The Role of Ultraviolet Photons in Circumstellar Astrochemistry
TThe Role of Ultraviolet Photons in Circumstellar Astrochemistry
T J Millar a) Astrophysics Research Centre, School of Mathematics and Physics,Queen’s University Belfast, Belfast BT7 1NN, UK (Dated: 1 January 2021)
Stars with masses between 1 and 8 solar masses (M (cid:12) ) lose large amounts of material inthe form of gas and dust in the late stages of stellar evolution, during their AsymptoticGiant Branch phase. Such stars supply up to 35% of the dust in the interstellarmedium and thus contribute to the material out of which our solar system formed.In addition, the circumstellar envelopes of these stars are sites of complex, organicchemistry with over 80 molecules detected in them. We show that internal ultravioletphotons, either emitted by the star itself or from a close-in, orbiting companion,can significantly alter the chemistry that occurs in the envelopes particularly if theenvelope is clumpy in nature. At least for the cases explored here, we find that thepresence of a stellar companion, such as a white dwarf star, the high flux of UVphotons destroys H O in the inner regions of carbon-rich AGB stars to levels belowthose observed and produces species such as C + deep in the envelope in contrast tothe expectations of traditional descriptions of circumstellar chemistry. a) [email protected] a r X i v : . [ a s t r o - ph . S R ] D ec . INTRODUCTION Mass loss from stars on the Asymptotic Giant Branch (AGB) phase typically lasts a fewtimes 10 years. Despite this short astronomical time-scale, this period of stellar evolutionis one of intense study for a number of reasons: (i) their atmospheres are a major siteof dust formation in the Universe; (ii) through their stellar winds, they provide at least30% of the dust found in the interstellar medium; (iii) the measurement of isotopic ratiosfrom molecular lines allows one to probe nucleosynthetic processes deep inside the star;(iv) a simple dynamical environment that allows physical properties of the wind, such asdensity, temperature, expansion velocities and chemical abundances, to be determined as afunction of radial distance through the circumstellar envelope (CSE), and (v) a relativelysimple ‘astrochemical laboratory’ in the outer CSE, having spherical symmetry, a large-scaleconstant-velocity expansion and with well-defined chemical processes that are dependent onradial distance from the star.These CSEs, particularly those around carbon-rich AGB stars - notably IRC+10216 (alsoknown as CW Leo) - are rich in linear carbon-chain species, such as C n H ( n = 1-8), C n O ( n =1-3,5), C n N ( n = 1-3,5), C n S ( n = 1-3,5), HC n N ( n = 1-5,7,9), the anions C n N − ( n = 1,3,5)and C n H − ( n = 4,6,8). One should note, however, that the linear nature of these speciesprovides a favourable aspect for radio astronomical detection of rotational transitions sinceit minimises the value of the rotational partition function - the intrinsic energy of rotationis spread over fewer energy levels than is the case for non-linear molecules.The CSE around IRC+10216 is a particular object of interest since over 80 moleculeshave been detected in it, indeed many for the very first, and some the only, time. In part,this is due to the carbon-rich nature of the wind since the carbon atom bonds easily to itselfand other elements, in part to its very high mass-loss rate, ˙ M , in excess of 10 − solar massesper year (M (cid:12) yr − ), and in part to its proximity to Earth, around 130 parsecs (pc). It has ahuge CO envelope extending to an angular radius of some 200 arcsec, or about 1 light year.At its distance from Earth, 1 arcsec is equivalent to about 2 × cm. Given its expansionvelocity, v e of about 15 km s − , material takes about 10 yr to move from the dust formationzone at a few stellar radii (R ∗ ) to the interstellar medium.Early observations of this source indicated that molecules could be grouped into twocategories, one in which they appeared close to the stellar photosphere and the other in2hich they appeared in shells of radii 12-20 arcsec and with widths of 2-4 arcsec . Theseobservations were shown to be consistent with a model in which parent species, such asC H , HCN and CO, were formed in the high-temperature chemistry near the photosphere,accelerated to terminal velocity through collisions with dust grains, and photodissociatedby interstellar UV photons as they moved outwards into a region of high interstellar UVflux. The formation of radical daughter products leads to a rapid chemistry that builds upmore complex molecules before they too are photodissociated by the interstellar field as theymove outward through the envelope. The high mass-loss rate of IRC+10216 ensures thatdensities are high and reactive time-scales short, on the order of a few hundred years, in thisinteraction zone.The early models describing molecule formation in the outer CSE were all based on thisdescription . The detection of abundant hot water at a temperature of several hundreddegrees, with a fractional abundance of around 10 − , in IRC+10216 led to a fundamentalreappraisal of these models since they predicted most oxygen would be locked up in COand very little would be free to form water in the warm inner CSE. Although a numberof suggestions were made for the formation of this hot water, that currently favoured isthat the CSE is clumpy enough to allow interstellar UV photons to penetrate unhinderedto the dense inner envelope. Once in this inner region, the photons can dissociate CO andSiO with the released O atoms able to react with H to form water . The importance ofnon-Local Thermodynamic Equilibrium (LTE) chemistry in the inner CSE was strengthenedfurther by the detection of methyl cyanide, CH CN, on an angular scale of 1-2 arcsec, amolecule which is not made efficiently through LTE chemistry.
II. CHEMICAL STRUCTURE
In the following sub-sections, I describe briefly the dominant chemistry as a function ofradial distance in the CSE.
A. The Photosphere
The photospheres of AGB stars consists of hot ( ∼ n = 10 -10 cm − ) gas in which LTE determines the chemical composition of the gas. After H , CO is3he most stable molecule and essentially takes up all of the available oxygen in an C-richstar and all the available carbon in an O-rich star. The excess abundance of oxygen in thelatter results in large abundances of molecules such as H O, SiO and SO, while the excessof carbon in the former leads to high abundances of C H and HCN.Sharp and Wasserburg present the results of LTE abundances and condensation se-quences of molecules as a function of the C/O ratio. Although these condensation cal-culations can give some information on the refractory species in which the elements aresequestered as dust grains condense from the gas, they ignore the detailed physics of grainnucleation and growth as well as the physical changes, for example, large-scale pulsations,thermal pulses, dredge-up of material from the stellar core to the surface, that the star itselfcan undergo.A much more detailed description of chemical equilibrium in O-rich, C-rich and S-type(where C/O ∼
1) AGB stars that takes into account both gas-phase and condensed-phasespecies among 34 elements has been presented by Ag´undez et al. . Their detailed predic-tions for molecular abundances within 5 R ∗ , calculated through mimimising the total Gibbsfree energy of the mixture, are compared to observational determinations where these areavailable. They show excellent agreement for many species, including C H , HCN, CS, SiS,SiO, SiC , HCP, HF and HCl in C-rich stars. For O-rich AGB stars, they find such agree-ment for H O, CO , H S, SO, SiO and PO. Many inorganic species are also observed inagreement with predictions in the inner envelope, including cyanides and isocyanides suchas MgCN, MgNC, NaCN, KCN and CaNC, halides such as AlF, AlCl, NaCl and KCl, andoxides such as TiO, TiO and AlO.Ag´undez et al. also note some significant failures in of the modelling, most importantlyfor the hydrides H O, SiH and PH in C-rich stars and NH in both C-rich and O-rich stars.The differences are very large, with calculated abundances falling some five to six orders ofmagnitude below those observed. Such failings have led to suggestions for the formation ofthese species through non-LTE chemistry, including shock and surface chemistry as discussedbelow. In addition to including simple diatomic and triatomic species, they have also usedDensity Functional Theory to calculate the thermochemical data for Ti x C y species up to x = 13 and y = 22 to identify the key condensation nuclei of the titanium carbide particlesoften found at the centre of extra-solar carbonaceous dust grains.4 . Pulsational Shock Waves Although LTE chemistry is treated in a ‘steady-state’ fashion, AGB stars undergo convec-tive motions, large-scale pulsations and thermal pulses, all of which can lead to spatial andtemporal inhomogeneities in physical conditions and to deviations from LTE abundances aswell as to isotopic compositions. The effects of pulsational shocks on the LTE abundanceshave been studied in detail in a series of papers by Cherchneff and co-workers . Theseperiodic shocks drive large changes in both density and especially in temperature whichessentially destroy all LTE molecules and allow a new gas-phase chemistry in the coolingpost-shock gas. In addition, these dense cooling flows also allow dust grains to nucleate andgrow. The shocked gas follows a ballistic trajectory, it is subject to repeated shocks, risingup and falling back in the atmosphere, thus enhancing the time-scale over which dust cangrow over several pulsation cycles before radiation pressure on the grains eventually enablesboth the gas and the dust to escape to the circumstellar envelope. The composition of thisgas can be significantly different from that predicted by the LTE models.In particular, Cherchneff has shown that hot water can be produced at an abundanceclose to that observed in IRC+10216 from O atoms released in the collisional destruction ofCO in the hot post-shock gas. C. Dust Formation
The formation of dust grains in AGB stars has traditionally been described by nucleationtheory in which grains grow by the addition of monomers to seed particles and assumeschemical equilibrium . More recently, there have been attempts to describe the kineticgrowth of dust grains, or more precisely, grain seeds, through using quantum mechanicalcalculations to determine the lowest energy structures and pathways to growth. Thus,Goumans and Bromley performed DFT calculations to identify the lowest energy pathwayfrom SiO to Mg Si O H , through the successive additions of either an oxygen or an Mgor Si atom at each intermediate step. Their calculations showed a common problem onforming grains, namely that the first steps in growth are often highly endoergic. Similarapproaches have been made by Bromley et al. , Gobrecht et al. and Boulangier et al. who combine DFT calculations with a chemical kinetic theory of growth and a new approach5o nucleation. D. Gas-Grain Chemistry
With the exception of grain formation at very high temperatures, gas-grain chemistryhas been neglected in essentially all circumstellar chemical models to date. This neglect isdue to the fact that the time-scales for collisions of the gas with the dust is shorter thanthe expansion time-scale only at radial distances where the grains are warm enough thatfew species can remain bound to their surfaces. Observations do indicate, however, that thegas-grain interaction may be significant even in the warm (T ∼ , NH , C H , and SiH , have abundances that appearto increase at radial distances of around 10-40 stellar radii in IRC+10216. In the interstellarmedium, large abundances of fully saturated molecules are associated with Hot MolecularCores, regions of high mass star formation with temperatures in the range 100–300 K and H number densities of 10 –10 cm − . Such high abundances result from the desorption of icemantles in which these hydrides have formed through hydrogen atom addition to C, N andO atoms on the ice surface. Although there is no evidence that C-rich AGB envelopes haveice-covered mantles, it is possible that the formation of these hydrides could be the result ofreactions involving chemisorbed species on warm, bare carbonaceous grains. The availabilityof chemisorption sites on bare grains may also serve as a trap for gas-phase molecules andradicals and lead to the removal of species from the gas. In particular, molecules involvingsilicon, such as SiO, SiC, SiS, SiC , and Si C, are often seen to have gas-phase abundancesthat decrease in this region of the CSE .Van de Sande et al. have recently produced the first model of the circumstellar chem-istry that includes the gas-grain interaction, with applications to both C-rich and O-richenvelopes. Their model includes the accretion of gas-phase species on to the dust grainstogether with surface chemistry involving hydrogenation and reactions between atoms andradicals. The ice mantles that form can be removed through thermal desorption, photodes-orption and sputtering of ice with abundant gas-phase molecules due to differential velocitiesin the outflow between the gas and the dust particles. The authors find that abundancescan be significantly altered in some circumstances depending on the choice of model param-6ters: mass-loss rate and expansion velocity – increasing ˙ M /v e increases the density in theCSE and thereby shortens the collisional time between gas and grains; grain temperature– which depends on the material composition, size and morphology of the dust particles.Surface chemistry is enhanced by faster diffusion rates on warmer grains; and drift velocity– sputtering rates increase as this increases. Although the binding energies of the gas-phasespecies are taken from laboratory studies of those in water ice mantles rather than on barecarbonaceous or silicate materials, these models are an important first step in consideringthe interaction of gas and dust in CSEs. Subsequently, Van de Sande et al. considered theeffects of different grain size distributions and performed radiative transfer calculations inorder to compare with molecular line observations finding that, in general terms, a combina-tion of their gas-grain model with observation may be able to constrain the size distributionof dust grains in CSE envelopes. E. The Outer CSE
Chemistry in the outer region of the CSE is dominated by radiation chemistry, that is, bythe interaction of the outflowing wind with the external UV radiation field produced by thegalactic stars in its neighbourhood. Since this interaction generates reactive radicals andions, it is important to treat the photodissociation of abundant molecules as accurately aspossible. In recent years, important advances in this regard have been made in accountingfor the self-shielding of CO and N . Given the significance of photons to determining the abundances and radial distribu-tions of molecules, we devote the following Section to the important topic of photon-drivenchemistry.
III. PHOTOCHEMISTRYA. External (Interstellar) UV Photons
Many of the molecules detected through micro- and millimeter-wave rotational spec-troscopy show clumpy, shell-like distributions on angular sizes of 10-20 arcsec. These dis-tributions have been interpreted, rather successfully, as arising from the photochemistryinduced by the destruction of outflowing, or ‘parent’, molecules from the inner CSE by in-7oming interstellar UV radiation. For stars such as IRC+10216, an extinction at visiblewavelengths of A V = 1 mag falls in a region of high density, n ∼ cm − so that radicalsand ions produced by UV photons collide and react to build more complex species on shorttime scales. Millar et al. showed that a photochemical model could explain both the de-creasing column densities of the cyanopolyynes (HC n +1 N, n = 1–4) and the increasing radiiof their peak abundances as their size increased. Such models, which assume a sphericallysymmetric CSE at constant mass-loss rate and outflow velocity, were very successful but donot address some of the more recent evidence that the mass-loss rate is not in steady statenor symmetric. For example, Mauron and Huggins showed that the CSE of IRC+10216contains a series of high density shells, while high spatial resolution observations of thecyanopolyynes and other hydrocarbon chains show that the molecular gas in these shells isclumped.Brown and Millar and Cordiner and Millar considered a simple model for thesedensity-enhanced shells and showed that they has an impact on the chemistry due to bothshorter collisional time scales and enhanced extinction against UV photons within the shells.The first ‘clumpy’ model of the outflow was developed to explain the detection of hot waterin IRC+10216, mentioned above in Sect. I. This model essentially allows a few percentof interstellar UV photons to penetrate deep into the molecular CSE and dissociate COand SiO unimpeded by the 40 mag or so of dust extinction at UV wavelengths, appropriatefor a mass-loss rate of 2 × − M (cid:12) yr − at a radius of 2 × cm. The liberated Oatoms then react quickly with H at these warm temperatures to form H O. The radicalOH, the photodissociation product of water is also detected in IRC+10216 . Note that theabundant CO species is not photodissociated since it self-shields very efficiently .Our detailed chemical kinetic models of the chemistry in the CSEs use the codes andreaction rate coefficients publicly available from the UMIST Database for Astrochem-istry website , with updated photodissociation rates calculated using the cross-sections provided in the Leiden photochemistry database . The initial, or parent, molecular abun-dances, that is for those molecules which are formed close to the stellar surface, are takenfrom Ag´undez et al. and shown in Table I. In this paper, we shall consider fractionalabundances of species i as a function of radial distance r , x i ( r ) = n i ( r ) /n H ( r ), where wenote that the H molecule is not photodissociated by the incident radiation field, so that n H ( r ) is proportional to r − for an envelope expanding at constant velocity v e .8 ABLE I. Parent species and their initial fractional abundances relative to H .Species Abund Species AbundHe 1.7 × − CO 8.0 × − N × − C H × − HCN 2.0 × − SiS 1.0 × − SiO 1.2 × − CS 5.0 × − SiC × − HCP 2.5 × − We can solve for the fractional abundance, x i ( r ), of species i as a function of radius. TheODE that describes the evolution of the fractional abundance of i due to both the expansionand chemistry can be written as:d x i d r = 1 v e (cid:88) j,k k jk x j x k n H ( r ) + (cid:88) l k l x l − x i (cid:34)(cid:88) m k im x m n H ( r ) + (cid:88) n k n (cid:35) (1)The first and third terms on the right hand side are the summation over all two-bodyreactions leading the formation and destruction of species i , respectively, while the sec-ond and fourth terms represent one-body reactions, that is photo-processes and cosmic-rayionisations, leading to the formation and destruction of i , respectively.We assume that the radial distribution of the gas temperature is given by a power-lawof the form T ( r ) = T star ( r/R star ) p , where T star and R star are the stellar temperature andradius, respectively, and p = -0.7.Fig. 1 shows the radial distribution of water and OH for both a smooth flow and forthe ‘low extinction-type’ model proposed by Ag´undez et al. for parameters typical ofIRC+10216, i.e. ˙ M = 2 × − M (cid:12) yr − and v e = 14.5 km s − . In the latter case Iadopt the ad hoc assumption of Ag´undez et al. that 2.5% of interstellar UV photonsare not extincted by dust and can penetrate down to the innermost envelope with theremaining 97.5% of photons extinguished by dust. The results confirm those of Ag´undezet al. For the standard smooth model, although water can be made in the internal CSE,that is, at radii less than 10 cm, its abundance is more than two orders of magnitude lessthan that observed. The clumpy model on the other hand efficiently photodissociates theinitial abundance of SiO and converts the oxygen atoms released into H O at an abundancewhich agrees with the range derived from observation , (4-24) × − . Note that the9hotodissociation rate adopted for SiO at 10 cm, the start of the outflow, is equivalentto an effective UV extinction of 3.7 in the clumpy medium, much less than the its value ofabout 420 in a smooth outflow. -11 -10 -9 -8 -7 -6 -5 H2O O OH F r a c t i ona l abundan c e Radius (cm)
FIG. 1. Molecular abundances relative to H as a function of radius in a model of IRC+10216that assumes 2.5% of interstellar UV photons are able to penetrate to 10 cm without beingextinguished by dust grains. The solid curves refer to a ‘smooth’ outflow, that is one in which thedensity distribution follows a 1 /r distribution. Dashed lines refer to the clumpy model. Colourcode: Green, H O; Red, OH; Black, O.
This simple model was improved by Van de Sande et al. who investigated the role ofclumps and pores on the transfer of interstellar photons to the inner CSE. Instead of an ad hoc assumption of the fraction of photons able to be transported free of the effects ofextinction, they assumed that the CSE is composed of a size distribution of clumps thattakes up a fraction f vol of the CSE and which are embedded in an interclump mediumcharacterised by the parameter f ic = ρ ic /ρ sm , the ratio of the interclump density to that ofa smooth, uniform outflow. Thus, f ic = 1 is equivalent to a smooth outflow, while f ic = 0represents a void interclump medium, that is a one-component outflow.Van de Sande et al. calculate an effective UV optical depth for external, interstellarphotons, τ eff , from radial distance r to infinity for an exponential distribution of clumps, f ( τ ) = 1 τ cl exp( − τ /τ cl ) (2)10here τ cl is the average optical depth of the clumps. This approach was applied to thechemistries of both O-rich and C-rich CSEs over a range of mass-loss rates from 10 − to10 − M (cid:12) yr − .Fig. 2 shows the abundance distributions when the approach by Van de Sande et al. is taken for the same physical parameters as used in Fig. 1. The particular case shownhere is a one-component model, which minimises the dust extinction seen by interstellarphotons, with f vol = 0.1, f ic = 0, that is where the mass of the outflow is contained inclumps that take up one-tenth of the total volume. Note that the calculations presented byVan de Sande et al. contained an error in that CO self-shielding was not included - seethe correction published by Van de Sande et al. . This has a large effect on abundancesin the inner envelopes of the one-component flows at the highest mass-loss rates, 10 − M (cid:12) yr − . In particular, the large enhancements derived by Van de Sande et al. for HCN inthe O-rich case and for H O in the C-rich case have been over-estimated. Note also thatthe effects for lower mass-loss rates are less sensitive to this omission since column densitiesof CO are reduced and therefore less sensitive to the effects of self-shielding in these cases.Fig. 2 does, however, include the correct CO self-shielding, although the Van de Sandemodels do not consider that of N , an omission that may affect their conclusions to somedegree, particularly for lower mas-loss rates. One sees here that, for this mass-loss rate, 2 × − M (cid:12) yr − , and volume filling factor, the radial distribution of the water abundanceis essentially identical for both the smooth and clumped outflows and much less than itsobserved value.Fig. 3 shows, again for a one-component model, that if the outflow is extremely clumpy, f vol = 0.01, then external photons can penetrate to the inner CSE, at a radial distance of lessthan 10 cm, and increase the water abundance by a factor of a few and the OH abundanceby several orders of magnitude. It is noticeable that the radial distribution of OH movesinward in this case due to the increased photodissociation rate of H O in the inner envelope.However, such small filling factors are inconsistent with the observations of IRC+10216.
B. Internal (Stellar) UV Photons
Since AGB stars are cool, with effective temperatures generally less than 3000 K, andform copious amounts of dust, it was rarely considered that they might emit sufficient UV11 -11 -10 -9 -8 -7 -6 -5 H2O O OH F r a c t i ona l abundan c e Radius (cm)
FIG. 2. As Fig. 1, except for a porous, clumpy, mass distribution in the CSE. In particular, theseresults are for a one-component distribution of mass, taking up a fraction 0.1 of the total volumeof the CSE. The solid curves refer to the smooth flow, dashed curves to the one-component model.Colour code: Green, H O; Red, OH; Black, O. -11 -10 -9 -8 -7 -6 -5 H2O O OH F r a c t i ona l abundan c e Radius (cm)
FIG. 3. As Fig. 2, except that the results are for a one-component distribution of mass, takingup a fraction f vol = 0.01 of the total volume of the CSE. The solid curves refer to the smooth flow,dashed curves to the one-component model. Colour code: Green, H O; Red, OH; Black, O. was the first to suggest that internally generated stellar(blackbody) photons might affect the chemistry of the internal CSE of IRC+10216 ( T eff =2330 K). At 50 R ∗ (or about 1 arcsec at the distance of IRC+10216), the flux of unshieldedstellar photons falls to more than 100 times less than the interstellar UV flux for λ < , are unaffected by the presence of thesephotons. Nevertheless, in a clumpy medium, internal stellar photons can play a significantrole in driving a selective chemistry on the spatial scales now being probed by the ALMAinterferometer.For a smooth outflow, the radial extinction in the UV from radius r to infinity is pro-portional to 1/ r . Thus, for the cool AGB stars, internal photons have a very large dustextinction as they propagate outwards and play no, or at most a very limited, role in chem-istry for mass-loss rates above 10 − M (cid:12) yr − . If the flows are porous, however, internalphotons can find pathways of low extinction to the external CSE although their effects aresmall since, in addition to dust extinction, the photon flux falls off as 1/ r due to geometricdilution.Van de Sande and Millar applied the porosity formalism to investigate the effects ofinternal stellar photons on chemistry. They found that for mass-loss rates above 10 − M (cid:12) yr − , the very large effective UV optical depths that occur between the dust formation zoneand around 10 R ∗ , that is within a radial distance of about 3–5 × cm, means that thereis no effective photochemistry. For smaller mass-loss rates, however, smaller effective opticaldepths mean that these photons can affect chemistry, again in a selective manner, and withthe largest effects seen in the one-component models which have the lowest optical depths.Thus, a point at radius r from the star sees external UV photons at an optical depth τ eff ( r )and stellar UV photons at an optical depth,∆ τ eff ( r ) = τ eff ( r d ) − τ eff ( r ) (3)where τ eff ( r d ) is the optical depth from the dust formation radius, r d , to infinity.Fig. 4 shows the effective extinction in the UV for internal photons propagating outwardsfrom the star for a variety of mass-loss rates for smooth, one-component and two-component(weighted) models. The appropriate rates for photodestruction by internal photons arecalculated using the cross-sections from Heays et al. as: β i ( r ) = β i ( r sc ) (cid:18) r sc r (cid:19) exp( − γ i ∆ A V ( r )) (4)13 ABLE II. Model parameters.Species Abund Species Abund˙ M × − M (cid:12) yr − v e − T star star × cmR dust × cm p -0.7No. Reactions 6516 No. Species 468 where β i ( r sc ) is the unshielded photorate of species i at a scaling radius r sc , and ∆ A V ( r )is the visual extinction from the dust formation radius to radial distance r . For thosespecies for which cross-sections are unknown, we use the scaling formula commonly used inastrochemical studies of interstellar clouds in which the unshielded interstellar rate, β IS0 , ismultiplied by the ratio of the integrated fluxes of stellar to interstellar photons (integratedover 6–13.6 eV): β IP0 = (cid:18) G ∗ G IS (cid:19) β IS0 (5)where G = (cid:90) ˚ A ˚ A F ( λ )d λ (6)and F ( λ ) is the photon flux.This approach can significantly overestimate the photoionisation rates for molecules sincetheir ionization potentials generally fall at energies where the flux of stellar UV photonsdepends sensitively on the assumed blackbody temperature of the source. For these specieswe have used a reduction factor determined from comparing photoionisation rates calculatedfor atomic ionisation, for which the exact cross-sections are known, to those calculated usingthe integrated approach. We include 336 photochannels due to stellar internal photons. Ourtotal chemical kinetic network thus includes, when internal photons from a companion object(see next Section) are also included, some 6516 reactions among 468 species.Table II gives the stellar parameters adopted for the models in this Section and Fig. 5shows the results for a model similar to that in Fig. 2 with the addition of stellar photons ata blackbody temperature of 2330 K, the effective temperature of IRC+10216. In this case,we see that the internal, stellar photons do not play any role in increasing the abundanceof water. Such low-energy photons can affect molecular distributions for smaller mass-loss14 f ic = f vol = A U V ( i n t e r na l ) Radius (cm)
FIG. 4. Effective radial extinction in magnitudes of internally generated UV photons for mass-lossrates of 10 − M (cid:12) yr − (solid lines), 2 × − M (cid:12) yr − (dashed lines), and 2 × − M (cid:12) yr − (dotted lines). The cases of smooth, one-component and two-component (weighted) outflows arecolor coded. rates and Fig. 6 shows the distributions for ˙ M = 10 − M (cid:12) yr − and an extremely clumpedoutflow with f vol = 0.01. Here one sees an enhancement in the fractional abundance ofwater by about an order of magnitude at 10 cm. One should note that the amount ofdust and hence extinction is directly proportional to the mass-loss rate. Thus, at radius r ,both the total and effective extinctions are an order of magnitude less in Fig. 6 as those inFigs. 2 and 5. As a result, the distributions of water lie closer to the star in the case oflower mass-loss rate since interstellar photons do not suffer as much extinction while stellarblackbody photons also suffer less extinction as they propagate outwards through the CSE. C. Internal (Companion) UV Photons
Stellar blackbody photons may not be the only source of internal UV photons in someAGB stars. Broadband
GALEX observations show that a significant fraction of AGB starsare detectable at UV wavelengths. In a survey of 316 AGB stars, Montez et al. findthat 179 (57%) are detected at NUV (2310˚A) and 38 (12%) detected at FUV (1528˚A)wavelengths. In a careful study, they show that de-reddened, distance-corrected NUV fluxes15 -11 -10 -9 -8 -7 -6 -5 H2O O OH F r a c t i ona l abundan c e Radius (cm)
FIG. 5. Water abundance in a model of IRC+10216 that assumes a porous, one component,clump mass distribution in the CSE with f vol = 0.1 and includes a source of internal UV photonsfrom a stellar blackbody at a temperature of 2330 K. The solid curves refer to the smooth flow,dashed curves to the one-component model. Colour code: Green, H O; Red, OH; Black, O. correlate inversely with ˙
M /v e , a measure of the H number density per unit volume in theCSE, and that in some cases the UV fluxes correlate with the optical light curves, evidenceconsistent with a stellar, or intrinsic, source for the UV radiation.In a similar manner, Ortiz and Guerrero have shown that main-sequence binary com-panions of AGB stars can be inferred from the detection of an AGB star in the GALEXfar-UV band and with an observed flux ratio more than 20 times that predicted in theGALEX near-UV band. They show that 34 stars out of a volume-limited sample of 58 fulfillthese criteria indicating that they have a main-sequence companion earlier than spectraltype K0. Furthermore, they argue that the excess UV emission is not due to a single tem-perature companion, as might be expected from a star, but may reflect either absorptionby the extended atmosphere and CSE of the AGB star or be produced by an accretionflow. Subsequently, Ortiz et al. argued from a survey of some 20 UV-emitting AGB starsthat the far-UV, i.e. the highest energy, photons might arise from a hot companion or anaccretion disk.These results indicate that internal UV radiation may be present in a significant fractionof AGB stars, generated either by a stellar companion or by the accretion disk around a star16 -11 -10 -9 -8 -7 -6 -5 H2O O OH F r a c t i ona l abundan c e Radius (cm)
FIG. 6. As Fig. 3, but for a mass-loss rate of 10 − M (cid:12) yr − and a source of internal UV photonsfrom a stellar blackbody at a temperature of 2330 K. Here f vol = 0.01. The solid curves refer tothe smooth flow, dashed curves to the one-component model. Colour code: Green, H O; Red, OH;Black, O. or a planet.The physical effects of companion objects may also be imprinted on the density struc-ture of the CSE gas. Thus the beautiful spiral patterns detected in IRC+10216 and RSculptoris , LL Peg and the equatorial density enhancement in L Pup , as well as thecomplex density structures seen in all O-rich AGB stars studied at high spatial resolution inthe ALMA Large Programme ATOMIUM , can all be interpreted in terms of an orbitingstellar or planetary companion that perturbs the radial outflow from the AGB star. Re-cently, Homan et al. used ALMA to study the CO and SiO emission in the CSE of theO-rich AGB star EP Aqr at high angular resolution. They found evidence of complex hy-drodynamic flows in the inner envelope including a central equatorial density enhancement,which itself contains spiral structures, a bi-conical outflow and a spherical void in the SiOemission at a distance of ∼
55 au from the star. They argued that the void is due to UV de-struction of SiO by a white dwarf companion at a temperature of around 6000 K and a massbetween 0.65 and 0.8 M (cid:12) and, furthermore, that it is this companion that perturbs non-radial motions in the wind of the AGB star. Several theoretical models have been presentedshowing that the nature of these complex structures depends on the radial momentum in17he wind compared to the orbital angular momentum of the companion and therefore onparameters such as the mass-loss rate, the mass ratio of the primary and companion, theorbital radius of the companion, and the stellar wind velocity at the orbital distance of thecompanion, amongst others.
In order to examine the effects of UV flux from a companion object, we show in Fig. 7results from a series of representative models for a carbon-rich outflow that combine ourporosity approach with three sources of UV radiation: (i) the external interstellar flux, (ii)a cool (2330 K) blackbody AGB stellar flux, as discussed in Sect.III B, and (iii) a hotterblackbody flux from a companion object such as a white dwarf or an accretion disk. Inthese models, we choose a white dwarf companion with temperature equal to 6000 K anda radius of 1.8 × cm (0.26 R (cid:12) ). We note that, at this temperature, the neglect of N self-shielding does have an effect on the abundances calculated for N in the inner envelopefor the one-component models. In particular, the models may severely underestimate the N abundance for radii less than a few times 10 cm, although its impact on the abundances ofC + and H O, discussed below, is likely to be minimal. In these figures, we show the fractionalabundances as a function of radius calculated for three models: green curves are for ‘smooth’outflows, i.e. with density proportional to r − ; red curves are for ‘one-component’ models inwhich the interclump density is zero, i.e. f ic = 0; and black curves represent the fractionalabundance weighted over those calculated for the interclump and clumpy media. For thiswe use the formula provided by Van de Sande et al. : x wt ( r ) = x cl ( r ) + f ic (1 − f vol )( x ic ( r ) − x cl ( r )) (7)where x wt , x cl and x ic are the weighted, clump and interclump fractional abundances, respec-tively. These particular models are for the case of f ic = 0.1 and f vol = 0.2 and for mass-lossrates of 10 − M (cid:12) yr − , 2 × − M (cid:12) yr − , and 2 × − M (cid:12) yr − .The impact of internal, companion UV photons is very significant in the case of lowmass-loss rates with the entire CSE showing a significant degree of ionisation from thephoto-degradation of parent C H , HCN and CH . In these cases it can be seen that, evenfor mass-loss rates on the order of 2 × − M (cid:12) yr − , abundant C and C + can be formed justoutside the dust formation zone, although the latter’s abundance falls rapidly as internalphotons from the white dwarf get extinguished by dust grains. These species are due to thephotodissociation of parent HCN and C H with C + most abundant in the highly clumped,18 -12 -11 -10 -9 -8 -7 -6 -5 f ic = f vol = + C Smooth1compWeighted F r a c t i ona l abundan c e Radius (cm) -12 -11 -10 -9 -8 -7 -6 -5 f ic = f vol = + C Smooth1compWeighted F r a c t i ona l abundan c e Radius (cm) -12 -11 -10 -9 -8 -7 -6 -5 f ic = f vol = + C Smooth1compWeighted F r a c t i ona l abundan c e Radius (cm)
FIG. 7. Distribution of C, C + and CH fractional abundances for a stellar BB at 2330 K and awhite dwarf companion at 6000 K. Mass-loss rates are 10 − M (cid:12) yr − ( top), 2 × − M (cid:12) yr − (middle), and 2 × − M (cid:12) yr − (bottom). Solid lines show the CH abundance, dashed lines thatof C, and dotted lines C + . one-component outflows with f vol = 0.2 (Fig. 7). As f vol increases, the outflow becomes‘smoother’ ( f vol = 1) and the ability of internal photons to produce C + decreases (‘smooth’curves, Fig. 7).Finally, we discuss the effect of companion UV photons on the radial distribution of water,19hich we discussed previously in Sec. III A and Sec. III B. In both cases we found that thefractional abundance of H O increased somewhat depending on the value of the mass-lossrate and the degree of porosity with the largest effect seen in the one-component models atlow values of ˙ M . Fig. 8 shows the distribution of H O, OH and O for mass-loss rates of 10 − M (cid:12) yr − , 2 × − M (cid:12) yr − , and 2 × − M (cid:12) yr − with an additional companion UV fieldfrom a 6000 K blackbody.Unlike the cases discussed earlier in Sec. III B, in which internal radiation is providedsolely by a cool stellar blackbody, the addition of an internal 6000 K radiation field from awhite dwarf companion destroys H O in the inner regions and its abundance is much less,by more than an order of magnitude, than that found when the companion field is absent(see Fig. 5) and much less than its observed fractional abundance of ∼ − . IV. CONCLUSIONS
Models of the chemical processes in the circumstellar envelopes of AGB stars that adoptspherical symmetry are still important in describing the observation of molecular emission inthe outer envelopes where the majority of molecules are found. It is clear, however, that thedensity distributions of the inner CSEs, in particular, can no longer be described in termsof spherically symmetric, constant velocity outflows irradiated solely by external interstellarUV photons. Furthermore, the fact that AGB stars are cool, with effective temperaturesless than 3500 K, typically, means that stellar photons are unable to photodissociate or pho-toionise many of the common molecules produced near the stellar surface, thereby limitingtheir effect on chemistry. Non-smooth outflows are not only driven by stellar phenomenasuch as thermal pulses or surface inhomogeneities but also by the presence of (sub-)stellarcompanions. As shown conclusively by the ATOMIUM results , it is highly likely that themajority of O-rich AGB stars have a stellar or planetary companion that affects the physicalstructure of the outflow and which may contribute to the internal UV flux that permeatesthe dust formation zone. While the evidence of companions objects in C-rich objects is lesscomprehensive, there is no reason to believe that the presence of companions will be any lesslikely in them than those in O-rich stars. It may be the case, however, that the nature ofthe density perturbations differ in both types of star due to their different dust compositionswhich can drive larger mass-loss rates in C-rich than in O-rich stars as carbonaceous grains20 -12 -11 -10 -9 -8 -7 -6 -5 f ic = f vol = F r a c t i ona l abundan c e Radius (cm) -12 -11 -10 -9 -8 -7 -6 -5 f ic = f vol = F r a c t i ona l abundan c e Radius (cm) -12 -11 -10 -9 -8 -7 -6 -5 f ic = f vol = F r a c t i ona l abundan c e Radius (cm)
FIG. 8. Distribution of H O, OH and O fractional abundances for a stellar BB at 2330 K and awhite dwarf companion at 6000 K. Mass-loss rates are 10 − M (cid:12) yr − (top), 2 × − M (cid:12) yr − (middle), and 2 × − M (cid:12) yr − (bottom). Solid lines show the H O abundance, dashed lines thatof OH, and dotted lines O. are more efficient absorbers of stellar radiation than the silicates present in O-rich CSEs.Thus the ratio of radial momentum to orbital angular momentum can be larger in C-richthan O-rich stars, making the radially directed winds from the former harder to perturb.Furthermore, the presence of a non-central, and non-blackbody, UV source, such as a21tellar chromosphere, a (sub-)stellar companion, or an accretion disk, means that the trans-port of photons in a non-symmetric, clumpy medium and its effect on chemistry will becomplex to model. The chemical effects of far-UV photons implies that the initial stagesof dust formation may involve not only to neutral-neutral reactions, as has been commonlyassumed, but also reactions between ions and neutrals. Depending on the nature of theradiation source and the wavelength dependence of the UV flux, chemistry in such regionsmight be much more selective than is the case in the interstellar medium. That is, only cer-tain species may be dissociated or ionised. For example there may be no photons energeticenough to ionise carbon or sulfur atoms and, as a result, their chemistries may be morerestricted than they are in interstellar clouds.In Sect. III A, we showed that external, interstellar UV photons cannot affect the chem-istry in the inner CSEs of AGB stars unless either the mass-loss rate is low, less than about10 − M (cid:12) yr − , or the material is highly clumped so that the effective extinction is aroundtwo orders of magnitude less than that observed in a smooth outflow. An alternative meansby which UV photons can affect the inner chemistry is to consider the role of UV photonsgenerated by the AGB star itself (Sect. III B) or by a companion object (Sect. III C). In theformer case, internal stellar photons are unable to affect the chemistry for mass-loss ratesmuch above 10 − M (cid:12) yr − due to the effects of dust extinction . In particular, the largeabundance of water detected in IRC+10216 is not reproduced in a model in which f vol = 0.1due to the large effective extinction in the inner envelope. Indeed Fig. 5 shows that stellarphotons do not alter the abundance of H O at all for radii less than a few times 10 cm.For a much more porous envelope, for example with f vol = 0.01, then the water abundanceincreases by about a factor of 3–4 at 10 cm, although still at a level about an order ofmagnitude less than that observed.If the mass-loss rate is much smaller than that in IRC+10216, for example, 10 − M (cid:12) yr − ,then the water abundance does increase somewhat but its maximum fractional abundanceis 10 − at 10 cm, even for a highly porous outflow with f vol = 0.01, though still more thanan order of magnitude less than observed (Fig. 6).The inclusion of an internal, ‘hot’ source of UV photons, for example from a stellar chro-mosphere, a stellar companion, or an accretion disk around a companion, can change theinternal abundances appreciably even for cases in which f vol is relatively large, as shown inFigs. 7 and 8. The nature of the changes made depends very sensitively on the particular22hysical parameters chosen, including those associated with the companion – size, temper-ature, the wavelength dependence of the UV flux – and on those associated with the AGBstar – mass-loss rate, wind velocity, clumpiness and porosity of the circumstellar envelope,for example. These sensitivities will be explored more fully in a future publication. ACKNOWLEDGMENTS
This manuscript has been improved by the comments of the referees for which I amgrateful. I would like to thank the STFC for support under grant number ST/P000312/1as well as the organisers, in particular Dr Xiaohu Li, of the International Workshop onAstrochemistry, Xi’an, 2019, for their hospitality during my time in Xi’an.
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