Charge-dependent spectral softenings of primary cosmic-rays below the knee

Using nine years of data from the Dark Matter Particle Explorer, this study reports the first direct detection of distinct spectral softenings in carbon, oxygen, and iron cosmic rays that universally occur at a rigidity of approximately 15 teravolts, thereby rejecting a mass-dependent softening scenario with high confidence and supporting charge-dependent acceleration or propagation models.

The Gist

Imagine the universe is filled with a constant, invisible rain of tiny, super-fast particles called cosmic rays. Most of these are just single protons (hydrogen nuclei), but some are heavier, like carbon, oxygen, and even iron. Scientists have been trying to figure out how these particles get their incredible speeds and how they travel across the galaxy.

For a long time, there was a big debate: Does the "speed limit" or the "turning point" for these particles depend on their electric charge (how many protons they have) or their mass (how heavy they are)?

Think of it like a race. If the rules of the race depend on the charge, a light but highly charged particle might hit a wall at the same "speed" as a heavy, highly charged one. If the rules depend on mass, then a heavy truck would hit a wall at a different speed than a light motorcycle, regardless of how charged they are.

The Discovery: A Universal "Speed Bump"

The DAMPE satellite (a space telescope designed to catch these particles) spent nine years collecting data. It looked at the energy spectra (the "speed distribution") of protons, helium, carbon, oxygen, and iron.

What they found was a surprise:

1. The Hardening: At a certain speed (around 500–1,000 billion volts), all these particles suddenly got a bit "stiffer" or "harder" to slow down.
2. The Softening: Then, at a much higher speed (around 15 trillion volts), all of them suddenly hit a "speed bump" and started to drop off in numbers. This is called "spectral softening."

The Big Reveal: It's About Charge, Not Weight

The most exciting part of this paper is how they figured out why this speed bump happens.

They compared the "speed bump" for each element:

• Protons (Charge 1) hit the bump at ~15 trillion volts.
• Helium (Charge 2) hit it at ~30 trillion volts.
• Carbon (Charge 6) hit it at ~90 trillion volts.
• Iron (Charge 26) hit it at ~390 trillion volts.

The Analogy: Imagine a toll booth on a highway. The toll isn't based on how heavy your car is (mass); it's based on how many "charge tags" you have.

• If you have 1 tag, you pay 15.
• If you have 2 tags, you pay 30.
• If you have 26 tags, you pay 390.

The paper proves that the "speed limit" is strictly proportional to the electric charge. They ruled out the idea that it depends on mass with a confidence level of 99.999%. This is a huge deal because it tells us the physics governing these particles is tied to their electric charge, likely due to how they interact with magnetic fields in space.

What Caused This? Two Main Theories

The scientists propose two main ideas for what created this universal "speed bump":

1. The "Nearby Neighbor" Theory
Imagine the galaxy is a dark room filled with a faint, steady hum of light (background cosmic rays from distant sources). Suddenly, a bright flashlight turns on nearby.

• The paper suggests there might be a nearby cosmic ray source, possibly a supernova explosion associated with the Geminga pulsar (a dead star spinning rapidly).
• This nearby source adds a "bump" to the total light. Because the particles from this source haven't had enough time to spread out perfectly, they create a specific shape in the data that looks like a hardening followed by a softening.
• The energy required for this "flashlight" fits perfectly with what a typical supernova explosion produces.

2. The "Traffic Jam" Theory (Propagation)
Alternatively, the speed bump might not be from a specific source, but from how the particles travel through the galaxy.

• Imagine the galaxy is a forest. As the particles (hikers) move through, they create their own "turbulence" or "wind" in the magnetic fields.
• This self-generated turbulence changes how easily the particles can move. At a certain "charge" level, the traffic rules change, causing the particles to slow down or scatter differently. This is a "propagation effect."

Why Does This Matter?

Before this, we only had precise measurements for the lightest particles (protons and helium) at these high energies. We didn't know if the heavy stuff (like iron) followed the same rules.

This paper confirms that the rules are the same for everyone, from the lightest proton to the heaviest iron nucleus. It's like discovering that the laws of physics for a bicycle and a semi-truck are identical when it comes to hitting a specific speed limit. This helps scientists narrow down the list of possible explanations for where cosmic rays come from and how they travel through our universe.

In short: The universe has a universal speed limit for cosmic rays that depends entirely on their electric charge, not their weight. This limit was likely caused either by a nearby cosmic "factory" (like a supernova) or by the way the particles interact with the galaxy's magnetic "traffic."

Technical Summary

1. Problem Statement

Understanding the origin and propagation of Galactic Cosmic Rays (CRs) is a fundamental challenge in high-energy astrophysics. While standard theories predict that spectral features (such as breaks or "knees") in CR energy spectra should be charge-dependent (due to magnetic rigidity effects in acceleration or propagation) or mass-dependent (due to interaction thresholds), observational evidence has been lacking.

• The Gap: Previous measurements by experiments like AMS-02 and CALET have revealed spectral hardenings around a few hundred GV and softenings around 10–30 TeV for protons and helium. However, precise measurements for heavier nuclei (Carbon, Oxygen, Iron) at these high energies were limited.
• The Question: Do the spectral breaks observed in primary CRs depend on the particle's charge ($Z$) or its mass number ($A$)? Resolving this is crucial for distinguishing between acceleration limits (e.g., in supernova remnants) and propagation effects (e.g., diffusion changes in the interstellar medium).

2. Methodology

The study utilizes data from the Dark Matter Particle Explorer (DAMPE) satellite, a space-borne calorimeter-type detector.

• Data Source: 9 years of on-orbit data (January 1, 2016 – December 31, 2024), resulting in a live time fraction of ~76.2% after excluding calibration periods, South Atlantic Anomaly (SAA) passages, and a major solar flare event.
• Detector Capabilities: DAMPE employs a Plastic Scintillator Detector (PSD), Silicon-Tungsten Tracker (STK), Bismuth Germanium Oxide (BGO) calorimeter, and Neutron Detector (NUD). The thick BGO calorimeter (~32 radiation lengths) allows for precise energy measurement up to PeV energies.
• Particle Identification:
  • Charge ($Z$): Measured via PSD and STK. Specific charge windows were defined for Carbon ($5.7 < Q < 6.3 + \dots$), Oxygen, and Iron to suppress backgrounds from lighter nuclei.
  • Energy ($E$): Derived from the total deposited energy in the BGO calorimeter.
  • Background Rejection: A Monte Carlo (MC) template fitting method was used to estimate and subtract residual backgrounds (e.g., fragmentation products, back-scattered secondaries).
• Analysis Techniques:
  • Unfolding: A Bayesian unfolding procedure was applied to correct for bin-to-bin migration caused by finite energy resolution.
  • Spectral Fitting: The data were fitted using a Smoothly Broken Power Law (SBPL) model to identify hardening and softening features. The significance of these breaks was evaluated by comparing $\chi^2$ values between a simple Power Law (PL) and the SBPL model.
  • Modeling: Two theoretical scenarios were tested:
    1. Nearby Source Model: Superposition of a background population and a single nearby source (e.g., Geminga pulsar).
    2. Propagation Model: Changes in the diffusion coefficient of CRs in the Galaxy, potentially due to self-generated turbulence.

3. Key Contributions

• First High-Energy Measurements: Provided the first precise direct measurements of Carbon, Oxygen, and Iron spectra up to 100 TeV (rigidity) and ~60 TeV (rigidity for Iron), extending significantly beyond previous limits (few TeV).
• Universal Softening Discovery: Directly detected spectral softening features in C, O, and Fe spectra for the first time, confirming they occur at the same rigidity as protons and helium.
• Charge vs. Mass Discrimination: Rigorously tested the dependence of the break energy on charge ($Z$) versus mass ($A$), providing a definitive statistical rejection of the mass-dependent hypothesis.

4. Key Results

• Spectral Structures: All five species (Proton, Helium, Carbon, Oxygen, Iron) exhibit a similar spectral structure:
  1. Hardening: A break at $\sim$500–1000 GV rigidity (significance $2.7\sigma$ to $29\sigma$).
  2. Softening: A distinct softening (break) at a rigidity of $\sim$15 TV.
• Break Rigidity Values:
  • Proton: $14.6 \pm 1.3$ TV
  • Helium: $15.3 \pm 2.3$ TV
  • Carbon: $16.1 \pm 5.6$ TV
  • Oxygen: $15.4 \pm 4.8$ TV
  • Iron: $13.8 \pm 6.0$ TV
• Charge Dependence: The break energy ($E_{br}$) scales linearly with the particle charge ($Z$). The fit yields $E_{br}/\text{TeV} \approx (15.3 \pm 1.6) \times Z$.
• Rejection of Mass Dependence: The hypothesis that the break energy depends on the mass number ($A$) is rejected with a confidence level of > 99.999% ($>4.4\sigma$).
• Model Interpretations:
  • Nearby Source: A model adding a nearby source (consistent with the Geminga pulsar, age $\sim 3.4 \times 10^5$ years, distance $\sim 250$ pc) with an exponential cutoff at $\sim$30 TV successfully reproduces the observed "bump" structure and dipole anisotropies. The source appears to have slightly higher metallicity than the background.
  • Propagation: A propagation model with two breaks in the diffusion coefficient (mimicking changes in turbulence damping) can also reproduce the spectral shapes, though explaining the anisotropies requires further study.

5. Significance

• Fundamental Physics: The confirmation that spectral breaks are charge-dependent rather than mass-dependent strongly suggests that the underlying mechanism is related to magnetic rigidity. This supports scenarios where the break is caused by acceleration limits (e.g., maximum energy achievable in a supernova remnant) or propagation effects (e.g., rigidity-dependent diffusion) rather than interaction thresholds.
• Source Identification: The results provide strong evidence for the existence of a nearby, dominant cosmic-ray source contributing to the local flux, with the Geminga pulsar being a prime candidate.
• Paradigm Shift: These findings challenge the standard paradigm of a single, uniform power-law source population, indicating that the local CR spectrum is a complex superposition of background galactic sources and specific nearby contributors.
• Future Directions: The results set stringent constraints for future CR propagation models and source identification efforts, emphasizing the need to account for local source contributions in the TeV–PeV energy range.