A pulsar wind nebula has a magnetic field

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres

Stars from the Inside, Ch Hot and fast electrons: bremsstrahlung, Compton scattering and synchrotron emission

Problem

A pulsar wind nebula has a magnetic field B=1.0×10−6 TB = 1.0\times10^{-6}\,\mathrm{T}. Electrons with Lorentz factor γ=1.0×106\gamma = 1.0\times10^{6} radiate synchrotron X-rays there. Using the magnetic energy density UB=B2/2μ0U_B = B^2/2\mu_0 and the synchrotron cooling time tcool=3mec4σTUBγ,t_{\rm cool} = \frac{3m_ec}{4\sigma_TU_B\gamma}, compute tcoolt_{\rm cool} in seconds and in years, and compare it with a nebula age of 100 yr100\,\mathrm{yr} to decide whether these X-ray-emitting electrons must be continuously supplied.

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