On Presolar Stardust Grains from CO Classical Novae

Christian IliadisDepartment of Physics & Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255

Triangle Universities Nuclear Laboratory, Durham, NC 27708-0308, USA

iliadis@unc.edu

Lori N. DownenDepartment of Physics & Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255

Triangle Universities Nuclear Laboratory, Durham, NC 27708-0308, USA

Jordi JoseDepartament de Fısica, EEBE, Universitat Politecnica de Catalunya, c/Eduard Maristany 10,

E-08930 Barcelona, Spain

Institut d’Estudis Espacials de Catalunya, c/Gran Capita 2-4, Ed. Nexus-201, E-08034Barcelona, Spain

Larry R. NittlerDepartment of Terrestrial Magnetism, Carnegie Institution for Science, Washington, DC 20015,

USA

Sumner StarrfieldEarth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA

ABSTRACT

About 30% to 40% of classical novae produce dust 20 − 100 days after the outburst,but no presolar stardust grains from classical novae have been unambiguously identifiedyet. Although several studies claimed a nova paternity for certain grains, the mea-sured and simulated isotopic ratios could only be reconciled assuming that the grainscondensed after the nova ejecta mixed with a much larger amount of close-to-solar mat-ter. However, the source and mechanism of this potential post-explosion dilution of theejecta remains a mystery. A major problem with previous studies is the small numberof simulations performed and the implied poor exploration of the large nova parameterspace. We report the results of a different strategy, based on a Monte Carlo technique,that involves the random sampling over the most important nova model parameters: thewhite dwarf composition; the mixing of the outer white dwarf layers with the accretedmaterial before the explosion; the peak temperature and density; the explosion timescales; and the possible dilution of the ejecta after the outburst. We discuss and takeinto account the systematic uncertainties for both the presolar grain measurements andthe simulation results. Only those simulations that are consistent with all measuredisotopic ratios of a given grain are accepted for further analysis. We also present the nu-merical results of the model parameters. We identify 18 presolar grains with measuredisotopic signatures consistent with a CO nova origin, without assuming any dilution ofthe ejecta. Among these, the grains G270 2, M11-334-2, G278, M11-347-4, M11-151-4,and Ag2 6 have the highest probability of a CO nova paternity.

Subject headings: circumstellar matter, dust - meteorites - novae, cataclysmic variables - nuclearreactions, nucleosynthesis, abundances

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1. Introduction

Primitive meteorites contain dust grainswith isotopic compositions vastly differentfrom those of any other matter found in thesolar system (Zinner 2014). The only viableexplanation for their existence is that theycondensed in stellar winds or the ejecta of ex-ploding stars. These tiny grains survived thejourney through the interstellar medium tothe region in which the presolar cloud formedabout 4.6 Gy ago. Some of these grains alsosurvived the homogenization process duringthe formation of the solar system and wereincorporated into meteorites. They are calledpresolar stardust grains and retain the dis-tinct isotopic composition of the stellar out-flows at the time of grain condensation. Thelaboratory measurement of their isotopic ra-tios provides an exceptional opportunity tostudy stellar evolution, stellar explosions, nu-cleosynthesis, dust formation, and galacticchemical evolution.

The analysis and interpretation of presolarstardust grains requires an iterative approach(Nittler & Cielsa 2016). First, the stellarsource for a group of grains needs to be identi-fied on the basis of the available isotopic data.Once the source is identified, the preciselymeasured isotopic ratios provide strong con-straints for understanding the physical andchemical processes that occurred inside theparent stars. According to current think-ing, most analyzed stardust grains formed inAsymptotic Giant Branch (AGB) stars of aprevious generation. This insight was impor-tant for a quantitative understanding of AGBstars, and also for demonstrating how one halfof all elements beyond iron are synthesizedin the astrophysical s-process. A fraction ofthe measured stardust grains (≈ 1% − 5% ofSiC; up to 10% of oxides and silicates; ≈ 50%of graphite) originate presumably from core-collapse supernovae (Zinner 2014). Their iso-topic signatures may shed light on explosivenucleosynthesis, the mixing between different

layers in the ejecta, grain condensation, andhow much dust survived the reverse shock be-fore injection into the interstellar medium.

A few presolar stardust grains are char-acterized by very low 12C/13C and 14N/15Nratios and large 30Si excesses (Amari et al.2001). These signatures imply an increasedproduction of the minor isotopes, 13C and15N, compared to the major ones, 12C and14N, and are difficult to explain by AGBstar or supernova nucleosynthesis. Explosivehydrogen burning in classical novae, on theother hand, seems to reproduce qualitativelysome of the isotopic signatures measured inthese grains (Amari et al. 2001; Jose et al.2004; Jose & Hernanz 2007; Haenecour et al.2016).

A classical nova is thought to be one conse-quence of the accretion of hydrogen-rich ma-terial onto a white dwarf in a close binary sys-tem (Jose et al. 2016; Starrfield, Iliadis, & Hix2016). Some of the key processes are sketchedin Figure 1. Over long periods of time, thematerial being accreted from the secondarystar forms a layer of nuclear fuel (green regionin Figure 1a) on the white dwarf surface. Thebottom of this layer is gradually compressedby the surface gravity and becomes electrondegenerate. Once the temperature at the bot-tom of the accreted layer reaches the Fermitemperature (≈ 30 MK), the layer begins toexpand, but by this time the temperature isincreasing so fast that a thermonuclear run-away results. During the steep temperaturerise, matter from the outermost white dwarfcore layer is dredged up into the accreted mat-ter (red region in Figure 1b), as first sug-gested by Ferland & Shields (1978). This sig-nificantly enriches the burning layer in CNOnuclei, which is crucial for ensuring a strongnuclear energy release and a violent outburst;it also helps to explain the observed abun-dances inferred from the ejecta. The ejectedmaterial (blue region in Figure 1c) consists ofa mixture of white dwarf and accreted matterthat has been processed by explosive hydro-

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gen burning.

Spectroscopic studies identified two dis-tinct types of classical novae. Nova ejecta richin CNO material point to an underlying COwhite dwarf, which represents the evolution-ary fate of a low-mass star after the cessationof core helium burning (Section 3.3.1). Theseobjects are called “CO novae”. On the otherhand, elemental enrichments in the range ofNe to Ar have been attributed to the pres-ence of an underlying, massive ONe whitedwarf, representing the evolutionary fate ofan intermediate-mass star after completion ofcore carbon burning. The latter explosions,often referred to as “neon novae” or “ONenovae”, tend to be more energetic than COnovae (Starrfield, Sparks, & Truran 1986).

About 20-100 days after the outburst,many classical nova light curves show a rapiddecline in the optical flux because of ex-tinction, and a corresponding rise in themid-infrared luminosity because of thermalemission (Shore 2012; Evans & Gehrz 2012).This observation strongly suggests that dustgrains, with radii up to ≈ 10 µm (Stratton& Manning 1939; Gehrz et al. 1998; Gehrz2008), form in the ejecta when they cool totemperatures below ≈ 1700 K. Overall, about30-40% of novae produce dust, including bothCO and ONe novae (Evans & Gehrz 2012). Anumber of CO novae are known to have beenprolific dust producers (see Table 1). Whendust forms, its observed mass fraction in novaejecta is about 10−3, corresponding to a massbetween 10−10 M� and 10−6 M�.

Unlike most other sources, classical novaehave been observed to produce carbon-richand oxygen-rich dust simultaneously (Gehrz1992). In principle, the composition of thedust that forms in a given environment de-pends sensitively on the carbon-to-oxygen ra-tio. When the number abundance ratio ofC/O exceeds unity, and all oxygen atoms arelocked up in strongly bound CO molecules,carbon-rich dust forms; similarly, oxygen-richdust forms when the value of C/O is less than

WDcore

nuclearashes

WDcore

convec/veenvelope

nuclearburning

accretedma7erfromcompanion

WDcore

nuclearashes

ejecta

(a) (b) (c)

Fig. 1.— Sketch of processes during a classi-cal nova outburst. (a) Nuclear ashes from aprevious outburst (He plus metals; light greyregion) sit on top of a CO-rich white dwarfcore (dark grey region), consisting mainlyof 12C and 16O; the white dwarf accreteshydrogen-rich matter (green region) from acompanion. (b) The temperature increases atthe base of the envelope until a thermonuclearrunaway (TNR) occurs; during the TNR,mixing and diffusion takes place at the inter-face of accreted and white dwarf outer corematter (red region); the convective envelope(orange region) extends to the surface. (c) Afraction of the nuclearly processed accreted-plus-core matter is ejected (blue region) anda fraction remains on the white dwarf (lightgrey region) to take part in the next event.

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unity (Waters 2004). This assumes that theCO abundance reaches its saturation value.However, if CO does not form to saturation,neither carbon nor oxygen will be entirelybound in CO molecules, leaving both ele-ments available for dust condensation (Evans& Rawlings 2008). In addition, Jose et al.(2004) found that the presence of significantamounts of intermediate-mass elements, suchas Al, Ca, Mg, or Si, may dramatically alterthe condensation process, allowing for the for-mation of carbon-rich dust even in an oxygen-rich environment. Table 1 summarizes themeasured carbon and oxygen abundances (bymass) in CO nova shells, together with theobservation of dust species.

A classical nova is not an ideal environmentfor dust condensation. Diatomic and poly-atomic molecules can only form in the ejectaif they are shielded from ionization by the co-pious UV radiation of the white dwarf, whichremains a supersoft X-ray source after theoutburst (Schwarz et al. 2011). The shieldingcan be provided only by spatially inhomoge-neous regions of the ejecta that have a muchhigher than average gas density. Clumpyejecta have been inferred spectroscopically formany classical novae (Williams 1992; Saizar &Ferland 1994), but the physical origin remainsan open question.

The above discussion implies that measur-ing the isotopic signatures of presolar stardustgrains originating from classical novae couldshed light on the explosion mechanism, themixing of matter during the outburst, andthe formation of molecules and dust in theexpanding ejecta. While several authors haveclaimed a nova paternity for certain stardustgrains, no grains from novae have been unam-biguously identified yet. Therefore, they arereferred to in the literature as “nova candi-date” or “putative nova” grains.

A significant problem is that most classicalnova simulations result in ejecta with muchmore anomalous isotopic ratios compared towhat has been measured in the grains (Nittler

& Hoppe 2005; Gyngard et al. 2010; Leitneret al. 2012; Nguyen & Messenger 2014). Toexplain the measurements, it has been specu-lated (Amari et al. 2001) that these grainsmay have condensed after the nova ejectamixed with a much larger amount (& 90%)of close-to-solar matter. However, the originof the latter contribution is not well under-stood. In addition, counter-arguments favora supernova origin for some of these “novacandidate” grains (Nittler & Hoppe 2005; Liuet al. 2016). Recently, the “first plausiblegrain of CO nova origin” has been reported,based on the measured C, N, Si, and S isotopiccompositions, without requiring any mixingwith solar-like matter (Haenecour et al. 2016).This would imply that dust from classical no-vae contributed to the building blocks of thesolar system. A severe problem with this in-terpretation is the mismatch of the simulatedand measured 16O/17O and 16O/18O ratios inthat particular stardust grain, with the devi-ations amounting to several orders of magni-tude.

Although the total amount of matterejected by classical novae per year in ourgalaxy is much smaller when compared tothe contributions of AGB stars or type II su-pernovae, it is puzzling that among severalthousand presolar stardust grains identifiedso far, we cannot claim with confidence aclassical nova paternity for a single grain. Amajor problem is that hydrodynamic novasimulations have a poorly constrained pa-rameter space, and that these CPU-intensivesimulations sample a restricted number ofparameter combinations before the computedisotopic ratios are compared with stardustgrain measurements. Here, we follow a differ-ent approach that explores a large region ofthe nova parameter space. Since we need toperform a large number of simulations, ourmethod does not depend on specific classi-cal nova hydrodynamic modeling, but is bynecessity model independent.

We will focus on CO novae and leave an

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investigation of ONe novae to future work. InSection 2, we present our strategy. Section 3discusses our simulation procedure, togetherwith the various parameters entering the cal-culations. Results are presented in Section 4.A summary and conclusions are given in Sec-tion 5.

2. Strategy

The two questions we attempt to answerare: (1) Does a given presolar stardust grainoriginate from a classical nova? (2) Whatare the conditions that gave rise to the mea-sured isotopic ratios? These questions are in-tricately connected. If we cannot identify anyviable nova conditions that could give rise tothe data, we may not claim that a given star-dust grain has a nova paternity. These ques-tions have been partially addressed using one-dimensional hydrodynamic nova simulations(Jose et al. 2004). As with any stellar model,such simulations depend on many assump-tions and parameters. Some model param-eters are constrained by observation or ex-periment (e.g., thermonuclear reaction ratesand the nuclear energy release), while onlyindirect information is available for other pa-rameters (e.g., the rate of mass accretionfrom the companion, the initial compositionof the fuel, initial luminosity and mass ofthe white dwarf, the amount of white dwarfmatter dredged up into the accreted enve-lope, and the effects of multicycle nova evolu-tion). Some effects have remained nearly un-explored, e.g., the impact of a magnetic fieldor rotation on the nova outburst. The sim-ulation of dust formation introduces a hostof additional assumptions, e.g., the shield-ing of molecules from the radiation of thewhite dwarf, the formation of clumpy ejecta,mixing of the ejecta with matter of the in-terstellar medium or the accretion disk, andgrain nucleation and growth to macroscopicsize. The main disadvantage of studying thenova paternity of stardust grains with a hy-

drodynamic computer code is that only a rel-atively small number of simulations can beperformed. Since the nova parameter spaceis only sparsely explored, parameter valuecombinations favorable for reproducing iso-topic signatures of nova grains may easily bemissed.

We seek a more comprehensive explorationof the nova parameter space. To this end,our strategy involves three key ingredients:(i) a simple and fast simulation that can berepeated many times using different combi-nations of parameter values; (ii) the assump-tion of a reasonable parameter range and theindependent sampling of all parameters; and(iii) the comparison of simulated and observedisotopic ratios for all elements measured in agiven stardust grain. The latter point is im-portant: the grains condensed at a given timeand location in the expanding ejecta1. Unlesswe can explain all the measured isotopic sig-natures simultaneously, we may not claim anova paternity.

In the following, we will discuss each ofthese ingredients. We start with a descriptionof a schematic model, then add realistic as-sumptions pertaining to nova outbursts, andfinally discuss how to compare our simulationresults to stardust grain data.

3. Procedures

3.1. Nuclear reaction network andthermonuclear rates

We compute the nucleosynthesis using areaction network consisting of 213 nuclides,ranging from p, n, 4He, to 55Cr. These nu-

1We assume in the present work that the presolar graincomposition is not significantly altered by ion implan-tation. While implantation may be important for con-centrations of either noble gases (Verchovsky, Wright& Pillinger 2003) or trace elements (Clayton et al.2002), it is highly unlikely that this process will altersignificantly the major-element (e.g., carbon, oxygen,or silicon) isotopic composition of the grains studiedhere.

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clides are linked by 2373 nuclear interactions(proton and α-particle captures, β-decays,light-particle reactions, etc.). Thermonuclearreaction rates are adopted from STARLIBv6.5 (09/2017)2. This library has a tabularformat and contains reaction rates and rateprobability density functions on a grid of tem-peratures between 10 MK and 10 GK (Sal-laska et al. 2013). The probability densitiescan be used to derive statistically meaning-ful reaction rate uncertainties at any desiredtemperature. Many of the reaction rates im-portant for the present work that are listed inSTARLIB have been computed using a MonteCarlo method, which randomly samples allexperimental nuclear physics input parame-ters (Longland et al. 2010). Most of the re-action rates important for studying hydrogenburning in CO novae are based on experi-mental nuclear physics information and pro-vide a reliable foundation for robust predic-tions. For some reactions of interest to classi-cal novae (Iliadis 2015), however, experimen-tal rates are not available yet, and the ratesincluded in STARLIB are adopted from nu-clear statistical model calculations using thecode TALYS (Goriely et al. 2008). In suchcases, a reaction rate uncertainty factor of 10is assumed.

Stellar weak interaction rates, which de-pend on both temperature and density, forall species in our network are adopted fromOda et al. (1994) and, if not listed there, fromFuller, Fowler & Newman (1982). The stellarweak decay constants are tabulated at tem-peratures from T = 10 MK to 30 GK, anddensities of ρYe = 10 − 1011 g/cm3, whereYe denotes the electron mole fraction. Forall stellar weak interaction rates, we assumeda factor of two uncertainty. Short-lived nu-clides, e.g., 13N (T1/2 = 10 min), 14O (T1/2

= 71 s), 15O (T1/2 = 122 s), 17F (T1/2 = 64 s),and 18F (T1/2 = 110 min), present at the end

2The STARLIB site has moved to:https://starlib.github.io/Rate-Library/.

of a network calculation were assumed to de-cay to their stable daughter nuclides.

To explore the effects of thermonuclear re-action rate uncertainties, we perform someof our calculations by randomly sampling allrates simultaneously using the rate proba-bility densities provided by STARLIB. Thismethod is discussed in detail in Iliadis et al.(2015) and was recently applied to explainabundance anomalies in globular clusters (Il-iadis et al. 2016). It suffices to mention herethat we adopt a lognormal distribution for thenuclear rates, given by

f(x) =1

σ√

2π

1

xe−(ln x−µ)2/(2σ2) (1)

where the lognormal parameters µ and σ de-termine the location and the width, respec-tively, of the distribution. For a lognormalprobability density, samples, i, of a nuclearrate, y, are computed from

yi = ymed(f.u.)pi (2)

where ymed and f.u. are the median value andthe factor uncertainty, respectively, which areboth provided by STARLIB. The quantity piis a random variable that is normally dis-tributed, i.e., according to a Gaussian dis-tribution with an expectation value of zeroand a standard deviation of unity. We em-phasize that the factor uncertainty of exper-imental Monte Carlo reaction rates dependsexplicitly on stellar temperature (Iliadis et al.2010; Longland 2012).

3.2. A schematic model of explosivehydrogen burning

We adopt a simple, one-zone analytical pa-rameterization for the thermodynamic trajec-tories of the explosion,

T (t) = Tpeake−t/τT , ρ(t) = ρpeake

−t/τρ (3)

where t ≥ 0 is the time since peak tempera-ture, Tpeak, or peak density, ρpeak; τT and τρ

6

are the times at which temperature and den-sity, respectively, have fallen to 1/e of theirpeak values. Notice that we do not assumean adiabatic expansion since we treat τT andτρ as independent parameters. This is consis-tent with the results of one-dimensional hy-drodynamic nova simulations, which predictnon-adiabatic T − ρ evolutions.

It is necessary to demonstrate that our sim-ple simulation has some predictive power asregards to nova nucleosynthesis. In a firststep, we generated a hydrodynamic CO novamodel using the one-dimensional code SHIVA(Jose & Hernanz 1998), assuming a whitedwarf mass and initial luminosity of MWD =1.0 M� and LWD = 10−2 L�, respectively,and accretion of solar-like material at a rateof Macc = 2 × 10−10 M� yr−1. The com-position of the nuclear fuel was obtained bypre-mixing equal amounts of solar-like matterwith carbon-oxygen white dwarf matter (as-sumed to be 50% 12C and 50% 16O, by mass).The model included 45 envelope zones con-taining all material involved in the thermonu-clear runaway. The deepest zone achieved apeak temperature of 179 MK, while the in-nermost ejected zone reached a peak tem-perature of 163 MK. Final isotopic abun-dances for matter that exceeds escape veloc-ity (i.e., the fraction of the envelope ejected)are determined 1 hr after peak temperature isachieved, and the abundance of each nuclideis mass-averaged over all ejected zones.

In a second step, we adjusted the parame-ters of our simple one-zone simulation by trialand error to see if we can approximately re-produce the final isotopic ratios of the multi-zone hydrodynamic model, assuming exactlythe same initial abundances in both calcula-tions. The resulting isotopic ratios for themost important elements (C, N, O, Si, and S)are shown in Figure 2. The solid lines corre-spond to the time evolutions predicted by thesimple one-zone simulation and were obtainedwith the following parameter values: Tpeak =177 MK, ρpeak = 200 g/cm3, τT = 2500 s,

τρ = 38 s. The total time was 10,000 s, butthe results are not sensitive to this parame-ter once peak temperature and density havesignificantly declined from their peak values.The dotted line in each panel indicates themass-zone-averaged ejected final abundanceratios predicted by the multi-zone hydrody-namic calculation. The interesting finding isthat the one-zone simulation reproduces theresults of the multi-zone hydrodynamic calcu-lation within a factor of 2. We repeated thetest for other CO white dwarf masses, andeven for models of ONe novae, and again ob-tained agreement within a factor of 2.

This level of agreement may be at first sur-prising, considering that our simulation, un-like the hydrodynamic model, follows a sin-gle zone only, and disregards accretion, con-vection, and ejection of matter. However, re-call that we are mainly interested in isotopicratios instead of absolute isotopic or elemen-tal abundances, which are very likely moresensitive to such effects. We emphasize thatthe parameters (Tpeak, ρpeak, τT , τρ) derivedfrom the simple simulation correspond neitherto the averages over different mass zones, norto a given zone, of the hydrodynamic sim-ulation. They nevertheless provide, albeitcrude, approximations of the physical condi-tions during the nuclear burning, mainly be-cause thermonuclear reaction rates are highlysensitive to the plasma temperature.

It is also interesting to note that the valueρpeak = 200 g/cm3 of the exponentially decay-ing density profile in Figure 2 does not cor-respond to any maximum density in the one-dimensional hydrodynamic simulation, but isapproximately equal to the density at maxi-mum temperature in the innermost zones ofthe hydrodynamic calculation. In the lattersimulation, the density declines from a maxi-mum value, which typically amounts to a fewthousand grams per cubic centimeter and isachieved well before the temperature peaks,to a very small value.

A factor of two agreement is sufficient for

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12C/13C

100 101 102 103 1040.01

0.1

1

10

14N/15N

100 101 102 103 1041

10

100

1000

16O/17O

100 101 102 103 104

10

100

1000

16O/18O

100 101 102 103 104104

105

106

107

108

28Si/29Si

100 101 102 103 104

10

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28Si/30Si

100 101 102 103 104

10

100

32S/33S

100 101 102 103 10450

100

200

32S/34S

100 101 102 103 10410

20

50

Time(s)

Massfrac.on

ra.o

Fig. 2.— Time evolution of C, N, O, Si, and S isotopic ratios as predicted by a parametric, one-zonesimulation (solid lines), assuming exponentially decaying temperature and density trajectories. Thesimulation parameters were Tpeak = 177 MK, ρpeak = 200 g/cm3, τT = 2500 s, τρ = 38 s. Initialabundances were obtained by pre-mixing solar-like matter with carbon-oxygen white dwarf matter(assumed to be 50% 12C and 50% 16O, by mass) in equal amounts. The dotted lines show the final,mass-zone-averaged results of a one-dimensional hydrodynamic simulation using the same initialcomposition, where the deepest zone reached a peak temperature of 179 MK during the outburst.

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the purposes of the present work, as will beshown below. The advantage of our simpleprocedure is that we can independently sam-ple over the parameters and repeat the simu-lation many times. If a given stardust grainhas indeed a nova paternity, we would expectthat certain combinations of parameter values(Tpeak, ρpeak, τT , τρ) approximately repro-duce the measured isotopic ratios, with mag-nitudes near the ranges typical for classicalnovae.

Before we can discuss the presolar stardustgrain data, however, we need to introducethree more parameters that will be importantfor our study: the 12C/16O ratio of the outerwhite dwarf core, the mixing of matter at theinterface of the white dwarf and the envelope,and the dilution of the ejecta by mixing withsolar-like matter.

3.3. Key parameters for nova nucle-osynthesis

3.3.1. The white dwarf composition

Stars with masses between ≈ 0.8 − 8 M�undergo hydrogen and helium burning in theircores and end their lives as white dwarfs(Karakas & Lattanzio 2014), composed of car-bon and oxygen (CO white dwarfs). Thecomposition of the white dwarf depends sensi-tively on the 12C(α,γ)16O reaction rate. MostCO nova studies assume a white dwarf corecomposition of 50% 12C and 50% 16O, bymass. A rare exception is the work of Kovetz& Prialnik (1997), who performed nova sim-ulations for core compositions of pure 12C,pure 16O, and an equal mixture of 12C and16O. However, what is most relevant for novasimulations is the composition of the outer-most core of the white dwarf, since only thislayer is expected to be dredged up duringthe outburst. Recently, Jose et al. (2016)evolved an 8 M� progenitor star throughsuccessive hydrogen burning, helium burn-ing, and thermally pulsing asymptotic gi-ant branch phases, and used the resulting

outer core composition at several locations ofthe nascent white dwarf as starting points ofthe CO nova simulations. This resulted incarbon-rich ejecta and the possibility of theformation of carbon-rich dust.

One problem with this assumption is thatthe white dwarf needs some time to cool be-fore a nova outburst can take place; if thewhite dwarf is initially too luminous, the en-velope is not highly degenerate and only amild thermonuclear runaway with no massejection will occur. For this reason, almost allnova simulations have been performed withan initial white dwarf luminosity in the rangeof LWD = 10−3 − 10−2 L�. A few studiesassumed higher luminosities, see Starrfield,Sparks, & Truran (1985); Yaron et al. (2005);Hernanz & Jose (2008). The important pointis that the composition of the outer corechanges while the white dwarf evolves on itscooling track. This question was studied byBravo et al. (2011) in connection with mod-els for thermonuclear supernovae. The outercore composition of their 1 M� model whitedwarf changed from a 12C/16O mass fractionratio of 1.8 at the beginning of the coolingtrack, to 7.2 at the end of core crystallization(see their Figure 1). These compositions arevastly different than the mass fraction ratioof 12C/16O = 1 that is commonly assumed instudies of CO novae.

We do not know the actual 12C/16O massfraction ratio in the outer white dwarf corethat gave rise to the isotopic signatures ina given nova presolar grain. Therefore, wewill randomly sample this parameter over therange predicted by white dwarf models (1.5≤ 12C/16O ≤ 8.0) to see which values, if any,reproduce the stardust grain data.

Another problem with assuming an outercore composition of equal 12C and 16O abun-dances is that classical novae are expected torecur on time scales of ≈ 104 − 105 yr. Eachnova outburst leaves behind a remnant layercomposed of helium and other nuclear burn-ing products, and of unburned hydrogen, on

9

top of the outer white dwarf core (light greyarea in Figure 1a and c). Since this layer takespart in the burning during the next flash (Fu-jimoto & Iben 1992; Prialnik & Livio 1995), itimpacts the composition of the nuclear fuel.

3.3.2. Mixing between white dwarf and ac-creted matter during the flash

Spectroscopic observations show that CNOelements are considerably enriched relative tohydrogen in many nova ejecta (Gehrz et al.1998). This enrichment plays a critical rolefor the dynamic ejection of a portion of theenvelope and presumably results from mixingof the outer core white dwarf matter with theaccreted matter (red region in Figure 1b). Re-cent two- and three-dimensional simulationsnow yield encouraging results by demonstrat-ing that Kelvin-Helmholtz instabilities dur-ing the thermonuclear runaway can lead toan enrichment of the accreted envelope withmaterial from the underlying white dwarf atlevels that approximately agree with observa-tions (Glasner & Livne 1995; Glasner, Livne& Truran 2012; Casanova et al. 2011, 2016).

So far, multi-dimensional nova simulationsincorporate very small nuclear reaction net-works (≈ 30 nuclides only), and are not suit-able for studying the nucleosynthesis in de-tail. Consequently, one-dimensional simula-tions are indispensible for this purpose, butcannot account self-consistently for the mix-ing at the interface between the outer whitedwarf core and the accreted matter. Mostone-dimensional simulations work around thisproblem by artificially enriching the envelopewith outer core matter to a predetermined de-gree. The enriched matter is then accretedand its history is followed through the nuclearburning and mass ejection stages.

Frequently, one-dimensional nova simula-tions assume that the accreted matter fromthe companion and the white dwarf core ma-terial pre-mix with equal mass fractions. Re-cent work, albeit in the context of ONe no-

vae, hinted at a pre-mixing fraction of 25%white dwarf matter and 75% accreted mat-ter (Kelly et al. 2013), which provides a sig-nificantly better fit to the measured elemen-tal abundances in several, but not all, novaejecta.

While these are encouraging first steps, weare far from being able to predict the degreeof element mixing in a given observed nova.In particular, the pre-mixing parameter, fpre,is poorly constrained at present. We define itby mixing one part of outer white dwarf corematter with fpre parts of accreted solar-likematter,

Xpre ≡XWD + fpreXacc

1 + fpre(4)

where Xi denotes mass fraction. We will ran-domly sample this parameter over a reason-able range (0.5 ≤ fpre ≤ 5.0) to see whichvalues best reproduce the stardust grain data.The outer bounds of this interval correspondto white dwarf admixtures of 67% and 17%,respectively.

3.3.3. Dilution of the ejecta

We already mentioned that previous clas-sical nova simulations result in much moreanomalous isotopic ratios compared to thevalues measured in nova candidate grains. Toexplain the observations, an additional mix-ing episode, after the outburst, has been pos-tulated (which we will term “post-mixing”),whereby the ejecta processed by nuclear burn-ing mix with more than ten times the amountof unprocessed, solar-like matter before graincondensation (Amari et al. 2001). However,the source and mechanism of this potentialdilution is not understood.

The grains we are considering here con-densed at temperatures well over 1000 K and,therefore, it is difficult to explain the forma-tion of SiC or olivine grains by mixing of novaejecta with the interstellar medium.

One idea was pursued by Figueira et al.

10

(2017), who studied the collision of the novaejecta initially with the accretion disk andsubsequently with the companion. Theyfound that the matter escaping from the bi-nary system is predominantly composed ofthe ejecta, i.e., the contribution of the accre-tion desk or the companion is small. Underthese conditions, we expect on average onlyminor post-mixing, although enhanced dilu-tion may perhaps occur in local regions. Ifgrains can condense in this environment, wenevertheless expect that only a small frac-tion will show signatures of significant post-mixing.

More studies of this important issue areneeded, since we neither know the source ofthe solar-like matter for post-mixing, nor ifany post-mixing took place at all. At thistime, we conclude the following. If we con-sider two measured stardust grains, and forone grain all data agree with CO nova simu-lations without the need for any post-mixing,while the other grain requires dilution tomatch data to the CO nova simulations, thenthe former grain is more likely to originatefrom a CO nova. We will return to this argu-ment in Section 4.2.

Since the post-mixing process is poorlyconstrained, our simulations will account forit using a post-mixing parameter, fpost, de-fined by

Xpost ≡Xproc + fpostXpris

1 + fpost(5)

where Xproc and Xpris denote the mass frac-tions from the reaction network output (i.e.,processed matter) and the pristine matter(i.e., solar-like), respectively. We will sam-ple this parameter over a range of 0 ≤ fpost≤ 104 to see which values best reproduce thestardust grain data.

3.4. Comparison of simulations topresolar stardust grain data

Isotopic data for all presolar stardustgrains that have been suggested over the

years to originate from novae are compiledin Table 2. The data are separated accordingto grain chemistry (SiC, silicate, graphite,and oxide). As already noted above, wehave no unambiguous evidence linking any ofthese grains to a nova paternity. Neither canwe exclude unambiguously a nova paternityfor many other grains among the thousandsof stardust samples measured so far. Ourgoal is to investigate the conditions, if any,that could give rise to the measured isotopicanomalies.

The values listed for C, N, and O representisotopic number abundance ratios, while forMg, Si, and S the data correspond to parts-per-thousand deviations from solar matter,e.g.,

δ(25Mg/24Mg

)≡ δ25Mg

≡

[(25Mg/24Mg

)exp

(25Mg/24Mg)�− 1

]× 1000

(6)

where the most abundant isotope of the ele-ment (i.e., of even mass number) appears inthe denominator.

We chose to exclude consideration ofδ26Mg values and inferred 26Al/27Al ratios.First, for grains with significant amounts ofboth Mg and Al, some of the observed 26Mgmay have condensed originally as 26Al. Insuch cases, we cannot simply add the simu-lated 26Mg and 26Al abundances and comparethe total to the measured δ26Mg values be-cause the Al and Mg may have condensedin a particular grain with different efficien-cies. Although, in principle, this can be takeninto account if the Al/Mg ratio of a grain isknown, e.g., for MgAl2O4 grains (Zinner atal. 2005), this ratio has not been reportedfor many of the grains. Second, even forgrains like SiC with high Al/Mg ratios andhence purely radiogenic 26Mg, Al contamina-tion has been shown to have impacted nearlyall reported isotopic measurements (Zinner &Jadhav 2013; Groopman et al. 2015), leadingto an underestimate of the original 26Al/27Al

11

ratios by up to a factor of two. The magni-tude of such contamination can be estimatedfor a given grain through detailed analysis ofthe original measurement data (Groopman etal. 2015), but this information has not beenreported for the nova candidate grains of thisstudy.

When comparing grain measurements toresults from nucleosynthesis simulations, twoimportant issues need to be addressed. First,we cannot reasonably expect that a sim-ulation will precisely reproduce the grainmeasurements, since there are too many ap-proximations involved in any nucleosynthesismodel. If the simulation results are “close”to the data, say, within some factor, we mayaccept the computed results as a possible so-lution. Second, we need to account for thesystematic bias in the grain measurements,in addition to the statistical uncertainty thatis included in the reported error. Systematiceffects arise from contamination, e.g., fromsampling the meteorite material surroundingthe grain, or from sample preparation. It isimportant to emphasize that this bias couldmove a data point into the direction of lessanomalous values only, i.e., contaminationwill not make a grain appear more anoma-lous than it really is.

We will adopt the following procedure fordetermining approximate agreement betweensimulation and measurement (“acceptable so-lutions”). The simulated mass fraction of anuclide with atomic number Z and mass num-ber A, denoted by Xsim(AZ), is divided andmultiplied by a systematic uncertainty factor,nsim, according to

Xsim(AZ)/nsim ≤ Xsim(AZ)

≤ Xsim(AZ)× nsim(7)

This range is then transformed into a rangeof simulated δ-values, δAZsim,

[δAZlowsim, δAZhighsim ] (8)

Next, using an experimental uncertainty fac-tor, nexp, we define a range for a measured

value of δAZmeanexp ± δAZerrexp,

[n(1−π)/2exp × δAZmeanexp − nexp × δAZerrexp,

n(1+π)/2exp × δAZmeanexp + nexp × δAZerrexp](9)

where π = sign(δAZmeanexp ) = ±1 denotes thesign of the experimental mean value. We de-fine an acceptable solution if the two regionsgiven by Equations 8 and 9 overlap. For thetwo factors containing the effects of the sim-ulation and measurement bias, we adopt val-ues of nsim = 1.7 and nexp = 2. The for-mer value implies an uncertainty factor fora simulated abundance ratio of 1.72 ≈ 3. Itwas chosen to exceed the factor of 2 withinwhich our one-zone simulations reproduce theresults of the multi-zone hydrodynamic calcu-lation (Section 3.2). As already pointed outin Section 2, we will only accept solutions forwhich simulated and measured δ-values over-lap for all measured isotopic ratios.

To gain a better understanding of this pro-cedure, consider the following numerical ex-ample. Suppose a value of δ13Cmeanexp ±δ13Cerrexp

= 12734 ± 167 has been measured for a hy-pothetical grain. Accounting both for sta-tistical and systematic effects, we translatethis experimental result into an experimen-tal interval of [12400, 25802], according toEquation 9. Furthermore, suppose that oneamong many reaction network runs resultsin final mass fractions of Xsim(12C) = 0.203and Xsim(13C) = 0.0193. According to Equa-tion 7, these values are translated to ranges of0.1194 ≤ Xsim(12C) ≤ 0.3451 and 0.011353≤ Xsim(13C) ≤ 0.03281. The interval forthe corresponding Xsim(13C)/Xsim(12C) ra-tios is then given by [0.03289, 0.2748], result-ing in a range of simulated δ13Csim values of[1701, 21568]. In this case, the experimentaland simulation ranges overlap. Only if thesame applies to all other isotopic ratios mea-sured for this particular grain do we retain thesolutions (i.e., the model parameters, such aspeak temperatures and densities, mixing pa-rameters, etc.) of this particular reaction net-

12

work calculation.

4. Results

We will first show what results can be ob-tained with our method by using grain LAP-149 as an example. We then summarize re-sults for all nova candidate grains. Finally wediscuss those grains that most likely originatefrom CO novae.

4.1. Example: grain LAP-149

The nova candidate graphite grain LAP-149 has a diameter of about 1 µm and ex-hibits one of the lowest 12C/13C ratios evermeasured (Table 2). The 14N/15N ratio ishigh, but the oxygen, silicon, and sulfur iso-topic ratios are close to solar within experi-mental uncertainties. Haenecour et al. (2016)found that the C, N, Si, and S isotopic ratioscould be reproduced by a CO nova model in-volving a 0.6 M� white dwarf with 50% pre-mixing (fpre = 1; Equation 4) without assum-ing any post-mixing. However, the measuredand simulated 17O/16O and 18O/16O ratiosdisagreed by orders of magnitude. The otherCO nova models, for white dwarf masses inthe range of MWD = 0.8 − 1.15 M�, did notprovide a match to any of the measured iso-topic ratios. Notice that LAP-149 is the onlynova candidate grain with eight measured iso-topic ratios (see Table 2).

Our results for LAP-149 are shown in Fig-ure 3, which was obtained after computing25,000 network samples. The top row dis-plays the measured isotopic ratios (red) to-gether with the simulations. Only those sim-ulation results are displayed that simultane-ously agree with all data, according to Equa-tions 8 and 9. The different colors for the sim-ulation results correspond to different peaktemperature values (blue: Tpeak < 0.20 GK,green: Tpeak ≥ 0.20 GK). The correspondingsampled model parameters are shown in thebottom row.

We obtain acceptable solutions for a wide

range of pre-mixing fractions, between fpre= 1 and fpre = 5 (first bottom panel), cor-responding to outer white dwarf core admix-tures between 50% and 16%, respectively.Post-mixing fractions are in the range offpost = 30 − 100, implying a significantadmixture of solar-like matter after the ex-plosion. In particular, no acceptable solu-tions are obtained without post-mixing, inagreement with the findings of Haenecouret al. (2016). Acceptable peak tempera-ture and peak density values (second bottompanel) scatter throughout the sampled ranges(150 MK ≤ Tpeak ≤ 250 MK, 5 g/cm3 ≤ρpeak ≤ 5 × 103 g/cm3). The 1/e exponen-tial decay times for temperature and density(third bottom panel) scatter within the rangeof 103 s ≤ τT ≤ 104 s and 102 s ≤ τρ ≤ 104 s,respectively. Solutions are obtained for theentire range of sampled outer white dwarfcore composition, 0.6 ≤ XWD(12C) ≤ 0.9, 0.1≤ XWD(16O) ≤ 0.4 (fourth bottom panel).Lastly, the ratios of elemental carbon to oxy-gen, after post-mixing, are in the range ofX(C)/X(O) = 0.6 − 1.0 (fifth bottom panel).

So far, we used in the simulations for allrates of thermonuclear reactions and weakinteractions the recommended (i.e., median)values provided by STARLIB. However, thenuclear rates have uncertainties, either de-rived from experimental nuclear physics in-put or from theoretical models (Section 3.1).For this reason, we repeated the above MonteCarlo procedure of computing 25,000 net-work samples, but this time included the ran-dom sampling of the nuclear rates accord-ing to their probability densities contained inSTARLIB (Section 3). As a result, the scatterof the simulation points (black, blue, green)in Figure 3 increased slightly, but all relevantfeatures discussed above are preserved. Inother words, current reaction rate uncertain-ties have only a small impact on our resultsfor this particular grain.

The above results do not prove a CO novaorigin for LAP-149, because we are not con-

13

0 0.20.40.60.8

−1

−0.5

0

δ13C

δ15N

x105

x103

●

1 2 3 4 5 6

10−410−2100102104

Pre −mixing

Post−

mixi

ng

−2 0 2 4 6−3

−2

−1

0

1

2

δ17O

δ18O

x102

x102

●

0.1 0.2

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

−2−1 0 1 2 3−1.5−1

−0.50

0.51

δ26Mg

δ25M

g

x100

x102

102 103 104 105101102103104105

τT (s)

τ ρ (s

)

−2 −1 0 1−1.5−1

−0.50

0.51

δ30Si

δ29Si

x102

x102

●

0.60.70.80.9

0.1

0.2

0.3

0.4

XWD(12C)

X WD(

16O

)

−2 0 2 4

−5

0

5

δ34S

δ33S

x102

x102

●

10−3 10−2 10−110−3

10−2

10−1

X(C)

X(O)

Fig. 3.— Summary results for the presolar stardust graphite grain LAP-149, the only nova candi-date grain with eight different measured isotopic ratios. (Top row) Isotopic ratios for C, N, O, Mg,Si, and S. The data points are shown in red; simulations that reproduce all data simultaneously (seeEquations 8 and 9) are displayed in blue and green, depending on the sampled peak temperature(see below). (Bottom row) From left to right: post-mixing fraction versus pre-mixing; peak densityversus peak temperature; 1/e exponential decay times for the density evolution versus temperatureevolution; outer white dwarf mass fractions of 16O versus 12C; and elemental oxygen versus carbonmass fractions after post-mixing. The blue and green simulation results correspond to peak tem-peratures of Tpeak < 0.20 GK and Tpeak ≥ 0.20 GK, respectively. The simulation results shownwere obtained with recommended nuclear interaction rates only, i.e., without Monte Carlo samplingof the nuclear rates.

14

sidering here the production in sites otherthan novae (e.g., supernovae or AGB stars).But we can conclude that this grain couldonly have been produced by the tempera-ture and density conditions, and composi-tions, typical of CO novae if the ejecta mixedwith a large fraction of solar-like matter, i.e.,1 part of ejecta with at least 30 parts of solar-like matter.

We carefully repeated the random sam-pling using different random number seedsand total numbers of simulations. All resultsshown in this work, including Figure 3, are ro-bust, in the sense that they are reproducibleapart from small statistical fluctuations.

4.2. Results for all nova candidategrains

Similar to grain LAP-149 discussed in theprevious section, we investigated for each ofthe 39 grains listed in Table 2 if our simu-lations can reproduce the measured isotopicratios according to Equations 8 and 9. Threepoints need to be considered for the followingdiscussion.

First, the number of measured isotopic ra-tios will strongly impact the likelihood that agiven grain originates from a CO nova. Inother words, if simulations reproduce to asimilar degree the data for grains A and B,and only two isotopic ratios have been mea-sured in grain A compared to six ratios ingrain B, then the latter grain is more likelyto be of CO nova paternity. Clearly, the moreisotopic ratios measured, the tighter the con-straints on the grain origin.

Second, the relative number of networkruns (“acceptable solutions”) that provide si-multaneous solutions for all measured isotopicratios of a given grain is also important inthis regard. We cannot claim that the ab-solute number of acceptable solutions reflectsthe probability of a CO nova paternity. Butwe can conclude that a low number of solu-tions indicates a fine-tuning of model param-

eters, while a high number of solutions resultsfrom model parameter combinations that oc-cupy a larger volume of the parameter space.In other words, the relative number of accept-able solutions reflects the likelihood of a COnova paternity.

Third, we discussed in Section 3.3.3 thatthe origin and mechanism for a possible dilu-tion of the ejecta by solar-like matter (“post-mixing”) is not well understood, and that it islikely that a fraction of CO nova grains con-dense in the ejecta with little, if any, post-mixing. For this reason, we assume that agiven grain has a higher chance of a CO novapaternity if its measured isotopic ratios canbe simulated without any post-mixing.

If we allow for post-mixing of various de-grees, we find acceptable solutions for almostall grains listed in Table 2. The only excep-tions are grains 8-9-3 and KFC1a-551. Forthese, not a single acceptable solution is ob-tained, and thus a CO nova paternity is highlyunlikely. Also, it would be a fortuitous coinci-dence if all the other 37 stardust grains listedin Table 2 would be of CO nova origin. There-fore, we conclude that only a weak case canbe made for a CO nova paternity if signifi-cant post-mixing must be invoked to matchobserved and simulated isotopic ratios.

Table 3 lists all grains for which we foundacceptable solutions without assuming anypost-mixing. For each grain we show the min-eralogy, the number of measured isotopic ra-tios, and the measured elements. The lastcolumn shows the total number of networkruns that provide simultaneous solutions forall measured isotopic ratios of a given grainaccording to Equations 8 and 9. The grainsare rank ordered, from top to bottom, accord-ing to the plausibility of a CO nova paternity.As discussed above, we ranked the grains ac-cording to the number of measured isotopicratios (column 3) and the number of accept-able simulations (column 5).

We find that six grains, all of them of the

15

SiC variety, have a high plausibility of a COnova origin (from G270-2 to Ag2 6 in Ta-ble 3). These grains will be discussed in moredetail in Section 4.3. In this case, we obtainacceptable solutions without any post-mixing,and we have several measured isotopic ratios(≥4) or many acceptable solutions (≥10).

The next group consists of twelve grains(from Ag2 to 1 07 in Table 3) that do not re-quire any post-mixing. These have a mediumplausibility of a CO nova paternity. We rankthem below the top group because they eitherhave a small number of measured isotopic ra-tios (i.e., fewer experimental constraints) or asmall number of acceptable simulations.

Figure 4 shows the measured C, N, O, Si,and S isotopic ratios of all grains listed in Ta-ble 2. The colors red and green indicate grainsof high and medium plausibility, respectively,of a CO nova paternity. For these two groups,acceptable solutions are obtained without as-suming any post-mixing of the ejecta. Grainsshown in blue require post-mixing to matchthe measured isotopic ratios and correspondto a low plausibility of a CO nova paternity.For the two grains shown in black, no so-lutions are obtained with or without post-mixing of the ejecta, and thus they most likelydo not originate from CO novae.

4.3. High-plausibility CO nova grains

The SiC grains G270-2, G278, Ag2 6 (Liuet al. 2016), and M11-334-2, M11-347-4, M11-151-4 (Nittler & Hoppe 2005), shown in bold-face in Table 3, have the highest plausibilityof a CO nova paternity. For these grains, be-tween four and six isotopic ratios of the ele-ments C, N, Si, and S have been measured,and our simulations sampling the CO novaparameter space provide simultaneous solu-tions to all data without requiring any dilu-tion of the ejecta with solar-like matter.

Interestingly, most of these have been ar-gued to originate from supernovae rather thannovae on the basis of their isotopic signatures.

For example, M11-334-2 has 28Si, 44Ca, and49Ti excesses and a very high inferred initial26Al abundance, similar to those seen in typeX SiC grains from supernovae, and M11-151-4 has an unexplained 47Ti anomaly. The 32Sexcesses seen in G270-2 and AG2 6 and thestrong 28Si depletion seen in G278 have notbeen predicted by previous nova models.

We will now consider the simulated COnova peak temperature and peak density con-ditions that are obtained for these grains, as-suming no post-mixing. They are shown inFigure 5, using the same color scheme thatwas employed in Figure 3 (black, blue, andgreen for Tpeak ≤ 0.15 GK, 0.15 GK < Tpeak< 0.20 GK, and Tpeak ≥ 0.20 GK, respec-tively). The simulation results are not uni-formly spread over the Tpeak − ρpeak plane.Instead, the solutions occupy select regions.Black simulation points are not apparent, ex-cept for a small number of points for grainsG278 and M11-334-2. This indicates that allsix grains likely originate in nova explosionswith peak temperatures in excess of 150 MK,involving higher-mass CO white dwarfs. Forgrains G270 2 and Ag2 6, the most likelypeak temperature exceeds 200 MK, as can beseen from the relative number of green simu-lation points. Figure 6 shows for the same sixgrains the exponential 1/e decay time scaleof the density profile versus the exponential1/e decay time scale of the temperature pro-file. The simulation points occupy a parame-ter space typical for CO nova conditions.

It is interesting to consider the measuredelemental carbon and oxygen abundances inCO nova ejecta, and compare the observa-tions to the simulations. The observationalresults are summarized in Table 1. Thecarbon-to-oxygen mass fraction ratios rangefrom 0.084 (for GQ Mus) to 5.4 (for V827Her). Dust has been directly observed inPW Vul, QV Vul, V827 Her, V842 Cen, andV1668 Cyg (column 5). At least two of these,QV Vul and V842 Cen, have produced SiCdust. The simulated elemental oxygen versus

16

0 2 4 6 80123456

δ13C

δ15 N

x104

x104

●●

●●

●●

●●

●

●

●

●

●● ●

●

●● ●

●

●

0 2 4 6 8 10 12−1

−0.8−0.6−0.4−0.2

00.2

δ17O

δ18 O

x104

x103

●●

●●

●

●●

●

●

●●

●

●

●●

●

●

−0.5 0 0.5 1 1.5−0.5

00.51

1.52

δ30Siδ2

9 Si

x103

x103

●●

●

●●●●

●

●●

● ●●●●●●●●●●●● ●●●

●●

−8 −6 −4 −2 0 2

−10

−5

0

5

δ34S

δ33 S

x102

x102

●

●●●●

Fig. 4.— Measured isotopic ratios for the elements C, N, Si, and S (see Table 2). The colors redand green indicate grains of high and medium plausibility, respectively, of a CO nova paternity (seediscussion in the text); for these two groups, acceptable solutions are obtained without requiringany post-mixing of the ejecta. Grains shown in blue require post-mixing to match the measuredisotopic ratios and correspond to a low plausibility of a CO nova paternity. For the two grainsshown in black, no solutions are obtained with or without post-mixing of the ejecta; thus it ishighly unlikely that they originate from CO novae.

17

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

G270_2

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

M11−334−2

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

G278

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

M11−347−4

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

M11−151−4

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

Ag2_6

Fig. 5.— Peak density, ρpeak, versus peak temperature, Tpeak, for the six presolar stardust grainswith the highest plausibility of a CO nova paternity. These are shown in boldface in column 5 ofTable 3. The colors have the same meaning as in Figure 3. The simulation results, using 50,000network calculations, were obtained assuming no post-mixing of ejecta with solar-like matter (fpost= 0) and without any variations of thermonuclear reaction rates.

18

100 101 102 103 104 105100

101

102

103

104

105

τT (s)

τ ρ (s

)

G270_2

100 101 102 103 104 105100

101

102

103

104

105

τT (s)

τ ρ (s

)

M11−334−2

100 101 102 103 104 105100

101

102

103

104

105

τT (s)

τ ρ (s

)G278

100 101 102 103 104 105100

101

102

103

104

105

τT (s)

τ ρ (s

)

M11−347−4

100 101 102 103 104 105100

101

102

103

104

105

τT (s)

τ ρ (s

)

M11−151−4

100 101 102 103 104 105100

101

102

103

104

105

τT (s)

τ ρ (s

)

Ag2_6

Fig. 6.— Exponential 1/e decay time scale of the density profile versus the exponential 1/e decaytime scale of the temperature profile, for the six presolar stardust grains with the highest plausibilityof a CO nova paternity (shown in boldface in column 5 of Table 3). The colors have the samemeaning as in Figure 3. The simulation results, using 50,000 network calculations, were obtainedassuming no post-mixing of ejecta with solar-like matter (fpost = 0) and without any variations ofthermonuclear reaction rates.

19

carbon abundances (by mass) are shown inFigure 7, without assuming any post-mixing.Most of the simulation results scatter aboutthe dotted line, corresponding to equal carbonand oxygen mass fractions. A few simulationpoints, for grain G278 only, exhibit ratios ofX(O)/X(C). 0.3 (i.e., the points on the farleft in the second top panel), which wouldbe unfavorable for the condensation of SiCgrains. For all solutions shown in Figure 7,the median of the elemental silicon mass frac-tion amounts to Xmed(Si) ≈ 6× 10−4, whichis close to the solar value, X�(Si) ≈ 8×10−4.

Finally, we repeated the simulations un-der exactly the same conditions, except thatwe included this time thermonuclear reactionrate variations. As mentioned in Section 3.1,all reaction rates in the network were sampledsimultaneously according to their rate prob-ability densities given by STARLIB. The re-sults for the peak density versus peak tem-perature are shown in Figure 8. Compari-son to Figure 5, which was obtained with-out thermonuclear rate variations, shows thatthe thermonuclear rate uncertainties increasethe scatter of the simulation points (black,blue, green) noticeably. A detailed analysisof which nuclear reaction rate variations havethe largest impact on the scatter is beyondthe scope of the present work and will be pre-sented in a forthcoming publication. Never-theless, all relevant features discussed aboveare preserved, even when taking into accountthermonuclear rate variations.

5. Summary

We discussed a new method to analyze theCO nova paternity of presolar stardust grains.Previously, a small number of simulations wasperformed, assuming fixed values for key pa-rameters (e.g., white dwarf composition, mix-ing during the explosion, peak temperaturesand densities, explosion time scales, dilutionof the ejecta after the outburst, and ther-

monuclear reaction rates) that are sometimesweakly constrained. Such a method will al-ways result in a poor exploration of the largenova parameter space and, consequently, in aweak predictive power of the applied model.In addition, previous comparisons betweenpredicted and observed isotopic abundanceratios were not based on a rigorous statisti-cal procedure, resulting in conflicting claimsof CO nova paternities.

In this work, we applied a Monte Carlomethod by randomly sampling over realisticparameter ranges. We adopted thermonu-clear reaction rates, and their associatedprobability densities, from the STARLIB li-brary. We also provide a statistical interpre-tation for what we mean by “agreement” or“disagreement” between observed and pre-dicted isotopic ratios (Equations 8 and 9).

Based on the numerical results for the pa-rameters of our model, we identify 18 presolargrains with measured isotopic signatures con-sistent with a CO nova origin, without requir-ing any dilution of the ejecta. Among these,the grains G270 2, M11-334-2, G278, M11-347-4, M11-151-4, and Ag2 6 have the high-est plausibility of a CO nova paternity. As isthe case with all previous studies, we cannotdetermine the absolute probability that anygiven grain originates in a CO nova. Sucha conclusion can only be drawn if a studysimilar to the one presented here is appliedto competing astrophysical scenarios, e.g., su-pernovae and AGB stars. Such an investiga-tion is planned for the future. Numerical re-sults for any of the grains listed in Table 2can be requested from the first author.

We would like to thank Andrea Derdzin-ski, Bob Gehrz, Ann Nguyen, David Little,Jack Dermigny, and Maitrayee Bose for help-ful comments. This work was supportedby the U.S. Department of Energy underContract No. DE-FG02-97ER41041 and byNASA under the Astrophysics Theory Pro-gram Grant 14-ATP14-0007. JJ ackowledges

20

10−3 10−2 10−1 10010−3

10−2

10−1

100

X(C)

X(O)

G270_2

10−3 10−2 10−1 10010−3

10−2

10−1

100

X(C)

X(O)

M11−334−2

10−3 10−2 10−1 10010−3

10−2

10−1

100

X(C)

X(O)

G278

10−3 10−2 10−1 10010−3

10−2

10−1

100

X(C)

X(O)

M11−347−4

10−3 10−2 10−1 10010−3

10−2

10−1

100

X(C)

X(O)

M11−151−4

10−3 10−2 10−1 10010−3

10−2

10−1

100

X(C)

X(O)

Ag2_6

Fig. 7.— Elemental oxygen versus elemental carbon abundance (by mass) in the ejecta, for the sixpresolar stardust grains with the highest plausibility of a CO nova paternity (shown in boldface incolumn 5 of Table 3). The colors have the same meaning as in Figure 3. The simulation results,using 50,000 network calculations, were obtained assuming no post-mixing of ejecta with solar-likematter (fpost = 0) and without any variations of thermonuclear reaction rates. The dotted linescorrespond to equal mass fractions.

21

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

G270_2

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

M11−334−2

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

G278

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

M11−347−4

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

M11−151−4

0.15 0.2 0.25

101

102

103

104

Tpeak (GK)

ρ pea

k (g/

cm3 )

Ag2_6

Fig. 8.— Same as Figure 5, except that the random sampling of thermonuclear reaction rates isincluded in the results. An increase in the scatter of the simulation points (black, blue, green)compared to Figure 5 is apparent.

22

partial support by the Spanish MINECOthrough grant AYA2014-59084-P, and bythe AGAUR/Generalitat de Catalunya grantSGR0038/2014.

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This 2-column preprint was prepared with the AASLATEX macros v5.2.

25

Table 1

Carbon, oxygen, and dust observations in CO novae.a

CO nova Xobs(C)b Xobs(O)b Xobs(C)/Xobs(O) Type of dustc Mass of dust (M�)

GQ Mus 0.0080 0.095 0.084 none detected · · ·HR Del · · · 0.047 · · · · · · · · ·LMC 1991 · · · · · · 0.27f · · · · · ·LW Ser · · · · · · · · · C 3.6×10−7

NQ Vul · · · · · · · · · C 2×10−7

PW Vul 0.031 0.047 0.66 C 5.1×10−10

QV Vul · · · 0.041 · · · C, SiO2, HC, SiC 1.0×10−6j

V339 Del · · · · · · · · · · · · 5×10−9m

V443 Sct · · · 0.007 · · · · · · · · ·V705 Casn · · · · · · · · · C, HC, SiO2 8.2×10−7j

V827 Her 0.087 0.016 5.4 C · · ·V842 Cen 0.12 0.03 4.0 C, SiC, HC · · ·V1186 Sco · · · · · · · · · none detectedi · · ·V1280 Sco · · · · · · · · · C, SiO2

g 1.0×10−7l

V1425 Aql 0.030d 0.085d 0.35 · · · · · ·V1668 Cyg · · · · · · · · · C 2.1×10−8j

V2214 Oph · · · 0.060 · · · · · · · · ·V2362 Cyg · · · 0.163e · · · · · · ≈ 2 × 10−10 − 2 × 10−8k

V2676 Oph · · · · · · · · · C, SiO2h · · ·

aFrom Gehrz et al. (1998), unless noted otherwise; if more than one value is quoted, we adopt the arithmeticaverage value. Only those novae are listed for which the white dwarf paternity (i.e., CO) has been established.

bAbundance by mass.

cC=amorphous carbon; HC=hydrocarbons; SiO2=silicate.

dFrom Lyke et al. (2001).

eFrom Munari et al. (2008).

fFrom Schwarz et al. (2001).

gFrom Sakon et al. (2016).

hFrom Kawakita et al. (2017); also reported by Kawakita et al. (2015): 12C/13C ≈ 4 and 14N/15N ≈ 2.

iFrom Schwarz et al. (2007).

jFrom Gehrz (2008).

kFrom Arai et al. (2010).

lFrom Chesneau et al. (2008).

mFrom Evans et al. (2017).

nHric et al. (1998) suggest a white dwarf mass of 0.79 ± 0.06 M�.

26

Table2

Measu

red

isotopic

ratiosin

novacandidatepreso

larstardust

grains.

Grain

12C

/13C

14N

/15N

17O

/16O

18O

/16O

δ25M

g/24M

gδ29Si/

28Siδ30Si/

28Siδ33S/32S

δ34S/32S

(×

10−

4)

(×

10−

3)

SiC

Grain

s

AF

15bB

-429-3

19.4

±0.2

···

···

···

···

28

±30

1118

±44

···

···

AF

15bC

-126-3

16.8

±0.2

5.2

2±

0.1

1···

···

···

-105

±17

237

±20

···

···

Ag22

2.5

±0.1

7.0

±0.1

···

···

···

-304

±26

319

±38

-92

±222

162

±106

Ag2

62

16.0

±0.4

9.0

±0.1

···

···

···

-340

±57

263

±82

48

±334

-394

±106

KJC

1121

4.0

±0.2

6.7

±0.3

···

···

···

···

···

···

···

KJG

M4C

-100-3

15.1

±0.1

19.7

±0.3

···

···

···

55

±5

119

±6

···

···

KJG

M4C

-311-6

18.4

±0.1

13.7

±0.1

···

···

···

-4±

5149

±6

···

···

G16142

9.2

±0.0

735.0

±0.7

···

···

···

34

±5

121

±6

···

···

G16972

2.5

±0.0

133.0

±0.8

···

···

···

-42

±12

40

±15

···

···

G17482

5.4

±0.0

219.0

±0.2

···

···

···

21

±4

83

±5

···

···

G270

22

11.0

±0.3

13.0

±0.3

···

···

···

-282

±101

-3±

131

-615

±385

-542

±175

G2832

12.0

±0.1

41.0

±0.5

···

···

···

-15

±3

75

±4

···

···

G2782

1.9

0±

0.0

37.0

±0.2

···

···

···

1570

±112

1673

±138

···

···

G13422

6.4

0±

0.0

87.0

0±

0.1

4···

···

···

445

±34

513

±43

···

···

GA

B2

1.6

0±

0.0

213.0

±0.2

···

···

···

230

±6

426

±7

-82

±279

-6±

122

G240-1

21.0

0±

0.0

17.0

±0.1

···

···

···

138

±14

313

±23

···

···

M11-1

51-4

3,a

4.0

2±

0.0

711.6

±0.1

···

···

···

-438

±9

510

±18

···

···

M11-3

34-2

3,b

6.4

8±

0.0

815.8

±0.2

···

···

···

-489

±9

-491

±18

···

···

M11-3

47-4

35.5

9±

0.1

36.8

±0.2

···

···

···

-166

±12

927

±30

···

···

M26a-5

3-8

44.7

5±

0.2

3···

···

···

···

10

±13

222

±25

···

···

Silic

ate

Grain

s

1075

···

···

49.1

±3.6

1.3

6±

0.1

9···

···

···

···

···

426

···

···

128.0

±1.4

1.7

4±

0.0

51025

±29

24

±40

134

±52

···

···

476

···

···

149.0

±2.0

1.3

0±

0.0

6213

±56

136

±46

-49

±80

···

···

A094

TS67

···

···

95.4

±1.1

1.5

0±

0.0

1···

29

±43

43

±54

···

···

AH

-106a8

···

···

50.1

±2.2

1.7

8±

0.0

7···

15

±59

80

±67

···

···

B2-7

9···

···

133.0

±1.0

1.4

3±

0.0

4···

21

±56

57

±69

···

···

GR

95

13

2910

···

···

62.5

±2.5

1.9

6±

0.1

479

±21

-16

±63

379

±92

···

···

Graphit

eG

rain

s

KF

B1a-1

614,1

13.8

±0.1

312

±43

···

···

-28

±62

-133

±81

37

±87

···

···

KF

C1a-5

514,c

8.4

6±

0.0

4273

±8

···

···

-157

±443

84

±54

761

±72

···

···

LA

P-1

4912

1.4

1±

0.0

1941

±81

3.8

6±

0.3

41.9

4±

0.0

7···

-8±

24

-23

±29

-23

±143

6±

70

Oxid

eG

rain

s

12-2

0-1

013

···

···

88.0

±3.0

1.1

8±

0.1

1···

···

···

···

···

8-9

-313

···

···

51.4

±1.1

1.8

9±

0.0

7-6

6±

21

···

···

···

···

C4-8

13

···

···

440.4

±1.2

1.1

0±

0.0

2949

±8

···

···

···

···

KC

2314

···

···

58.5

±1.8

2.1

9±

0.0

645

±35

···

···

···

···

KC

3314

···

···

82.2

±0.6

0.6

8±

0.0

8···

···

···

···

···

MC

G6710

···

···

47.3

±1.4

1.7

7±

0.0

3···

···

···

···

···

MC

G6810

···

···

62.6

±1.1

1.8

9±

0.0

2···

···

···

···

···

S-C

608715

···

···

75.2

±0.3

2.1

8±

0.0

336

±22

···

···

···

···

T5416

···

···

141

±5

0.5

±0.2

···

···

···

···

···

Sola

r89

272

3.8

2.0

0.0

0.0

0.0

0.0

0.0

Note.—

Presented

errors

are

1σ

.Som

eratio

sare

presented

as

devia

tio

ns

from

sola

rabundances

inperm

il,δiX

/jX

≡[(iX

/jX

)/(iX

/jX

)�

–1]×

1000.

12C

/13C

and

14N

/15N

(ratio

inair

)are

from

Jose

et

al.

(2004)

and

refe

rences

therein

;17O

/16O

and

18O

/16O

sola

rvalu

es

are

from

Leit

ner

et

al.

(2012).

aA

ddit

ional

isotopic

ratio

sfo

rG

rain

M11-1

51-4

are

giv

en

inN

ittle

r&

Hoppe

(2005):

26A

l/27A

l=

0.2

7±

0.0

5,δ46T

i/δ48T

i=

28

±59,δ47T

i/δ48T

i=

215

±57,δ49T

i/δ48T

i=

82

±55,δ50T

i/δ48T

i=

-100

±123.

bA

ddit

ional

isotopic

ratio

sfo

rG

rain

M11-3

34-2

are

giv

en

inN

ittle

r&

Hoppe

(2005):

26A

l/27A

l=

0.3

9±

0.0

6,δ42C

a/δ40C

a=

-70

±200,δ44C

a/δ40C

a=

535

±150,δ46T

i/δ48T

i=

-61

±33,δ47T

i/δ48T

i=

-5±

36,δ49T

i/δ48T

i=

380

±47,δ50T

i/δ48T

i=

-20

±59.

cM

ult

iple

valu

es

exis

tfo

rthe

16O

/18O

(or

18O

/16O

)ratio

of

Grain

KF

C1a-5

51

and

are

not

giv

en

here

(see:

Am

ari,

Zin

ner,

&L

ew

is(1995);

M.

Bose,

priv

.com

m.

(2017);

and

http:/

/presola

r.w

ustl.edu/˜

pgd).

Refe

rences.

—1A

mari

et

al.

(2001);

2L

iuet

al.

(2016);

3N

ittle

r&

Hoppe

(2005);

4N

ittle

r&

Ale

xander

(2003);

5V

ollm

er

et

al.

(2007);

6N

guyen

&M

essenger

(2014);

7N

guyen

et

al.

(2007);

8N

guyen

et

al.

(2010);

9B

ose

et

al.

(2010);

10L

eit

ner

et

al.

(2012);

11Jose

&H

ernanz

(2007);

12H

aenecour

et

al.

(2016);

13G

yngard

et

al.

(2010);

14N

ittle

ret

al.

(2008);

15C

hoi,

Wasserburg,

&H

uss

(1999);

16N

ittle

ret

al.

(1997).

27

Table 3

Summary results of our simulationsa . The order, from top to bottom, reflectsapproximately the likelihood that a given presolar stardust grain originated

from a CO nova.

Grainb Mineralogyb Number of Measured Number of

isotopic ratiosc elementsc solutionsd

G270-2 SiC 6 C, N, Si, S 67M11-334-2 SiC 4 C, N, Si 1228G278 SiC 4 C, N, Si 425M11-347-4 SiC 4 C, N, Si 56M11-151-4 SiC 4 C, N, Si 43Ag2 6 SiC 6 C, N, Si, S 10Ag2 SiC 6 C, N, Si, S 3G1342 SiC 4 C, N, Si 11AF15bC-126-3 SiC 4 C, N, Si 5G240-1 SiC 4 C, N, Si 8KJGM4C-311-6 SiC 4 C, N, Si 2AF15bB-429-3 SiC 3 C, Si 102M26a-53-8 SiC 3 C, Si 7T54 oxide 2 O 11048KC33 oxide 2 O 8840KJC112 SiC 2 C, N 131512 20 10 oxide 2 O 3301 07 silicate 2 O 3

aThe table shows all presolar stardust grains for which we found acceptablesolutions without assuming any post-mixing, i.e., without any dilution of the ejectabefore grain condensation.

bSee Table 2; the grains in boldface have the highest plausibility for a CO novapaternity.

cMeasured number of isotopic ratios and elements in grain.

dThe number of network runs, out of a total of 50,000 simulations, that providesimultaneous solutions for all measured isotopic ratios of a given grain.

28