---
title: "Solar Neutrino Flavor Observatory Interactive Lab | Sandbox Physics"
description: "How can you tell a fainter Sun from neutrinos that change flavor on the way? Count the neutrinos two ways."
canonical_url: "https://sandboxphysics.com/labs/solar-neutrino-flux/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/solar-neutrino-flux/"
last_modified: "2026-10-27"
---

Neutrinos · D03 · SNO and the missing flavors

# Solar Neutrino Flavor Observatory

**How can you tell a fainter Sun from neutrinos that change flavor on the way?** Count the neutrinos two ways. One reaction sees only electron neutrinos; the neutral-current reaction counts all active flavors alike. If electron neutrinos come up short while the all-flavor total does not drop, the Sun is not fainter. Some of its electron neutrinos have turned into other flavors on the way.

Look inside a heavy-water detector and replay the three reactions it can see. Record a simulated exposure, then find where the flux limits from the three channels cross. Can a fainter Sun that emits only electron neutrinos explain the same counts?

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

This teaching model is inspired by SNO: a 12 m vessel and an 18 m sensor sphere, both rounded, with 384 enlarged sensors. The three channels are perfectly separated Poisson counts with a stated response matrix and exactly known backgrounds. They are not SNO data, and SNO’s correlated event extraction is not reproduced. The elastic-scattering flavor weight is fixed, and the neutrino spectrum, thresholds, MSW propagation and detector calibration are left out. The optical examples are sketches, not the events used to sort the total counts into channels. The fits are unconstrained weighted least squares, and the counting bands are not confidence regions or discovery significance.

Three responses to the same exposure

## Comparing the channels reveals the missing flavor

CC

### Charged current

Use in fit

Electron flavor only

$\nu_e+d\to p+p+e^-$

Recorded count $\text{—}$

Prediction at the inspected point, with background $\text{—}$

NC

### Neutral current

Use in fit

All active flavors

$\nu_\alpha+d\to p+n+\nu_\alpha$

Recorded count $\text{—}$

Prediction at the inspected point, with background $\text{—}$

ES

### Elastic scattering

Use in fit

A weighted flavor mixture

$\nu_\alpha+e^-\to\nu_\alpha+e^-$

Recorded count $\text{—}$

Prediction at the inspected point, with background $\text{—}$

Solid bars are observed counts; thin bars are predictions at the inspected flux point. Every channel shares one count scale. Channel labels are ideal here; real SNO extracted overlapping populations with a joint statistical analysis.

### Where the channel constraints cross

Click a flux point, or use arrow keys on the chart. Shading shows one counting-fluctuation scale for each selected channel.

Both axes use $10^6\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$

CC NC ES Best fit

Inferred from these counts

### How much changed flavor?

Electron flavor $\text{—}$

Other active flavors $\text{—}$

Values include a local counting-error scale, assuming known response and background. Negative estimates are displayed, with a warning; no physical-boundary interval is claimed.

Best electron-only explanation

$\text{—}$

Weighted residual: best / electron-only$\text{—}$

Residual scores compare this teaching record only. They are not SNO’s significance or calibrated p-values.

Inspected flux point $\text{—}$ Reveal simulated source

Response matrix, exact counts & optical hits

Counts per unit exposure and flux. The rows correspond to CC, NC and ES; backgrounds per exposure are shown separately. These are teaching coefficients, not measured SNO efficiencies.

$$
A=\begin{pmatrix}300&0\\100&100\\60&9.24\end{pmatrix},\qquad B=bT\begin{pmatrix}20\\35\\8\end{pmatrix}
$$

Compare with the historical result

SNO’s 2002 paper reported electron and total active fluxes, under its stated boron-8 spectrum assumption. These published values are a separate reference; this simulator neither fits them nor reproduces the collaboration’s analysis.

$$
\begin{aligned}\Phi_e&=1.76\pm0.05\,\mathrm{(stat.)}\pm0.09\,\mathrm{(syst.)}\\\Phi_{\mathrm{NC}}&=5.09^{+0.44}_{-0.43}\,\mathrm{(stat.)}^{+0.46}_{-0.43}\,\mathrm{(syst.)}\end{aligned}
$$

$10^6\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$

[SNO · 2002 original paper ↗](https://arxiv.org/abs/nucl-ex/0204008)

[Why heavy water changed the question →](https://sandboxphysics.com/stories/neutrinos/sno-flavor-transformation/) [Explore how flavor propagates →](https://sandboxphysics.com/labs/neutrino-flavor-propagation/)

Before heavy water: two radiochemical targets

## Two targets see the same Sun differently

Chlorine misses the pp component; gallium sees it. Change what arrives, then watch each published response add up.

This is a separate calculation with BP2000 responses. These controls do not change the SNO exposure recorded above.

Prescribed component averages pp survival $P_{pp}$ $0.55$ Intermediate-component survival $P_{\mathrm{mid}}$ $0.45$ Boron-8 and hep survival $P_{\mathrm{high}}$ $0.33$ Common source scale $f$ $1$ Exposure in days $T$ $30$

### Chlorine · Homestake

$\nu_e+{}^{37}\mathrm{Cl}\to{}^{37}\mathrm{Ar}+e^-$

Capture threshold $0.814\,\mathrm{MeV}$

$2.72\,\mathrm{SNU}$

Bar scale: 150% of this target’s unchanged BP2000 rate.

- **Relative to no flavor change**: $0.358$
- **Expected extracted atoms**: $4.78$

### Gallium · GALLEX / GNO / SAGE

$\nu_e+{}^{71}\mathrm{Ga}\to{}^{71}\mathrm{Ge}+e^-$

Capture threshold $0.233\,\mathrm{MeV}$

$63.06\,\mathrm{SNU}$

Bar scale: 150% of this target’s unchanged BP2000 rate.

- **Relative to no flavor change**: $0.493$
- **Expected extracted atoms**: $67.75$

pp component Intermediate components High-energy components

Equal illustrative populations of target isotope atoms; constant production, radioactive loss during exposure and 90% extraction. Values are expectations, not recorded integer counts. $N_{\mathrm{target}}=10^{30}$

Inspect every component and the calculation

Rounded BP2000 Table 7 components, multiplied by the prescribed survival and source scale. All rates in SNU.

| Source | Chlorine baseline | Chlorine current | Gallium baseline | Gallium current |
| --- | --- | --- | --- | --- |
| $pp$ | 0.00 | 0.00 | 69.70 | 38.34 |
| $pep$ | 0.22 | 0.10 | 2.80 | 1.26 |
| $\mathrm{hep}$ | 0.04 | 0.01 | 0.10 | 0.03 |
| ${}^7\mathrm{Be}$ | 1.15 | 0.52 | 34.20 | 15.39 |
| ${}^8\mathrm{B}$ | 5.76 | 1.90 | 12.10 | 3.99 |
| ${}^{13}\mathrm{N}$ | 0.09 | 0.04 | 3.40 | 1.53 |
| ${}^{15}\mathrm{O}$ | 0.33 | 0.15 | 5.50 | 2.48 |
| ${}^{17}\mathrm{F}$ | 0.00 | 0.00 | 0.10 | 0.05 |

$$
R_d=f\sum_i c_{di}P_i,\qquad 1\,\mathrm{SNU}=10^{-36}\,\mathrm{atom}^{-1}\,\mathrm{s}^{-1}
$$

$$
N_{\mathrm{ext}}=\epsilon\frac{q}{\lambda}(1-e^{-\lambda T}),\quad\lambda=\frac{\ln2}{t_{1/2}}
$$

Production is in atoms per day. Half-lives: argon 35.0 days, germanium 11.43 days. The intermediate group combines pep, beryllium-7 and CNO; the high group combines boron-8 and hep. These prescribed averages are not exact energy intervals or a numerical matter-propagation solution.

Separate historical measurements · 2001 snapshot

BP2000 Table 8 reports these measurements. They stay fixed while you move the controls; no joint fit, discovery significance or present-day best value is claimed.

$$
\begin{aligned}R_{\mathrm{Cl}}&=2.56\pm0.23\,\mathrm{SNU}\\R_{\mathrm{GALLEX+GNO}}&=74.1^{+6.7}_{-7.8}\,\mathrm{SNU}\\R_{\mathrm{SAGE}}&=75.4^{+7.8}_{-7.4}\,\mathrm{SNU}\end{aligned}
$$

Fixed historical spectrum and rounded integrated coefficients; no solar luminosity constraint, correlated flux/cross-section uncertainties, extraction fluctuations or counter backgrounds. Radiochemistry integrates captures and loses event direction and capture time.

[BP2000 · Tables 7–8 ↗](https://www.sns.ias.edu/~jnb/Papers/Preprints/BP2000/paper.pdf) [Gallium cross sections ↗](https://arxiv.org/abs/hep-ph/9710491) [Homestake →](https://sandboxphysics.com/stories/neutrinos/homestake-solar-neutrino-problem/) [GALLEX / SAGE →](https://sandboxphysics.com/stories/neutrinos/gallium-low-energy-solar-neutrinos/)

Physics tutorial

## One source. Three different questions.

**Background** Radiochemical experiments found too few solar electron neutrinos. SNO used heavy water to ask an additional question: how many active neutrinos arrived, regardless of flavor? Comparing the charged-current, neutral-current and elastic-scattering rates told a faint source apart from a change of flavor.

**Why it matters** Each channel picks out a band on a plane whose axes are the two flux components. A single rate that is sensitive to electron flavor cannot tell a weaker source from a change of flavor; channels with different sensitivities can.

Start with the essentials

- **Focus question**: Can the same electron-channel count come from two Suns with different total active fluxes?
- **One-sentence intuition**: The neutral-current rate counts all active flavors together, so a low electron-flavor rate does not have to mean a low total active flux.

### Core mathematical model

#### Two flux components

$$
\Phi_x=\Phi_\mu+\Phi_\tau,\qquad\Phi=\Phi_e+\Phi_x
$$

The second component contains the other two active flavors. This model cannot distinguish muon from tau flavor, and does not include sterile states.

#### Expected counts in the three channels

$$
\begin{aligned}\lambda_{\mathrm{CC}}&=300T\Phi_e+20bT\\\lambda_{\mathrm{NC}}&=100T(\Phi_e+\Phi_x)+35bT\\\lambda_{\mathrm{ES}}&=60T(\Phi_e+0.154\Phi_x)+8bT\end{aligned}
$$

Flux is in millions per square centimeter per second, and exposure is relative. The coefficients and known backgrounds are chosen for teaching. The fixed scattering weight stands in for a response that really depends on the spectrum; it is not a universal ratio.

#### Sampling the counts

$$
N_i\sim\operatorname{Poisson}(\lambda_i)
$$

Each of the three channels, perfectly separated here, is sampled independently. The real SNO analysis had to fit overlapping event populations with correlated uncertainties. The optical examples are not used to assign these total counts to channels.

#### Fitting only the selected channels

$$
Q=\sum_{i\in\mathcal S}\frac{[N_i-B_i-T(A\boldsymbol\Phi)_i]^2}{\max(N_i,1)}
$$

The unconstrained weighted least-squares fit uses each observed count as its variance estimate, but never less than one. Its local covariance and residual scores describe this approximation; neither is a calibrated confidence region or significance.

#### Light travel time to each sensor

$$
t_j=\frac{n\,|\mathbf r_j-\mathbf r_v|}{c}
$$

Every ray in the scene ends at a stored sensor position, 9 meters from the center. The clock starts when the electron effectively emits light, and the water index is 1.33. Refraction at the acrylic, dispersion, scattering and the neutron capture delay are left out.

### Common difficulties

#### A neutral-current flash is not a direct neutrino image

**Typical misconception** A neutron emits the light shown in the NC scene.

**Better mental model** The freed neutron is captured, the capture gamma rays scatter electrons, and those electrons emit the Cherenkov light. The illustration is averaged over directions, starts at that effective emission point and leaves out the capture delay and the neutron’s diffusion.

#### A negative fit result warns about the approximation

**Typical misconception** A negative other-flavor estimate is a physical negative flux.

**Better mental model** The fit is deliberately unconstrained, so near zero, counting fluctuations can push the estimate outside the physical range. A physical inference needs a proper treatment of that boundary, which this Lab does not provide.

### Run the experiment

1. 01

   #### Compare the reactions

   Select CC, NC and ES above the detector. Drag along the light-flight timeline and check the side and interaction views.

   **What to observe:** CC and ES show broadened cones of light from electrons. NC shows a capture flash averaged over directions, because the neutron is neutral and is not the particle that emits the Cherenkov light.

2. 02

   #### Make two similar electron counts

   Acquire Faint Sun, then Changed flavors. Compare CC and NC on the shared count scale.

   **What to observe:** Both presets have the same electron-flavor flux. The larger total active flux raises the NC count; losing electron flavor is not the same as dimming the source.

3. 03

   #### Remove a channel

   Turn off NC, then ES. Keep only CC in the fit, then restore a second channel.

   **What to observe:** One rate only confines the fluxes to a line, not a single point. With this response, CC plus ES can also separate the two components, but its error on the other-flavor flux is larger than with CC plus NC.

4. 04

   #### Test an electron-only explanation

   Look at the best electron-only hypothesis and compare its predicted bars with the recorded counts.

   **What to observe:** That hypothesis gets its own best fit to the selected channels. When the counts need another active component, matching one channel leaves the others unmatched.

5. 05

   #### Separate truth from inference

   Reveal the simulated source, vary the seed, and acquire a long exposure. Export the CSV.

   **What to observe:** The truth marker plays no part in the fit. Counts fluctuate, so the best fit need not land exactly on the source. The export contains every displayed count, response, illustrative hit and sensor coordinate.

Physical conclusion

Channels with different flavor sensitivities turn a missing electron rate into a test of the total active flux. This Lab shows that logic on its own; it does not reproduce the historical analysis.

## Related experiments and articles

Continue exploring

### How flavor change is predicted and tested

Propagation through vacuum and matter predicts a flavor probability. How do solar, atmospheric, reactor and beam experiments test it?

1. [Lab **Neutrino Flavor Propagation** Start with coherent vacuum propagation and ideal flavor trials.](https://sandboxphysics.com/labs/neutrino-flavor-propagation/)
2. [Lab **Neutrino Matter Resonance** Follow a rotating matter Hamiltonian and compare slow with sudden conversion.](https://sandboxphysics.com/labs/neutrino-matter-resonance/)
3. [You are here **Solar Neutrino Flavor Observatory** Separate electron flavor from total active solar flux with three reaction responses.](https://sandboxphysics.com/labs/solar-neutrino-flux/)
4. [Lab **Atmospheric Neutrino Zenith Experiment** Turn Earth-crossing baselines into direction-dependent event counts.](https://sandboxphysics.com/labs/atmospheric-neutrino-zenith/)
5. [Lab **Reactor Near–Far Spectra** Fit the same near and far counts while testing calibration and normalization.](https://sandboxphysics.com/labs/reactor-near-far-spectra/)
6. [Lab **Long-Baseline CP Observatory** Compare both accelerator beam polarities on frozen spectra and separate CP phase, matter and response assumptions.](https://sandboxphysics.com/labs/long-baseline-cp/)

Neutrinos · Reading path

### What happened to the Sun’s neutrinos?

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How do you know those neutrinos came from the Sun?**](https://sandboxphysics.com/stories/neutrinos/kamiokande-real-time-solar-neutrinos/)
2. [Lab **Cherenkov Light & Detector Rings**](https://sandboxphysics.com/labs/cherenkov-rings/)
3. [Article **SNO: where did the Sun’s missing neutrinos go?**](https://sandboxphysics.com/stories/neutrinos/sno-flavor-transformation/)
4. [Article **Why does passing through the Sun change a neutrino’s flavor?**](https://sandboxphysics.com/stories/neutrinos/solar-matter-msw-effect/)
5. [Lab **Neutrino Matter Resonance**](https://sandboxphysics.com/labs/neutrino-matter-resonance/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)