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Proton Acceleration by Collisionless Shocks in Supermassive Black Hole Coronae: Implications for High-Energy Neutrinos

This study uses Particle-in-cell simulations to demonstrate that diffusive shock acceleration in AGN coronae efficiently accelerates protons to high energies while remaining inefficient for electrons, thereby providing a first-principles explanation for the observed high-energy neutrinos from Seyfert galaxies without a corresponding gamma-ray flux.

Original authors: Minh Nhat Ly, Yoshiyuki Inoue, Yasuhiko Sentoku, Takayoshi Sano

Published 2026-06-23

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CC BY 4.0

Original authors: Minh Nhat Ly, Yoshiyuki Inoue, Yasuhiko Sentoku, Takayoshi Sano

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a supermassive black hole at the center of a galaxy. Around it, there isn't just empty space; there is a super-hot, chaotic "corona" of plasma (a soup of charged particles like protons and electrons). Scientists have recently detected high-energy neutrinos (ghostly particles that rarely interact with anything) coming from these black holes, specifically from a galaxy called NGC 1068.

Here is the mystery: If these neutrinos are made by smashing protons together, we should also see a lot of high-energy gamma rays (light). But we don't. The gamma rays are missing. This suggests the protons are being smashed in a place so thick with light that the gamma rays get trapped and eaten, but the neutrinos escape.

The big question was: How do these protons get moving fast enough to make such powerful neutrinos?

This paper uses supercomputer simulations to answer that question. Here is what they found, explained simply:

1. The "Cosmic Slingshot" (The Shock Wave)

Think of the black hole's corona as a busy highway. Sometimes, material falls in, or winds crash into each other, creating a "shock wave." This is like a traffic jam moving at incredible speeds. When particles hit this moving wall, they can get bounced back and forth, like a ping-pong ball between two moving paddles. Every time they cross the wall, they get a little faster. This process is called Diffusive Shock Acceleration (DSA).

2. The Heavy vs. The Light (Protons vs. Electrons)

The researchers simulated this "ping-pong" game with two types of players: heavy protons and light electrons.

The Protons (The Heavyweights): They are like big, sturdy bowling balls. The simulations showed that the shock wave is incredibly good at accelerating them. No matter how "weak" the shock is (even if it's just a gentle traffic jam), the protons consistently grab about 10% of the total energy available and turn it into high-speed motion. They are the stars of the show.
The Electrons (The Featherweights): They are like tiny ping-pong balls. The shock wave is much less efficient at speeding them up. In most cases, they get less than 1% of the energy. In fact, in some scenarios, the "wind" from the protons gets so turbulent that it actually blocks the electrons from getting a good run, leaving them relatively slow.

3. The "Missing Light" Explained

Why don't we see the gamma rays? The paper suggests that because the protons are doing all the heavy lifting, they are creating the neutrinos. But the environment is so dense with X-ray light (like being in a foggy room with a bright spotlight) that any gamma rays produced are immediately absorbed. The neutrinos, however, are like ghosts; they walk right through the fog and reach our detectors (IceCube) on Earth.

4. The "Goldilocks" Zone

The researchers tested many different conditions:

Speed: Even when the shock wave wasn't moving at "super-fast" speeds, it still worked great for protons.
Temperature: Even when the protons were much hotter than the electrons (which is expected in black hole coronas), the protons still got accelerated efficiently.
Magnetic Fields: The magnetic fields acted like the rails for the train, guiding the particles. As long as the fields weren't too weak or impossibly strong, the protons kept gaining speed.

The Bottom Line

The paper concludes that collisionless shock waves in the hot corona of a black hole are the perfect "proton accelerators." They are robust, efficient, and work even in "weak" conditions.

This explains the IceCube observations perfectly:

Protons get accelerated to the necessary high speeds (around 100 TeV) to make neutrinos.
Electrons don't get accelerated as much, which helps explain why we don't see the expected flood of gamma rays (which usually come from high-energy electrons).
The neutrinos escape the trap, while the gamma rays get stuck, solving the mystery of the "missing light."

In short, the black hole's corona acts like a natural, ultra-powerful particle accelerator that is very good at making neutrinos but very bad at making the light we usually expect to see alongside them.

Technical Summary: Proton Acceleration by Collisionless Shocks in Supermassive Black Hole Coronae

Problem Statement
Recent observations by the IceCube Neutrino Observatory have detected a significant excess of high-energy neutrinos from nearby radio-quiet active galactic nuclei (AGNs), most notably the Seyfert galaxy NGC 1068. These observations present a discrepancy: while high-energy neutrinos are detected, the corresponding flux of high-energy gamma-rays is significantly lower than predicted by standard hadronic interaction models. This suggests that neutrinos are produced in a region opaque to gamma-rays, likely the hot corona surrounding the central supermassive black hole (SMBH), where gamma-rays are attenuated via $\gamma\gamma$ pair production with X-ray photons.

To explain the observed neutrino spectrum, parent protons must be accelerated to energies of $\sim 100$ TeV within this corona. However, the dominant acceleration mechanism in SMBH coronae remains unestablished. While Diffusive Shock Acceleration (DSA) is a leading candidate, its viability is uncertain under coronal conditions. Specifically, coronal shocks are expected to have low sonic Mach numbers ( $M_s \sim 2-10$ ) and trans-relativistic velocities, regimes traditionally considered inefficient for particle acceleration. Furthermore, the behavior of two-temperature plasmas ( $T_i \gg T_e$ ) and the specific efficiency of proton versus electron acceleration in these environments lack first-principles constraints.

Methodology
To address these uncertainties, the authors employ first-principles, one-dimensional particle-in-cell (PIC) simulations using the SMILEI code. The study focuses on quasi-parallel collisionless shocks ( $\theta = 30^\circ$ ) tuned to the physical parameters of SMBH coronae.

The simulation survey systematically explores a broad parameter space motivated by observational constraints for Seyfert galaxies:

Sonic Mach Number ( $M_s$ ): Ranging from trans-sonic ( $M_s \approx 2$ ) to higher values ( $M_s \approx 30$ ).
Alfvénic Mach Number ( $M_A$ ): Ranging from $4$ to $46$.
Shock Velocity ( $v_{sh}$ ): Trans-relativistic speeds ( $v_{sh}/c \approx 0.17 - 0.66$ ).
Ion-to-Electron Temperature Ratio ( $T_i/T_e$ ): Ranging from $0.01$ to $50$, reflecting the decoupled thermal states expected in collisionless coronae.

The simulations utilize a reduced ion-to-electron mass ratio ( $m_i/m_e = 100$ ) to ensure computational feasibility while preserving key dimensionless parameters. The runs are evolved for sufficient time ( $t \gtrsim 400 \Omega_{ci}^{-1}$ ) to allow for the saturation of electromagnetic instabilities and the development of nonthermal power-law tails.

Key Results

Robust Proton Acceleration: The study finds that DSA is a robust and efficient mechanism for proton acceleration in SMBH coronae. Despite the low sonic Mach numbers, shocks consistently channel approximately 10% of the shock's kinetic energy into nonthermal ions. This efficiency remains stable across the entire parameter survey, including cases with $M_s \approx 2$ , challenging the notion that low- $M_s$ shocks are ineffective accelerators.
Acceleration Dynamics: The maximum energy of accelerated protons increases linearly with time after the shock structure reaches a quasi-steady state. The acceleration rate follows the scaling predicted by DSA theory, $t_{acc} \propto \gamma \beta_{sh}^{-2} \Omega_{ci}^{-1}$ . The authors derive a normalized acceleration coefficient, $C^{-1} \equiv d(\gamma \beta_{sh}^{-2})/d(t\Omega_{ci})$ , which exhibits a universal value of $C^{-1} \approx 0.1$ , varying by less than a factor of two across all tested parameters.
Inefficiency of Electron Acceleration: In contrast to protons, electron acceleration is highly inefficient, with nonthermal electron energy fractions remaining below 1% (typically $\sim 10^{-3}$ for coronal-like $T_i/T_e$ ratios). The efficiency of electron acceleration decreases as the $T_i/T_e$ ratio increases. In specific trans-relativistic cases with strong magnetic field amplification, the electron power-law tail fails to extend to higher energies over time, suggesting that sustained DSA is inhibited when amplified fields intermittently render the shock effectively superluminal for electrons.
Instability Mechanisms: The upstream magnetic turbulence required for scattering is driven primarily by the nonresonant instability (NRI, or Bell's instability) across most of the parameter space. Resonant instability (RI) becomes dominant only at very low Alfvénic Mach numbers ( $M_A \lesssim 8$ ).

Implications for NGC 1068 and Neutrino Production
Applying these results to NGC 1068, the authors demonstrate that:

Timescales: Protons can be accelerated to $\sim 100$ TeV on timescales shorter than the relevant cooling (Bethe-Heitler, photomeson, $pp$) and dynamical (free-fall) timescales.
Energy Budget: The nonthermal proton power required to explain the observed neutrino luminosity is estimated to be $\sim 3\%$ of the total shock power. This is well within the $\sim 10\%$ acceleration efficiency measured in the simulations.
Gamma-ray Deficit: The low efficiency of electron acceleration and the high opacity of the corona to gamma-rays naturally explain the observed deficit in high-energy gamma-rays while allowing neutrinos to escape.

Significance and Claims
The paper claims to provide the first first-principles, self-consistent constraints on DSA in the specific context of SMBH coronae. The primary significance lies in establishing that collisionless shocks are a viable and efficient mechanism for producing the high-energy protons necessary to explain the IceCube neutrino signal from NGC 1068, even under the challenging conditions of low sonic Mach numbers and high ion-to-electron temperature ratios.

The authors explicitly state that while their results strongly support the hadronic model for neutrino production in AGN coronae, the application of local kinetic simulation results to a complex astrophysical object like an AGN corona requires careful consideration. The energy budget analysis is presented as an order-of-magnitude assessment based on the microphysics established in the paper, bridging the gap between microscopic plasma physics and macroscopic high-energy phenomena. The study does not claim to resolve all uncertainties regarding the maximum proton energy or the detailed transition of instabilities in 3D, noting that these require further investigation.

1. The "Cosmic Slingshot" (The Shock Wave)

2. The Heavy vs. The Light (Protons vs. Electrons)

3. The "Missing Light" Explained

4. The "Goldilocks" Zone

The Bottom Line

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