. 17
( 28)


(b) Rotation velocity as a function
of distance from the center of a
galaxy, for ¬ve spiral galaxies.The
fact that the rotation velocity is
large at great distances from the
center of the galaxy is taken as
evidence for the existence of dark
matter. [Vera Rubin, Department

of Terrestrial Magnetism; (b)
Reprinted with permission from
Rubin,V., Science, 220, 1339,
Fig.1 © (1983) AAAS.]

0 10 20 30 40 50 100


not be stable. The galaxies are more stable if the
Rotation curves can be determined from the
dark mass has a spherical distribution. This
measurement of Doppler shifts in spectral lines.
would mean that the dark matter is most likely in
This can be done with optical lines, such as H .
the halo. Remember, the halo is not a ring
Extensive studies have been carried out by Vera
around the galaxy. It is a spherically symmetric
Rubin (Fig. 17.21 a), at the Carnegie Institution.
mass distribution.
Typical results are shown in Fig. 17.21 (b). We find

We can use the rotation curve to give us the objects. This is the ratio of mass, expressed in
mass distribution in the halo. If M(r) is the mass solar masses, to the luminosity, expressed in
interior to radius r, then v(r) is related to it by the solar luminosities. By definition, the mass-to-
fact that the acceleration of gravity must provide light ratio of the Sun is one. The mass-to-light
the acceleration for a circular orbit (v2/r), so ratios of main sequence stars are given in the
v2 1r2
mass“luminosity relationship discussed in
Section 5.5. If we know the mass-to-light ratio of a
r2 r
galaxy, we can see what types of objects have
similar mass-to-light ratios. For spiral galaxies,
Solving for M(r) gives
rv2 1r2
the mass-to-light ratio is 1:3 near the center. This
means that most of the mass near the center
M1r2 (17.3)
G probably comes from normal stars. However, near
the edge of the visible disk, the ratio climbs to
We can relate M(r) to the density distribution
20:1, and is above 100:1 for the farthest points to
(r) by the equation of mass continuity (equation
which rotation curves have been measured.
9.33), which was one of the equations of stellar
It has been suggested that the halos might
4 r 2 1r2
consist of faint, old red stars. These stars would
dM>dr (17.4)
have masses less than 1M . There is even some
direct observational evidence for such stars in
Solving for (r) gives
the halos of nearby galaxies. The mass-to-light
1r2 a ba b
ratio of such stars is about 20:1. They might
4 r2 dr
therefore provide the dark matter out to the edge
of the visible disk, but something else is needed
If we take v(r) v0, a constant, then differen-
beyond that. More recent observations seem to
tiating equation (17.3) with respect to r gives
rule out all nuclear burning material as a signif-
dM1r2 0
icant part of the halo. Some astronomers have
suggested that a lot of mass could be hidden in
Jupiter-sized objects, which are obviously not very
Finally, substituting equation (17.6) into equation
(17.5) gives
Recently a new technique has been employed
to search for massive compact halo objects (MACHOs) .
4 Gr 2
If these objects are massive and small then they
The density in the halo therefore falls off as should bend starlight passing close to their sur-
1/r . It is not nearly as fast as the exponential face. The bending of light is a prediction of gen-
falloff in the light of the disk. eral relativity, as discussed in Chapter 8. When a
With a 1/r 2 falloff in density, it might seem MACHO passes in front of a star in another
that there is not much matter very far out. nearby galaxy (such as the LMC) there will be a
However, if we divide the galaxy into spherical very brief change in the intensity of that light.
shells, each of thickness dr, the volume of each This is known as microlensing. Systematic searches
shell is 4 r 2dr. This means that the mass of each for microlensing events have been carried out.
shell is constant! As far out as the rotation curve There have been some detections of such events,
remains flat, we are adding significant amounts in which light from stars in the LMC shows varia-
of matter to the galaxy. This is particularly impor- tions suggestive of microlensing. However, there
tant, since the rotation curves seem flat as far out is still a question about whether we are seeing
as we can measure. It may also be that there is still microlensing due to a star in the halo of our
a significant amount of matter beyond those galaxy, or due to one near the target star in the
points. LMC. (The LMC is used for such studies because it
What is the dark matter in the halo? We can provides us with a large number of stars to study,
get a clue by looking at mass-to-light ratios of various and it is far from our galactic plane, so, if we see

lensing events, it is more likely that they are galaxy. The idea of neutrinos as dark matter in
caused by objects in the halo of our galaxy, than galaxies is still not generally accepted.
the disk.) The rotation curves of galaxies are our first
It has been suggested that the dark matter evidence for the existence of dark matter. We
could be in the form of neutrinos, if neutrinos know it is there because we can measure its
have a small rest mass. Remember, we saw in gravitational effects, but we cannot see it. When
Chapter 9 that there is growing evidence that the astronomers were not sure the matter was there,
neutrino mass is in about the 10 2 eV range This there was a ˜missing mass problem™. However, the
is small enough to have been overlooked in mass isn™t missing; it is just nonluminous. As we
previous experiments. However, there are so go to larger scales in the universe, we will see
many neutrinos in the universe that even a small that we will find evidence that dark matter
mass for each neutrino can add a lot of mass to a becomes more and more important.

Chapter summary
In this chapter we looked at the properties of We applied some of the ideas of star forma-
various types of galaxies. tion, discussed in previous chapters, to look at
Elliptical galaxies have no evidence for recent star formation in the LMC and in spirals. We also
star formation. However, the metal abundances looked at how the density wave theory might
are high. Ellipticals are classified according to explain spiral structure.
the eccentricity of their appearance. Spirals have In studying rotation curves of galaxies we
an evident interstellar medium, as well as O and found that the masses of galaxies are greater
B stars, meaning that star formation is still tak- than would be determined from luminous mate-
ing place. Spirals are classified according to the rial. It has been suggested that most of the
tightness of the spiral arms and the relative sizes matter is distributed in a spherically symmetric
of the nucleus and disk. halo.

17.1. If we see a spiral galaxy edge-on, how do we 17.6. How do the relative abundances of atomic
know that it is a spiral? and molecular hydrogen vary within a spiral
17.2. (a) Why is it not likely that single spirals galaxy?
formed from single ellipticals? (b) Why is it 17.7. What parts of the interstellar medium would
not likely that ellipticals formed from spirals? you expect to best trace out spiral arms?
(Hint: Think of the effects of rotation.) Explain your answer.
17.3. Compare the properties of dwarf ellipticals 17.8. What are the differences between grand design
with the properties of globular clusters in our and flocculent spiral galaxies (a) in their
own galaxy. appearance and (b) in the scenario by which
17.4. What features of S0 galaxies make them the spiral arms are formed and maintained?
similar to (a) spirals, (b) ellipticals? *17.9. In equation (17.4) we used the relationship
17.5. Assume there is some way, either by between mass and density for a spherically
spectroscopy or by some aspect of the shape symmetric system. However, spiral galaxies
of the galaxy, to determine the luminosity have a disklike appearance. Why is the use of
class for a galaxy. How can this information equation (17.4) valid?
be used, along with other observations, to 17.10.How does the density wave theory help us
determine the distance to a galaxy? explain spiral structure?

17.1. Given the luminosity profile in equation 17.6. Suppose we are observing a galaxy to meas-
(17.1), what would the luminosity be at ure its rotation curve. By how much would
(a) r r0, (b) 2r0? the wavelength of the 21 cm line shift as we
17.2. Given the luminosity profile in equation (17.2), moved from the center to the edge of the
what is the luminosity at (a) r D, (b) r 2 D? galaxy, which has an orbital speed of 200 km/s
(Express your answer in terms of L0.) (a) if we are in the plane of the galaxy, (b) if
17.3. Given the luminosity profile in equation the galaxy is tilted at a 45 angle to our line
(17.2), for a given galaxy how far out would of sight?
you have to go before you have 95% of the 17.7. If we measure the rotation curve of a galaxy,
galactic luminosity? Express your answer as how far out would the orbital speed have to
a multiple of D. be 300 km/s, to give the largest measured
mass, 2 1012M ?
17.4. Given the luminosity profile in equation
(17.2) and the density profile in equation 17.8. For a galaxy, with a flat rotation curve, whose
(17.7), find an expression for the mass-to- density distribution is given by equation (17.7)
light ratio as a function of distance from the out to a radius of 20 kpc, calculate (leaving
center of the galaxy r. Assume that the ratio your answer in terms of v0) (a) the total mass
is unity at r D. out to 20 kpc, (b) the gravitational potential
17.5. The Andromeda Galaxy is at a distance of energy, (c) the rotational kinetic energy.
700 kpc. (a) Suppose we observe the CO(2“1) (d) Compare (b) and (c) and note if they obey
transition at a wavelength of 1.3 mm, with a the virial theorem.
30 m diameter telescope. What is the linear 17.9. Calculate the mass of a galaxy with a flat
resolution? rotation curve, with v 300 km/s, out to
(b) Suppose we use a millimeter interfero- r 20 kpc. (Express your answer in M .)
17.10. If neutrinos have a rest mass equal to 10 4 of
meter with a maximum baseline of 1 km?
(c) Repeat these calculations for the the electron rest mass, how many neutrinos
do you need to give 1012M ?
Whirlpool Galaxy, at a distance of 9.6 Mpc.

Computer problems

17.3. Draw a graph of the luminosity profile, L(r)/L0 vs. r,
17.1. Use the mass“luminosity relationship discussed
for spiral galaxies (equation 17.2), for D
in Chapter 5 to draw a graph of the mass-to-light 2.5, 5,
ratio for main sequence stars as a function of 10 kpc.
spectral type. 17.4. Use the rotation curves in Fig. 17.21(b) to deter-
17.2. Draw a graph of the luminosity profile, L(r)/L(0) vs. mine the mass interior to the largest radius out to
r, for elliptical galaxies (equation 17.1), for r0 5, which the rotation curve has been measured.
(Express your answer in M .)
10, 20 kpc.
Chapter 18

Clusters of galaxies

gravitationally. As such, they are interesting sys-
18.1 Distribution of galaxies tems to understand. In addition, by studying the
gravitational interactions, we learn about the
If we look at the distribution of galaxies, such as masses of the individual galaxies and the cluster
that shown in Fig. 18.1, we see that the galaxies as a whole. It has been found that the number of
are not randomly arranged on the sky. Among the galaxies per unit area in a cluster falls off approx-
imately as exp[ (r/r0)1/4]. This is the same as the
patterns we see distinct groupings, called clusters
of galaxies. surface brightness in elliptical galaxies. We know
Clusters are interesting for a number of rea- that ellipticals are dynamically relaxed systems.
sons. They may provide us with clues on the for- If clusters and ellipticals have similar density dis-
mation of galaxies themselves. This is especially tributions, then this suggests that some of the
true if, as many think, cluster-sized objects formed clusters are dynamically relaxed also.
first and then broke into galaxy-sized objects. (The
Example 18.1 Crossing time for a cluster of
alternative view is that galaxies formed first and
then gathered into clusters.) Clusters also pose us
The time for a galaxy to cross from one side of a
with interesting dynamical problems, including a
cluster to the other is called the crossing time. Find
dark matter problem of their own. Finally, when
the crossing time for a cluster of galaxies with an
we reach the scale of clusters of galaxies, we are
extent of 1 Mpc, and galaxies moving at 103 km/s.
beginning to reach a scale which has some signifi-
cance in the overall structure of the universe. SOLUTION
The cluster of galaxies to which the Milky Way The time for a galaxy to cross is the diameter
belongs is called the Local Group. As clusters go, it divided by the speed, so
is not a very rich one. Besides the Milky Way, it
1106 pc 2 13 1018 cm pc 2 1108 cm s2
contains several irregulars, including our com-
panions, the Large and Small Magellanic Clouds, 1016 s
the spiral galaxies M31 and M33, and a number of
109 yr
dwarf ellipticals. Other nearby clusters are
named by the constellation in which they are We think that clusters of galaxies have been
around for over 1010 years (the age of our galaxy as
centered. For example the Virgo, Coma, Hercules
and Centaurus clusters are shown in Fig. 18.2. determined from globular cluster HR diagrams). If
they were not gravitationally bound they would
have had many crossing times to evaporate. We
18.2 Cluster dynamics therefore think that clusters are gravitationally
bound. They have also had sufficient time to
Just as with clusters of stars, clusters of galaxies become relaxed, so we can apply the virial theo-
may be isolated collections of masses interacting rem to analyze their internal motions (Fig. 18.3).

Fig 18.1. Distribution of galax-
ies.This is a two-dimensional view
as seen from the Earth. It is from
the APM Galaxy Survey, which
detected over two million galaxies,
covering approximately one-tenth
of the whole sky.This image cov-
ers a region of about 100 50
about the South Galactic Pole.The
intensities of each pixel are scaled
by the number of galaxies in that
pixel. [Steven Maddox, Nottingham

Example 18.2 Virial mass of cluster
In terms of the internal motions, the virial
mass is given by equation (13.47): For the Coma cluster we have vrms 860 km/s and
a cluster radius of 6.1 Mpc. Find the virial mass of
5 vR
M the cluster.
In terms of observed Doppler shifts, the virial
From equation (18.1) we have
mass is given by equation (13.52)
152 18.6 107 cm s2 2 16.1 Mpc2 13.1 1024 cm Mpc2
5 v2 R
16.67 dyn cm2 g2 2
r M
M (18.1) 8
1015 M

Fig 18.2. Nearby clusters of galaxies. (a) Virgo.This is a
rich cluster, with a few thousand members, but it is not very
strongly concentrated towards the center. (b) Coma
Berenices.This cluster contains more than 1000 galaxies,
with a large number of types E and S0.

Fig 18.2. (Continued) (c) Hercules.This is a small irregular
cluster at a distance of 120 Mpc. (d) Centaurus, in the halos. We should only add the dark matter that
southern hemisphere. [NOAO/AURA/NSF]
we know is there, so we only add enough to
account for the observed rotation curves in dif-
ferent types of galaxies. (We suspect that there
When we add up all the mass that we can see may be more dark matter beyond the points
in the cluster, we find that it does not add up to where the rotation curves have been measured,
the amount required by the virial theorem. This because there is no evidence of the rotational
was originally done by using just the mass of the velocities beginning to fall off.) Even this amount
luminous matter in the galaxies. However, we saw of dark matter is not enough to account for the
in Chapter 17 that the halos of galaxies may con- virial mass.
tain dark matter. Even if we don™t know what that Some of the mass may be in the form of low
dark matter is, we know it is there, and can add density gas within the cluster, but between the
its mass to that of the luminous matter in each galaxies. This gas has either been ejected from
galaxy. However, clusters have many ellipticals the galaxies, or has fallen into the cluster. In
and S0 galaxies which may not have massive either case, we would expect this gas to be very
hot, about 107 K. It should be hot enough to give
off faint X-ray emission. In fact, such emission is
Motion of Cluster observed. In Figs. 18.4 and 18.5, we see X-ray
images of two clusters. The hot gas contributes a
significant amount of mass, but doesn™t com-
Motion of Net Motion
Galaxy within of Galaxy pletely solve the problem.
Cluster There are still two possible solutions. One is
that the individual galaxies have, as some have
suspected, halos that go out even farther than
the rotation curves can be measured. There is evi-
dence to support this in studies of the interac-
tions of binary galaxies. The advantage of a
binary galaxy over the rotation curve studies is
Fig 18.3. Motions of a galaxy in a cluster.The blue arrow
that the galaxies in a binary system are far
shows the overall motion of the cluster.The green arrows
show the motions of the galaxies within the cluster.The net enough apart to sample the full mass of each
motion for each galaxy (shown in red) is the vector sum of other. The other possibility is that the clusters
its internal motion with the overall motion of the cluster.
contain their own dark matter. This matter may

Luminous Matter
Dark Matter
Fig 18.6. Possible distribution of dark matter in a cluster
of galaxies. Each blue patch indicates the position of lumi-
Fig 18.4. ROSAT X-ray image of the Virgo cluster (Fig. 18.2a)
nous matter within the cluster.The red areas indicate the
shows the hot intracluster, intergalactic gas. [NASA/MPI]
locations of the dark matter.The darker the areas are, the
greater the concentration of dark matter.

be the same as that in the halos of galaxies, but
there just may be additional amounts in the clus-
individual galaxies or the generally distributed
ter, not bound to any one galaxy. If a rich cluster
dark matter. A possible distribution of dark mat-
has the mass implied by the virial theorem, then
ter in a cluster of galaxies is shown schematically
the mass-to-light ratio is about 200. This would
in Fig. 18.6.
be consistent with either the extended halos in
Another interesting feature about clusters of
galaxies is that giant elliptical galaxies are
found near the centers of some clusters (such as
M87, in Fig. 17.2a). These galaxies are central dom-
inant or cD galaxies. Some cD galaxies also seem
to have multiple nuclei. It has been noted that
the center of a cluster is the most likely place for
galaxies to pass near each other. Some galaxy col-
lisions result in galaxy mergers. Once a few
galaxies have merged, they can swallow galaxies
that pass too close. The process is called galactic
The whole subject of galaxy encounters is
under active study. Numerical simulations have
been carried out to find out what happens to the
stars and gas in each of the two colliding galaxies,
both for very close encounters and for direct col-
lisions. The result of one such calculation is
shown in Fig. 18.7. Some examples of interacting
galaxies are shown in Fig. 18.8. As you can see, the
Fig 18.5. Chandra X-ray image of the Centaurus cluster calculations produce results that look like objects
(Fig. 18.2d), showing more detail in the hot gas [NASA]. that are actually observed.



Fig 18.7. Interacting galaxies. Steps in the computer simu-
lation. (a) The galaxies are far apart. (b) They are closer
together, and the effects of the interaction are showing.
Note that the tidal effects, tending to stretch the structures, Fig 18.8. Observations of interacting galaxies. (a) A pair of
are very important. In encounters, individual stars never
galaxies, NGC 4038 and 4039, which have an appearance sim-
actually touch. [Visualization by Frank Summers (STScI);
ilar to the simulation. Because of their appearance, these are
simulation by Chris Mihos (Case Western Reserve
called ˜The Antennae™. (b) HST image of the nucleus of the
University) and Lars Hemquist (Harvard University)]
elliptical galaxy NGC 1316.There is an unusually large number
of bright young clusters in this image, suggesting that they were
formed in some encounter with another galaxy. [STScI/NASA]
18.3 Expansion of the universe
where v is the speed of the galaxy, d is the dis-
18.3.1 Hubble™s law tance, and H0 is a constant, called the Hubble con-
In Hubble™s study of galaxies, he found that all
stant. (The subscript zero on the H indicates that
galaxies have redshifted spectral lines. The red-
this is the current value. As we will see in Chapter
shift means that they are all moving away from
20, H is constant in the sense that it is the same
us. Furthermore, the rate at which any galaxy is
at every place, but can change with time.) The
receding from us is proportional to its distance
relationship given by equation (18.2) is called
from us. We can write this in the simple form:
Hubble™s law. Results of more recent studies are
shown in Fig. 18.9.
v H0 d (18.2)

Suppose the rate of expansion has been con-
stant over the age of the universe. If all objects
started very close together at t 0 (whatever that
time means), then the current distance between
any two objects would be
d vt0

where t0 is the current age of the universe. Solving
for v gives
v (1/t0)d (18.3)

Fig 18.9. Hubble™s law.The distance is plotted on the ver-
tical axis, and the radial velocity (from the redshift) is plotted
on the horizontal axis.This is the result of the HST Key
Project to study Hubble™s law, and data using different dis-
tance indicators are shown with different colored symbols.
The labelled lines show lines corresponding to different
values of H. [John Huchra, CFA]

At first it might seem unusual that we are in
some special part of the universe, so that all things
are moving away from us in a very particular way.
However, we interpret Hubble™s law as telling us
that all galaxies are moving away from each other.
This motion represents the overall expansion of
the universe. (We will discuss this in more detail
in Chapter 20.) To visualize this, we can imagine
the galaxies as dots on the surface of a balloon, as
shown in Fig. 18.10. As the balloon is blown up, all
the dots move away from all the other dots. In
Fig. 18.11, we see that the separations between
any pair of galaxies increases, and that the larger
separations increase faster. This means that we
could observe from any of the galaxies, and we
would still obtain Hubble™s law.
Suppose that in some time t, the balloon
expands so that all distances are multiplied by a
factor (1 f ). If two objects were initially a dis-
tance d apart, their distance at the end of the Fig 18.10. The universe as an expanding balloon.The
interval is (1 f )d. The change in the distance galaxies are painted on the surface of the balloon. As the
balloon expands, each galaxy moves away from every other
between the two objects is fd, so the average rela-
galaxy.This is a two-dimensional analogy to help us with the
tive velocity of the two objects is fd/ t. This is the
same form as Hubble™s law.

both distance and velocity in convenient units. A
#1 #2

value of 500 km/s/Mpc works out to a Hubble time
of 2 109 yr (2 Gyr; see Problem 18.6). This was a
cause for concern, since our understanding of
stellar evolution and the HR diagrams of globular
clusters in our galaxy tell us that these clusters
Separations at are about 10 Gyr old. (In fact, radioactive dating
Earlier Time
places the age of the Solar System at over 4 Gyr.)
It is disconcerting to have the universe younger
than things in it. However, there is an immediate
error in Hubble™s value due to confusion between
type I and type II Cepheids as distance indicators.
Separations at
Over the years, other refinements have been
Later Time
made. As we will see below, the currently accepted
value for the Hubble constant is in the range
50“100 km/s/Mpc.
Apart from telling us something interesting
about the universe, Hubble™s law is also of great
Change in Separation value when determining distances to distant
objects. It is important that this only be used for
Fig 18.11. The effect of all galaxies moving away from
objects that are far enough away that their veloc-
each other.The two frames show the positions of the galax-
ities relative to us are dominated by the expan-
ies at different times, with the bottom frame being later. In
sion of the universe, as shown in Fig. 18.12. We
the top frame the green arrows show the separations at the
say that objects must be far enough away to be in
earlier time. In the bottom frame, the blue arrows show the
the Hubble flow. Objects within our own cluster of
separations at the later time.The red arrows show the
change in separation between the two times for each pair of galaxies are not in the Hubble flow. Their
galaxies (the difference between the blue and green arrows). motions are dominated by the dynamics of our
You can see that the galaxies that were initially farther apart
cluster. Even nearby clusters have random veloci-
have the greatest change in separation, and the galaxies that
ties relative to us that are a significant fraction of
were closest have the least change in separation.
their Hubble law velocity.
Example 18.3 Hubble™s law and distance
This is the same as Hubble™s law, if we make For some cluster, we measure v 103 km/s. What is
the identification the distance? Take H0 65 km/s/Mpc.
H0 1/t0 (18.4)
Then, 1/H0 , called the Hubble time, is the age of
We find the distance from
the universe if the expansion has been constant.
d v H0
Actually, as we will discuss in Chapter 20, the
1103 km s 2
expansion is not constant. If the expansion is slow-
165 km s Mpc2
ing down, the actual age of the universe is less
than the Hubble time. If the expansion is speeding
15 Mpc
up, the actual age of the universe is greater than
the Hubble time.
18.3.2 Determining the Hubble constant
The value that Hubble obtained for H0 was
Of course, if we are going to apply Hubble™s law to
500 km/s/Mpc. Note that the units of the Hubble
determine distances, we need an accurate value
constant may seem strange, but there is a dis-
for the Hubble constant. This means that we need
tance in the numerator (km) and in the denomi-
an independent way of measuring distances to
nator (Mpc), so the units really work out to 1/time.
objects that are far enough away to be in the
We use km/s/Mpc because with it we can express

(a) (b)
Fig 18.12. Expansion of the universe and random velocities of galaxies. (a) We see just the motion due to the expansion of
the universe.The center can be any reference galaxy, such as our own.The red arrows show the motions of galaxies at different
distances from us solely due to the expansion of the universe. Notice that all the red arrows are pointed directly away from us,
and that they are longer as we look at more distant galaxies. (b) We add in the random motions of the galaxies (green arrows).
The random motions point in any direction, and they are the same throughout the universe.The net motion of any galaxy is the
sum of its random and expansion motions.

Hubble flow. The importance of an object being around these two points: (1) what are the correct
far away is illustrated in Fig. 18.13. Suppose an distance indicators, and (2) where does the Hubble
object has a velocity of H0d from the Hubble flow flow start?
and v from other sources. This v probably results We now turn to the problem of measuring dis-
from random motions of the galaxies, just as the tances to distant clusters of galaxies. The procedure
gas in the room has random motions superim- involves using our most secure distance indicators
posed on any regular flow. Note that v can be to measure the distances to nearby galaxies, and
positive or negative. The actual radial velocity that then building up a series of distance indicators,
we measure will be useful at greater and greater distances. The prob-
lem can be involved, as shown in Table 18.1.
vr H 0d v (18.5)
We start the process by looking at Cepheids to
In general, v is independent of d. Thus, for find the distances to nearby galaxies. Of course, we
more distant objects, H0d increases while v stays must calibrate the Cepheid period“luminosity rela-
the same. For more distant objects, v represents tionship within our own galaxy. This involves start-
a smaller fraction of H0d, and introduces a smaller ing with trigonometric parallax observations of
fractional error into the determination of H0. nearby stars and moving cluster observations of
It would seem a simple task to get around this nearby star clusters to produce a calibrated HR dia-
problem. All we have to do is use the most distant gram. The calibrated HR diagram allows us to use
objects we can observe. Unfortunately, our dis- spectroscopic parallax for individual stars, and for
tance indicators work best for nearby galaxies, main sequence fitting for globular clusters con-
where we can still see individual stars such as taining Cepheids. This gives a calibrated period“
Cepheids. Therein lies the problem. We can meas- luminosity relation for Cepheids as well as RR Lyrae
ure distances more accurately for nearby objects, stars. We can then use the Cepheids and RR Lyrae
but we are not sure if they are in the Hubble flow. stars as distance indicators for galaxies that are
Arguments over the proper value of H0 center close enough for us to see these stars individually.

Distance indicators.
Table 18.1.
Method range (Mpc)

Recession Speed (km/s)

Cepheids 0“100

Novae 0“20
RR Lyrae stars 0“0.2
W Virginis stars 0“1
Eclipsing binaries 0“1
4000 Red giants 0“1
Globular clusters 0“50
Supergiants 0“1
Stellar luminosity function 0“1
HII region diameters 0“25
HII region luminosities 0“100
HII loop diameters 0“4
0 Brightest blue star 0“25
0 50 100 Brightest red stars 0“15
Distance Supernovae 0“400
21 cm linewidths 0“100
(Millions of Parsecs)
Disk luminosity gradients 0“100
Fig 18.13. Sources of error in measuring the Hubble con-
U”B colors 0“100
stant. For both nearby and distant galaxies, uncertainties are
Luminosity classi¬cation 0“100
indicated schematically by error bars. Straight lines from the
Brightest elliptical in cluster 50“5000
origin are then drawn at the widest angle that can still lie
within one of the error bars.The error bar that determines
this widest angle is the one that generates the largest uncer-
the apparent magnitude, we have a measure of the
tainty in H0 since H0 would be determined by the slope of a
distance. The problem is to come up with inde-
line from our measured point to the origin.
pendent indicators of galactic luminosity. Hubble
made the simple assumption that all galaxies have
HST has greatly expanded the distance over which the same absolute visual magnitude. We know
we can study Cepheids up to 100 Mpc. that this is not the case. Instead, it has been sug-
For galaxies that are somewhat farther away, gested that the brightest ellipticals in each cluster
we can still use individual objects within the have the same absolute magnitude. The luminosi-
galaxy, but they have to be brighter than Cepheids. ties of the brightest ellipticals seem to vary, how-
We can, for example, measure the angular sizes ever. For this reason, rather than using the brightest
of HII regions. Since we think we know what their elliptical in a cluster, we use the second or third
linear sizes should be, this gives us a measure of brightest elliptical in a cluster.
distance. One promising technique is the use of With the recent recognition that galaxies have
supernovae. From the light curve we can tell luminosity classes, much effort has gone into find-
whether the supernova is a type I or type II. Type ing luminosity class indicators. In this way, we can
I supernovae appear to have similar peak lumi- observe a galaxy, determine its morphological type
nosities. By measuring their apparent magnitude (Sa, Sb, etc.), and then have some indicator of its
at peak brightness, we can find the distances. luminosity class. If we know absolute magnitude
Eventually we reach a point where individual as a function of morphological type and luminos-
objects within galaxies cannot be measured. We ity classes, and we measure the apparent magni-
must rely on being able to know the total lumi- tude, we can convert the difference into a distance.
nosity of the galaxy. If we know the absolute mag- Another recent discovery, indicated in Fig. 18.14,
nitude of a given type of galaxy, and we measure is that the width of the 21 cm line in a galaxy seems

calibration is complicated by the fact that the
I Band
relationship may depend on the type of galaxy.
24 Calibrators
Even with these methods, there is another nag-
16 Fornax ( µ= 31.24)
38 Ursa Major ( µ= 31.34)
ging problem. When we look at a distant galaxy, we
53 Pisces ( µ= 33.89)

are seeing it as it was a long time ago. However, we
28 Coma ( µ= 34.67)
20 Abell 1367 ( µ= 34.70)
absolute magnitude

know that galaxies evolve. As they evolve, their
179 Total

luminosity changes. Luminosity calibrations on
nearby galaxies might not apply to distant galaxies.
More recently supernovae have been an impor-
’20 tant tool. We can see supernovae far away, espe-
cially with HST. One is shown in Fig. 18.15(a). From


2 2.2 2.4 2.6 2.8

log W ir
Fig 18.14. Tully“Fisher relation. For various selections of
test galaxies, each plotted with a different symbol and color,
we plot the 21 cm line width on the horizontal axis, and
absolute magnitude in the I band on the vertical axis, for
galaxies whose distances are determined by other methods.
[Brent Tully, Institute for Astronomy, Hawaii]

to correlate with its absolute infrared luminosity.
This is called the Tully“Fisher relation. Therefore,
we can observe the 21 cm line, measure its width,
and know the absolute magnitude of the galaxy.
Of course, this relation must be calibrated. The

Fig 18.15. (a) HST image of a
supernova in a distant galaxy.The
larger image shows the cluster of
galaxies in which this event took
place.The box on the left shows
the location of the individual galaxy
in which the supernova took place,
and the blowup on the right shows
the supernova.The brightness of
the supernova places the distance
to this cluster at 3 Gpc. (b)
Measurements of H0 since 1970,
with error bars shown for each
measurement. [(a) STScI/NASA;
(b) John Huchra, CFA]

the light curve, we can tell what type of supernova better idea of clustering if we also know distances
it is. It turns out that type I supernovae (which to galaxies. We obtain the distances from meas-
occur in close binary systems, discussed in uring the redshifts of clusters.
Chapter 12), have a reasonably narrow range of It might seem that we can determine the mass
peak absolute magnitudes. We can therefore use of a supercluster by using the virial theorem, in
them as ˜standard candles™ at great distances. much the same way as we did for clusters of
So you see that there is a problem at every step galaxies. However, the crossing time for a cluster
of the determination of the Hubble constant. For in a supercluster is greater than the current age
this reason, no one indicator is used at any step of the universe (as estimated by the Hubble time).
along the way. For example, when the distance to This means that superclusters are not dynami-
the Hyades, as determined from the moving cluster cally relaxed, and the virial theorem should not
method, was revised by 10%, it only affected the apply. It is even possible that superclusters are
extragalactic distance scale by 5%. not gravitationally bound.
Currently accepted values of the Hubble con- In addition to superclusters, there appear to be
voids of comparable size. As their name implies,
stant fall in the range 50 to 100 km/s/Mpc. The
corresponding Hubble times are 20 Gyr to 10 Gyr, voids are large regions of space that are essentially
the latter time being small enough to be some- devoid of galaxies.
what worrisome. Measurements since 1970 are One of the major breakthroughs in these stud-
shown in Fig. 18.15(b). A number of recent studies ies has come from the ability to measure a large
suggest values of 70 km/s/Mpc with an uncer- number of redshifts in a relatively short time.
These redshift surveys are carried out at radio
tainty of 10 km/s/Mpc.
In Chaper 20, when we begin to look at theo- (21 cm) and optical (H ) wavelengths. They cover
ries of the large-scale structure of the universe, large sections of the sky, and also cover a large
we will see that H0 shows in various equations. It range of redshifts. Having surveys in both the
is useful to be able to do calculations using a optical and radio parts of the spectrum provides
value of H0, but for which the results can be an important check on the results.
scaled for a different value. We therefore define a Presenting the results of these redshift sur-
dimensionless parameter, h, such that veys can be difficult. Not only are there millions
of data points, we have the location of each galaxy
H0 h [100 km/s/Mpc] (18.6)
as a function of three coordinates “ two for the
So, if H0 turns out to be 70 km/s/Mpc, then position on the sky, and one for the redshift. We
h 0.7. can leave the third coordinate in terms of red-
shift, or convert it to a distance, using Hubble™s
law. In any case, we are still stuck with trying to
18.4 Superclusters and voids plot a three-dimensional distribution of galaxies.
One way of doing this is to make slices through
Now that we have seen that galaxies are gathered our data, and then for each slice make a two-
into clusters, we might ask if the clusters are gath- dimensional picture of the resulting distribution
ered into larger groupings, called superclusters. The of galaxies. In Fig. 18.16, we show how we might
answer is that they are. The first supercluster iden- uses slices through a three-dimensional Earth to
tified (in the 1950s) is the one in which we live, produce a series of two-dimensional images,
called the local supercluster. The Virgo cluster of which, taken together, give us a feel for the three-
galaxies is near the center of the local supercluster. dimensional structure. For the redshift surveys,
The local group, our cluster of galaxies, is near the we can make our slices showing distribution on
edge. The local supercluster contains 106 galaxies the sky in a series of redshift ranges, or showing
in a volume of about 1023 cubic light years! distribution in one sky coordinate and redshift
Studies of more distant superclusters have for a range of the other sky coordinate.
been made difficult by a lack of extensive data on Some representative survey results are shown
distances to galaxies. After all, we only see two in Fig. 18.17. In these figures, each dot represents
dimensions projected on the sky. We can get a a galaxy; a concentration of dots is a cluster; a

even more complicated. Some have made analo-
gies with sponges and swiss cheese, with the typi-
cal sizes of the holes being tens to a hundred mil-
lion parsecs across. This shows us that the galaxies
are distributed in a much more complicated way
than is implied by simply talking about super-
clusters and voids.
From these surveys, we can also deduce the
motions of the galaxies with respect to their
neighbors. Remember, earlier in this chapter we
saw that any galaxy has motion associated with
the expansion of the universe, and local motions
in response to the gravitational attraction of its
neighbors. When we analyze these local motions
of the galaxies, we find that they are are not com-
pletely random. They are organized, with galaxies
in some part of a shell having similar motions.
This suggests that there are large amounts of mat-
ter attracting the galaxies to produce the organized
We can also see a similar effect in the motion
of our galaxy (or the Local Group) through space.
How do we detect that motion? Think of the fol-
lowing analogy. Imagine that you are in a room
full of people, all standing still. You start to walk
through the room. All of a sudden, it appears that
people on one side of the room are coming towards
you, while people on the other side of the room
are moving away from you. Your first thought
might be that this is the way that the people are
actually moving. On farther thought, you realize
that you are seeing your own motion reflected in
the apparent motions of the people.
The situation is a little more complicated with
galaxies, because the universe is expanding. We
start with all of the galaxies moving away from
Fig 18.16. How we might use slices through a three-
us. If we then start moving in some direction, we
dimensional object to let a series of two-dimensional images
represent our three-dimensional structure. will be overtaking some galaxies, and moving
away from others in the opposite side of the sky.
On average, galaxies in one half of the sky will
appear to be moving away from us slightly faster
concentration of clusters is a supercluster, and a
than in the other half of the sky. This effect is
lack of dots is a void. From these figures, we see
actually observed. By seeing which half of the sky
that superclusters and voids are quite common.
appears to be moving away from us a little faster,
There is a very distinctive feature to the distribu-
and which half is moving a little slower, we can
tion. It looks like the galaxies are concentrated
determine how fast we are moving and in what
on the surfaces of various shapes. The first
direction. What we actually measure is the total
astronomers studying these distributions thought
motion of the Earth. We must then correct for
that the surfaces may be like soap or beer foam
the motion of the Earth around the Sun, the
bubbles, but it now seems that the structures are

12 h Fig 18.17. The results of red-
11 h shift surveys. (a) The ¬rst Center
for Astrophysics slice, based on
h 10 h
15 optical observations. Around the
outside are markings indicating
right ascension (in hours) of the


galaxy. All of the galaxies in the
indicated declination range, cover-
ing six degrees, are plotted in this
single slice.The redshifts are plot-
ted on the straight axis moving
away from the point. (b) Two addi-
cz (km/s)
First CfA Strip
tional slices, showing different
26.5 ¤ δ < 32.5
declination ranges. [John Huchra,
mB ¤ 15.5

18.5 Where did all this structure
come from?

One of the great questions that we try to answer
in astronomy is, ˜How did we get here?™ In this
book, we have already talked about how star for-
mation takes place in various types of galaxies.
Therefore, the next step is to ask, ˜Where do the
galaxies and clusters (and other such structures)
come from?™
For many years, attempts to answer this ques-
tion have been quite vague. Astronomers loosely
talked about two general scenarios, a ˜top-down™
and a ˜bottom-up™. These are indicated in Fig.
18.18. In the top-down scenario, the largest-scale
structures form first, and then everything else
fragments. So, somehow, in the early universe,
objects with the masses of superclusters sepa-
rated out and began to contract gravitationally.
Eventually, a density was reached where less
motion of the Sun around the galactic center, massive structures, with the masses of clusters
and the motion of the galaxy within the Local of galaxies, could contract. Finally, these objects
Group. When we do this, we find that our cluster fragmented into the galaxies themselves. In the
is moving in the general direction of the Virgo bottom-up picture, the galaxies form first.
cluster, at a speed of approximately 300 km/s. Galaxies near each other would then attract
Other clusters, including the Virgo cluster, show themselves into clusters, and clusters near each
a similar motion. This suggests that there is a other would then attract themselves into super-
very massive object out there beyond the Virgo clusters.
cluster, providing a strong pull. We have no idea The thing that has changed recently is that
what it is, and, for lack of a better name, it is the redshift surveys have provided a large body
called the great attractor. of data. In addition, the advent of supercomputers

Fig 18.18. Diagram showing (a) top-down and (b) bot-
tom-up scenarios for galaxy formation.
Part of the problem involves dark matter. We
have already seen that there is more dark matter
has made it possible to simulate the evolution of than luminous matter around us. In clusters of
the universe and galaxy formation under vari- galaxies, the domination of dark matter is even
ous conditions. The results of the computer sim- greater. Since galaxy formation is initiated by
ulations can then be compared with the large gravitational attraction, most of that attraction
body of data. If a particular simulation can will be provided by most of the matter. This means
reproduce the distributions of galaxies and that, even though we see galaxies and clusters as
their large-scale motions, then it is possible that luminous objects, their formation is governed by
the physical ideas that went into that simula- dark matter. Therefore, to make a successful com-
tion might be important in the real universe. puter simulation of galaxy formation, we must
However, to date, no single simulation has been start with the right type of dark matter. However,
able to produce structure on all of the scales we have said that we don™t know what the dark
that we see. matter is. We don™t even know if the dark matter

in individual galaxies is the same as that in clus- early universe, we still haven™t addressed the issue
ters of galaxies. of where those initial enhancements came from.
While this may seem like an insurmountable To do that we must look at the history of the uni-
problem, theoreticians have managed to turn it verse, the field called cosmology, and we do that
around. They first realized that, even if we don™t in Chapters 20 and 21.
know the details of the dark matter, there are
probably classes that can be treated as a whole.
18.6 The Hubble Deep Field
For example, if the dark matter in individual
galaxies is in the form of Jupiter mass objects,
then, from the point of view of gravity, it doesn™t With the sensitivity and imaging quality of the
matter whether we have a certain number of refurbished HST, it was decided to devote a large
Jupiter mass objects or ten times as many objects amount of observing time to a small region of the
whose mass is one-tenth that of Jupiter. The point sky to look for the faintest (presumably) most dis-
would be that we were dealing with ordinary mat- tant objects that could be detected. This resulted
in the Hubble Deep Field. This field was chosen to
ter, but not in quantities large enough to form
luminous stars. be far from any local bright sources (like the
By analyzing the various possibilities, theo- galactic plane). The image was released so that
reticians have been able to group the dark matter any astronomer could study it. This also spurred
into two general types, according to how it coordinated observations of this field and objects
behaves. The two types are called cold dark matter within it, using a wide range of telescopes.
and hot dark matter. These don™t have to do with The field is approximately 1 arc min across.
the temperature, but with how the material An image of a one-quarter of that field is shown
behaves. An example of hot dark matter would be in Fig. 18.19(a). This image contains objects as
neutrinos, if they had even a very small rest mass. faint as 30th mag. (The diffraction spikes are
We will talk about what particles these might around a 20th mag star.) This picture shows a
actually be in Chapter 21, when we talk about the large number of spiral and elliptical galaxies.
earliest times in the universe. For now, we only
need to know that these produce different types
of structures.
So we have gone from vague notions of top-
down and bottom-up scenarios to asking a very
specific question: What is the dark matter that dom-
inates galaxy formation? The hope is that we can
answer that question by comparing the simula-
tions with the data. Unfortunately, at this
point, neither one works completely. The cold
dark matter is good at producing the small-
scale structures (the galaxies) but not the large-
scale structures (the clusters and superclusters,
or the ˜bubbles™). The hot dark matter is just the
opposite. It appears that cold dark matter does a
better job of describing the structures we see,
provided we add some modifications that come
from general relativity, which we will discuss in
Chapter 20.
Even when we correctly identify the dark mat- (a)
ter, and show how galaxies and clusters can grow
Fig 18.19. Images of the Hubble Deep Field. (a) A true
from some small density enhancements in the
color image of one-quarter of the ¬eld.

Fig 18.19. (Continued) (b) Detailed and (c) more detailed
views of part of the HDF. [STScI/NASA]

Chapter summary
Galaxies have a very irregular distribution on the ever, it can change with time. Measuring the
sky. The highest concentrations are called clus- Hubble constant is very difficult. We need meas-
ters. We think that the clusters are gravitation- urements of the distances to galaxies that don™t
ally bound. However, the galaxies that we see in a involve using the redshift. These are more accu-
cluster do not appear to have enough mass to rate for nearby galaxies. However, it is only for the
hold the cluster together, even if we allow for the distant galaxies that the effect of the expansion
dark matter that we know to be in the galaxies. of the universe is much greater than the effect of
This means that there must be dark matter in the the random motions of the galaxies. The most
clusters that is not associated with the individual likely values of the Hubble constant are between
galaxies. 50 and 100 km/s/Mpc, with much recent work
Virtually all of the galaxies that we see are suggesting a value of 70 km/s/Mpc.
moving away from us. The more distant galaxies On larger scales, the clusters are gathered into
are moving away faster. There is a simple rela- superclusters, which are tens of megaparsecs in
tionship between how far away a galaxy is and extent. Of comparable size are large volumes with
how fast it is moving away. This relationship is no galaxies, called voids. We learn about this
called Hubble™s law. This simple relationship large-scale structure from redshift surveys, in
results from the expansion of the universe. We which we measure the redshifts of thousands of
can also use Hubble™s law to tell us the distance to galaxies. (These are done both in the visible and
galaxies whose redshift we can measure. radio parts of the spectrum, depending on the
The quantity that currently tells us the actual types of galaxies we are looking at.)
distance to a galaxy with a given redshift is called Efforts to understand all of this structure are
the Hubble constant. It is constant in that it has just getting under way. An important problem is
the same value everywhere in the universe; how- that we don™t know how much dark matter there

is on the largest scales, and we don™t know the nature of the dark matter. No matter what we try,
nature of that dark matter. Some have even tried no single theory (or type of dark matter) can
to turn the problem around, using the distribu- explain the large- and small-scale structures that
tion of galaxies to tell us something about the we see, but CDM appears to be doing a better job.

18.1. Discuss the following statement: ˜For 18.11. What makes us think that there is dark mat-
Hubble™s law to be true, we must be at the ter in the Virgo cluster?
center of the universe.™ 18.12. Why do we expect a cluster of galaxies to
18.2. Draw a diagram, like Fig. 18.11, showing that obey the virial theorem but not a
the argument presented works even if the supercluster?
three galaxies are in a triangle, rather than 18.13. In adding up the ˜visible™ mass in clusters,
in a straight line. what is the problem in accounting for the
18.3. Why do we call the Hubble time an ˜upper masses of the galaxies that we can see?
limit™ or a ˜lower limit™ to the age of the uni- 18.14. Why would we expect intergalactic gas to be
verse? able to emit X-rays?
18.4. What are the main problems in the accurate 18.15. What are the current possibilities for the
determination of the Hubble constant? dark matter in clusters?
18.5. What do we mean by ˜Hubble flow™? 18.16. If we cannot see the dark matter in clusters
18.6. Can we use Hubble™s law to determine dis- of galaxies, how do we know that it is there?
tances within our own galaxy? 18.17. Explain how we might determine the mass
18.7. Of the distance measurement techniques of a binary galaxy system. Why is this impor-
listed in Table 18.1, which ones depend on tant, since we already have masses deter-
knowing the intrinsic luminosity of some mined from rotation curves?
type of object? 18.18. Why are redshift surveys important in study-
18.8. What is the value of supernovae as distance ing clustering of galaxies?
indicators? 18.19. How are hot and dark cold matter related to
18.9. When we look at a distant galaxy, we see it various scenarios of galaxy formation?
as it was a long time ago. How does this make 18.20. What type of structure is hot dark matter
the use of distance indicators more difficult? best at explaining? What types for cold dark
18.10. What is the evidence for the existence of matter?
clusters and superclusters of galaxies?

the whole cluster. What density of gas would
For all problems, unless otherwise stated, use H0 70
this require?
18.5. For the galaxies represented in Fig. 18.11,
18.1. For the cluster in Example 18.2, what is the
draw a graph of the length of the red line vs.
total kinetic energy?
distance. Do this three times, each time
18.2. For some cluster of galaxies, the radius is
using a different galaxy as your reference
500 kpc, and the rms radial velocity is
300 km/s. What is the mass of the cluster?
18.6. Find a relationship between the Hubble con-
18.3. Rewrite equation (18.1) so that if velocities
stant, expressed in km/s/Mpc, and the
are entered in km/s and distances in Mpc,
Hubble time, expressed in years. Use this to
the mass results in solar masses.
find the Hubble times corresponding to
18.4. Suppose that one-half of the mass of the
Hubble constants of 50, 65, 100 and
cluster in Example 18.2 is in the form of hot
500 km/s/Mpc.
intergalactic gas, spread out uniformly over

18.7. Suppose we have a universe whose size 18.11. Suppose that we can use supernovae to
increases by 1% in 1 Gyr. Show that the aver- measure distances out to 200 Mpc. What is
age rate of separation between any two the recession speed at that distance?
points is proportional to their distance, and 18.12. What is the crossing time for a cluster mov-
ing at 103 km/s through a typical superclus-
find the proportionality constant.
18.8. For some galaxy, we measure a recession ter-sized object?
velocity of 2000 km/s. How far away is the *18.13. What are the Jeans mass and length if we
have 1016 M worth of H spread out over
18.9. Rewrite Hubble™s law so that you can put in 10 Mpc, with random internal motions of
recession velocities in km/s and get dis- 1000 km/s?
18.14. What is the density of galaxies (galaxies/ly3)
tances in Mpc.
18.10. If the typical random velocity in a cluster is in the local supercluster?
300 km/s, how far out must we go before
this is only 1% of the expansion speed at
that distance?
Chapter 19

Active galaxies

In this chapter we look at galaxies with unusual of obscuration from dust near the center. In Fig.
activity within and around them. For many years 19.1 (b), we have a combined image, which shows
astronomers thought of these various types of various tracers of massive star formation (includ-
activity as being distinct. We now realize that many ing UV, IR and H ). We see a small ring of bright
of them have similar origins, but differ in the spe- young stars, close to the center. The dust lanes
cific conditions within the galaxy or its environ- that we see correspond to giant molecular clouds.
ment. We realize that all of this activity takes place In Fig. 19.2, we see a spectrum of a starburst
in the nucleus of the galaxy, or is driven by activity galaxy M82. Notice the large number of emis-
in the nucleus. We say that these phenomena are sion lines. These generally signify the presence
associated with active galactic nuclei (AGN). of hot gas.
In Chapter 15, we saw that star formation
takes place in molecular clouds. We detect molec-
19.1 Starburst galaxies ular clouds by emission from carbon monoxide
(CO) in the millimeter part of the spectrum. If the
Some galaxies appear to be giving out excessive strong infrared emission is really telling us that
amounts of radiation in the infrared. When we there is a lot of star formation taking place, then
studied star formation in Chapter 15, we saw that we should be able to ˜see™ the molecular clouds in
regions with recent star formation give off a lot which the stars are forming. We ˜see™ them by
of infrared radiation. The energy comes from the looking for the CO emission from those clouds.
newly formed stars, and heats the dust (from the Indeed, this CO emission is observed. By compar-
parent cloud) surrounding the stars. The dust ing the CO maps with far infrared maps, we see
then glows in the infrared. The more energy the that the CO and far infrared emissions are
young stars put into the cloud, the more infrared strongest in the same place. This is basically what
radiation is released. The excess infrared radia- we see in our galaxy, when we have star forma-
tion from some galaxies suggests that those tion in a molecular cloud (as depicted in Fig.
galaxies have very high rates of star formation. 15.2). This suggests that starburst galaxies really
The rate is so high that it cannot be sustained for do have a lot of star formation in complexes of
very long, or it would use up all of the interstellar molecular clouds.
material. This leads to the idea that this excessive We can form a better picture of the individ-
star formation is a short-lived phenomenon. We ual star forming regions by looking at near
therefore call such galaxies starburst galaxies. infrared images. The near infrared image has two
Fig. 19.1 shows a typical starburst galaxy. In advantages: (1) since the wavelength is shorter
Fig. 19.1 (a), we see an optical image of the whole than the far infrared, it corresponds to hotter
galaxy. Notice that it doesn™t look very unusual in temperatures, and allows us to isolate hotter
this optical image. There does appear to be a lot objects; (2) because of the shorter wavelength, we

Fig 19.1. Images of the starbust
galaxy NGC 4314, at a distance of
13 Mpc. (a) A normal image of the
whole galaxy, a barred spiral.
(b) An HST image of the central
region.This is a composite of
images taken in through ultravio-
let, blue, visible, infrared and H
¬lters. It shows that most of the
recent star formation is in a small
ring about the center of the
galaxy.We also see dust lanes
inside the ring, showing the loca-
tions of the giant molecular
clouds. [(a) McDonald
Observatory; (b) STScI/NASA]

(a) (b)

can produce images with better angular resolu- nova remnants are detected by their radio emis-
tion than at longer wavelengths. These near sion. The centers of starburst galaxies also have
infrared images show clusters of recently formed radio emission that is characteristic of supernova
massive stars. remnants. This tells us that the star formation
How do we know that the stars that have must have included high mass stars.
formed are truly massive? That is, how do we When we look at the amount of molecular
know that the emission comes from some num- material out of which the stars could have
ber of massive stars, rather than a larger number formed, and we look at the stars that have
of less massive stars? We know that after a rela- formed, we come to another interesting conclu-
tively short time, massive stars must undergo sion. The star formation must have been very
supernova explosions (Chapter 11). This means efficient. That is, a large fraction of the available
that some number of the stars that have formed molecular cloud mass was converted into stars
should have had time to go supernova. These in a short period of time. This is in contrast to
should no longer be visible as stars, but as super- what we found in the nearby star forming
nova remnants. As we saw in Chapter 11, super- regions, like Orion. In those cases, a very small
fraction of the available cloud mass has been
converted into stars. We discussed the fact that,
in general, in our galaxy, star formation has a
1000 low efficiency. That is, something appears to be
Flux Density (Jy)

supporting the clouds until the conditions are
100 just right for star formation. In starburst galax-
ies, the clouds are not as well supported, and
10 more easily form massive stars (as discussed in
Chapter 15). There is some evidence that the
density of molecular material is much higher
than in normal GMCs near us. They are more
3 5 10 20 40
like the GMCs in our galactic center, which also
Wavelength (µm)
have high densities.
Fig 19.2. A spectrum of a starburst galaxy, M82 (also
What creates the conditions that favor a star-
shown in Fig. 17.9). [ESA/ISO, SWS, R. Gerzel and D. Lutz]
burst? This is a topic of current research. Some

their sources. With the development of interfer-
Motions of Galaxies
ometers, with better angular resolution, the find-
ing of optical counterparts has been easier. Many
of the strong radio sources appear in the direc-
tions of other galaxies. Galaxies with strong radio
emission are called radio galaxies.

19.2.1 Properties of radio galaxies
The radio energy output of the radio galaxies is
enormous, typically 106 times the total output of
Gas Clouds
a normal galaxy. The radio spectrum of a typical
radio galaxy is shown in Fig. 19.4. The shape has
the power law characteristic of synchrotron radi-
ation. The radiation is also found to be polarized,
another signature of synchrotron radiation.
Synchrotron radiation requires a strong mag-
netic field and high energy particles, most likely
The actual synchrotron spectrum depends on
the energy distribution of the electrons. The
greater the proportion of the highest energy elec-
trons, the greater is the proportion of high
Fig 19.3. Diagram showing a model for how a starburst
energy photons. As the electrons radiate, they
might occur when two galaxies pass close together.
lose energy. Therefore the synchrotron spectrum
evolves over time. The most energetic electrons
astronomers think that starbursts occur in galaxies lose their energy the fastest, so the proportion of
that have nearby neighbors, and can steal inter-
stellar gas from those neighbors. This is illustrated,
schematically, in Fig. 19.3. The galaxies pass close
to each other, and one galaxy manages to draw a
large quantity of interstellar material from the
other. Most of this new material finds its way to
the center of the galaxy. This provides a lot of
material for star formation. In addition, that
material is denser than the typical molecular
log I

clouds that we have encountered. This means that
it is more likely to give birth to stars. The result is
very efficient star formation “ a starburst.

19.2 Radio galaxies

Many strong radio sources are not objects in our
own galaxy. When a radio source is found, it is
log ν
interesting to see if there is an identifiable opti-
Fig 19.4. Schematic evolution of a radio galaxy spectrum.
cal object at the same position. In the past this
As the more energetic electrons give off energy, they
could not always be done because the poor angu-
become less energetic, so the evolved spectrum has propor-
lar resolution in single-dish observations left
tionately less energy at higher frequencies.
radio astronomers with uncertain positions for


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