Determination of the ${\nu }_e$ and total ${}^8\mathrm{B}$ solar neutrino fluxes using the Sudbury Neutrino Observatory Phase I data set

This article provides the complete description of results from the Phase I data set of the Sudbury Neutrino Observatory (SNO). The Phase I data set is based on a 0.65 kiloton-year exposure of ${}^2{\mathrm{H}}_2$O (in the following denoted as ${\mathrm{D}}_2$O) to the solar ${}^8\mathrm{B}$ neutrino flux. Included here are details of the SNO physics and detector model, evaluations of systematic uncertainties, and estimates of backgrounds. Also discussed are SNO's approach to statistical extraction of the signals from the three neutrino reactions (charged current, neutral current, and elastic scattering) and the results of a search for a day-night asymmetry in the ${\nu }_e$ flux. Under the assumption that the ${}^8\mathrm{B}$ spectrum is undistorted, the measurements from this phase yield a solar ${\nu }_e$ flux of $\varphi ({\nu }_e)=1.{76}_{-0.05}^{+0.05}(\mathrm{stat}.){}_{-0.09}^{+0.09}(\mathrm{syst}.)\times {10}^6$ cm${}^{-2}$ s${}^{-1}$ and a non-${\nu }_e$ component of $\varphi ({\nu }_{\mu \tau })=3.{41}_{-0.45}^{+0.45}(\mathrm{stat}.){}_{-0.45}^{+0.48}(\mathrm{syst}.)\times {10}^6$ cm${}^{-2}$ s${}^{-1}$. The sum of these components provides a total flux in excellent agreement with the predictions of standard solar models. The day-night asymmetry in the ${\nu }_e$ flux is found to be $A_e=7.0\pm 4.9(\mathrm{stat}.){}_{-1.2}^{+1.3}\%(\mathrm{syst}.)$, when the asymmetry in the total flux is constrained to be zero.

Figure 1

Schematic of SNO detector.

Figure 2

The energy (top row), radial (middle row), and directional (bottom row) distributions used to build probability density functions to fit the SNO signal data. $T_{\mathrm{eff}}$ is the effective kinetic energy of the γ from neutron capture or the electron from the ES or CC reactions, and $R$ is the reconstructed event radius, normalized to the 600-cm radius of the AV.

Figure 3

(Left) Optical light paths within the detector. (Right) PMT time residual distribution for laser data.

Figure 4

Measured $D_2$O attenuation lengths, compared to the data of Boivin et al. [47].

Figure 5

Measured H${}_2$O attenuation lengths compared to the data of Smith and Baker [48], Boivin et al. [47], Quickenden and Irvin [49], and Pope and Fry [50].

Figure 6

PMT angular response model compared to laser source data and to the hybrid model that adjusts the ex situ measurements to agree with the data, for two wavelengths. Note that the zero has been suppressed.

Figure 7

Time residual histograms from ${}^{16}\mathrm{N}$ calibration data at (a) center of the detector and (b) $r=500$ cm. The prepulsing and late pulsing peaks are properties of the PMTs and do not depend on the source position, whereas the reflection peaks from the PMT support sphere vary with source position. The shape and fraction of light in the main peak used for energy calibration (shaded) are reasonably insensitive to source position.

Figure 8

The reduction in the total number of events, as a function of the number of hit PMTs, for successive applications of the instrumental background cuts. In the figure, 1 MeV corresponds to roughly 8.5 hit PMTs.

Figure 9

Comparison of the number of events remaining after application of the two separate sets of instrumental background cuts, as a function of the number of hit PMTs. As can be seen, the differences between the data sets are very minor.

Figure 10

A plot of the distribution of PMT hit times from a laser calibration run. Overlaid on the data are the pdfs used in the fitter to characterize the direct light (dashed curve) and the pdf describing the nondirect light (dotted curve). The summed pdf is also displayed (solid curve). As only the relative times of the PMT hits are relevant in the event reconstruction, the offset of the “prompt” peak from zero is unimportant.

Figure 11

Parametrized angular distribution of Cherenkov photons relative to the initial direction of a Monte Carlo 5-MeV electron. This distribution is used as the pdf for the direct PMT hits in reconstruction.

Figure 12

The distribution of the difference between the reconstructed $x$ position ($x_{\mathrm{fit}}$) and the true position $x_{\mathrm{true}}$ for a sample of Monte Carlo-simulated CC electrons.

Figure 13

$N_{\mathrm{hit}}$ distributions for data (dots) and Monte Carlo simulation (line) for a ${}^{16}\mathrm{N}$ calibration at the detector center, on both linear and logarithmic scales.

Figure 14

Photon collection efficiency ($P_{\mathrm{hit}}$) vs time. Shown is the value of the peak of the $N_{\mathrm{eff}}^{\prime }$ distribution from ${}^{16}\mathrm{N}$ calibration runs at the detector center, relative to the average over the data set. The dashed line is used as ${\epsilon }_{\mathrm{drift}}$, the correction to the absolute energy scale.

Figure 15

Fractional deviation of mean $N_{\mathrm{win}}$ for ${}^{16}\mathrm{N}$ source calibration runs after drift correction applied. Only a subset of the data in Fig. 14 is shown.

Figure 16

${}^{16}\mathrm{N}$ $E_{\mathrm{eff}}$ spectra for calibration data and a Monte Carlo calculation for a deployment near the center of the detector.

Figure 17

Fraction of in-time light for an event vs its mean PMT pair angle (${\theta }_{\mathit{ij}}$). Events that pass the low-level cuts (gray) and those that fail (black) are plotted on the high-level cut axes. ${}^{16}\mathrm{N}$ calibration source events are plotted in blue.

Figure 18

Projection of reconstructed positions of events within the SNO detector onto the $z‐y$ plane for an energy threshold of $T_{\mathrm{eff}}>5.0$ MeV. The dashed line shows the radius of the PMT support sphere (PSUP), the solid line the AV, and the dotted line the fiducial volume cut used by SNO.

Figure 19

Difference between ${}^{16}\mathrm{N}$ source data and ${}^{16}\mathrm{N}$ Monte Carlo simulations of the vertex accuracy, using a precision $z$-axis source scan. Vertex accuracy is defined here as the difference between expected source position (based on the measurements by the source-positioning mechanism for data and the true source position for Monte Carlo-simulated events) and reconstructed position. The shift between the Monte Carlo prediction and the data are consistent with a model that scales each event's reconstructed radial position by ±1%.

Figure 20

Comparison of vertex accuracy in for ${}^{16}\mathrm{N}$ and ${}^8\mathrm{Li}$ data for the October 2000 ${}^{16}\mathrm{N}$ $z$ scan and the December 2000 ${}^8\mathrm{Li}$ scan. Vertex accuracy is defined here as the difference between expected source position (based on the measurements by the source-positioning mechanism for data and the true source position for Monte Carlo-simulated events) and reconstructed position. The shifts between the Monte Carlo prediction and the data for both sources are consistent with a model that scales each event's reconstructed radial position by ±1%.

Figure 21

Difference between vertex resolution for October 2000 high-rate $z$ scan as a function of $z$ and Monte Carlo prediction.

Figure 22

Vertex resolution for high-rate ${}^{16}\mathrm{N}$ data as a function of $N_{\mathrm{hit}}$ compared to Monte Carlo prediction.

Figure 23

Vertex resolution for ${}^8\mathrm{Li}$ data as a function of $N_{\mathrm{hit}}$ compared to Monte Carlo prediction.

Figure 24

Diagram showing vectors involved in measurement of angular resolution using the ${}^{16}\mathrm{N}$ γ-ray calibration source.

Figure 25

The angular resolution tail from ${}^{16}\mathrm{N}$, showing good agreement with Monte Carlo simulation.

Figure 26

Angular resolution for Monte Carlo-simulated CC electrons. Shown is the distribution of angle between the Monte Carlo–predicted initial electron direction and fit direction for $N_{\mathrm{hit}}>65$ and $R_{\mathrm{fit}}<550$ cm. Roughly 68% of the distribution is contained within 26.7 degrees.

Figure 27

Fractional deviation in effective kinetic energy peak μ from the Monte Carlo prediction ${\mu }_0$ for December 1999 position scans. Shown on the left is the deviation vs source position. The right frame shows the distribution of deviations weighted by volume. A conservative $1\sigma$ limit of $0.72\%$ is obtained by adding the mean offset and distribution width linearly. The scatter in the left frame for points at the same radius results from these source locations having different $(x,y,z)$ coordinates that gave the same radial positions.

Figure 28

Fractional deviation in effective kinetic energy peak μ from Monte Carlo prediction ${\mu }_0$ for the January 2001 position scans. Shown in the left frame is the deviation vs source position. The right frame shows the distribution of deviations weighted by volume.

Figure 29

Fractional deviation in kinetic energy peak for all calibration sources including low-rate neutron and ${}^{16}\mathrm{N}$ data. Here, μ is the value at the peak for the data, and ${\mu }_0$ is the Monte Carlo simulation's prediction for the peak.

Figure 30

Comparison of the ex situ and in situ results as a function of time.

Figure 31

Monte Carlo-predicted event isotropy distributions for ${}^{208}\mathrm{Tl}$ and ${}^{214}\mathrm{Bi}$ decays. The isotropy parameter shown here on the abscissa, ${\theta }_{\mathit{ij}}$, is the average opening angle between all fired photomultiplier tube pairs centered at the reconstructed event vertex. More isotropic light distribution in an event results in a higher ${\theta }_{\mathit{ij}}$ value.

Figure 32

Comparison of Monte Carlo predictions of $\beta -\gamma$ background energy spectrum within the $D_2$O to the total neutrino data set. The curves are not fit to the data; they are normalized by the in situ and ex situ estimates and simply overlaid on the neutrino energy spectrum.

Figure 33

Comparison between the PDF obtained from the high-low radon study and the H${}_2$O pdf derived from acrylic source data. A value of $R^3=1$ corresponds to the radius of the AV.

Figure 34

Fit of of $R^3$ pdfs created by using calibration source data to the neutrino data set, using an energy threshold of $T_{\mathrm{eff}}>4.0$ MeV. The extended maximum likelihood method was used in the fit, and the band represents the systematic uncertainties. The $y$ axis is in units of events/0.03 cubic AV radius.

Figure 35

The distribution of live time and calendar time in 480 zenith angle bins for the $D_2$O data set. The dotted line labeled “Total time” is the distribution of live time that would have resulted if the SNO detector were 100% live during the entire calendar time spanned by the full $D_2$O data set. The asymmetric structure in the figure corresponds to the effects of the Earth's axial tilt and the latitude of Sudbury. The numerical values for the bin-by-bin live times are given in Tables 32 and 33.

Figure 36

The signal loss measured from various calibrations sources as a function of the number of hit PMTs.

Figure 37

The signal loss of the high-level cuts for ${}^{16}\mathrm{N}$ γ rays from data and Monte Carlo simulation (a), and the ratio of the two distributions (b).

Figure 38

Radial profile of neutron captures for a ${}^{252}\mathrm{Cf}$ source deployed at the center of the detector, compared to Monte Carlo simulation of the source. In (a) we compare the raw data distribution of events to the Monte Carlo simulation, and we see that the data have an excess owing to the associated γs and βs produced by the source. The difference between the two curves is shown in (b), and the ratio of difference to the data is shown in (c). The dropoff around 80 cm motivates the cut to remove the non-neutron events in the calculation of the efficiency.

Figure 39

Energy spectrum of γ rays from neutron capture for deployment of a ${}^{252}\mathrm{Cf}$ source at the center of the detector.

Figure 40

Capture efficiency for neutrons from a ${}^{252}\mathrm{Cf}$ source at several locations throughout the detector volume. In (a) we compare the measurements (filled dots) to the analytic calculation (solid curve), and in (b) the difference between them.

Figure 41

Flux of ${}^8\mathrm{B}$ solar neutrinos that are μ or τ flavor vs flux of electron neutrinos deduced from the three neutrino reactions in SNO. The diagonal bands show the total ${}^8\mathrm{B}$ flux as predicted by the BP2000 SSM [78] (dashed lines) and that measured with the NC reaction in SNO (solid band). The intercepts of these bands with the axes represent the $\pm 1\sigma$ errors. The bands intersect at the fit values for ${\varphi }_e$ and ${\varphi }_{\mu \tau }$, indicating that the combined flux results are consistent with neutrino flavor transformation with no distortion in the ${}^8\mathrm{B}$ neutrino energy spectrum.

Figure 42

(a) Distribution of $\cos {\theta }_{\odot }$ for $R_{\mathrm{fit}}\le 550$ cm. (b) Distribution of the radial variable $R^3=(R_{\mathrm{fit}}/R_{\mathrm{AV}}){}^3$. (c) Kinetic energy for $R_{\mathrm{fit}}\le 550$ cm. Also shown are the Monte Carlo predictions for CC, ES, and NC + background neutron events scaled to the fit results and the calculated spectrum of $\beta -\gamma$ background (Bkgd) events. The dashed lines represent the summed components, and the bands show $\pm 1\sigma$ statistical uncertainties from the signal-extraction fit. All distributions are for events with $T_{\mathrm{eff}}\ge 5$ MeV.

Figure 43

Relative energy scale for ${}^{16}\mathrm{N}$ calibration data vs calendar time. The black curve is the measured energy drift. The red and blue curves represent “worst-case” energy drift models designed to maximize the relative energy scale difference between day and night data. The energy estimate “$N_{\mathrm{win}}$” is discussed in Sec. 5e.

Figure 44

Run-by-run day and night event rates from the acrylic hot spot.

Figure 45

(a) Energy spectra for day and night. All signals and backgrounds contribute. The final bin extends from 13.0 to 20.0 MeV. Numerical values for each bin are given in Table 31. (b) Difference ($\mathrm{night}-\mathrm{day}$) between the spectra. The day rate was $9.23\pm 0.27$ events/day, and the night rate was $9.79\pm 0.24$ events/day.

Figure 46

Joint probability contours for $A_{\mathrm{tot}}$ and $A_e$. The points indicate the results when $A_{\mathrm{tot}}$ is allowed to float and when it is constrained to zero. The diagonal band indicates the 68% joint contour for the Super-Kamiokande $A_{\mathrm{ES}}$ measurement.