Neutrino physics: Theory and experiment (SS2021) Solar neutrinos Teresa Marrod´anUndagoitia Max-Planck-Institut f¨urKernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany E-mail: [email protected] Contents 1 Lecture 3: Solar neutrinos2 1.1 Standard solar model.............................2 1.2 Neutrino production.............................3 1.3 Radiochemical experiments..........................5 1.4 Real time experiments............................8 1.5 Reminder: Neutrino oscillations in matter................. 14 1.6 Summary................................... 15 1 LECTURE 3: SOLAR NEUTRINOS 1. Lecture 3: Solar neutrinos This lecture discusses the emission of neutrinos by the Sun and some of the measurements performed so far. Solar neutrinos help to understand better the Sun itself but they also provide an intense source of ν's to investigate their properties. Indeed solar neutrinos have played a key role to understand neutrino oscillations. 1.1. Standard solar model Our Sun is in the most stable and long evolutionary phase of a star where hydrogen is consumed in its core (in the main sequence). A common tool to learn about the interior of the Sun is helioseismology, a methodology which employs oscillation frequencies (many modes, more than 1015) to determine the internal structure of the Sun, specifically: • density profiles • constraints on solar composition • the extension of the convective envelope ... The standard solar model (SSM) results from all these observations. Nuclear reactions in the Sun: Typically the reaction in the Sun are of the type: T1 + T2 ! T3 + T4 or T1 + T2 ! T3 + T4 + T5: (1) The temperature in the solar core is ∼ (10 -15)×106 eV corresponding to keV energies. The Coulomb barriers for nuclear reactions are however of ∼ MeV energies. ! The dominant process for charged particles to undergo a reaction of the type above is quantum mechanical tunnelling. The cross section for a nuclear reaction can be given as: S(E) Z Z e2 σ(E) = exp(−2πη) η = 1 2 (2) E ~v S(E) is a nuclear physics factor (smooth when there are no resonances) and the exponential term is the tunnelling factor which represents the Coulomb barrier. Z1;Z2 are the charges of the reacting nuclei and v their relative velocity. The reaction rate can then be written as: n1n2 R = < σv >12 (3) 1 + δ12 ni are the particle densities, δ12 a term to avoid double counting of particles and < σv >12 the thermally averaged cross section. For < σv >, a Maxwell-Boltzmann distribution 2 1 LECTURE 3: SOLAR NEUTRINOS for the velocity of the particles inside the Sun is assumed. Figure1 illustrates the probability for two particles to undergo a nuclear reaction by overcoming the Coulomb barrier. The interplay between the Maxwell-Boltzmann distribution of particle velocities Figure 1. Illustration of the relative probability for two nuclear particles to undergo a nuclear reaction. and the tunnelling probability gives rise to an increased probability which is known as Gamov peak. 1.2. Neutrino production The nuclear energy generation occurs in the Sun by the fusion of hydrogen into helium being the net reaction: 4 + 4p ! He + 2e + 2νe (4) where 26.7 MeV are released per reaction. There are two reaction chains that both result into the burning of equation4: the pp-cycle (makes 99% of the energy in the Sun) and the CNO-cycle (figure2). Within these cycles, there are 8 reactions producing neutrinos. Each ν is typically called as its production reaction. Consequently, there are pp-ν, pep-ν, 7Be-ν, 8B-ν ... The reactions happen at different depths in the interior of the Sun. As general rule, the higher the nuclear charge of the ion involved in the reaction the stronger the dependence of the nuclear cross section on temperature. Accordingly, the more localized is the occurrence of reactions towards regions of higher temperature (at the Sun's center). 3 1 LECTURE 3: SOLAR NEUTRINOS Figure 2. Burning inside the Sun: pp-chain (left) and CNO-chain (right). Figure from Borexino Collaboration, 2018 [1]. • pp-, pep- and hep-neutrinos have a broad spatial distribution (see figure3) • 7Be-, 8B, 15N-, 15O- and 17F- neutrinos are more localized Figure 3. Normalized production profiles of solar neutrinos as a function of solar radius. Figure from Antonelli et al. 2013 [2]. 4 1 LECTURE 3: SOLAR NEUTRINOS The neutrino spectrum is calculated [3] using input parameters such as: • Solar age and luminosity • the equation of state • nuclear parameters (as discussed above) • chemical abundances • opacities (due to processes like Thomson scattering ...) With all these ingredients, the solar model predicts fluxes of ∼ 1010 neutrinos·cm−2·s−1 with % precision (see figure4). Figure 4. Predicted solar neutrino spectrum by Bahcall and Serenelli. Figure from Borexino Collaboration, 2018 [1]. • dominant flux from the pp-reaction featuring a continuous spectrum up to 0.42 MeV • A 7Be line at 0.86 MeV has the second highest rate (another 7Be line at 0.38 MeV) • At highest energies: 8B and hep-neutrinos with continuous spectra up to 14.06 MeV and 18.77 MeV, respectively. 1.3. Radiochemical experiments The search for solar neutrinos began with radiochemical experiments in the 1960s. Raymond Davis and his collaborators carried out the Homestake experiment (see figure5, left) which aim was to collect and count solar neutrinos. 5 1 LECTURE 3: SOLAR NEUTRINOS The detection reaction employed was the inverse beta decay of neutrinos on chlorine: 37 37 − νe + Cl ! Ar + e (5) 37 37 − Ar ! Cl + e + νe (6) • Energy threshold: 0.81 MeV • Half-life of 37Ar: 35 days • Target volume: 615 tons of C2Cl4 (carbon tetrachloride) • 37Cl natural abundance: 24% • Detection working principle: Argon atoms produced by solar neutrinos are collected in the target over several days. Next, the argon atoms are extracted by purging the tank with helium and passing the gas through a charcoal trap. Finally, the argon decays (equation9) are counted in low noise proportional counters. Figure 5. Chlorine Homestake experiment: picture of the tank (R. Davis, Brookhaven National Laboratory) on the left and results of the experiment. Figure from Cleveland et al., 1998 [4]. After about 20 years measuring time the rate measured by the experiment was: R = (2:56 ± 0:22) SNU (7) where SNU is a solar neutrino unit, introduced for convenience, corresponding to: 1 SNU = 1036 captures per target atom and per second. This rate is 1/3 of the expected rate constituting what was called at that time the "solar neutrino puzzle". The right side of figure5 shows the data acquired between 1970 and 1995. Important features of this measurement are: • No sensitivity to neutrino energy (only counting) • Energy threshold above the pp-neutrino spectrum 6 1 LECTURE 3: SOLAR NEUTRINOS Later on, similar experiments were performed with gallium as capture element: gallium experiments. This experiments were targeted to be sensitive to the pp- neutrino flux. The detection reaction is: 71 71 − νe + Ga ! Ge + e (8) 71 − 71 Ge + e ! Ga + νe (9) • Energy threshold: 0.233 MeV • Reminder: end-point of pp-ν spectrum: 0.42 MeV • Half-life of 71Ge EC-decay: 11.4 days Two experiments of this type were performed in the 90s: • SAGE in the Baksan tunnel in Russia, 4 700 meters water equivalent (m.w.e.) under the Caucasus. • GALLEX and its successor GNO at the LNGS underground laboratory, 3 600 m.w.e. under the Apennine mountains (see figure6) Both experiments were similar in the concept. While SAGE used a metallic gallium target (50 tons), GALLEX employed a gallium chlorine solution (30 ton of GaCl3). Figure 6. Schematics of the GALLEX experiment. Figure from the collaboration. 7 1 LECTURE 3: SOLAR NEUTRINOS For simplicity, only details on GALLEX are given in the following. • Runs of ∼ 30 days are acquired to collect enough statistics • Afterwards, 71Ge was extracted by flushing nitrogen gas • GeCl4 is then synthesized • Overall extraction efficiency of 95.7% derived using stable isotopes (70Ge, 72Ge ...) • 71Ge EC-decay is measured in proportional counters. Lines at 10.4 keV and 1.2 keV (Auger electrons and X-rays) appear from the K- and L-shell captures, respectively. The results of the gallium experiments: +3:5 +3:5 • SAGE R = 66:53:4 (stat) 3:2 (syst) • GALLEX R = 69:3 ± 4:1 (stat) ±3:6 (syst) The combined result of GALLEX/GNO and SAGE was ∼ 50% of the prediction. 1.4. Real time experiments In real time experiments, the events are detected as they happen. This is different from the experiments described in the last section were the isotopes created during a certain time (a month for example) are collected at the end of that time period. The first real time solar neutrino detector, Kamiokande, was built in Japan in 1982. Its successor Superkamiokande was built at the beginning of the 90s and has been taking data since then. Some characteristics of Superkamiokande include: • 50 kton ultra-pure water Cherenkov detector (22.5 kton used for analysis) • Cylindrical stainless steel tank about 40 m in height and diameter • Light detected with about 13 000 PMTs • Energy threshold at ∼ 5:5 MeV Neutrinos are detected in Superkamiokande over the elastic scattering reaction: − − νx + e ! νx + e (10) where νx represent the neutrino in all flavours x = e; µ, τ. The experiment uses the directionality of the Cherenkov photons to reconstruct the direction of the incoming neutrino. Figure7 shows the event rate in Superkamiokande as function of angle. The direction has to be converted to a system relative to the Sun's position. For the energy region between 5 and 20 MeV, a clear excess of events appears for the angle corresponding to the Sun position. 8 1 LECTURE 3: SOLAR NEUTRINOS Figure 7. Angular distribution of events for (5 − 20) MeV energy range in Superkamiokande.