3. Rotation curve and Dark matter
•The milky way galaxy is rotating. We can measure galactic rotation speed by
observing the Doppler shift of a 21cm emission line.
m
v2
r
= G
Mm
r2
Equation of motion for each star
r
v =
GM
r
∝ r−1/2
r
v
4. Dark matter in the universe
•We have already seen that the Milky Way Galaxy contains dark matter
•Invisible by the electromagnetic
wave
•But, dark matter does gravitational
interaction.
The properties of dark matter
Do other galaxies also contain dark matter other than the
Milky Way Galaxy??
✗ Electromagnetic wave
◯ Gravity
5. Dark matter in the universe
Do other galaxies also contain dark matter other than the Milky Way
Galaxy??
Yes, other galaxies also contain dark matter.
Rotation curves for other galaxies
•We can see that other galaxies also should contain
dark matter in order to explain their rotation curves.
•As I will explain later, ~90% of matter in the
universe is dark matter!
6. Dark matter in the universe
Do other galaxies also contain dark matter other than the Milky Way
Galaxy??
Yes, other galaxies also contain dark matter.
Rotation curves for other galaxies
•We can see that other galaxies also should contain
dark matter in order to explain their rotation curves.
•As I will explain later, ~90% of matter in the
universe is dark matter!
7. How can we observe dark matter?
✗ Electromagnetic wave
◯ Gravity
•Dark matter is not visible in electromagnetic
waves. Thus, we cannot observe dark matter by
electromagnetic wave.
•But, dark matter has gravity. We can use
this dark matter’s property!
Rμν −
1
2
gμνR + Λgμν =
8πG
c4
Tμν
Remember Einstein's Equation.
物质（能量）
时空的扭曲
Because dark matter does gravitation interaction, dark matter
distorts space-time.
8. Gravitational lensing
d2
xα
dτ2
+ Γα
βγ
dxβ
dτ
dxγ
dτ
= 0
Equation of motion in curved space-time (Geodesic equation).
•This equation tells us how particles (and
light) move in curved space-time.
Dark matter’s gravity distorts space-time
Rμν −
1
2
gμνR + Λgμν =
8πG
c4
Tμν
d2
xα
dτ2
+ Γα
βγ
dxβ
dτ
dxγ
dτ
= 0
The light travels in the curved space-time
Dark matter’s gravity is
associated with the path
of light.
Gravitational lensing effect
Dark matter
11. By using gravitational lensing, we can
reconstruct the 3D distribution of dark
matter.
3D map of dark matter in the universe
12. Hot gas observed by X-ray
Dark matter
Another observation of dark matter
•When bullet galaxy clusters collide(相撞), the hot gas contained in galaxy clusters
stopped. But, because dark matter less interacts with each other, dark matter moves on.
Dark matter
13.
14.
15. Hierarchical structure formation in the universe
Why is dark matter important?
Dark matter plays an important role in the structure formation in the universe.
Step.1
Dark matter particles come together in self-gravity to form dark matter halos.
Dark matter halo
16. Hierarchical structure formation in the universe
Why is dark matter important?
Dark matter plays an important role in the structure formation in the universe.
Step.1
Dark matter particles come together in self-gravity to form dark matter halos.
Dark matter halo
17. Hierarchical structure formation in the universe
Why is dark matter important?
Dark matter plays an important role in the structure formation in the universe.
Step.2
In the dark matter halo, the gravity of dark matter attracts gas. Then, stars and
galaxies are formed from interstellar gas.
18.
19.
20. Hierarchical structure formation in the universe
Why is dark matter important?
Dark matter plays an important role in the structure formation in the universe.
Step.3
Galaxies merge and produce more massive galaxies.
21.
22.
23. The Milky Way Galaxy also merges with Andromeda galaxy and makes the
“Milkomeda ” galaxy in 4 billion years (40亿年后)
24. The Milky Way Galaxy also merges with Andromeda galaxy and makes the
“Milkomeda ” galaxy in 4 billion years (40亿年后)
25. The universe on large scales
Structure formation in the universe
Dark matter particles Dark matter halos
Galaxy in dark matter halo
Galaxy mergers
26. What is a larger structure in the universe?
A cluster of galaxies is one biggest objects in the
universe. It contains ~100-10’000 galaxies
27. The universe on large scales
Much lager scales?
•This figure shows galaxies
discovered by the Sloan Digital Sky
Survey (SDSS).
•We can see that the distribution of
galaxies on large scales is not
random.
•The galaxies appear to be arranged in
a network, or filaments surrounding
voids (regions where number density is
low).
This structure is called a
large-scale structure
Void
