Super-AGB Stars and their role as Electron Capture Supernova progenitors
Carolyn L. Doherty, Pilar Gil-Pons, Lionel Siess, John C. Lattanzio
aa r X i v : . [ a s t r o - ph . S R ] M a r Publications of the Astronomical Society of Australia (PASA)c (cid:13)
Astronomical Society of Australia 2017; published by Cambridge University Press.doi: 10.1017/pas.2017.xxx.
Super-AGB Stars and their role as Electron Capture Supernovaprogenitors
Carolyn L. Doherty , , Pilar Gil-Pons , Lionel Siess , and John C. Lattanzio Konkoly Observatory, Hungarian Academy of Sciences, 1121 Budapest Monash Centre for Astrophysics, School of Physics and Astronomy, Monash University, Australia Polytechnical University of Catalonia, Barcelona, Spain Institut d’Estudis Espacials de Catalunya, Barcelona, Spain Institut d’Astronomie et d’Astrophysique, Universit´e Libre de Bruxelles, ULB, Belgium
Abstract
We review the lives, deaths and nucleosynthetic signatures of intermediate mass stars in the range ≈ . ⊙ ,which form super-AGB stars near the end of their lives. We examine the critical mass boundaries both between differenttypes of massive white dwarfs (CO, CO-Ne, ONe) and between white dwarfs and supernovae and discuss the relativefraction of super-AGB stars that end life as either an ONe white dwarf or as a neutron star (or an ONeFe white dwarf), af-ter undergoing an electron capture supernova. We also discuss the contribution of the other potential single-star channelsto electron-capture supernovae, that of the failed massive stars. We describe the factors that influence these different finalfates and mass limits, such as composition, the efficiency of convection, rotation, nuclear reaction rates, mass loss rates,and third dredge-up efficiency. We stress the importance of the binary evolution channels for producing electron-capturesupernovae. We discuss recent nucleosynthesis calculations and elemental yield results and present a new set of s-processheavy element yield predictions. We assess the contribution from super-AGB star nucleosynthesis in a Galactic perspec-tive, and consider the (super-)AGB scenario in the context of the multiple stellar populations seen in globular clusters. Abrief summary of recent works on dust production is included. Lastly we conclude with a discussion of the observationalconstraints and potential future advances for study into these stars on the low mass/high mass star boundary . Keywords: stars: AGB and post-AGB – stars: evolution – supernovae: general – white dwarfs– nuclear reactions, nucle-osynthesis, abundances
Stars in the mass range ≈ . ⊙ bridge the dividebetween high mass stars and low mass stars, and evolvethrough a super asymptotic giant branch (super-AGB) phasecharacterised by degenerate off-centre carbon ignition priorto the thermally pulsing phase. While super-AGB modelsfor the first few thermal pulses have existed for quite sometime (e.g. Garcia-Berro & Iben, 1994; Ritossa et al., 1996),it is only relatively recently that there has been a resur-gence in their study and that full evolutionary models havebeen computed for the entire thermally pulsing phase (e.g.Siess, 2010; Ventura & D’Antona, 2011; Lau et al., 2012;Karakas et al., 2012; Gil-Pons et al., 2013; Ventura et al.,2013; Jones et al., 2013; Doherty et al., 2015). Two majorreasons why this class of star had remained relatively un-derstudied for so long are the computational difficulties offollowing degenerate off-centre carbon ignition and the verylarge number of thermal pulses expected for super-AGBstars, ranging from tens to even thousands. One important and highly desirable outcome from stel-lar calculations for this mass range is a determination of thefinal fate of such objects. The three critical masses for in-termediate mass stars, each of which depends on the stellarcomposition are:1. M up , the minimum mass required to ignite carbon;2. M n , the minimum mass for creation of a neutronstar;3. M mas , the minimum mass defining the regime ofmassive stars, specifically those which undergo allstages of nuclear burning and explode as iron corecollapse supernovae (FeCC-SNe) .In the standard picture, a star with a mass below M up will end its life as a CO white dwarf (WD). Stars withmasses between M up and M n leave either a CO-Ne or These masses are often given different names in the literature; M up is alsoknown as M CO , M n is also know as M EC and M mas is also known as M up , M up ′ , M up ∗ , M min , M W , M mass M crit and M ccsn . We use SN for “supernova” and SNe for the plural “supernovae”. Doherty et al.
ONe WD remnant, whilst stars with masses between M n and M mas undergo an electron-capture supernova (EC-SN),ending their lives as neutron stars (e.g. Nomoto, 1984;Ritossa et al., 1999; Siess, 2007; Poelarends et al., 2008;Jones et al., 2013; Doherty et al., 2015).A considerable amount of study had been devoted to theexplosive deaths of stars in mass range 8 – 12 M ⊙ , in partic-ular their potential demise as EC-SNe. The earliest works(e.g. Miyaji et al., 1980; Nomoto, 1984; Hillebrandt et al.,1984; Nomoto, 1987) involved the evolution of “heliumballs” with core masses ∼ . ⊙ through He and Cburning with the resultant ONe cores then evolved to condi-tions very close to the expected explosion. Electron captureSNe are caused by the reduction of pressure support due toelectron capture reactions on Mg and Ne in stars withH-exhausted core masses ∼ ⊙ (Miyaji et al., 1980;Hillebrandt et al., 1984; Nomoto, 1987) . The electron cap-tures on these isotopes lead to a reduction both in electronfraction ( Y e ) and the Chandrasekhar mass, which triggerscontraction (Miyaji et al., 1980; Nomoto, 1987). Within thiscollapsing core, the competition between the energy releaseby O burning and the reduction in electron pressure due toelectron capture reactions determines the fate of the ONecore. Oxygen is ignited centrally and forms a deflagrationthat burns the central regions into nuclear statistical equi-librium. The electron capture reactions on this equilibratedmaterial work to further reduce the central density and thesubsequent rapid contraction leads to a core collapse. Dueto their formation history, EC-SNe are expected to receive alow natal kick (Podsiadlowski et al., 2004; van den Heuvel,2007; Wanajo et al., 2011), have a low explosion energy andsmall Ni production (Kitaura et al., 2006; Wanajo et al.,2017).The study of Ritossa et al. (1999) was the first to fol-low the stellar structure of a thermally pulsing super-AGBstar, including the stellar envelope, to conditions close tocollapse. In recent years a new generation of progenitormodels of EC-SNe has been computed which now evolvesuper-AGB stars to conditions of collapse (Takahashi et al.,2013) including along the entire thermally pulsing super-AGB phase (Jones et al., 2013).Determining the mass boundary between stars that do anddo not explode as supernovae is a topic of vital importancein astrophysics, for many reasons. For example, the super-nova rate in part determines the number of neutron starsand the total energy released by supernovae into the envi-ronment. Based on a standard initial mass function (IMF),there are as many stars born with masses between 5 and 10M ⊙ as there are with masses greater than 10 M ⊙ , so howthese elusive stars live and die is of interest to many sub-fields of astrophysics. This mass boundary is also importantfor galactic chemical evolution and dust evolution modelsbecause stars on either side of this divide have significantly This value can vary slightly between calculations, with a slightly lowervalue of 1.367 M ⊙ found by Takahashi et al. (2013) different chemical and dust production properties. Due to theshape of the IMF, super-AGB stars are both the rarest of thelow/intermediate mass stars, and also the most common ofthe stars on the more massive side of the boundary. Henceif they do indeed produce EC-SNe then they may make asignificant contribution to the overall SN rate.Until recently there have been few chemical yields avail-able for these stars. Chemical evolution calculations had touse some strategy to deal with missing yields for this massrange. The two most common strategies were to either to-tally ignore the yields for this mass range or interpolate inmass between yields for the low and high mass stars. Eitheris likely to introduce significant errors.The evolution of massive AGB stars (at the low mass end)and massive stars (at the high mass end) is very differentand the evolution between these is qualitatively different toboth, so interpolation is very unlikely to be close to the ac-tual yields. Because reliable yields have been missing, super-AGB stars have long been suspected to contribute to solv-ing various astrophysical problems, such as the origin of themultiple populations in globular clusters. We return to thisquestion later.Super-AGB stars are very difficult to identify obser-vationally, with no confirmed detections extant. There isonly one strong candidate, the very long period (1749days) and high luminosity ( M bol ≃ − .
0) star MSX SMC055 (Groenewegen et al., 2009). Another hindrance to iden-tifying super-AGB stars is that their high luminositiesand very large, cool, red stellar envelopes make them al-most indistinguishable from their slightly more massive redsuper-giant counterparts. Indirect evidence for super-AGBstars comes from observations of massive O-rich whitedwarfs (G¨ansicke et al., 2010), and also from neon novae(Jose & Hernanz, 1998; Wanajo et al., 1999; Downen et al.,2013), with the neon from which their name derives assumedto have been dredged-up from the interior of ONe WDs, theremains of an earlier super-AGB phase.In Section 2 we discuss the main evolution characteristicsof intermediate mass stars including the thermally pulsingsuper-AGB phase. In Section 3 we examine the mass limitsdefining the various evolutionary channels, in particular thefinal fates of super-AGB stars, including the importance ofthe binary star channel for formation of EC-SNe. In Section4 we describe the nucleosynthesis and stellar yields fromsuper-AGB stars. We apply these yields to the globular clus-ter abundance anomaly problems and examine their relativegalactic contribution, and briefly touch upon dust productionby super-AGB stars. Lastly in Section 5 we discuss the ob-servational studies, reiterate the most critical uncertaintiesand discuss future directions in super-AGB star research. Inthis review we do not consider super-AGB stars in the earlyuniverse. For an review on the evolution of primordial andextremely metal-poor super-AGB stars we refer to the com-panion paper by Gil-Pons (2017) in this edition.
PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars Figure 1.
Evolution in the Hertzsprung-Russell diagram (top panel) andin the log central density versus log central temperature diagram (bottompanel) of the 8 M ⊙ models of super-AGB stars of metallicities Z=0.02 and10 − from Doherty et al. (2015). CHB, CHeB and CCB refer to central H,He and C burning, respectively The main nuclear burning stages of intermediate-mass starsare well known, with the stars undergoing convective coreH-burning (CHB) via the CNO cycles followed by con-vective core He-burning (CHeB). In Figure 1 we show theHertzsprung-Russell diagram for two 8M ⊙ models of metal-licities Z = .
02 and 10 − through to the super-AGB phase.Clearly seen in this figure is the impact of metallicity on theevolution, with the lower metallicity object both more lu-minous and hotter for the same initial mass. At decreasingmetallicity, stars attain higher central temperatures to coun-teract fewer CNO seeds (and associated energy generation).These factors result in a larger core mass for the same initialmass. Due to the more rapid ignition of CHeB in the lowermetallicity model the (first) giant branch is avoided and thestar does not undergo a first dredge-up event (Girardi et al.,1996). Figure 1 also shows the evolution of central temper-ature T c versus central density ρ c for the models previouslydescribed. We clearly see the occurrence of central H burn-ing at higher temperatures for the lower metallicity model.Once central H is exhausted, the evolution of the stars in the T c – ρ c diagram becomes very similar because of the strongdependence of the nuclear burning rates on temperature. During CHeB the core is converted to C and O via thetriple- α and C( α , γ ) O reactions with the N producedfrom previous CNO cycling being converted to Ne via thereaction chain N( α , γ ) F( β + ν ) O( α , γ ) Ne. The cen-tral C content varies strongly with the core mass, withmore massive cores having less residual carbon due tohigher internal temperatures (Siess, 2007). Typically, inter-mediate mass stars have carbon mass fractions of ∼ . . C( α , γ ) O reaction rate and treatment of mixing(Imbriani et al., 2001; Straniero et al., 2003).The duration of the CHB and CHeB phases varies withmetallicity and a variety of other factors such as treatmentof convective boundaries, semiconvection, rotation and nu-clear reaction rates, particularly the rate of the C( α , γ ) Oreaction during the later phases of CHeB. Typically the mainsequence lifetime of intermediate mass stars in the massrange considered here ( ≈ . ⊙ ) is between about 18 –60 Myr with the CHeB phase being considerably shorter, ofthe order 2 – 5 Myr. For the same initial mass, intermediate-mass stars of lower metallicity will have a shorter lifetimealbeit only slightly, with the 8M ⊙ models presented hereshowing a difference in main sequence lifetime of only ∼ Very detailed descriptions of the carbon burning phasewithin super-AGB stars can be found in works such asGarcia-Berro & Iben (1994), Siess (2006) and Farmer et al.(2015) whilst here we provide a brief overview.Once CHeB has ceased, the resulting CO core begins tocontract causing an increase in the central density whichleads to neutrino energy losses becoming important for theinnermost regions of the star. This results in cooling and theformation of a temperature inversion. When the peak tem-perature reaches approximately 640MK, and the density atthat point is about 1.6 × g cm − , carbon is ignited. Thisignition takes place off-centre and under conditions of partialdegeneracy ( η ∼ L ⊙ and the large energy release drives the forma-tion of a convective zone. After a short period this first car-bon flash is quenched and contraction of the core resumes,to be followed by another carbon flash. In this second flashthe degeneracy is lower ( η ∼
1) and the convective regionthat forms (classified as a “flame”’) subsequently burns in-wards until it reaches the centre. Carbon burning however is The main sequence lifetime of intermediate mass stars is well know toincrease due to rotational mixing with an approx 20-25% increase foundby Ekstr¨om et al. (2012). However differences in this lifetime between ro-tating and non-rotating models are lower at only about 5% in the recentMIST calculations (Choi et al., 2016) which use a less efficient rotationalmixing. The contraction time from the cessation of CHeB to C ignition is a functionof core mass with larger core masses evolving more rapidly, with typicalvalues of 1 . × yr (Doherty et al., 2010).PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al. not complete and continues radiatively outwards, generatingsecondary convective flashes when regions of high carboncontent are encountered. The specific number of flashes de-pends on the degeneracy of the core, and thus on the star’sinitial mass. In general lower mass objects tend to experi-ence a higher number of secondary flashes and with higherintensity.The effect of the carbon burning flashes and flame on thecentral region can be seen in the bottom panel of Figure 1.For the Z=10 − model the initial flash causes a sharp dropin both temperature and density (down to log T ∼ . ρ ∼ ρ ∼ . The strength of the initial carbon flash is larger in themore degenerate (i.e. less massive) models, with the carbonflash luminosities ranging from ∼ to 10 L ⊙ . The moremassive models also ignite carbon closer to the centre, inconditions of milder degeneracy than the lower mass cases.Figure 2 is a Kippenhahn diagram of an 8.5 M ⊙ Z=0.02model and illustrates the typical multi-step burning process,consisting of an off-centre flash, a flame that propagates to-wards the centre, then subsequent secondary carbon flashesin the outer parts of the core. In the top panel the evolutionof the H, He, C, neutrino and total luminosities is shown.Clearly seen are the carbon burning flashes/flame with peaksin L C . The total luminosity of the star is almost constantthrough the carbon burning phase with its behaviour decou-pled from the central burning regions. During the steady car-bon burning flame phase, all of the energy released by carbonburning is carried away by neutrinos, in what is called the“balanced power condition” (Timmes et al., 1994), as seenin Figure 2. The carbon burning flame speed is quite slow ∼ − – 10 − cm s − (Timmes et al., 1994; Ritossa et al.,1996; Siess, 2006). The duration of the carbon burning phasedecreases with increasing core mass (i.e. initial mass) andranges between about 10,000 and 40,000 years.The minimum core mass for C-burning occurs for starswhich have CO core masses & M ⊙ at the start of carbonburning.The main nuclear reactions during the carbon burningphase are C( C,p) Na and C( C, α ) Ne, followed by Na(p, α ) Ne and O( α , γ ) Ne. The carbon burning ratesare quite uncertain and it has been suggested that there maybe unmeasured resonances (Spillane et al., 2007) or hin-drances (Jiang et al., 2007) which may alter the rates bymore than a factor of 1000 compared to the standard ratesfrom Caughlan & Fowler (1988). Due to their importancefor a variety of stellar environments, in particular in Type 1aSN studies, these reaction rates are currently under much in-vestigation (e.g. Bucher et al., 2015). Chen et al. (2014) ex-amined the impact of variations to the C+ C rates on car-bon burning within super-AGB stars and found that if the For the Z=0.02 model there is only one flash and then the core cools with-out any further C burning. This star forms a hybrid CO-Ne white dwarf(Section. 2.2.1).
Figure 2.
Kippenhahn and luminosity diagram during the carbon burningphase for an 8 . ⊙ model with Z = .
02 from Doherty et al. (2015). Timehas been set to zero when L C first exceeds 1 L ⊙ . In the upper panel weshow different luminosity sources: H in green, He in dashed red, C in blue,surface in magenta, and the negative of the neutrino luminosity is in black.In the lower panel the mass coordinate of the HBS is shown in blue, theHeBS in red, and the hatched regions represent convection. rates were multiplied by factors of 1000 and 0.01 the mini-mum CO core mass for carbon ignition became 0.93 M ⊙ and1.10M ⊙ respectively.After the completion of CCB the core has been con-verted to mostly O (50 – 70%), Ne (15 – 35%) and traceamounts of Na, , , Mg, , Ne and Al (Siess, 2007).The third most common element in the cores varies betweencalculations and is either Mg (Nomoto, 1984; Miyaji et al.,1980; Takahashi et al., 2013) or Na (Garcia-Berro & Iben,1994; Siess, 2006) which results in either ONeMg or ONeNacores . There is also a small abundance of C remainingthroughout the ONe core of about 0 . ⊙ at the end of C-burning will igniteneon and undergo all stages of further burning (Nomoto,1984). Therefore ONe cores are expected to be producedwith masses ∼ .
05 – 1 . M ⊙ . The amount of Mg or Na may have important implications in the subse-quent evolution if the stellar core grows to conditions for an EC-SN e.gGuti´errez et al. (2005). This value for neon ignition for a pure Ne core was found to be slightlylower at 1.35 M ⊙ by Schwab et al. (2016) their Figure C2.PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars In stars with initial mass slightly above M up carbon ignitesin the very outer regions of the core. In some cases, afterthe primary flash has occurred, no further carbon burningtakes place. These aborted carbon ignition models have aninterior comprised of a very large central CO region sur-rounded by a thin ONe layer and a further outer CO region(e.g Doherty et al., 2010; Ventura & D’Antona, 2011). Theinitial mass range for creation of this class of hybrid CO-Ne cores is very narrow, being at most about 0.1M ⊙ . CO-Ne cores can also be formed when the carbon burning flamestalls on its journey towards the centre.Due to off-centre (convective) carbon burning in super-AGB stars a molecular weight inversion is created whichcan drive thermohaline mixing (Siess, 2009). The resultantmixing transports carbon from the inner region toward theburning flame, replacing it with the heavier products of car-bon burning. Thermohaline mixing below the C-convectiveshell is thus able to decrease significantly the C content inthe zones ahead of the C-burning flame, and deprived of fuel,this causes the extinction of the flame before it reaches thecentre. The result is a hybrid degenerate core, comprisingan inner zone of unburnt (but depleted) CO and an outerONe zone. In such a case, in contrast to evolution ignor-ing thermohaline mixing, the ONe core is left with a largeramount of unburned C, between 2 – 5%, in the centre. Laterusing downward revised values of the thermohaline mixingcoefficient based on multidimensional hydrodynamic simu-lations, Denissenkov et al. (2013) discounted the ability ofthermohaline mixing to stall the carbon burning flame, sug-gesting that the mechanism was too inefficient. They didhowever suggest another mechanism that may be active dur-ing the carbon burning phase within super-AGB stars andwhich could work to halt flame propagation. It is well knownthat convective flows may lead to mixing beyond the strictSchwarzschild boundary, often known as convective bound-ary mixing (CBM). This was applied by Denissenkov et al.(2013) to the base of the C-burning convective shell of super-AGB stars. These authors used their results from hydrody-namical simulations to simulate the propagation of the C-burning flame and determined that it was actually deprivedof fuel, and that the C-burning process was halted and hybridCO-Ne cores were formed. For determining the compositionof stellar material, the main difference between thermohalinemixing and CBM concerns the extent of the induced mixing.Thermohaline mixing connects the entire interior to the re-gion with the higher molecular weight that is being producedby the burning flame. With overshoot the mixing only occursdirectly below the convection over a region whose width isdetermined by some model or algorithm. In contrast to ther-mohaline mixing, this leaves a pristine CO core interior tothe maximum extent of the overshoot. Thus CBM also findshybrid CO-Ne cores, but these hybrids can be produced witha range of configurations and quite widely varying widths ofthe ONe shell. This is unlike the structures produced from the lower mass super-AGB stars which have thin ONe shellsin the far outer core.Chen et al. (2014) investigated the effects of CBM and thequite uncertain C reaction rates on hybrid core creation.They found that varying the efficiency of CBM in additionto the C reaction rates resulted in the formation of hybridCO-Ne cores over a wide range of core masses from ≈ .
93 –1 .
30 M ⊙ . This corresponds to an initial mass range for hy-brid CO-Ne core creation (defined as ∆ M CO − Ne ) of up to 1M ⊙ which would make the CO-Ne cores very common. Thisvery large core mass of 1.30 M ⊙ for hybrid CO-Ne WDscould have important implications for the rate of Type 1aSNe (e.g. Meng & Podsiadlowski, 2014; Wang et al., 2014;Liu et al., 2015).Farmer et al. (2015) studied carbon ignition within inter-mediate/massive stars with an extensive grid of models look-ing at the effects of rotation, convective overshooting , ther-mohaline mixing and combinations of these processes. Intheir study they found that a substantial number of starswhich ignited carbon off-centre went on to form CO-Necores. In particular, in agreement with Denissenkov et al.(2013) and Chen et al. (2014), models with efficient over-shooting at the base of the convective carbon burning regionled to a very wide initial mass range for hybrid CO-Ne WDs.Recently, work by Lecoanet et al. (2016) using 3D hydro-dynamic simulations has suggested that convective mixingcannot stall the carbon burning flame due to the large buoy-ancy barrier that needs to be crossed to reach the radiativeburning front and hence formation of CO-Ne WDs wouldnot be typical. Irrespective of whether CO-Ne cores couldactually form, Brooks et al. (2016) showed that a structurecomposed of a higher density ONe mantle above a CO corewould be unstable to rapid mixing shortly after the onset ofthe WD cooling sequence. Thus the actual occurrence of hy-brid cores and their possibility to remain unmixed through-out the latest stages of stellar lives is still a matter of debate.One of the main interests in hybrid cores is related to thepotential eventual fates of SNIa. The amount of available Cwould probably be high enough so that, if the degeneratecore were able to increase in mass up to M Ch , a thermonu-clear (single) SN explosion would result (Poelarends et al.,2008). Alternatively, if the super-AGB star were the primarycomponent of a close binary system with specific initial or-bital parameters, SNIa explosions might occur.This possibility was explored by Bravo et al. (2016), whocomputed the hydrodynamical explosion of white dwarfshosting hybrid cores, under different conditions (size of thehybrid cores, and ignition by deflagration or detonation).These authors showed that SNIa harboring hybrid coreswould be characterised by lower kinetic energies and lower This followed the work of Herwig et al. (1997) by using a diffusionco-efficient D OV beyond the formal convective border where D OV = D exp (cid:16) − zf over H p (cid:17) where D is the diffusion coefficient near the convectiveboundary, z is the radial distance from the edge of the convective zone, and H p is the pressure scale height at the convective edge. They examined f over in the range 0–0 . Doherty et al. amounts of ejected Ni than their pure CO WD counter-parts. Explosions of these hybrid cores may be the theoreti-cal counterparts of the sub-luminous class of SN2002 cx-likeSN or SNIax. Denissenkov et al. (2015) also pointed out thefact that hybrid CO-Ne cores might be one possible reasonfor the inhomogeneity of observed SNIa. More recent mul-tidimensional hydrodynamical simulations by Willcox et al.(2016) reproduce the same trend, that is, their SNIa modelshosting hybrid degenerate cores also produce less Ni andrelease less kinetic energy.
The ability of the Ne burning flame to propagate to the cen-tre is of crucial importance in determining if the star endsit life as an EC-SN or an FeCC-SN. As mentioned in Sec-tion. 2.2 if the ONe core mass exceeds 1.37 M ⊙ it is as-sumed that Ne shall ignite and the star will follow the mas-sive star channel. However there are slight complications tothis standard picture. The behavior of Ne burning is verysimilar to that seen during the earlier phase of C burn-ing. Efficient neutrino cooling causes the temperature maxi-mum to move away from the centre, resulting in Ne ignitionoccurring further off-centre for lower masses. Akin to theaborted carbon ignition models described in Section 2.2.1,if neon is ignited at the very outer edge of the core therewill be a brief neon flash but no subsequent burning norflame propagation (Timmes et al., 1994; Ritossa et al., 1999;Eldridge & Tout, 2004). It is expected that these stars withcore masses so close to the Chandrasekhar mass will endlife as EC-SNe after a very brief thermally pulsing phase.Doherty et al. (2015) proposed a new nomenclature for mod-els which undergo only very slight off-centre neon burn-ing and then later reach the TP-(S)AGB phase, calling them“hyper-AGB” stars.In addition to the super-AGB evolution towards an EC-SN a second possible single star EC-SN channel exists, thatof “failed massive stars” (FMS) (Jones et al., 2013, 2014).A FMS is formed in stars with ONe core masses slightlyabove the value for Ne ignition. If Ne is ignited far enoughoff-centre and convective boundary mixing is employed atthe base of the Ne burning shell, then instead of a flame pro-gressing smoothly towards the centre, the Ne burning can bestalled and undergo multiple flashes. After each flash there isa period of contraction which, given enough time, can ulti-mately result in the core reaching sufficient densities for theURCA processes to be activated and the star to subsequentlyreach conditions for an EC-SN prior to the Ne flame beingable to reach the centre. However, if no CBM is employedand the strict Schwarzschild boundary is used at the base ofthe Ne convective region, as seen in Jones et al. (2014), thenthe class of FMS ceases to exist and the Ne flame is freeto propagate inward towards the centre with the star mostlikely becoming an FeCC-SN. The exact contribution fromthe FMS to the EC-SN channel is highly uncertain but if thisclass of star only occur for models in which the H-exhausted Figure 3.
Mass of the H-exhausted core before (open circles connected bya dashed line) and after (triangles/diamonds connected by a solid line) theoperation of the SDU for two metallicities. The left/magenta and right/cyanlines correspond to models with a metallicity Z = − (with core over-shooting) and Z = .
04 (without core overshooting), respectively. The dot-ted horizontal line represents the Chandrasekhar mass. Models are fromSiess (2007) with overshoot as described in Herwig et al. (1997) with avalue f over = .
016 (see footnote 9). core has been reduced to precisely the Chandrasekhar mass,(refer to next section. 2.3) then we expect a narrow channel.
For intermediate mass stars, the H-exhausted core masses af-ter CHe burning are in the range ≈ . . ⊙ . Hence afterCHeB all future super-AGB stars will eventually grow de-generate core masses far exceeding the Chandrasekhar mass( M Ch ) and therefore if no process takes place to reduce thecore mass, these stars will undergo all stages of core burning,just as do massive stars.Prior to the thermally pulsing phase two processes can re-duce this H-exhausted core mass, these being second dredge-up (hereafter SDU) and dredge-out. Figure 3 shows the H-exhausted core mass both before and after SDU. Clearlyseen in the sharp divide between stars that undergo SDU andthose that do not. This figure also highlights that this samebehaviour occurs over a large spread in metallicity, and bothwith and without convective overshooting. Due to the gravitational contraction of the core after CHeB,the envelope expands and cools, with convection penetratinginwards into the H exhausted core (Becker & Iben, 1979).The SDU event occurs at different stages of the C-burning
PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars C(and O, e.g. Becker & Iben, 1979; Herwig, 2004), whilein the more massive models corrosive SDU also enrichesthe surface with substantial amounts of O. The masses ofthe stellar cores for which corrosive SDU occurs vary be-tween studies, with about 1 .
15 – 1 .
28 M ⊙ in Doherty et al.(2014b), down to 1.03 M ⊙ in Herwig (2004). These valuesare generally lower for lower metallicity models due to theirbroader residual He shells. The degree of metal enrichmentfrom SDU in the envelope of low metallicity stars is criticalfor their future evolution. Ritossa et al. (1999) first named, described and provided anextensive analysis of the phenomenon known as dredge-out. It was later reported by Siess (2007), Poelarends et al.(2008), Takahashi et al. (2013), Gil-Pons et al. (2013),Doherty et al. (2015) and Jones et al. (2016a) using differ-ent evolutionary codes and different input physics (in partic-ular the treatment of mixing and treatment of convective bor-ders). This phenomena occurs for massive super-AGB starsregardless of their metallicity (e.g. Gil-Pons et al., 2013) andoccurs for stars in the upper ≈ ⊙ range of super-AGBstars.Figure 4 shows the evolution during C-burning anddredge-out phase for a 9.5 M ⊙ Z=0.001 star from Siess(2007). Nearing the end of the carbon burning phase a con-vective He shell develops near the upper boundary of the par-tially degenerate core. This shell is initially separated fromthe base of the convective envelope by a relatively extendedradiative region (about 1M ⊙ ) and a thin semiconvective re-gion near the He-H interface. As described in Ritossa et al.(1999) the He convective shell is initially sustained mainlyby C-burning, and gravothermal energy, but He-burningpowers its final approach towards the base of the convectiveenvelope. Eventually these convective regions meet and pro-tons are ingested into very high temperature ( & K) He-and C-rich regions. These ingested protons rapidly undergothe C(p, γ ) N reaction leading to a H-flash with peak lu-minosities of L H ∼ L ⊙ . The associated total energy re-lease from the H-flash is vast, and generated in a very smallregion. According to estimates by Jones et al. (2016a) theenergy released by this process represents about 11% of thestar’s internal energy and about 8% of its binding energy. Itis likely that this has hydrodynamical consequences and theassumption of hydrostatic equilibrium should be doubted. At the very least, it is likely that time-dependent convectionis required (Herwig et al., 2011). Jones et al. (2016a) sug-gest that this dredge-out may provoke a global oscillation ofshell-H ingestion (GOSH) event (Herwig et al., 2014) whichcould potentially drive more powerful and non-radial hydro-dynamic events leading to mass ejection.With an abundant supply of C now in a high temper-ature, helium-rich region, the C( α ,n) O reaction is ex-pected to take place at a rapid pace and produce a substantialnumber of free neutrons (Doherty et al., 2015; Jones et al.,2016a). A dredge-out event is expected to produce neutrondensities of the order N n ≈ cm − corresponding to theintermediate n-capture regime (known as the “i-process”, seeCowan & Rose, 1977). This process in super-AGB stars wassuggested by Jones et al. (2016a) to be responsible for theoccurrence of some carbon-enhanced metal poor stars en-riched in s- and r-process elements (the CEMP s/r stars, seeBeers & Christlieb, 2005). But based on an IMF argument,the relatively few super-AGB stars seem unlikely to be a ma-jor source of pollution of the CEMP s/r stars (Abate et al.,2016).Besides the possibility of ejection of heavier-than-ironelements, the dredge-out process also alters surface abun-dances of light elements, in particular He and the He-burningproduct C (Ritossa et al., 1999). This results in the mostmassive super-AGB stars becoming carbon stars.In models of slightly lower mass than those that undergodredge-out, near the end of carbon burning and prior to theSDU there is also the formation of a convective He region.However this convective zone decays before the convectiveenvelope penetrates inwards and therefore does not mergewith the proton-rich region. This material will be highly en-riched in C (e.g. Herwig et al., 2012).
After the cessation of core carbon burning a super-AGB starconsists of a massive ONe core surrounded by a CO shell, aH-burning shell and a very extended H-rich envelope. Qui-escent H-burning is eventually interrupted by unstable He-burning, a thermal pulse ensues and the thermally-pulsingsuper-AGB (TP-SAGB) phase begins. Early He-flashes tendto be relatively mild, but their peak luminosities grow as theevolution progresses. When the TP-SAGB is established, H-burning and He-burning in shells alternate as nuclear energysuppliers. Figure 5 gives a schematic overview of the typi-cal values from the literature associated with the thermallypulsing phase of super-AGB stars.Whilst qualitatively similar to their lower mass coun-terparts , super-AGB stars present some important differ-ences. The most obvious is that the stellar cores and en-velopes are more massive, between ≈ .
05 – 1 .
37 M ⊙ , and ∼ ⊙ respectively. Due to their larger, hotter andmore compact cores the recurrence time between thermal For a recent review of AGB stars refer to Karakas & Lattanzio (2014).PASA (2017)doi:10.1017/pas.2017.xxx
Doherty et al.
Figure 4.
Kippenhahn and luminosity diagram during the carbon burningphase and dredge-out episode for an 9 . ⊙ Z = .
001 model from Siess(2007). Time is counted backwards from the last computed model. pulses (the interpulse period) is much shorter (10s-1000s yr)in super-AGB stars and due to this they can undergo from be-tween tens to multiple thousands of thermal pulses, typicallywith more pulses at lower metallicity. The thermal pulse du-ration is also greatly reduced in comparison to lower massAGB stars, with pulses lasting only about 0 . − to 10 − M ⊙ .The maximum temperature within the HeB convectivezone steadily increases throughout the evolution along theTP-SAGB and also increases with increasing initial mass,with the most massive super-AGB star models achievingtemperatures in the range 350 – 430 MK. This high temper-ature has important implications for the activation of the Ne neutron source and heavy element production (see Sec-tion. 4.3.2). The strength of the thermal pulses, as measuredby the HeB luminosity L He , decreases for super-AGB starswith increasing (initial) core mass. This is due to the reducedtemperature sensitivity of the triple α reaction, the higherradiation pressure and the lower degree of degeneracy (e.g.Sackmann, 1977; Sugimoto & Fujimoto, 1978; Siess, 2006).This L He value varies widely between computations fromdifferent research groups and typically those with less vi-olent thermal pulses have lower dredge-up efficiency. Theoverlap factor r is defined by r = M over / M TP where M over isthe mass contained in the previous intershell convective zonethat is engulfed in the next pulse (see Figure 5) and M TP isthe mass of the intershell convective zone at the current ther-mal pulse. This parameter is important in particular in rela- tion to heavy element production because it determines theamount of material that experiences multiple neutron expo-sures in subsequent thermal pulses.Due to the activation of nuclear burning at the base of theirconvective envelopes super-AGB stars are more luminousthan the classical AGB limit (Paczy´nski, 1970). The mostmetal poor models can reach in excess of 10 L ⊙ ( M bol ∼− . λ parameter, defined as ∆ M dredge / ∆ M H where ∆ M H is the increase in the core massduring the previous interpulse phase and ∆ M dredge is thedepth of the dredge-up (see Figure 5). By this definition a λ value of one represents the case where the entire region pro-cessed by the H shell during the previous interpulse phaseis mixed to the surface during the subsequent TDU episodeand there is no overall core growth. We note that there is nophysical reason why λ cannot exceed unity.In super-AGB star modelling the amount (and even oc-currence) of TDU is hotly debated, with computations find-ing no TDU (e.g. Siess, 2010; Ventura et al., 2013), lowefficiency TDU with λ ∼ . − . λ ∼ . − . λ > AGB stars to super-AGB stars (andlarger core masses).Jones et al. (2016a) examined the variations to the effi-ciency of TDU caused by modifying the amount of con-vective boundary mixing at both the base of the intershellconvective zone and the convective envelope. With signifi-cant convective boundary mixing included they uncovered anew potential convective-reactive site, where the TDU be-gins whilst the convective thermal pulse was still activated(i.e. ∆ t < < T eff < R & ⊙ . During their lives they can lose a substantialamount of material, up to about 90% of their initial mass,through stellar winds. During the majority of the TP-SAGB We define massive AGB stars as those with initial masses & ⊙ but notmassive enough to ignite carbon.PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars Figure 5.
Schematic Kippenhahn diagram of two consecutive thermal pulses showing typical values for super-AGB stars. The upper light grey shaded regionrepresents the convective envelope and the two thin shaded regions represent the convective shells associated with two consecutive flashes. phase the mass loss is in the superwind phase, with massloss rates up to ∼ − M ⊙ yr − , and expansion velocitiesup to about 25 km s − . When commonly used AGB starmass loss rates such as those by Vassiliadis & Wood (1993)or Bloecker (1995) are applied to super-AGB stars the aver-age mass loss rate during the TP-(S)AGB phase ranges from0 . × − M ⊙ yr − . Rapid mass loss from super-AGBstars means that their thermally pulsing lifetimes are quiteshort, of the order of 10 to 10 years.Super-AGB star model computations cease due to conver-gence problems prior to the removal of the entire envelope.This can occur when the amount of remaining envelope isstill quite large, up to ∼ ⊙ . The loss of convergence gen-erally occurs just after a thermal pulse when the radiationpressure is very high and the contribution of the gas pres-sure to total pressure tends to zero in shells near the base ofthe convective envelope. This results in super-Eddington lu-minosities (Wood & Faulkner, 1986; Wagenhuber & Weiss,1994). This instability has been attributed to the presenceof an opacity peak due to iron in these layers of the star(Sweigart, 1999; Lau et al., 2012). This will likely leadto the inflation of the envelope and either its entire ejec-tion or a period of enhanced mass loss. Envelope infla-tion due to the Fe opacity also occurs in massive stars(e.g. Petrovic et al., 2006; Gr¨afener et al., 2011). We ex-pect that multi-dimensional hydrodynamics will be requiredto understand the occurrence and outcome of such events(Jiang et al., 2015). After leaving the thermally pulsing phase, super-AGBstars are expected to go through a short lived planetary neb-ula (PN) phase before reaching the white dwarf coolingtrack. The precise lower and upper initial mass limits for stars thatwill enter the super-AGB phase depend on the input physicsand on numerical aspects of the calculations. As mentionedin the introduction there are three important mass limits inthe intermediate mass regime: M up , M n and M mas . The dif-ference between the M up and M mas values sets the maxi-mum (initial) mass range for super-AGB stars. In the follow-ing subsection we will examine how these boundary valueschange with differing compositions and mixing approachesand also discuss complications to this standard picture. M up and M mass Figure 6 is a compilation of M up (bottom panel) and M mas (top panel) values from the literature and illustrates both thelarge spread in results between different research groups andalso the behavior of these quantities with initial metallicity.The mass boundaries M up and M mas are highly dependenton the maximum convective core mass obtained during CHBand CHeB. As seen in section 2.2 the minimum CO coremass for carbon ignition is ∼ ⊙ , whilst neon ignitionrequires ONe core masses ∼ ⊙ . PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al.3.1.1 Composition
As the initial stellar metallicity decreases, stars attain highercentral temperatures and luminosities during the main se-quence to counteract fewer CNO seeds. This results in alarger He core mass for the same initial mass and also moremassive cores during CHeB and hence resultant CO cores.Due to this the M up values are seen to decrease with de-creasing metallicity until reaching a plateau (or minimume.g. Cassisi & Castellani 1993; Bono et al. 2000) at aboutZ=10 − to 10 − . As seen in Figure 6 the behaviour of M mas with metallicity echoes that of M up albeit with an offset ofabout 1 . . ⊙ to higher initial masses.Models that employ the strict Schwarzschild criterionfor convective boundaries such as those from Siess (2007)typically produce the smallest HeB core and hence rep-resent a reasonable upper limit to the values of M up and M mas . For near solar composition (Z=0.02) and using thestrict Schwarzschild criterion the M up and M mas valuesare ∼ ⊙ respectively (Garcia-Berro & Iben,1994; Ritossa et al., 1999; Siess, 2007; Doherty et al., 2010;Takahashi et al., 2013). We note the other recent values of M mas from the literature are in reasonable agreement withthese values e.g. for Z = .
015 Woosley & Heger (2015) find9 M ⊙ , while Jones et al. (2013) find 8.8–9.5 M ⊙ .Even assuming the same convective approach during thepre-carbon burning phases, the M up values vary consider-ably between studies. For example the work by Girardi et al.(2000) find very low values of about 4.5–5M ⊙ at Z=0.02. Thecauses of the differences are hard to attribute in some cases,as discussed in Siess (2007).The values of M up and M mas also show large variationsdue to the He content (e.g. Becker & Iben, 1979; Bono et al.,2000). Stars with larger initial He contents are more lu-minous and develop more massive convective cores duringCHB. Their CHB lifetime is also substantially shorter due toboth the reduced amount of H fuel and the hotter, larger coreswhich burn the fuel more efficiently. This larger core followsthrough to the CHeB phase resulting in a larger CO corewhich leads to a reductions of ∼ . ⊙ in M up and M mas when enrichments of Y ∼ Convective overshooting during the core H and He burningphases mixes in additional fuel to the core and increases theduration of these phases. It also increases the maximum sizeof the convective cores with this effect being more promi-nent during CHeB. Even moderate amounts of core over-shoot e.g. f over = 0.016 (see footnote 9) reduce the M up and M mas values by generally 2–2.5 M ⊙ (e.g Bertelli et al., 1985;Siess, 2007; Gil-Pons et al., 2007; Poelarends et al., 2008;Farmer et al., 2015). This is highlighted in Figure 6 by com-paring the small/large open square value from Siess (2007)which are for models without/with overshoot respectively. Similar to the impact of overshooting, stellar rotation in-creases both the duration and the size of the convective coreduring CHB (e.g Maeder & Meynet, 2000; Ekstr¨om et al.,2012). This larger core is inherited during CHeB and hencewe expect a larger CO core and presumably this would leadto a reduction in the initial mass for carbon ignition with in-creasing rotation rate. However, in their grid of intermediatemass Z=0.02 metallicity models with overshooting ( f over )Farmer et al. (2015) found that for a given initial mass, theCO core mass at carbon ignition was practically the same,irrespective of the initial rotation rate which ranged from Ω / Ω crit = . M up and M mas values providedthat overshoot is efficient enough. The C + C reaction rates can either hasten or de-lay the onset of C burning and hence alter the contrac-tion time between He burning and C ignition. The COcore grows considerably during this phase and the im-pact of this should not be overlooked. The carbon burn-ing C + C reaction rates can also modify the M up value. It has been suggested that there exists a possible un-known/unmeasured resonance (Spillane et al., 2007) whichwould increase the reaction rate above that currently rec-ommended (Caughlan & Fowler 1988, hereafter CF88) andlead to a reduction in the core mass which ignites carbonand hence reduce M up . Straniero et al. (2016) examined theimpact of including a narrow resonance at 1.45 MeV in thestandard carbon burning rate. They found the minimum COcore mass for carbon burning was shifted from ∼ ⊙ down to 0.95 M ⊙ , and this resulted in a uniform decreaseof M up by about 2 M ⊙ for their study over metallicities Z = . .
03. This can be seen in Figure 6 by the extentof the arrows representing models with the modified carbonburning rate. This reduction in M up with increased carbonreaction rate is in agreement with the results of Chen et al.(2014). However with their maximum rate (1000 × CF88)they find a lesser decrease, at about 1.3 M ⊙ (to M up ∼ ⊙ at metallicity Z=0.01).In Fraser et al. (2011) the M mas value was seen to de-crease by 1 M ⊙ (to 7 M ⊙ at metallicity Z=0.02) when the C + C reaction rates were enhanced by a factor of 10 compared to the standard CF88 rates.Given the shape of the IMF and the decrease in M mas withdecreasing metallicity, we expect that the SN rate was higherin the past. In summary, the two limiting masses M up and M mas are very uncertain and even with “reasonable” choicesof input physics their values may vary by over 3 M ⊙ . Forexample at close to solar metallicity (Z=0.02) M up can varybetween about to 5 . ⊙ . In Section 5 we discuss the ob-servational probes that are being used to aid in constrainingthese important mass boundaries. PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars Figure 6.
Values for M up (bottom panel) and M mas (top panel) as a func-tion of metallicity. Solid lines represent models calculated using the strictSchwarzschild condition for convective boundaries, dotted lines representmodels calculated using mechanical overshooting during the core burningphases, whilst points joined with dashed lines represent models calculatedusing some other way of calculating the convective border, such as inducedovershooting, a search for convective neutrality, or semiconvection. Valuesare from Becker & Iben (1979), Bono et al. (2000), Cassisi & Castellani(1993), Doherty et al. (2015), Dominguez et al. (1999), Eldridge & Tout(2004), Girardi et al. (2000), Ibeling & Heger (2013), Poelarends (2007),Siess (2007), Straniero et al. (2016) and Umeda et al. (1999). The error baron the Z=0.04 model from Bono et al. (2000) represents the variation in M up with initial helium content ranging from 0.29 to 0.37. M n After SDU or dredge-out has reduced the core mass to below M Ch , the final fate of super-AGB stars is dictated by the com-petition between core growth and mass loss from the stellarenvelope during the TP-SAGB phase. If the stellar wind re-moves the envelope prior to the core reaching M Ch then thestar will end its life as an ONe WD. Otherwise if the coregrowth is sufficient to reach M Ch then the star will undergoan EC-SN and end its life as a neutron star. The boundarybetween these two differing final fates is called M n the min-imum mass for neutron star formation. Here we describethe competing factors that determine the final fate includingthe complications from possible mass ejection events, andsummarise the results from both synthetic/parametric anddetailed calculation that have examined this problem.The core growth rate is dictated by the outward movementof the H burning shell and progresses at ∼ − M ⊙ yr − (Ritossa et al., 1999; Poelarends et al., 2008; Siess, 2010;Doherty et al., 2015) with typically faster growth rates in themore massive and/or metal-rich models.An important factor that influences the effective coregrowth rate is the TDU. Unfortunately, whilst the effi-ciency of TDU is a very important quantity, it is also oneof the most poorly constrained aspects of AGB model-ing, especially at larger core masses. It depends on manyfactors such as the resolution (Straniero et al., 1997), nu-merics (Stancliffe et al., 2004; Stancliffe, 2006) and treat-ment of convective boundaries (Frost & Lattanzio, 1996;Herwig et al., 1997; Mowlavi, 1999; Jones et al., 2016a). Asmentioned in section 2.4, in super-AGB stars the efficiencyof TDU varies considerably between studies and ranges from λ = λ >
1, typically being smaller for more mas-sive models. There is some evidence for TDU in massiveAGB stars of high metallicities. This is in the form of Rbover-abundances observed in bright O-rich AGB stars inthe Galaxy and Magellanic Clouds (Garc´ıa-Hern´andez et al.,2006, 2009). The existence of very luminous carbon richstars in the Magellanic Clouds is suspected to arise fromTDU events after the cessation of HBB (Frost et al., 1998;van Loon et al., 1999). Unfortunately we are yet to unam-biguously identify any super-AGB stars (see sections 5.1 and5.3), and there are no constraints from lower metallicity ob-jects, because such stars have long since died. A standardtracer of AGB nucleosynthesis is Tc which is produced byneutron captures in the deep layers of the star. Technetiumhas no stable isotope, and its longest lived isotope is Tcwith a half-life of 0.21 Myr. Therefore the detection of Tc inthe stellar spectra is the signature of recent nucleosyntheticactivity and the presence of TDU. Unfortunately super-AGBstars are not expected to be produce large enough amounts ofTc for it to be observable (e.g. from the massive AGB starsstudy by Garc´ıa-Hern´andez et al., 2013). We note here that the end result of an EC-SN either as a neutron staror remnant ONeFe WD is debated e.g. Isern et al. (1991); Canal et al.(1992); Jones et al. (2016b).PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al.
Figure 7.
Final fates of intermediate-mass stars from Poelarends (2007)(top panel) and Doherty et al. (2015) (bottom panel). Solid lines delineate M up , M n and M mas . The dashed line in the top panel represents the M n valuein the case where no metallicity factor is applied to the mass loss rate. Thehatched region represents the width of the EC-SNe channel. As mentionedin Section 3.1 there is a slight offset in the M up and M mas values betweenthe two sets of models, with this due to the different method for treatment ofconvective boundaries during CHeB, with Poelarends (2007) using convec-tive overshooting via the method of Herwig et al. (1997) with an overshootparameter of f over = . M n = M mas . The lowest metal-licity examined in Doherty et al. (2015) was Z=10 − , but here we presentnew models for Z=10 − calculated using the same methodology as in theprevious work. Whilst the mass loss rate is fundamental to determiningthe final fates of super-AGB stars, unfortunately it is alsohighly uncertain especially at lower metallicities. Mass lossin (super-)AGB stars is thought to be via pulsation aideddust-driven winds. Firstly large amplitude pulsations are re-sponsible for forcing material to large enough radii and in-creasing the density enough for dust grains to form. The ra-diation pressure from the star is then able to accelerate thesedust particles which also work to drag along the gas, withthis leading to quite efficient mass loss (Wood, 1979). Al-though there is no mass loss rate derived specifically forsuper-AGB stars it is common to use rates derived for lowermass AGB stars (e.g. Vassiliadis & Wood, 1993; Bloecker,1995), or for rates taken from red super-giant and O-richAGB stars (van Loon et al., 2005). Using these prescriptionsthe mass loss rates in super-AGB stars are of the order 10 − to 10 − M ⊙ yr − . The mass loss rate for super-AGB stars atlow metallicity is an unknown and we can only rely on andapply prescriptions which were derived using observationsof solar metallicity, or moderately metal-poor stars. Due totheir more compact structure, low metallicity stars are ex-pected to have slower mass loss rates. Kudritzki et al. (1987)proposed a metallicity scaling proportional to p Z / Z ⊙ in anto attempt to take this into account. We note however thatthis scaling was derived for radiative line-driven winds ofhot luminous O stars whose conditions are quite unlike thecool super-AGB stars we are considering here.Another important factor which determines the mass lossrate in super-AGB stars is the envelope opacity. The useof low temperature molecular opacities that take into ac-count the envelope composition variations during the super-AGB phase is crucial for cases where the envelope com-position ratio C/O exceeds unity. The change in molec-ular chemistry when a star becomes carbon rich leadsto an increase in opacity which results in a cooler andmore extended stellar envelope and a higher mass loss rate(Marigo, 2002; Cristallo et al., 2007; Ventura & Marigo,2010; Constantino et al., 2014; Doherty et al., 2014b). Thiseffect may play an important role for low metallicity super-AGB stars. This is especially true for the most massivestars, with post SDU/dredge-out core masses closest to M Ch .These stars have often had their surface enriched in C dueto dredge-out events and are carbon rich (with C/O >
10 insome cases) already, at the start of the TP-SAGB phase.The final fates of metal poor super-AGB stars alsostrongly influenced by the efficiency of SDU/dredge-outprior to the TP-SAGB phase. These processes are able to mixsignificant amounts of metals from the stellar interior lead-ing to surface metallicities up to Z = − , with the amountof enrichment increasing with stellar mass (Gil-Pons et al.,2013). Furthermore, the nucleosynthesis and mixing pro-cesses which occur during the TP-SAGB also alter their totalsurface metallicity. As a consequence, their envelope opacityvalues, surface luminosities and radii become very similar totheir higher Z counterparts. Envelope metallicity during theTP-SAGB is critical in terms of the strength of stellar winds, PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars < M up tobe able to grow enough to reach M Ch and explode as Type 1.5SNe (Iben & Renzini, 1983; Zijlstra, 2004; Gil-Pons et al.,2007; Lau et al., 2008; Wood, 2011).In addition to standard super-wind mass loss from super-AGB stars there have also been two suggested potentialmass expulsions events, from either the Fe-peak instabil-ity (Lau et al., 2012) or as a result of global oscillationsof shell-H ingestion (GOSH) events (Jones et al., 2016a).These phenomena are expected to occur at different evolu-tionary phases, with the Fe-instability generally seen nearthe end stages of the TP-AGB when the envelope has re-duced below about 3 M ⊙ , whilst the GOSH could potentiallyoccur prior to the start of the thermally pulsing phase duringthe dredge-out phase. These types of mass ejections makedetermining the final fates of super-AGB stars, in particularthe most massive near the EC-SN boundary, quite problem-atic.Whilst the final fates of thermally pulsing super-AGBstars had been examined for individual models of Z = . ∆ M EC − SN and ∆ M ONe asthe range of initial masses that produces EC-SNe and ONeWDs respectively. For Z = .
02 this EC-SN channel is nar-row with ∆ M EC − SN ∼ ⊙ , but at the lowest metallic-ity, all super-AGB stars would end life as EC-SNe, giving ∆ M EC − SN ∼ ⊙ , and leaving no ONe WDs. Interest-ingly at Z = − even the most massive CO cores are ableto grow to M Ch and explode as Type 1.5 SN. The cause ofthis increase in the EC-SN rate with decreasing metallic-ity is primarily the application of the metallicity scaling onthe mass loss rate. In the case with no metallicity scalingapplied to the mass loss (dashed line in Figure 7) we find ∆ M EC − SN ∼ .
25 – 0 .
55 M ⊙ with the wider range at lowermetallicity. Also critical to the width of the EC-SN channel is theoccurrence of TDU, with lower efficiencies resulting in awider channel. However, we expect the impact of the metal-licity scaling upon the mass loss rate to be greater thanthe possible lack of TDU. In Poelarends et al. (2008) thewidth of the EC-SN channel was explored for solar metal-licity using a selection of commonly used mass loss rates(Reimers, 1975; Vassiliadis & Wood, 1993; Bloecker, 1995;van Loon et al., 2005) as well as the efficiency of TDU, find-ing ∆ M EC − SN ranging from ∼ . . ⊙ . For a rough es-timation, the order of increasing mass loss rate is: Reimers(1975), van Loon et al. (2005), Vassiliadis & Wood (1993)and Bloecker (1995), with approximate values for a typicalmetal-rich super-AGB star being 0.2, 0.4, 0.8 and 3 × − M ⊙ yr − respectively (see Figure 7 in Doherty et al. 2014a).In Siess (2007) post SDU/dredge-out core masses weretaken from detailed calculations and then the further evolu-tion during the TP-SAGB phase was extrapolated based onthe ratio of the average envelope mass loss rates ˙ M env to av-erage effective core growth rates ˙ M core characterised by a ζ parameter defined as ζ = | ˙ M env ˙ M core | . With best estimate val-ues of ˙ M core = × − M ⊙ yr − , TDU efficiency λ valuesbetween 0 . . M env = 5 × − M ⊙ yr − the ζ val-ues range from 140 – 1000. With these values the ∆ M EC − SN ranged from ∼ ⊙ ( ζ = ∼ . . ⊙ ( ζ = Z = .
04 – 10 − . When the metallicity scal-ing of Kudritzki et al. (1987) was applied to the mass lossrate then a very similar result to that of Poelarends (2007)was found with ∆ M EC − SN increasing substantially at lowermetallicity and at Z=10 − the ONe WD channel disappearsentirely.Using detailed evolutionary calculations Doherty et al.(2015) confirmed the results of these earlier parametric stud-ies. They found that when using reasonable mass loss rates(Vassiliadis & Wood, 1993), without an explicit metallicityscaling but with efficient TDU, then the width of the EC-SN channel from TP-SAGB stars is narrow with ∆ M EC − SN ∼ . . ⊙ (bottom panel of Figure 7). This Figureshows that the vast majority of stars that enter the thermallypulsing super-AGB phase will end life as ONe WDs, in sharpcontrast with the favored set by Poelarends (2007).By taking the mass range of the EC-SN channel andweighting it with an IMF, the importance and fractional con-tribution towards the overall core-collapse supernovae ratecan be determined. Using a Salpeter IMF and the EC-SNwidth and mass limits from the synthetic calculations ofPoelarends (2007) results in 5, 17 and 38 % of all TypeII SN coming from the EC-SN channel for metallicitiesZ=0.02, 0.001 and 10 − .In contrast using the results from Doherty et al. (2015)over these same metallicities we find a far smaller percent-age, of about 2 – 5% of all Type II SNe will be EC-SNe. This We assume for our calculations that the maximum mass for a Type II SNis 18M ⊙ based on the analysis of SN observations by Smartt (2015)PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al. large variation in frequency of EC-SNe highlights the impor-tance of constraining the mass loss rate at low metallicity.We note here that models that undergo core overshootingwill have far smaller envelopes (by as much as 2 – 3 M ⊙ )to remove in order for a star to avoid the EC-SN channel.This will result in fewer SNe for models with larger valuesof overshooting. The calculations presented in the previous section haveshown that the EC-SN channel for single super-AGB starsstrongly depends on the mass loss rate and the efficiencyof the TDU, both of which are highly uncertain and re-main poorly constrained. Using standard prescriptions forthe wind mass loss which has no explicit dependenceon metallicity , Siess (2007), Poelarends et al. (2008) andDoherty et al. (2015) showed that the initial mass range forsingle stars to evolve toward EC-SNe is narrow, being of theorder of 0 . . ⊙ . However, this picture does not con-sider binary evolution which opens new channels for the for-mation of such SNe and ONe WDs. This is particularly rele-vant considering the high fraction of stars having a compan-ion (Raghavan et al., 2010) and that about 70% of all starsmore massive than 15M ⊙ will interact at some point with abinary companion (Sana et al., 2012).We will start our discussion with the accretion onto anONe WD in a short period system. These systems representthe massive counterparts of cataclysmic variables and followa similar evolutionary scenario for their formation but withdifferent initial conditions (for a review on the formation ofcataclysmic variables see e.g. Ritter, 2012). The evolutionstarts with a super-AGB progenitor and a lower mass com-panion. If the initial period is long enough, mass transferby Roche lobe overflow starts when an ONe core is formedand the super-AGB star has entered the TP-SAGB phase.Because the TP-SAGB star has a deep convective envelope,mass transfer is likely to become dynamically unstable re-sulting in the formation of a common envelope. When themass transfer timescale becomes shorter than the thermaltimescale of the accreting component, the gainer star cannotassimilate the incoming material and the matter soon engulfsthe binary system. The friction of the stars with the gas willproduce a spiralling-in with transfer of orbital angular mo-mentum and potential energy to the envelope. The outcomeof this process is either the merger of the two stars if the en-velope is not ejected sufficiently rapidly or the formation ofa short(er) period binary system if the common envelope israpidly dispersed. This phase is short lived ( ∼ The metallicity is implicitly included via its effect on the structural vari-ables that appear in the formula. Note however that if the mass ratio is less than ∼ . − . during that short period of time, the companion is not ex-pected to accrete a significant amount of mass. Today, thedetermination of final orbital parameters is still subject tolarge uncertainties associated with our understanding of theenergetics involved (for a review of common envelope evo-lution see Ivanova et al., 2013).If the system avoids merging, we are left with a detachedsystem. The hot core of the super-AGB star ionizes the ex-panding envelope, enabling it to shine for ∼ yr as a plan-etary nebula. Subsequently the companion may fill its Rochelobe driving a second phase of (reversed) mass transfer. Thiscan be initiated either by the star expanding as a result ofits nuclear evolution, or by the loss of orbital angular mo-mentum due to gravitational wave emission and/or magneticcoupling.On the other hand, for shorter periods, mass transfermay be initiated while the super-AGB star progenitor ison the red giant branch. Because of the extended convec-tive envelope, this case B Roche lobe overflow is unsta-ble and, for the reason mentioned before, a common en-velope develops. The H-rich envelope of the primary isejected and the outcome is the formation of a short pe-riod system composed of a naked He star and a low masscompanion. The evolution of this post-common-envelope bi-nary has been investigated by Law & Ritter (1983) and de-tailed stellar models were computed by Dominguez et al.(1993) and Gil-Pons & Garc´ıa-Berro (2001, 2002). Thesesimulations indicate that a second episode of mass trans-fer is triggered after the onset of He shell burning (re-ferred to as case BB) and because the He star has a radia-tive envelope, the mass loss from the primary is stable. Intheir study of a 10M ⊙ primary with a lower mass compan-ion, Gil-Pons & Garc´ıa-Berro (2001) showed that the sec-ond mass transfer episode is stable and that the system de-taches when carbon ignites leading to the formation of a cat-aclysmic variable with an ONe WD. On the other hand, start-ing with a 9M ⊙ initial model, the primary looses so muchmass that it does not ignite carbon and ends up as a CO WD(Gil-Pons & Garc´ıa-Berro, 2002).The fate of the accreting WD depends mainly on the massaccretion rate (e.g. Nomoto, 1982): if it is too low, recur-rent H shell flashes (nova outbursts) eject more mass thanhas been accreted and the accretor loses mass. On the otherhand if the accretion rate is higher than the core growth rate(which is controlled by the H-burning shell), the accretedenvelope expands and a common-envelope may ensue fol-lowed by a spiral-in phase. In the intermediate regime, Hburning is steady and stable accretion allows the ONe coreto grow. When the central density reaches 4 × g cm − foran ONe core mass of ∼ . ⊙ (Nomoto, 1984), electroncapture reactions on Mg, Na and Ne are successivelyactivated. They induce the collapse of the white dwarf andthe heat released by γ -ray emission ignites oxygen burning.The outcome of this accretion-induced collapse depends onwhether or not the timescale for electron capture (which in-duces contraction) is shorter than the timescale associated PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars − M ⊙ yr − , close to theEddington limit. As initially investigated by Saio & Nomoto(1985), in this double degenerate scenario the fast accretionleads to off-center ignition of carbon and the inward prop-agation of a burning front that incinerates the CO WD intoan ONe core that may eventually collapse into a neutron starif it is massive enough. However, this picture is oversim-plified. Hydrodynamical simulations (e.g. Guerrero et al.,2004; Pakmor et al., 2012) reveal that soon after the dis-ruption of the WD, a “quasi-static” configuration devel-ops in which the cold WD core is enshrouded in a hot,rapidly rotating CO envelope surrounded by a thick Kep-lerian disk. Using these new and more realistic initial con-ditions, Yoon et al. (2007) re-investigated the conditions foroff-centre carbon ignition and showed that it depends on the temperature in the hot envelope, the mass accretion rateand the mass of the WD. Recent 3D SPH simulations (e.g.Sato et al., 2016, and reference therein) also predict that theoutcome, accretion-induced collapse or Type Ia explosion,depends sensitively on the initial mass ratio.The evolution of single super-AGB stars tell us that theSDU can significantly reduce the mass of the H-exhaustedcore below the Chandrasekhar limit as illustrated in Fig-ure 3. Models also show that the core growth during thesubsequent TP-SAGB phase is very modest and that veryfew stars reach the conditions for EC-SNe. This promptedPodsiadlowski et al. (2004) to suggest that binary interactionmay be able to remove the envelope before the SDU occursand thus allow more super-AGB stars to become EC-SNe.In some early papers, Nomoto (1984, 1987) investigatedthe fate of He cores representative of the evolution of 8-10 M ⊙ models and showed that for He core masses in therange 2-2.5M ⊙ , the evolution proceeds toward EC-SNe.Therefore a new channel to EC-SNe will open if, at theend of a case A or B mass transfer, the super-AGB donorkeeps a helium core mass in the range 2-2.5 M ⊙ . How-ever, Podsiadlowski et al. (2004) also pointed out that thissimple picture does not take into account the effects of bi-nary interactions which can substantially alter the stellarstructure. In particular, the size of the helium core dependson the mass of the hydrogen envelope. Previous studies(e.g. Wellstein & Langer, 1999; Gil-Pons et al., 2003a) in-deed show that the helium core mass can be dramaticallyreduced in short period systems compared to the evolutionof a single star. Furthermore, binary interactions contributeto redistributing the angular momentum inside the star. Thisis likely to generate additional mixing which will also af-fect the He core mass. This promising scenario remains tobe explored with self-consistent models, so that the range ofinitial periods and stellar masses can be identified.Investigating the origin of unusual fast and faint opticaltransients, Tauris et al. (2013, 2015) studied the evolutionof binary systems composed of a neutron star orbiting ahelium-star companion. This initial set-up is the result ofprevious binary evolution which can be summarized as fol-lows. The starting point is two main sequence stars withthe primary being a typical B star (3 M ⊙ . M . M ⊙ ).Depending on the initial period and mass ratio, the moremassive component undergoes Roche lobe overflow whileon the main sequence (case A) or after core H-exhaustion(case B). As a result of this conservative mass transfer, thesystem is composed of a naked He-star (the initially moremassive star stripped of its H-rich envelope) and a relativelymassive (8 M ⊙ . M . M ⊙ ) main sequence companion(which has accreted a substantial fraction of the primary’senvelope) in a wide orbit. The more evolved He star even-tually explodes as a supernovae (possibly an EC-SN!) leav-ing a neutron star remnant. If the explosion does not disruptthe system, the neutron star can accrete some of the windfrom the secondary (likely a Be star) and may show up asan X-ray source. Thereafter the secondary fills its Roche PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al. lobe but because of the extreme mass ratio, mass transferis dynamically unstable and leads to common-envelope evo-lution. After spiral-in, and provided merging is avoided, thefinal system consists of a short period neutron star orbitingthe naked He core of the secondary. The subsequent evolu-tion is similar to the previous one. After core He exhaustion,the He-star expands and a new episode of mass transfer be-gins (Habets, 1986; Dewi et al., 2002) which is temporarilyhalted during central C burning. At this stage, the exchangeof mass is highly non-conservative because the mass trans-fer rate is 3–4 orders of magnitude larger than the Eddingtonaccretion limit of the neutron star (a few 10 − M ⊙ yr − ). Intheir study, Tauris et al. (2015) showed that by gradually in-creasing the initial period (from 0.06 to 2.0 days) and themass of the He-star, the remnant of the He-star varies fromCO WD to ONe WD, to neutron stars formed by EC-SN orFeCC-SN as a consequence of mass transfer occurring dur-ing core helium burning (case BA), He shell burning (caseBB) or beyond (case BC). In some cases, the mass transferruns away and a common-envelope episode follows leadingto a merger or the formation of a very tight system. In thisscenario, EC-SN will mainly be observed as weak Type IcSNe. A variety of mixing episodes can occur in intermediate massstars prior to the TP-(S)AGB phase. Super-AGB stars of highand moderate metallicities undergo the first dredge-up eventthat mixes to the surface material from regions that have un-dergone partial hydrogen burning in which the CNO cycle isactive but with only marginal activation of the heavier hydro-gen burning cycles/chains. There are increases in the surfaceabundances of He, N, C, O and to a lesser extent in-creases in Na, Ne, and Mg. Simultaneously there is adecrease in the surface abundances of H, Li, C, N and O.As with the FDU, SDU mixes to the surface species in-volved in H burning, with the main nucleosynthetic signa-ture being a very large enhancement of He by up to ∼ Nand Na. In addition to the enrichment from standard SDU,models with corrosive SDU also increase the surface abun-dance of C, and in some cases , O and Ne. Dredge-outevents also have the ability to enrich the surface in prod-ucts of partial He burning, in particular C. As mentionedin Doherty et al. (2015) and Jones et al. (2016a) the C pro-duced via proton capture on C will subsequently undergothe C( α ,n) O reaction with the neutrons produced lead-ing to potentially significant heavy element production.Once the star reaches the TP-super-AGB phase the nu-cleosynthesis is dictated by hot bottom burning and (poten-tially) third dredge-up.
Hot bottom burning (hereafter HBB) occurs during the in-terpulse phase when the material in a very thin region atthe base of the convective envelope is hot enough to un-dergo nuclear burning. An equivalent, and perhaps more in-tuitive, way to think of this is that the bottom of the con-vective envelope extends into the top of the H-burning shell.The maximum temperature found at the bottom of the enve-lope is a function of initial metallicity and mass, with moremassive and/or metal-poor models achieving higher temper-atures. For super-AGB stars this temperature ranges fromabout 100 – 160 MK with a density of about 10 g cm − . Withsuch high temperatures there is activation of the CNO, Ne-Na, Mg-Al chains/cycles and potentially proton-capture re-actions involving heavier species such as Ar and K (see Fig-ure 8).Another consequence of HBB in super-AGB starsis the activation of the Cameron-Fowler mechanism(Cameron & Fowler, 1971). Here Be is created from He( He, γ ) Be and is quickly mixed to a cooler regionwhere it undergoes electron capture to form Li. Super-AGBstars can indeed become very lithium rich, with A( Li) up to ∼ , for a short time at the start, or just prior to the TP-(S)AGB phase. But once the He in the envelope is depletedthe Li production ceases and Li is efficiently destroyed. HBBalso produces He, but unless the TP-SAGB phase is veryextended, the main contribution to the surface of He willremain SDU/dredge-out.Activation of the CNO cycles leads to the production of C and N to the detriment of C, with this efficient de-struction being able to decrease the C/O ratio to below unityin the cases where the surface has been enriched from cor-rosive SDU, dredge-out or efficient TDU. However, at hightemperatures ( > O(p, γ ) F channel opens anddepletes O. In the most metal-poor/massive super-AGBstar models this can lead to the creation of a carbon star(C/O >
1) not from C enrichment but from the depletionof O (Siess, 2010). The C/ C and N/ N number ratiosreach their equilibrium values.Within the Ne-Na cycle very hot HBB leads to the de-struction of , Ne and Na to the benefit of the alreadyvery abundant Ne.For super-AGB stars the most obvious result from the Mg-Al burning is the very large reduction of Mg which is al-most completely destroyed to form Mg. Al is also pro-duced (Siess & Arnould, 2008; Doherty et al., 2014a) but atthese high temperatures the Al(p, γ ) Si( β + ) Al channelopens which bypasses the Mg. As the temperatures in-crease even further (T >
110 MK) there is activation of the Al(p, γ ) Si reaction (Ventura et al., 2011).If the HBB temperatures in super-AGB stars are extreme( >
150 MK) the argon-potassium (Ar-K) chain (refer Fig-ure 8) may also be activated (Ventura et al., 2012c), with this A( Li) = log (n[Li]/n[H]) + 12, where n is number abundancePASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars Na(p, α ) Ne.Near the end of evolution when the envelope mass dropsbelow about 1 – 2 M ⊙ , the temperature reduces below thecritical value required to sustain HBB and this processceases. Within the intershell convective zone during a thermal pulsethe main product is C produced by the triple- α reactionwith subsequent production also of the α capture species O, Ne, Mg, and Si. The abundant N in the inter-shell from the preceding CNO cycling is converted to Nethrough the reactions N( α , γ ) F( β + ν ) O( α , γ ) Ne.Due to the large temperature in the helium burning intershellconvective zone, the Ne( α ,n) Mg and Ne( α , γ ) Mg re-actions are activated. There is a substantial neutron flux re-sulting from the Ne( α ,n) Mg reaction with neutron den-sities of up to 10 − n/cm . These free neutrons can becaptured by Fe seeds within the convective pulse and lead toheavy element production via the slow (s) neutron captureprocess.Relevant to heavy element production in super-AGB starsis the occurrence of hot TDU events, where the tempera-ture at the base of the convective envelope during the TDUis still high enough for nuclear burning to be active (e.gChieffi et al., 2001; Herwig, 2004). From theoretical predic-tions (Goriely & Siess, 2004) these hot TDUs are expectedto inhibit the formation of C pockets. With no C pocketformation, in the standard picture, the main neutron sourcein S-AGB stars for the production of elements heavier thanFe is assumed to be the Ne neutron source during the con-vective thermal pulses. Recently Jones et al. (2016a) foundproton ingestion episodes during the later thermal pulsescreating C which may lead to i -process nucleosynthesis(Cowan & Rose, 1977) via the C( α ,n) O neutron source.We shall discuss the heavy element production yields fromsuper-AGB stars in Section. 4.3.2. Owing to the very nar-row mass of the convective He shell instability, even witha substantial number of thermal pulses, the total amount ofmaterial dredged to the surface of super-AGB stars is quitemodest, at most about 0.1 M ⊙ . ChainAr−K Cl Ar Ar Ar K K CaK (p, ) γ β + e
53 d (lab)88 y ( =10 g/cm ) ρ Ne−Na Cycle Mg−Al Chain Na
22 25 2620 21 Ne Mg Mg Mg Si SiAl Al NaNaNe
AlNe (p, ) γ β + (p, ) α CNO Cycles
C C
12 13 1513
F F β + (p, ) γ (p, ) α CNO IV CNO I CNO II CNO III N N
15 181716
N OO O O F
Figure 8.
A section of the chart of the nuclides (with atomic mass numberon the x-axis and proton number on the y-axis) showing the CNO and Ne-Na cycles and Mg-Al and Ar-K chains.
Super-AGB star yields for the production of elements lighterthan Fe have only quite recently become available. There isnow a variety of calculations from different research groupswhich cover a large range of masses and metallicities includ-ing a wide variety of input physics. Grids of nucleosynthesiscalculations of super-AGB stars have been produced fromthree main groups: those using
STAREVOL (Siess, 2010),
ATON (Ventura et al., 2013; Di Criscienzo et al., 2016) and
MONSTAR / MONSOON (Doherty et al., 2014a,b). For full de-tails of choices of stellar model parameters the reader shouldrefer to these publications. Here we briefly describe the ma-jor differences between the different set of models.In contrast to the model grids using
MONSTAR , thoseusing
STAREVOL and
ATON do not undergo TDU eventsand therefore show the abundance patterns of pure HBB.
PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al.
Another significant difference between models is that
STAREVOL and
MONSTAR use standard mixing-length the-ory with an alpha value calibrated to solar value. The
ATON models utilize the FST (Canuto & Mazzitelli, 1991) modelfor convection, which produces higher temperatures duringHBB, with the result that these models undergoing more ad-vanced nucleosynthesis.The mass loss prescriptions also vary. The standard modelsets for
STAREVOL and
MONSTAR both use the mass lossprescription from Vassiliadis & Wood (1993), whilst
ATON use the more rapid Bloecker (1995) rate with an η valueof 0.01. Slower mass loss rates lead to more TDU enrich-ment (if TDU is occurring) and the longer duration on thesuper-AGB gives HBB more time to process material. This,together with higher temperatures at the bottom of the con-vective envelope, will lead to more advanced nucleosynthe-sis. Another important factor is the nuclear reaction rates,especially for the heavier proton capture reactions.A common feature of all super-AGB models at all metal-licities is the large production of HBB products C and Oas well as He with the bulk amount coming from efficientSDU. Lithium is temperamental and is either destroyed orproduced in super-AGB stars dependent primarily on themass loss rate. When HBB begins we see production of Li,but once the He is all used, the destruction of Li domi-nates. So if the mass-loss is sufficiently high that the starends its life early, before the He is all destroyed, then thestar may be a nett producer of Li. If the mass-loss rate islower, and the Li is destroyed before most of the mass isejected, then the Li yield is negative. (Ventura & D’Antona,2010; Doherty et al., 2014a). N is increased at all dredge-up events and is also greatly increased through HBB. TheTDU products C, O and Ne are also subsequently pro-cessed via HBB.Models of very (and extremely) metal-poor super-AGBstars create similar isotopes to their metal rich counterparts.However, in lower metallicity models that experience TDU,such as those by Doherty et al. (2014b), one find positiveyields of the species C, O, N, Si, which is not thecase for the more metal-rich super-AGB stars.In Figure 9 we compare light element super-AGB staryields (in [X/Fe]) for models with Z = . Z = . where [A/B] = log ( n (A) / n (B)) ∗ − log ( n (A)/ n (B)) ⊙ Figure 9.
Comparison of a selection of light element yields for models of9.0 M ⊙ Z = .
02 and 7.5 M ⊙ Z = . Z = . the relative TDU contribution higher at lower metallicity. Atthe very low metallicity the yield of many major elementssuch as C, O, F, Ne, Na and Mg differ so much betweencalculations that there is no consensus on whether these el-ements are either produced or destroyed within super-AGBstars.We stress that although agreement between results fromdifferent groups at high metallicity is somewhat comfort-ing, the principal test of the validity of our results will comewhen we can compare against observations, which requiresus to positively identify super-AGB stars.For details of nucleosynthesis in extremely metal-poor (Z ≤ − ) and primordial super-AGB stars we refer to the re-view by Gil-pons (2017) in this volume. Due to both the numerical complexities and time consum-ing nature of the calculations, currently published heavyelement nucleosynthesis yield predictions of super-AGBstars are limited to a small selection of individual mod-els in Fishlock et al. (2014), Shingles et al. (2015) andKarakas & Lugaro (2016) . In these works heavy elementproduction is limited to predominantly Rb and in not largequantities. This nucleosynthesis is illustrated by Figure 10in which we present a new set of super-AGB heavy ele-ment (s-process nucleosynthesis) yields for a range of metal- Note also the super-AGB star nucleosynthesis calculations for selectedspecies in Karakas et al. (2012) and Lugaro et al. (2014)PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars Z = . − . ∼ ⊙ ), thermally pulsing dura-tions ( ∼ × yrs) and number of thermal pulses ( ≈ Ne neutron source withvery high peak neutron densities N n ∼ cm − reached.However, with the very short thermal pulse duration, the in-tegrated neutron exposure τ is not very high, at most ∼ − . This results in a large production of Rb (Z=37),Kr (Z=36) and light s-process elements Sr, Y, and Zr (Z=38,39, 40), and a small synthesis of heavy s-process elementsand Pb. The heavy element abundance patterns are similarbetween models of the different metallicities even with theassociated large variation in availability of Fe-seeds. This isdue to the low neutron exposure which inhibits formation ofsubstantial amounts of elements past the light s-process peakas well as the small overlap factor between successive ther-mal pulses which leads to little build up of heavy elements tobe subsequently reprocessed. Even with their large numberof thermal pulses, heavy element production within super-AGB stars (at least of the moderate metallicities presentedhere), is reasonably modest, with the yield of no heavier thanFe element exceeding unity in [X/Fe]. . This is due primarilyto the small mass contained within each convective thermalpulse ( ∼ × − M ⊙ ) and therefore considerable dilutionof s-process enriched intershell material within a massive en-velope.The super-AGB models of Jones et al. (2016a) found pro-ton ingestion during TPs where protons from the envelopewere making contact with the convective HeB during thethermal pulse. This leads to rapid production of C, whichthen undergoes the C( α ,n) O reaction. The neutrons pro-duced during this event are available to then form heavyelements via the intermediate capture process. Jones et al.(2016a) estimated the potential i-process heavy element pro-duction within super-AGB stars to be of the order of 1–2 dex,comparable to the maximum 1–2.5 dex production from the Ne source as estimated by Doherty et al. (2014a,b).
Due to a lack of stellar yield calculations, super-AGB starshad long been missing in galactic chemical evolution studies,with this mass range either treated by interpolating betweenlower mass AGB stars and massive stars (e.g Romano et al.,2010; Kobayashi et al., 2011), or even neglected entirely.Now, with the recent availability of grids of super-AGB stel-lar yields (from a variety of research groups and utilisingquite different input physics), we are beginning to be able toanswer the question of how important are these stars, withina galactic perspective.
Figure 10.
Heavy element nucleosynthesis yields for super-AGB stars fora range of metallicities (in [X/Fe]) all scaled to the solar abundances ofAsplund et al. (2009). The breaks in the distribution are for the elements Tc(Z=43) and Pm (Z=61) which have no stable isotopes. The shaded regionsrepresent the elements used to represent the three s-process peaks ls , hs andPb. The maximum production is for the element Rb (Z=37). In Doherty et al. (2014a) metal-rich super-AGB yieldswere weighted by a standard IMF and compared to the con-tribution from lower mass AGB stars to assess their relativeimportance. This showed that whilst metal-rich super-AGBstars are large producers of isotopes such as He, C, N, O, Ne and Na, from a galactic context their contribu-tion is minimal. In Figure 11 we have selected two illustra-tive isotopes, Li and C. For C the overall contributionis practically negligible compared to that from the interme-diate mass AGB stars. However, depending on the choice ofmass loss rate, super-AGB stars at high/moderate metallici-ties may make a contribution to the Galactic inventory of Li, , Mg and Al. Super (and massive) AGB stars also con-tribute a non-negligible amount ( ≈
10 per cent) to the galac-tic value of the radioactive isotope Al (Siess & Arnould,2008; Doherty et al., 2014a). As mentioned in Section 4.3,the yields of super-AGB stars vary quite considerably be-tween the results from different research groups. Howeverthis is less pronounced at higher metallicities. This makesthese models reasonably robust.Based on current model predictions, super-AGB stars (atleast of mid to high metallicity) are not expected to make asubstantial contribution to the heavy elements in the Galaxy.This is of course dependent on the choice of mass loss rate,with a larger contribution expected for a slower mass lossrate. In super-AGB stars there is considerable dilution of s-process enriched intershell material within the massive enve-lope. Yet super-AGB stars may still make an important con-tribution to the light s-process elements, in particular Rb, Srand Y in the early Galaxy. Currently the impact of the possi-ble heavy element (i-process) nucleosynthesis in dredge-outevents (Doherty et al., 2015; Jones et al., 2016a) and protoningestion during thermal pulses (Jones et al., 2016a) awaitsdetailed nucleosynthesis calculations.
PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al.
Figure 11.
Stellar yields weighted by the Kroupa et al. (1993) IMF, withthe shaded regions representing the mass range for super-AGB stars. Formasses lower than 6 M ⊙ AGB yields are from Karakas (2010). The errorbars on the 8.5 M ⊙ Z=0.02 are mass loss tests cases from Doherty et al.(2014a).
The “abundance anomaly problem” in globular clusters in-volves explaining the origin of the unusual compositionspresent in a substantial fraction (often a majority) of thestars in globular clusters. These patterns are not seen infield stars, and include, for example, He enrichment andanti-correlations in the element pairs C-N, O-Na, Mg-Aland Mg-Si (Carretta et al., 2009a,b; Bragaglia et al., 2010).These abundance patterns are characteristic of the resultsof hot hydrogen burning (Denisenkov & Denisenkova, 1990;Prantzos et al., 2007). Crucially in the majority of clustersthere is no variation, from star to star, in the Fe and heavy (s-process) element abundances (e.g. Yong et al., 2006, 2008).There also seems to be a near constancy in the total C+N+Oabundance (e.g. Smith et al., 1996; Ivans et al., 1999), withsome exceptions (e.g. NGC1851, Yong et al., 2009). Thiswould limit the amount of dredged-up material as this con-tains primary carbon (and its burning products) whereas Hburning simply cycles CNO elements among each other,leaving C+N+O constant.The leading theory to explain these anomalies is thatglobular clusters are made of multiple generations ofstars, with the anomalous stars being formed from theenriched material from a first generation of stars (fora review refer to Gratton et al. 2012). Many candidatessites have been proposed as the source of the enrich-ing gas such as: (super-)AGB stars (Cottrell & Da Costa, 1981; Ventura et al., 2001; D’Ercole et al., 2008); rapidlyrotating massive stars (Decressin et al., 2007); massivebinary stars (de Mink et al., 2009); super-massive stars(Denissenkov & Hartwick, 2014) and novae (Smith & Kraft,1996; Maccarone & Zurek, 2012).Currently each of the suspected polluters has prob-lems matching certain observed abundance patterns(Gratton et al., 2012) as well as larger problems such as themass budget for the different populations and the pollutedmaterial (e.g. Bastian & Lardo, 2015). The entire pictureof multiple stellar generations seems incompatible withobservations from young massive clusters (the best currentday globular cluster analogues) that show a lack of availablegas, and no evidence for multiple bursts of star formation(see Bastian, 2015, and references therein).Whilst there are problems with the (super-)AGB scenario,as well argued by Renzini et al. (2015) and D’Antona et al.(2016), using solely nucleosynthetic considerations super-AGB and massive AGBs are perhaps the only barely plausi-ble progenitor candidate remaining. This is based on theirability to (qualitatively) reproduce many of the necessaryfeatures, such as high helium content (primarily from SDU)and Li production. They also reach high enough tempera-tures to activate not only the CNO cycles but also the Ne-Naand Mg-Al chains/cycles.Observations of Mg-K anti-correlations in the lowmetallicity globular clusters NCG2419 and NCG2808(Mucciarelli et al., 2012; Cohen & Kirby, 2012;Mucciarelli et al., 2015) have been explained as beingproduced from (very) hot hydrogen burning and the argon-potassium (Ar-K) chain (Ventura et al., 2012c). This isshown in Figure 8. Under laboratory conditions the half lifeof Ar to electron capture is 53 days whilst at conditionsfound in super-AGB star envelopes with ρ ∼
10 g/cm thishalf-life is increased to 88 years. Due to this, Iliadis et al.(2016) argued that the main path to K would be viathe Ar(p, γ ) K( β + ν ) Ar(p, γ ) K( β + ν ) Ar(p, γ ) Kchannel. Iliadis et al. (2016) used Monto Carlo nuclearreaction network calculations to identify a temperatureand density regime that could explain all the abundancepatterns in the cluster NGC2419, in particular the Mg-Kanti-correlation. They ruled out the majority of pollutercandidates but concluded that super-AGB stars may be aviable solution if the HBB temperatures could be increasedslightly, such as results from the use of the FST theory ofconvection.Probably the major nucleosynthetic problem with the(super-)AGB scenario currently is the fine balance of con-ditions required to produce Na instead of destroy it. Toachieve the high depletion of O (and Mg) that is observed,the duration of the TP-(S)AGB phase needs to be quiteextended. However this leads also to destruction of Na, Nova also may reach the correct temperature/density conditions, howeverwithout any detailed nova model calculations at low metallicity this needsfurther exploration and remains quite speculative.PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars Na. A rem-edy to this problem could come from a decrease in the reac-tion rate of Na(p, α ) Ne destruction channel by a factor of2–5 (Ventura & D’Antona, 2006). We note however that thisvalue is outside the current uncertainties. An experimentalre-evaluation of this reaction rate is sorely needed.Another nucleosynthetic obstacle for the (super-)AGBstar scenario (and all other polluter candidates) is the pro-duction of too much He to match the observed spread in themajority of clusters (Bastian et al., 2015). Helium in massiveAGB and super-AGB stars is produced primarily from SDU,with a smaller contribution from HBB. These processes arequite independent, so there is some potential scope to mod-ify the He production.Another important and often overlooked point is the im-pact of rotation on the surface composition. Decressin et al.(2009) showed that rotation in intermediate mass stars mayact like deep (corrosive) SDU and increase the surface in car-bon (and total metallicity), which would make (super-)AGBstars unviable polluter candidates.As we saw in Section 4.3 the predictions of super-AGBstar nucleosynthesis at low metallicity (applicable to themajority of globular clusters) vary widely between differ-ent research groups. For super-AGB star models to matchas the polluter we must fit rather strict evolutionary con-straints. These are: no, or very inefficient TDU; very ad-vanced HBB, driven either by more efficient convective mix-ing (e.g. through use of FST), or standard mixing-length the-ory with increased mixing length α ; a relatively slow massloss rate. In addition, as discussed in Pumo et al. (2008), themost massive super-AGB stars, which undergo dredge-outevents, must all end their lives as EC-SNe to avoid pollutingthe cluster with C enriched material.However, if (super-)AGB stars are indeed the source ofthe material from which the later generation(s) formed thiswould prove invaluable to constraining theoretical modellingof this class of star. AGB and super-AGB stars make substantial contribu-tions to the galactic dust inventory (e.g. Gehrz, 1989;Matsuura et al., 2009; Schneider et al., 2014). The type ofdust formed during the (S-)AGB phase is determined bythe surface composition of the star, primarily the C/O ratio,and is classified into two main groups: either carbon-rich oroxygen-rich dust. As seen in the previous sections, due toHBB the surface composition in super-AGB stars is typi-cally C/O < Z = . − .
018 (Ventura et al., 2012a,b,2014; Dell’Agli et al., 2017). The amount of dust generated depends critically on thedensity in the stellar outflow, with more rapid mass lossleading to higher density and greater dust production. Thisresults in dust mass yields (and silicate dust grain sizes)which are correlated with initial mass, with the most mas-sive super-AGB stars producing ∼ − to 10 − M ⊙ withgrain size . µ m (Dell’Agli et al., 2017). Models of O-rich super-AGB stars from Ventura et al. (2012b) find theamount of dust production is strongly metallicity depen-dent, with decreasing dust yields at lower metallicity. Thisis due to the reduced availability of the key elements Si,Al, Fe and O at lower metallicity, as well as the far lowerO abundance due to the more efficient HBB at low metal-licity. Since these elements are not produced in substantialamounts within the stars themselves, dust formation is ex-pected to be inhibited. At the metallicity of Z = × − Di Criscienzo et al. (2013) found the Si abundance was toolow for non-negligible silicate production. They suggesteda metallicity threshold of Z = .
001 as the limit for silicateproduction for super-AGB stars. As yet, there are no dustyield calculations from models that have undergone dredge-out and become C-rich at the start of the super-AGB phase,nor of super-AGB star models which have become carbonrich due to either 3DU or very efficient O destruction. Thesemodels would result in substantially different dust chemistryand warrant exploration.
Here we discuss some of the observational probes and stud-ies that can and are being used to aid in the understanding ofthe evolution of stars that bridge the low/high mass divide.
As mentioned in the introduction, a fundamental problem isthat there are at present no definite detections of super-AGBstars. Super-AGB stars with their very rapid mass loss ratesare expected to be dust enshrouded OH/IR stars and more lu-minous than their lower mass AGB star counterparts. How-ever, models that undergo more efficient convective mix-ing (e.g. through using the FST theory of convection or alarger mixing-length within the MLT formulation) will at-tain higher luminosities, making clear identification betweena massive AGB and a super-AGB star practically impossi-ble. Furthermore, from a nucleosynthetic point of view a lowmass super-AGB star and a massive AGB star are expectedto produce very similar element distributions, in particularfor the heavier than Fe elements. At present abundance de-terminations in massive (potentially super-)AGB stars arelimited to a small sample of stars in the Galaxy and Mag-ellanic clouds (Garc´ıa-Hern´andez et al., 2006, 2007, 2009).These stars are found to be Rb-rich, which is suggestive thatthey have undergone TDU events. Determining the exactamount of enrichment is problematic as it has been shownthat accounting for an extended circumstellar envelope can
PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al. substantially modify the abundance determinations in thisclass of star (Zamora et al., 2014). Super-AGB stars mayalso be identified in the large infrared surveys of Magellanicclouds(e.g. Kraemer et al., 2017), or in young stellar clus-ters.Super-AGB stars also share the same stellar luminositiesand surface temperatures as the slightly more massive redsuper-giants. Hence a careful analysis of red super-giant sur-veys may yield super-AGB star candidates. One such ob-ject is the star HV2112 (Levesque et al., 2014), which hasbeen suggested potentially as a super-AGB star, or even aThorne- ˙Zytkow object (Tout et al., 2014). Their stellar vari-ability may be a key to distinguish between red super-giantsand super-AGB stars with super-giants found to have loweramplitude pulsations, with maximum variations of about 0.5mag (Wood et al., 1983; Groenewegen et al., 2009).
Planetary nebula abundances may be used as probes ofthe resultant nucleosynthesis in super-AGB stars (e.g.Ventura et al., 2015, 2016; Garc´ıa-Hern´andez et al., 2016).However as these stars represent only a relatively scarce (andshort-lived) mass range we expect only a small number ofsuch PNe.White dwarfs can be used to explore the evolutionaryproperties of super-AGB stars in a variety of ways, such asWD mass distributions/population studies, initial-final massrelations and analysis of individual massive WDs.We note that observations of ultra-massive white dwarfsare particularly difficult due to their relative scarcity, inher-ently low luminosity due to more compact nature, as wellas more rapid cooling (Althaus et al., 2007). Recent worksby Cummings et al. (2016a,b) and Raddi et al. (2016) havederived semi-empirical initial-final mass relations for ultra-massive WDs using observations from young open clusters.However, the procedure to derive an initial-final mass rela-tion is quite involved and is affected by quite a range of un-certainties. Firstly, the WD effective temperature and grav-ity are determined from observations and the mass is thendetermined from a mass to radius relation. Next the clus-ter age is found from isochrone fitting with this procedurereliant on stellar evolution models with their inherent uncer-tainties. The initial mass of the WD is determined by esti-mating the cooling time, which is dependent on compositione.g. CO (Salaris et al., 1997, 2010) or ONe (Althaus et al.,2007), and then subtracting this from the cluster age to findthe stellar lifetime. Lastly this duration is compared to theo-retical stellar models to derive the initial mass. With the stel-lar lifetimes of super-AGB stars quite short ( ∼
20 – 60 Myr)and dependent on rotational mixing and overshoot amongother effects, the determination of an initial mass for a ultra-massive WD will be hampered by large uncertainties. Hencethis method seems unlikely to be able to accurately deter- Massive WDs have masses greater than 0.8 M ⊙ whilst ultra massive havemasses greater than 1.1M ⊙ mine the exact upper mass limit for WD formation. Based oncurrent estimates of the initial-final mass relation the maxi-mum mass for a WD progenitor is estimated to be in range ∼ ⊙ or more (Salaris et al., 2009; Williams et al.,2009; Cummings et al., 2016a).Theoretical calculations from single or binary inter-mediate mass stars predict a veritable zoo of massiveWDs including: CO, CONe, ONe, Si and ONeFe WDs.Yet observationally distinguishing these cores may proveto be practically impossible. Two ultra-massive ( ∼ ⊙ ) O-rich (G¨ansicke et al., 2010) WDs have been ob-served. In principle differentiating between the CO or ONecore composition of a massive WD can be accomplishedfrom asteroseismology of pulsating WDs (C´orsico et al.,2004). Another way to probe WD interiors comes fromeither classical or neon novae which are hosted on COand ONe WDs(Jose & Hernanz, 1998; Wanajo et al., 1999;Gil-Pons et al., 2003b; Downen et al., 2013) respectively,however these observations will most likely probe only theouter core.
There is the potential to learn about the final fates of interme-diate mass stars through studies of SNe and their remnants.The most common approach is to identify particular eventsand make direct comparison between models and observedproperties such as chemistry, mass-loss history, light curvesetc. The overall SN rate may be used to estimate the min-imum mass for a SN. In addition, it may also be possibleto use predicted nucleosynthetic properties to determine thefrequency of certain types of SN events.Have we already seen the death throes of a supernovafrom a super-AGB star? With their H rich envelopes, singlesuper-AGBs are expected to explode as Type II SN. EC-SNeare expected to have lower explosion energies of ≈ ergand very small Ni masses ∼ × − M ⊙ (Kitaura et al.,2006) compared to their more massive FeCC-SN counter-parts ( ≈ erg, ∼ × − M ⊙ ). The envelopes of super-AGB star progenitors of EC-SNe may be either C-rich orO-rich prior to explosion, with dredge-out events being ableto form carbon stars, albeit only for a short time before effi-cient HBB would burn this C to N resulting in C/O < The first WD with an atmosphere of O, Ne and Mg has been recently dis-covered (Kepler et al., 2016) . However, unexpectedly the surface gravityof this WD corresponds to a mass of ≈ ⊙ , far below that expectedfrom theoretical predictions. One possible explanation is that this WDformed via a binary channel.PASA (2017)doi:10.1017/pas.2017.xxx uper-AGB Stars ∼ ⊙ (i.e Spiro et al., 2014).Whilst there are some very promising candidate EC-SN, inparticular SN1054 and SN2008S, as yet there has been nodefinitive confirmed super-AGB EC-SN events.Based on observations of Type II-P SNe which also hadpre-SN progenitor imaging, the review by Smartt (2009) es-timated the lower initial mass for CC-SN explosions to be8 . + − . M ⊙ . However with an increased data set, this valuewas revised to 9 . + . − M ⊙ or 10 + . − M ⊙ depending on choiceof stellar models (Smartt, 2015). These values for M n arein reasonable agreement with the theoretical stellar evolu-tionary calculations discussed in Section 3.1 which take intoaccount a moderate amount of overshooting. Under the as-sumption of the minimum initial mass for a CC-SN to be 8M ⊙ , the recent SUDARE supernova survey (Botticella et al.,2017) found the expected CC-SN rate to be higher than thevalue deduced from observations by about a factor of two. Apossible remedy to this discrepancy is if the minimum massfor a CC-SN was increased to 10 M ⊙ .From an explosive nucleosynthesis perspective super-AGB stars that undergo an EC-SN may produce a wide vari-ety of elements from Zn to Zr (Wanajo et al., 2011), and iso-topes Ca and Fe (Wanajo et al., 2013a,b). Based on theirnucleosynthesis calculations of Kr, Wanajo et al. (2011)suggested the frequency of EC-SNe relative to all CC-SNemust be ∼ ⊙ wide in initial mass, if these events arethe main source of elements Zn to Zr in the Galaxy.Recent determinations of the neutron star mass distribu-tion have suggested that it may be bimodal (Schwab et al.,2010; Knigge et al., 2011; Valentim et al., 2011), withthe lower mass peak suspected to arise from EC-SNe(van den Heuvel, 2004; Podsiadlowski et al., 2004). Due tothe steep density gradient at the core edge, it is expected thatEC-SNe result in neutron star masses very close to that ofthe original ONeMg core and with relatively small veloc-ities (Podsiadlowski et al., 2005; Radice et al., 2017). How-ever, recent low mass FeCC-SN and EC-SN progenitor mod-els show smaller differences in the density gradients than inprevious calculations (e.g. see Figure 1 in M¨uller, 2016) anddue to this have far more similar explosion properties than inprevious works, with these lowest mass FeCC-SNe dubbed“EC-SN like”. Owing to their similarity in explosion prop-erties the resulting neutron star masses may not be as clearlydistinguishable as was thought, making it harder to separateneutron stars from the lowest mass FeCC-SN and EC-Se.As described in Sect. 3.3, binary evolution opens new evo-lutionary channels to EC-SNe. In the scenario that involvesthe merger of two WDs, the signature is expected to be thatof a SN of Type Ib (Nomoto & Hashimoto, 1987). If we con-sider a CV-like configuration of an accreting ONe WD, theexplosion properties depend on the mass transfer rate. If ac-cretion is slow, helium will build up at the surface of the WDand eventually ignite off-center. The detonation will thenproduce observational signatures similar to those of a SNIa(Marquardt et al., 2015). In the other class of models wherethe progenitor loses its H-rich envelope and becomes a Hestar, the EC-SN explosion would be observed as a SNIb orIc depending of the mass and composition of the envelopesurrounding the collapsing ONe core (Tauris et al., 2015).According to Moriya & Eldridge (2016), the explosion ofstripped-envelope EC-SNe could give rise to fast evolvingtransients and the newly-formed neutron star would have alow kick velocity. The very large uncertainty in the mass loss rates for super-AGB stars, particularly at low metallicity, is a major im-pediment to determining the final fates of this class of star.Whilst there are observational studies examining the impactof metallicity on the mass loss rates of AGB and red super-giant stars (e.g. Goldman et al., 2017), these works can onlyprobe the relatively metal rich populations, because the lowmetallicity super-AGB stars are long since dead. However,there are valiant efforts underway in theoretical modelling ofAGB star atmospheres and circumstellar envelopes to derivea predictive theory of mass loss for (super-)AGB stars (seeH¨ofner 2016 and reference therein). In addition to the impor-tance of determining the “standard” mass loss from super-
PASA (2017)doi:10.1017/pas.2017.xxx Doherty et al.
AGB stars, there may also be mass expulsions from eitherthe Fe-peak instability (Lau et al., 2012) or global oscillationof shell-H ingestion (GOSH, see Herwig et al., 2014). Bothof these phenomena may have a substantial impact on thefrequency of EC-SNe, as well as potentially modify super-AGB nucleosynthesis and need further examination. Basedon observations of evolved massive AGB stars de Vries et al.(2014, 2015) have suggested the need for a “hyper”-wind of10 − -10 − M ⊙ yr − to account for the very short superwindduration and lack of extended structure (Cox et al., 2012).Could this hyperwind be as a result of an Fe peak instabil-ity? Our current theory of convection, in particular the treatmentof convective boundaries, lies at the heart of the majority ofthe uncertainties in this mass range. Arguably the most im-portant factor that effects the mass boundaries M up and M mas is the treatment of convective borders, in particular duringcore He burning. Multidimensional hydrodynamical simula-tions of convection are key to understanding this mass range.A new theory of convection, such as the 321D theory un-der development (Arnett et al., 2015; Campbell et al., 2016),would help to constrain the WD/SN boundary .Is convective boundary mixing efficient enough to stall C,and/or Ne burning i.e. Do CO-Ne WDs or FMS exist? Whilethe study of Lecoanet et al. (2016) suggested the C-burningwould most likely not be stalled by CBM, the results from Cburning flame propagation cannot simply be applied to thatof neon-oxygen burning flames to rule out the formation ofFMS. This is due to the structure between C and Ne flamesbeing quite different with Ne burning flames far thinner andfaster moving (e.g. Timmes et al., 1994). Multi dimensionalcalculations of Ne flames are crucial to determine if FMSexist.What is the impact of convective boundary mixing on theoccurrence and efficiency of third dredge-up? Are super-AGB stars the site of the i-process heavy element productionfrom during proton ingestion TPs (Jones et al., 2016a)? There are a number of investigations that could be done inthe near future, and which would dramatically advance thisfield. We list a selection of these here. • an analysis of red super-giant surveys to possibly iden-tify super-AGB; • further analysis of GOSH events, to determine theirimplications for super-AGB stars; • the problem of convergence and the Fe opacity peak;this will require hydrodynamical models but couldyield significant advances in our understanding of themasses and progenitors of various SNe; • hydrodynamical multi-dimensional flame propagationcalculations, especially for the Ne flame; • reevaluation/measurement of the critical nuclear reac-tion rates: Na + p, C+ C; • details of dust production from super-AGB and mas-sive AGB stars; • proton ingestion and the resulting i-process neutroncaptures; this may have implications well beyondsuper-AGB stars. The last decade has seen real advances in the study of thelives and deaths of super-AGB stars. There are now fullydetailed interior stellar evolutionary models along the entireTP-SAGB for a wide range of metallicities from Z = . Z = − (see companion review by Gil Pons, 2017).Furthermore super-AGB star nucleosynthesis predictions forboth light and heavy elements are now available for somecompositions, and the composition range is being extendedall the time. The first detailed dust yields are also now avail-able.The study of EC-SNe has also flourished in recent years.The production of a new generation of single star EC-SNprogenitor models is an important update on the previousmodels from the early 1980s. There are now detailed singleand multi-dimensional simulations of EC-SNe (and EC-SNlike) explosions as well as detailed nucleosynthetic calcula-tions from EC-SNe. In addition, recent works have calcu-lated synthetic light-curves of EC-SNe within super-AGBstar envelopes. There have also been important advances inthe role of binary stars in producing EC-SNe.All of these above results have produced predictions thatcan and are being tested against observation to further con-strain these stars on the low/high mass star boundary.Nevertheless, some of the most important questions re-main, for example the recent multi-dimensional simulationsof O-deflagration in ONe cores has reopened the debate ofthe final fate of an EC-SN on whether they explode by oxy-gen deflagration, or collapse by electron captures to form aneutron star.We have highlighted/identified areas that need attention,which may help us finally answer some of these importantquestions. This work was supported in part by the National Science Founda-tion under Grant No. PHY-1430152 (JINA Center for the Evolutionof the Elements). CD acknowledges support from the Lendulet-2014 Programme of the Hungarian Academy of Sciences. CDwould like to thank S.W Campbell and S. Jones for interesting dis-cussions. LS is a senior FNRS researcher.
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