Supernova $ν$ flavour conversions in DUNE: the slow, the fast and the standard

This study evaluates the Deep Underground Neutrino Experiment's (DUNE) capability to distinguish between slow collective, fast collective, and standard MSW neutrino flavor conversion mechanisms in a future supernova signal by combining GLoBES and MultiNest to analyze flux parameter extraction.

The Gist

Imagine a massive star in our galaxy runs out of fuel and collapses in on itself, creating a spectacular explosion called a supernova. This event is like a cosmic firework, but instead of light, it shoots out an unimaginable flood of tiny, ghostly particles called neutrinos.

Scientists are building a giant underwater detector called DUNE (Deep Underground Neutrino Experiment) in South Dakota. Its job is to catch these neutrinos when they arrive at Earth. If a supernova goes off nearby, DUNE will be the first to see it, acting like a cosmic seismograph.

However, there's a catch. These neutrinos don't just travel in a straight line from the star to Earth. As they zoom through the incredibly dense soup of the exploding star, they interact with each other and change their "identity" (or flavor). It's like a game of musical chairs where the players swap seats constantly.

This paper asks a simple but crucial question: If DUNE catches these neutrinos, can we figure out what the explosion looked like at the source, even after all this identity swapping?

Here is a breakdown of the three main "identity swapping" games the paper studies, using simple analogies:

1. The Three Types of "Identity Swaps"

The authors look at three different ways neutrinos change flavors:

• The "Slow" Swap (Spectral Swaps):

  • The Analogy: Imagine a slow-motion dance where two groups of dancers (neutrinos of different energies) slowly trade partners. This happens over tens of milliseconds.
  • What it does: It creates a sharp "cut" in the energy spectrum. Below a certain energy, the neutrinos stay the same; above it, they completely swap identities. It's like a river that suddenly changes color halfway through its path.
  • The Result: If this happens, the neutrinos arriving at Earth have a very specific, jagged pattern in their energy levels.

• The "Fast" Swap (Fast Flavor Conversions):

  • The Analogy: This is like a sudden, chaotic mosh pit. It happens in a split second (microseconds). If the neutrinos are moving in slightly different directions, they instantly scramble their identities.
  • What it does: It tends to mix everything up equally. Instead of distinct groups, you get a "smoothie" where all flavors are blended together.
  • The Result: The distinct differences between the types of neutrinos disappear, making them look very similar to each other.

• The "Standard" Swap (MSW Effect):

  • The Analogy: This is the "classic" version. Imagine neutrinos walking through a thick fog (the star's matter). As the fog gets thinner, they naturally shift into a different form, like a chameleon changing color based on the background.
  • What it does: This depends on the "mass ordering" of the neutrinos (a fundamental property of the universe). It acts like a filter, letting some flavors pass through while blocking or converting others.

2. The Detective Work at DUNE

The scientists used computer simulations to ask: If DUNE sees a specific pattern of neutrinos, can we tell which "swap" happened?

They tested two different "recipes" for the initial explosion (Benchmark A and Benchmark B) and ran them through the three scenarios above.

The Good News:

• We can tell if any swapping happened. If the data looks like a smooth, unswapped flow, DUNE will know immediately that something is wrong with our models.
• We can likely figure out the "Mass Ordering." DUNE is sensitive enough to tell if the neutrinos are arranged in the "Normal" or "Inverted" order, which is a huge mystery in physics.
• We can still guess the explosion's power. Even with all the swapping, DUNE can still estimate how much energy the star released and the average energy of the particles.

The Bad News (The Tricky Part):

• It's hard to tell "Slow" from "Fast" if they happen together. If the "Slow" dance happens first, followed by the "Fast" mosh pit, the final result looks very similar to just the "Fast" mosh pit alone. DUNE might not be able to tell the difference.
• The "Standard" swap hides the truth. The standard MSW effect is so powerful that it often overwrites the subtle signatures of the other effects. It's like if someone painted over a detailed mural with a single coat of white paint; you can see the white paint, but you can't easily see the original art underneath.
• The "Inverted" ordering is confusing. If the universe has an "Inverted" mass ordering, the different swapping scenarios look almost identical to DUNE. It's like trying to distinguish between a red apple and a red ball when they are both painted the exact same shade of red.

3. The Big Takeaway

The paper concludes that DUNE is a powerful tool, but it needs a good map.

If we don't understand the complex "swapping" rules (the collective effects), we might misinterpret the data. We might think a star exploded with a certain energy when it actually exploded with a different one, simply because we didn't account for the neutrinos changing their clothes on the way to Earth.

In summary:

• The Star: A cosmic explosion sending out neutrinos.
• The Journey: A chaotic trip where neutrinos swap identities (Slowly, Quickly, or Standardly).
• The Detector (DUNE): A giant net catching the survivors.
• The Challenge: The net catches the neutrinos, but the "clothes" they are wearing have changed. The scientists are trying to figure out if DUNE is smart enough to reverse-engineer the original outfit, even after the chaotic journey.

The answer is: Yes, mostly. DUNE will be able to tell us a lot about the explosion and the nature of neutrinos, but we must be careful not to get fooled by the most complex mixing scenarios, especially if the universe has the "Inverted" mass ordering.

Technical Summary

Here is a detailed technical summary of the paper "Supernova $\nu$ flavour conversions in DUNE: the slow, the fast and the standard" by A. Giarnetti and J. T. Penedo.

1. Problem Statement

Core-collapse supernovae (SNe) act as extreme neutrino factories, producing a massive flux of neutrinos. However, the flavor composition of these neutrinos as they reach Earth is significantly altered by three distinct conversion mechanisms:

1. Standard MSW Conversions: Matter-enhanced oscillations dependent on the neutrino mass ordering (Normal Ordering - NO, or Inverted Ordering - IO).
2. Slow Collective Oscillations: Energy-dependent spectral swaps driven by neutrino-neutrino forward scattering, occurring over tens of milliseconds.
3. Fast Collective Oscillations (FFCs): Energy-independent flavor conversions driven by angular crossings in the neutrino distribution, occurring on sub-microsecond timescales.

The challenge lies in the fact that these mechanisms often operate simultaneously and non-linearly. Current analyses of future supernova signals (specifically for the Deep Underground Neutrino Experiment, DUNE) often treat these effects in isolation or assume complete flavor equilibration, potentially leading to a misinterpretation of the original supernova flux parameters (luminosity, average energy, spectral pinching) and the underlying physics (mass ordering, collective effects).

2. Methodology

The authors employ a phenomenological approach to bridge the gap between supernova evolution simulations and terrestrial detector response.

• Flux Parameterization:

  • The initial neutrino fluxes are modeled using "pinched" thermal spectra defined by luminosity ($\epsilon_i$), average energy ($\langle E_i \rangle$), and a pinching parameter ($\alpha_i$).
  • Angular distributions are modeled as Gaussian functions centered in the forward direction, characterized by a spread parameter ($\sigma_i$).
  • Two benchmark scenarios (A and B) are defined with specific parameter sets to test the sensitivity of the analysis.

• Flavor Conversion Modeling:

  • Slow Instabilities: Modeled via spectral swaps (splits) determined by the zeros of the spectral difference function $g(1/E)$. The swap windows depend on the mass ordering and the crossing energies.
  • Fast Instabilities: Modeled via angular crossings of the Electron Lepton Number (ELN) and non-electron Lepton Number (XLN) distributions. The authors use an analytical prescription (based on Ref. [59]) to calculate the survival probability $P_{ee}(v)$, leading to partial or full flavor equilibration depending on the angular region.
  • Sequential Application: The study assumes a specific temporal order: Slow instabilities develop first, followed by Fast instabilities, and finally MSW conversions as neutrinos exit the star. This addresses the complexity of non-linear interplay.

• Detector Simulation & Inference:

  • Detector: DUNE Far Detector (40 kt Liquid Argon Time Projection Chamber).
  • Channels: The analysis includes $\nu_e$ Charged Current (CC), $\bar{\nu}_e$ CC, Neutral Current (NC) on Argon, and Neutrino-Electron Elastic Scattering (ES).
  • Tools: The General Long Baseline Experiment Simulator (GLoBES) is used to compute event rates and energy smearing. This is interfaced with MultiNest, a nested sampling algorithm, to perform Bayesian inference.
  • Goal: To reconstruct the source flux parameters ($\epsilon, \alpha, \langle E \rangle$) and distinguish between different conversion scenarios (Unoscillated, MSW-only, Slow+MSW, Slow+Fast+MSW) for both NO and IO mass orderings.

3. Key Contributions

• Integrated Framework: The paper provides a comprehensive framework that simultaneously incorporates slow collective effects, fast collective effects, and standard MSW conversions in a sequential manner, rather than treating them as mutually exclusive or assuming full equilibration.
• DUNE Sensitivity Analysis: It offers the first detailed assessment of DUNE's ability to disentangle these specific collective effects from standard oscillations using Bayesian model comparison.
• Parameter Reconstruction: It quantifies how the presence of collective effects impacts the precision of reconstructing the original supernova flux parameters (luminosity, pinching, average energy).
• Benchmark Comparison: By comparing two distinct flux benchmarks (differing in pinching parameters), the study highlights how the initial spectral shape influences the ability to distinguish conversion scenarios.

4. Key Results

A. Spectral Fluence Modifications

• Fast Conversions: Tend to equalize fluences across species, diminishing distinctions between $\nu_e$ and $\nu_x$.
• MSW Effects: Depend heavily on mass ordering. In NO, $\nu_e$ converts to $\nu_x$; in IO, $\bar{\nu}_e$ converts to $\bar{\nu}_x$.
• Slow Conversions: Induce sharp spectral swaps. In NO, a swap occurs above 20 MeV; in IO, two swaps occur, causing significant depletion of $\nu_e$ at lower energies (8 MeV).
• Combined Effects: When all three are active, fast conversions partially "soften" the dramatic spectral swaps induced by slow instabilities before MSW effects further reshape the spectrum.

B. Flux Parameter Reconstruction

• Unoscillated Case: DUNE can reconstruct $\nu_e$ parameters with high precision due to the large $\nu_e$ CC cross-section. $\bar{\nu}_e$ parameters are poorly constrained due to high energy thresholds and low cross-sections.
• Impact of MSW: MSW conversions drastically reduce sensitivity to original $\nu_e$ parameters (as they convert to $\nu_x$) but improve constraints on original $\nu_x$ parameters (which convert to $\nu_e$).
• Impact of Collective Effects: The presence of slow and fast instabilities does not significantly degrade the ability to reconstruct flux parameters if the correct model is used. The dominant factor degrading reconstruction quality is the MSW effect (due to flavor swapping), not the collective effects themselves.
• Priors: Physics-informed priors (e.g., $\langle E_{\nu_e} \rangle \le \langle E_{\bar{\nu}_e} \rangle \le \langle E_{\nu_x} \rangle$) are crucial for constraining parameters that are otherwise poorly measured.

C. Model Discrimination (Bayesian Evidence)

• Unoscillated vs. Converted: The unoscillated scenario is decisively distinguishable from any scenario involving MSW conversions ($\log_{10} B > 20$).
• Mass Ordering: DUNE can almost always distinguish between NO and IO scenarios with strong evidence, regardless of the collective effects present.
• Collective Effects (Slow vs. Fast):
  • NO Case: An MSW-only scenario is decisively distinguishable from scenarios involving collective effects.
  • IO Case: Different collective mechanisms (Slow, Fast, or both) produce observationally similar spectra. DUNE cannot decisively distinguish between "Slow+MSW" and "Slow+Fast+MSW" in the IO case.
  • Fast Conversions: DUNE lacks the sensitivity to resolve the subtle spectral imprints of fast flavor conversions when slow instabilities and MSW effects are also active. The "fast" component is effectively hidden by the "slow" and MSW reshuffling.

5. Significance

This work underscores that while DUNE will be a powerful observatory for supernova neutrinos, the interpretation of its data is highly model-dependent.

1. Risk of Misinterpretation: Neglecting collective effects or assuming incorrect mass orderings can lead to substantial errors in inferring the supernova's intrinsic properties (e.g., luminosity and temperature).
2. Limitations on Fast Instabilities: The study suggests that detecting the specific signature of fast flavor conversions (FFCs) in a single Galactic supernova event using DUNE alone may be impossible if slow instabilities are also active, as their spectral signatures are degenerate or masked.
3. Need for Multi-Model Analysis: Future analyses of supernova data must employ flexible frameworks that test multiple conversion hypotheses simultaneously rather than assuming a single mechanism.
4. Bridge to Simulations: The paper highlights the need for tighter integration between radiation-hydrodynamics simulations (which predict the initial flux and angular distributions) and detector analysis to fully exploit the potential of next-generation neutrino observatories.

In conclusion, DUNE will successfully determine the neutrino mass ordering and constrain the supernova flux parameters, but distinguishing between complex collective oscillation scenarios (specifically the presence of fast conversions) remains a significant challenge requiring precise knowledge of the initial neutrino phase-space distribution.