Wfpc2

(a) Optical image of the radio galaxy Centaurus A. (b) Optical HST image of Centaurus A, showing the inner region with the suspected black hole. [(a) ESO; (b) STScI/NASA]

(a) Optical image of the radio galaxy Centaurus A. (b) Optical HST image of Centaurus A, showing the inner region with the suspected black hole. [(a) ESO; (b) STScI/NASA]

Lobe

Lobe

Nucleus Jet

10 Million Parsecs

Lobe

Nucleus Jet

10 Million Parsecs

Nucleus k-H

1 parsec k-H

1 parsec

100 light seconds

Accretion Disk Black Hole

Matter

Radiation spiraling in Accretion Disk

Matter

Radiation spiraling in Accretion Disk

Black Hole (c)

Fig 19.10.

Structure of radio galaxies. (a) Large-scale schematic.The shaded areas are the large lobes. Closer to the center is the jet pointing to one lobe or the other. (b) Small-scale schematic.A series of three frames, each blown up by a factor of 1000. (c) Schematic of central region.

Black Hole (c)

Fig 19.10.

Structure of radio galaxies. (a) Large-scale schematic.The shaded areas are the large lobes. Closer to the center is the jet pointing to one lobe or the other. (b) Small-scale schematic.A series of three frames, each blown up by a factor of 1000. (c) Schematic of central region.

Infalling Material

Infalling Material

Confining Material

Infalling Material

Infalling Material

Fig 19.11.

Jet collimation mechanism. Material flows out of the small source in the center. It is confined by the ring of material, forming the nozzles for the jets.The shading of the confining material indicates that the density is higher on the inner side.The confining material is stabilized by material falling in from farther out.

The confining material may be held in place by material falling in from even farther out, as shown in the figure.

It is possible to have two openings on opposite sides. However, higher resolution observations show that clumps on opposite sides of the center were not ejected at the same time. We also see single jets, but two lobes, in many radio galaxies. It therefore seems that only one nozzle operates at a time. Some flip-flopping of the nozzles is needed to produce the two lobes.

We now turn to the source of the energy in the nucleus of the galaxy. The energy requirements are enormous, since any of the energy ultimately given off in radio waves has its source in the galactic nucleus. At first we might think that nuclear reactions are the most efficient possible energy source. After all, they convert about 0.7% of the available mass into energy. However, if we look at the mass available in the nucleus of a radio galaxy, a higher fraction is being converted into energy. What energy source can be more efficient (by a factor of almost 100) than nuclear reactions?

The answer is mass falling into a black hole. As we saw in Chapter 8, a black hole is important because it allows us to have a large mass in a small radius, and hence strong gravitational forces. We can estimate the amount of energy available in dropping a particle of mass m from far away to the Schwarzschild radius. (Once the mass has passed the Schwarzschild radius, we can no longer get any energy out.) The energy gained by this mass is the negative of the potential energy at RS, so the maximum energy we can extract is

Emax = GMmR

Substituting RS = 2GM/c2 gives Emax = (1/2)mc2

This tells us that we can take out up to half the rest energy of the infalling mass. The rate at which energy is generated then depends on the rate at which mass falls into the black hole, dm/dt. The maximum luminosity, dE/dt, is given by

Example 19.1 Luminosity for mass falling into a black hole

Calculate the energy generation rate for mass falling into a black hole at the rate of 1 M0/yr.

solution

Using equation (19.3) gives

Remember, the luminosity of the Sun is 3.8 X 1033 erg/s, so this is almost 1013 solar luminosities!

However, extracting energy is not a simple as dropping mass into any black hole. If the mass is dropped straight in, most of the energy will be sucked into the black hole. In order to have most of the energy escape, it is necessary for the infalling matter to be in orbit around the black hole, slowly spiraling in. In this case approximately 40% of mc2 is available to power the galaxy. This 40% is very close to the limit of one-half that we found in our simple calculation, equation (19.3).

In equation (19.3), we see that the luminosity does not depend on the mass of the black hole. However, when we take into consideration the spiraling trajectory for extracting most of the energy, the mass of the black hole, becomes important. The more massive the black hole, the greater the rate at which we can drop in material.

We can think of a more massive black hole as having a larger surface area. Calculations show that, in order to produce the luminosities we see in radio galaxies, black holes with masses of about 107 M0 are needed!

19.2.3 The problem of superluminal expansion

An interesting problem with some radio sources is that they appear to have small components that are moving faster than the speed of light! This is called the problem of superluminal expansion. Of course, we do not actually observe the velocities of these components. We observe the rate of change of the angular separation from the center of the source, d0/dt, as shown in Fig. 19.12. We can convert this to a velocity only if we know the distance d to the source. If 0 is measured in radians, then the speed is v = (d0/dt)d

If our derived velocity is greater than c, then either (1) the sources are much closer than Hubble's law suggests, or (2) the apparent velocity doesn't represent a true physical velocity.

One explanation is based on the premise that we are not seeing one source moving. Instead, we are seeing a series of sources. Each source turns on as the previous one fades. This creates the illusion of motion, much as do the lights on a movie marquee. Unfortunately, this doesn't solve the problem. It is unlikely that the individual sources will turn on in sequence by chance. Some signal must be coordinating the time when each turns on. In order for us to see the superluminal expansion, the coordinating signal must be traveling faster than the speed of light. Having a signal traveling faster than the speed of light is just as bad as having an object travel faster than c.

There is an alternative explanation, involving a special relativistic effect. The situation is illustrated in Fig. 19.13. Suppose we have an object starting at point O and traveling to P, a distance r away. The object has a speed v, making an angle 0 with the line of sight. In this arrangement, we take the x-direction to be along the line of sight. The y-direction is perpendicular to the line of sight, and the motion along the y-direction will

0 0

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