Regular variations in X-ray emissions from black hole accretion disks, revealing spin and dynamics.Quasi-periodic oscillations (QPOs) are regular, repeating variations in the X-ray brightness of accreting black holes and neutron stars. They appear as distinct peaks in the power spectrum of the observed light curve, indicating that the emission is modulated at specific frequencies, typically ranging from millihertz to hundreds of hertz. These oscillations are not perfectly periodic like a clock, but rather quasi-periodic, meaning their frequency and amplitude can drift over time. QPOs are a powerful diagnostic tool for probing the extreme physics of accretion disks and the strong gravitational fields near compact objects.
QPOs were first discovered in the 1980s in X-ray binaries, with the launch of the EXOSAT satellite. The term was coined to describe the broad, peaked features seen in the power spectra of sources like Cygnus X-1 and GX 5-1. Since then, they have been observed in many systems, including microquasars and, more recently, in some active galactic nuclei.
The exact mechanism behind QPOs is still debated, but the leading models involve instabilities and resonances in the accretion disk. One prominent idea is that QPOs arise from orbital motion of hot spots or clumps of matter in the inner disk, where the orbital frequency is set by the black hole's mass and spin. Another model invokes disk oscillations, where the disk itself vibrates at characteristic frequencies due to pressure and gravity restoring forces. The observed frequencies and their ratios can be used to infer the black hole's mass and spin, as well as the geometry of the accretion flow.
QPOs are used to measure black hole spins and masses, test general relativity in strong-field regimes, and probe the structure of accretion disks. They also serve as a tool to study the interaction between the disk and the black hole's magnetosphere.
In 2020, astronomers detected quasi-periodic oscillations in gamma-ray bursts, suggesting that the central engine of these explosions may be a hyper-accreting black hole with a disk that oscillates in a similar way to stellar-mass black holes in our galaxy.
| T(r) | variable | disk temperature at radius r — temperature kelvin |
| r | variable | radial distance from the central object — radius metre |
| M | variable | mass of the central object — mass kilogram |
| \dot{M} | variable | mass accretion rate — mass flow rate kilogram per second |
| G | constant | Constant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \sigma | constant | Constant relating blackbody radiated power to temperature. — stefan boltzmann constant = 5.670374419e-8 watt per square metre per kelvin to the fourth |
| H_eff | variable | effective static Hamiltonian — hamiltonian joule |
| H_0 | variable | time-averaged Hamiltonian — hamiltonian joule |
| H_{-1} | variable | first negative Fourier component of the Hamiltonian — hamiltonian joule |
| H_{+1} | variable | first positive Fourier component of the Hamiltonian — hamiltonian joule |
| frequency | variable | driving frequency — angular frequency radian per second |
| [ , ] | operator | measures the non-commutativity of two operators — commutator |
| r | variable | radial coordinate — radial coordinate metre |
| M | variable | black hole mass — mass kilogram |
| a | variable | specific angular momentum (spin parameter) — angular momentum per unit mass metre |
| Q | variable | electric charge — electric charge coulomb |











