Category Archives: Solar neutrinos

Comprehensive measurement of pp-chain solar neutrinos with Borexino

In autumn 2018, the Borexino collaboration publishes [Nature 562, 505 (2018)] the first complete study of all neutrinos components  from the proton-proton fusion process in the Sun.

About 99% of the solar energy is produced through sequences of nuclear reactions, initiated by the so-called pp (proton-proton) fusion, in which hydrogen is converted into helium. Neutrinos emitted by this nuclear fusion chain represent a unique tool for solar and neutrino physics.

Here we report the first comprehensive measurement of the interaction rates of pp, ^7Be, and pep neutrinos with the highest precision to date, together with that of ^8B neutrinos with the lowest-threshold. We also set a limit on the hep neutrino flux.

These measurements provide  a first indication that the temperature profile in the Sun is more compatible with solar models assuming high surface metallicity, and a direct determination of the pp-II/pp-I  branching ratio. At the same time, we determined the survival probability of solar electron neutrinos at different energies, thus probing simultaneously and with high precision the MSW-LMA flavor conversion paradigm in both the vacuum and the matter dominated regimes.

This plot (as given in Fig. 2a of the 2018 Nature paper) reports the distribution of events after selection cuts, and the fit of the Borexino Low-Energy-Region (LER, [0.19-2.93] MeV) spectrum. Neutrino and background components are depicted over the Three Fold Coincidence (TFC) subtracted energy spectrum with suppressed ^{11}C background. The properties of the data bins and residuals are available here. For this specific fit we also report the correlation matrix for both the Monte Carlo and the analytical approach. 

As regards the High-Energy-Region (HER, [3.2-16] MeV) of the Borexino spectrum, this plot (Fig. 2b of the 2018 Nature paper) reports the radial distribution of events belonging to HER-I ([3.2-5.7] MeV), after selection cuts. Fit with neutrino and background components are depicted as well. Data bins content and residuals are available here

Borexino provides the most precise measurement of the electron neutrino survival probability (P_{\mathrm{ee}}) in the low energy region, and it is so far the only experiment being able to simultaneously test neutrino flavour conversion in both the vacuum and the matter dominated regime.  

As in Fig. 3 of  Nature (2018), the above plot shows the  electron neutrino survival probability as a function of neutrino energy. We report the P_{\mathrm{ee}} from the Borexino experimental measurements of pp, ^7Be, pep and ^8B solar neutrino flux, as well as the ± 1\sigma theoretical prediction of P_{\mathrm{ee}} according to the MSW-LMA and Vacuum-LMA solutions. The theoretical bands contours are reported here while Borexino experimental P_{\mathrm{ee}} points can be found here.

To further probe the robustness of the Borexino results,  we performed a statistical study to compare our P_{\mathrm{ee}} measurements with two theoretical oscillation scenarios: the MSW-LMA and the Vacuum-LMA.  The test was carried out as a frequentist analysis where we adopted a test statistics t based on the ratio between the likelihood obtained assuming the MSW-LMA and the Vacuum-LMA oscillation hypothesis. This ratio test pointed out how our data disfavour the Vacuum-LMA hypothesis at 98.2% C.L., and are in excellent agreement with the expectation from the MSW-LMA paradigm.

The plot above as in “Extended Data” Fig. 2 of our 2018 Nature paper (online version only)  shows the probability distribution of the test statistics t, obtained by simulating thousands of sets of P_{\mathrm{ee}}  values (at the pp, ^7Be, pep and ^8B energies) in the MSW-LMA and the Vacuum-LMA hypothesis. Data bins content for the two distributions can be found here. The dotted black line corresponds to the actual Borexino  P_{\mathrm{ee}} results, which gives a value of t_{BX}=-4.16 .

This plot (Fig. 4 of the Borexino 2018 Nature paper) compares the Borexino experimental results with the theoretical predictions from the low metallicity (SSM-LZ) and high metallicity (SSM-HZ) Standard Solar Models in the \Phi(^7Be)-\Phi(^8B) space. Allowed contour obtained by combining the Borexino new results with all solar and KamLAND data, and leaving free the oscillation parameters \theta_{12} and \Delta \mathrm{m}^2_{21}, is also shown.  All contours correspond to 68.27% C.L. 
Best fit values are available here while the global analysis \chi^2 profile can be found here. The contours describing the Borexino measurements and the SSM-HZ (SSM-LZ) expectations are obtained taking into account the specific \Phi(^7Be) and \Phi(^8B) evaluations (the best fit values and the related uncertainties) as well as their correlation, if any.

The Borexino results on the ^7Be and ^8B solar neutrino fluxes are compatible with the temperature profiles predicted by both the  high and low metallicity Standard Solar Models. However, the combination of the Borexino measurements provides an interesting hint in favour of the solar temperature profile predicted by the SSM-HZ. This results was obtained by performing both a frequentist and a Bayesian hypothesis test. As regards the frequentist analysis, our data disfavour the SSM-LZ at 96.6% C.L., a constraint which is slightly stronger than our sensitivity (median sensitivity, 94.2% C.L.). The Bayesan analysis confirms the mild preference for the SSM-HZ, yielding a Bayes factor of 4.9.

The above plot, as in “Extended Data” Fig. 3 of the 2018 Nature paper (online version only),  shows the probability distribution of the frequency test for the SSM-LZ and the SSM-HZ. The test statistics t is obtained by simulating thousands of fake sets of ^7Be–^8B values in the HZ and LZ hypothesis. Data bins content for the two distributions can be found here. The dotted black line corresponds to the actual Borexino ^7Be and ^8B results, which gives a value of t_{BX}=-3.49 .

Seasonal Modulation of the 7Be Solar Neutrino Rate in Borexino

On June 2017, the Borexino collaboration published [Astroparticle Physics 92 (2017) 21-29] an improved measurement of time periodicities of the 7Be solar neutrino interaction rate.

This yearly modulation was observed on 4 years (December 2011 – December 2015) of Borexino Phase II data.

The period, amplitude, and phase of the observed time evolution of the signal are consistent with its solar origin, and the absence of an annual modulation is rejected at 99.99% C.L.

The data were analyzed using three methods:

  1. the sinusoidal fit;
  2. the Lomb-Scargle method;
  3. the Empirical Mode Decomposition techniques.

All the analysis methods clearly confirm the presence of an annual modulation of the 7Be solar neutrino interaction rate and show no signs of other periodic time variations.

This plot (as given in Fig.4 of our paper) shows the \beta-like event rate [cpd/100 ton] along with the best fit in 30.4-days long bins, starting from Dec 11, 2011 . The red line describes the analytical fit equation:

    \[\mathrm{R(t)=R_0 + \overline{R}} \left[ 1 +  \epsilon \cos \frac {2 \pi} {\mathrm{T}}  \left( \mathrm{t} - \phi \right) \right]^2.\]

Related data (Nbin, rate and errors) are available here.

The robustness of the fit was studied by varying the bin size and the fitting methods. The following plot (as given in Fig. 5 of the publication) shows the rate of \beta-like events passing selection cuts in 7-days long bins. This time, the red line is the best fit resulting from the Lomb-Scargle analysis. Associated data (Nbin, rate and errors) can be found here.

Neutrinos from the primary proton-proton fusion process in the Sun

In 2014, the Borexino collaboration published (Nature 512, pp 383 2014) the first real-time measurement of neutrinos from the proton-proton fusion process.

In the core of the Sun, energy is released through sequences of nuclear reactions that convert hydrogen into helium. The primary reaction is thought to be the fusion of two protons with the emission of a low-energy neutrino. These so-called pp neutrinos constitute nearly the entirety of the solar neutrino flux, vastly outnumbering those emitted in the reactions that follow. Although solar neutrinos from secondary processes have been observed, proving the nuclear origin of the Sun’s energy and contributing to the discovery of neutrino oscillations, those from proton–proton fusion have hitherto eluded direct detection. Here we report spectral observations of pp neutrinos, demonstrating that about 99% of the power of the Sun, 3.84 × 1033 ergs per second, is generated by the proton–proton fusion process.

Fig3This plot (as given in Fig. 3 of the Borexino Nature paper) reports the fit of the Borexino energy spectrum between 165 and 590 keV and the relative residuals. The properties of the data bins and residuals are available here.

FigExt2This plot, as shown in “Extended Data Figure 2″ of the Borexino Nature paper, reports the ± 1\sigma prediction of the MSW-LMA solution for the electron survival probability as well as the survival probability points associated to the Borexino experimental measurements of pp, 7Be, pep and 8B solar neutrino flux.

Numerical values for the electron survival probability band are available here  while the coordinates of the experimental Borexino measurements can be found here.