Pulsar Halos in Gamma-Ray Astronomy

• Pulsar halos are extended gamma-ray structures produced by high-energy electrons and positrons escaping pulsar wind nebulae, serving as indicators of local cosmic-ray propagation.
• Observations combine gamma-ray imaging with diffusion-loss models to distinguish halos from compact X-ray PWNe, demonstrating sizes tens of parsecs larger than the nebular emissions.
• Multiwavelength studies, using TeV gamma rays and keV X-rays, constrain diffusion coefficients and magnetic fields, linking halo morphology to underlying interstellar transport physics.

Pulsar halos, also termed TeV halos, are extended gamma-ray structures generated by electrons and positrons escaping from pulsar wind nebulae, and are now recognized as an emerging class of Galactic gamma-ray sources. In the late evolution stage of middle-aged pulsars, these leptons diffuse into the interstellar medium and produce GeV–TeV emission primarily through inverse Compton scattering of CMB and interstellar photons; the resulting halos are much larger than the compact X-ray PWN and act as indicators of cosmic-ray propagation in localized regions of the Galaxy and of the particle escape process from PWNe (Fang, 2022, Liu, 2022).

1. Definition and observational criteria

The observational definition of a pulsar halo is phenomenological but relatively specific. The source is expected to be spatially coincident with a pulsar, to have a pulsar energetic enough to power the observed emission, to be substantially more extended than the associated X-ray PWN, and to admit a diffusion-loss interpretation for the gamma-ray morphology and spectrum (Fang, 2022). In the evolutionary picture summarized for pulsar halos, the relevant systems are typically middle-aged pulsars, often in the range $10^5$–$10^6$ yr, after the pulsar wind nebula can no longer confine the highest-energy $e^\pm$ and the particles escape into the ambient interstellar medium (Liu, 2022).

A concrete application of these criteria was given for HESS J1831$-$098. Its gamma-ray emission is spatially coincident with PSR J1831$-$0952; the best-fit centroid is within $\sim 0.08^\circ$ of the pulsar; the pulsar has a spin-down luminosity of $1.08\times10^{36}$ erg s$^{-1}$ and an age of 128 kyr; the gamma-ray emission has $\sigma_{\rm src}=0.30^\circ$, whereas the X-ray PWN is $\sim 0.1$ pc; and no evidence links the emission to nearby SNR Kes 69 or other sources. On that basis, the source was found to meet all the criteria for a pulsar halo (2207.13533).

The class is therefore distinguished from classical PWNe not only by angular extent but also by transport regime. In the review literature, the gamma-ray extensions of known halos are tens of parsecs, whereas compact X-ray PWNe are typically $10^6$0 pc (Fang, 2022). This scale separation is central: it is the observational signature that the emitting particles have escaped the nebular confinement region and are probing the local interstellar transport environment.

2. Radiative and transport framework

The standard description of a pulsar halo uses a diffusion-loss equation for the electron and positron distribution. A representative form is

$10^6$1

with energy-dependent diffusion, radiative losses, and a source term for continuous injection (2207.13533). Reviews of the subject use the closely related spherical form

$10^6$2

and parameterize the diffusion coefficient as

$10^6$3

with $10^6$4 in Galactic transport models (Fang, 2022).

The injected lepton spectrum is commonly modeled as a power law with an exponential or super-exponential cutoff. For HESS J1831$10^6$5098 the injection spectrum was written as

$10^6$6

while broader pulsar-halo modeling also uses

$10^6$7

These forms connect the gamma-ray spectrum to the lepton injection index, cutoff scale, and total conversion efficiency from pulsar spin-down power into high-energy pairs (2207.13533, Guo et al., 2024).

The dominant gamma-ray radiation mechanism is inverse Compton scattering of ambient photon fields by the escaped $10^6$8. Synchrotron losses are also important, and the same particles are expected to produce diffuse X-ray emission in the ambient magnetic field. A commonly quoted scaling for IC scattering on the CMB is

$10^6$9

while the corresponding synchrotron photon energy is

$e^\pm$0

These relations explain why TeV gamma rays and keV X rays jointly constrain the same lepton population (Liu, 2022).

At ultra-high energies, the radiative mapping between $e^\pm$1 and $e^\pm$2 ceases to be simple. The morphology depends not only on $e^\pm$3 but also on the spectral curvature of the electrons and on Klein–Nishina suppression of IC cooling. This produces a degeneracy between the electron spectrum and the energy-dependence of the diffusion coefficient when morphology is inferred from $e^\pm$4 TeV data (Guo et al., 2024).

3. Morphology and transport models

The simplest pulsar-halo model assumes isotropic diffusion with a spatially and temporally independent coefficient. For HESS J1831$e^\pm$5098, that “basic” model required an extremely hard injection spectrum, $e^\pm$6 with 68% confidence interval $e^\pm$7, in order to satisfy the \textit{Fermi}-LAT upper limits while fitting the H.E.S.S. spectrum. The underlying issue is that early-injected, lower-energy electrons remain trapped and overproduce gamma-ray flux at GeV energies unless the spectrum is very hard. The same study showed that both a two-zone diffusion model,

$e^\pm$8

with $e^\pm$9 pc, and a time-delayed slow-diffusion model,

$-$0

with $-$1 kyr, can reproduce the H.E.S.S. and \textit{Fermi}-LAT data with a milder $-$2 (2207.13533).

A different challenge to slow diffusion invoked fast, isotropic transport plus a ballistic phase for newly injected particles. Using the generalized Jüttner propagator, that scenario could marginally fit the Geminga halo morphology, but it required a conversion efficiency of $-$3; for PSR J0622$-$43749 it failed more strongly, requiring $-$5 and yielding $-$6. The conclusion of that study was that slow diffusion is necessary to account for the gamma-ray halos around pulsars (Bao et al., 2021).

Anisotropic diffusion offers a different interpretation of compact and asymmetric morphologies. In that framework the transport equation is written with parallel and perpendicular diffusion coefficients relative to a mean magnetic field, and for sub-Alfvénic turbulence one has

$-$7

The measured asymmetric morphologies of the Geminga and Monogem halos were interpreted with this model in terms of different mean magnetic-field orientations, comparable Alfvénic Mach numbers $-$8, and a local magnetic-field coherence length of approximately 100 pc (Wu et al., 7 Mar 2026). A related diagnostic relation for the projected axis ratio is

$-$9

which links the observed elongation to turbulence level and viewing geometry (Li et al., 8 Dec 2025).

Morphology is also shaped by effects that can masquerade as transport physics. At ultra-high gamma-ray energies, the surface-brightness evolution can shrink or expand with energy depending on the electron spectral cutoff, spectral hardness, and Klein–Nishina cooling, so size–energy relations do not by themselves uniquely determine $-$0 in $-$1 (Guo et al., 2024). Proper motion produces further complexity: below 10 TeV, halos can be double peaked or single peaked with an extended tail, whereas above 10 TeV they become nearly spherical because the cooling time of tens-of-TeV electrons is $-$2 kyr; offsets above 10 TeV are usually too small to be observable by HAWC or LHAASO (Zhang et al., 2020).

Finally, anisotropic models become less restrictive when the mean magnetic field is not treated as a single infinite-coherence structure. Random changes of field direction over realistic coherence lengths of $-$3–200 pc make halos rounder, steepen the surface brightness near the pulsar, flatten the outer profile, and reduce apparent asymmetry after PSF convolution. This was proposed as a way to reconcile anisotropic diffusion with the lack of strong asymmetry in many currently observed halos (Yan et al., 11 Jul 2025).

4. Representative systems

The currently discussed pulsar-halo sample spans nearby archetypes, more distant candidates, and recent southern-hemisphere detections. The table summarizes several systems for which specific physical parameters were reported.

Halo or source	Associated pulsar	Reported features
Geminga halo	Geminga	$-$4 cm$-$5 s$-$6, $-$7
Monogem halo	B0656+14	$-$8 cm$-$9 s$\sim 0.08^\circ$0, $\sim 0.08^\circ$1
LHAASO J0621+3755	J0622+3749	$\sim 0.08^\circ$2 cm$\sim 0.08^\circ$3 s$\sim 0.08^\circ$4, $\sim 0.08^\circ$5
HESS J1831$\sim 0.08^\circ$6098	J1831$\sim 0.08^\circ$70952	$\sim 0.08^\circ$8 cm$\sim 0.08^\circ$9 s$1.08\times10^{36}$0, $1.08\times10^{36}$1
PSR B1055$1.08\times10^{36}$252 halo	PSR B1055$1.08\times10^{36}$352	First southern-hemisphere TeV halo; $1.08\times10^{36}$4 extension $1.08\times10^{36}$5

The first four entries correspond to the compilation of known halos in a dedicated review, where the diffusion coefficients inferred from halo modeling are all far below the canonical Galactic average at 100 TeV (Fang, 2022). Geminga and Monogem remain the canonical nearby examples against which other sources are calibrated.

HESS J1831$1.08\times10^{36}$6098 is notable because detailed joint use of H.E.S.S. morphology and H.E.S.S./\textit{Fermi}-LAT spectral information showed that its diffusion coefficient and spin-down-to-electron conversion efficiency are both similar to the Geminga halo, with best-fit values $1.08\times10^{36}$7 cm$1.08\times10^{36}$8 s$1.08\times10^{36}$9 and $^{-1}$0. In the spatially and temporally uniform model the required injection spectrum was very hard, $^{-1}$1, whereas two-zone and time-delayed slow-diffusion models allowed more typical $^{-1}$2 (2207.13533). A later H.E.S.S. spectro-morphological analysis using Gammapy and Naima found that the emission is well described with a pulsar halo model, although a simple 2D Gaussian morphology could not be rejected (Sabri et al., 3 Oct 2025).

LHAASO J0621$^{-1}$33755 established that not all halos need look Geminga-like in detail. Combined LHAASO-KM2A, \textit{Fermi}-LAT, VERITAS, and XMM-Newton constraints revealed a spectral break at $^{-1}$4–10 TeV, a smaller diffusion suppression zone of $^{-1}$5 pc, a harder electron injection spectrum with $^{-1}$6, and an X-ray-derived magnetic-field limit $^{-1}$7 (Adams et al., 3 Apr 2025).

PSR B1055$^{-1}$852 added a new benchmark. H.E.S.S. reported the first detection of extended VHE gamma-ray emission around this middle-aged pulsar, making it the third detected TeV pulsar halo and the first discovered in the southern hemisphere. The emission has a one-sigma extension of $^{-1}$9, no significant spectral variation across the emission region, and a diffusion coefficient at 100 TeV in the $\sigma_{\rm src}=0.30^\circ$0 cm$\sigma_{\rm src}=0.30^\circ$1 s$\sigma_{\rm src}=0.30^\circ$2 range, again much lower than the standard ISM value (Wach et al., 3 Oct 2025).

5. Multiwavelength constraints and experimental methodologies

Gamma-ray data alone do not fully determine the transport physics, because the same morphology can arise from different combinations of diffusion, cooling, injection history, and field geometry. This is why X-ray observations have become central. For Geminga, a broad-band $\sigma_{\rm src}=0.30^\circ$3–79 keV analysis with XMM-Newton and NuSTAR found no significant diffuse X-ray emission and translated the non-detection into strong constraints on the ambient magnetic field and diffusion coefficient. Within a physical model tuned to the GeV–TeV data, the X-ray limits implied $\sigma_{\rm src}=0.30^\circ$4; for a fixed $\sigma_{\rm src}=0.30^\circ$5, the X-ray upper limits required $\sigma_{\rm src}=0.30^\circ$6 cm$\sigma_{\rm src}=0.30^\circ$7 s$\sigma_{\rm src}=0.30^\circ$8 (Manconi et al., 2024).

The expected X-ray surface-brightness profiles differ across the leading transport models. In the isotropic suppressed-diffusion model the X-ray halo is centrally peaked because particles accumulate near the pulsar; in the ballistic-to-diffusive picture the profile is broader and less sharply peaked; in anisotropic diffusion it is flatter because particles escape rapidly along the ordered field. On that basis, sensitive X-ray detectors of a large field of view, explicitly including eROSITA and Einstein Probe, were proposed as decisive tools for distinguishing between the competing transport scenarios (Wu et al., 2024).

Morphological confirmation of distant halos remains difficult with current gamma-ray instruments. Simulations for LHAASO-KM2A and CTA showed that the main challenges are limited angular resolution and photon statistics, especially when the intrinsic angular extension $\sigma_{\rm src}=0.30^\circ$9 falls below the instrument PSF. In that study, CTA benefited from a PSF of $\sim 0.1$0 at 30 TeV, whereas LHAASO-KM2A had $\sim 0.1$1 at the same energy; CTA could resolve most candidate halos beyond 1.5 kpc in 50 h, while LHAASO-KM2A could currently morphologically discriminate only the closest and largest halos, such as Geminga and Monogem (Wei et al., 5 Mar 2026).

CTA-specific studies have further emphasized the power of spatial-spectral likelihood methods. Using CTA prod5 IRFs and a full 3D Poisson likelihood in the planned Galactic Plane Survey, one study concluded that, under Geminga-like assumptions for all middle-aged pulsars, CTA could detect $\sim 0.1$2 halos, identify significant energy-dependent morphology in $\sim 0.1$3, and decompose $\sim 0.1$4 for detailed transport studies. The same analysis emphasized systematic uncertainties from interstellar emission and instrumental response, especially for large extended sources (Eckner, 2023).

6. Population-level implications and outstanding questions

At the population level, pulsar halos have been proposed as a major component of the very-high-energy Galactic sky. A population synthesis that linked SNRs, PWNe, and halos in a coherent evolutionary framework found that the number of detectable halos in HESS. and HAWC surveys can range from 30 to 80% of the number of detectable PWNe, and that CTA’s Galactic Plane Survey could detect 250–300 sources including 170 PWNe and up to 100 halos. In that calculation, unresolved halos dominate the diffuse emission from unresolved source populations and become comparable to large-scale interstellar radiation powered by cosmic rays above $\sim 0.1$5–1 TeV (Martin et al., 2022).

This broader role connects pulsar halos to the long-standing TeV diffuse-emission problem. A dedicated population study argued that TeV emission from pulsars naturally explains the Milagro “TeV excess,” with the total gamma-ray flux from TeV halos expected to exceed the hadronic gamma-ray flux above $\sim 0.1$6 GeV. In that model the halo contribution exceeds standard hadronic expectations by factors of $\sim 0.1$7 at 3.5 TeV and $\sim 0.1$8 at 15 TeV, and a full HAWC survey was expected to resolve about 50 individual TeV halos in the Milagro region of interest (Linden et al., 2017).

Their role in the local positron flux is more contested. In the review literature, if the suppressed diffusion inferred from Geminga extended all the way to Earth, Geminga would not explain the positron excess; in a two-zone model with a finite slow-diffusion region, enough positrons can escape to contribute at Earth (Fang, 2022). By contrast, a study explicitly asking whether pulsar halos are rare found that if all nearby middle-aged pulsars developed halos with diffusion suppression extents as small as 30 pc, their combined positron flux would saturate the $\sim 0.1$9 GeV AMS-02 measurement for injection efficiencies much smaller than those inferred for Geminga and Monogem. That work concluded that it seems a simpler scenario to assume that most middle-aged pulsars do not develop halos (Martin et al., 2022).

The physical origin of slow diffusion remains unsettled. The literature summarized here repeatedly contrasts self-excited turbulence with pre-existing ISM or SNR-driven turbulence, and more recent anisotropic models relocate the problem from a strongly suppressed isotropic diffusion coefficient to the structure, coherence, and sub-Alfvénic character of the interstellar magnetic field (2207.13533, Li et al., 8 Dec 2025). This suggests that the central open problem is not merely whether diffusion is “slow,” but what magnetic configuration and injection history are required to turn escaped pulsar pairs into a measurable halo. Future progress is expected from larger samples, energy-dependent morphology, joint TeV/X-ray analyses, and more accurate measurements of halo asymmetry and surface-brightness profiles.