PHECT: A lightweight computation tool for pulsar halo emission

TL;DR

The paper tackles modeling gamma-ray halos around pulsars to probe small-scale Galactic CR propagation. It introduces PHECT, a lightweight C-based tool with YAML configuration that supports multiple transport models beyond standard diffusion and uses stable finite-volume discretization. The authors validate PHECT against standard diffusion and external benchmarks, demonstrate its outputs (SB profiles/maps, spectra, and electron densities), and discuss its readiness for upcoming high-precision halo data. The work enables self-consistent, model-driven comparisons and lays out a path for incorporating additional physics like pulsar motion and synchrotron emission, enhancing interpretability of pulsar halos as CR probes.

Abstract

$γ$-ray pulsar halos, most likely formed by inverse Compton scattering of electrons and positrons propagating in the pulsar-surrounding interstellar medium with background photons, serve as an ideal probe for Galactic cosmic-ray propagation on small scales (typically tens of parsecs). While the associated electron and positron propagation is often modeled using homogeneous and isotropic diffusion, termed here as standard diffusion, the actual transport process is expected to be more complex. This work introduces the Pulsar Halo Emission Computation Tool (PHECT), a lightweight software designed for modeling pulsar halo emission. PHECT incorporates multiple transport models extending beyond standard diffusion, accounting for different possible origins of pulsar halos. Users can conduct necessary computations simply by configuring a YAML file without manual code edits. Furthermore, the tool adopts finite-volume discretizations that remain stable on non-uniform grids and in the presence of discontinuous diffusion coefficients. PHECT is ready for the increasingly precise observational data and the rapidly growing sample of pulsar halos.

Figures (10)

• Figure 1: Schematic illustrations of two of the possible slow-diffusion interpretations. The star symbols denote the current position of the pulsar. Left: SNR-induced model. The slow diffusion originates from a strong turbulence region (blue area) generated by the associated SNR or the progenitor stellar wind of the pulsar. The small green parabolic zone near the pulsar schematically represents the bow-shock PWN. $D_\mathrm{in}$ and $D_\mathrm{out}$ are the diffusion coefficients inside and outside the SNR, respectively. Right: Anisotropic diffusion model. The apparent slow diffusion results from the projection effects of anisotropic diffusion. The blue region illustrates the asymmetric electron distribution due to anisotropic diffusion conditions. $D_{zz}$ and $D_{rr}$ are the diffusion coefficients parallel and perpendicular to the mean magnetic field around the pulsar, respectively.
• Figure 2: One-dimensional $\gamma$SB of the Geminga halo computed by the standard diffusion (StdDiff_N) and superdiffusion (Super_A) models, in comparison with the HAWC data Abeysekara:2017old. The parameters used are the default settings in param_config.yaml, with the following exceptions: D0=4.1e27 and eta=0.049 for the StdDiff_N model; alpha=1.6, D0=1.5e20, and eta=0.070 for the Super_A model.
• Figure 3: Two-dimensional $\gamma$SB of the Geminga halo predicted by models SNR2Z_N (left) and Aniso_N (right). The parameters used are the default settings in param_config.yaml, with the following exceptions: PHI=270 for the SNR2Z_N model (indicating the pulsar motion is horizontally to the right); z_ref=300 for the Aniso_N model.
• Figure 4: Average of $\gamma$SB over different azimuthal intervals for models SNR2Z_N (left) and Aniso_N (right). The parameters used are identical to those in Fig. \ref{['fig:map']}.
• Figure 5: $\gamma$-ray spectra of the Geminga halo within $10^\circ$ around the pulsar computed using the StdDiff_N and 2Zone_N models, in comparison with the HAWC data. For the StdDiff_N model: $\texttt{eta=0.06}$, $\texttt{Ec=165}$, and $\texttt{D0=4.5e27}$. For the 2Zone_N model: $\texttt{eta=0.09}$, $\texttt{Ec=125}$, $\texttt{D0=7e27}$, and $\texttt{r\_2z=35}$, where the last two parameters are suggested by Ref. Fang:2023xla. Other parameters are set to their default values.