Alpha Fusion in Stars An explanation of how elements on the periodic table, from He to Fe, are produced in stars such as Red Giants and Super Giants. AUTHORS: Jasmeet K Dhaliwal, Scripps Institution of Oceanography, UCSD Jason Moore, Mira Mesa High School, San Diego SUMMARY: This lesson focuses on the formation of elements heavier than helium up to iron through helium burning or alpha processes. This includes an introduction to Red Giant and Red SuperGiant stars and the types of alpha fusion in each of them. CONTEXT FOR USE: Building on the previous lesson, more complicated alpha processes are used to introduce the origin of heavier elements within the cores of stars. This relates the topics of stellar evolution, nuclear fusion and the origin of the elements. MISCONCEPTIONS Stars get their energy from burning light Red giants are like Jupiter Stars burn the same things their entire lives Stars do not die

Stellar Evolution Main Sequence Stars derive their energy from hydrogen fusion. Red Giants generate their energy through helium (alpha particle) fusion. MAIN POINT: As stars evolve, their energy sources for nuclear fusion change, meaning that different elements are “burned” at different stages in a star’s life. TEACHER NOTES: In the evolution of stars, they grow and exhaust their fuel, changing to a different source of energy (i.e. a different element). For a typical main sequence star, the stars begin producing energy from hydrogen burning (proton-proton fusion) as explained in the previous lesson. Eventually, the supply of hydrogen begins to decrease and finally the core is entirely depleted and consists only of helium. Low-mass stars, which are less than 0.5 solar mass, continue burning hydrogen, increasing in temperature and luminosity over time; they eventually collapse directly into the white dwarf stage. However, mid-sized stars like the Sun will continue along the main sequence for ~10 billion years, and when there is a small amount of hydrogen burning in the shell (hydrogen shell fusion), the star will increase in size into a Red Giant. Eventually, the helium in the core begins to fuse and becomes the main source of energy for the star. Massive stars (>5 solar masses) evolve away from the main sequence within a few million years and become red supergiants, and immediately have enough energy to begin helium fusion within their cores. They can also burn progressively heavier elements (onion shell ; slide 6-8), eventually ending in iron cores. As the helium atoms (alpha particles) fuse together, they begin to form elements heavier than helium. This is a method for the formation of all the even elements up to iron. REFERENCES: Stellar Evolution: http://en.wikipedia.org/wiki/Stellar_evolution Red Giant: http://en.wikipedia.org/wiki/Red_giant PICTURE/GRAPHICS CREDITS: http://kepler.nasa.gov/files/mws/kasc1.jpg 2

Red Giants As a star uses up its hydrogen, helium accumulates in its core, and will eventually burn. The remaining hydrogen continues to burn in a shell around the core The hydrogen-shell burning increases the thermal pressure, which causes the star to expand into a Red Giant. MAIN POINT: An explanation of the balance of pressure and gravity in a Red Giant. TEACHER NOTES: As a star runs out of its supply of hydrogen, the helium in the core results in an increase in temperature. This results in an outward thermal pressure, which pushes the remaining hydrogen into a shell around the helium core; this is called the hydrogen-burning shell. As the star begins to burn helium, its temperature increases and eventually the thermal pressure is stronger than the gravitational pressure. This results in an expansion of a large, outer-atmosphere of the star, resulting in a large radius and a low surface temperature. This is a characteristic Red Giant. It is a luminous giant star with low to intermediate mass (0.3-8 solar masses), and a relatively low density (because of the expanded radius). REFERENCES: Red Giant: http://en.wikipedia.org/wiki/Red_giant PICTURE/GRAPHICS CREDITS: http://outreach.atnf.csiro.au/education/senior/astrophysics/images/stellarevolution/hshellburningsml.jpg 3

Triple-Alpha Process: Step 1 The fusion of He-4 (alpha particles) is also called alpha fusion. In a triple-alpha process, typical of many red giants, the helium atoms combine to form carbon. In the first step, two alpha particles combine to make Be- 8 nucleus (A= 8; Z= 4) MAIN POINT: The Triple-Alpha process is a common form of alpha fusion in Red Giant Stars. TEACHER NOTES: Alpha fusion refers to the fusion of alpha particles (helium nuclei). Specifically, a triple-alpha process is the fusion of three alpha particles to form a Carbon-12 nucleus. This occurs in two steps. In the first step, two helium nuclei combine to form a beryllium nucleus. There is a conservation of atomic mass and the resulting nucleus has 4 protons and 4 neutrons (with an atomic number of 8). REFERENCES: Triple-Alpha Process: http://en.wikipedia.org/wiki/Triple-alpha_process PICTURE/GRAPHICS CREDITS: http://upload.wikimedia.org/wikipedia/commons/8/8d/Triple-Alpha_Process.png

Triple-Alpha Process: Step 2 In the second step of the triple-alpha process, one alpha particles combines with the Be-8 nucleus to form a C- 12 nucleus (A= 12; Z= 6) MAIN POINT: The Triple-Alpha process in Red Giant stars results in the formation of Carbon-12. TEACHER NOTES: Here, the beryllium nucleus formed in the previous step fuses with an additional alpha particle, resulting in a carbon nucleus. The beryllium-8 produced from the previous reaction is highly unstable and therefore either decays rapidly or reacts with an alpha particle to produce carbon. It should be noted that not all the products of fusion in stars are stable. In this example, the formation of beryllium-8 is important for the formation of carbon-12, but the majority of beryllium actually formed during the Big Bang (this is possible because it is such a light element). REFERENCES: Triple-Alpha Process: http://en.wikipedia.org/wiki/Triple-alpha_process Beryllium: http://en.wikipedia.org/wiki/Beryllium#Isotopes_and_nucleosynthesis Nucleosynthesis: http://en.wikipedia.org/wiki/Nucleosynthesis PICTURE/GRAPHICS CREDITS: http://upload.wikimedia.org/wikipedia/commons/8/8d/Triple-Alpha_Process.png 5

Super Giant Stars More massive stars (>5 solar masses) can evolve to become Super Giants. These are important in the synthesis of heavier elements up to iron (Fe). In these stars, alpha fusion continues past the triple-alpha process. This forms a chain of alpha processes that result in subsequently heavier nuclei. MAIN POINT: Supergiant stars can continue past the triple-alpha process to produce elements up to iron. TEACHER NOTES: The image above is of Betelgeuse, a Red SuperGiant star. The image is taken with the Hubble Telescope. Massive stars (>5 solar masses) can eventually evolve into Supergiant stars. They have sufficient mass and thermal energy to continue beyond the triple-alpha process, and can result in the formation of heavier elements. This occurs through the fusion of alpha particles to increasingly heavier nuclei. This stops at iron, because it has the highest binding energy and the addition of an alpha particle to an Fe-nucleus does not generate energy (rather, it consumes it). In the end, a core of an exhausted Supergiant will consist of iron (see slide 9). REFERENCES: Super Giant: http://en.wikipedia.org/wiki/Supergiant PICTURE/GRAPHICS CREDITS: http://apod.nasa.gov/apod/ap990605.html 6

Chain of Alpha Processes This chain of Alpha Processes is also termed the alpha ladder. In this, an alpha particle is added to an atomic nucleus (such as carbon) to form oxygen. The addition of an alpha particle to an atom adds 2 protons (and therefore the atomic number of the product is 2 larger than the original) 12 C + 4 He → 16 O 16 O + 4 He → 20 Ne 20 Ne + 4 He → 24 Mg 24 Mg + 4 He → 28 Si 24 Si + 4 He → 32 S 32 S + 4 He → 36 Ar 36 Ar + 4 He → 40 Ca 40 Ca + 4 He → 44 Ti 44 Ti + 4 He → 48 Cr 48 Cr + 4 He → 52 Fe Carbon Burning Oxygen Burning Silicon Burning MAIN POINT: Alpha particles are the building-blocks of heavier nuclei, which are formed through fusion. TEACHER NOTES: The general process, in which an alpha particle is added to a nucleus results in a chain of reactions. This set of reactions is also known as the alpha ladder. It can form all the even elements from beryllium to iron. The reactions proceed at a very low rate and do not contribute significantly to the energy production in stars, but are important for the generation of the elements. REFERENCES: Alpha Process: http://en.wikipedia.org/wiki/Alpha_process PICTURE/GRAPHICS CREDITS: Authors (Dhaliwal, Moore) 7

Formation of Odd Elements Odd elements are not formed through the alpha ladder in stars. The Oddo-Harkins rule states that even numbered elements are inherently more stable (and therefore more common) than odd elements. Odd elements can be formed during the Big Bang, radioactive decay or supernova nucleosynthesis. MAIN POINT: An explanation of the elements up to Fe that are odd and do not form through the alpha ladder. TEACHER NOTES: The odd elements between He and Fe are less abundant that the even elements. This is partially a result of stability, as well as the fact that these elements are not formed in the alpha ladder. The Oddo-Harkins rule states that elements with even atomic numbers are more common than elements with odd numbers (this can be noted on the diagram of Solar System abundances); this applies to all elements on the periodic table. This is demonstrated by the saw-tooth shape of the graph above. Some of the elements above can be formed through the radioactive decay of even elements within stars, such as N and Al. Other elements, such as Li and B formed during the Big Bang. Finally, many of these elements reach measurable quantities after supernovae, through neutron capture processes (r- and s- processes). These are beyond the scope of this lesson, but it is important to explain to the students that there are other processes responsible for the formation of elements besides hydrogen burning and alpha fusion. REFERENCES: Nucleosynthesis: http://en.wikipedia.org/wiki/Nucleosynthesis Oddo-Harkins Rule: http://en.wikipedia.org/wiki/Oddo-Harkins_rule PICTURE/GRAPHICS CREDITS: http://en.wikipedia.org/wiki/File:SolarSystemAbundances.png 8

Conclusions During a star’s lifetime, it burns heavier and heavier elements. Heavier elements burn faster (see table on right) When it accumulates Fe in the core and can no longer maintain a balance of temperature and pressure, the star will undergo core collapse MAIN POINT: The sequence of element formation is from light to heavier, because the heavier nuclei are formed from lighter nuclei. TEACHER NOTES: A large star (larger than our Sun) that is massive enough to continue past He burning to carbon, oxygen and silicon burning will eventually result in a layered structure (like an onion). As each element is begins to burn, the lighter element moves into a shell around it (like the hydrogen-burning shell in slide 2). Therefore, when the star begins to burn carbon, there would be a shell of helium-burning, surrounded by another shell of hydrogen-burning. This continues through to silicon-burning, which deposits iron in the core and continues in a small shell around it. During these different stages of fusion, the star is able to balance the inward force of gravity with outward thermal pressure. This is because of the energy and heat generated from the fusion in the shells. When fusion stops, however, and the core consists of Fe, the star can no longer generate energy from fusion. This is because Fe has a high binding energy and its fusion is an energy-consuming process. Therefore, the star can no longer balance the inward force of gravity with an outward thermal pressure; without the generation of heat and energy, the star will collapse and then explode into a supernova type II. This is explained further in the next lesson. REFERENCES: Type II Supernova: http://en.wikipedia.org/wiki/Type_II_supernova PICTURE/GRAPHICS CREDITS: http://astronomy.swin.edu.au/cms/cpg15x/albums/userpics/core-collapse1.jpg

Summary After hydrogen fusion, larger stars can continue with the fusion of heavier elements. Red Giants can fuse helium and form carbon (triple-alpha process). Super Giant Stars can form elements from later steps of alpha fusion. The alpha ladder can form the even elements lighter than iron. The odd elements can be formed in supernova or through nuclear decay. Even elements are more common than odd elements. After a star is exhausted of energy, its core will consist of Fe (and outer shells of lighter elements). 10