Multi-band Emission up to PeV Energy from the Crab Nebula in a Spatially Dependent Lepto-hadronic Model

Abstract

Multi-band emission from radio to ultra-high energy gamma-rays in the Crab Nebula has been detected. To explain the observed results, non-thermal photon production \textbf{in} the Crab Nebula is carefully studied in a spatially dependent lepto-hadronic model. In our model, the dynamical evolution of the PWN is simulated in a spherically symmetric system. Both electrons and protons are accelerated at the termination shock. The relevant particle propagation equations as well as the photon evolving equation are simultaneously solved. For the Crab Nebula, our results reveal that the observed multi-band photon spectra can be well reproduced with reasonable model parameters. In particular, the photons with energy $\gtrsim 200$ TeV are mainly contributed by the hadronic component via proton-proton interaction. The contribution of the hadronic component depends on both proton spectral index ${\alpha }_{\mathrm{p}}$ and number density $n_{\mathrm{H}}$ of medium within the PWN. Besides, high energy neutrino fluxes are predicted with variable proton spectral indices. The predicted fluxes are not only far below the sensitivities of current neutrino observatories, but also beneath the atmospheric neutrino background with energy less than $\sim 40$ TeV. Moreover, the calculated radial profiles of surface brightness and spectral index are presented.

11 pages, 7 figures, ApJ accepted

References in corpus (10)

• Observations of the Crab Nebula with H.E.S.S
• All-sky search for time-integrated neutrino emission from astrophysical sources with 7 years of IceCube data
• VHE Gamma-Ray Observation of the Crab Nebula and its Pulsar with the MAGIC telescope
• Peta-electron volt gamma-ray emission from the Crab Nebula
• A Dynamical Model for the Evolution of a Pulsar Wind Nebula inside a Non-Radiative Supernova Remnant
• Spitzer Space Telescope Infrared Imaging and Spectroscopy of the Crab Nebula
• Evolution of a Pulsar Wind Nebula within a Composite Supernova Remnant
• Local Kelvin-Helmholtz instability and synchrotron modulation in Pulsar Wind Nebulae
• Detection of UHE gamma rays from the Crab Nebula: Physical Implications
• Modeling the broadest spectral band of the Crab nebula and constraining the ions acceleration efficiency

Cited by in corpus (10)

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• Ultra-High-Energy Gamma-Ray Astronomy
• Phenomenological modelling of the Crab Nebula's broad band energy spectrum and its apparent extension
• Probing LHAASO Galactic PeVatrons through gamma-ray and neutrino correspondence
• Exploring the high energy frontiers of the Milky Way with ground-based gamma-ray astronomy: PeVatrons and the quest for the origin of Galactic cosmic-rays
• Hadronic emission from the environment of the Crab Pulsar Wind Nebula by re-accelerated particles
• Spatio-spectral-temporal Modelling of Two Young Pulsar Wind Nebulae
• Investigating the Role of Pre-supernova Massive Stars in the Acceleration of Galactic Cosmic Rays
• The Potential for Hadronic Particle Acceleration in Galactic Pulsar Wind Nebulae
• Energy-dependent extension of the Crab Nebula as a diagnostic of ultrahigh-energy hadronic emission