Anatomy of the Solar Neutrino Spectrum

The Sun emits neutrinos through every fusion reaction in its core. From the simplest proton-proton reaction at the start of the chain to the rare CNO cycle in heavier-element catalysis, each step that involves a beta decay or electron capture produces a small flux of electron neutrinos that escape immediately and traverse the Sun’s interior in seconds.

The total flux at Earth is enormous — approximately $7\times 10^{10}$ neutrinos per square centimetre per second pass through us, dominated by the lowest-energy sources. But the spectrum of this flux is structured: discrete lines (from electron-capture reactions) and continuous spectra (from beta-decay reactions) at characteristic energies, each tied to a specific nuclear reaction in the solar core.

Different experiments have, over the decades, probed different parts of this spectrum. Each source was first measured by the experiment whose threshold and sensitivity matched its energy and abundance. The combined picture is one of the most thoroughly studied solar phenomena, and it continues to refine.

This post is about the structure of the solar neutrino spectrum, what each source tells us, and which experiments have measured them.

The major sources

The dominant solar neutrino sources are six:

• pp — proton-proton reaction, the first step of the pp chain. By far the most abundant.
• pep — proton-electron-proton reaction, monoenergetic at 1.44 MeV.
• 7Be — electron capture on beryllium-7, two monoenergetic lines (mostly 0.86 MeV).
• 8B — beta decay of boron-8, continuous spectrum up to 15 MeV.
• hep — helium-electron-proton reaction, the rarest and highest-energy source.
• CNO — neutrinos from beta decays of 13N, 15O, 17F in the CNO cycle.

The pp source

The pp reaction is the first step of the proton-proton chain: $p+p\to {}^2\text{H}+e^{+}+{\nu }_e(Q\approx 0.42\text{ MeV})$

The neutrino energy spectrum is continuous from zero up to 0.42 MeV. The flux at Earth is approximately $6\times 10^{10}$ cm⁻²s⁻¹, by far the largest solar neutrino source. The corresponding interaction rate in any detector is, however, low because the cross-section grows linearly with energy.

The pp flux was first directly measured by Borexino in 2014 — an extraordinary technical achievement requiring extreme low-energy radiopurity. Earlier experiments (GALLEX/SAGE) detected pp neutrinos via inverse beta decay on gallium, which has a 233-keV threshold; this gives an integrated count above threshold but does not directly measure the spectrum.

The pp source provides direct confirmation that the standard pp chain operates as predicted. Its measurement, with current Borexino precision around 10%, is consistent with the standard solar model.

The 7Be source

Electron capture on ${}^7$Be produces a monoenergetic neutrino line: ${}^7\text{Be}+e^{-}\to {}^7\text{Li}+{\nu }_e(E_{\nu }\approx 0.86\text{ MeV})$

A small fraction (about 10%) of the captures populate the excited 478-keV state of ${}^7$Li, producing 0.38 MeV neutrinos in addition. The combined 7Be flux is approximately $5\times 10^9$ cm⁻²s⁻¹.

The 7Be line was first directly measured by Borexino in 2007. The result was a high-precision (5%) confirmation of the standard solar model prediction. The 7Be measurement was the first use of an electronic detector to do high-precision solar neutrino spectroscopy — measuring a specific spectral feature rather than an integrated rate.

The 8B source

Beta decay of boron-8 in the solar core: ${}^8\text{B}\to {}^8\text{Be}+e^{+}+{\nu }_e(Q\approx 15\text{ MeV})$

The neutrino spectrum is continuous from threshold up to approximately 15 MeV, with average energy around 7 MeV. The flux at Earth is approximately $5\times 10^6$ cm⁻²s⁻¹ — much smaller than pp, but the higher-energy neutrinos have much larger cross-sections, making them detectable in water-Cherenkov and heavy-water experiments.

The 8B flux was the first solar neutrino source to be detected in real time (Kamiokande in 1989), the first to be detected through neutral-current interactions (SNO in 2001), and the first to provide a direct measurement of solar neutrino flavor change. It remains the most precisely measured solar source.

The 8B production rate is exquisitely sensitive to the solar core temperature. Each percent shift in the core temperature changes the 8B flux by approximately 30%. This makes 8B a useful probe of solar interior conditions, complementary to helioseismology.

The hep source

Hydrogen-helium-electron-proton reaction: ${}^3\text{He}+p\to {}^4\text{He}+e^{+}+{\nu }_e(Q\approx 19\text{ MeV})$

This is the rarest source — about 1000 times less abundant than 8B — but extends to the highest neutrino energy in the spectrum. The flux at Earth is approximately $8\times 10^3$ cm⁻²s⁻¹.

hep neutrinos have been searched for in the high-energy tail of the 8B spectrum at SNO and Super-Kamiokande. Both experiments have reported upper bounds consistent with the small predicted flux. A definitive detection requires more sensitive future experiments.

The pep source

Proton-electron-proton reaction: $p+e^{-}+p\to {}^2\text{H}+{\nu }_e(E_{\nu }\approx 1.44\text{ MeV})$

This is a monoenergetic line, similar to 7Be in structure but at higher energy. The flux is approximately $1.4\times 10^8$ cm⁻²s⁻¹.

The pep flux was first directly measured by Borexino in 2012. It is a useful test of the standard solar model: pep is closely related to pp through the underlying reaction physics, and the two should be in a fixed ratio. Borexino’s measurement is consistent with this expectation.

The pep flux is also relevant for the CNO measurement, as both contribute to the energy region where CNO neutrinos are sought, and pep must be carefully subtracted.

The CNO source

The CNO cycle, an alternative to the pp chain, contributes about 1% of solar luminosity but produces neutrinos through beta decays of ${}^{13}$N, ${}^{15}$O, and ${}^{17}$F. The combined CNO neutrino flux is approximately $5\times 10^8$ cm⁻²s⁻¹.

CNO neutrinos were not directly detected until Borexino’s 2020 measurement, due to their overlap with pep and natural-radioactivity backgrounds. The Borexino result confirms the CNO cycle operates in the Sun and provides constraints on the solar metallicity. Future experiments will improve the precision substantially.

The combined picture

Each source has been measured. The integrated picture confirms the standard solar model — the framework that describes the Sun’s nuclear-fusion-powered structure — to high precision across the full energy range.

The remaining open questions are not whether the solar neutrinos exist as predicted (they do) but rather:

• The precise solar metallicity (resolved by improved CNO measurements)
• Sub-percent corrections to fluxes from helioseismic and nuclear-physics inputs
• Time variations (e.g., solar-cycle-dependent fluxes — searched but not detected)
• Possible new physics in solar neutrino propagation (NSI, sterile mixing — not detected at current sensitivities)

Detection thresholds and energy ranges

Different experiments have probed different parts of the spectrum based on their thresholds:

Experiment	Threshold	Sources detected
Homestake (Cl)	~0.8 MeV	7Be, 8B (integrated)
GALLEX/SAGE (Ga)	~0.23 MeV	pp + others (integrated)
Kamiokande/Super-K	~5 MeV	8B (real-time spectrum)
SNO	~5 MeV	8B (flavour-resolved)
Borexino	~150 keV	pp, 7Be, pep, 8B, CNO (spectroscopic)

Borexino’s low threshold and excellent radiopurity made it the first experiment to spectroscopically resolve all the major solar sources (with the exception of hep, which remains too rare for current sensitivities).

What it all confirms

The solar neutrino programme — running for more than 50 years from Homestake’s first detection through Borexino’s CNO measurement — has produced one of the most thoroughly characterised neutrino sources in physics. The combined data set:

• Confirms that the Sun fuses hydrogen via both the pp and CNO cycles, exactly as theoretically predicted
• Confirms the solar interior structure (temperature, density, composition) to better than 1% in many regions
• Provides flavor-resolved measurements that established neutrino oscillation in the early 2000s
• Continues to provide tests of standard solar physics through fluxes that change systematically with solar core temperature

The Sun is the most studied neutrino source. It is also the closest one. We can probe it in real time, with multiple complementary techniques. The accumulated understanding is the foundation on which all solar physics now rests.

The spectrum, in its full structure, is among the most beautiful results of decades of patient experimental work. Each line and continuous shape corresponds to a specific nuclear process happening 8 light-minutes away. The Sun’s interior is open to us through neutrinos in a way that no other technique can match.