12.2 Accretion processes and jet formation

Accretion Processes and Jet Formation

Supermassive black holes at the centers of galaxies pull in surrounding matter, forming luminous accretion disks that power active galactic nuclei (AGN). Understanding how matter falls onto these black holes, and how some of that energy gets redirected into enormous jets, is central to explaining why AGN rank among the most energetic objects in the universe.

Accretion Processes in AGN

Accretion around supermassive black holes

Gas and dust in the vicinity of a supermassive black hole feel its immense gravitational pull, but they don't fall straight in. Because of conservation of angular momentum, infalling material enters orbital motion and gradually settles into a flattened, rotating structure: the accretion disk.

Within the disk, viscous forces (driven largely by turbulence from the magnetorotational instability, or MRI) transfer angular momentum outward, allowing material to spiral slowly inward toward the event horizon. As it spirals in, the material converts gravitational potential energy into thermal energy through friction and compression. The result is extreme heating, and the disk radiates across the electromagnetic spectrum, from radio waves to gamma rays.

Beyond this thermal emission, non-thermal processes contribute significantly. Electrons spiraling in magnetic fields produce synchrotron radiation, and inverse Compton scattering can boost photon energies into the X-ray and gamma-ray bands.

Accretion disk structure

Two broad regimes describe accretion disk geometry:

• Thin disk (Shakura-Sunyaev model): The disk is optically thick and geometrically thin. This applies when the accretion rate is a moderate fraction of the Eddington rate. The disk radiates efficiently, producing a characteristic multi-temperature blackbody spectrum.
• Hot corona: The inner regions can become geometrically thick and optically thin, forming a hot corona above and below the disk. This corona is responsible for much of the hard X-ray emission through inverse Compton scattering of disk photons.

Energy release in the disk comes from viscous dissipation of gravitational energy, amplified by magnetic field interactions. The resulting spectral energy distribution (SED) spans many decades in wavelength and serves as a diagnostic tool for disk properties.

Two key quantities govern how much luminosity the disk can produce:

• Eddington luminosity $L_{\text{Edd}} = \frac{4\pi G M m_p c}{\sigma_T}$ sets the maximum luminosity at which radiation pressure balances gravitational infall. Exceeding this limit can drive powerful outflows.
• Radiative efficiency $\eta$ determines what fraction of the accreted rest-mass energy $\dot{M}c^2$ is converted to radiation. For a non-spinning (Schwarzschild) black hole, $\eta \approx 0.057$. For a maximally spinning (Kerr) black hole, $\eta$ can reach roughly 0.42. Black hole spin therefore has a dramatic effect on AGN luminosity.

Jet Formation and Propagation

Relativistic jets in radio-loud AGN

Not all AGN produce jets, but those classified as radio-loud launch collimated outflows of plasma at relativistic speeds. Two primary mechanisms explain how jets are powered and launched:

1. Blandford-Znajek (BZ) process: Magnetic field lines threading the ergosphere of a spinning black hole extract rotational energy from the black hole itself. This is thought to be the dominant mechanism for the most powerful jets.
2. Blandford-Payne (BP) mechanism: Material on the surface of the accretion disk is accelerated centrifugally along magnetic field lines anchored in the disk. This contributes to the mass loading of the jet.

Once launched, the outflow is collimated into a narrow jet by a combination of magnetic hoop stress (from toroidal field components) and external pressure from the surrounding medium.

Several observable consequences follow from relativistic jet speeds:

• Apparent superluminal motion: A jet moving close to the speed of light at a small angle to our line of sight can appear to travel faster than $c$ in projection on the sky. This is a geometric illusion, not a violation of relativity.
• Doppler boosting: The approaching jet appears dramatically brighter than the receding one due to relativistic beaming, which compresses photon arrival times and blueshifts the emission.

The jet plasma composition remains debated. It may consist of electron-positron pairs, electron-proton plasma, or a mixture. As jets propagate through the interstellar and intergalactic medium, they drive shocks, inflate radio lobes, and interact with ambient gas on scales of hundreds of kiloparsecs.

Efficiency of accretion and the disk-jet connection

What determines whether an AGN is radio-loud or radio-quiet? Several factors interact:

• Black hole spin: Higher spin (larger Kerr parameter $a$) provides more rotational energy for the BZ process, favoring stronger jets.
• Accretion rate regime: Sub-Eddington thin disks, super-Eddington flows, and radiatively inefficient advection-dominated accretion flows (ADAFs) each produce different jet and radiative properties. ADAFs, common at low accretion rates, tend to be associated with relatively stronger jet output compared to their radiative luminosity.
• Magnetic flux: In magnetically arrested disks (MADs), accumulated magnetic flux near the black hole becomes dynamically important, potentially enhancing jet power significantly.
• Environment: The availability of gas to fuel accretion and the density of the surrounding medium both affect how jets propagate and how long accretion episodes last.

The disk-jet connection ties these factors together: jet luminosity correlates with accretion power, but the relationship is not one-to-one. AGN feedback, both radiative (radiation pressure driving winds) and mechanical (jets depositing energy into the host galaxy and cluster), regulates the accretion supply itself. This creates a feedback loop that helps explain the co-evolution of supermassive black holes and their host galaxies, and why only a fraction of AGN end up radio-loud.