TeV Halos: Extended Pulsar Gamma Emission

• TeV Halos are extended, very-high-energy gamma-ray sources observed around middle-aged pulsars, defined by large angular extents and hard spectra.
• They are interpreted as inverse-Compton emission from relativistic electrons and positrons confined by suppressed diffusion zones, challenging standard ISM models.
• TeV Halos offer crucial insights into pulsar evolution, local cosmic-ray propagation, and the origins of high-energy gamma rays and cosmic-ray leptons.

TeV halos are extended very-high-energy (VHE; $0.1$–$100$ TeV) gamma-ray sources surrounding pulsars, especially middle-aged systems, and are generally interpreted as inverse-Compton emission from relativistic electrons and positrons that have escaped the compact pulsar wind nebula (PWN) but remain confined within a larger region where diffusion is strongly inhibited relative to the average interstellar medium (ISM). Observationally, they are much larger than classical X-ray PWNe yet much smaller than expected if particles propagated with the standard Galactic diffusion coefficient. Their formation mechanism remains under debate, and current work links them to questions of local transport suppression, pulsar evolution, diffuse Galactic gamma-ray emission, and the origin of high-energy cosmic-ray leptons (Fleischhack et al., 2019, Amato et al., 2024).

1. Definition and observational phenomenology

The defining observational properties of TeV halos are their large angular extent, hard TeV spectra, and association with pulsars rather than with compact nebulae or shell-type remnants. The archetypal cases are Geminga and PSR B0656+14 (Monogem), which HAWC and H.E.S.S. resolved as extended TeV sources with angular extension $\theta_{\rm halo}\simeq2^\circ$–$3^\circ$, corresponding to physical radii $R_{\rm halo}\simeq20$–$30$ pc at distances of order $250$–$290$ pc. Surface-brightness profiles fall off rapidly beyond $\theta\simeq2^\circ$, and the differential photon flux is commonly parameterized as $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$ (Amato et al., 2024).

Geminga and Monogem established the phenomenological template. Geminga was observed as a $100$0-radius gamma-ray source, with $100$1 pc, a $100$2 TeV differential flux $100$3, photon index $100$4, and luminosity $100$5. Monogem shows a comparable size, $100$6–$100$7 pc, and a similar spectrum. Later work identified additional candidates and detections, including the LHAASO source associated with PSR J0622+3749 and a HAWC detection at the location of the radio-quiet pulsar PSR J0359+5414 with $100$8 significance (Sudoh et al., 2019, Albert et al., 2023).

Several selection studies have formalized the empirical characteristics of candidate halos. Six LHAASO-based candidates were reported to share a middle-aged, gamma-ray-bright pulsar in the positional error circle, a rather clean field without any common Galactic VHE-emitting supernova remnants or bright PWNe, and an absence of any gamma-ray emissions in $100$9–$\theta_{\rm halo}\simeq2^\circ$0 GeV after removing the pulsars’ emissions. Their luminosities at $\theta_{\rm halo}\simeq2^\circ$1 TeV satisfy $\theta_{\rm halo}\simeq2^\circ$2 and $\theta_{\rm halo}\simeq2^\circ$3, nearly identical to previously reported relations (Zheng et al., 2024). This suggests that TeV halos form a distinct observational class, although some extended VHE sources remain potentially complex or ambiguous.

2. Diffusion-loss framework and halo morphology

The standard theoretical description of TeV halos uses the diffusion-loss equation for the electron-positron population: $\theta_{\rm halo}\simeq2^\circ$4 Here $\theta_{\rm halo}\simeq2^\circ$5 is the differential density of $\theta_{\rm halo}\simeq2^\circ$6, $\theta_{\rm halo}\simeq2^\circ$7 is the spatial diffusion coefficient, $\theta_{\rm halo}\simeq2^\circ$8 is the energy-loss rate, and $\theta_{\rm halo}\simeq2^\circ$9 is the source term (Amato et al., 2024).

For multi-TeV leptons, inverse-Compton and synchrotron losses dominate, and one frequently writes $3^\circ$0, with $3^\circ$1, implying a characteristic cooling time

$3^\circ$2

Assuming spherical symmetry and neglecting advection, the halo radius satisfies

$3^\circ$3

With $3^\circ$4 and $3^\circ$5–$3^\circ$6 around these pulsars, one finds $3^\circ$7–$3^\circ$8 pc, in agreement with Geminga and Monogem (Sudoh et al., 2019).

A central empirical fact is that the diffusion coefficient inferred inside TeV halos is far below the Galactic average. HAWC-based analyses yield $3^\circ$9 at $R_{\rm halo}\simeq20$0 TeV, a factor $R_{\rm halo}\simeq20$1 below the standard ISM value. Joint fits to Geminga and Monogem have also been summarized as $R_{\rm halo}\simeq20$2 (Evoli et al., 2018, Amato et al., 2024). More generally, TeV halos require $R_{\rm halo}\simeq20$3–$R_{\rm halo}\simeq20$4, or suppression by $R_{\rm halo}\simeq20$5–$R_{\rm halo}\simeq20$6, over scales of order $R_{\rm halo}\simeq20$7 pc (Sudoh et al., 2019).

Morphological fitting often uses either a two-dimensional Gaussian or a diffusion profile. In one HAWC stacking analysis, the standard diffusion profile was written as

$R_{\rm halo}\simeq20$8

with $R_{\rm halo}\simeq20$9, while single-source studies also use Gaussian extensions scaled from Geminga. These descriptions encode the same basic result: the halos are extended, roughly symmetric sources whose size is set by the competition between diffusion and radiative losses (Albert et al., 30 Apr 2025).

3. Transport suppression and competing formation scenarios

The main theoretical problem is not the gamma-ray production mechanism, which is generally inverse-Compton scattering, but the origin of the slow-diffusion zone. One class of models invokes self-generated turbulence. In these models, the steep cosmic-ray gradient produced by particles escaping a pulsar drives resonant Alfvén waves; the turbulence then scatters the same particle population and lowers the effective diffusion coefficient. The wave transport equation can be written schematically as

$30$0

and quasi-linear theory gives

$30$1

Numerical solutions produce suppression factors $30$2–$30$3 over radii $30$4 pc for pulsar ages $30$5–$30$6 yr (Evoli et al., 2018).

Self-confinement models have also been developed in spherical geometry for the observed morphology. In this formulation, the resonant growth rate is

$30$7

and the diffusion coefficient remains suppressed by $30$8–$30$9 at multi-TeV energies. At $250$0 TeV and $250$1 pc around a $250$2 kyr pulsar like Geminga, one finds $250$3–$250$4, versus the ISM value $250$5 (Mukhopadhyay et al., 2021).

A second class of models ties confinement to the pulsar’s environment. A recent progenitor-environment study modeled pulsars from birth in core-collapse explosions through their motion in supernova remnants, wind-blown bubbles, or superbubbles, and concluded that pulsars escape into the ISM at around $250$6 kyr, significantly later than the values most commonly used in the literature. The majority of known pulsars with a confirmed TeV halo have high probabilities of still being in their parent environment, which suggests that efficient pair confinement is connected to the region influenced by progenitor stars (Bourguinat et al., 2 Jul 2025).

A third proposal invokes anisotropic diffusion in sub-Alfvénic turbulence, with $250$7. This can make a halo appear compact if the line of sight is aligned with the local mean magnetic field. However, one study concluded that only a tiny wedge of parameter space, $250$8–$250$9 with $290$0, can simultaneously satisfy size and symmetry for a single halo, and estimated a probability of $290$1 for $290$2 of the $290$3 brightest TeV halos all to be aligned within $290$4 (Luque et al., 2022). Another study, using the anisotropic-diffusion framework to forecast LHAASO detections, argued that a selection effect may explain why the morphologies of all three detected TeV halos so far are consistent with being spherical, and that LHAASO is capable of detecting asymmetric TeV halos after several-year operation (Yan et al., 2022). The controversy therefore remains open at the level of interpretation, although isotropic low-diffusion zones presently provide the more direct match to the existing population.

4. Demographics, ubiquity, and pulsar subclasses

Population studies have shifted the field from case-by-case interpretation to source-class inference. An early empirical argument proposed that TeV halos are ubiquitous and predicted that future HAWC and CTA observations will detect in total $290$5–$290$6 TeV halos, while the existing HESS source catalog could contain $290$7–$290$8 TeV halos that are presently classified as unidentified sources or PWN candidates (Sudoh et al., 2019).

A later HAWC stacking analysis of $290$9 isolated middle-aged pulsars using $\theta\simeq2^\circ$0 days of data identified TeV halo-like emission at a significance level of $\theta\simeq2^\circ$1. In that analysis, the real data yielded $\theta\simeq2^\circ$2, corresponding to $\theta\simeq2^\circ$3, and after a trials factor of $\theta\simeq2^\circ$4 the significance remained $\theta\simeq2^\circ$5. The inferred diffusion scale was $\theta\simeq2^\circ$6 pc at $\theta\simeq2^\circ$7 TeV, corresponding to $\theta\simeq2^\circ$8 (Albert et al., 30 Apr 2025). This result supports the statement that extended TeV halos may commonly exist around middle-aged pulsars.

Individual source discoveries reinforce that conclusion. HAWC detected VHE gamma-ray emission at the location of the radio-quiet pulsar PSR J0359+5414 with $\theta\simeq2^\circ$9 significance. The excess was found to be consistent with a TeV halo associated with PSR J0359+5414, and the source was noted to share similar properties with other halos while having a younger and radio-quiet pulsar (Albert et al., 2023). This supports the use of halos as tracers of pulsars that are invisible in radio-beam geometry.

The status of millisecond pulsars (MSPs) is different. An earlier HAWC-based study of $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$0 MSPs reported a stacked likelihood preference with $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$1 and concluded that MSPs might produce VHE gamma rays with $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$2–$$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$3 (Hooper et al., 2021). A later HAWC analysis of $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$4 MSPs in $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$5 days of data found no significant emission from individual pulsars, and the stacked excess was consistent with a background. The resulting $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$6 C.L. upper limits imply $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$7 at $$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$8–$$\phi(E_\gamma)=\phi_0(E_\gamma/E_0)^{-\Gamma}\exp(-E_\gamma/E_{\rm cut})$$9 TeV and suggest that MSPs are not as efficient as isolated pulsars in producing TeV halos (Abeysekara et al., 30 Apr 2025). For TeV halos as a source class, the current observational picture therefore favors isolated middle-aged pulsars rather than MSPs.

5. Astrophysical implications

TeV halos bear directly on the origin of the positron excess. In self-confinement models, the halo evolves through a growth phase and a relaxation phase. Multi-TeV $100$00 are confined efficiently and produce the TeV gamma rays, while lower-energy $100$01 with $100$02 TeV can escape before the halo is fully formed; if they also escape their parent supernova remnant, they would provide a natural explanation for the positron excess observed by PAMELA and AMS-02 (Evoli et al., 2018). At the same time, broader transport reviews emphasize that a one-zone suppressed-diffusion model makes Geminga-like sources ineffective suppliers of the local positron excess, whereas two-zone models with $100$03–$100$04 pc and $100$05 can allow Geminga and Monogem to contribute at $100$06 GeV–$100$07 TeV (Amato et al., 2024). The observational data therefore constrain, but do not uniquely settle, the positron problem.

TeV halos have also been proposed as the source of the Galactic “TeV excess.” A Galactic pulsar population model concluded that TeV halo emission is expected to exceed the hadronic gamma-ray flux at energies above $100$08 GeV and naturally matches the Milagro excess, with the combined spectrum remaining $100$09 (Linden et al., 2017). More recently, diffuse gamma-ray measurements by LHAASO between $100$10 TeV and $100$11 PeV were interpreted as being in good agreement with the summed emission of the Milky Way’s TeV halos. In that framework, the excess intensity, spectrum, and morphology are matched if TeV halos convert $100$12 of their total spindown power into very-high and ultra-high-energy photons, with a power-law photon spectrum of index $100$13 between $100$14 TeV and $100$15 TeV (Dekker et al., 2023).

Beyond the Galaxy, TeV halos have been argued to contribute significantly to the isotropic gamma-ray background. A population calculation for Andromeda and the cosmological halo ensemble found that TeV halos should contribute significantly to the isotropic gamma-ray background at the highest measured energies, constituting up to $100$16 of the signal observed above $100$17 TeV (Xu et al., 2021). This has direct implications for source population studies and for neutrino-gamma comparisons, because a leptonic TeV component reduces the hadronic fraction that would otherwise be associated with neutrino production (Linden et al., 2017).

6. Multi-wavelength diagnostics and future observational tests

Because the same $100$18 that produce TeV inverse-Compton emission also emit synchrotron radiation, TeV halos are expected to have X-ray counterparts. One modeling study of $100$19 middle-aged pulsars concluded that, for a benchmark magnetic field $100$20, most of the X-ray halos are bright enough to be detectable by eROSITA in the $100$21–$100$22 keV band during its four-year all-sky survey, and that three should exceed the sensitivity of the first all-sky survey. The predicted X-ray fluxes span $100$23–$100$24, and the spatial profiles were proposed as diagnostics of the magnetic field and the energy dependence of diffusion (Li et al., 2021).

An observational search with the first four eROSITA all-sky surveys, however, did not detect degree-wide diffuse emission around Geminga, PSR B0656+14, B0540+23, J0633+0632, or J0631+1036. The resulting $100$25 upper limits on the ambient magnetic field were $100$26 for Geminga, $100$27 for B0656+14, $100$28 for J0633+0632, $100$29 for J0631+1036, and $100$30 for B0540+23 (Khokhriakova et al., 2023). These non-detections constrain the synchrotron efficiency and support the view that inverse-Compton losses dominate on degree scales.

Future TeV observations are expected to sharpen source classification. Candidate-selection studies of unidentified extended sources emphasize that TeV halos should exhibit a characteristic radial profile, hard spectra, and energy-dependent shrinkage of the angular size. Simulations for the Cherenkov Telescope Array Observatory and the ASTRI Mini-Array show that next-generation imaging atmospheric Cherenkov telescopes can distinguish a TeV-halo template from simpler Gaussian or shell morphologies, and can measure shrinkage between bands such as $100$31–$100$32 TeV and $100$33–$100$34 TeV (Rigoselli et al., 18 Sep 2025). Population forecasts similarly indicate that deep HAWC and CTA surveys should detect tens to hundreds of halos, while LHAASO and future southern wide-field facilities can test whether asymmetric halos exist and whether the slow-diffusion phenomenon is generic (Sudoh et al., 2019, Yan et al., 2022).

The central unresolved issue is still the origin of the low-diffusion zone. Current evidence establishes TeV halos as a major source class and as a practical probe of electron transport on scales of tens of parsecs. Whether that transport suppression is self-generated, environmentally inherited, or partly geometry-dependent remains the key question that ties TeV halos to pulsar wind physics and Galactic cosmic-ray propagation (Amato et al., 2024).