Download 3 The lives of galaxies

Discovering Astronomy : Galaxies and Cosmology
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The lives of galaxies
In this section, we look at how galaxies formed and evolved, and likewise how the large scale pattern
of galaxies formed. But before we can understand those issues, we need to understand the mysterious
dark matter, as it plays a key role.
3.1 The dark universe
Lecture 5 : Cosmic Perspective 22.1, 22.2
What are galaxies made of ? We can do a reasonably accurate census of the contents of the solar
neighbourhood, i.e. the region within a few tens of parsecs of the Sun. The result, by fraction of
mass, is :
• 37% stars
• 13% failed or dead stars (brown dwarfs, white dwarfs, neutron stars)
• 50% gas
However, if we average over the whole of a typical galaxy, we get a rather different story :
• 90% dark matter
• 8% stars
• 2% gas
How we do know about this dark matter, and what is it ?
Two ways of estimating mass.
(1) Measure the amount of light L from a galaxy.
Assume that on average this light is coming from stars quite like the Sun. The Sun has mass-to-light
ratio = M /L . Then our estimate of the mass is M = ⇥ L. This should give us the mass in
stars.
[Actually of course there is a mixture of stars of different types. Detailed calculations show that the best
multiplying factor to use is about = 2 ]
(2) Measure rotation speed V of a galaxy.
We measure rotation speed at distance R around the galaxy, just like we did for the Milky Way. Then
we use V 2 = GM/R, for the velocity expected according to Newton’s laws. This should give us the
total gravitating mass. However material only feels a pull from material inside radius R; pulls from
material further out cancels out. So this method gives us the mass within radius R:
M (< R) = RV 2 /G
Do these two methods give us the same answer ?
Measuring rotation.
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l
Figure 30: Examples of real measured rotation curves for various galaxies
We rely once again on our trusty friend the Doppler effect. Using spectral features (e.g. stellar absorption lines,
ionised gas emission lines, or neutral hydrogen radio emission) we measure the Doppler shift in different parts of the
galaxy, as indicated in Fig. 29. If we see a blueshift on
one side and a redshift on the other side, this is a sign of
rotation. If the shift in wavelength is
then the rotation
velocity must be Vrot = c ·
/ . We can do this measurement at a series of different radial distances, and see
how rotation velocity changes with radius, V (R). This is
known as the rotation curve. Rotation curves have now
been measured for many spiral galaxies, and a consistent
pattern emerges, as shown in Fig. 30. In the inner parts of
galaxies, rotation velocity starts off low and rises as you Figure 29: Measuring rotation from the
move outwards, then it flattens off and stays flat out to very Doppler shift of spectral features.
large distances from the centre. Is this what we expect ?
Types of rotation curve. (1) A solid body, rotating with a fixed angular rotation speed, would show
velocity following V / R, increasing outwards. (2) Material orbiting a central point mass, like
the planets orbiting the Sun, would have V / 1/R1/2 . (3) Galaxies don’t do either : they show
V / const. This is because the matter is not all in a central point, as in the solar system case - the
material is distributed. But we can measure how the light at least is distributed - does that help us to
get a better prediction for galaxy rotation curves?
Observed vs predicted rotation curves.
First, we measure the light profile of a galaxy from
an image. As described above, this can enable us to
estimate the mass in stars within each radius, M⇤ (<
R). If we assume that those stars constitute all the
relevant mass, then we can predict the rotation within
that same radius as Vpred (R) = (GM⇤ (< R)/R)1/2 .
The typical result of this exercise (see Fig. 31 is that
it agrees well in the inner parts, but falls short by a
factor 3 in the outer parts. This means that at those
outer radii, the total enclosed mass is about 9 times
bigger than the visible stelllar mass - the remainder
of the mass is something dark.
Figure 31: Comparing predicted and observed
rotation curves for the galaxy NGC 3998.
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Figure 32: Left : Illustrating the orbits of stars in Elliptical galaxies. Right : Effect on the width of absorption
lines seen in the spectrum
Dark Matter halos. For a typical spiral galaxy, 90% of its mass is dark matter. The luminous matter
is more concentrated than the total gravitating matter. In the central parts, including the radius in the
Milky Way where the Sun resides, dark matter is present but negligible. Most of the dark matter is in
an extended “halo”. Fig. 31 shows how you can get a much better fit if you include such an extended
dark halo in the calculation.
Finding dark matter in elliptical galaxies. Elliptical galaxies do not rotate. The stars are on random
orbits, like the stars in the Milky Way bulge and halo. Some individual stars may be on circular orbits,
but in many different directions; other stars are on highly elliptical orbits, or more complicated orbits.
The result is no net rotation. However the typical stellar velocity is still given by V 2 = GM/R. How
do we measure this typical random velocity?
Line velocity broadening. Fig. 32 shows an absorption line seen in a galaxy spectrum at some radius
R. The light we see comes from all the stars in the same line of sight, looking through the galaxy.
Because of the random motions, some of these stars are moving away from us and stretch the line to
the red; and some are moving towards us and stretch the line to the blue. This results in net velocity
broadening. If we see a line of width
then the spread of velocities is V ⇠
/ . This tells us
the typical random velocity at R, and then we estimate M (< R) ⇠ R V 2 /G.
The result is that, just as with spiral galaxies, in ellipticals we find Mtotal ⇠ 10 ⇥ Mstars .
Dark matter in clusters. Clusters of galaxies contain hundreds to thousands of galaxies. These are
moving around at random, rather like the stars in an elliptical galaxy. We can use this to estimate the
total mass of the whole cluster. We measure V for each individual galaxy from the Doppler shift as
normal, and subtract the mean V for the cluster, and then calculate the spread V around that mean.
Finally, we measure the size R of the cluster, and calculate the mass as M ⇠ R V 2 /G.
Cluster masses. The result is even more dark matter than we already found in the halos of galaxies.
A good example is the Coma cluster. It has size R ⇠ 1.5Mpc and the spread of velocities is V ⇠
1700km s 1 . This gives Mclus ⇠ 1.0 ⇥ 1015 M . Coma has ⇠ 1000 galaxies with ⇠ 1010 stars each.
So we have :
• Stellar mass : ⇠ 1013 M
• Summed halo mass : ⇠ 1014 M
• Total cluster mass : ⇠ 1015 M
In other words, while individual galaxies are 90% dark matter, clusters are 99% dark matter. Rich
clusters are the most massive objects known.
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Figure 33: Left : Galaxies and hot gas in the cluster Abell 1689. The whiteish light is the visible light image.
The purplish light is the X-ray emission. Right : gravitational lensing by dark matter in the cluster Abell 2218.
The light from background galaxies is distoprted into arcs.
Dark matter in clusters Take 2 : hot gas. Smooth X-ray emission shows the presence of hot gas
filling the space between the galaxies. (See Fig. 33.) It is very hot : T⇠ 108 K. At this temperature,
gas will be highly ionised : the electrons are stripped from the Hydrogen atoms, so that electrons
and protons move separately. The gas temperature tells us how fast the protons are moving. Thermal
physics says that at temperature T the speed of protons is vp = (3kT /mp )1/2 . (Here mp = 1.67 ⇥
10 27 kg is the mass of the proton, and k = 1.38 ⇥ 10 23 J K 1 is Boltzmann’s constant.)
For the Coma cluster T = 8 ⇥ 107 K so vp = 1492 km s 1 . Note that this is quite similar to the speed
of a typical galaxy. This is not a coincidence. It is because the protons follow v 2 = GM/R in just
the same way as the galaxies. So the gas temperature also tells us the total gravitating mass ... and
gives us the same answer.
Gravitational lensing by dark matter. Gravity bends light. Light from background galaxies gets
distorted as it passes through the gravitational field of the massive cluster. Because the cluster is
symmetrical, this results in stretched-out arcs of light. (See Fig. 33.) This gives us another way of
estimating the mass but also allows the dark matter to be mapped.
What is Dark Matter? Is it Gas? Well, gas isn’t really “dark”. Hot gas shines in spectral emission
lines. Very hot gas shines in X-rays. Even very cold gas emits easily detectable radio waves.
What is Dark Matter? Compact objects?
Dead stars leave behind compact remnants - white
dwarfs, neutrons stars, and black holes. We know
such objects exist in the disk of the Milky Way.
Perhaps the halo of our Galaxy has large numbers of them ?
Such hypothetical objects are
known as “Massive Compact Halo Objects” or MACHOs. They might be detected indirectly, because
they can make background stars temporarily brighten,
as illustrated in Fig.
34.
If an invisible MACHO passes in front of a distant star, the gravitational lensing effect will make the star temporarily get
brighter. This effect has been seen but not as often as it should have been if all dark matter is mae
of MACHOs. So it seems this is not the answer. Figure 34: As a background star passes be-
hind a MACHO, its light is focused by gravitational lensing and so it gets temporarily
brighter.
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What is Dark Matter? Particles pervading space? We
know in fact that dark matter can be any kind of ordinary
matter. In later lectures we will see that Helium and other elements are made during the Big Bang by
nuclear fusion; the amount made depends on the density of the Universe. The density of dark matter
that we see implies that much more heavy elements should have been made than we see. Ordinary
atomic matter is also called “baryonic matter”. So we need a non-baryonic particle. Are there any ?
What is Dark Matter? Neutrinos? Neutrinos don’t contribute to the creation of elements. They are
also very hard to detect. Traditionally they were thought to have zero mass, but now they are thought
to have a tiny but non-zero mass. If there are lots of them, could they make the dark matter ? As
we will see in the next section, the dark matter gradually clumps during the history of the universe,
allowing galaxies to form. As neutrinos are light, they would move around very quickly, making “hot
dark matter”. Computer simulations show that this gives the wrong pattern of clustering.
What is Dark Matter? We are left with Cold Dark Matter. We need a non-baryonic particle that
is massive so that it moves slowly (“cold”). It also needs to interact poorly with ordinary matter, so
that it plays no part in element creation - it is a Weakly Interacting Massive Particle (WIMP). No
such particle is definitely known to exist. But several have been proposed to exist as part of particle
physics theories. So whether they do exist is doubly important!
Looking for Dark Matter. It is possible that dark matter particles could be directly detected by their
scattering effect on ordinary matter. But this behaviour is mimicked by cosmic rays, so experiments
have to be placed underground where cosmic rays don’t reach. A handful of underground experiments
are underway worldwide. There are no positive results yet, but watch this space...