A compact quasar radio core

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres · Radiation, radiative transfer and stellar atmospheres

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

Problem

A compact quasar radio core, resolved only by very-long-baseline interferometry, has flux densities Sν=3 JyS_\nu = 3\,\mathrm{Jy} at ν=2 GHz\nu = 2\,\mathrm{GHz} and Sν=1.2 JyS_\nu = 1.2\,\mathrm{Jy} at ν=8 GHz\nu = 8\,\mathrm{GHz}, and an angular size of 1 mas1\,\mathrm{mas} FWHM modelled as a Gaussian, for which Ω≈1.13 θ2\Omega \approx 1.13\,\theta^2 (1 mas=4.848×10−9 rad1\,\mathrm{mas} = 4.848\times10^{-9}\,\mathrm{rad}). ((a)) Translate the two flux densities into a spectral index α\alpha, defined by Sν∝ν−αS_\nu \propto \nu^{-\alpha}. ((b)) Translate α\alpha into the electron power-law index pp. ((c)) Translate the 2 GHz2\,\mathrm{GHz} flux density and the angular size into a brightness temperature, and classify the emission as thermal or non-thermal, and as incoherent or coherent.

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