. 18
( 28)


Fig 19.5. VLA radio image of Hercules A (z 0.15).The
resolution of the image is 1.4 arc sec; the image itself is a
stacked image of four frequencies (18 21 22 23 cm) and
three con¬gurations (A B C). It is of the highest sensitiv-
ity of any map of any radio source. Notice the narrowness of
the jet, and then the much larger extent of the lobes. [Nectaria
A. B. Gizani, Observatorio Astronomico de Lisboa, Portugal]

high energy electrons decreases with time. This
means that the spectrum evolves, with more and
more of the radiation coming out at long wave- Fig 19.7. VLA radio image of 3C465 (z 0.03) at 327 MHz
lengths as shown in Fig. 19.4. By studying the . Notice the bent appearance. It is not due to the galaxy
synchrotron spectrum of a radio galaxy, we can motion (we know it™s moving too slowly). Probably it is due to
¬‚ows in the cluster atmosphere, relative to the central cD.
estimate how long it has been radiating.
Such ¬‚ows can be induced by cluster mergers. [Jean Eilek
Maps of radio galaxies, such as those shown in
(NMTech) and Frazer Owen (NRAO/AUI/NSF, STScI/NASA)]
Figs. 19.5“19.7, show us what truly amazing
objects they are. (In order to determine the linear
bending of the lobes. Higher resolution observa-
size, we must know the distance to the radio
tions show narrow structures, called radio jets,
galaxy. This is found from the redshift of the visi-
pointing from the center of the galaxy to the
ble associated galaxy, using Hubble™s law.) A typi-
larger radio lobes. Some images of jets are shown
cal radio galaxy has a small source near the center
of the galaxy, and then two large sources far
beyond the optical limits of the galaxy. The opti-
cal galaxy is generally a giant elliptical. The two
sources, or radio lobes, may be separated by up to
107 pc (10 Mpc), and be as wide as 106 pc (1 Mpc).
Sometimes, multiple pairs of lobes are seen. The
structure of these sources is suggestive of matter
being ejected from the galaxy. We sometimes see

Fig 19.8. M87 on different scales. At upper left is a VLA
image of the large-scale structure.To the right is an optical
(HST) image of the jet. Below is a VLBA radio image of the
Fig 19.6. VLA radio image of Cygnus A (z 0.06). center and start of the jet. An optical image of M87 is shown
[Courtesy C. Carilli and R. Perley, NRAO/AUI/NSF] in Fig. 17.2(a). [NOAO/AURA/NSF]

in Fig. 19.8. An optical image of Cen A is shown in gas, it takes a long time for collisions to establish
Fig. 19.9. an equilibrium (Maxwell“Boltzmann) velocity
distribution. The time is longer than the age of
19.2.2 Model for radio galaxies the universe, so this never happens. This is how
The generally accepted picture of what is going we can have an unusually large number of high
on in radio galaxies is shown in Fig. 19.10. We energy electrons. The high energy electrons lose
have interesting phenomena on a wide variety of their energy by synchrotron radiation, rather
length scales. On the largest scale we have the than by collisions with lower energy electrons.
radio lobes themselves. The density in these lobes The magnetic fields in the lobes are thought to
is very low, 10 4 to 10 3 electrons/cm3. Because be in the range 10“100 G. The lobes contain
smaller-scale structures with extents of 103 pc
of this low density, collisions are infrequent.
Therefore, when energy is deposited into this and smaller.
The jets are highly collimated, being some
10 pc long by 104 pc wide. The flow velocities in

the jets are hard to measure, but estimates
range from 103 to 105 km/s. (Some jets are mov-
ing close to the speed of light, as discussed in
Section 19.2.3.) The densities are about 10 2 elec-
trons/cm3. The magnetic fields are comparable
to those in the lobes.
Figure 19.11 shows one mechanism by which
the jets can be collimated. We assume that there
is material flowing outward in all directions.
However, the source of the flow is surrounded by
denser gas. This denser gas has a hole in it, and
the outflowing material just follows the path of
least resistance. Effectively, the material forms
itself into a nozzle. One problem with this pic-
ture is that we would expect the outflowing
material to drive the confining material outward.

Fig 19.9. (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

1 Million Parsecs
Nucleus Jet

10 Million Parsecs

Jet Jet
1 parsec

X 1000
Jet Jet
1 light day
X 1000

100 Fig 19.11. Jet collimation mechanism. Material ¬‚ows out of
light the small source in the center. It is con¬ned by the ring of
seconds material, forming the nozzles for the jets.The shading of the
(b) con¬ning material indicates that the density is higher on the
inner side.The con¬ning material is stabilized by material
falling in from farther out.
spiraling in Accretion Disk

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
Black Hole nucleus of the galaxy. The energy requirements
(c) are enormous, since any of the energy ultimately
Fig 19.10. Structure of radio galaxies. (a) Large-scale given off in radio waves has its source in the galac-
schematic.The shaded areas are the large lobes. Closer to tic nucleus. At first we might think that nuclear
the center is the jet pointing to one lobe or the other.
reactions are the most efficient possible energy
(b) Small-scale schematic. A series of three frames, each
source. After all, they convert about 0.7% of the
blown up by a factor of 1000. (c) Schematic of central
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
The confining material may be held in place by energy. What energy source can be more efficient
material falling in from even farther out, as (by a factor of almost 100) than nuclear reactions?
shown in the figure. The answer is mass falling into a black hole. As
It is possible to have two openings on opposite we saw in Chapter 8, a black hole is important
sides. However, higher resolution observations because it allows us to have a large mass in a small
show that clumps on opposite sides of the center radius, and hence strong gravitational forces. We
were not ejected at the same time. We also see can estimate the amount of energy available in
single jets, but two lobes, in many radio galaxies. dropping a particle of mass m from far away to the
It therefore seems that only one nozzle operates Schwarzschild radius. (Once the mass has passed

the Schwarzschild radius, we can no longer get We can think of a more massive black hole as hav-
any energy out.) The energy gained by this mass is ing a larger surface area. Calculations show that,
the negative of the potential energy at RS, so the in order to produce the luminosities we see in
maximum energy we can extract is radio galaxies, black holes with masses of about
107 M are needed!
Emax GMm/RS (19.1)

2GM/c2 gives 19.2.3 The problem of superluminal
Substituting RS
Emax (19.2)
An interesting problem with some radio sources is
This tells us that we can take out up to half the that they appear to have small components that
rest energy of the infalling mass. The rate at are moving faster than the speed of light! This is
which energy is generated then depends on the called the problem of superluminal expansion. Of
rate at which mass falls into the black hole, dm/dt. course, we do not actually observe the velocities of
The maximum luminosity, dE/dt, is given by these components. We observe the rate of change
of the angular separation from the center of the
Lmax (19.3)
source, d /dt, as shown in Fig. 19.12. We can con-
vert this to a velocity only if we know the distance
Example 19.1 Luminosity for mass falling into a d to the source. If is measured in radians, then
black hole the speed is
Calculate the energy generation rate for mass
falling into a black hole at the rate of 1 M >yr. v (d /dt)d

If our derived velocity is greater than c, then
either (1) the sources are much closer than
Using equation (19.3) gives Hubble™s law suggests, or (2) the apparent velocity
1 12 1033 g 2 13 1010 cm>s 2 2 doesn™t represent a true physical velocity.
13 107 s 2
L One explanation is based on the premise that
we are not seeing one source moving. Instead, we
1046 erg/s
3 are seeing a series of sources. Each source turns
on as the previous one fades. This creates the illu-
Remember, the luminosity of the Sun is 3.8 1033
sion of motion, much as do the lights on a movie
erg/s, so this is almost 1013 solar luminosities!
marquee. Unfortunately, this doesn™t solve the
However, extracting energy is not a simple as problem. It is unlikely that the individual
dropping mass into any black hole. If the mass is sources will turn on in sequence by chance.
dropped straight in, most of the energy will be Some signal must be coordinating the time
sucked into the black hole. In order to have most when each turns on. In order for us to see the
of the energy escape, it is necessary for the superluminal expansion, the coordinating signal
infalling matter to be in orbit around the black must be traveling faster than the speed of light.
hole, slowly spiraling in. In this case approxi- Having a signal traveling faster than the speed of
mately 40% of mc2 is available to power the light is just as bad as having an object travel
galaxy. This 40% is very close to the limit of one- faster than c.
half that we found in our simple calculation, There is an alternative explanation, involving
equation (19.3). a special relativistic effect. The situation is illus-
In equation (19.3), we see that the luminosity trated in Fig. 19.13. Suppose we have an object
does not depend on the mass of the black hole. starting at point O and traveling to P, a distance r
However, when we take into consideration the away. The object has a speed v, making an angle
spiraling trajectory for extracting most of the with the line of sight. In this arrangement, we
energy, the mass of the black hole, becomes take the x-direction to be along the line of sight.
important. The more massive the black hole, the The y-direction is perpendicular to the line of
greater the rate at which we can drop in material. sight, and the motion along the y-direction will

v (dt)



Time (yrs)


Fig 19.12. Superluminal expansion. (a) VLBA image of the
radio jet 3C279, which shows apparent superluminal ¬‚ows.
Superluminal motion is shown in a ˜movie™ mosaic of ¬ve radio
images made over seven years.The stationary core is the bright
1998 red spot to the left of each image.The observed location of
the rightmost blue/green blob moved about 25 light years from
1991 to 1998, hence the changes appear to an observer to be
faster than the speed of light, or ˜superluminal™.The blue/green
20 40 60 80
blob is part of a jet pointing within 2 to our line of sight, and
Light Years
moving at a speed of 0.997 times the speed of light. (b)The
(a) geometry of the problem.We measure a change in angular
position d and relate that to a tangential velocity v by knowing
the distance d. [(a) Ann Wehrle (Caltech/NASA/Wehrle, A.
be detected as the proper motion. The distances x et al., Astrophys. J. Suppl., 133, 297, 2001]
and y traveled along these two directions are
x r cos
Substituting from equations (19.4) and (19.5),
y r sin (19.4) we have
The time for the object to move the distance r is tapp (r/v) (r/c) cos
t r/v (19.5) (r/v) (1 cos ) (19.6)
However, a light or radio wave emitted from P v/c. The apparent velocity
where we have set
has to travel a shorter distance than one emitted across the sky, vapp, is then
from O before reaching the observer. The path
from P to the observer is shorter than the path vapp
from O to the observer by a distance x. This
means that a light wave emitted from P takes x/c
r sin
1r v 2 11 cos 2
less time to reach us than one emitted at O.
Therefore, from the point of view of the observer,
Eliminating r gives
the apparent time, tapp, for the object to travel
from O to P is
v sin
11 cos 2
vapp (19.7)
tapp t x/c

O Substituting back into equation (19.7), we
Fig 19.13. Apparent superlu-
minal motion as a clump of
material moves from O to P. vapp
a b
11 2
2 1>2
v max
This is just the quantity that appears in the
Lorentz transformations. We know that this quan-
tity can become quite large as v approaches c.
x Example 19.2 Superluminal expansion
For an object moving away from the nucleus of a
galaxy at v 0.95c, find the maximum value of
vapp and the angle at which it must be moving to
reach this maximum.

We have


so 18.2 . From equation (19.8) we have

11 0.952 2 1>2
To Observer

For v V c, is close to zero, and vapp v sin ,
the expected result. However, for v close to c, vapp There is a way to test this explanation. For a
can be greater than v. In fact, vapp can be so much given speed and direction of motion, there
greater than v that it exceeds c. should be a specific Doppler shift for radiation
To see this, we can find the angle that gives from the moving object. Unfortunately, these
the maximum vapp for a given v. Taking equation radio sources do not have any lines in their spec-
(19.7), dividing by v, differentiating the result tra. The Doppler shift alters the shape of the syn-
with respect to , and setting the result equal to chrotron spectrum, but the interpretation is dif-
zero, gives ficult. Studies of the spectra of these sources are
11 cos 2 11 cos 2 2

19.3 Seyfert galaxies
cos )2 gives
Multiplying through by (1
cos2 sin2
cos 0
Seyfert galaxies are characterized by having
Remembering that sin2 cos2 1, this simpli- nuclei that strongly dominate the total light
fies to from the galaxy. On a short exposure, they look
like stars with a fuzzy patch around them and
cos 0
like a spiral galaxy on longer exposures (Fig.
or 19.14). For comparison, normal spirals never look
like a star, even on a short exposure. This suggests
that we are not resolving the nuclei of Seyferts in
most of our images of them. (There are a few
We find sin from
Seyferts for which the source of narrow emission
cos2 )1/2
sin (1
lines has been resolved.) When we can study the
2 1/2 fuzzy patch around the nucleus, it seems like the
(1 )

times the width of lines in normal galaxies. If the
broadening is thermal Doppler broadening, this
would imply a temperature in excess of 107 K (see
problem 19.10).
There are some differences among Seyferts in
the appearance of lines called ˜forbidden lines™.
These are spectral lines that are not strong under
normal circumstances. In some Seyferts, the for-
bidden lines are broad, and in others they are nar-
row. The ones with narrow lines are called type I,
and the others are called type II. In addition,
infrared emission from type I Seyferts is non-ther-
mal, while that from type II Seyferts is thermal
emission from dust. Also, type I Seyferts are weak
radio sources, while half of the type II have mod-
erate radio emission. Type I Seyferts also have
strong X-ray emission, with a correlation between
optical and X-ray luminosity. In Fig. 19.15, we see
that the Seyfert spectra have similarities with
other types of active galaxies.
(c) (d) The brightest Seyfert is shown in Fig. 19.14. It
is an 11th magnitude galaxy in Coma Venatici.
Fig 19.14. The Seyfert galaxy NGC 1566.This is at a dis-
Ultraviolet emission lines from this galaxy show
tance 15 Mpc.The active region in the center is found to
rapid variations in strength and width. To
vary on a time scale of less than a month. (a) HST Wide
explain this phenomena, a nucleus with a black
Field Planetary Camera 2 (WFPC2) image of the oxygen
hole of mass 109 M has been proposed.
emission (5007 …) from the gas at the heart of NGC 4151.
Though the twin cone structure can be seen, the image does Another type of active galaxy is called a BL Lac
not provide any information about the motion of the oxygen
object, named after the first one of this type
gas. (b) In this STIS (imaging spectrometer) spectral image of
observed. A spectrum of a BL Lac object is shown
the oxygen gas, the velocities of the knots are determined by
in Fig. 19.16.
comparing the knots of gas in the stationary WFPC2 image
to the horizontal location of the knots in the STIS image. (c)
This STIS spectral image shows the velocity distribution of
19.4 Quasars
the carbon emission from the gas in the core of NGC 4151.
It requires more energy to make the carbon gas glow (CIV
19.4.1 Discovery of quasars
at 1549 …) than it does to ionize the oxygen gas seen in the
other images. (d) In this false color image the two emission In our discussion of radio galaxies we mentioned
lines of oxygen gas (the weaker one at 4959 … and the the importance of predicting accurate radio posi-
stronger one at 5007 …) are clearly visible.The horizontal
tions for the purposes of finding optical counter-
line passing through the image is from the light generated by
parts. Before the use of interferometry, some
matter falling into the black hole at the center of NGC
sources were studied by lunar occultation. In
4151. [STScI/NASA]
such an experiment, the source is observed as the
Moon passes in front of the source. Since we
know the position of the edge of the Moon very
accurately, we can determine the location of a
disk of a spiral galaxy. This suggests that we are
radio source by noting the times at which the
seeing spiral galaxies with unusually bright
source disappears and reappears.
This technique was used at the Parkes radio
The optical spectra (Fig. 19.15) are character-
telescope in Australia to study the radio source
ized by strong, broad emission lines. The lines are
more than 103 km/s wide. This is more than ten 3C273. (The designation means that it is the 273rd

Fig 19.15. Line spectra of vari-
ous types of active galaxies.
[William Keel, University of

source in the 3rd Cambridge catalog of radio a fuzzy patch around it. The most detailed photo-
sources.) When photographs of the area around graphs show a jet extending from the core, just as
the radio source were examined, a faint (13th in radio galaxies.
magnitude) star was noted. This was an interest- The optical spectrum of 3C273, shown in Fig.
ing discovery, since no radio stars were known at 19.18, is quite unusual. The spectrum puzzled
the time. Closer observations, producing photo- astronomers for some time. It was finally noted
graphs like that in Fig. 19.17, have shown that that a series of lines looked like the Balmer series,
3C273 is not really a star. It looks like a star with but with a very large redshift. For example, the

VLA HST UIT EUVE ROSAT EGRET Cerenkov Fig 19.16. A BL Lac object,
Markarian 421, showing its full
spectrum over all wavelength
ranges. [William Keel, University
of Alabama]

Optical UV X rays
+ +++ +
+ +++
Flux per decade (νFν), erg/cm2 second

++ +
++ +
+ +
+++ +
+++ + ++
++ flaring
+++ + ++
+ +++ +

+ Markarian 421 broad band spectrum
15 20
10 25
log frequency (Hertz)

is not proper to think of the redshift as being a
Doppler shift. We will see in Chapter 20 that a
wavelength shift of 15% means that, in the time
it takes light to get from 3C273 to us, the separa-
tions between all pairs of objects have increased
by 15%. If we approximate the expansion rate as
constant, then this means that the light has had
to travel for 15% of the Hubble time to reach us. If
the distance is d, then the travel time is d/c, so
d/c 0.15 (1/H0)

10.15 2 c

10.15 2 13 105 km>s 2
170 km>s>Mpc 2

640 Mpc
Fig 19.17. An optical image of the quasar 3C273. Notice
the jet to the lower right. [H.-J. Roeser, ESO, and William We find the distance modulus, m M,
Keel, University of Alabama]
m M 5 log10 (d/10 pc)
5 log10 (6.0
H line, whose rest wavelength is 656.3 nm, was
observed at about 760.0 nm. This is a 15% shift in 39.0
Since the apparent magnitude is 13, the abso-
In Chapter 20 we will see that Hubble™s law, as
lute magnitude is 26. For comparison the abso-
presented in Chapter 18, is not a useful descrip-
lute visual magnitude of the Sun is 5. A difference
tion for finding the distance modulus to an
of 31 magnitudes corresponds to a brightness
object with a very large redshift. This is because it
ratio of a little more than 1012. This means that
3C273 gives off 1012 times as much visible light as
does the Sun. What makes this even more
remarkable is that 3C273 gives off more energy in
the radio part of the spectrum than in the visible!
The proposal that the spectrum of 3C273
could be explained with a large redshift was
made in 1963 by the Caltech astronomer Maarten
Schmidt. At that time, the existence of a similar
object, 3C48, was known. It had been noted in
1960 that there is a possible correspondence
between the radio source and a 16th magnitude
star. The spectrum of this star showed an even
greater redshift than 3C273, corresponding to a
37% shift. These objects were given the name
Fig 19.18. Spectrum of 3C273, showing the Lyman alpha
quasi-stellar radio sources, because of the starlike
line in emission and a number of other lines in absorption.The
lower spectrum is of a quasar with z 3.48, in which there appearance on short-exposure photographs. The
are many absorption lines at lower redshift, the Lyman-alpha name was shortened to QSR or quasar. Further
forest, corresponding to intervening material. [William Keel,
studies have revealed a class of objects that are
University of Alabama, NASA, and L. Lu, Keck Observatory]
like QSRs in optical photographs, and also have

large redshifts, but don™t have any radio emis- plate archives and find its image as far back as
sion. These are called quasi-stellar objects, or QSOs. 100 years ago.
We now loosely call both types of objects quasars. An important feature of this variability is that
it allows us to place an upper limit on the size of
19.4.2 Properties of quasars the emitting region. We discussed this idea in our
The spectra of many quasars show a large ultravi- study of masers, in Chapter 15. If a significant
olet excess. This means that they are brighter in fraction of the total power varies on a time scale
t, then the emitting region can be no larger than
the ultraviolet than one would expect from just
ct (as long as motions close to the speed of light
knowing their visual brightness. This provides us
with a way of searching for quasars. We cannot are not involved). In the case of quasars, varia-
take spectra of all stars to see if they have large tions on a time scale of a few months limit the
size of the emitting region to about 1012 km. (This
redshifts. Since quasars are so faint, it takes a
is only about 104 AU.)
long time to observe a spectrum. We can study
radio sources, but not all quasars are radio The spectra of quasars, such as that in Fig.
sources. However, we can compare visible, blue 19.20, show both emission lines and absorption
and (now with space observations) ultraviolet lines. Generally, all of the emission lines can be
explained by a single redshift z, but a few groups
images of large fields to find objects with a large
ultraviolet excess. Spectra of these objects can of absorption lines appear with different red-
then be taken to see if they have large redshifts. shifts, always less than or equal to that of the
Some quasars are quite variable in their emission lines. Often the spectrum is dominated
energy output (Fig. 19.19). We have good records by the Lyman-alpha line at various redshifts.
of the visible and radio variability of quasars for (Remember, Ly is the lowest transition and is
the past 30 years as a result of specific studies. often the most easily excited.) We sometimes
refer to this as the Lyman-alpha forest. Over the
However, we have optical records going back even
farther, since observatories save photographic years, extensive absorption line surveys have been
plates. A quasar may be on a plate exposed for an carried out, providing good statistical informa-
entirely different purpose. Once the quasar is dis- tion on absorption line properties. The absorption
covered, an astronomer can go back through lines are generally narrow, less than 300 km/s

300 Fig 19.19. Light curves for vari-
NGC 5548
IRAS 13224“3809 ous active galaxies. [William Keel,
emission line f lux
X-ray intensity

University of Alabama]
6 Ly ±


0 0
0 10 20 30 0 50 100 150 200 250
time, days time, days

NGC 5548 1350A
3.8 cm radio flux

continuum flux

BL Lacertae 6
10 1840A


5 °

0 0
1970 1975 1980 1985 1990 1995 2000 0 50 100 150 200 250
year time, days

Fig 19.20. Spectrum of the

quasar Q0103-294, at z 3.11.
15 Z=3.11




Relative Intensity







400 500 600 700 800 900
Wavelength (nm)

wide. They are also mostly from the ground states One possible source of redshift is gravitational.
of atoms, indicating a low temperature. All of this We have already seen that photons are redshifted
suggests that the absorption lines arise in mate- as they leave the surface of any object. One prob-
rial between us and the quasar. lem with this explanation arises from the limited
At the time of this writing, the largest range of redshifts seen in the emission lines. This
observed quasar redshift is 6.28. The light from tells us that the emitting gas would have to be in
the most distant quasars has been traveling over a thin shell around some massive object. An
90% of the age of the universe to reach us. This analysis of such systems shows that quasars
means that we are seeing the universe as it was would have to be so close or so massive that our
before our own galaxy formed. Therefore, quasars local part of the galaxy would be greatly affected
by their presence. Even with a mass of 1011 M ,
provide us with an important link to our past.
the objects would still be within our galaxy.
19.4.3 Energy“redshift problem There is an additional problem. For the larger
The immediate problem that astronomers recog- redshifts, we need black holes. Even with a black
nized with quasars was explaining their enormous hole to get a redshift greater than 100%, the pho-
energy output. What makes the problem even tons must be emitted from very close to the
more difficult is the fact that the energy must be Schwarzschild radius. We cannot think of any
generated in a small volume. One way out of the way to come up with a hot radiating gas close to
RS, especially given the narrow range of redshifts
problem is to say that quasars are not as far away
as we think they are. After all, we only observe in a given quasar. The accretion disks responsible
their apparent brightness. We infer their absolute for X-ray emission around objects like Cyg X-1 are
brightness by knowing their distances, deter- generally outside the photon sphere (defined in
Section 8.4.2), which is at 1.5 RS.
mined from the redshifts and Hubble™s law. (It
should be noted that even the factor of two uncer- Another possible source of redshift is called
tainty in the Hubble constant has no real bearing kinematic. This means that we are observing a
on this particular problem.) If we are saying that high velocity due to something other than the
the distances are wrong, we are saying that the expansion of the universe. For example, they
quasars do not obey Hubble™s law. If that is the might be shot out of galaxies. However, if this
case, we must explain the large redshifts. This is were the case, we might expect to see some
the basic problem. Either we have to explain the blueshifts comparable to the redshifts seen in
large energy output, or we have to come up with quasars. To get them all moving away from us, we
another redshift mechanism. For this reason, we might think that they have been ejected from our
can think of this as the energy“redshift problem. galaxy, but the kinetic energy becomes quite large.

Also, if there were nearby objects moving at high In addition, there are direct pieces of evidence
speeds, we would expect to see some proper that quasars are at cosmological (Hubble™s law)
motion, and we don™t. distances. The absorption lines in quasar spectra
In an effort to see if some kinematic explana- are one example. As we have said they are gener-
tion is possible, some effort has been made to ally at redshifts that are less than the emission
search for galaxies and associated quasars, where lines, and the most natural explanation is that
the quasar and galaxy have very different red- they are from material between us and the
shifts. If it can be shown that a galaxy and a quasar. If the intervening material obeys Hubble™s
quasar are directly connected, then they must be law, then the quasars must be at cosmological
at approximately the same distance from us. distances. Also, the fact that Seyferts appear to be
Presumably the distance is accurately indicated galaxies supports the belief that quasars are also
by the redshift of the galaxy. If the quasar has a galactic in scale and far away, rather than small
different redshift, then it doesn™t obey Hubble™s and nearby. Finally, the observation of the gravi-
law. Examples have been found of galaxies and tational lensing of quasars by massive interven-
quasars that appear near each other on the sky, ing galaxies (discussed in the next section) means
but have different redshifts. The problem, how- that the quasars must be more distant than the
ever, is in proving that the quasar and galaxy are intervening galaxies.
associated. Just because two objects appear along Much of the concern over the energy“redshift
almost the same line of sight doesn™t mean that problem faded in the 1990s. Astrophysicists now
they are at the same distance. A galaxy and a feel that the energy generation requirements in
quasar don™t have to be at the same distance any quasars are not as outrageous as they seemed in
more than two stars in the same constellation the 1970s. This is partly because of the number of
have to be at the same distance. high energy phenomena that have been observed
Sometimes arguments over whether galaxies and understood, at least partially. More specifi-
and quasars that appear near each other are asso- cally, our understanding of radio galaxies has
ciated come down to questions of probability and reached the point where we think that quasars
statistics. For example, we might ask, given a may be a different manifestation of the same phe-
quasar, what is the probability that there will be an nomenon. The energy requirements for quasars
unassociated galaxy along the same line of sight? are large, but not much larger than those for the
Arguments such as this are difficult to frame, and most luminous radio galaxies. This point will be
also can lead to fallacious conclusions, akin to a discussed farther in Section 19.6.
person who takes a bomb on board an airplane to The quasar problem is in many ways typical
safeguard his passage, on the assumption that if of problems in astronomy. On the observational
the probability of one person having a bomb on a side, it provides an excellent example of the
plane is low, the probability of two people having interplay among observations in various parts of
bombs is much lower. To date, the statistical argu- the spectrum. Radio and optical observations
ments seem to allow all of the cases of galaxies and were important in the discovery of the phenom-
quasars in the same direction as being coinci- enon. Radio, optical, infrared, ultraviolet and X-
dences, with the two being unassociated. ray observations have been important in under-
Some effort has also gone into trying to standing the phenomenon. In addition, our
observe direct connections between the galaxy understanding of quasars has required the
and quasar in such situations. Connections results of extensive systematic surveys of quasar
would be in the form of a detectable trail of lumi- properties. Such surveys don™t receive the same
nous material between the galaxy and the quasar. glory as the initial discovery, but they provide
Even this problem is not easy, because there are the data on which a solution can ultimately
photographic artifacts which can resemble such be based.
a bridge between two objects. To date, no con- The quasar problem is also typical in another
vincing evidence has been presented to demon- way. Many problems in astronomy come upon the
strate a bridge between a quasar and a galaxy. scene in a spectacular fashion, often with an

unexpected observation of a new phenomenon. and the quasar. (Clearly, the alignment of the
The solutions, however, do not come in a single, quasar and galaxy are completely accidental. The
spectacular step. For our understanding of two have no physical connection.) Let™s first look
quasars, it has been important to have the prob- at the ray from the quasar that passes over the
lem around long enough for astrophysicists to top of the galaxy. It is bent slightly downward.
become more comfortable with the energies When that ray reaches us, we would see an image
required. Part of the process is the discovery of of the quasar back along the line of the ray reach-
other high energy phenomena. For example, ing us. The image would appear higher than the
when it was suggested in the 1980s that quasars quasar itself. We can also look at the ray going
might involve some form of black hole, the ideas under the quasar. It is bent upward, and results
was not taken seriously by most. After all, black in the image of the quasar being below the actual
holes were theoretic playthings. However, the quasar. In fact, if we analyzed rays that go all
observations of objects such as Cyg X-1 have made around the galaxy, each produces an image in a
the existence of black holes seem more likely. It is slightly different position. When you look at the
a large jump from a few M black hole to a 108 M quasar, you will see a ring of images around the
galaxy. This is called an Einstein ring.
one, but it is not as big a jump as from no black
holes to a few M black hole. In addition, the suc- In real situations we are not likely to find
cess in explaining many of the details of radio the quasar exactly in line with the galaxy. If it is
galaxies has made astrophysicists more confi- slightly off line, the ring breaks up into a group
dent of the model that places a massive black of distinct images. Also, if it is off line, the vari-
hole in the center of a galaxy. (We may even ous rays will travel different distances to reach
have one at the center of our galaxy, as noted in us. This means that each image of the quasar is
Chapter 16.) a ˜snapshot™ of the quasar at a slightly different
time. If the quasar is varying in brightness, the
variations will appear in all of the images, but
19.5 Gravitationally lensed quasars there will be a delay from one image to the
When we discussed general relativity and black Gravitational lensing of quasars has been
holes in Chapter 8, we saw that a strong gravita- observed, but the first detection was quite acci-
tional field can bend the path of a light ray. In dental. Astronomers simply noticed two quasars
Chapter 4, we saw that when we allowed glass (a that appeared virtually identical. They had the
lens) to bend light rays, images were moved or same spectra and redshifts. The two quasars had
altered. Is it possible that gravitational bending the same variations in brightness, but with the
of light can also produce a lens effect? variations in one quasar following those in the
By looking at Fig. 19.21, we can see how this other by a fixed time delay. It was not obvious
might happen. In this case we imagine that the that this was a lensing situation, because the
light is coming from a distant quasar, and the intervening galaxy was not bright enough to be
bending is caused by a galaxy midway between us seen in the original images. Further observations
revealed its presence.
Now that we know that such lensing situa-
Observer Galaxy
tions exist, astronomers have searched systemati-
cally for more of them. These searches have been
done both in the optical and radio parts of the
spectrum. Some sample optical images of lensed
Quasar quasars are shown in Fig. 19.22. The observation
of gravitationally lensed quasars is important for
Fig 19.21. Diagram of geometry for the gravitational
a number of reasons. Probably most important, it
lensing of a quasar.The size of the shift is hot to scale.
is a demonstration that the quasars must be at

Fig 19.22. Observations of
lensing of quasars. (a) Lensing in a
rich galaxy cluster Abell 2218. In
this HST image, some background
objects appear as arcs. (b) PG115
080.This ring is the result of
gravitational lensing of a quasar.
The original image is on the left.
The image on the right is
processed so that the quasar is
removed and the ring remains
(See also Fig. 8.1). [STScI/NASA]



the distances indicated by their redshifts. This is SOLUTION
because the quasar must be at least as far away as From equation (8.1) we have
the intervening galaxy. Usually the lensing will
4 GM bc2
brighten the image of the quasar. This allows us
to study quasars at larger redshifts than we might where is the angle of deflection in radians and b
normally be able to detect. Also, it provides a way is the impact parameter. Solving for M:
of measuring the mass of the intervening galaxy.
This allows us to tell how much dark vs. luminous
matter there is in that galaxy. 4G

15 arc sec2 150 kpc2 13.08 1021cm kpc 2 13 1010cm s 2 2
Example 19.3 Mass of lensing galaxy
12.06 105arc sec 1 rad2 14 2 16.67 dyn cm2 s2 2
Suppose we observe the image of a quasar to be 8
shifted by 5 arc sec on the sky. What is the mass of
1046 g
the intervening galaxy? Assume that the light 1
passes past the edge of the galaxy™s disk, which has
a radius of 50 kpc.

early universe indicate that black holes with
19.6 A uni¬ed picture of masses in the range 106 to 109 M were formed in
active galaxies? the process, and are naturally found at the cen-
ters of galaxies. These black holes are probably
19.6.1 A common picture rotating, so they will not have the simple struc-
When we look at the various examples of AGNs, ture discussed in Chapter 8. These black holes
we see many features in common: large energy would become more massive in their active
output, rapid variability meaning small sources phase. We might wonder about the fate of these
of energy, and jets. The explanations involve mas- black holes. If their host galaxies are isolated,
sive black holes fed by material passing through then we might expect the black holes to sit qui-
an accretion disk. There are also uniform out- etly in the centers, long after the fuel to feed the
flows that can be collimated into narrow jets. engine has run out. However, if there are other
This leads us to ask whether radio galaxies, galaxies nearby, then black holes might be
Seyferts and quasars are different manifestations ejected in three-galaxy encounters. So, in the
of the same basic phenomenon. present (nearby) universe, we might expect to
The common features would be supermassive find some galaxies with black holes and others
black holes in the centers of galaxies. These black without. We describe below searches for super-
holes would be surrounded by accretion disks, massive black holes in galactic nuclei.
with material being fed in, converting gravita- We would expect that the gas surrounding
tional potential energy into kinetic energy and, the black hole would settle into a disk. Material
ultimately, radiation. There are also outflows spirals in and liberates energy as it becomes
that are collimated into jets. There are also dense closer. The energy can be in the form of radiation,
clouds close to the center which give rise to the but there are also some mechanical ways in
emission lines that we see. which the energy can be extracted. The simplest
The particulars of any AGN phenomenon then models suggest a thin disk, but theoreticians are
depend on various parameters. For example, the now able to make more complicated models, and
total luminosity would depend on the mass of the possibility of thicker disks has been sug-
the black hole (the more massive, the greater the gested. It may also be that the structure of the
rate at which we can drop in material and effi- disk is affected by magnetic forces.
ciently get energy out) and the amount of mate- The continuum emission comes mostly from a
rial that is available to spiral into the black hole region that is several Schwarzschild radii across.
(the amount of fuel that is available for the This region would have a temperature of a few
times 105 K, and would therefore give off black-
engine). Some particulars of what we observe will
depend on the orientation of the disk with body radiation that peaks in the ultraviolet, as
respect to the line of sight. The existence of radio observed. Other processes also contribute to the
lobes would depend on the AGN having been on continuum, so we don™t see exactly a blackbody
long enough for the material to accumulate at spectrum. The radiation that we see also depends
the end of the jets. on the optical depth of the disk and its orienta-
In this picture massive black holes are present tion relative to the line of sight.
in the nuclei of most large (i.e. not irregular or In the simplest version of the model, the
dwarf) galaxies. Where did these black holes broad emission lines come from a number of
small dense clouds (densities of about 109 cm 3
come from? Their universality, and the fact that
we see quasars as being quite prominent in the and sizes of about 1 AU). These clouds are in ran-
early universe, suggest that these massive black dom orbits about the central source. They are at a
holes must be a natural byproduct of galaxy for- distance from the central source where the den-
sity of ionizing photons is about 108 cm 3 (see
mation. We will discuss the issue of galaxy for-
mation and dark matter in Chapter 21, but for Problem 19.17 for the energy density). More
now we will note that some computer simula- detailed analyses indicate that this gas can exist
tions on how galaxies might have formed in the over a larger range of distances from the center,

so there is a wider range of physical conditions. we might infer that the AGN phase is something
Also, recent studies have shown that there is a lot many galaxies went through in the past. If this is
of molecular material close to the centers of AGN. the case, then even nearby galaxies with no
This molecular material can be quite opaque, nuclear activity might have black holes left over
and, if viewed from the right angle, can hide from an earlier active phase. Presumably there is
material on the far side of the center, resulting in currently no activity because there is no material
asymmetric line profiles. to fall in (no fuel to feed the engine). We might
A further suggestion of how a massive black therefore find supermassive black holes in nearby
hole could exist in the nucleus of a starburst galaxies. The study of nearby galaxies is important
galaxy is that the starburst could provide a very since we can study them in the most detail.
rich cluster near the center. The total mass of the The presence of a massive object in the center
stars in the cluster could be in excess of 106 M . of a galaxy can be inferred from its gravitational
Of course, when the cluster is formed, it will not effects on the motions of surrounding objects. In
be contained within its Schwarzschild radius. the nuclei of galaxies we have many stars, and,
Initially, the motions of the stars within the clus- depending on the type of galaxy, we may or not
ter will keep it from collapsing farther. However, have a lot of gas. Both the stars and the gas will
there may be dissipative processes which allow move in response to the presence of a massive
the stars to lose some of their kinetic energy, object near the center of the galaxy. From the
motions (essentially vr vs. distance from the cen-
and settle closer together. If enough energy is
disspipated, the cluster can eventually contract ter) we can learn about the mass of the central
to its Schwarzschild radius and become a massive object. There is a slight complication because the
black hole. motions that we are studying are due to rotation
and to random motions. In this case we can write
19.6.2 Black holes in galactic nuclei? the mass interior to radius r as
Obviously, if this general picture is to work then
(r / G) [ vrot2 2
M(r) ]
there must be supermassive black holes in the
where vrot is the rotational speed and is the rms
centers of active galaxies. This suggests that we
velocity dispersion for the random motion. When
search for observational evidence of those black
possible, studying the motions of the stars is
holes. Also, since quasars seem to have been more
more reliable than the gas, since the stars are less
prevalent in the past (higher redshift) than now,

Fig 19.23. Evidence for massive
black holes in galactic nuclei.
(a) HST image of NGC 7052,
showing what may be a massive
dusty disk, edge-on.


Fig 19.23. (Continued)
(b) Spectra on opposite sides of
the center of M87.These show a
very large velocity shift across the
center. (c) Imaging spectrometer
(STIS) map of M84.The image on
the left is a regular (WFPC2)
image, with the blue outline
showing the line along which
spectra were taken. On the right
we see the spectrum, showing a
very large velocity shift across the
nucleus. [STScI/NASA]



likely to have their velocities affected by other So, we can hope to show that there are condensed
processes (such as supernova explosions). supermassive objects in AGNs, but to this point
So, the first step in looking for a black hole is we cannot conclusively show that such objects
to use the motions of surrounding objects to are black holes.
measure the mass of the central object. However, To date, studies of motions near the centers
this is not enough. We must also show that the of 14 galaxies have produced evidence for a mas-
supermassive object is contained within the sive compact object. Some of these are AGNs and
109 km for a 109 M
Schwarzschild radius (3 others are ˜normal™ nearby galaxies. For exam-
black hole). This is hard, because, even with the ple, one of the best cases is M31, the Andromeda
galaxy, with a central object mass of 3 107 M .
resolution of HST or VLBI on the nearest galaxies
(see Problem 19.18), we can only reach about 105 RS. As discussed in Chapter 16, there is evidence

that the Milky Way contains a 3 106 M con- tions between the mass of the central object and
other properties of the galaxy. The strongest cor-
densed object. The most massive object found to
date is 3 109 M in the well studied active relation is with the brightness of the bulge.
There is no correlation with the total mass of
galaxy, M87 (Fig. 19.8). Enough of these objects
the galaxy.
have been studied to begin to look for correla-

Chapter summary
We find a number of galaxies with large amounts by a disk close to the center. The most likely
of energy coming from a relatively small region source of energy for the jets is a massive black
in the center of the galaxy. While these used to be hole (up to 10 million solar masses of material)
thought of independently, we now realize that into which matter falls. Up to 40% of the rest
there are many common physical features of energy of that matter is converted into energy
these systems, and we discuss them collectively as flowing out.
active galactic nuclei, or AGNs. Seyferts appear to be spiral galaxies with
Starburst galaxies appear to have recently active nuclei. They have spectra that are charac-
undergone a large episode of massive star forma- terized by strong broad emission lines.
tion near their centers. While many of them look Quasars are also galaxies that seem to have
quite normal in the visible part of the spectrum, many properties in common with radio galaxies.
since dust blocks the light from most of the stars, Many of them have large redshifts, suggesting
that dust is heated and glows strongly in the that they are at great distances. For quasars to
infrared. In relatively nearby starburst galaxies, appear as bright as they do and be so far away,
we can make CO maps of the molecular clouds they must be giving off large amounts of energy.
out of which the stars are forming. We think that Also, the energy output varies rapidly, meaning
starbursts can occur when two galaxies pass close that the source of that energy must be very small.
together, and interstellar matter from one galaxy We now think that quasars are powered by mat-
is transferred to the center of the other. This gas ter falling into very massive black holes near
provides the fuel for the starburst. their centers. If quasars are as far away as their
Some galaxies give off tremendous amounts redshifts indicate, then we are seeing them as
of radiation in the radio part of the spectrum. they were a long time ago, and they give us a way
These are the radio galaxies. They typically give of looking back to see how the universe was at a
off a million times as much energy as a normal much earlier time.
galaxy. The radiation is polarized, and much Quasars have both emission and absorption
more energy is given off at longer wavelengths lines. We think that the absorption lines are pro-
than shorter wavelengths. These two features sug- duced by material between us and the quasar. We
gest that we are observing synchrotron radiation, have now also detected quasar images that are
which means a strong magnetic field and a good produced by gravitational lensing by intervening
supply of high energy electrons. For most galaxies material.
we see the emission coming from two large lobes Searches for supermassive black holes in
on either side of the optical part of the galaxy. galactic nuclei have produced more than a dozen
objects with masses ranging from 3 107 M to
The lobes are typically 10 Mpc long by 1 Mpc wide.
3 109 M . We still do not have sufficient angular
Narrow jets point from the center of the galaxy
resolution to say definitively that these central
out to the lobe.
objects are contained within the Schwarzschild
We think that the jets can be produced by a
flow in all directions at the center, but collimated

onto a black hole? Why is it important for
19.1. What is the evidence that the Lyman alpha
the black hole to be very massive?
forest arises in material between us and the
19.13. In calculating the energy we can extract by
dropping matter into a black hole, we only
19.2. In this chapter, we saw various examples of
considered the energy gained in falling to
active galactic nuclei. List these types. What
the Schwarzschild radius. However, matter
are the similarities among them? What are
will still accelerate after crossing RS. Why
the differences that distinguish one type
from another? don™t we add this extra energy to what we
19.3. What makes us think that starburst galaxies can extract?
are sites of very active star formation? 19.14. If we have a particle and an antiparticle
19.4. Why is it unlikely that the current rate of annihilating and producing energy, what is
star formation in a starburst galaxy can be the efficiency of that reaction (in terms of
sustained for a long time? the fraction of the mass converted into
19.5. What does the detection of many supernova energy)?
remnants tell us about starburst galaxies? 19.15. What are the similarities between radio
19.6. In studying starburst galaxies, we make galaxies and quasars?
observations in various parts of the spec- 19.16. Why were lunar occultations important in
trum. List them, and state briefly what we the discovery of quasars? How might the dis-
learn from each. covery of quasars have come sooner if radio
19.7. What is the suspected role of galaxy interac- interferometry had come sooner?
tions in creating starbursts? 19.17. What is the problem that was posed by
19.8. How do we know that the radio emission quasars being at the distances indicated by
from radio galaxies is synchrotron? What their redshifts (that is, at cosmological
does this tell us about the regions that are distances)?
emitting? 19.18. Why is the variability of quasars important?
19.9. In a radio galaxy, emission comes from a 19.19. How would you carry out a search for radio-
very large area. What makes us think that quiet quasars?
the ultimate source of this energy is the 19.20. What do we mean by the ˜energy“redshift
nucleus of the galaxy? problem™?
19.10. In radio galaxies, high energy particles are 19.21. What evidence is there that quasars are
transported from the inner parts of the truly at the distances implied by their
galaxy to the lobes. Once at the lobes, why redshifts?
don™t they quickly lose their energy? 19.22. How do quasars allow us to see the universe
19.11. In a radio galaxy, how do we think that the as it was in the distant past?
observed jets are formed? 19.23. Why is the discovery of gravitationally
19.12. Why do we think that the ultimate source of lensed quasars important?
energy in a radio galaxy is matter falling

magnetic energy, and compare it with the
[For all problems, unless otherwise stated, use H0
answer in (a).
70 km/s/Mpc.]
19.2. For the sizes, densities and speeds given in
19.1. (a) To the extent that we can ascribe a tem-
the chapter, estimate the kinetic energy in
perature to the large lobes of radio galaxies,
it is about 106 K. For the numbers given in the flow of the jets of radio galaxies.
19.3. A radio galaxy has an angular extent of 2 ,
this chapter, estimate the thermal energy
and the associated optical galaxy has its
stored in one of these lobes. (b) Calculate the

spectral lines shifted by 15% of their rest 19.14. At what rate must mass be falling into a
wavelength. What is the diameter of the black hole to produce the luminosity of a
radio galaxy? typical radio galaxy?
19.4. What are wavelengths of the H and H *19.15. Suppose we try to explain the redshift of
lines in 3C273? 3C273 as a gravitational redshift, rather
19.5. What are the wavelengths of the H and H than cosmological. (a) From what radius,
relative to RS, is the radiation emerging?
lines in 3C48?
19.6. Using the same reasoning as was used for (b) If the width of the lines is 0.1% of their
3C273, estimate the distance to 3C48. wavelength, what is the range of radii (rela-
tive to RS ) from which the radiation can be
19.7. A quasar is observed with its H line at
800.0 nm. Estimate its distance. emitted?
19.8. Estimate the redshift of a quasar whose 19.16. What are the Schwarzschild radius and den-
sity for a 109 M black hole?
light has been traveling 1 Gyr to reach us.
19.9. What redshift would be needed to shift the 19.17. What is the energy density if the density of
photons is 108 cm 3 ? Assume that the pho-
Ly line into the visible part of the
spectrum? tons are all at the peak wavelength of a
For the 103 km/s wide emission lines in 105 K blackbody.
Seyferts, what temperature would be 19.18. Compare the angular resolution for HST
required for thermal Doppler broadening? observations and for VLBI observations with
19.11. For the superluminal source discussed in the Schwarzschild radii for the M31 and
Example 19.2 (with 0.95), what is the M87 central objects at their respective
range of angles about 18.2 for vapp to be distances.
greater than c? 19.19. For the galaxy NGC 3115 we find a rotational
19.12. What is required , assuming the optimal speed of 150 km/s and the dispersion for
angle, to produce a superluminal source random motions of 270 km/s at an angular
with vapp 10c? radius of 1.0 arc sec. What is the mass of the
19.13. If a quasar varies on a time scale of four central object?
months, how does the maximum size of the 19.20. For the galaxy M87 we find negligible rota-
emitting region compare with the tion and the dispersion for random motions
Schwarzschild radius for a 109 M black of 350 km/s at an angular radius of 1.5 arc
hole? sec. What is the mass of the central object?

Computer problems

19.1. You drop an object of mass m into a black 19.3. Estimate the angular sizes of the RS for
106 M , 107 M , 108 M , 109 M black holes
hole. Calculate the energy it has acquired
when it reaches 2 RS, 1.5 RS, 1.1 RS and 1.01 RS. for an object in the Virgo cluster and for an
Express your answer as a fraction of the maxi- object at redshift 1.
mum energy (when reaching RS ). 19.4. What are the orbital speeds at 2 RS, for
objects in circular orbits around 106 M ,
19.2. Plot a graph of vapp vs. for v/c 0.50, 0.90,
107 M , 108 M and 109 M black holes?
0.95, 0.99.
Chapter 20


fluid and ignore the lumps. The only force that
Einstein once said that the most incomprehensi-
currently affects the large-scale structure is grav-
ble thing about the universe is that it is compre-
ity. We can apply gravity as described by general
hensible. It is amazing that we can apparently
relativity, though for many things Newtonian grav-
describe the universe with what are very simple
itation is a sufficiently accurate approximation.
theories. We can ask truly fundamental questions
The electromagnetic force is important in that
of where we have come from and where we are
electromagnetic radiation carries information,
going and expect scientific answers. In this chap-
but it doesn™t affect the large-scale structure. We
ter and the next, we will study cosmology, the
will see in the next chapter that there was a time
large-scale structure of the universe. We can
when radiation was dominant and all of
learn a great deal using only the physics we have
the forces we know had an important effect on
introduced in this book. With the introduction of
the structure of the universe.
some more physics, namely elementary particle
Until recently, we have had very few observa-
physics (in Chapter 21), we will see that even
tional clues about the large-scale structure of the
more fascinating concepts are within our grasp.
universe. We will see that recent experiments,
some characterized by great difficulty and
20.1 The scale of the universe resourcefulness, have greatly added to our knowl-
edge. The field of observational cosmology is a
growing one. In studying cosmology, as with
When we study the gas in a room, we must deal
other fields of astrophysics, we combine theory
with it as a collection of molecules. We don™t care
and observations to increase our insight into
about the fact that the molecules are made up of
what is happening.
atoms or that the atoms are made up of protons,
In making theoretical models of the uni-
neutrons and electrons; or that the protons and
verse, we start with an assumption, called the
neutrons are made up of other particles. All we
cosmological principle. It says that on the largest
care about is how the molecules interact with
scales the universe is both homogeneous and isotropic.
one another, and how that affects the large-scale
By homogeneous, we mean that, at any instant,
properties of the gas. When we study the uni-
the general properties, such as density and com-
verse, we also treat it as a gas. The molecules of
position, are the same everywhere. By isotropic,
the gas are galaxies. In the big picture, stars, plan-
we mean that, at any instant, the universe
ets, etc., don™t matter. Of course these smaller
appears the same in all directions. We know
objects can still contain some hidden clues for us
that our everyday world is neither homoge-
to learn about the larger structure. They simply
neous nor isotropic, but for the universe, on the
don™t affect the larger structure themselves.
scales of many superclusters, this is a very good
How do we study cosmology? On the theoreti-
cal side, we look at the universe as large-scale

There is another assumption that we might be will discuss this radiation in detail in Chapter 21.
tempted to make, namely that the universe is the For now, we note that this discovery ended, for
same at all times. Cosmological theories which most astronomers, the debate over whether the
incorporate this assumption are called steady-state universe is steady-state.
theories. Until the early 1970s, there were vigorous
debates about whether or not the universe is
20.2 Expansion of the universe
steady-state. The theory was favored by many
because it had a certain philosophical simplicity.
20.2.1 Olbers™s paradox
If the universe had no beginning, then there is no
There is a very simple observation that we can
need to worry about what went on “before” the
make every day that tells us about the history and
structure of the universe. This simple observation
However, a long chain of observational evi-
is that the sky is dark at night. The mystery in
dence has been amassed against the steady-state
this observation was noted by Heinrich Olbers in
theory, and very few hold it today. For example,
1823. We refer to the problem as Olbers™s paradox.


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