Cosmic Ray Electrons Accounting for the North Polar Spur and the Acceleration Efficiency of Weak Shocks 后印本

摘要: The parameters of cosmic ray electrons (CRe) and the strength of magnetic field are crucial for studying the particle acceleration of shocks. The recent confirmation of the bipolarity of the eROSITA bubbles suggests that the well-known NPS/Loop I should be a 10--kpc sized relic in the Galactic halo instead of a small local structure near the Sun. By deriving the energy density of CRe and magnetic field strength accounting for the NPS, unprecedentedly precise parameter constraints on particle acceleration for weak shocks in the halo medium can be provided. The parameters of CRe and magnetic field can be derived independently by modeling the gamma-ray and the radio data of the NPS via inverse Compton scattering and synchrotron emission, respectively. Our main results are: (1), the energy density of CRe is (3-6)$\times 10^{-14}$ erg cm$^{-3}$, and the spectral index is $p\simeq 2.0\pm 0.1$ below the cooling break energy of about 5 GeV; (2), the magnetic field strength is 3 $\mu$G; (3), the shock acceleration efficiency of CRe is close to 1%. Given the Mach number of 1.5, the high acceleration efficiency and flat spectrum of CRe suggest that re-acceleration of preexisting relativistic electrons could exist in the NPS. Alternatively, they could be accelerated by a faster shock in the early epoch, and transport to the current position with an unusually large perpendicular diffusion coefficient. In addition, the cooling break energy suggests that the cooling timescale is $10^7$ yr, in agreement with the age of the eROSITA bubbles.