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Astrophysical origins of TeV features in the cosmic-ray lepton spectrum

This paper investigates the origins of spectral features in the TeV cosmic-ray lepton spectrum by modeling the diffuse background and nearby pulsar contributions within a unified propagation framework, demonstrating that the spectral shapes of such features can effectively distinguish between nearby astrophysical sources and exotic interpretations like dark matter.

Original authors: Zhen Xie, Ruizhi Yang

Published 2026-08-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Zhen Xie, Ruizhi Yang

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 the universe as a giant, chaotic ocean, and the Earth as a small boat floating on its surface. In this ocean, there are tiny, invisible messengers called cosmic rays—high-energy particles that zoom through space at nearly the speed of light. Most of these messengers are heavy and tough, like boulders, but a special, lighter group consists of electrons and their antimatter twins, positrons. These lightweight travelers are like delicate soap bubbles; as they zip through the galaxy, they constantly bump into magnetic fields and light waves, losing their energy and slowing down very quickly. Because they lose energy so fast, if we see a high-energy bubble near our boat, it must have come from a nearby source, not from the distant horizon. Scientists have been measuring these bubbles for decades, and recently, some of the most precise measurements have shown something strange: the number of these particles doesn't just slowly fade away as expected. Instead, the data shows bumps, kinks, and sudden drops, like a smooth road that suddenly has a pothole or a speed bump. This has sparked a huge debate: are these weird shapes caused by something exotic and new, like dark matter exploding, or are they just the result of a few nearby cosmic "fireworks" that we haven't fully understood yet?

This paper, written by Zhen Xie and Ruizhi Yang, dives deep into that debate to see if the "fireworks" explanation is enough. The authors act like cosmic detectives, trying to figure out if the strange shapes in the data can be explained by ordinary astrophysical sources, specifically pulsars (which are the super-dense, spinning remains of exploded stars) and supernova remnants. They start by building a very detailed model of what the "background noise" of the universe should look like if there were no nearby fireworks at all. Using a sophisticated computer program called GALPROP, they simulate how electrons travel through the galaxy, accounting for how they lose energy and spread out. They find that this background is smooth and predictable, slowly curving downward as energy increases, much like a gentle hill.

Next, the team tests the "nearby pulsar" theory. They imagine two different scenarios for how these pulsars might shoot out particles. The first is a "burst" scenario, where a mature pulsar releases a massive cloud of particles all at once, like a sudden geyser. The second is a "continuous" scenario, where a young pulsar steadily leaks particles over thousands of years, like a dripping faucet. The authors run complex simulations to see what these signals would look like when they finally reach Earth. They discover that while pulsars can create bumps and drops in the data, the shape of these features depends heavily on how the particles lose energy. A key finding is that when they account for the fact that high-energy particles lose energy in a random, "stochastic" way (like a pinball bouncing unpredictably) rather than a perfectly smooth slide, the sharp, sudden drops predicted by older models become much softer and more spread out.

The paper then looks at a specific set of data from the DAMPE satellite, which showed a slight bump near 1 TeV (a trillion electron volts). The authors use their models to ask: "Could a nearby pulsar or a supernova remnant explain this bump?" They find that it is possible. A nearby pulsar that is about 10,000 years old, or a supernova remnant about 10,000 years old, could produce a signal that matches the data, provided the source is energetic enough. However, they also point out a catch: if the source were very young (only a few hundred years old), it would need to be impossibly powerful to explain the data. Furthermore, the "sharpness" of the drop-off in the data is a crucial clue. The authors show that while pulsars can create a drop-off, it tends to be a bit "fuzzy" or broad due to the random cooling effects. If future measurements show a drop-off that is incredibly sharp and sudden—like a cliff edge rather than a gentle slope—it would be very hard to explain with just a pulsar, and might point toward something more exotic, like dark matter.

In short, the paper suggests that the strange features in the cosmic-ray electron spectrum are likely just the result of nearby cosmic accelerators, like pulsars, doing their thing. The "bumps" and "drops" are probably just the natural signature of particles traveling from a specific distance and age. The authors conclude that we don't need to call in the aliens or invent new physics just yet. Instead, they argue that we need better, higher-resolution measurements in the future to see exactly how sharp or fuzzy these features really are. If the features turn out to be smooth and broad, the case for nearby pulsars gets stronger; if they turn out to be razor-sharp, then the search for something truly exotic might just be getting started.

Problem Statement
High-energy cosmic-ray electron and positron measurements from experiments such as PAMELA, AMS-02, ATIC, H.E.S.S., and DAMPE have revealed spectral structures that deviate from a single smooth power-law background. Notably, the rising positron fraction and the all-electron spectrum features (including a spectral break near 0.9 TeV reported by DAMPE) have motivated interpretations ranging from nearby astrophysical accelerators to dark matter annihilation or decay. A significant challenge remains in distinguishing whether these spectral features arise from conventional astrophysical sources (such as nearby pulsars or supernova remnants) or from new particle physics. Existing data often suffer from degeneracy, where both astrophysical source cutoffs and dark matter endpoints can produce hard spectra with sharp edges. This work aims to revisit the conventional diffuse electron background and quantify the contribution of nearby discrete sources, specifically pulsars, to determine if they can reproduce particle-physics-like spectral structures.

Methodology
The authors employ a two-component framework within a common propagation model:

Diffuse Background Modeling: The conventional diffuse electron background is constructed using GALPROP v54 calculations. The model parameters are calibrated using cosmic-ray nuclei data (specifically the $^{9}\text{Be}/^{10}\text{Be}$ ratio) and diffuse gamma-ray observations. The authors utilize an ensemble of 64 GALPROP models with varying halo heights, source distributions, and gas density profiles. The local interstellar spectrum at the Earth's position is derived by summing primary electrons, secondary electrons, and secondary positrons. This background is normalized to AMS-02 data at 100 GeV to isolate spectral shape variations at higher energies.
Nearby Source Propagation: The contribution of nearby discrete sources is modeled using Green-function solutions for electron propagation with radiative losses. The study considers two injection histories:
- Burst-like Injection: Approximating mature nearby pulsars (e.g., Geminga, Monogem) where pairs are released over a short interval.
- Continuous Injection: Approximating young pulsars injecting pairs over their finite lifetimes.
The injected spectrum is parameterized as a power law with an exponential or super-exponential cutoff. Crucially, the authors incorporate stochastic inverse-Compton (IC) cooling using a Monte Carlo approach. Unlike standard deterministic continuous-loss approximations ( $b(E) \propto E^2$ ), this method samples individual IC scatterings using the Klein-Nishina kernel and a path-averaged interstellar radiation field (ISRF) model (Popescu et al.). Synchrotron cooling is treated as a continuous loss. The propagation kernel accounts for spatial diffusion and the finite age of the source.
Spectral Analysis: The propagated spectra are fitted with an empirical form $AE^{-p} \exp[-(E/E_{\text{eff}})^{\beta_{\text{eff}}}]$ to quantify the sharpness of the spectral cutoff ( $\beta_{\text{eff}}$ ). The authors compare these theoretical templates against the highest-energy data points from DAMPE and H.E.S.S. to estimate the energetic requirements for a potential local component.

Key Results

Diffuse Background Characteristics: The GALPROP ensemble produces a smooth all-electron spectrum above $\sim$ 100 GeV. The spectrum softens gradually toward higher energies due to the combination of the primary source spectrum (modeled as a broken power law) and radiative cooling during propagation. The ensemble does not generate narrow bumps, abrupt cutoffs, or edge-like structures; the effective spectral index transitions smoothly from $\sim$ 3.1 to $\sim$ 4.5.
Stochastic Cooling Effects: The inclusion of stochastic IC cooling significantly alters the spectral shape compared to deterministic models. For burst-like pulsar sources, the sharp "cooling edge" predicted by continuous-loss approximations is broadened. The effective sharpness parameter $\beta_{\text{eff}}$ decreases to values of order a few (e.g., 1.3 to 3.6 depending on age), rather than remaining extremely sharp.
Continuous Injection vs. Burst:
- Burst-like Pulsars: The spectral turnover is jointly shaped by radiative cooling and the source cutoff. For older sources (e.g., 300 kyr), cooling dominates, shifting the peak to lower energies and broadening the decline.
- Continuous Injection: A rapidly falling feature in this scenario is primarily inherited from the intrinsic super-exponential cutoff of the source injection spectrum, not generated by propagation. Propagation effects (diffusion and cooling) mildly broaden this intrinsic cutoff.
Energetic Constraints:
- For a burst-like mature pulsar at 500 pc to contribute 10% of the background at 1 TeV, the required total injected pair energy is $\sim 5 \times 10^{47}$ erg (for 100 kyr) to $\sim 5 \times 10^{48}$ erg (for 300 kyr). These values are within the range typically invoked for positron excess interpretations, though the 300 kyr case is demanding.
- For a young continuous-injection pulsar (10 kyr, 100 pc), the required power is $\sim 10^{34}$ erg s $^{-1}$ , which is plausible. However, for very young sources (e.g., 300 yr), the required power rises to $\sim 10^{37}$ erg s $^{-1}$ , which is difficult to realize given typical pulsar spin-down powers and pair-conversion efficiencies.
DAMPE High-Energy Points: Using the two highest-energy DAMPE points as an illustrative case, the authors show that a mild residual could be explained by a nearby discrete source. A burst-like pulsar (20 kyr, 500 pc) requires $\sim 8 \times 10^{46}$ erg. A continuous pulsar (3 kyr, 100 pc) requires $\sim 6 \times 10^{33}$ erg s $^{-1}$ . An SNR-like burst source yields a broader, less endpoint-like contribution ( $\beta_{\text{eff}} \approx 2.7$ ).

Significance and Claims
The paper claims that the detailed shape of spectral features serves as a diagnostic tool for distinguishing between conventional astrophysical origins and exotic particle physics.

Astrophysical Plausibility: Nearby pulsars can produce structured high-energy spectra, but the "sharpness" of these features is limited. Stochastic IC cooling broadens the cooling edges of burst-like sources, and continuous injection relies on intrinsic source cutoffs that are naturally broadened by propagation.
Differentiation: The authors argue that if future high-resolution measurements (e.g., from DAMPE with increased exposure or the HERD mission) reveal a very sharp, stable, edge-like feature, it would be difficult to accommodate with ordinary pulsar propagation models. Such a feature would strengthen the case for alternative origins, such as dark matter. Conversely, a smooth cutoff or a cooling-broadened decline would remain naturally compatible with nearby astrophysical sources.
Conclusion: The work does not claim to definitively identify the origin of the DAMPE spectral break but provides a rigorous framework for testing the "nearby source" hypothesis against future data, emphasizing that the degeneracy between astrophysical and particle-physics interpretations can be broken by precise measurements of the spectral shape and sharpness.

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