SUPERNOVA MIXTURES REPRODUCING ISOTOPIC RATIOS OF PRESOLAR GRAINS

Transcription

1 The Astrophysical Journal, 666:1048Y1068, 2007 September 10 # The American Astronomical Society. All rights reserved. Printed in U.S.A. A SUPERNOVA MIXTURES REPRODUCING ISOTOPIC RATIOS OF PRESOLAR GRAINS Takashi Yoshida National Astronomical Observatory of Japan, Mitaka, Tokyo , Japan; takashi.yoshida@nao.ac.jp Received 2006 July 11; accepted 2007 May 25 ABSTRACT Most of supernova-originating presolar grains, such as silicon carbide type X (SiC X) and low-density graphite, show excesses of 28 Si. Some of them also indicate evidence for the original presence of short-lived nuclei 44 Ti. In order to reproduce isotopic and elemental signatures of these grains, large-scale heterogeneous mixing in supernova ejecta is required. I investigate supernova mixtures that reproduce as many isotopic ratios as possible of 18 individual SiC X and 26 individual low-density graphite grains. The supernova ejecta are divided into seven layers, i.e., the Ni, Si/S, O/Si, O/Ne, C/O or O/C, He/C, and He/N layers. Then, mixtures indicating isotopic ratios with small differences from those of individual single grains are sought. Mixtures reproducing five isotopic ratios in 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti are obtained for three SiC grains. For 10 SiC X grains for which five, four, or three isotopic ratios have been measured, the mixtures reproducing all measured isotopic ratios are also found. For 20 low-density graphite grains, the mixtures reproducing six isotopic ratios in 12 C/ 13 C, 14 N/ 15 N, 16 O/ 17 O, 16 O/ 18 O, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti are obtained. The mixing ratios of each mixture strongly depend on reproduced isotopic ratios. The main component of most mixtures is one of the Ni, He/C, and He/N layers. The carbon-to-oxygen ratio of the mixtures is larger than unity for most cases. The ratios of Fe/C and Fe/Si in the mixtures have large varieties. Most of the mixtures for low-density graphite indicate Fe/Si larger than unity. The elemental signatures of the mixtures will constrain grain formation in supernovae. Subject headings: dust, extinction nuclear reactions, nucleosynthesis, abundances solar system: formation supernovae: general Online material: additional figures, machine-readable table 1. INTRODUCTION 1048 Primitive meteorites contain tiny, nanometer to micron sized grains, the isotopic compositions of which are far from the solar system composition. Since the isotopic and elemental compositions of the grains are considered to reflect nucleosynthesis in stars or Galactic chemical evolution in their birth, they are called presolar grains (for reviews, see Zinner 1998; Clayton & Nittler 2004; Lodders & Amari 2005). After the success in isolating silicon carbides (SiC) ( Bernatowicz et al. 1987), graphite (Amari et al. 1990), titanium carbide (Bernatowicz et al. 1991), and silicon nitride ( Nittler et al. 1995) were isolated as presolar grains. Presolar oxide grains such as corundum ( Hutcheon et al. 1994; Nittler et al. 1994), spinel (Nittler et al. 1997), and hibonite (Choi et al. 1999) have also been isolated. Recent progress of mass spectroscopy in the micron and submicron area has revealed the existence of presolar silicate grains ( Nguyen & Zinner 2004; Nagashima et al. 2004). Silicon carbide type X (SiC X) (Amari et al. 1992), lowdensity graphite (Amari et al. 1995), and some silicon nitride (Nittler et al. 1995) are believed to originate from supernovae. Most of these grains have excesses of 28 Si and some of them show evidence for the original presence of short-lived nuclei 44 Ti (Nittler et al. 1996). In most of the grains, C, N, and Si isotopic ratios have been measured (e.g., Amari et al. 1992; Hoppe et al. 2000). For low-density graphite, oxygen isotopic ratios have been measured and excesses of 18 O have been found (Amari et al. 1995). Isotopic ratios of heavy elements such as Sr, Zr, Mo, Ru, and Ba have been measured (Pellin et al. 1999, 2000, 2006; Davis et al. 2002). Oxide grains from supernovae have been found, but they are still very rare (Nittler et al. 1998; Choi et al. 1998). Recent astronomical observations of the Type II supernova 2003gd showed that core-collapse supernovae can be a major dust supplier in the universe (Sugerman et al. 2006). Since the discovery of SiC X, isotopic ratios of the grains have been compared with those evaluated from supernova nucleosynthesis models. Amari et al. (1992) required large-scale heterogeneous mixing in supernova ejecta to reproduce excesses of 28 Si and a carbon-enriched composition. In general, a large 28 Si excess is obtained in a deep region through explosive oxygen burning. The carbon-enriched region is mainly in the He layer and is on an oxygen-rich layer. Therefore, the 28 Si-enriched deep region should mix into the carbon-enriched region. The mixture should be appropriate for the formation of C-enriched grains. Mixing processes in supernovae have been studied to explain observational results of supernova explosions. In order to explaintheearlyemergenceofhardx-raysand-rays observed in SN 1987A, it is necessary to consider mixing that carries 56 Ni produced in the innermost region into the outer H-rich envelope in a short time. Linear stability analysis showed that the Rayleigh- Taylor instability at the boundary of the He and H layers can cause large-scale mixing ( Ebisuzaki et al. 1989). Several studies of hydrodynamic simulations have shown that fluid elements in deep regions penetrate into the outer H-rich region if the initial velocity perturbation is not too small (Arnett et al. 1989; Hachisu et al. 1990). Recent hydrodynamic simulations have revealed that some Ni is carried to the He layer by mixing induced by Rayleigh-Taylor instabilities at the Si/O and (C+O)/ He interfaces ( Kifonidis et al. 2003). Travaglio et al. (1999) considered two mixing models of supernova ejecta to reproduce isotopic and elemental signatures of low-density graphite grains. They first considered diffusive mixing from an onion-like composition structure to a homogeneous one using a 15 M supernova model from Woosley &

2 SUPERNOVA MIXTURES FOR PRESOLAR GRAINS 1049 Weaver (1995). However, the mixed compositions did not satisfy both the 28 Si excess and the carbon-enriched feature. They further investigated isotopic ratios of the supernova ejecta considering heterogeneous mixing. Such mixing is considered to be induced by the Rayleigh-Taylor instabilities, as shown above. They divided the supernova model into seven distinct zones. Then, they investigated possible ranges of isotopic ratios by changing the mixing ratios of these zones widely under carbonenriched conditions. They compared with the isotopic ratios of low-density graphite grains. The obtained ranges of 12 C/ 13 C, 16 O/ 18 O, and 30 Si/ 28 Si covered the corresponding ratios measured in low-density graphite grains. The excesses of 44 Ti and 41 Ca are also reproduced. The obtained mixtures consist of C-rich He and Si-rich zones. The mixing ratios of the Si/S+Si/O zone should be small in order to reproduce the isotopic ratios of the grains. Yoshida et al. (2005b) investigated possible ranges of 29 Si/ 28 Si and 30 Si/ 28 Si of supernova mixtures. They took into account a variety of stellar mass and hypernova explosions to reproduce the 29 Si/ 28 Si > 30 Si/ 28 Si shown in most SiC X grains, where (X/Y) ½(N X /N Y )/(N X /N Y ) 1Š ; 1000 and N X and N Y are the abundances of isotopes X and Y. The obtained ranges covered the Si isotopic ratios of most SiC X in less massive supernovae and hypernovae. They also pointed out the importance of the Ni layer in reproducing the Si isotopic ratios of these grains. The above studies focused on finding possible ranges of isotopic ratios by changing the mixing ratios. Usually, the ranges are shown on the plane of two isotopic ratios such as 12 C/ 13 C versus 14 N/ 15 N. In this case, even if a mixture reproduces two isotopic ratios of a grain on the isotopic ratio plane, it is still difficult to find out whether the mixture reproduces other isotopic ratios. It is important to find out how many isotopic ratios of individual presolar grains from supernovae are reproduced by supernova mixtures. The mixing ratios and the elemental compositions of mixtures should provide information important for nucleosynthesis in massive stars and grain formation in supernova ejecta. Yoshida & Hashimoto (2004) sought the mixtures reproducing six isotopic ratios for 15 supernova-originating grains having evidence for the original presence of 44 Ti. They used the supernova ejecta of a 4 M He star model. They divided the ejecta into seven layers, i.e., the Ni, Si/S, O/Si, O/Ne, C/O, He/C, and He/N layers. Then, they sought the mixtures reproducing the isotopic ratios of individual grains considering four layers such as (Si/S, O/Ne, He/C, and He/N) and (Ni, Si/S, He/C, and He/N). They found the mixtures reproducing four isotopic ratios for two grains. The mixing ratios of the Ni, Si/S, O/ Ne, and He/C layers are occasionally smaller than This result strongly suggests that microscopic mixing should occur in addition to the macroscopic mixing. However, they did not consider all seven layers to mix. Therefore, mixtures with all seven layers should be investigated to reproduce isotopic ratios of presolar grains from supernovae. In this study, I seek mixtures reproducing as many isotopic ratios as possible for individual SiC X and low-density graphite grains considering all seven layers of supernova ejecta. The compared isotopic ratios are 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti for SiC X grains. They are 12 C/ 13 C, 14 N/ 15 N, 16 O/ 17 O, 16 O/ 18 O, 26 Al/ 27 Al, 29 Si/ 28 Si, and 30 Si/ 28 Si for low-density graphite grains (and 44 Ti/ 48 Ti for some grains). I investigate characteristics of the mixtures for elemental compositions and the mixing ratios. The mixtures reproducing isotopic ratios of individual grains provide their elemental compositions. The elemental compositions are important when they are compared with elemental conditions deduced from grain condensation theory. The C/O ratio of the mixtures forming SiC X and low-density graphite grains has been discussed (e.g., Lodders & Fegley 1997; Clayton et al. 1999; Ebel & Grossman 2001; Deneault et al. 2006). The condensation condition for the inclusion of TiC and Fe-rich metal subgrains in graphite has also been discussed ( Lodders 2006). The conditions of elemental compositions of mixtures should be provided from the viewpoint of isotopic ratios and nucleosynthesis studies. In x 2 the SiC X and low-density graphite grains and their isotopic ratios compared in this study are described. In x 3the characteristics of the chemical compositions of the supernova ejecta of 3.3, 4, 6, and 8 M He star models calculated in Yoshida et al. (2005b) are shown. Then, the seven-layer mixing model in this study and the conditions under which a mixture reproduces isotopic ratios of a given grain are described. Section 4 shows typical examples of seven-layer mixtures reproducing isotopic ratios of individual single SiC X and low-density graphite grains. The characteristics of the mixing ratios of the mixtures are also shown. In x 5 characteristics of elemental compositions that will be important for grain condensation theory are discussed. The relation of the isotopic ratios to the mixing ratios of specific layers is also discussed. The conclusions of this study are shown in x 6. In the Appendix, a minimization method to find mixtures having isotopic ratios with the smallest differences from those of a single grain is described. 2. PRESOLAR GRAINS FROM SUPERNOVAE In this study, the measured data of isotopic ratios are adopted from 18 SiC X grains and 26 low-density graphite grains. The selected isotopic ratios and their values are listed in Table 1. Six SiC X grains having evidence for the original presence of short-lived nuclei 44 Ti are picked up from Amari et al. (1992) and Nittler et al. (1996). The isotopic ratios 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti have been measured in these grains. From Hoppe et al. (2000) one grain in which 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti were measured and four grains with the three isotopic ratios 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti are chosen. Seven grains measured by NanoSIMS (Besmehn & Hoppe 2003) are used; 12 C/ 13 C, 14 N/ 15 N, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti have been measured for one grain and 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti for the other grains. For low-density graphite grains, 22 grains having isotopic ratios of 16 O/ 17 O < 1000 or 16 O/ 18 O < 250 are picked up. Amari et al. (1995) suggested that presolar grains having excesses of 18 O compared with the solar 16 O/ 18 O ratio should be originating from supernovae. Most of the 18 O is produced only in the He layer during massive-star evolution. The isotopic ratios 12 C/ 13 C, 14 N/ 15 N, 16 O/ 17 O, 16 O/ 18 O, 26 Al/ 27 Al, 29 Si/ 28 Si, and 30 Si/ 28 Si of these grains are compared. Four graphite grains having evidence for the original presence of 44 Ti are also adopted. For three of them, the isotopic ratios of 12 C/ 13 C, 14 N/ 15 N, 16 O/ 17 O, 16 O/ 18 O, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti are taken. The isotopic ratios 12 C/ 13 C, 14 N/ 15 N, 16 O/ 18 O, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti of another grain are prepared. Data for all the lowdensity graphite grains except KFA1f-302 are listed in Travaglio et al. (1999). The isotopic ratios of KFA1f-302 are adopted from Nittler et al. (1996). 3. SUPERNOVA MIXING MODELS 3.1. Composition Distribution of Supernova Ejecta The chemical composition distributions of the supernova ejecta aretakenfrom3.3,4,6,and8m He star supernova models

3 1050 YOSHIDA Vol. 666 TABLE 1 Isotopic Ratios of Supernova-Originating Presolar Grains Adopted in This Study Grains 12 C/ 13 C 14 N/ 15 N 16 O/ 17 O 16 O/ 18 O 26 Al/ 27 Al 29 Si/ 28 Si 30 Si/ 28 Si 44 Ti / 48 Ti SiC Type X KJGM a KJGM a KJGM a KJGM a KJGM a KJH-X2 a,b KJD57 c KJC58 c KJC59 c KJC72 c KJC74 c M d M d M d M d M6-8-3 d M d M d Low-Density Graphite e KE3a KE3a KFA1f-302 a < KE3a KE3a KE3a KE3a KE3a KE3a-351b KE3a KE3a KE3a KE3a KE3a KE3a KE3a KE3c KE3c KE3c KE3c KE3c KE3c KE3c-551b KE3c KE3c KE3c a Nittler et al. (1996). b Amari et al. (1992). c Hoppe et al. (2000). d Besmehn & Hoppe (2003). e All data are adopted from Travaglio et al. (1999) except KFA1f-302. calculated in the study of Yoshida et al. (2005b). The He-star models with masses of 3.3, 4, 6, and 8 M correspond to the latestage evolution of stars with masses of 13, 15, 20, and 25 M at the zero-age main sequence stage. Details of these models are shown in Yoshida et al. (2005b). The mass fraction distributions of major elements in the supernova ejecta of the 3.3, 4, 6, and 8 M He star models are shown in Figure 1. In this study, the supernova ejecta are divided into seven layers based on the characteristics of the chemical composition distribution,i.e.,theni,si/s,o/si,o/ne,c/ooro/c,he/c,and He/N layers. In the 3.3 and 4 M models, there is a thin layer, in which the main composition is carbon, inside the He/C layer (see Figs. 1a and 1b). This layer is set as the C/O layer. Then, the region of the O/C layer is added to the O/Ne layer. In the 6 and 8 M models, the O/C layer is set inside the He/C layer (see Figs. 1c and 1d). The locations of the mass cut and the outer boundary of each layer in the supernova models are listed in Table 2. In the mixing calculations for the supernova ejecta, the chemical

4 No. 2, 2007 SUPERNOVA MIXTURES FOR PRESOLAR GRAINS 1051 TABLE 2 Locations of the Mass Cut and the Outer Boundaries of Every Layer in the He-Star Supernova Models Stellar Mass M cut Ni Si/S O/Si O/Ne C/O He/C He/ N a a Note. Values are in units of M. a O/C layer in the case of the 6 and 8 M models. Fig. 1. Mass fraction distributions of the main elements in the supernova ejecta of (a)3.3m,(b)4m,(c)6m,and(d )8M He-star supernova models. The Ni, Si /S, O/Si, O/ Ne, C/O (3.3 and 4 M models) or O/C (6 and 8 M models), He/C, and He/ N layers are indicated as shaded and unshaded regions appearing alternately. The scale of the mass coordinate changes at (a)1.75,(b)2.2, (c) 2.5, and (d )3M, each of which is indicated by a thin vertical dotted line. [See the electronic edition of the Journal for panels byd ofthisfigure.] composition is averaged for each layer. The abundances, isotopic ratios, and C/O ratios of each layer in the supernova ejecta of the 3.3, 4, 6, and 8 M models are listed in Table 3. As an example, the mass fraction distributions for the C, N, O, Al, and Si isotopes, 44 Ti, and 48 Ti in the 4 M model are shown in Figure 2. The main characteristics of each layer in the supernova ejecta are described as follows. The Ni layer mainly contains 56 Ni, which decays to 56 Fe via 56 Co. The isotopic ratios of 12 C/ 13 C and 14 N/ 15 N are much smaller than those of the solar ratios. On the other hand, 26 Al/ 27 Al is larger than unity. The Si isotopic ratios depend on the stellar mass, as pointed out in Yoshida et al. (2005b). The contribution of Si in the Ni layer to mixtures is important to reproduce Si isotopic ratios of presolar grains from supernovae. The Ni layer shows the largest 44 Ti/ 48 Ti in all layers of the supernova ejecta. The 44 Ti/ 48 Ti is 0.45Y0.48. The main component of the Si/S layer is 28 Si. The values of 29 Si/ 28 Si and 30 Si/ 28 Si are close to The 44 Ti/ 48 Ti in this layer is the second largest in all layers: 44 Ti/ 48 Ti (5Y8) ; In order to reproduce 44 Ti/ 48 Ti larger than this ratio in some grains, the contribution of the Ni layer is necessary. The O/Si layer is enriched in oxygen and silicon. The 12 C/ 13 C is of order The 14 N abundance is smaller than that of 15 N. This layer shows excesses of 30 Si rather than 29 Si compared with the solar ratio. The value of 30 Si/ 28 Si is much larger than 29 Si/ 28 Si, as shown in Yoshida et al. (2005b). The 44 Ti/ 48 Ti is much smaller than in the inner two layers. The O/Ne layer is enriched in oxygen and neon. The 12 C/ 13 C is of order The ratio of 26 Al/ 27 Al is about (5Y6) ; 10 3 in the 3.3 and 4 M models and about 1 ; 10 3 in the 6 and 8 M models. The ratio of 30 Si/ 28 Si to 29 Si/ 28 Si is not as large as that in the O/Si layer. The C/O layer is set outside the O/Ne layer in the 3.3 and 4 M models. The C/O layer is enriched in carbon rather than oxygen. The C/O ratio r(c/o) is about 1.8. On the other hand, in the 6 and 8 M models, the O/C layer is set. In the O/C layer, the C/O ratio is about 0.3. In this region, 12 C/ 13 Cis4; 10 4 to 1 ; The mass fraction of 17 O in this layer is the largest of all layers. The He/C layer shows the largest C/O ratio of all layers. The 12 C/ 13 C ratio is also the largest except for the 4 M model. The 14 N/ 15 N is smaller than the solar ratio. A large amount of 18 Ois produced in this layer, so that the 16 O/ 18 O is the smallest. This layer determines the smallest 16 O/ 18 O of the mixtures of supernova ejecta with a given stellar mass. The He/C layer in less massive stars indicates smaller 16 O/ 18 O. Thus, 16 O/ 18 Oofsome grains indicating small 16 O/ 18 O is not reproduced by the mixturesofthe6or8m models. The Si isotopic ratios are slightly larger than the corresponding solar ratios. In the He/N layer, the C/O ratio is slightly larger than unity. Therefore, it should be one of the main components of the mixtures (Yoshida & Hashimoto 2004). The isotopic ratios of C, N, O, and Al have been affected by the CNO cycle. The Si isotopic ratios are almost equal to the solar ratios. Large 14 N/ 15 Nanda large amount of 14 N in this layer make it difficult to reproduce the 14 N/ 15 N of presolar grains from supernovae (e.g., Travaglio et al. 1999) Seven-Layer Mixing Model I seek the mixing ratios of a mixture reproducing N iso isotopic ratios of a single grain by the following method. First, a mixing ratio of layer a of a mixture is denoted by x a and the abundance of isotope i averaged in layer a is denoted by y ia.then,theisotopic ratio iso of isotope i to isotope j as a function of a vector x characterized by the mixing ratios x a of the mixture is set to be r iso;mix (x) ¼ ( P a y iax a )/( P a y jax a ). The corresponding isotopic ratio and its -value of the grain are denoted by r iso,grain and iso,grain. Here the 2 value of N iso isotopic ratios for the mixture and the grain is defined as 2 ¼ X iso ½r iso; mix (x) r iso;grain Š 2 : ð1þ 2 iso;grain The 2 value is a function of the mixing-ratio vector x. The mix- ratios have domain constraints 0 x a 1 and an equality Ping a x a ¼ 1. So, the minimum value of 2 is sought under the constraints. In general, the 2 value presented by equation (1) is a nonlinear function of x and has many local minima. The minimum value should be found while avoiding the local minima. Furthermore, some mixing ratios corresponding to the minimum 2 value may be much smaller than unity, e.g., of order 10 5,as shown in Yoshida & Hashimoto (2004). Therefore, I seek the minimum 2 value using a minimization method with a genetic algorithm with floating-point representation ( Michalewicz 1996, p. 121). Details of the minimization method are given in the Appendix. This minimization method is very useful for avoiding local minima but it needs to take many steps to reach the minimum value after avoiding the local minima. Thus, after avoiding local minima, a downhill-simplex method is used to find the minimum value (Press et al. 1999, p. 402). After obtaining the minimum 2 value and the mixing ratios of the corresponding mixture, one

5 1052 YOSHIDA Vol. 666 TABLE 3 Abundances, Isotopic Ratios, and the C/O Ratio of Each Layer in the Supernova Ejecta of the 3.3, 4, 6, and 8 M He Star Models Species Ni Si/S O/Si O/ Ne C/O He/C He/ N 3.3 M Model 12 C E E E E E E E C E E E E E E E N E E E E E E E N E E E E E E E O E E E E E E E O E E E E E E E O E E E E E E E Al E E E E E E E Al E E E E E E E Si E E E E E E E Si E E E E E E E Si E E E E E E E Ti E E E E E E E Ti E E E E E E E 07 C E E E E E E E 05 O E E E E E E E 05 Si E E E E E E E 04 Ti E E E E E E E 07 Fe E E E E E E E C/ 13 C E E E E E E E N/ 15 N E E E E E E E O/ 17 O E E E E E E E O/ 18 O E E E E E E E Al/ 27 Al E E E E E E E Si/ 28 Si E E E E E E E Si/ 28 Si E E E E E E E Ti / 48 Ti E E E E E E E 10 r (C/O) E E E E E E E+00 Note. Table 3 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content. can determine whether the mixture reproduces N iso isotopic ratios of the grain. I consider that the mixture reproduces N iso isotopic ratios of the grain if the minimum 2 value is smaller than 4N iso. This condition means that the average of the deviations from N iso isotopic ratios of the grain is roughly within 2. Note that 1000 is artificially added to the 2 value when the C/O ratio of the corresponding mixture is smaller than unity in the minimization of the 2 value. A priority is given to mixtures with r(c/o) 1. This is because equilibrium condensation theory shows that SiC and graphite grains can be formed in the environment of r(c/o) > 0:98 (Lodders & Fegley 1997). However, it should be noted that this treatment does not completely exclude oxygen-enriched mixtures. It has been reported that even if a supernova mixture is enriched in oxygen, the energetic electrons created by -rays dissociate CO molecules to form carbon atoms. This process may cause the condensation of graphite grains in oxygen-enriched mixtures (Clayton et al. 1999; see also x 5.1 for details). When the minimum 2 value in mixtures is sought, it is sought for every set of isotopic ratios. For example, consider the search for mixtures reproducing five isotopic ratios of a SiC X grain. First, the minimum 2 value of the mixtures is sought taking account of 12 C/ 13 C, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti. Then, the minimum value of mixtures is sought for a different set 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti, and so on. It is possible that the minimum 2 value of the former mixture is smaller than that of the latter mixture and that both of the values are smaller than 4N iso (=20 in this case). In this case, I consider that both of the mixtures reproduce five isotopic ratios of the grain. All mixtures satisfying the condition of 2 4N iso should be candidates for reproducing N iso isotopic ratios of the grain. There are uncertainties in stellar evolution, the supernova explosion mechanism, and the variety of supernova explosions. Therefore, it is important to seek many possibilities of mixtures reproducing isotopic ratios of grains, rather than to constrain strictly the conditions of the mixtures. Conditions of elemental composition deduced from grain formation theory will constrain the mixtures further. I note that the mixtures reproducing isotopic ratios of a grain should be represented by regions in the coordinates of the mixing ratios x a. In practice, it is difficult to represent the regions in the mixing-ratio coordinates. The mixtures are shown only as points in the coordinates and do not show all of the range. Nevertheless, the mixing ratios provide important information for the knowledge of isotopic and elemental compositions of the mixtures reproducing isotopic ratios of the grain. 4. MIXTURES REPRODUCING ISOTOPIC RATIOS OF PRESOLAR GRAINS FROM SUPERNOVAE I conduct a search for mixing ratios of supernova mixtures that reproduce as many isotopic ratios of SiC X and low-density graphite grains as possible. The obtained mixtures reproduce five isotopic ratios of the SiC X grains and six isotopic ratios of the low-density graphite grains. The mixing ratios of the mixtures strongly depend on reproduced isotopic ratios. I now show the characteristics of the mixing ratios of the mixtures reproducing isotopic ratios of supernova-originating grains.

6 No. 2, 2007 SUPERNOVA MIXTURES FOR PRESOLAR GRAINS 1053 Fig. 2. Mass fraction distributions of (a) 12 C, 13 C, 14 N, and 15 N; (b) 16 O, 17 O, and 18 O; (c) 28 Si, 29 Si, and 30 Si; and (d ) 26 Al, 27 Ai, 44 Ti, and 48 Ti in the supernova ejecta of the 4 M model. The scale of the mass coordinate changes at 2.2 M, indicated by the thin vertical dotted line Silicon Carbide Type X Fourteen mixtures reproducing five isotopic ratios of four SiC X grains are found. The isotopic ratios and abundance ratios of the mixtures are listed in Table 4. The corresponding mixing ratios and 2 values are listed in Table 5. The same information is also listed for 26 mixtures reproducing all isotopic ratios of eight SiC X grains, of which three or four isotopic ratios have been measured. The mixtures corresponding to KJGM , KJGM , and KJH-X2 are classified into three groups by reproduced isotopic ratios. The mixtures reproducing 12 C/ 13 C but not reproducing 14 N/ 15 N are classified into group C. The mixtures reproducing 14 N/ 15 N but not 12 C/ 13 CareclassifiedintogroupN. The ones reproducing both 12 C/ 13 Cand 14 N/ 15 N are classified into group CN Group C Three mixtures reproducing five isotopic ratios of KJGM are classified into group C. The isotopic ratios of the mixtures of the 3.3, 6, and 8 M models are shown in Figure 3a.The mixing ratios, 2 values, and C/O ratios of the mixtures are showninfigure3b. The isotopic ratios of KJGM are alsoshowninfigure3a. The three mixtures well reproduce the isotopic ratios 12 C/ 13 C, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti of KJGM On the other hand, 14 N/ 15 Nofthe mixtures is larger than 10 4, whereas 14 N/ 15 N of the grain is The main component of the mixtures is commonly the He/N layer. The mixing ratios of the He/N layer are larger than The second component depends on the stellar mass. In the case of the 3.3 M model, the second component is the C/O layer. In the other two models, the second component is the He/C layer. The C/O ratio of the C/O layer is larger than unity but smaller than that of the He/C layer. On the other hand, the O/C layer is enriched in oxygen. Including the He/C layer prevents the decreasing of the C/O ratio by including oxygen-rich layers. The mixing ratios of the Ni layer and the Si/S layer are (1Y2) ; 10 4 and (3Y5) ; 10 4, respectively, among these mixtures. The mixing ratios are small but including the Si/S layer is required to reproduce the excess of 28 Si. The small mixing ratio of the Si/S layer does not supply enough 44 Ti to reproduce 44 Ti/ 48 Ti in the grain. The additional 44 Ti is provided from the Ni layer. The O/Si layer is not included in the mixtures to avoid 30 Si excesses. The C/O ratio of the mixture is 1.0 for the 3.3 and 6 M models and 2.0 for the 8 M model. There are two mixtures reproducing the five isotopic ratios of KJH-X2 using the 6 and 8 M models. The mixtures show 14 N/ 15 Nlargerthan10 4, similar to the case of KJGM The characteristics of mixing ratios are similar to the mixtures for KJGM The main component of the mixtures is the He/N layer; the mixing ratios are The second component is the He/C layer. The mixing ratio is about 0.21, which is much larger than that for the case of KJGM This is because KJH-X2 has relatively large 12 C/ 13 C(300). The mixing ratio of the Ni layer is 4 ; 10 4 and 9 ; 10 4 for the 6 and 8 M models, respectively. These values are also larger than those of the mixtures for KJGM and are favorable for reproducing 44 Ti/ 48 Ti = 0.23 for KJH-X2. The mixing ratios of the O/Si and O/Ne layers are smaller than 1 ; The small mixing ratios of these layers avoid the small C/O ratio of the mixtures. The

7 TABLE 4 Isotopic Ratios and Abundance Ratios of the Mixtures Reproducing Five Isotopic Ratios of SiC X Grains Grains He-Star Mass 12 C/ 13 C 14 N/ 15 N 26 Al/ 27 Al 29 Si/ 28 Si 30 Si/ 28 Si 44 Ti / 48 Ti r(c/o) r (Si/C) r (Fe/C) Group C KJGM E KJGM E KJGM E KJH-X E KJH-X E Group N KJGM E E E 3 KJGM KJGM E KJGM E E E 3 KJGM E Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, and 44 Ti / 48 Ti KJGM E E Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 30 Si/ 28 Si, and 44 Ti / 48 Ti KJGM E E Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, and 30 Si/ 28 Si KJH-X Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti M E E Mixtures Reproducing 26 Al / 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti of KJD57 KJD KJD E KJD KJD Mixtures Reproducing 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti KJC E KJC E KJC E KJC KJC E KJC E KJC E KJC E KJC E E E 3 KJC E E KJC E KJC E E KJC E KJC E KJC E KJC E M E M E E M E E M M E M

8 TABLE 5 Mixing Ratios and 2 Values of the Mixtures Reproducing Five Isotopic Ratios of SiC XGrains Grains He-Star Mass x(ni) x(si/s) x(o/si) x(o/ Ne) x(c/o) x(he/c) x(he/ N) 2 Group C KJGM E E E E E KJGM E E E KJGM E E E E KJH-X E E E E KJH-X E E E Group N KJGM E E KJGM E E KJGM E E E KJGM E E E KJGM E E E Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 26 Al / 27 Al, 29 Si/ 28 Si, and 44 Ti / 48 Ti KJGM E E E Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 30 Si/ 28 Si, and 44 Ti / 48 Ti KJGM E E E Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, and 30 Si/ 28 Si KJH-X E E E E E Group CN: Mixtures Reproducing 12 C/ 13 C, 14 N/ 15 N, 29 S/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti M E E 3 Mixtures Reproducing 26 Al / 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti of KJD57 KJD E E KJD E E KJD E E E E KJD E E E E Mixtures Reproducing 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti KJC E E E E 2 KJC E E E E E 2 KJC E E E E E 2 KJC E E 2 KJC E E E E E E E 24 KJC E E KJC E E E 2 KJC E E E E KJC E E E E E 24 KJC E E E E E E E 24 KJC E E E E E E E 24 KJC E E E E E E 24 KJC E E E E E 24 KJC E E E E E 3 KJC E E E E E E E 25 KJC E E E E E 3 M E M E E 24 M E E 24 M E E E E E E 24 M E E E E E E E 24 M E E E E E E

9 1056 YOSHIDA Vol. 666 The mixtures of the 3.3 and 6 M models reproduce 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti of KJGM These mixtures belong to group N. The isotopic ratios of the mixtures are shown in Figure 3c, and the mixing ratios, 2 values, and C/O ratios are shown in Figure 3d. The isotopic ratios of KJGM are also shown in Figure 3c. Although the 44 Ti/ 48 Ti values of the mixtures are slightly larger than the observed one, the 2 value is smaller than 10. However, the mixtures show 12 C/ 13 C much larger than the observed one. The main component of the mixtures is the He/C layer. The He/N layer with a mixing ratio of 7 ; 10 3 is commonly included. In the case of the 3.3 M model, the mixing ratio of the C/O layer is For inner oxygen-rich layers, the Si/S layer with a mixing ratio of about 2 ; 10 3 is included in the mixtures to reproduce the Si isotopic ratios. The Ni and O/Si layers are not included. This grain shows 44 Ti/ 48 Ti of 0.024, which is smaller than the value in the Si/S layer of the 3.3 and 6 M models. So, the 44 Ti/ 48 Ti of the grain is reproduced by including the Si/S layers. Mixtures reproducing the five isotopic ratios of KJGM are also obtained in the 3.3, 6, and 8 M models. Although they belong to group N, their mixing ratios are quite different (see Table 5). The main components of the mixtures are the C/O layer, the O/Ne layer, and the He/C layer for the 3.3, 6, and 8 M models, respectively. The 8 M model mixture indicates mixing ratios similar to the mixtures for KJGM The difference in the main component reflects the C/O ratio of the mixtures. In the 3.3 M model mixture, the C/O ratio is 1.2. The mixture of the 6 M model indicates a C/O ratio of because of including the O/Ne layer. The mixture of the 8 M model has a C/O ratio of 3.5 probably because the mixing ratios of the oxygenrich layers are small. The Si/S layer is commonly included and the O/Si layer is not included to reproduce Si isotopic ratios. Fig. 3. (a) Isotopic ratios of 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti / 48 Ti of KJGM (SiC X) and the mixtures reproducing five isotopic ratios of the grain. Open circles with error bars are the isotopic ratios of KJGM The solid, dotted, and dash-dotted lines indicate the mixtures of the3.3,6,and8m models. 29 Si / 28 Si and 30 Si/ 28 Si are represented by -value notation. ( 29 Si / 28 Si) and ( 30 Si / 28 Si) are equal to 5:065 ; 10 2 and 3:362 ; 10 2, respectively (Anders & Grevesse 1989). (b) The mixing ratios, 2 values, and C/O ratio r (C/O) of the mixtures of the 3.3 M (solid line), 6 M (dotted line), and 8 M (dash-dotted line)models.(c, d ) The same as in (a)and(b), but for KJGM The solid and dotted lines indicate the mixtures of the 3.3 and 6 M models. (e, f ) KJH-X2. The solid lines indicate the mixture of the 6 M model. (g, h) KJGM The solid and dotted lines indicate the two mixtures of the 4 M model. (i, j) M The solid lines indicate the mixture of the 8 M model. (k, l) KJD57. The solid, dotted, dashed, and dash-dotted lines indicate the mixtures of the 3.3, 4, 6, and 8 M models, respectively. [See the electronic edition of the Journal for panels byl ofthisfigure.] C/O ratios of the mixtures of the 6 and 8 M models are 2.0 and 1.5, indicating a carbon-rich environment Group N Group CN A mixture of the 6 M model reproduces the isotopic ratios of 12 C/ 13 C, 14 N/ 15 N, 26 Al/ 27 Al, 29 Si/ 28 Si, and 30 Si/ 28 Si of KJH- X2. This mixture reproduces both 12 C/ 13 Cand 14 N/ 15 N, so that it belongs to group CN. Figure 3e shows the isotopic ratios of KJH-X2 and the mixture, and Figure 3f shows the mixing ratios, 2 value, and C/O ratio of the mixture. The mixture reproduces the isotopic ratios of KJH-X2, except for 44 Ti/ 48 Ti. The 44 Ti/ 48 Ti ratioofkjh-x2is0.15,whichisrelativelylarge.however, 44 Ti/ 48 Ti of the mixture is 0.48, which is larger than the ratio of the grain. The mixing ratios of the mixture are different from those of the mixtures shown above; the main component of the mixtures is the Ni layer. The mixing ratio of the Ni layer is The second main component of the mixture is the He/N layer, the mixing ratio of which is The mixing ratio of the Si/S layer is 3 ; 10 3 in order to reproduce the 28 Si excess. Although the grain shows 30 Si/ 28 Si slightly larger than 29 Si/ 28 Si, the mixing ratio of the O/Si layer is smaller than 1 ; Note that the C/O ratio is ; the mixture is enriched in oxygen. There are two mixtures reproducing five isotopic ratios, including 29 Si/ 28 Si and 30 Si/ 28 Si. Figure 3g shows the isotopic ratios of two mixtures of the 4 M model for KJGM , and Figure 3h shows the mixing ratios, 2 values, and C/O ratios of the mixtures. Although the grain shows 29 Si/ 28 Si larger than 30 Si/ 28 Si, both of the mixtures indicate 30 Si/ 28 Si larger than 29 Si/ 28 Si. They show large mixing ratios of the Si/S and O/Si layers and very small mixing ratios of the outer C-rich layers (of order 10 4 ). Therefore, the C/O ratios of the mixtures are smaller than 2 ; 10 3, which is largely enriched in oxygen. Although the mixtures reproduce five isotopic ratios of the grain, it might be difficult to form SiC from the O-rich mixtures. M is a submicron SiC X for which 12 C/ 13 C, 14 N/ 15 N, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti have been measured by NanoSIMS. Large excesses of 12 C, 28 Si, and 44 Ti have been obtained. A mixture of the 8 M model reproducing the five isotopic ratios of this grain is found. Figure 3i shows the isotopic ratios of M and the mixture, and Figure 3j shows the mixing ratios, 2 value, and C/O ratio of the mixture. The mixture also shows 26 Al/ 27 Al of 8 ; The mixture is very homogeneously mixed compared with the mixtures already shown; the mixing ratios of the Ni, Si/S, O/Si, O/Ne, and He/N layers are larger than 0.1. Only the O/C layer indicates a small mixing ratio. However, the large mixing ratios of the inner four layers bring about the O-rich composition of the mixture; the C/O ratio is 9 ; Therefore, it may be difficult to form SiC X from this mixture from the viewpoint of chemical composition Grains with Four or Three Isotopic Ratios KJD57 is a grain for which 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti have been measured. This grain shows 44 Ti/ 48 Ti of 0.45 and 30 Si/ 28 Si larger than 29 Si/ 28 Si. There are mixtures reproducing the four isotopic ratios of the grain for all supernova models. Figure 3k shows the isotopic ratios of KJD57 and the mixtures. Figure 3l shows the mixing ratios, 2 values, and C/O ratios of the mixtures. The mixtures show that 12 C/ 13 Cand 14 N/ 15 N are larger than the corresponding solar system ratios. The mixing ratios of the mixtures are roughly similar to the mixtures in group C. The He/C layer is included with a relatively large mixing ratio, except for the 4 M model. The Ni layer is also included with a large mixing ratio, with a logarithmic scale.

10 No. 2, 2007 SUPERNOVA MIXTURES FOR PRESOLAR GRAINS 1057 This is due to large 44 Ti/ 48 Ti in the grain. Differences according to stellar mass are seen in the mixing ratios of the C/O, O/C, and He/C layers. The mixtures of the 3.3 and 4 M models include the C/O layer with mixing ratios of about 0.2. However, the mixing ratios of the He/C layer in the 6 and 8 M model mixtures are also about 0.2. This difference is also seen in the mixtures reproducing five isotopic ratios ( 14 N/ 15 N is the exception) of KJGM (see also Fig. 3b). In Hoppe et al. (2000) and Besmehn & Hoppe (2003) there are 10 SiC grains for which 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti have been measured. Mixtures reproducing the isotopic ratios of seven grains are found (see Tables 4 and 5). There are three characteristic patterns of the mixing ratios. The first pattern indicates the main component of the He/N layer. This pattern is obtained in the mixtures reproducing the isotopic ratios of KJC59, KJC74, and M This pattern is similar to that of the mixtures in group C (see Fig. 3a for KJGM ). These mixtures commonly indicate 14 N/ 15 Nof order 10 4, which is much larger than the ratios measured in SiC X. In most mixtures the 12 C/ 13 C ratio is smaller than the solar system ratio and 26 Al/ 27 Al is of order In the case of M , the Ni layer is not included in the mixture because 44 Ti / 48 Ti of the grain is small. The second pattern shows the main component of the He/C and/or C/O layers. This pattern is obtained in the mixtures for KJC58, KJC72, and M It is roughly similar to that of the mixtures in group N (see Fig. 3c). The mixtures commonly indicate 12 C/ 13 C larger than The obtained 14 N/ 15 N is smaller than the solar system ratio for most of the cases. The last pattern indicates the main component of the Ni layer. This pattern is obtained in the mixtures for KJC58 and M It is roughly similar to that of the mixture in group CN (see Fig. 3e). These mixtures also indicate 12 C/ 13 Coforder10 3 and 14 N/ 15 N smaller than the solar system ratio. At the same time, their 26 Al/ 27 Al ratio is larger than 0.1; their 26 Al/ 27 Al is very large. Note that the C/O ratio is larger than unity, which is different from the value of the mixture corresponding to KJH-X Unsuccessful Cases Although reproducing isotopic ratios of six SiC X grains with mixtures has been attempted, there are three grains for which five isotopic ratios are not reproduced. One example is a mixture of the 8 M model corresponding to KJGM When the isotopic ratios of 12 C/ 13 C, 26 Al/ 27 Al, 29 Si/ 28 Si, 30 Si/ 28 Si, and 44 Ti/ 48 Ti are compared, a smallest 2 value of 91 is obtained. This mixture does not reproduce 29 Si/ 28 Si and 30 Si/ 28 Si. The 2 values of 29 Si/ 28 Si and 30 Si/ 28 Si are 33 and 45, respectively. The grain showed that 29 Si/ 28 Si is larger than 30 Si/ 28 Si ( 29 Si/ 28 Si = , 30 Si/ 28 Si = ). On the other hand, the mixture indicates 29 Si/ 28 Si = and 30 Si/ 28 Si = The isotopic ratios of this mixture are similar to those of the mixtures in group C (see Fig. 3a). The mixing ratios are also similar to those of these mixtures; the main component is the He/N layer and the second one is the He/C layer. These characteristics of the isotopic ratios and mixing ratios are seen in the mixtures corresponding to KJGM and KJGM For both of the grains, the mixtures with the smallest 2 values are obtained using the 8 M model. Although 29 Si/ 28 Si is larger than 30 Si/ 28 Si in these grains, the corresponding mixtures do not reproduce this isotopic signature. In the SiC X grains studied by Besmehn & Hoppe (2003) three isotopic ratios are not reproduced for M , M , and M The mixture of the 3.3 M model has the smallest 2 value for each grain. These three grains have 29 Si/ 28 Si larger than 30 Si/ 28 Si. This isotopic signature is also obtained in the mixtures. However, the difference between 29 Si/ 28 Si and 30 Si/ 28 Si of each mixture is smaller than that of the corresponding grain. The mixing ratios of the mixtures corresponding to M and M are roughly similar to those of the mixtures in group C. The main component of the mixtures is the He/N layer. On the other hand, the isotopic ratios of the mixture corresponding to M are roughly similar to those of the mixtures in group N. The main component of the mixture is the C/O layer. There are some grains of which five or three isotopic ratios are not reproduced by supernova mixtures. However, the mixtures indicating the smallest 2 values for the corresponding grains have mixing ratios similar to those of the mixtures reproducing five isotopic ratios of the SiC X grains Low-Density Graphite Now I conduct a search for mixtures that reproduce as many isotopic ratios of 26 low-density graphite grains as possible. First, I focus on 12 C/ 13 C, 14 N/ 15 N, 16 O/ 17 O, 16 O/ 18 O, 26 Al/ 27 Al, 29 Si/ 28 Si, and 30 Si/ 28 Si of 22 grains, for which 44 Ti/ 48 Ti has not been measured. There are 46 mixtures reproducing six isotopic ratios of 19 grains. The isotopic ratios and abundance ratios of the mixtures are listed in Table 6. The corresponding mixing ratios and 2 values are listed in Table 7. The mixtures are classified into three groups that are denoted as group C, group N, and group CN, as classified in x Group C The mixtures in group C reproduce six isotopic ratios ( 14 N/ 15 N is the exception) of the grains. Twelve mixtures are found for reproducing the isotopic ratios of eight grains. The isotopic ratios of KE3a-157 and the mixtures of the 3.3 and 4 M models are shown in Figure 4a. The mixing ratios, 2 values, and C/O ratios of the mixtures are shown in Figure 4b. These two mixtures well reproduce six isotopic ratios and indicate 14 N/ 15 N of about 2 ; 10 4, which is much larger than the ratio of KE3a-157. They also indicate 44 Ti/ 48 Ti of about 0.4. The mixing ratios of the two mixtures are roughly similar. The main component is commonly the He/N layer; the mixing ratios are larger than The Ni and He/C layers are commonly included with mixing ratios of The mixing ratios of the Si/S layer are about The O/Si layer is not practically included. The mixture of the 4 M model reproduces the Si isotopic ratios indicating 29 Si/ 28 Si larger than 30 Si/ 28 Si. The 3.3 M model mixture does not reproduce this signature, but its Si ratios are within the error bars. The above isotopic signatures are also seen in the other mixtures in group C. A large 14 N/ 15 N ratio is seen in all of the mixtures. Most of the mixtures indicate 14 N/ 15 N larger than The Si isotopic ratios of eight mixtures are reproduced within the error bars. There are seven grains having 29 Si/ 28 Si larger than 30 Si/ 28 Si. The main component of the mixtures in group C is the He/N layer. The mixing ratio of the He/N layer is larger than 0.7 for 11 mixtures and 0.9 for seven mixtures. The Ni and He/C layers are included with smaller mixing ratios, but occasionally they are the second or third main components. The mixing ratios of the Ni and He/C layers are larger than 0.01 for nine mixtures. Exceptional mixtures show the He/C layer with a mixing ratio larger than 0.1, and the corresponding grains have large 12 C/ 13 C. Not extremely large (but still large) 14 N/ 15 N is due to the relatively large mixing ratio of the He/C layer. The Ni layer is included in 11 mixtures to reproduce 26 Al/ 27 Al. Including the Ni layer raises 44 Ti / 48 Ti of the mixtures. The mixtures (except for the one corresponding to KE3a-141) do not include the O/Si