxies, to the mechanisms behind the formation of globular clusters. Among all the uncertainties affecting the theoretical modelling of this phase, and described in the literature, it remains to be fully clarified which results are severely affected by the use of inadequate low-tempe…
Context. The circumstellar environment of evolved stars is generally rich in molecular gas and dust. Typically, the entire environment is either oxygen-rich or carbon-rich, depending on the evolution of the central star. Aims. In this paper we discuss three evolved disc sources with evidence of atypical emission lines in their infrared spectra. The stars were taken from a larger sample of post-AGB binaries for which we have Spitzer infrared spectra, characterised by the presence of a stable oxygen-rich circumbinary disc. Our previous studies have shown that the infrared spectra of post-AGB dis…
Context. The recent detection of warm H$_2$O vapor emission from the outflows of carbon-rich asymptotic giant branch (AGB) stars challenges the current understanding of circumstellar chemistry. Two mechanisms have been invoked to explain warm H$_2$O vapor formation. In the first, periodic shocks passing through the medium immediately above the stellar surface lead to H$_2$O formation. In the second, penetration of ultraviolet interstellar radiation through a clumpy circumstellar medium leads to the formation of H$_2$O molecules in the intermediate wind. Aims. We aim to determine the properties…
Context: We present the physical and chemical properties of intermediate-mass stars models of low metallicity, evolved along the thermal pulse phase. Aims: The target of this work is to extend to low metallicities, Z=1,2 and 6 x 10^{-4}, the models previously computed for chemistries typical of Globular Clusters of an intermediate metallicity (Z=0.001), and for the most metal-rich clusters found in our Galaxy (Z=0.004); the main goal is to test the self-enrichment scenario also for metal poor Globular Clusters Methods: We calculated three grids of intermediate-mass models with metallicities Z=…
Phosphorus-bearing compounds have only been studied in the circumstellar environments (CSEs) of the asymptotic giant branch (AGB) star IRC +10216 and the protoplanetary nebula CRL 2688, both C-rich objects, and the O-rich red supergiant VY CMa. The current chemical models cannot reproduce the high abundances of PO and PN derived from observations of VY CMa. No observations have been reported of phosphorus in the CSEs of O-rich AGB stars. We aim to set observational constraints on the phosphorous chemistry in the CSEs of O-rich AGB stars, by focussing on the Mira-type variable star IK Tau. Usin…
M1-92: AGB interruption and isotopic ratio paradox. Chemistry and morpho-kinematics from improved shapemol modelling
Observatorio Astronómico Nacional (OAN-IGN)（国家天文台（OAN-IGN））；Centro de Astrobiología (CAB), CSIC-INTA（天体生物学中心（CAB），西班牙国家研究委员会-西班牙航空航天技术研究所）；Institut de Radioastronomie Millimétrique（毫米波射电天文学研究所）；Ilumbra, AstroPhysical MediaStudio（Ilumbra 天体物理媒体工作室）；Department of Physics and Astronomy, University of Calgary（卡尔加里大学物理与天文学系）
During their asymptotic giant branch, evolution low-mass stars lose a significant fraction of their mass through an intense wind, enriching the interstellar medium with products of nucleosynthesis. We observed the nearby oxygen-rich asymptotic giant branch star IK Tau using the high-resolution HIFI spectrometer onboard Herschel. We report on the first detection of H_2^{16}O and the rarer isotopologues H_2^{17}O and H_2^{18}O in both the ortho and para states. We deduce a total water content (relative to molecular hydrogen) of 6.6x10^{-5}, and an ortho-to-para ratio of 3:1. These results are co…
A number of late [WC] stars have unique infrared properties, not found among the non-[WC] planetary nebulae, and together define a class of IR-[WC] stars. They have unusual IRAS colours, resembling stars in the earliest post-AGB evolution and possibly related to PAH formation. Most or all show a double chemistry, with both a neutral (molecular) oxygen-rich and an inner carbon-rich region. Their dense nebulae indicate recent evolution from the AGB, suggesting a fatal-thermal-pulse (FTP) scenario. Although both the colours and the stellar characteristics predict fast evolution, it is shown that …
The vital importance of composition-dependent low-temperature opacity in low-mass (M < 3Msun) asymptotic giant branch (AGB) stellar models of metallicity Z > 0.001 has recently been demonstrated (e.g. Marigo 2002; Ventura & Marigo 2010). Its significance to more metal-poor, intermediate mass (M > 2.5Msun) models has yet to be investigated. We show that its inclusion in lower-metallicity models ([Fe/H] < -2) is essential, and that there exists no threshold metallicity below which composition-dependent molecular opacity may be neglected. We find it to be crucial in all intermediate-mass models i…
We present results from the first application of the Grid of Red Supergiant and Asymptotic Giant Branch ModelS (GRAMS) model grid to the entire evolved stellar population of the Large Magellanic Cloud (LMC). GRAMS is a pre-computed grid of 80,843 radiative transfer (RT) models of evolved stars and circumstellar dust shells composed of either silicate or carbonaceous dust. We fit GRAMS models to ~30,000 Asymptotic Giant Branch (AGB) and Red Supergiant (RSG) stars in the LMC, using 12 bands of photometry from the optical to the mid-infrared. Our published dataset consists of thousands of evolved…
