Active galactic nuclei are extremely bright central regions of galaxies powered by matter falling into supermassive black holes. Quasars are among the most luminous examples and can be seen across billions of light-years. This cheat sheet helps students connect observations, such as redshift and brightness, to the physics of black holes, accretion, and jets.
It is useful for comparing AGN types and understanding why small regions can release enormous energy.
The core ideas include accretion disks converting gravitational energy into radiation, relativistic jets carrying energy outward, and redshift measuring cosmic distance and motion. Important formulas include redshift z = (lambda observed - lambda rest) / lambda rest, luminosity flux relation F = L / (4 pi d^2), and Eddington luminosity L_Edd = 1.3 x 10^31(M / M_sun) W. AGN brightness can vary quickly, which shows that the emitting region must be small because light travel time limits how fast a large object can change.
Spectra, radio emission, X-rays, and optical brightness all help astronomers classify and study active galaxies.
Key Facts
- An active galactic nucleus is powered mainly by accretion onto a supermassive black hole with a mass of about 10^6 to 10^10 solar masses.
- Redshift is calculated by z = (lambda observed - lambda rest) / lambda rest, where a larger positive z usually means the source is farther away in an expanding universe.
- For nearby objects, recessional velocity can be estimated by v = zc, where c = 3.00 x 10^8 m/s and z is much less than 1.
- Observed flux and luminosity are related by F = L / (4 pi d^2), so brightness decreases with the square of distance.
- The Eddington luminosity is L_Edd = 1.3 x 10^31(M / M_sun) W, giving the approximate maximum steady luminosity before radiation pressure balances gravity.
- The Schwarzschild radius is R_s = 2GM / c^2, which gives the event horizon size for a non-rotating black hole.
- Rapid variability limits source size by R <= c delta t, because a region cannot change coherently faster than light can cross it.
- Quasars are extremely luminous AGN viewed at great distances, often showing broad emission lines and strong radiation from radio to X-ray wavelengths.
Vocabulary
- Active Galactic Nucleus
- An active galactic nucleus is a bright, compact center of a galaxy powered by matter falling into a supermassive black hole.
- Quasar
- A quasar is a very luminous active galactic nucleus that is usually observed at great cosmic distances.
- Accretion Disk
- An accretion disk is a rotating disk of hot gas and dust spiraling toward a compact object such as a black hole.
- Relativistic Jet
- A relativistic jet is a narrow stream of particles and radiation launched near a black hole at speeds close to the speed of light.
- Redshift
- Redshift is the stretching of light to longer wavelengths, often caused by the expansion of the universe or motion away from the observer.
- Eddington Luminosity
- Eddington luminosity is the maximum steady luminosity where outward radiation pressure balances inward gravity for accreting matter.
Common Mistakes to Avoid
- Confusing a quasar with a star, which is wrong because a quasar is the active center of a distant galaxy powered by a supermassive black hole.
- Using v = zc for large redshifts without caution, which is wrong because this simple approximation only works well when z is much less than 1.
- Thinking higher apparent brightness always means higher luminosity, which is wrong because observed flux also depends strongly on distance through F = L / (4 pi d^2).
- Forgetting that rapid variability implies a small source size, which is wrong because no object can change coherently faster than light can travel across it.
- Assuming every galaxy has an active nucleus, which is wrong because many galaxies contain central black holes that are currently quiet due to low accretion rates.
Practice Questions
- 1 A quasar has a rest wavelength line at 486 nm observed at 729 nm. Calculate its redshift using z = (lambda observed - lambda rest) / lambda rest.
- 2 An AGN has luminosity L = 4.0 x 10^38 W and is at distance d = 2.0 x 10^25 m. Calculate its observed flux using F = L / (4 pi d^2).
- 3 A black hole has mass 10^8 M_sun. Estimate its Eddington luminosity using L_Edd = 1.3 x 10^31(M / M_sun) W.
- 4 If two AGN have similar luminosities but one appears much brighter from Earth, explain what this suggests about their distances and why.