Mirage Sources and Large TeV Halo-Pulsar Offsets: Exploring the Parameter Space

We investigate the asymmetric propagation of 100 TeV electrons (whose radiation mainly concentrates on 20–30 TeV) in turbulent magnetic fields around pulsars, using GPU-accelerated simulations to explore their trajectories and interactions within pulsar wind nebulae and the interstellar medium. Key results include the identification of ``mirage’’ sources indicating significant offsets in high-energy emissions from their originating pulsars, challenging the results of traditional symmetric diffusion models. By varying parameters like source distance, magnetic field strength, and electron injection spectral index, the study delineates their effects on observable phenomena such as the probability that a source has at least one mirage around it, as well as the source separation. Our results offer insights into some puzzling sources observed recently by the Large High Altitude Air Shower Observatory (LHAASO), and shed light on the cosmic-ray transport mechanism in the interstellar medium.

💡 Research Summary

The paper tackles a long‑standing puzzle in very‑high‑energy astrophysics: many TeV halos detected by LHAASO and HAWC show a centroid that is displaced by tens to hundreds of parsecs from the associated middle‑aged pulsar. Conventional isotropic diffusion models, which assume a uniform diffusion coefficient reduced by a factor of 10²–10³ relative to the Galactic average, cannot reproduce such offsets because the electrons would lose energy before traveling that far.

To address this, the authors develop a first‑principles, GPU‑accelerated test‑particle simulation that follows the trajectories of 100 TeV electrons (which radiate mainly at 20–30 TeV via inverse‑Compton scattering on the CMB) in a three‑dimensional turbulent magnetic field. The turbulent field is constructed in Fourier space with a Kolmogorov‑type power spectrum (E(k) ∝ k⁻¹¹⁄³), enforced to be divergence‑free, and composed of four nested grids spanning scales from 4 × 10⁻⁹ kpc to 5 × 10⁻⁴ kpc. By adjusting the RMS field strength σ_B, the coherence length L_c, and the ratio of regular to turbulent components, the authors can emulate a wide range of interstellar environments.

Electron dynamics are integrated with the Boris pusher using a timestep equal to 1/100 of the gyration period, and synchrotron plus inverse‑Compton losses are applied at each step. The initial electron spectrum follows dN/dE ∝ E⁻ᵅ exp(−E/E_cut) and is sampled logarithmically with 8192 energy bins; each bin is represented by a single macro‑particle whose statistical weight reflects the physical number of electrons in that bin. This weighted‑macro‑particle technique dramatically reduces computational cost while preserving the spectral fidelity of the full population.

The simulation outputs the spatial distribution of electrons at successive times, which is then converted into synthetic γ‑ray maps (25–40 TeV band) using an inverse‑Compton scattering matrix that includes the CMB and five interstellar radiation field components. The maps are convolved with the LHAASO point‑spread function (σ ≈ 0.43°) and overlaid with realistic Poisson background noise. Source detection is performed via a Bayesian model‑comparison framework: successive Gaussian templates are added until the improvement in log‑likelihood (Δlog L > 12, equivalent to TS > 25) ceases, thereby quantifying the number of statistically significant “mirage” sources.

Parameter scans reveal several key trends: (1) Harder injection spectra (α ≈ 1.5) increase the mirage ratio because higher‑energy electrons survive longer and travel farther before cooling. (2) Stronger turbulent fields (B_t ≈ 6 μG) raise synchrotron losses, reducing propagation distance, but also increase the magnetic rigidity, which can modestly enhance the probability of coherent deflection over a single L_c. (3) Larger coherence lengths dramatically boost the number of mirage sources; for L_c = 20 pc the average number of detectable offsets ξ rises from ≈0.5 to >2 per pulsar. (4) A higher regular‑to‑turbulent ratio (B_r/B_t) tends to align electron streams with the regular field, producing more pronounced, but fewer, offset spots.

The authors compare these findings with specific LHAASO detections that exhibit offsets of 30–80 pc. By selecting simulation parameters that match the estimated distance (d ≈ 2 kpc), magnetic field strength (B_t ≈ 3 μG), and coherence length (L_c ≈ 15–20 pc), the simulated mirage ratio reaches 10–15 %, consistent with the observed fraction of offset halos. This suggests that the observed offsets are a natural consequence of anisotropic propagation in a realistic turbulent magnetic environment rather than requiring exotic particle transport mechanisms.

In the discussion, the paper emphasizes that “mirage” sources are not separate astrophysical objects but projection effects arising from the line‑of‑sight alignment of magnetic field structures with the observer. Consequently, the morphology of TeV halos can be highly asymmetric, and the centroid of γ‑ray emission does not reliably indicate the true accelerator location. The authors propose that future high‑resolution observations (e.g., CTA) combined with polarization measurements of the surrounding magnetic field could test the predicted correlation between offset direction and magnetic field orientation.

Overall, the study provides a robust computational framework for exploring non‑diffusive, anisotropic cosmic‑ray transport, demonstrates that magnetic turbulence can naturally generate the observed TeV‑halo offsets, and opens a pathway to use γ‑ray morphology as a diagnostic of interstellar magnetic turbulence on scales of tens of parsecs.