Branduolinės sintezės keliai

Nuclear synthesis paths

Proton-proton chain vs. CNO cycle, and how nuclear temperature and mass determine fusion processes

At the heart of every shining main sequence star lies fusion engine, in which light nuclei combine to form heavier elements and release enormous amounts of energy. The specific processes that occur nuclear processes in the core of a star depends heavily on it masses, core temperature and chemical composition. For stars similar to or smaller than the Sun, proton–proton (p–p) chain dominates hydrogen synthesis, while massive, hotter stars relies on CNO cycle – a catalytic process involving isotopes of carbon, nitrogen and oxygen. Understanding these different synthesis pathways reveals how stars generate their enormous radiation and why higher-mass stars burn faster and brighter but have much shorter lives.

In this article we will delve into p–p chains the basics of synthesis, we will describe CNO cycle and explain how core temperature and stellar mass determine which pathway fuels a star's stable hydrogen-burning phase. We will also examine the observational evidence for both processes and consider how changing conditions in a star can alter the balance of fusion pathways over cosmic time.

1. Context: Hydrogen fusion in stellar cores

1.1 The central importance of hydrogen synthesis

Main sequence stars get their stable light from hydrogen synthesis in their cores, which creates radiation pressure that balances out the gravitational contraction. In this phase:

  • Hydrogen (the most common element) synthesizes into helium.
  • Mass → Energy: A small fraction of mass is converted into energy (E=mc2), which is released as photons, neutrinos, and thermal motion.

The total mass of a star determines its core temperature and density, determining which fusion pathway is possible or dominant. In lower-temperature nuclei (e.g., the Sun, ~1.3×107 Q) p–p circuit is most efficient; and in hotter, more massive stars (core temperature ≳1.5×107 Q) CNO cycle can outperform the p–p circuit, providing brighter radiation [1,2].

1.2 Energy production rate

The rate of hydrogen fusion is extremely sensitive to temperature. A small increase in core temperature can significantly enhance the reaction rate, a property that helps main-sequence stars maintain their hydrostatic balanceIf the star is compressed slightly, the core temperature increases, the fusion rate increases sharply, creating additional pressure that restores equilibrium, and vice versa.

2. Proton–proton (p–p) chain

2.1 Overview of steps

In low and medium mass stars (up to ~1.3–1.5 M⊙) p–p circuit is the dominant pathway for hydrogen synthesis. It occurs through a series of reactions that convert four protons (hydrogen nuclei) into one helium-4 nucleus (4He), releasing positrons, neutrinos, and energy. Simplified overall reaction:

4 p → 4He + 2e+ + 2ν + γ.

This chain can be divided into three subsections (p–p I, II, III), but the general principle remains the same: gradually build 4He from protons.Let us distinguish the main branches [3]:

p–p branch I

  1. p + p → 2H + e+ + νe
  2. 2H + p → 3He + γ
  3. 3Hey + 3Hey → 4He + 2p

p–p branches II and III

Next, the process involves 7Without or 8B, which capture electrons or emit alpha particles, producing different types of neutrinos with slightly different energies. These side branches become more important as the temperature rises, changing the neutrino tracks.

2.2 Main by-products: Neutrinos

One of the signs of p–p chain synthesis is neutrino production. These nearly massless particles escape from the star's core almost unencumbered. Solar neutrino experiments on Earth detect a fraction of these neutrinos, confirming that the p–p chain is indeed the main source of the Sun's energy. Early neutrino experiments revealed discrepancies (the so-called "solar neutrino problem"), which were eventually resolved by understanding neutrino oscillations and improving models of the Sun [4].

2.3 Temperature dependence

The rate of the p–p reaction increases approximately as T4 near the temperatures of the Sun's core, although the exact degree varies among sub-clusters. Despite its relatively moderate temperature sensitivity (compared to CNO), the p–p circuit is efficient enough to power stars up to about 1.3–1.5 solar masses. More massive stars tend to have higher central temperatures, favoring alternative, faster cycles.

3. CNO cycle

3.1 Carbon, nitrogen, oxygen as catalysts

In the case of hotter cores in more massive stars CNO cycle (carbon–nitrogen–oxygen) dominates in hydrogen synthesis. Although the overall reaction is still 4p → 4He, the mechanism uses C, N, and O nuclei as intermediate catalysts:

  1. 12C + p → 13N + γ
  2. 13N → 13C + e+ + νe
  3. 13C + p → 14N + γ
  4. 14N + p → 15O + γ
  5. 15Oh → 15N + e+ + νe
  6. 15N + p → 12C + 4Hey

The end result remains the same: four protons become helium-4 and neutrinos, but the presence of C, N, and O strongly affects the reaction rate.

3.2 Temperature sensitivity

The CNO cycle is much more sensitive to temperature than the p–p chain, its rate increasing approximately as T15–20 under typical conditions in the core of massive stars. As a result, small increases in temperature can dramatically increase the fusion rate, resulting in:

  • High radiation in massive stars.
  • Sudden dependence on core temperature, which helps massive stars maintain dynamical equilibrium.

Since the mass of a star determines the pressure and temperature of the core, only stars with masses exceeding about 1.3–1.5 M⊙, has a fairly hot interior (~1.5×107 K or higher) for the CNO cycle to dominate [5].

3.3 Metallicity and the CNO cycle

The abundance of CNO in the star's composition (its metallicity, i.e. elements heavier than helium) can slightly change the efficiency of the cycle. Higher initial amounts of C, N, and O lead to more catalysts, and thus a slightly faster reaction rate at a given temperature; this can change the lifetimes and evolutionary sequences of stars.Especially metal-poor stars rely on the p–p chain unless they reach very high temperatures.

4. Stellar mass, core temperature and fusion pathway

4.1 Mass–temperature–synthesis regime

Star initial mass determines its gravitational potential, which determines a higher or lower central temperature. Therefore:

  1. Small to medium weight (≲1.3 M⊙): p–p circuit is the main route for hydrogen synthesis, with a relatively moderate temperature (~1–1.5×107 K).
  2. High mass (≳1.3–1.5 M⊙): The core is hot enough (≳1.5×107 K), that CNO cycle would surpass the p–p circuit in energy production.

Many stars use a mixture of both processes at certain layers or temperatures; the center of the star may be dominated by one mechanism, while the other is active in the outer layers or at earlier/later stages of evolution [6,7].

4.2 Transition point around ~1.3–1.5 M⊙

The transition point is not abrupt, but approximately 1.3–1.5 At the solar mass limit, the CNO cycle becomes the dominant energy source. For example, Sun (~1) M⊙) obtains ~99% of its fusion energy through the p–p chain. 2 M⊙ In a star of greater mass, the CNO cycle dominates, with the op–p chain contributing to a smaller extent.

4.3 Consequences for stellar structure

  • p–p dominant stars: Often have larger convection layers, relatively slower fusion rates, and longer lifetimes.
  • CNO dominant stars: Very high fusion rates, large radiation belts, short main sequence lifetimes, and powerful stellar winds capable of stripping away material.

5. Observable signs

5.1 Neutrino flux

Solar neutrino spectrum is evidence for the operation of the p–p chain. In more massive stars (e.g., high-radiation dwarfs or giant stars), an additional neutrino flux caused by the CNO cycle could in principle be detected. Future advanced neutrino detectors could theoretically resolve these signals, providing a direct glimpse into nuclear processes.

5.2 Star structure and HR diagrams

The color–amplitude diagrams of star clusters reflect the mass–radiation relationship formed by stellar core fusion. High-mass clusters are dominated by bright, short-lived main-sequence stars with steep slopes in the upper HR diagram (CNO stars), while lower-mass clusters are dominated by p–p chain stars that survive billions of years on the main sequence.

5.3 Helioseismology and asteroseismology

Solar internal oscillations (helioseismology) confirms details such as core temperature that support p–p chain models. For other stars, asteroseismology missions such as Kepler whether TESS, helps reveal the internal structure – showing how energy production processes can vary depending on mass and composition [8,9].

6. Evolution after hydrogen combustion

6.1 Post-main sequence divergence

When hydrogen is released in the nucleus:

  • Low-mass p–p stars expand into red giants, eventually igniting helium in a degenerate core.
  • Massive CNO stars quickly transitions to advanced burning phases (He, C, Ne, O, Si), which end with core collapse in the form of a supernova.

6.2 Changing core conditions

During mantle hydrogen burning, stars can reintroduce CNO processes in individual layers or rely on p–p chaining in other parts as temperature profiles change. The interplay of fusion modes in multilayer burning is complex and is often revealed through elemental product data from supernovae or planetary nebula emissions.

7. Theoretical and numerical models

7.1 Stellar Evolution Codes

Codes such as MASS, Geneva, KEPLER whether GARSTEC, incorporate nuclear reaction rates for both p–p and CNO cycles by iterating the stellar structure equations over time. By adjusting parameters such as mass, metallicity, and rotation rate, these codes generate evolutionary paths that are consistent with observed data from star clusters or well-defined stars.

7.2 Reaction rate data

Accurate nuclear cross-section data (e.g. from MOON experiments in underground laboratories for the p–p chain, or the NACRE or REACLIB databases for the CNO cycle) provide targeted modeling of stellar luminosities and neutrino fluxes. Small changes in the cross sections can significantly change the predicted lifetime of stars or the location of the p–p/CNO boundary [10].

7.3 Multilayer simulations

While 1D codes satisfy many stellar parameters, some processes – such as convection, MHD instabilities, or advanced stages of burning – can benefit from 2D/3D hydrodynamical simulations, which reveal how local phenomena can affect the global fusion rate or mixing of materials.

8. Wider implications

8.1 Chemical evolution of galaxies

Main-sequence hydrogen fusion strongly influences the rate of star formation and the distribution of stellar lifetimes throughout the galaxy. While heavier elements are formed at later stages (e.g., helium burning, supernovae), the main hydrogen-to-helium conversion in the galactic population is shaped by p–p or CNO regimes, depending on the mass of the stars.

8.2 Habitability of exoplanets

Lower-mass, p–p-sequence stars (such as the Sun or red dwarfs) have stable lifetimes of billions to trillions of years, giving potential planetary systems enough time for biological or geological evolution. In contrast, short-lived CNO stars (O, B-type) have short lifetimes that are likely insufficient for the emergence of complex life.

8.3 Future observation missions

As research into exoplanets and asteroseismology grows, we are gaining more knowledge about the internal processes of stars, perhaps even distinguishing p–p and CNO signatures in stellar populations. Missions such as PLATO, or ground-based spectroscopic surveys will further refine the mass–metallicity–radiance relationships in main-sequence stars operating under different fusion regimes.

9. Conclusions

Hydrogen synthesis there are stellar lives spine: it drives main sequence radiation, stabilizes stars against gravitational collapse, and sets evolutionary time scales. Choosing between proton-proton chains and CNO cycle depends essentially on core temperature, which is itself related to the star massLow- and intermediate-mass stars, such as the Sun, rely on p–p chain reactions to ensure long and stable lifetimes, while more massive stars use the faster CNO cycle, radiating brilliantly but with short lifetimes.

Too detailed observations, solar neutrino detection and theoretical models Astronomers are validating these fusion pathways and refining how they shape stellar structure, population dynamics, and ultimately the fate of galaxies. Looking back to the very earliest times of the universe and the distant remnants of stars, these fusion processes remain a fundamental explanation for both the light in the universe and the distribution of stars that fill it.

Sources and further reading

  1. Eddington, A. S. (1920). “The internal constitution of stars.” The Scientific Monthly, 11, 297–303.
  2. Bethe, H. A. (1939). “Energy production in stars.” Physical Review, 55, 434–456.
  3. Adelberger, EG, et al. (1998). “Solar fusion cross sections.” Reviews of Modern Physics, 70, 1265–1292.
  4. Davis, R., Harmer, DS, & Hoffman, KC (1968). “Searching for neutrinos from the Sun.” Physical Review Letters, 20, 1205–1209.
  5. Salaris, M., & Cassisi, S. (2005). Evolution of stars and stellar populations. John Wiley & Sons.
  6. Kippenhahn, R., Weigert, A., & Weiss, A. (2012). Stellar structure and evolution, 2nd edition. Springer.
  7. Arnett, D. (1996). Supernovae and nucleosynthesis. Princeton University Press.
  8. Christensen-Dalsgaard, J. (2002). “Helioseismology.” Reviews of Modern Physics, 74, 1073–1129.
  9. Chaplin, WJ, & Miglio, A. (2013). “Asteroseismology of solar-type and red giants.” Annual Review of Astronomy and Astrophysics, 51, 353–392.
  10. Iliadis, C. (2015). Stellar nuclear physics, 2nd edition. Wiley-VCH.
Return to the blog