The Sun's Composition and Fusion Dynamics

The Sun’s primary energy source is the proton-proton chain, a fusion reaction converting hydrogen (H) to helium (He), releasing energy via photons and neutrinos. This document addresses the Sun’s composition, the fractions of hydrogen and helium, minor constituents, their rate of change, and how long the Sun’s current luminosity (radiative output) will persist.

1. Composition of the Sun: Hydrogen, Helium, and Minor Constituents

The Sun’s composition is primarily hydrogen and helium, with trace amounts of other elements. Based on current solar models and observations (e.g., spectroscopy, helioseismology, and standard solar models):

• Initial Composition (at formation, ~4.6 billion years ago):
• Hydrogen (H): ~73.5% by mass (X ≈ 0.735)
• Helium (He): ~24.9% by mass (Y ≈ 0.249)
• Other elements (collectively called "metals" in astrophysics, Z): ~1.6% by mass. These include oxygen (~0.8%), carbon (~0.3%), neon (~0.2%), iron (~0.2%), and trace amounts of nitrogen, silicon, magnesium, and others.
• Current Core Composition (after ~4.6 billion years of fusion):
• In the Sun’s core, where fusion occurs, hydrogen is gradually converted to helium. Current estimates suggest:
• Hydrogen: ~35–40% by mass in the core (down from ~73.5% initially).
• Helium: ~60–65% by mass in the core (up from ~24.9%).
• Other elements: Remain largely unchanged (~1.6%), as they are not significantly involved in the proton-proton chain.
• The outer layers (convective zone) retain the initial composition, as they are not mixed with the core.
• Overall Sun Composition (averaged):
• Hydrogen: ~70% by mass.
• Helium: ~28% by mass.
• Metals: ~1–2% by mass.

These values are derived from solar models calibrated with helioseismology and spectroscopic data, such as those from the Solar and Heliospheric Observatory (SOHO) and studies like Asplund et al. (2009, 2021).

2. Rate of Change of Hydrogen and Helium

The Sun converts hydrogen to helium via the proton-proton chain in its core, where four hydrogen nuclei (protons) fuse to form one helium-4 nucleus, releasing energy. The rate of this process can be estimated from the Sun’s luminosity and fusion efficiency:

• Luminosity and Fusion Rate:
• The Sun’s current luminosity is \( L_\odot \approx 3.828 \times 10^{26} \) watts.
• Each fusion reaction (4H → He) releases ~26.7 MeV of energy, with ~0.7% of the hydrogen’s mass converted to energy (via \( E = mc^2 \)).
• The Sun consumes ~600 million metric tons of hydrogen per second, producing ~596 million tons of helium, with ~4 million tons converted to energy.
• Mass Conversion:
• Total hydrogen consumed over 4.6 billion years: ~\( 2 \times 10^{30} \) kg (about 1% of the Sun’s initial hydrogen).
• The Sun’s total mass is \( 1.989 \times 10^{30} \) kg, with ~10% of its mass (the core) undergoing fusion.
• Core hydrogen mass initially: ~\( 1.46 \times 10^{29} \) kg (73.5% of core mass).
• Current core hydrogen: ~40% of core mass, meaning ~\( 5.8 \times 10^{28} \) kg of hydrogen remain in the core.
• Rate of Change:
• Hydrogen decreases by ~\( 1.89 \times 10^{17} \) kg/year.
• Helium increases by ~\( 1.88 \times 10^{17} \) kg/year.
• This corresponds to a fractional change of ~0.00013% of the Sun’s hydrogen mass per year.

3. How Long Will the Sun’s Current Luminosity Persist?

The Sun’s luminosity is not static; it increases over time due to changes in the core’s density and temperature as hydrogen is depleted and helium accumulates. The Sun is currently in its main sequence phase, where it fuses hydrogen in the core.

• Main Sequence Lifetime:
• The Sun’s total main sequence lifetime is estimated at ~10 billion years (from formation to the end of core hydrogen burning).
• Age now: ~4.6 billion years.
• Remaining main sequence time: ~5.4 billion years (until ~10 billion years from formation).
• Luminosity Evolution:
• The Sun’s luminosity has increased by ~30–40% since its formation (zero-age main sequence, ZAMS).
• Current models predict the Sun’s luminosity will continue to increase gradually, by ~1% every 100 million years, due to increasing core density and temperature.
• The Sun’s current luminosity will remain roughly stable (within ~10%) for another ~1–2 billion years. Beyond that, it will brighten significantly as it approaches the end of the main sequence.
• End of Main Sequence:
• When core hydrogen is depleted (~5.4 billion years from now), the Sun will exit the main sequence, becoming a subgiant and then a red giant. Its luminosity will increase dramatically (100–1000 times current levels) as it fuses hydrogen in a shell around the inert helium core.
• The Sun’s current radiative output will not persist indefinitely but will remain relatively stable for ~1–2 billion years before significant changes occur.

4. Photon Emission and Consistency with Fusion

The photons emitted from the Sun’s surface (photosphere) are primarily in the visible spectrum, peaking at ~500 nm (yellow-green), consistent with a blackbody temperature of ~5772 K. These photons originate from the photosphere, not directly from the core fusion reactions:

• Fusion Photons: Gamma rays produced in the core take ~1 million years to reach the surface, scattering and losing energy to emerge as visible light.
• Neutrinos: These are direct evidence of the proton-proton chain, detected on Earth (e.g., by the Sudbury Neutrino Observatory). Their flux matches predictions for hydrogen-to-helium fusion.

The consistency of photon and neutrino emissions confirms the proton-proton chain as the dominant reaction. Other reactions (e.g., CNO cycle) contribute <2% of the Sun’s energy.

5. Summary

• Current Composition (by mass, approximate):
• Whole Sun: ~70% H, ~28% He, ~1–2% metals.
• Core: ~35–40% H, ~60–65% He, ~1–2% metals.
• Rate of Change:
• Hydrogen consumed: ~600 million tons/second (~0.00013% of Sun’s H per year).
• Helium produced: ~596 million tons/second.
• Luminosity Duration:
• The Sun’s current luminosity (~3.828 × 10²⁶ W) will remain within ~10% for ~1–2 billion years.
• Main sequence ends in ~5.4 billion years, followed by a dramatic increase in luminosity as a red giant.

6. Chart: Sun’s Composition by Mass

Below is a chart comparing the Sun’s overall composition and core composition by mass percentage (hydrogen, helium, and metals).

The chart shows the approximate mass fractions: 70% H, 28% He, 2% metals for the whole Sun, and 37.5% H, 61.5% He, 1% metals for the core (using midpoint estimates for the core’s hydrogen and helium ranges).

References

• Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. (2009). The chemical composition of the Sun. Annual Review of Astronomy and Astrophysics, 47, 481–522.
• Asplund, M., Amarsi, A. M., & Grevesse, N. (2021). The chemical make-up of the Sun: A 2020 vision. Astronomy & Astrophysics, 653, A141.
• Bahcall, J. N., Pinsonneault, M. H., & Basu, S. (2001). Solar models: Current epoch and time dependences, neutrinos, and helioseismological properties. The Astrophysical Journal, 555(2), 990–1012.
• Christensen-Dalsgaard, J. (2002). Helioseismology. Reviews of Modern Physics, 74(4), 1073–1129.
• Turck-Chièze, S., & Couvidat, S. (2011). Solar neutrinos, helioseismology and the solar internal dynamics. Reports on Progress in Physics, 74(8), 086901.