1. dark matter and the Fate of the Universe
Lecture 40:
dark matter
and the Fate of the Universe

2. dark matter: do we need it?
motions of stars/gas within galaxies
motions of galaxies within groups and clusters
hot gas in clusters
gravitational lensing by galaxies and clusters

3. clusters are full of hot gas

4. another way to weigh a cluster
assuming that the hot gas in clusters is in gravitational equilibrium, we can use the temperature of the gas to estimate the mass of the cluster
v = (0.1 km/s) x (T/Kelvin)1/2
then use v in the usual formula
M = (v2 x r)/G

5. Example: the Coma cluster
The galaxies in the Coma cluster have an average orbital velocity of 1200 km/s within a radius of 1.5 Mpc. The hot gas has an average temperature of 108 K. Find the mass of the Coma cluster using both methods. Do they agree?

6. a third way: gravitational lensing

8. Abell 2218

9. cluster mass-to-light ratios
all three methods (galaxy velocities, hot gas temperatures, and gravitational lensing) show that clusters have mass-to-light ratios of Msun/Lsun!

10. dark matter: what is it? there are two basic possibilities:
baryonic dark matter – ‘ordinary matter’ (i.e. protons, neutrons, electrons, etc.) perhaps faint stars, brown dwarfs, planets, gas?
non-baryonic dark matter – a new kind of particle that we have never seen directly!

11. the search for MACHOs
perhaps the dark “halo” of our Galaxy is made up of normal material (like faint stars or brown dwarfs)
these are called Massive Compact Halo Objects (MACHOs).
they might be detected by microlensing

13. not very MACHO…
results from microlensing surveys (in which millions of stars were monitored over many years) show that at most about ten percent of the mass of our galactic halo is made of MACHOs

14. exotic dark matter: WIMPs
WIMPs stands for Weakly Interacting Massive Particles
the definition of a WIMP is a kind of particle that interacts with other matter only via gravity and the weak force (not the strong force and electromagnetic force)

15. hot and cold dark matter
hot dark matter is made of particles that move very close to the speed of light (such as neutrinos)
cold dark matter is made of particles that move much slower than the speed of light

16. structure formation
theoretical calculations show that if most of the dark matter were “hot”, it would not be able to clump together, and galaxies and clusters would not be able to form
“cold” dark matter readily forms dense structures bound together by gravity, perhaps producing the structures we see

17. large scale structure

19. where does structure come from?
assume: dark matter is cold, and initially very smooth with small lumps
calculate what happens to the matter, including only the force of gravity and the expansion of the Universe

21. observations
simulation

22. the fate of the Universe
the pull of gravity acts to slow the expansion
the more mass, the stronger the gravity
whether expansion will continue in the future depends on the total amount of mass in the Universe

23. the options:
expansion continues forever at about the same rate (coasting)
expansion continues forever, but slows down all the time, until eventually the expansion is infinitely slow (critical)
at some point, gravity wins, and the Universe starts to contract (recollapsing)
expansion accelerates (accelerating)

24. critical density
the dividing line between a Universe that goes on expanding forever and one that recollapses is called the critical density
the value of the critical density (for H0 = 70 km/s/Mpc) is 9.2 x kg/m3 or 1.36 x 1011 Msun/Mpc3

25. the density parameter W
astronomers like to express the density of the Universe today in terms of the critical density: W = r0/rc
then
W < 1  recollapse (closed)
W = 1  critical
W > 1  expand forever (open)

27. closed
flat
open

28. Measuring the expansion rate of the Universe
the relationship between distance and velocity (Hubble’s Law) tells us how fast the Universe is expanding
if we could measure the expansion rate in the past, we can also tell how the expansion rate is changing
for example, if we could find high redshift standard candles…

31. white dwarf supernovae
for a long time, people hoped that quasars could be used in this way – but it turns out they are not good standard candles.
white dwarf supernovae seem to be good standard candles, and are bright enough to be seen at very high redshifts (z=1, or about half the age of the Universe)

33. the surprising result…
white dwarf supernovae used as standard candles indicate that the expansion of the Universe is accelerating! (galaxies are moving away from each other faster now than they were in the past)
this means that there must be a repulsive force that pushes matter apart (sort of the opposite of gravity)

34. dark energy
we basically have no idea what could cause this repulsive force
it goes by names like “dark energy”, “quintessence”, and “cosmological constant”
this leaves us in a slightly embarrassing situation…

35. Cosmic budget of mass and energy:
Wbaryons = 0.1
Wmatter = 0.3
Wdark energy = 0.7
Wmatter + energy = 1