Fusion Reactions in Stars: Proton-Proton Chain and CNO Cycle Reaction

Jiachen Li
May 29, 2018

Submitted as coursework for PH241, Stanford University, Winter 2018


Fig. 1: Schematics of Proton-Proton Chain Reaction. (Source: J. Li, after Adelberger et al. [2])

Nuclear fusion reaction powers a star for most of its life. When a protostar born from nebulae or molecular settles down, it becomes a main-sequence star, and fusion reaction happens in its core. The primary nuclear fusion happens in the star core is the conversion of proton to helium. However, depended by the mass, stars achieve this conversion in different ways. The proton-proton chain reaction dominates in stars the size of the Sun or smaller, while the Carbon-Nitrogen-Oxigen (CNO) cycle reaction dominates in stars that are more than 1.3 times as massive as the Sun. [1]

Proton-Proton Chain Reaction

In the cores of lower-mass main-sequence stars such as the Sun, the dominant energy production process is the protonproton chain reaction. This creates a He-4 nucleus through a sequence of chain reactions that begin with the fusion of two protons to form a deuterium nucleus along with an ejected positron and neutrino. During this process, two hydrogen atoms are firstly merged together into a deuterium atom, which can then be merged with another hydrogen to form He-3. Then two of the He-3 nuclei can be merged together to form a He-4 atom. This whole reaction releases a large amount of energy in the form of gamma rays. [2]

CNO Cycle Reaction

Fig. 2: Schematics of CNO Cycle Reaction. (Source: J. Li, after Wiescher et al. [4])

In higher-mass stars, the dominant energy production process is the CNO cycle, which is a catalytic cycle that uses nuclei of carbon, nitrogen and oxygen as intermediaries and in the end produces a helium nucleus as with the proton-proton chain. CNO reaction is a very temperature sensitive process. [3] Under typical conditions found in stars, catalytic hydrogen burning by the CNO cycles is limited by proton captures. Specifically, the timescale for beta decay of the radioactive nuclei produced is faster than the timescale for fusion. Thus, this kind of CNO cycle converts hydrogen to helium slowly, and is called cold CNO cycle. [4] Under conditions of higher temperature and pressure, the rate of proton captures exceeds the rate of beta- decay, pushing the burning to the proton drip line. The essential idea is that a radioactive species will capture a proton before it can beta decay, opening new nuclear burning pathways that are otherwise inaccessible. Because of the higher temperatures involved, these catalytic cycles are typically referred to as the hot CNO cycles. [4]


The type of hydrogen fusion process that dominates in a star is determined by the temperature dependency differences between the two reactions. The protonproton chain reaction starts at temperatures about 4 × 106 °K, making it the dominant fusion mechanism in smaller stars. A self-maintaining CNO chain requires a higher temperature of approximately 16 × 106 °K, but thereafter it increases more rapidly in efficiency as the temperature rises, than does the proton-proton reaction. Above approximately 17 ×106 °K, the CNO cycle becomes the dominant source of energy. [5]

© Jiachen Li. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] M. Salaris and S. Cassisi, Evolution of Stars and Stellar Populations (Wiley, 2005).

[2] E. G. Adelberger et al., "Solar Fusion Cross Sections. II. The p-p Chain and CNO Cycles", Rev. Mod. Phys. 83, 195 (2011).

[3] B. E. Reddy, Principles and Perspectives in Cosmochemistry (Springer, 2010).

[4] M. Wiescher et al., "The Cold and Hot CNO Cycles," Annu. Rev. Nucl. Part. Sci. 60, 381 (2010).

[5] N. Reid and S. Hawley, New Light on Dark Stars: Red Dwarfs, Low-Mass Stars, Brown Dwarfs, 2nd Ed. (Springer, 2005).