No abstract

The Crab Nebula is a bright source of gamma-rays powered by the Crab Pulsar's rotational energy, through the formation and termination of a relativistic electron-positron wind. We report the detection of γ-rays from this source with energies from 5 × 10−4 to 1.1 petaelectronvolts (PeV), with a spectrum showing gradual steepening over three energy decades. The ultra-high-energy photons imply the presence of a PeV electron accelerator (a pevatron) in the nebula, with an acceleration rate exceeding 15% of the theoretical limit. We constrain the pevatron's size between 0.025 and 0.1 pc, and magnetic field ≈110 μG. The production rate of PeV electrons, 2.5 × 1036 erg s−1, constitutes 0.5% of the pulsar spin-down luminosity, although we cannot exclude a contribution of PeV protons to the production of the highest energy γ-rays.

Since the gravitational waves were detected by LIGO and Virgo, it has been promising that lots of information about the primordial Universe could be learned by further observations on stochastic gravitational waves background. The studies on gravitational waves induced by primordial curvature perturbations are of great interest. The aim of this paper is to investigate the third order induced gravitational waves. Based on the theory of cosmological perturbations, the first order scalar induces the second order scalar, vector and tensor perturbations. At the next iteration, the first order scalar, the second order scalar, vector and tensor perturbations all induce the third order tensor perturbations. We present the two point function 〈h λ,(3) h λ',(3)〉 and corresponding energy density spectrum of the third order gravitational waves for a monochromatic primordial power spectrum. The shape of the energy density spectrum of the third order gravitational waves is different from that of the second order scalar induced gravitational waves. And it is found that the third order gravitational waves sourced by the second order scalar perturbations dominate the two point function 〈h λ,(3) h λ',(3)〉 and corresponding energy density spectrum of third order scalar induced gravitational waves.