The Crab Nebula is the brightest pulsar wind nebula in the Galaxy, powered by the pulsar PSR B0531+21. Its emission is observed across the entire electromagnetic spectrum, from radio to gamma rays with energies of 1.1 PeV, detected by the LHAASO observatory. The standard leptonic model explains the spectrum via synchrotron radiation from electrons and inverse Compton scattering, but it cannot reproduce the observed energy-dependent expansion of the nebula in the X-ray and TeV ranges. Nearby in the archive are works on gamma-ray records from quasars, cosmic accelerators, and neutrino signals from the Fermi bubbles; all of them address the origin of ultra-high-energy particles, but none links spatial morphology to the hadronic channel in the Crab as directly.
The authors built a spatially resolved pulsar wind nebula model in which the pulsar's energy is distributed among the magnetic field, electrons, protons, and turbulent waves. Particle evolution is described by an advection-diffusion equation that includes synchrotron, inverse Compton, and proton-proton losses. Electron injection is given by a broken power-law spectrum, while protons follow a relativistic Maxwellian distribution with a non-power-law tail, as in PIC simulations. The equations for particles and turbulent waves were solved numerically using the Crank-Nicolson method. The spatial emission profile was calculated using a previously described method and compared with data on the 68% energy containment radius.
The hybrid lepto-hadronic model simultaneously reproduces the multi-wavelength spectrum and the energy-dependent size of the Crab Nebula. The fraction of hadronic emission from neutral pion decay increases with energy: from ~15% at 1 TeV to ~50% at ~400 TeV and nearly 100% at PeV. The purely leptonic scenario yields too compact a source at TeV energies, while the purely hadronic one is too extended. The predicted 68% radius at 1.1 PeV is about 1.43 arcminutes, roughly six times larger than in the leptonic model. This difference is an observable criterion for the origin of ultra-high-energy gamma rays.
This work shows that the energy-dependent extent of the Crab Nebula can serve as a direct diagnostic of hadronic acceleration to PeV energies. Unlike neighboring studies that focus on spectra or neutrinos, here spatial morphology is used for the first time as a discriminator between leptonic and hadronic channels. This opens the way to testing hybrid models with future next-generation Cherenkov telescopes.
The topic could evolve toward detailed modeling of turbulence and magnetic field inhomogeneities that affect proton transport. It is also promising to apply a similar approach to other pulsar wind nebulae with detected PeV emission. A joint analysis of morphology, spectrum, and neutrino data would help refine the hadronic contribution fraction.
The results will affect the interpretation of data from gamma-ray observatories and neutrino telescopes, as well as models of particle acceleration in astrophysical sources.
The next step will be to verify the predicted size at 1.1 PeV with the future LACT array and to search for correlations with neutrino events.
This work is directly related to the unresolved problem of the origin of ultra-high-energy gamma rays in pulsar wind nebulae: whether they result from leptonic or hadronic processes. This is a key question for understanding where and how protons are accelerated to PeV energies in our Galaxy.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors constructed a spatially resolved lepto-hadronic model of the Crab Nebula that simultaneously reproduces the spectrum and the energy-dependent size from X-rays to PeV. They found that above ~400 TeV, hadronic emission from neutral pion decay dominates, and the predicted radius at 1.1 PeV is six times larger than in the leptonic scenario.
Where its strength is
Using energy-dependent morphology as a discriminator between leptonic and hadronic channels provides a concrete, observable criterion that future telescopes can test.
Where it could go next
Worth trying
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.54, against a usual 0.64. It looks like few have drilled nearby.
The Crab Nebula is the remnant of the supernova of 1054, which was observed by Chinese and Arab astronomers. Its pulsar rotates 30 times per second, and the energy stored in its magnetic field is comparable to the energy of the supernova explosion.