Relativistic accretion discs

Artist's impression of an accretion disc around a black hole (credit: NASA / JPL-Caltech)

The figure above is an artist's impression of an accretion disc around a black hole. Above the disc, flowing away from the black hole, is a jet-like structure. The base of the jet is glowing brightly, and illuminating the inner part of the accretion disc. This bright source is called the "corona". Note that this picture is somewhat simplified, e.g., it doesn't show the relativistic warping of space-time; there might not be a jet; the geometry of the corona isn't well known; the disc might not have such a simple geometry; the flow might be different close to the event horizon. It does, however, help set the scene and I believe it is a useful picture to have in mind.

These accretion flows can broadly be divided into two categories: 1) accretion flows around stellar mass objects, typically X-ray binaries in our Galaxy, and 2) accretion flows around super-massive black holes in Active Galactic Nuclei (AGN), the luminous cores of other galaxies. In the latter case, these are the engines of the most powerful sustained energy sources in the Universe.

Fundamentally, these types of thin disc accretion flows are very efficient at converting gravitational potential energy of infalling matter into kinetic energy (the gas flows along approximately Keplerian orbits which are faster closer to the centre) and radiation. The innermost radius of these accretion flows can be deep in the gravitational potential of the black hole which is why they can be so efficient. A significant fraction of the rest-mass energy of the accreting matter, infalling at a rate $\dot{m}$, can emerge as radiation with a luminosity $L = 0.1 - 0.4 \dot{m} c^2$. The luminosity increases as the black hole spins faster (some of the review articles linked below will explain this).

Above the accretion disc is a very hot, tenuous corona, that must be continuously energised by the accretion disc. One model is that the corona is powered by magnetic reconnection, i.e., sudden reconfigurations of the magnetic field geometry, which provide a burst of power that accelerates electrons up to relativistic speeds in the corona. This hot corona can then up-scatter photons from the disc to X-ray energies via inverse-Compton scattering, a process in which relativistic electrons with Lorentz factor $\gamma$ boost the energy of photons from the disc by a factor $\gamma^2$ (this is the opposite of normal Compton scattering where the photons lose energy to the electrons). This means that the corona is a powerful source of continuum X-rays above the disc. However, due to the stochastic nature of the magnetic reconnection events the corona is often observed to be highly variable on very short timescales (meaning it is quite compact and close to the black hole).

Review articles

• "Supermassive Black Holes in X-Rays: From Standard Accretion to Extreme Transients" by Kara and García (2025)
• "Fluorescent iron lines as a probe of astrophysical black hole systems" by Reynolds and Nowak (2003)
• "Measuring Black Hole Spin Using X-Ray Reflection Spectroscopy" by Reynolds (2014)