lecture25

1. Introduction to modern astronomy 25 島袋隼⼠(Hayato Shimabukuro)（云南⼤学、 SWIFAR） ©GETTYIMAGES

2. 15. Galaxies and Dark matter （星系和暗物质）

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

9. Gravitational lensing The path of light is distorted by the gravity of the dark matter (and also galaxy cluster)

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

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.

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.

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

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