1. Astronomy 1143 – Spring 2014 Lecture 21: The Evidence for Dark Matter

2. Key Ideas: Dark Matter - detected by its gravitational pull Gravity appears stronger than can be accounted for by “normal” matter Expected: speeds lower if the star is very distant from the galaxy center Mass-to-Light Ratios Evidence for Dark Matter Rotation curves of spiral galaxies Hot gas halos around elliptical galaxie Velocities of Galaxies in Cluster Gravitational Lensing Candidates for Dark Matter – stay tuned for evidence

3. Is that all there is? We have measured many forms of normal matter from light Stars – absorption-line spectra Low-density gas – emission-line spectra Dust – blocks optical/emits in the far infrared Is that amount of matter enough to explain the gravitational force pulling on stars in a galaxy or on galaxies in a cluster?

4. Matter produces gravity Gravity depends on mass and distance d M2M2 M1M1

5. Planets in the Solar System

6. More distant planets move more slowly

7. From Solar System to Galaxy Planets have smaller speeds the further they are from the Sun Sun has about 99.8% of the mass in the Solar System No substantial contribution from dark matter When we look at the same idea in a galaxy it is a little more complicated because the mass isn’t essentially concentrated in the center. Clearest signal looking relatively far out from center

8. Inside the Galaxy Gravity depends on mass and distance r M2M2 M(r) M(r) is the mass inside of radius (r)

9. Rotation of the Disk Measure using the Doppler Effect Stars: Doppler shifts of stellar absorption lines Ionized Gas: Doppler shifts of emission lines from HII regions Atomic Hydrogen (HI) Gas: Cold H clouds emit a radio emission line at a wavelength of 21-cm Can trace nearly the entire disk beyond where the stars have begun to thin out.

10. Measuring Masses of Galaxies Star or Gas cloud is held in its orbit by the gravity of the mass interior to its orbit. Newton’s Gravity: M(R) = mass interior to radius R V rot = rotation speed Similar to how we calculated the mass of the Sun in Lecture 8

11. Rotating Disk Rotation Axis Approaching Side BLUESHIFT Receding Side REDSHIFT

12. Which galaxy is good for measuring rotation curves?

13. Example: Milky Way Sun: r=8 kpc, v circ =220 km/sec Gives: M = 9  10 10 M sun inside r=8 kpc Gas Cloud in Outer Disk: r=16 kpc, V circ =275 km/sec Gives: M=2.8  10 11 M sun inside r=16 kpc Measuring the rotation curves gives us a good way to measure the masses of Spiral Galaxies.

14. How much mass can we find? Gravity holding stars in their orbits tells us how much matter there needs to be How much of that gravity is caused by the stars/gas/dust that we see? Difference between mass needed and mass observed  evidence for dark matter Turns out that counting up the mass that we see is a little tricky, because what we see is light and what we want is mass

15. Mass-to-light Ratio Some of the mass in a galaxy comes from “normal” matter – stars, gas, & dust How do we find the amount of material? Use the light we see from stars, gas and dust Stars – optical/near infrared light Gas – emission lines in radio Dust – emission in far infrared

16. Example A spiral galaxy has a luminosity of 2.5x10 10 L Sun If each star is like the Sun, the mass is 2.5x10 10 M sun But not every star has the same mass as the Sun – a 10 M sun main-sequence star radiates about 10 4 L sun. If each star is 10 M Sun, the total mass of the Galaxy is

17. Example A lot smaller! The kind of stars in a galaxy makes a big difference in the amount of matter you infer

18. Mass in stars, gas, & dust Measuring the amount of matter in stars, gas and dust is not easy Mass-to-light ratio of stars depends on age and composition Luminosity of starlight may be difficult to measure because of dust Radio and far-infrared maps need to measure gas and dust

19. Rotation Curve if no dark matter

20. Typical Spiral Galaxy Rotation Curve 0 0 25 200 100 5101520 Radius from the Center (kpc) Rotation Speed (km/sec)

21. Picture of rotation curve on galaxy

22. Dark matter Dark matter = stuff that doesn’t emit, absorb, or otherwise interact with photons. dark matter Other galaxies are found to have dark matter, too. Andromeda Galaxy

23. Galaxies are surrounded by dark matter halos

24. Escape Velocity One measure of the strength of the gravitational force is the escape velocity How fast you need to be traveling to leave a gravitating mass and never come back Earth: 11 km/s Jupiter: 59.5 km/s

25. Velocities < Escape Velocities For long-lived systems: Planets in a solar system Stars in a galaxy Galaxies in a galaxy cluster velocities should be less than the escape velocity, otherwise structures would disperse Measure a velocity Calculate how much mass is needed for the escape velocity to be larger than observed velocities

26. Velocity Dispersions in Ellipticals Elliptical Galaxies have little to no organized rotation But stars still bound to galaxy – cannot exceed escape velocity Measure the velocity dispersion for ellipticals Shows that dark matter is needed But it’s not just stars that have velocities – gas particles do too!

27. Hot Gas in Ellipticals We see hot X-ray emitting gas around ellipticals. The gas is gravitationally bound to the galaxy. Velocities of gas particles must be smaller than escape velocity Velocity from Temperature of Gas

28. Example The T of X-ray gas in NGC 4636 is 11.6 million K. How much mass is needed to hold onto that gas? T=11.6 million K  velocity of proton = 437,740 m/s 60 kpc from the center = 1.85 x 10 21 m Only about 1x10 11 M Sun in stars, gas & dust. Need dark matter!

30. Velocities of Galaxies in Clusters Additional evidence for the presence of dark matter comes from the high velocities of galaxies in clusters Galaxies are moving at 800-1000 km/s compared to the cluster center Amount of matter we measure from the light is not enough to prevent their escape! 90-99% of the matter in clusters is dark matter

31. Zwicky in action Where’s the matter?

32. Insight from Einstein: Gravitational Lensing

33. Gravitational Lensing The amount of gravitational lensing depends on the curvature of spacetime We see lots of bending – lots of matter Conclusion: cluster masses are dominated by dark matter

34. Possible candidates Stellar remnants Black holes Neutron stars White dwarfs Brown Dwarfs & Planets Particle Neutrino New Particle – Weakly Interacting Massive Particles (WIMPs) MACHOs -- MAssive COmpact Halo Objects

35. Is “Dark Matter” the only possible explanation? It is not easy to believe that we are unaware of the nature of something that has 5-6 times more mass than “normal” matter However, many lines of evidence are pointing to the same conclusion! Possible counter explanation: Neither Newton nor Einstein got the law of gravity quite right. On galaxy-sized scales, gravity stronger than what Law of Universal Gravity states