Other mixing processes in CEMP-no stars
In Fig. 4.17, some observed evolved CEMP-no stars may also have experienced other mixing processes like thermohaline (cf. Sect. 2.4). As discussed, however, a significant fraction of CEMP-no stars may CEMP-not have experienced too much mixing, except the most evolved stars (cf. Fig. 2.6).
Also, it has to be noted that unevolved CEMP-no stars lie globally at similar positions than evolved CEMP-no stars in Fig. 4.17. If the internal mixing processes had a strong impact on the surface C/N and12C/13C ratios, we should probably see distinct groups of CEMP-no stars: the bulk of evolved CEMP-no stars on the one hand, the bulk of unevolved CEMP-no stars on the other hand. The fact that it is not the case may finally indicate that the composition of the evolved CEMP-no stars shown in Fig. 4.17 reflects quite well the composition of the cloud in which they formed.
4.5 The late mixing process in the source star
A solution to the C/N−12C/13C puzzle is to introduce alate mixing processin the source star, occurring between the H- and He-burning shell, about 200 yr before the end of the evolution. Be-low I give more details on this process and discuss how it can naturally produce a material with a high C/N ratio and a low12C/13C ratio, able to improve the fit between models and observations.
In Sect. 4.8, I investigate whether other models available in the literature can provide a solution.
This mixing process was investigated in Choplin et al. (2017b, page 159 of this thesis). The main points of the paper are summarized in this section.
30 40 50 60 70 80
T [MK]
10 -2 10 0 10 2 10 4 10 6 10 8
τ eq [y r]
MS He
C O
O/N C/N
12
C/
13C
Figure 4.18: CNO equilibrium timescales of the O/N, C/N, and12C/13C ratios as a function of the temperature. A one-zone model at densityρ =1 g cm−3 is used. The shaded areas show the ranges of duration for the various burning stages (main sequence, He-, C-, and O-burning) of the models presented in Table 4.4.
CHAPTER 4. MIXING IN CEMP-NO SOURCE STARS
Envelope
H-shell
He-shell
C-core
CNO cycl
e
16O
12C
14N
13C
Core carbon burning
t left ~ 100 yr
r [R ]
☉
0 550
Mr [M ]
☉
0 5 10 15 20
0.1 3.9 48
Envelope
H-shell
He-shell
CO-core
12C
16O 13C
14N CNO
cycl e
Figure 4.19:Schematic view of the late mixing process at work in the source star. The mixing starts during the core carbon burning phase. The curved black arrows show the region where it operates.
The scheme is at scale in mass. Corresponding radii are indicated.
4.5.1 General idea
Figure 4.18 shows the time it takes for the C/N, O/N and12C/13C ratios to reach their CNO equilibrium value in a H-burning zone at30 < T < 80 MK. Results are obtained using the one-zone model described in Sect. 4.2. Equilibrium values are reached quicker when the temperature increases. Whatever the temperature, 12C/13C reaches equilibrium∼ 10 times faster than C/N, and C/N reaches equilibrium100−1000times faster than O/N. In the H-burning shell of a com-plete stellar model, there is a gradient of temperature and the temperature30 .T .80MK. The global equilibrium timescale of the shell cannot be deduced directly from Fig. 4.18. However, the relative difference between the different timescale stays the same.
Let us now assume that some 12C is injected in a single burning zone atT = 30 MK which is at CNO equilibrium. The extra12C disturbs the CNO equilibrium. Fig. 4.18 tells us that after 2000 yr, 12C/13C will have reached back its equilibrium value while C/N and O/N will not. It means that if the H-burning shell of the massive star is burning at 30 MK and some12C is injected 2000 yr before the end of the evolution, then, at the pre-SN stage, the H-shell will have C/N above equilibrium and 12C/13C at equilibrium. The average temperature in the H-burning shell of a massive source star is about40MK. Then, to obtain a partially processed CN material, with C/N above equilibrium and12C/13C at equilibrium, some12C has to be injected in the H-burning shell
∼100−200yr before the end of the evolution. At this time, the source star burns carbon in its core.
For20−60Mmodels, the core carbon burning stage lasts for10−1000yr (grey area in Fig. 4.18).
4.5. The late mixing process in the source star
Table 4.4: Properties of the source star models: model label (column 1) initial mass (column 2), υini/υcrit (column 3), initial equatorial velocity (column 4), total lifetime (column 5), duration of the main sequence, helium, carbon, neon, oxygen, and silicon-burning phases (column 6−11), mass of the model at the end of the evolution (column12), remnant mass according to the relation of Maeder (1992, column13).
Model Mini υini/υcrit υini τlife τMS τHe τC τNe τO τSi Mfinal Mrem
[M] [km/s] [Myr] [Myr] [Myr] [yr] [day] [day] [day] [M] [M]
No rotation
20s0 20 0 0 8.93 8.02 0.79 978 168 318 3.1 19.98 1.88
32s0 32 0 0 5.78 5.24 0.48 124 22 47 0.6 31.94 2.98
60s0 60 0 0 3.81 3.44 0.33 15 7 7 0.5 59.80 6.35
Rotation
20s7 20 0.7 610 11.0 10.1 0.76 400 277 128 1.4 19.50 2.20
32s7 32 0.7 680 7.14 6.61 0.47 45 7 15 0.6 30.71 3.69
60s7 60 0.7 770 4.69 4.33 0.32 5 1 3 0.2 47.65 8.88
No rotation, late mix
20s0mix 20 0 0 8.93 8.02 0.79 993 - - - 19.98 1.88
32s0mix 32 0 0 5.78 5.24 0.48 157 - - - 31.94 2.98
60s0mix 60 0 0 3.81 3.44 0.33 18 - - - 59.80 6.35
Rotation, late mix
20s7mix 20 0.7 610 11.0 10.1 0.76 412 - - - 19.50 2.20
32s7mix 32 0.7 680 7.14 6.61 0.47 51 - - - 30.70 3.69
60s7mix 60 0.7 770 4.69 4.33 0.32 5 - - - 47.64 8.73
4.5.2 Implementation in source star models
This mixing process was investigated for a grid of six models whose characteristics are given in Table 4.4. Small differences exist between the input parameters of these models and the models of the previous section. First, when log(Teff) ≥ 3.95, the mass-loss rates are from Kudritzki &
Puls (2000), instead of Vink et al. (2001). Radiative winds are generally small at low metallicity so that no big impact is expected. Second, following the study on Al discussed in Sect. 4.2, the nuclear rates from the literature that minimize the production of Al are selected: Angulo et al.
(1999) for26Mg(p, γ)27Al, Cyburt et al. (2010) for27Al(p, γ)28Si and27Al(p, α)24Mg. Third,fenergin the expression ofDshear(Eq. 3.10) was taken equal to 1 instead of 4.
First, the models were computed normally (without late mixing) until the end of the central silicon-burning phase. The computation is stepped when the mass fraction of 28Si in the core is less than 10−8. For rotating models, the effects of rotation were taken into account until the end of the carbon burning phase. Last stages were computed without rotation. It saves a lot of computational time and leads to only very small differences in the abundance profiles since the duration of the last stages is short (∼1−300days, cf. Table 4.4) compared to the rotational mixing timescale. In a second step, I have computed again the end of the evolution for the six models while triggering the late mixing process∼200 yr before the end of the evolution (Fig. 4.19 for a schematic view). For these models, the evolution was stopped at the end of core carbon burning.
Last stages are very short and change only the composition of the most inner layers. It gives four categories of models: (1) no rotation, no late mixing, (2) no rotation, late mixing, (3) fast rotation, no late mixing and (4) fast rotation, late mixing.
To model the late mixing process in rotating models, the shear diffusion coefficientDshear is multiplied by a factor of 100 in between the H- and He-shell. In non-rotating models, an artificial and constant diffusion coefficient Dno rot = 109cm s−1 is set in the mixing zone. This is a typical value of the diffusion coefficient found in rotating models including late mixing. Although mod-eled through the shear diffusion coefficient, it is not assumed that the physical origin of the late mixing process is linked to the shear. Its possible physical origin is discussed in Sect. 4.5.4.
CHAPTER 4. MIXING IN CEMP-NO SOURCE STARS
1H
4He
14N
12C
16O
23Na
22Ne
27Al
24Mg
13C
14N
1H
4He
12C
16O
23Na
22Ne
27Al
24Mg
13C
Late mixing zone
Figure 4.20: Abundance profiles of the 20Mmodels withυini/υcrit = 0.7at the end of the core carbon-burning phase with no late mixing (left) and with late mixing (right). Shaded areas show the convective zones. The zone where the late mixing process occurs is indicated on the top.
2 1 0 1 2
[C/N]
0.5 1.0 1.5 2.0 2.5
log
12C/
13C
SunISM
CN eq
20s0mix W+SN 32s0mix W+SN 60s0mix W+SN 20s0mix W 32s0mix W 60s0mix W
2 1 0 1 2
[C/N]
0.5 1.0 1.5 2.0 2.5
log
12C/
13C
SunISM
CN eq
20s7mix W+SN 32s7mix W+SN 60s7mix W+SN 20s7mix W 32s7mix W 60s7mix W
Figure 4.21: Same as Fig. 4.17 but for the 20, 32 and 60Mmodels of Table 4.4 including the late mixing process and withυini/υcrit = 0(left) and 0.7 (right). The red square, diamond and triangle show the composition of the ejecta of the 20M model when the mass cut is equal toMα,MCO, andMrem, respectively.
4.5.3 Comparison with CEMP-no stars
When the late mixing process is included, additional12C and16O enter into the H-shell, boost-ing the CNO cycle and then releasboost-ing more energy. The H-shell becomes convective, extends in mass so that more He-burning products are engulfed. The fresh12C starts to be transformed into
13C and14N in the H-shell. However, the time remaining before the end of the evolution being short, the [C/N] equilibrium value of∼ −2.3is not reached. The right panel of Fig. 4.20 shows the abundance profile of the rotating 20Mmodel with late mixing, at the end of core carbon burn-ing. We see that the convective H-shell contains a lot of CNO elements, and has X(C)/X(N)> 1 while X(12C)/X(13C) is at equilibrium, around 4. This process builds a zone which is, at the end of evolution, partially processed by the CN cycle in the source star, where C/N is high and12C/13C at equilibrium.
Fig. 4.21 shows the ejecta of the non-rotating (left panel) and rotating (right panel) 20, 32 and 60Mmodels including the late mixing process. With increasing mass, the tracks in Fig. 4.21 are
4.5. The late mixing process in the source star
shifted to the left, away from observations. This is mainly due to the fact that higher-mass models have a higher temperature in the H-burning shell. This implies that the CN cycle operates faster.
In this case, the injected 12C is transformed more rapidly into14N. Then, the [C/N] ratio in the H-burning shell is closer to the equilibrium value (∼ −2) at the end of evolution. It finally implies that the ejecta of higher-mass models cannot reach high [C/N] ratios together with low 12C/13C ratios. There are several reasons that may make the late mixing process more likely to occur in
∼20Msource stars than in∼60Msource stars:
• In a60 M model, the late mixing process should occur very late in the evolution, so as to end up with a high C/N (see above). If it occurs too early, C/N has enough time to reach back equilibrium. It means that the time window for the late mixing to operate is shorter in a 60Mmodel than in a20Mmodel.
• In more massive stars, the mixing process should be extremely strong so as to compensate for the short time available.
• In more massive stars, the distance between the H- and He-burning shells is greater, so that the connection between the two shells might be less likely.
Overall, ∼ 20M source stars might be better candidates for the late mixing process, hence for reproducing the observations.
Fig. 4.21 shows that both the non-rotating and rotating 20Mmodels can reproduce the bulk of observations. These two kind of models show however important differences regarding other elements. In fact, the late mixing process changes the distribution of chemical species in the source star (Fig. 4.20) but in the models presented here, it implies further nucleosynthesis almost only for the elements8 12C,13C and14N. This is because the burning timescales for the other species considered in the network (e.g. O, Ne, Na, Mg, Al) are longer compared to the remaining time before the end of the evolution. For instance, there is little time for the Ne-Na cycle to operate and produce additional23Na in models including late mixing. Instead, a progressive mixing, achieved by rotation during the core helium burning stage can form extra 23Na (Sect. 4.3.2 and Fig. 4.7).
This is an important difference between non-rotating (little Na) and rotating models (high Na) including late mixing. Many CEMP-no stars are enriched in Na. It may suggest that, at least for a part of the CEMP-no star sample, two kind of mixing are needed: rotational mixing (for Na) and the late mixing process (for a high C/N with a low12C/13C).
4.5.4 Physical origin
In the present work, the late mixing process is triggered artificially. It has to be noted that in some cases, similar events occur naturally. Indeed, various authors reported sudden ingestion events of H-burning material into the He-burning core or shell in low or zero metallicity mas-sive stellar models (with or without rotation, Hirschi 2007; Ekström et al. 2008; Heger & Woosley 2010; Limongi & Chieffi 2012, see also Sect. 4.8). Although observed in some stellar models, the occurrence conditions and physical process(es) responsible for such events remain unknown. No specific behaviour is observed with any stellar parameter.
The treatment of the convection in stellar evolution codes may impact the shell/shell inter-action or the core/shell interinter-action and thus the occurrence of the late mixing event. In GENEC, the convective boundaries are determined using the Schwarzschild criterion. The boundaries of the convective zones are sharp (step functions). During the main sequence and core He-burning phase, the convective core is extended using a penetrative overshoot. The overshoot is applied neither for the more advanced phases of stellar evolution, nor for the intermediate convective shells. This prescription probably does not capture the whole physics of convection (Arnett et al.
8This process may also form heavy elements through neutron captures, see Sect. 4.8.
CHAPTER 4. MIXING IN CEMP-NO SOURCE STARS
Figure 4.22: Radial profile of the averaged atomic weightA¯at the lower (left) and upper (right) convective boundary regions of the C-burning shell of a 15Mmodel. The radius of each profile is shifted such that the boundary position coincides with the boundary position of the vhrez model. The symbols denote the mesh points. The black profile is from GENEC while the other profiles are from 3D hydrodynamic simulations of various resolutions. The range of radius shown corresponds approximately to the range of mass coordinates 1.2−1.8M (figure from Cristini et al. 2017).
2015). Multi-dimension hydrodynamics numerical simulations of convection in deep stellar inte-rior show that the chemical composition of each side of the convective boundary makes a smooth transition and is not a step function. (Herwig et al. 2006; Meakin & Arnett 2007; Arnett & Meakin 2011; Cristini et al. 2017). Fig. 4.22 shows a comparison between 1D code (GENEC) and 3D simu-lations, for the carbon burning shell. We see that in 3D, the carbon shell extends further in mass compared to 1D models. Multi-D simulations of H/He burning-zones during earlier stages (e.g.
core He-burning stage) do not exist since they are computationally too expansive, mainly because the burning timescales are long.
It might be that improving the way convection is treated in classical 1D codes to follow more closely the behavior observed in multi-dimensional simulations strengthens the exchanges be-tween the H- and He-burning shells. This could naturally induce the creation of the late mixing zone. If so, the late mixing invoked in this work would result from an overly poor description of the convective boundaries in 1D stellar evolution models.