[Paper Review] Morphology of Gamma-Ray Halos around Middle-Aged Pulsars: Influence of the Pulsar Proper Motion

Yi Zhang, Ruo-Yu Liu+2 more|arXiv (Cornell University)|Oct 29, 2020

Pulsars and Gravitational Waves ResearchPhysics and Astronomy65 references14 citations

TL;DR

This paper models the morphology of gamma-ray halos around middle-aged pulsars, showing that pulsar proper motion induces distinct morphological phases: double-peaked or tail-like structures at GeV-TeV energies due to asymmetric electron diffusion, and nearly spherical halos above 10 TeV due to rapid electron cooling. The key result is that offsets between the pulsar and halo center are typically too small to resolve above 10 TeV, limiting observable signatures for HAWC and LHAASO unless the pulsar is nearby or has high velocity.

ABSTRACT

Recently, gamma-ray halos of a few degree extension have been detected around two middle-aged pulsars, namely, Geminga and PSR B0656+14, by the High Altitude Water Cherenkov observatory (HAWC). The gamma-ray radiation arise from relativistic electrons that escape the pulsar wind nebula and diffuse in the surrounding medium. The diffusion coefficient is found to be significantly lower than the average value in the Galactic disk. If so, given a typical transverse velocity of $300-500{\, m km /s}$ for a pulsar, its displacement could be important in shaping the morphology of its gamma-ray halos. Motivated by this, we study the morphology of pulsar halos considering the proper motion of pulsar. We define three evolutionary phases of pulsar halo to categorize its morphological features. The morphology of pulsar halos below 10$\,$TeV is double peaked or single peaked with an extended tail, which depends on the electron injection history. Above 10 TeV, the morphology of pulsar halos is nearly spherical, due to the short cooling timescale ($<50\,$kyr) for tens TeV electrons. We also quantitatively evaluate the separation between the pulsar and the center of the gamma-ray halo, as well as the influence of different assumptions for the pulsar characteristics and the injected electrons. Our results suggest that the separation between the center of the gamma-ray halo above 10$\,$TeV and the associated pulsar is usually too small to be observable by HAWC or LHAASO. Hence, our results provide a useful approach to constrain the origin of extended sources at very high energies.

Motivation & Objective

• To understand how pulsar proper motion shapes the morphology of gamma-ray halos around middle-aged pulsars.
• To determine the observable signatures of pulsar halo offsets in current and future instruments like HAWC and LHAASO.
• To evaluate the impact of electron injection history, diffusion properties, and cooling timescales on halo morphology.
• To provide a framework for constraining the origin of extended TeV-PeV gamma-ray sources.

Proposed method

• The study models gamma-ray emission from inverse Compton scattering of relativistic electrons diffusing in the interstellar medium.
• It divides halo evolution into three phases based on timescales: pulsar displacement relative to electron diffusion length (tpd), electron cooling timescale (tc), and pulsar age (tage).
• The model incorporates spatially varying diffusion coefficients, assuming a two-zone diffusion model with a slow-diffusion region centered at the pulsar's birthplace.
• Simulated halo morphologies are convolved with instrument-specific point spread functions (PSF) of Fermi-LAT, HESS, and LHAASO to mimic observational resolution.
• The separation between the pulsar and the halo's centroid (Θ) and brightest point (Θ′) is quantified as a function of energy and model parameters.
• Extreme-case analysis assumes electron injection ceases at tage − tc to derive maximum possible offset angles (Θmax, Θ′max).

Experimental results

Research questions

• RQ1 How does pulsar proper motion affect the spatial morphology of gamma-ray halos at GeV and TeV energies?
• RQ2 What are the observable signatures of halo offsets, and can they be resolved by current instruments like HAWC and LHAASO?
• RQ3 How do electron injection history and diffusion properties influence the asymmetry and peak structure of pulsar halos?
• RQ4 What is the maximum possible angular offset between the pulsar and the halo center under extreme assumptions, and what does it imply for source identification?

Key findings

• Pulsar halos below 10 TeV exhibit double-peaked or single-peaked with extended tails, depending on electron injection history, due to asymmetric diffusion from the pulsar's motion.
• Above 10 TeV, halos become nearly spherical due to electron cooling timescales shorter than 50 kyr, suppressing observable asymmetry.
• The angular separation between the pulsar and the halo's centroid (Θ) and brightest point (Θ′) decreases with increasing gamma-ray energy, becoming unresolvable above 10 TeV for typical pulsar distances and velocities.
• The maximum angular offset between the pulsar and halo centroid is empirically given by Θmax = 3°(Eγ/1 TeV)−0.77(vtr/400 km s−1)(d/2 kpc)−1 for a 3 µG magnetic field, indicating that large offsets are unlikely under standard assumptions.
• Magnetic field strength significantly affects the offset, while the electron injection spectrum and background photon field have weak influence, suggesting magnetic field structure is key to interpreting large observed offsets.
• If a large offset is observed, it likely indicates complex magnetic field configurations or non-pulsar-halo origins, necessitating high-resolution multiwavelength follow-up.