Black Holes and Quasars

Last: 13. The Realm of the Nebulae Next: 15. A Brief History of the Universe

Black holes represent the final victory of gravity over all other forces. Small ones are formed when massive stars collapse; big ones lurk in the centers of galaxies. They are almost invisible when isolated, but some of the most violent events in the universe involve matter falling into black holes.

Topics

Reading

  14.1 The Formation of a Stellar-Mass Black Hole   p. 325-326
  14.2 The Photon Sphere   p. 326
  14.3 The Event Horizon   p. 327-328
  14.7 Detecting a Black Hole   p. 330-334
  14.8 Supermassive Black Holes   p. 335-336
  17.1 Active Galactic Nuclei   p. 339-402
  17.3 How Are Quasars Powered?   p. 406-409

Properties

A black hole forms when an object's gravitational field is too powerful for light to escape. Once this happens, many details about the object -- its composition, for example -- become irrelevant. The simplest kind of black hole does not rotate, and all its properties are determined by just one thing: its mass.

A simple black hole of mass M has a radius RS ∝ M known as the Schwarzschild radius or the horizon radius. A ray of light launched upward from this radius can just barely escape the gravity of the black hole. Nothing inside this radius can get out; this region cannot influence the rest of the universe in any way.   Schematic of a black hole

At the center of a non-rotating black hole is a singularity -- a point where gravity becomes infinitely strong. Everything within the Schwarzschild radius is pulled into the singularity and destroyed.

Critical Orbits

The smallest possible circular orbit around a black hole has a radius of 1.5 RS. Light is the only thing fast enough to actually travel in this orbit, so this radius is called the photon sphere. Anything which comes within photon sphere will eventually fall into the hole unless it uses rocket power to escape.

The smallest orbit which is stable, meaning that small departures from a perfect circle are allowed, has a radius of 3 RS.

  Schematic of a black hole

Schwarzschild Radius: A Newtonian Derivation

In Newtonian physics, the velocity needed to escape an object of mass M and radius R is √2 times the velocity of a circular orbit at that radius, or

ve = &radic(2 G MR

where G is Newton's gravitational constant.

Setting ve = c, the speed of light, and solving for R yields the Schwarzschild radius:

RS  =  2 G M 

c2 

For an object with mass M = 1 MSun, the Schwarzschild radius is RS = 2.96 km. In other words, the Sun would have to contract to a radius of 2.96 km to become a black hole.

Note that RS ∝ M, so the Schwarzschild radius for any other mass is easily computed: multiply the mass in units of the Sun's mass by 2.96 km.

Rotating Black Holes

Most black holes probably rotate. A rotating black hole has a flattened region, the ergosphere, in which nothing can remain at rest; the hole's rotation drags space with it. The event horizon nests within the ergosphere.

Objects which fall into the ergosphere can extract energy from the black hole's rotation.

  Schematic of a black hole
Rotating black hole [Wikipedia]

In a rotating black hole the singularity is a ring instead of a point. Theoretically, it's possible to fall through this ring and avoid being shredded by infinite gravitational forces. We're not sure what happens next...

Detection

A black hole which is sitting quietly by itself is hard to detect. It has, of course, a strong gravitational field, but far away from the hole the field is no stronger than it would be for any other object of the same mass.

In theory, one way to detect a black hole is by its effect on light; light rays passing near the hole are deflected by its gravity. Here's what a 10 MSun back hole would look like from a distance of 600 km. Of course, anbody so close to a black hole of this size would be torn apart by the hole's gravitational field!

  Lensing by a black hole
Black hole [Wikipedia]

A more practical way to detect a black hole is to study the orbits of stars and/or gas orbiting around it.

The Black Hole in the Center of the Milky Way

Tracking individual stars in the center of the Milky Way shows that they move in elliptical orbits about an object with a mass of

MBH = 3.7×106 MSun .

This is too large a mass to be hidden in any star or star cluster! Some very contrived alternatives to a black hole exist, but most of these would naturally become black holes anyway. The most logical conclusion is that our galaxy has a large black hole at its center.

  Orbits of stars around MW's black hole
Stellar Orbits in the Central Parsec [UCLA]

Note: these orbits obey Kepler's laws, but because they are tilted, their foci don't always correspond to the position of the black hole.

Gas Disk in Giant Elliptical Galaxy M87

We can't track individual stars in other galaxies, but spectra of rotating disks of gas provide strong evidence for massive black holes.   Gas disk in M87
Hubble Confirms Existence of Massive Black Hole [STScI]

Black Hole in Giant Elliptical Galaxy M87

Spectra show that one side of this disk is red shifted (receding) while the other is blue shifted (approaching). This implies the disk is rotating with a speed of about 550 km ⁄ sec.

The mass at the center of the disk is roughly

MBH = 3×109 MSun .

This is almost 1000 times the mass of the black hole at the center of the Milky Way!

  Spectrum of gas disk in M87
Hubble Confirms Existence of Massive Black Hole [STScI]

Black Holes in other Galaxies

Studies of many galaxies have now turned up similar evidence. It appears that the black holes at the centers of galaxies are usually about 0.1% of the stellar mass of the bulge (counting elliptical galaxies as all bulge).   BH mass vs bulge mass

Activity

A black hole which is actively capturing matter is much easier to detect; the gas spiraling in toward the hole heats up and emits intense light, while high-speed jets may extend along the axis of a rotating hole.

These jets appear to be produced when a rotating black hole encounters a magnetic field. The black hole acts like a electrical generator, and the voltage accelerates charged particles.

  A BH and accretion disk
Black hole [Wikipedia]

SS 433

One dramatic case is SS 433, where two jets of gas emerge at roughly 25% the speed of light. The black hole is thought to have a mass

MBH = 16 MSun .

 
Radio image of SS433
Gigantic Cosmic Corkscrew [NRAO]
 
Model of SS433
Pileup on Cosmic Speedway [Harvard]

Jet in M87

Jets are also seen escaping the centers of galaxies. Here's the jet associated with the black hole in M87.   The jet from the nucleus of M87
A Cosmic Searchlight [StScI]

Double Jets in Merging Galaxies

In this composite X-ray (blue) + radio (pink) image, a pair of galaxies spiral toward a merger, with their respective jets tracing their gyrations. The optical image below shows the two galaxies; they're tiny compared to the jets they produce!


3C 75 in Abell 400 [Harvard]
 
3C 75 in Abell 400 [Harvard]

Quasars

Quasars are extremely luminous objects found in the centers of galaxies. They can outshine their hosts by factors of 100 or more. They may vary erratically, dimming or brightening by a factor of two in a few weeks.

These properties strongly support the idea that quasars are powered by matter falling into black holes.

  Quasar 3C 273 from HST
HST Images of Quasars [IAS]

Rapid Variations

The rapid variations in brightness tell us that quasars must be extremely small. An energy source one light year in radius can't turn on or off in less than one year; for example, even if the entire surface goes dark at the same instant, light from the edge is still arriving a year after the light from the center stops.   Constraint on size of QSO engine

To change brightness in just a few weeks, the central engines of quasars can be no more than a few light-weeks in radius.

Extreme Luminosity

The high luminosities of quasars require more energy than ordinary stars can possibly provide. At best, nuclear fusion converts about 1% of the available mass into energy, and in most stars the fraction converted is more like 0.1%. Matter swirling into a black hole can convert 10% to 30% of its mass into energy before it finally falls in.  
Astronomy Picture of the Day [NASA]

Quasar and Black Hole Demographics

If quasars are powered by matter falling into black holes, the amount of quasar light seen in the universe should be related to the amount of matter now locked up in black holes.

Although the details are still sketchy, this prediction seems to be correct. We now know that most galaxies of any size have central supermassive black holes. The quasar activity we observe can be produced when black holes like these form and grow. The surprising conclusion is that most galaxies are sleeping quasars; ready to reawaken whenever more matter falls into their central black holes.

Last: 13. The Realm of the Nebulae Next: 15. A Brief History of the Universe

Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: November 21, 2006
http://www.ifa.hawaii.edu/~barnes/ast110_06/bhaq.html
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