2 0
[X/H]
vini
/
vcritC N O F Ne Na Mg Al Si
[
12C/
13C]
0.70.5 0.40.3 0.20.1 0.0
Figure 4.8: Composition of the wind of 20M models atZ = 10−5 with various initial rotation rates. The dashed black pattern (superimposed with the red pattern) shows the composition of the ISM. Black circles and red triangles show main-sequence and giant CEMP stars respectively, with [Fe/H] < −3(Table 4.2). Recognized CEMP-r, -s and -r/s are excluded. Abundances with upper/lower limits are not plotted. The typical uncertainty is±0.3dex.
mostly during the main sequence phase because of its longer duration (the chemical species have more time to be transported). When reaching the stellar surface, chemical species are potentially expelled through winds. In these models however, the mass loss metallicity relation (M˙ ∝Z0.85, cf. Sect. 3.3.5) plays a major role and thus prevents significant radiative mass loss episodes. Also the mechanical mass loss (cf. Sect. 3.3.5) stays small for these models. The 20 M model with υini/υcrit = 0.7 loses about 0.12 M through mechanic mass loss and 0.6M through radiative mass loss. The total mass lost through winds is < 1Mfor all the 20Mmodels. We note that the mass loss may be strongly enhanced for higher mass stars.
4.3.3 Composition of the ejecta
The effect of varying the initial rotation, mass cut, dilution, efficiency of rotational mixing, mass and metallicity on the chemical composition of the source star ejecta is considered.
Initial rotation
Composition of the wind. Fig. 4.8 shows the [X/H] ratios in the wind of the models. For all models, the wind contribution is less than 1 M and comes from the H-rich region. The non-rotating model (red) is superimposed with the ISM pattern since the ejected material has kept exactly the same composition as the ISM. As rotation increases, the wind is overall more and more enriched in a material processed by the CNO cycle, Ne-Na and Mg-Al chains (cf. Sect. 4.3.2). For the faster rotators, the12C/13C ratio is equal to the CNO equilibrium value of∼ 4(equivalent to [12C/13C]=−1.35).
CHAPTER 4. MIXING IN CEMP-NO SOURCE STARS
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0
[X/H]
vini/vcrit
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
0.70.5 0.40.3 0.20.1 0.0
Figure 4.9: Same as Fig. 4.8 but for the composition of all the H-rich material. This material in-cludes the wind material plus the material from a supernova with a mass cut set at Mα. Mα
corresponds to the bottom of the H-envelope (the bottom of the H-envelope is defined where the
1H mass fraction drops below10−3). The dashed orange line shows theυini/υcrit = 0.4model with the rate of the27Al(p, γ)28Si reaction from Cyburt et al. (2010) instead of Iliadis et al. (2001).
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0 2
[X/H]
vini/vcrit
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
0.70.5 0.40.3 0.20.1 0.0
Figure 4.10: Same as Fig. 4.9 but for the composition of all the H-rich + He-rich material. This material includes the wind material plus the material from a supernova with a mass cut set at MCO.MCOcorresponds to the bottom of the He-shell (the bottom of the He-shell is defined where the4He mass fraction drops below10−3).MCOalso corresponds to the top of the CO-core.
4.3. Massive source stars with rotation
7.0 M☉ 7.58 M☉ 7.77 M 7.9 M☉ ☉8 M☉
12C
16O
22Ne
14N
23Na
24Mg
27Al
13C
4He 1H
Figure 4.11: Abundance profile of the 20 M model with Z = 10−5 and υini/υcrit = 0.4 at the pre-SN stage. Dashed vertical lines corresponds to the mass cuts of Fig. 4.12.
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0
[X/H]
Mcut=8.0 M¯
Mcut=7.9 M¯ Mcut=7.77M¯
Mcut=7.58M¯ Mcut=7.0 M¯
C N O F Ne Na Mg Al Si
[
12C/
13C]
ISM
Figure 4.12: Composition of the ejecta of a 20M model with Z = 10−5 andυini/υcrit = 0.4 for various mass cuts taken in between the H-shell and He-shell. These mass cuts are also represented in Fig. 4.11.
CHAPTER 4. MIXING IN CEMP-NO SOURCE STARS
Composition of the H-rich material. Fig. 4.9 shows the chemical composition of the ejecta when considering the wind plus all the material above the bottom of the H-rich region. In this case, Mcut = Mα, where Mα is the mass of the helium core set where the mass fraction of 1H drops below 10−3. From the top left panel of Fig. 4.6 we see that it corresponds to a total ejected mass of
∼12−14M, depending on the model. The typical CNO pattern appears for all the models (more N, less C and O) but the sum of CNO elements increases with rotation, as a result of12C and16O having diffused to the H-burning shell. [Na/H] spans∼2dex while [Mg/H], [Al/H] and [Si/H]
do not vary more than 0.5 dex. Mg and Al are overproduced with rotation (Fig. 4.7) but only in the He-rich region, which is not consider in the yields of Fig. 4.9.12C/13C is very close to the CNO equilibrium value.
Composition of the H-rich + He-rich material. Fig. 4.10 is similar as Fig. 4.9 but it considers the wind plus all the material above the bottom of the He-rich region. In this case, Mcut = MCO. The total ejected mass is about15−16M, depending on the model (Fig. 4.5). Compared to the previous case, the additional ∼ 2 M ejected are H-free, so that is raises a bit the [X/H] ratios (by < 0.5 dex). The CNO pattern is reversed compared to Fig. 4.9 because in He-burning regions,
14N is depleted while12C and 16O are abundant (Fig. 4.6). No or very little little additional 14N is added to the ejecta compared to Fig. 4.9. The ratios containing He-burning products ([Ne/H], [Na/H], [Mg/H] and [Al/H]) are largely boosted compared to Fig. 4.9. They also greatly increase with initial rotation as a result of the back-and-forth mixing process. In He-burning regions, 13C is destroyed by13C(α, n)16O so that the 12C/13C ratio is largely enhanced compared to the case where only H-rich ejecta is considered. Considering deeper mass cuts raise again C/H, O/H, Ne/H, Mg/H, and12C/13C but, overall, it does not change significantly the trends of Fig. 4.10.
Mass cut in the intershell region
Fig. 4.12 shows the chemical composition of the wind plus an ejecta defined with various mass cuts, for theυini/υcrit = 0.4model. The 5 considered mass cuts are represented in Fig. 4.11 which shows the abundance profile of the 20Mmodel withυini/υcrit = 0.4at the pre-SN stage. The zone between7.8.Mr.8Mcorresponds to the intershell region, in between the H- and He-burning shells. AsMcut decreases, deeper layers are ejected and we move progressively from the H-rich only ejecta to a mixed H+He ejecta. Varying the mass cut from 7 to 8Mleads to a quick increase of the [X/H] ratios, up to∼5dex for [C/H]. It illustrates the high sensitivity of the yields on the mass cut when varying it around the intershell region.
Dilution of the source star ejecta with ISM
The material ejected from the star can be mixed with the material in the ISM. The effect of the dilution depends on the composition of the ISM, which is not known at low metallicity (a choice has nevertheless to be made when computing low metallicity models, as done in this work).
Generally, in the case of the scenario proposing that CEMP-no stars were formed from one or very few source stars, we can probably just guess that the ISM is either metal-free or very metal-poor.
Table 4.1 reports how are affected the different abundance ratios in the source star ejecta while considering either a dilution with a poor ISM or a free ISM. A dilution with a metal-free ISM adds some H so that the [X/H] ratios are affected (where X refers to metals). On the other hand, such an ISM does not modify the [X/Fe] (where X refers to metals) or the isotopic ratios. In almost all the cases, when the [X/H] or [X/Fe] ratios are affected by dilution with ISM, they are reduced (cf. Fig. 4.13 and next paragraph). This is because in the source star ejecta, the H and Fe abundances are similar to the H and Fe abundances in the ISM while light metals (C to Al) are generally strongly overproduced by the source star compared to what is present in the ISM.
4.3. Massive source stars with rotation
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0
[X/H]
C N O F Ne Na Mg Al Si
[12C/13C]
ISM 01
10100 100010000
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0 2
[X/H]
C N O F Ne Na Mg Al Si
[12C/13C]
ISM 01
10100 100010000
Figure 4.13:Left panel: composition of the H-rich ejecta of the 20Mmodel withυini/υcrit= 0.7for various dilution factorsD. TheD = 0pattern corresponds to the green pattern in Fig. 4.9. Right panel: same as left panel but for H-rich + He-rich ejecta. TheD = 0pattern corresponds to the green pattern in Fig. 4.10.
Table 4.1:Effect of diluting the source star ejecta with two different kinds of ISM: metal-poor and metal-free. Different kinds of abundance ratios are considered. X refers to metals.
[X/H] [X/Fe] isotopic ratios
Metal-poor ISM towards ISM value towards ISM value towards ISM value Metal-free ISM towards ISM value unchanged unchanged
In this work, when diluting the source star ejecta with ISM, I consider that the ISM material is the same than the ISM material used to form the source star (α-enhanced ISM, cf. Sect. 3.3.4 for details on the initial composition). To be more quantitative, a dilution factorDcan be defined as
D= MISM
Mej (4.3)
withMejthe total mass ejected by the source star andMISM the mass of initial ISM added to the massive star ejecta. The left panel of Fig. 4.13 shows the chemical composition of the wind plus the H-rich ejecta for theυini/υcrit = 0.7model. Different dilution factors are considered. D= 100 means that there is 100Mof ISM for 1Mof source star ejecta. AsDincreases, the composition is shifted towards the ISM composition. The right panel of Fig. 4.13 is similar but for the H-rich + He-rich ejecta (like in Fig. 4.10). In this case, the amount of light elements is more important in the source star ejecta so that higher Dvalues are needed to reach back the ISM pattern. The ISM considered here isα-enhanced, which explains why the [C/H], [O/H]... ratios are enhanced compared to the [N/H], [F/H]... ratios. Also, in this ISM, [12C/13C]'0.5, which corresponds to
12C/13C= 300(cf. Sect. 3.3.4). A more extended discussion about the12C/13C ratio can be found in Sect. 4.4.
At the present day, the dilution factor cannot be strongly constrained. The point explosion or Sedov-Taylor explosion can be used as an approximation to estimate how fast will a shock wave travel and what would be left behind it. For a standard explosion energy of E51 = 1(E51is the SN energy in units of 1051 ergs) and typical ISM densities, the ejecta will be mixed with about MISM = 104 Mof ISM (Cioffi et al. 1988; Ryan et al. 1996; Wehmeyer et al. 2015). For the models of Fig. 4.13, the total mass ejected is between ∼ 12 and∼ 16 M. Taking104 M of ISM leads to a dilution factor of104/16 < D < 104/12, which gives 600 . D . 800(in between the cyan and blue patterns in Fig. 4.13). This would be for standard explosions energies. In the case of a
CHAPTER 4. MIXING IN CEMP-NO SOURCE STARS
low-energetic supernova withE51 = 0.1for instance,60 .D.80(i.e. Dis divided by 10, this is becauseD∼MISM ∼E510.95, Ryan et al. 1996, their Sect. 5.6.1).
Another way to constrain the dilution factor may be the surface Li abundance of the CEMP-no stars. We can assume that Li is completely destroyed in massive stars so that X(Li)ej, the Li mass fraction in the source star ejecta is 0. The Li mass fractionX(Li)CEMP in the CEMP-no star natal cloud (possibly different than the value observed today) is then
X(Li)CEMP = MejX(Li)ej+MISMX(Li)ISM
Mej+MISM = MISMX(Li)ISM
Mej+MISM (4.4)
whereMejis the mass ejected by the source star, andX(Li)ISM the Li abundance in the ISM. The dilution factor can then be expressed as
D= MISM
Mej = X(Li)CEMP
X(Li)ISM−X(Li)CEMP
. (4.5)
We can suppose that the Li abundance in the initial ISM is equal to the WMAP value ofA(Li)ISM = 2.72(Cyburt et al. 2008). If, as a first guess, we consider that in situ processes changing the Li abun-dance did not occur during the CEMP-no star life, we can takeX(Li)CEMP equal to the observed Li abundance. If the CEMP-no star has no Li at its surface,D= 0and the CEMP-no star is made of pure source star ejecta. If the Li abundance is high, more ISM is needed to form the CEMP-no star.
The maximal detected A(Li) for CEMP-no stars is about 2.1 (i.e. around the Spite Plateau value Spite & Spite 1982). It leads to a maximal dilution factor of Dmax ∼ 0.3, i.e. all CEMP-no stars would be made of almost pure source star ejecta, even the most Li-rich.
This estimation ofDstays correct as long as (1) in situ processes changing the Li abundance did not occur in CEMP stars and (2) the Li ISM abundance is indeedA(Li)ISM = 2.72(value from WMAP). If instead, A(Li)ISM = 2.2 for instance, Dmax ∼ 4, i.e. the source star ejecta may still largely dominate compared to the ISM (see Fig. 4.13). The main uncertainty in this method are the possible internal processes changing the surface Li abundance of the CEMP-no stars. Korn et al. (2009) have used models including atomic diffusion to estimate by how much the surface Li abundance of the dwarf CEMP-no star HE 1327-2326 was depleted since its birth. At maximum, Li was depleted by 1.2 dex. It would correspond to an initial Li ofA(Li)ini < 1.82for HE 1327-2326 and lead to a small Dvalue. Overall, this method of guessingDis uncertain so precaution is required. It nevertheless suggests very small dilution factors. This is inconsistent with the high Dvalues guessed from the Sedov-Taylor theory assuming standard explosions energies. It might nevertheless be more consistent with low energetic SNe (E51 <1), that give smallerDvalues (for E51= 0.1however, there is still 1 order of magnitude of difference at least).
Efficiency of the rotational mixing
The fenerg parameter in theDshear expression (Eq. 3.10) was taken equal to 4 in these mod-els. It is consistent with the surface N/H enrichments of observed10−20Mrotating stars (cf.
Sect. 3.3.1).fenerg= 4corresponds to a critical Richardson number6Ric= 2.fenerg= 1(Ric= 0.5) is also a reasonable choice, likely consistent with the observations (cf. Sect. 3.3.1).
Fig. 4.14 shows the effect of changingfenergfrom 1 to 4. The 2 top panels show the H-rich (left) and H-rich + He-rich ejecta (right) of the 20 M models with υini/υcrit = 0.2 and with various fenerg. The yields are barely affected when changingfenerg. The same plots for the 20M model withυini/υcrit= 0.7are shown below. In this case, the effect is much larger and leads to differences of1−1.5dex at maximum. Thefenerg = 1model withυini/υcrit = 0.7has similar yields than the fenerg = 4 model with υini/υcrit = 0.3. Changing fenerg does not change the general trends but shifts the yields upward or downward, for a given initial rotation. To obtain similar yields as the
6Physical values ofRicare likely between 0.25 and 2, cf. Sect 3.3.1.
4.3. Massive source stars with rotation
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0
[X/H]
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
fenerg=1 fenerg=2 fenerg=4
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0 2
[X/H]
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
fenerg=1 fenerg=2 fenerg=4
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0
[X/H]
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
fenerg=1 fenerg=2 fenerg=4
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0 2
[X/H]
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
fenerg=1 fenerg=2 fenerg=4
Figure 4.14: Effect of varying the efficiency of rotational mixing (fenerg) on the yields. The top panels show the 20M models withυini/υcrit = 0.2. The bottom panels show the 20M models with υini/υcrit = 0.7. The left panels show the H-rich ejecta. The right panels show the H-rich + He-rich ejecta.
υini/υcrit = 0.7,fenerg = 4 model while settingfenerg = 1, it is probably needed to raiseυini/υcrit up to about 1. Thefenerg ∼Ricparameter is important, especially for fast rotators, but its accurate value is not known.
Mass
Figure 4.15 shows the yields of 20, 40 and 60 M models withυini/υcrit = 0.4at Z = 10−5. The final yields are rather similar. The 60Mproduces more N because its H-shell is more active than in lower mass models. In the H-rich layers, more Na is produced in the 20 M models because the back-and-forth mixing process (Fig. 4.1) is more efficient in lower masses. It is mainly because the process has more time to operate due to the longer duration of the core helium burning stage. Also, Al and Si are overproduced in the H-rich layers of the 40 and 60 M because of the higher H-burning temperature, increasing the efficiency of the Mg-Al-Si chain. The yields of the 60 M in the H-rich + He-rich layers show significant differences compared to the other models (right panel). It is explained by the fact that the He-burning shell becomes convective in the 20 and 40 M models while it does not for the 60 M model. In the 60M model, the H-burning shell is very active and therefore limits the activation of the He-burning shell. In the 20 and 40 M models, while becoming convective, the He-shell engulfs some14N from the H-rich region. It boosts the production of F and Na through the chains 14N(n, γ)15N(α, γ)19F and
CHAPTER 4. MIXING IN CEMP-NO SOURCE STARS
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0
[X/H]
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
20 M¯ 40 M¯ 60 M¯
6 7 8 9 10 11 12 13 14 Atomic Number
4 2 0 2
[X/H]
ISM
C N O F Ne Na Mg Al Si
[12C/13C]
20 M¯ 40 M¯ 60 M¯
Figure 4.15: Composition of the H-rich (left panel, same as Fig. 4.9) and H-rich + He-rich (right panel, same as Fig. 4.10) ejecta ofZ = 10−5,υini/υcrit = 0.4models with different initial masses.
6 7 8 9 10 11 12 13 14 Atomic Number
6 4 2 0 2
[X/H]
C N O F Ne Na Mg Al Si
[12C/13C]
Z=10−5 Z=0
6 7 8 9 10 11 12 13 14 Atomic Number
6 4 2 0 2
[X/H]
C N O F Ne Na Mg Al Si
[12C/13C]
Z=10−5 Z=0
Figure 4.16: Same as Fig. 4.15 but for 20M models withυini/υcrit = 0.4and with two different initial metallicities.
14N(α, γ)18F(e+νe)18O(α, γ)22Ne(n, γ)23Ne(e−ν¯e)23Na. The neutrons required to activate this chain come from22Ne(α, n).
Metallicity
Figure 4.16 shows the yields (H-rich: left panel, H-rich + He-rich: right panel) of the 20M
models with υini/υcrit = 0.4atZ = 10−5 (green pattern) andZ = 0 (magenta). The two models are computed with the same physics. The [C/H], [N/H] and [O/H] ratios do not change by more than 0.5 dex from theZ = 10−5 theZ = 0model. The reason is that the transport by rotation of
12C and16O from the convective He-burning core to the convective H-burning shell operates at a similar efficiency in theZ = 0model. In the H-rich ejecta (left panel), the elements from Ne to Si are much less abundant in the Z = 0 model compared to theZ = 10−5 model. Considering also the He-rich ejecta raises considerably the abundances of these elements in both models. The exception is for the [Si/H] ratio in the Z = 0 model, which stays several dex below the [Si/H]
ratio of theZ = 10−5model. The differences are mainly due to the fact that the H-burning shell of theZ = 0model is more active, which limits the growth of the convective He-burning core (at the middle of the core He-burning phase, the size of the convective He-cores are 3.9Mand 2.7Min