Analytical modeling of the gamma-ray morphology of TeV halos around moving pulsars

@misc{recchia2026analytical,
  title = {{Analytical modeling of the gamma-ray morphology of TeV halos around moving pulsars}},
  author = {Sarah Recchia},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34515},
  eprint = {2610.34515},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34515},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Analytical modeling of the gamma-ray morphology of TeV halos around moving pulsars
AU  - Sarah Recchia
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34515
UR  - https://arxiv.org/abs/2610.34515
AB  - We aim to derive an analytical prescription for the line-of-sight-integrated particle distribution around moving pulsars, suitable for constructing spatial templates of the associated TeV-halo gamma-ray emission without resorting to computationally expensive numerical integrations. We consider electrons and positrons continuously injected by a moving source, undergoing isotropic diffusion and radiative energy losses. Assuming spatially uniform target photon fields, as appropriate for the cosmic microwave background and approximately valid for the interstellar radiation fields, the projected particle distribution provides a useful proxy for the inverse-Compton gamma-ray morphology. We show that the line-of-sight integration of the particle distribution can be performed exactly, reducing the calculation to a single numerical integral over the injection history. Under the additional assumptions of constant injection luminosity and a simplified treatment of energy losses, we derive a fully analytical expression that factorizes into an energy-dependent spectral term and a dimensionless spatial term describing the energy-dependent morphology. Comparison with the exact calculation shows good agreement over a broad range of energies and spatial scales, with appreciable deviations primarily at particle energies approaching the cutoff of the injection spectrum and at large distances from the source, where the emission becomes fainter. Our results enable the construction of physically motivated, energy-dependent spatial templates for gamma-ray halos around moving pulsars, capturing the morphological asymmetries induced by proper motion without computationally expensive numerical integrations. This makes them particularly suitable for systematic morphological and spectral analyses of extended gamma-ray sources.
ER  -