The $s$ process: Nuclear physics, stellar models, and observations

Nucleosynthesis in the $s$ process takes place in the He-burning layers of low-mass asymptotic giant branch (AGB) stars and during the He- and C-burning phases of massive stars. The $s$ process contributes about half of the element abundances between Cu and Bi in solar system material. Depending on stellar mass and metallicity the resulting $s$-abundance patterns exhibit characteristic features, which provide comprehensive information for our understanding of the stellar life cycle and for the chemical evolution of galaxies. The rapidly growing body of detailed abundance observations, in particular, for AGB and post-AGB stars, for objects in binary systems, and for the very faint metal-poor population represents exciting challenges and constraints for stellar model calculations. Based on updated and improved nuclear physics data for the $s$-process reaction network, current models are aiming at an ab initio solution for the stellar physics related to convection and mixing processes. Progress in the intimately related areas of observations, nuclear and atomic physics, and stellar modeling is reviewed and the corresponding interplay is illustrated by the general abundance patterns of the elements beyond iron and by the effect of sensitive branching points along the $s$-process path. The strong variations of the $s$-process efficiency with metallicity bear also interesting consequences for galactic chemical evolution.

Figure 1

Illustration of the neutron-capture processes responsible for the formation of the nuclei between iron and the actinides. The observed abundance distribution in the inset shows characteristic twin peaks. These result from the nuclear properties where the $s$- and $r$-reaction paths encounter magic neutron numbers. Note that a $p$ process has to be invoked for producing the proton-rich nuclei that are not reached by neutron-capture reactions. For details see discussion in text.

Figure 2

The characteristic product of cross section times $s$-process abundance $⟨\sigma ⟩N_s$ plotted as a function of mass number. The thick solid line represents the main component obtained by means of the classical model, and the thin line corresponds to the weak component in massive stars (see text). Symbols denote the empirical products for the $s$-only nuclei. Some important branchings of the neutron-capture chain are indicated as well.

Figure 3

$R$-matrix analysis of the second resonance in bismuth. The dashed line corresponds to the yield calculated with the resonance parameters from the ENDF/B-VI.8 evaluation which exhibits the effect of neutron sensitivity in previous data.

Figure 4

Nucleosynthesis yields between Fe and Nb showing the final $s$-process yields after shell C burning for a $25M_{\odot }$ star with solar metallicity. To illustrate the combined effect of new cross sections for ${}^{58}\mathrm{Fe}$, ${}^{59}\mathrm{Co}$, ${}^{64}\mathrm{Ni}$, and ${}^{63,65}\mathrm{Cu}$ the yield is plotted relative to the case obtained with the previous cross sections of 32. Even and odd Z elements are distinguished by black and open symbols, respectively. The thin lines demonstrate the uncertainties stemming from the extrapolation of the measured cross sections to higher and lower energies.

Figure 5

Stellar enhancement factor (SEF) for the ${}^{187}\mathrm{Os}(n,\gamma ){}^{188}\mathrm{Os}$ reaction. The first ten excited states in ${}^{187}\mathrm{Os}$, up to an excitation energy of 260 keV, have been included in the calculation. The difference between the results obtained with a spherical and a deformed optical model potential for the neutron-nucleus interaction could be used for estimating the uncertainties of the SEF results.

Figure 6

Uncertainties of the stellar ($n,\gamma$) cross sections for $s$-process nucleosynthesis. These values refer to a thermal energy of $kT=30\mathrm{keV}$, but may be considerably larger at lower and higher temperatures.

Figure 7

Schematic layout and main parameters of the Frankfurt intense neutron source (see text).

Figure 8

The $r$-process abundances (open squares) obtained via the $r$-process residual method, $N_r=N_{\odot }-N_s$, using the classical and stellar $s$-process model. The $r$-only nuclei are represented by solid squares. ($N_i$ relative to $\mathrm{Si}\equiv {10}^6$). From 26.

Figure 9

Structural characteristics vs the age of an AGB model with initial mass $M_{\mathrm{ini}}^{\mathrm{AGB}}=2$ $M_{\odot }$ and solar metallicity. Upper panel, top to bottom: Temporal evolution of the mass coordinates of the inner border of the convective envelope, the mass location of maximum energy production in the H-burning shell, and the maximum energy production within the H-depleted core. During each interpulse period, the flat segment of the lowest line corresponds to the location of the radiative burning of the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction in the pocket. Lower panel: Temporal evolution of the H-burning and He-burning contributions to luminosity. From 92.

Figure 10

The formation of the ${}^{13}\mathrm{C}$ pocket according to 328. The sequence of the panels shows the evolution of the chemical composition in the transition zone between the H-rich envelope and the H-exhausted core. The various lines represent the abundances of H (crosses), ${}^{12}\mathrm{C}$ (dotted), ${}^{13}\mathrm{C}$ (solid), and ${}^{14}\mathrm{N}$ (dashed). (a) The TDU just occurred and the convective envelope is receding. (b) Production of ${}^{13}\mathrm{C}$ by proton capture on the abundant ${}^{12}\mathrm{C}$ starts in the hotter region. (c) Some ${}^{14}\mathrm{N}$ is also produced, and (d) the ${}^{13}\mathrm{C}$ (and ${}^{14}\mathrm{N}$) pocket is fully developed.

Figure 11

Top panel: Theoretical results of $[\mathrm{El}/\mathrm{Fe}]$ vs atomic number at the last TDU episode in the envelope of an AGB star with initial mass $M=1.5M_{\odot }$ and $[\mathrm{Fe}/\mathrm{H}]=0$. Bottom panel: The same as the top panel but $[\mathrm{Fe}/\mathrm{H}]=-0.5$. Adapted from 162 and 50.

Figure 12

Top panel: Theoretical results of the $s$-process index $[\mathrm{hs}/\mathrm{ls}]$ as a function of $[\mathrm{Fe}/\mathrm{H}]$ for AGB models of initial mass $M=1.5M_{\odot }$ and a wide range of ${}^{13}\mathrm{C}$-pocket efficiencies. Spectroscopic observations are plotted for post-AGB stars (solid triangles, 359; 285; 292, 291), Ba stars (large open squares, 10; medium open squares, 313; small open squares, 215), carbon stars (large solid squares, 395; medium solid squares 6; small solid squares 95), CEMP-$s$ and CEMP-$s/r$ stars (solid diamonds are main-sequence turn-off stars; solid triangles are giants stars, see text for references). Bottom panel: Theoretical results of the $s$-process index $[\mathrm{Pb}/\mathrm{hs}]$ vs $[\mathrm{Fe}/\mathrm{H}]$. Spectroscopic observations: CEMP-$s$, CEMP-$s/r$, and galactic Ba stars for which Pb abundances have been reported. Symbols are the same as in the top panel. Typical error bars are indicated in the top left corner of the panels.

Figure 13

Theoretical predictions of the $s$-process index $[\mathrm{hs}/\mathrm{ls}]$ vs $[\mathrm{Fe}/\mathrm{H}]$ for AGB models with initial mass $M=1.3M_{\odot }$, a range of ${}^{13}\mathrm{C}$-pocket efficiencies, and an initial $r$-process enrichment $[r/\mathrm{Fe}{]}^{\mathrm{ini}}=2.0$. The symbols of the spectroscopic observations are as in Fig. 12.

Figure 14

Abundance patterns of the CEMP-$s/r$ stars CS 31062-050 and CS 29497-030 compared with AGB models. Both stars show large excesses of heavy neutron-capture elements. The data and the theoretical expectations are normalized to the solar photospheric abundances of 216. Top panel: CS 29497-030 compared with AGB models of $1.35M_{\odot }$ case ST/9 and no dilution. In this case an initial $r$-process enrichment of $[r/\mathrm{Fe}{]}^{\mathrm{ini}}=2.0$ was adopted. Bottom panel: CS 31062-050 compared with AGB models of $1.5M_{\odot }$ case ST/2.7 and $\mathrm{dil}=1.0$ dex, with and without initial $r$-process enrichment ($[r/\mathrm{Fe}{]}^{\mathrm{ini}}=1.6$ and 0.0, respectively).

Figure 15

Top panel: Solar $s$ abundances normalized to ${}^{150}\mathrm{Sm}$ vs atomic mass for the solar main component as in 26, but updated by 50. Bottom panel: The predicted $s$-process distribution at the epoch of the Solar System formation obtained with a galactic chemical evolution code (350) and AGB $s$-process yields at various metallicities. Note that ${}^{208}\mathrm{Pb}$ is boosted to about 95% of its solar abundance by the contribution from low-metallicity AGB stars. Note also the 20%–30% deficit in the GCE distribution below magic neutron number $N=82$. These are the two major changes compared to the 26 stellar model with the ST pocket and $[\mathrm{Fe}/\mathrm{H}]=-0.3$, which are AGB models reproducing the main $s$-process component but only about 34% of solar ${}^{208}\mathrm{Pb}$.

Figure 16

Comparison of spectra around the Ba II 4934 Å line for AGB, post-AGB, and CEMP stars. Spectral data were obtained with the high dispersion spectrograph of the Subaru telescope with a resolving power of 60 000 or higher. The spectrum of the metal-poor star is normalized to the continuum level (bottom panel). The atomic absorption lines are clearly seen in the spectrum and are useful for abundance analyses. In contrast, molecular absorption (mostly of ${\mathrm{C}}_2$) is dominant in the AGB star (top panel), and the continuum level is very uncertain. Molecular absorption of the post-AGB star is not as severe as in the AGB star, depending on stellar temperature.

Figure 17

The same as in the bottom panel of Fig. 14, but for AGB models with initial mass $M=1.3M_{\odot }$, case ST/10, and $\mathrm{dil}=0.2$ dex. This solution is obtained under the hypothesis of a turn-off star before the first dredge-up.

Figure 18

Measurements of Eu isotope ratios from the Eu II absorption line profile for an $r$-process-enhanced star (top panel) and CEMP-$s$ and CEMP-$s/r$ stars. Adapted from 23.

Figure 19

Top panel: The evolution of the $s$-process fractions of $[\mathrm{Ba}/\mathrm{Fe}]$ vs $[\mathrm{Fe}/\mathrm{H}]$ in the galactic halo as well as in the thick and thin disk (dashed lines) and theoretical predictions of the total $s/r$ abundances (solid lines) from 350 and 306. The spectroscopic data from observations of galactic disk and halo stars are collected from the literature (110; 136; 239; 238; 178; 345; 59; 127; 231; 242; 256; 90; 356; 19; 394; 14; 168; 232; 82; 118; 119; 254; 18; 16; 80; 201; 233; 295). Error bars are plotted only when reported for individual objects by the authors. The dotted line connects a star observed by different authors. Analogous plots are shown for $[\mathrm{Eu}/\mathrm{Fe}]$ (middle panel) and $[\mathrm{Ba}/\mathrm{Eu}]$ (bottom panel).

Figure 20

Same as Fig. 19, but for $[\mathrm{Y}/\mathrm{Fe}]$ (top panel) and $[\mathrm{Pb}/\mathrm{Fe}]$ (bottom panel). The observational data of Y are from the references given in Fig. 19. The Pb data are from 317, 351, 168, 18, 295, and 294.