The carbon stars (C-type stars) and S-stars are evolved stars of roughly solar mass and greater, up to approximately 10 solar masses, which are on the Asymptotic Giant Branch (AGB) region of the Hertsprung-Russell(HR) diagram. In this region of the HR diagram, the stars outer layers have expanded, their luminosity increased and their color turned redder compared to the pre-evolved state on the HR diagram. This diagram shows the HR diagram with evolutionary paths away from the main sequence into the AGB region.

 Ultimately these stars shed their outer layers into space as planetary nebulae and become white dwarfs. But it is during their short stint in the AGB region where a lot of very interesting action takes place.

            Stars, which have evolved into the AGB region, are variable stars of the Mira class or long period variables. While stars are in this region, they are undergoing a series of sequential shell burning episodes called thermal pulses (TP). This diagram enlarged from the previous HR figure highlights these pulses in the AGB region. Within one of these shells helium burning occurs which

 results in a region with high ¹²C levels. This carbon isotope, following some mixing with the mainly hydrogen containing regions above followed by proton capture nuclear reactions results in the synthesis of considerable quantities of the carbon isotope ¹³C. This is where things begin to get interesting! This ¹³C serves as a reactant, once the temperature reaches ~10⁸, in the following reaction:

¹³C + He  ---> ¹⁶O + n

Also occurring, but to a lesser degree and requiring greater reaction temperatures is this reaction:

²²Ne + He --> ²⁵Mg + n

Both of these reactions result in the production of neutrons, which serve in the “slow neutron capture” nuclear reactions. Carbon stars are, from what I understand of them, similar to S stars because they often have products in their atmospheres similar to S stars but have enhanced amount of carbon such that the C/O >1.

Slow Neutron Capture

           Many of the elements in the periodic table are synthesized in stars by the slow-neutron capture pathway in evolving stars. Some of the main elements made in this manner are highlighted in this figure of the Periodic Table.

This figure shows these same s-process elements in an isotope chart where proton number runs along the y-axis and neutron number along the x-axis. This chart shows many very interesting things about the elements and their isotopes.

 For example, the black region represents stable isotopes of particular elements. On either side of this “valley of stability” lies isotopes which are unstable (radioactive) and will decay ultimately attempting to get back to the ‘valley of stability”. The isotope of zirconium ⁹³Zr will beta decay to stable element niobium (⁹³Nb), while the unstable element of molybdenum (⁹³Mo) will undergo electron capture decay to get back to ⁹³Nb.

    The key in many respects to understanding what goes on in these stars is the element technetium. Technetium (Tc) has no stable isotopes and was first detected in S stars in the early 1950’s. The longest-lived isotope, ⁹⁹Tc, has a half-life of 2.6 x 10⁶ years. As a result, this element must have been recently made within the star and found its way to the surface in sufficient quantities to be detected spectroscopically. Since elements beyond Fe-Ni cannot be made by the more classical energy generating reactions (beyond Fe-Ni group, fusion to higher elements consume energy) a different mechanism such as neutron capture must be occurring.

This figure shows the actual s-process at work. The starting point for the sake of illustration begins at the nickel isotope ⁶²Ni. The red arrow to the right is the result of a capture of a neutron where the isotope generated (⁶³Ni) is unstable. Now the slow process is slow in that the neutron captures happen sufficiently slow that unstable isotopes decay before they have the chance to capture another neutron. Thus, ⁶³Ni decays via beta decay (blue arrows) to copper, ⁶³Cu, which can now capture another neutron to become ⁶⁴Cu. This unstable isotope can decay either by beta decay to ⁶⁴Zn or electron capture to become 64Ni. Complex webs of element isotopes are generated driven by the neutron release primarily from ¹³C burning. All of this occurring in a thin shell deep inside the AGB star. Once the burning of ¹³C is done, a variety of effects conspire to force the outer envelope of the star to become unstable toward convection with the result that convection can set in for a period of time between thermal pulses which will dredge up this s-element enhanced shell, ultimately to appear in the surface layers.

The amount of s-element enhancement can be 1000-10000 fold placing many of these elements into position such that they can be detected, even by amateur equipment. The figure below shows the spectrum of RS Cnc, an S-type star, which has enhanced levels of s-process elements present. Technetium lines are evident, as are lines from molybdenum, strontium, zirconium, niobium, rhenium and ruthenium. Zirconium oxide (ZrO) is particularly evident in the red region of the spectrum but are not demonstrated here. All isotopes of the technetium produced by the s-process are unstable and will decay as shown in this figure to either molybdenum or ruthenium via beta or electron capture decay, depending on which isotope you are talking about. Therefore if one is detecting technetium, one should also be able to see molybdenum and ruthenium as decay products and in fact you can. Of course the presence of these two elements can also result from the s-process so what you see is most likely a combination of s-process material AND technetium decay.

 Other Interesting Tidbits

          The burning of ¹³C to produce neutrons for the s-process is very temperature sensitive as is the reaction of ²²Ne to produce neutrons. The ¹³C reactions initiates just below a temperature of 10⁸ whereas the ²²Ne reaction is somewhat higher at 3 x 10⁸. The half-life of technetium at 10⁸ degrees is 2.6 x 10⁶ years whereas by the time the temperature gets to 3 x 10⁸, its half-life is measures in days. So even though more technetium probably gets made at the higher temperature, there may not be sufficient time for it to get dredged up out of this hot shell before it decays. This tells us that the source of the neutrons is ¹³C burning.

            The seed nuclei for the s-process are the Fe-Ni group of elements. The distribution and amount of heavy element isotopes made by the s-process depends on the amount of these seed nuclei. For solar metallicities, the distribution of heavy element synthesis is in the mid-range of atomic weights, from rubidium to palladium. For low metallicity stars such as those in the galactic halo, the s-process builds heavier nuclei up to lead and bismuth.