How the Sun and stars shine

Each second, fusion reactions in the Sun’s core fling approximately 60 billion neutrinos onto every square centimetre of the Earth. In the late 1990s, the Borexino experiment at Gran Sasso National Laboratory in Italy was conceived to measure these neutrinos right down to a few tens of keV, where the bulk of the flux lies. The detector’s name means “little Borex” and refers to an earlier idea for a large experiment with a boron-loaded liquid scintillator, which was shelved in favour of the present, smaller and more ambitious detector. Rather than studying rare but high-energy ⁸B neutrinos from a little-followed branch of the proton–proton (pp) fusion chain, Borexino would target the far more numerous but lower energy neutrinos produced in the Sun by electron captures on ⁷Be.

Three decades after its conception, Borexino has far exceeded this goal thanks to the exceptional radiopurity of the experimental apparatus (see “Detector design” panel. Special care taken in construction and commissioning has achieved a radiopurity about three orders of magnitude better than predicted, and 10 to 12 orders of magnitude below natural radioactivity. This has allowed the collaboration to probe the entire solar-neutrino spectrum, including not only the pp chain, but also the carbon–nitrogen–oxygen (CNO) cycle. This mechanism plays a minor role in the Sun but becomes important for more massive stars, dominating the energy production and the production of elements heavier than helium in the universe at large.

The heart of the Sun

The pp-chain generates 99% of the energy in the Sun: it begins when two protons fuse to produce a deuteron and an electron neutrino – the so-called pp neutrino (see “Chain and cycle” figure). Subsequent reactions produce light elements, such as ³He, ⁴He, ⁷Be, ⁷Li, ⁸B and more electron neutrinos. In Borexino, the sensitivity to pp neutrinos depends on the amount of ¹⁴C in the liquid scintillator: with an end-point energy of 0.156 MeV compared with a maximum visible energy for pp neutrinos of 0.264 MeV, the ¹⁴C → ¹⁴N + β^– + ν beta decay sets the detection threshold and the feasibility of probing pp-neutrinos. The Borexino scintillator was therefore made using petroleum from very old and deep geological layers, to ensure a low content of ¹⁴C.

Since data-taking began in 2007, Borexino has measured, for the first time, all the individual fluxes produced in the pp-chain. In 2014 the collaboration made the first definitive observation of pp neutrinos, using a comparison with the predicted energy spectrum. In 2018 the collaboration performed, with the same apparatus, a measurement of all the pp-chain components (pp, ⁷Be, pep and ⁸B neutrinos), demonstrating the large-scale energy-generation mechanism in the Sun for the first time (see “Energy spectrum” figure). This spectral fit allowed the collaboration to directly determine the ratio between the interaction rate of ³He + ³He fusions and that of ³He + ⁴He fusions – a crucial parameter for characterising the pp chain and its energy production.

The simultaneous measurement of pp-chain neutrino fluxes also gave Borexino a unique window onto the famous “vacuum-matter” transition, whereby coherent virtual W-boson interactions with electrons modify neutrino-oscillation probabilities as neutrinos propagate through matter, enhancing the oscillation probability as a function of energy. In 2018 Borexino measured the solar electron–neutrino survival probability, P_ee, in the energy range from a few tens of keV up to 15 MeV (see “Survival probability” figure). This was the first direct observation of the transition from a low-energy vacuum regime (P_ee~0.55) to a higher energy matter regime where neutrino propagation is dominantly affected by the solar interior (P_ee~0.32). The transition was measured by Borexino at the level of 98% confidence.

CNO cycle

A different way to burn hydrogen, the CNO cycle, was hypothesised independently by Carl Friedrich von Weizsäcker and Hans Albrecht Bethe between 1937 and 1939. Here, ¹²C acts as a catalyst, and electron neutrinos are produced by the beta decay of ¹³N and ¹⁵O, with a small contribution from ¹⁷F. The maximum energy of CNO neutrinos is about 1.7 MeV. In addition to making an important contribution to the production of elements heavier than helium, this cycle is important for the nucleosynthesis of ¹⁶O and ¹⁷O. In massive stars it also develops in more complex reactions producing ¹⁸F, ¹⁸O, ¹⁹F, ¹⁸Ne and ²⁰Ne.

The sensitivity to CNO neutrinos in Borexino mainly comes from events in the energy range from 0.8 to 1 MeV. In this region, the dominant background comes from ²¹⁰Bi, which is produced by the slow radioactive decay ²¹⁰Pb (22 y) → ²¹⁰Bi (5 d) + β^– + ν → ²¹⁰Po (138 d) + β^– + ν → ²⁰⁶Pb (stable) + α. The ²¹⁰Bi activity can be inferred from ²¹⁰Po, which can be efficiently tagged using pulse-shape discrimination. However, convective currents in the liquid scintillator bring into the central fiducial mass ²¹⁰Po produced by ²¹⁰Pb, which is most likely to be embedded on the nylon containment vessel. In order to reduce convection currents, a passive insulation system and a temperature control system were installed in 2016, significantly reducing the effect of seasonal temperature variations. 

Thanks to these and other efforts, in 2020 Borexino rejected the null hypothesis of no CNO reactions by more than five standard deviations, providing the first direct proof of the process. The energy production as a fraction of the solar luminosity was measured to be 1_-0.3^+0.4%, in agreement with the Solar Standard Model (SSM) prediction of roughly 0.6 ± 0.1% (which assumes the solar surface has a high metallicity – a topic discussed in  more detail later). Given that luminosity scales as M⁴ and number density as M^–2.5 for stars between one and 10 solar masses, the CNO cycle is thought to be the most important source of energy in massive hydrogen-burning stars. Borexino has provided the first experimental evidence for this hypothesis.

Probing solar metallicity using CNO neutrinos is of the utmost importance, and Borexino is hard at work on the problem

But, returning to the confines of our solar system, it’s important to remember that the SSM is not a closed book. Borexino’s results are thus far in agreement with its assumption of a protostar that had a uniform composition throughout its entire volume when fusion began (“zero-age homogeneity”). However, thanks to the ability of neutrinos to peek into the heart of the Sun, the experiment now has the potential to explore this assumption and weigh in on one of the most intriguing controversies in astrophysics.

The solar-abundance controversy

As stars evolve, the distribution of elements within them changes thanks to fusion reactions and convection currents. But the composition of the surface is thought to remain very nearly the same as that of the protostar, as it is not hot enough there for fusion to occur. Measuring the abundance of elements on a star’s surface therefore gives an idea of the protostar’s composition and is a powerful way to constrain the SSM. 

Currently, the best method to determine the surface abundance of elements heavier than helium (“metallicity”) uses measurements of photo-absorption lines. Since 2005, improved hydrodynamic calculations (which are needed to model atomic-line formation, and radiative and collisional processes which contribute to excitation and ionisation) indicate a much lower surface metallicity than was previously considered. However, helioseismology observables differ by roughly five standard deviations from SSM predictions that use the new surface metallicity to infer the protostar’s composition, when the sound–speed profile, surface–helium abundance and the depth of the convective envelope are taken into account. Helioseismology implies that the zero-age Sun’s core was richer in metallicity than the present surface composition, suggesting a violation of zero-age homogeneity and a break with the SSM. This is the solar-abundance controversy, which was discovered in 2005.

One possible explanation is that a late “dilution” of the Sun’s convective zone occurred due to a deposition of elements during the formation of the solar system. Were there to have been an accretion of dust and gas from the proto-planetary disc onto the central star during the evolution of the star–planet system, this could have changed the initial metallicity of the surface of the Sun – a hypothesis backed up by recent simulations that show that a metal-poor accretion could produce the present surface metallicity. 

As they are an excellent probe of metallicity, CNO neutrinos have an important role to play in settling the solar-abundance controversy. If Borexino were to measure the Sun’s present core metallicity, and by running simulations backwards prove that its surface metallicity must have been diluted right from its birth, this would violate one of the basic assumptions of the SSM. Probing solar metallicity using CNO neutrinos is, therefore, of the utmost importance, and Borexino is hard at work on the problem. Initial results favour the high-metallicity hypothesis with a significance of 2.1 standard deviations – a tentative first hint from Borexino that zero-age homogeneity may indeed be false.

The ancient question of why and how the Sun and stars shine finally has a comprehensive answer from Borexino, which has succeeded thanks to the detector’s extreme and unprecedented radio-purity – the hard work of hundreds of researchers over almost three decades.