The s-process in CEMP source stars
5.2 A new grid of massive stars with rotation and s-process
Figure 5.1:Final mass fractionX(normalized to solar) of heavy elements in a single burning zone atT = 300 MK and ρ = 500 g cm−3. The initial mass fraction of56Fe is10−7. The initial mass fraction of22Ne is varied from10−4 to 0.05.
more abundant, the16O(n, γ)17O(α, γ)21Ne chain is boosted, so that less neutrons are available for heavy elements.
5.2 A new grid of massive stars with rotation and s-process
Grids of massive stellar models including rotation and full s-process network are needed in order to investigate the role of such stars in the chemical enrichment of the Universe. To date, only Frischknecht et al. (2016) and very recently Limongi & Chieffi (2018) have provided such grids. An important part of my work was to compute a new grid of massive rotating star with full s-process, so as to extend the study of Frischknecht et al. (2016). The final goal being to gain knowledge on the nature of such massive stars by comparing their yields to the abundances of observed low-mass metal-poor stars enriched in s-elements.
In Choplin et al. (2018) we computed a new grid of massive stars with initial masses between 10 and 150M, at a metallicityZ = 0.001in mass fraction (corresponding to [Fe/H]=−1.8). The models were computed either without rotation or with υini/υcrit = 0.4. We considered only one metallicity but significantly extended the range of mass compared to the study of Frischknecht et al. (2016), that focused on15−40Mmodels. We also investigated the impact of a faster initial rotation and a different17O(α, γ)21Ne reaction rate. Most of the physical ingredients of this grid are the same than for the models discussed previously. The main change is the size of the nuclear network that now comprises 737 species, from1H to212Po instead of 31 species (cf. Sect 3.3.3).
The paper describing the models is directly included in the thesis (in the present section). It was very recently accepted in A&A and I have therefore almost no discussion to add yet. Before the paper itself, I discuss several aspects that were not published: several additional physical ingre-dients and some obstacles I had to overcome. In Appendix A.5, additional parameters, allowing to quantify the efficiency of the s-process, are defined and tabulated for the new grid of models.
The table was not published in the paper but it may be useful to have these quantities for future comparisons with other models.
CHAPTER 5. THE S-PROCESS IN CEMP SOURCE STARS
Figure 5.2: Same as Fig. 5.1 but when varying the initial mass fraction of 16O from 0.2 (solid pattern) to 0.5 (dot-dashed pattern).
5.2.1 Nuclear network and reaction rates
As shown in Table 2 of the paper below, 8 important nuclear reaction rates were updated com-pared to the study of Frischknecht et al. (2016). Originally, the reaction rate format in stellar evolu-tion codes is the following: one table for each reacevolu-tion rate with two columns, one for the tempera-ture, one for the associated rate. Then, interpolations are done in these tables to evaluate the rates at the desired temperatures. With large networks, it is convenient to use analytical reaction rates such as in the REACLIB format (Cyburt et al. 2010) in order to save computational time. Such a format allows to express a reaction rate withnsets of 7 parametersa0, .., a6. For 2-body reactions, it yields is respectively equal tohσviNA2 andλ, whereλrepresents the photodisintegration orβ-decay rate.
If just the standard tabulated rate exists, one has to find theaparameters that allow to fit correctly the rate. A leastsquare method is used to estimate these parameters from a temperature-rate table.
n > 1is often required to reach a reasonable accuracy. Finding the aparameters can sometime be challenging, mainly because of the large range of temperature to be covered (several orders of magnitude, it depends on the reactions). Once the a parameters are determined for the for-ward reaction, the arev parameters for the reverse reaction can be easily calculated (Rauscher &
Thielemann 2000).
Best et al. (2013) provided, in the tabular form, new rate measurements for the17O(α, n)20Ne and the 17O(α, γ)21Ne reactions, that are of crucial importance for the s-process in massive stars.
I used the fitting method described in Rauscher & Thielemann (2000, also nucastro.org) to con-vert these tabulated rates into theREACLIB format. For the two fits, I found thatn = 3provides satisfactory results: the final deviation is less than 5 % (Fig. 5.3, only one of the two fit is shown).
5.2. A new grid of massive stars with rotation and s-process
10 -2 10 -1 10 0 10 1 10 2
10 -40 10 -34 10 -28 10 -22 10 -16 10 10 10 10 10 10 10 10 10 -10 14 20 26 32 38 -4 2 8
Ra te [c m
3m ol
−1s
−1]
17O( α,γ )
21Ne rate Best+13 rate Best+13 (fit)
contrib 1 contrib 2 contrib 3
10 -2 10 -1 10 0 10 1 10 2
Temperature [GK]
10 0 5 5 10
deviation (%)
Figure 5.3: Rate of the 17O(α, γ)21Ne reaction. The thick black line corresponds to the recom-mended values tabulated in Best et al. (2013). Dashed lines show the different contributions, which were fitted according to the method described in Rauscher & Thielemann (2000, also nucastro.org).
Three different contributions (n= 3, see Eq. 5.1) were found to provide an acceptable fit. The thin red line shows the sum of the 3 contributions. The deviation from the original tabulated rate (Best et al. 2013) is shown in the bottom panel.
5.2.2 TheµandΩprofiles
When first trying to reproduce the results of Frischknecht et al. (2016), I found significantly different results: many s-elements were underproduced by a factor of 100 in the new models.
It was caused by strong oscillations of the Dshear coefficient in between the H- and He-burning zones, during the core He-burning stage. The green profile in the left panel of Fig. 5.4 shows such oscillations. The low values of Dshear at Mr ' 7.5 strongly reduces the exchanges of material between the He-core and the H-shell, leading to a smaller synthesis of primary 14N and 22Ne (Fig. 5.4, right panel, green line). SuchDshear oscillations are likely not physical since their shape change or disappear when changing the model resolution. An example is shown by the blue profiles in Fig. 5.4: the resolution of this model (res-model in Fig. 5.4) is reduced compared to the green model (res+model) but it is still enough to see the eventualDshearoscillations. In this case, theDshear does not oscillate so that the mixing is not cut and more14N and22Ne are synthesized compared to the green model (Fig. 5.4, right panel). While the changes induced by the presence or the absence of oscillations are not huge for 14N and 22Ne (factor of about 5), they are much more significant for s-elements (factor of about 100 at maximum, as shown in Fig. 5.5). Models of
CHAPTER 5. THE S-PROCESS IN CEMP SOURCE STARS
Mr [M ]
☉
res+SMO res+
res-SMO Yc = 0.5
res-Dshear [cm2 s-1 ]
res+SMO res+
res-SMO Yc = 0.2
Mr [M ]
14 N,22 Ne [mass frac.]
14N
22Ne
☉
res-Figure 5.4: Left panel: Dshear coefficient between the He-core and H-shell. Right panel: internal mass fraction of 14N and22Ne. Models shown are rotating 25 M atZ = 10−3, during the core helium burning phase (the central mass fraction of4He is 0.5 on the left panel and 0.2 on the right panel). Shaded area show convective zones. res+models (black and green) are computed with high resolution (about twice more shells thanres- models). SMOmodels (black and red) include the smoothing technique (see text and Appendix A.4).
30 40 50 60 70 80
Atomic number (Z) 2
1 0 1
[X/H]
res+
res-Figure 5.5:[X/H] ratios in the ejecta of the green (high resolution) and blue (low resolution) mod-els of Fig. 5.4.
5.2. A new grid of massive stars with rotation and s-process
Frischknecht et al. (2016) are similar to the blue lines in Fig. 5.4 and 5.5 while new models to the green lines.
To improve the stability of the code and find similar results when changing the mesh number, I improved the way of calculatingDshear(Eq. 3.10), by trying to better evaluate the derivative ofµ andΩ, that appeared to be responsible for the oscillation of theDshearcoefficient. The oscillation problem is solved if properly smoothing theµandΩprofiles when calculating their derivatives (see Appendix A.4 for more details). If applied, this technique gives similar results when chang-ing the mesh number (see Fig. 5.4, black and red profiles). It also gives similar s-process yields compared to the models of Frischknecht et al. (2016).
A&A 618, A133 (2018)
https://doi.org/10.1051/0004-6361/201833283 c
ESO 2018