Past exam of the relativistic Astrophysics and Cosmology course of the University of Cambridge / 2014 / Paper 1 / 3 / a / Solution

An active galactic nucleus is powered by accretion onto a central supermassive black hole. Binding-energy release gives $L\sim \eta \dot{M}{c}^2$, so a compact source can outshine its host without converting its entire mass into radiation. A disc produces a thermal continuum, a hot corona can Comptonize disc photons into X-rays, and surrounding gas produces broad and narrow emission lines. Dust can obscure and reradiate the central emission. Orientation explains part of the diversity between unobscured and obscured nuclei, but accretion state and intrinsic variability also matter.

relativistic jets channel energy and momentum into collimated magnetized outflows. Disc rotation and, in some models, black-hole rotation supply the energy; magnetic stresses accelerate the plasma and connect the engine to the outflow. synchrotron radiation traces relativistic electrons and magnetic fields, while inverse Compton scattering can produce higher-energy emission. Bright knots, terminal hotspots and large radio lobes show that the deposited energy is not confined to the unresolved nucleus.

For bulk speed $\beta c$ at viewing angle $i$, the Doppler factor is $\mathcal{D}=[\Gamma (1-\beta \cos i){]}^{-1}$, and an approaching feature hasLight-travel delay can therefore give apparent superluminal motion without any material or signal travelling locally faster than light. Beaming also makes approaching jets appear brighter and more rapidly variable; a one-sided image is not proof of a physically one-sided outflow. Spectral, polarization and resolved-motion measurements constrain the geometry and emission mechanisms. Jets can inflate cavities and heat surrounding gas, linking black-hole accretion to galaxy and cluster feedback.