1. DOES DARK MATTER REALLY EXIST? Prof. Megan Donahue Science Media Group MSU Physics & Astronomy Dept. Harvard-Smithsonian Center for Astrophysics

2. We can calculate the mass of a planet, star or galaxy by measuring how fast another object orbits around it. Where v is the measured velocity of the orbiting object, G is a constant, and M(<r) is the total mass enclosed within a sphere of radius r Example: The mass of the Earth can be calculated from the orbiting space shuttle using this equation. M r v

3. Given this equation, which of these animations depicts an orbital system that is not physical. Hint all the mass is in the center? Needs final animations! One is physical One rotates like a record.

4. 1.The quantity enclosed mass M(<r) is the total mass inside a sphere with radius r. Sphere with radius r

5. 1a.Which of these enclosed-mass plots (of M(<r)) is of a doughnut? ABC

6. 1b.Which of these enclosed-mass plots describes our solar system? ABC

7. 1c.Which enclosed-mass plot has most of the mass in the system concentrated in the center? ABC

8. 1d.Which enclosed-mass plot has mass spread out to radius R? ABC

9. 2.A plot of orbital velocity vs. radius is called a velocity curve. The mass within radius r is: So a plot of v(r) can be converted into M(r) and vice versa.

10. 2a.Which of these velocity curves describes our solar system? (Hint: over 99.9% of the mass is in the center.) ABC v

11. 2b.Which of these velocity curves is consistent with the enclosed mass M(<r) being proportional to r? ABC

12. 2c.Consider plot A and this orbital velocity law M(<r) = rv 2 /G:  If all the mass is concentrated in the center, the orbital speed v is proportional to: a)   b) 1 /r 2 c) 1 /  r d)r A Hint: solve for v in this orbital velocity law.

13. 3a.Consider plot B:  Is the orbital velocity v proportional to: a)   b)r c)r 2 d) 1 /r 2 B Hint: you do not need an equation to answer this question.

14. 3b.Consider plot B:  If v is proportional to  , and since M(<r) is proportional to v 2 r, M(<r) is proportional to: a)r b)r 2 c)r 3 d)r 4 B

15. 3c.If M(< r) is proportional to r 3, then the density of matter = mass / volume is proportional to: [Hint: the volume of a sphere is proportional to r 3 ] a) 1 /r 3 b) 1 /r 2 c) 1 /r d)Constant e)r f)r 2 g)r 3

16. 4. A look at galaxies

17. We can calculate the mass of a galaxy using the same equation: Where M(< r) is the mass enclosed with a radius r, v is the velocity of material orbiting at a radius r, and G is the gravitational constant.

18. And, we can measure the velocity curves of spiral galaxies using doppler shifts of matter orbiting the galaxy at different distances. Using these measurements and the equation for orbital velocities, we can determine the mass enclosed at different radii from the center.

19. 4a. At R = 1 kpc, order each system by increasing enclosed mass at M(r < 1kpc), where the dashed line is drawn. Add multiple choice picks this & next 2 slides

20. 4b.At r < 1kpc (inside of the dashed line), order each M(r < 1kpc) in increasing enclosed mass.

21. 4c. At any radius r > 1kpc, order the enclosed mass M(r > 1kpc) in increasing enclosed mass.

22. 5a.Consider plot C:  At large r, v is proportional to: a)r b)Constant c) 1 /r d) 1 /r 2 C

23. 5b.Consider plot C:  At large r (R 1 < r < R 2 ), M(r) is proportional to: a)r b)Constant c) 1 /r d) 1 /r 2 C

24. 5c.Consider plot C:  At small r (r < R 1 ), v is proportional to: a)r b)Constant c) 1 /r d) 1 /r 2 C

25. 5e.Implications for galaxy structure  If this were the measured velocity curve of a galaxy, then one could conclude that up to a small radius (r R 1 ), the velocity remains flat; this means the density of matter declines like 1 /r 2. C

26. 5f.Measured galaxies C  The velocity curves of a number of different galaxies have been measured, and they closely fit this pattern:

27. 5g.  These velocity curves are consistent with the idea that there is a large amount of mass in the galaxy’s halo - the region outside the visible spiral arms - astronomers call it “dark matter”.

28. 6a.If a galaxy has an edge at large r, (> R) what would you expect the velocity curve to look like?

29. 6b.If a galaxy has an edge at large r, what would you expect the enclosed mass curve M(< r) to look like?

30. 7. A look at galaxy clusters

31. Velocities toward or away from the observer of the galaxies in a cluster can be measured using doppler shifts - objects moving toward the observer are shifted blue, and those moving away from the observer are shifted toward the red.

32. 7a.Consider the following distributions of orbital velocities in three clusters of similar average radius. Note: assume the axes scale on each plot is identical  Order the clusters in order of largest velocity spread to smallest. Need explanation that in a galaxy cluster you can plot histogram (what is?) of the galaxies,Need to label Bottom axis. Add intro with a generic histogram - eg. numbers of people in a class with different grades

33. 7b.Consider the following distributions of orbital velocities in three clusters of similar average radius. Note: assume the axes scale on each plot is identical  Order the clusters in order of largest mass to smallest.

34. 7c.Consider the following distributions of orbital velocities in three clusters of similar average radius. Note: assume the axes scale on each plot is identical  Order the clusters in order of X-ray temperature. Hint: Think of the relationship between temperature & velocity. Need explanatory intro slide - Megan to send text.

35. 7d.Assume we have measured redshifts for every galaxy in these clusters and all the galaxies have the same luminosity.  Which galaxy cluster, A or C, has the largest M/L ratio?

36. 8a.What would happen to the galaxies in a cluster of galaxies if the dark matter “went away”?  Predict Optical Appearance: a)The cluster of galaxies would fly apart. b)The galaxies would continue orbiting as they were. c)The galaxies would collapse in a big collision.

37. 8b.What would happen to the galaxies in a cluster of galaxies if the dark matter “went away”?  Predict Optical Appearance:  How fast would they fly apart? (The galaxies are moving about 1000 km/s and the cluster is about 3 X 10 19 km across.) a)Fly apart immediately - no cluster visible the next day. b)Cluster would fly apart - no cluster visible after a couple of years. c)Cluster would fly apart - no cluster visible after a few hundred million to a billion years. d)Nothing would happen.

38. This simulation, created by Gus Evrard at Univ. of Michigan, shows what would happen to an evolving cluster of galaxies if dark matter were “turned off”.

39. Dark Matter Summary

40. If dark matter disappeared from the universe today we wouldn’t see the effects immediately.

41. So why do we think it is still there? 1.Clusters appear to be stable, long-lived structures. We can observe clusters over a wide range of cosmic history, and if they’re doing anything at all, they’re getting bigger with time, not smaller. The forces of gravity cause over-dense systems to grow with time. 2.Clusters of galaxies have old galaxies with old stars. 3.We don’t really know for sure but we think it would be cool if dark matter were real.