ATA 2010 DYNAMICS of the MILKY WAY

1. ATA 2010 DYNAMICS of the MILKY WAY Ken Freeman, ANU & UWA

2. Introduction Galaxies are collections of stars, gas, dust and dark matter Masses are between about 106 and 1012 M. The Milky Way is a disk galaxy and is near the upper end of the mass range.

3. NGC 2997 - a typical disk-like spiral galaxy

4. NGC 891 A spiral galaxy seen edge-on Note the small central bulge and the dust in the equatorial plane

5. Disk galaxies Flat rotating disk-like systems, often with spiral structure Surface brightness distribution I(R) = Io exp(-R / h) Io is the central surface brightness, typically around 150 pc-2 h is the scale length: 4 kpc for a large galaxy like the MW Ratio of stars/gas varies : for the MW stars 95%, gas 5% of the visible matter. Dark/visible mass ratio is about 10-20

6. The nearby spiral galaxy M83 in blue light (L) and at 2.2 (R) The blue image shows young star-forming regions and is affected by dust obscuration. The NIR image shows mainly the old stars and is unaffected by dust. Note how clearly the central bar can be seen in the NIR image

7. Rotation of spirals Mostly don’t rotate rigidly - wide variety of rotation curve morphology depending on their light distribution. Here are a couple of extremes - the one on the left is typical for lower luminosity disks, while the one on the rightis more typical of the brighter disks like the Milky Way

8. What keeps the disk in equilibrium ? (always ask this question for any stellar system) Most of the kinetic energy is in the rotation • in the radial direction, gravity provides the radial acceleration needed for the ~ circular motion of the stars and gas • in the vertical direction, gravity is balanced by the vertical pressure gradient associated with the random vertical motions of the disk stars.

9. Believed to be much like NGC 891, with weak bar like M83. Rotational velocity ~ 220 km/s Our Galaxy Schematic picture of our Galaxy, showing bulge, thin disk, thick disk, stellar halo and dark halo Our Galaxy at 2.4

10. MOVIE Start by showing a numerical simulation of galaxy formation. The simulation summarizes our current view of how a disk galaxy like the Milky Way came together from dark matter and baryons, through the merging of smaller objects in the cosmological hierarchy. • much dynamical and chemical evolution • halo formation starts at high z • dissipative formation of the disk

11. Simulation of galaxy formation • cool gas • warm gas • hot gas

12. Movie synopsis •z ~ 13 :star formation begins - drives gas out of the protogalactic dark matter mini-halos. Surviving stars will become part of the stellar halo - the oldest stars in the Galaxy • z ~ 3 :galaxy is partly assembled - surrounded by hot gas which is cooling out to form the disk • z ~ 2 :large lumps are falling in - now have a well defined rotating disk galaxy. You saw the evolution of the baryons. There is about 10 x more dark matter in a dark halo, underlying what you saw: it was built up from mergers of smaller sub-halos

13. Course Objectives To study the dynamics of the Milky Way. Most of its visible mass is in stars, so the dynamical theory is mostly stellar dynamics Following this basic descriptive introduction, I will go straight to the lectures on the theoretical dynamics. This will give you maximum opportunity to complete the assignments. We will then return to more advanced descriptive material on near-field cosmology: ie what we can learn about galaxy formation from studying the detailed properties of our own Galaxy.

14. Lecture times 2 to 4 pm on Monday 02, 09, 16 August 2010 ICRAR, UWA - ground floor

15. Assessment 30% on assignment work, 70% on examination Assignments: one problem sheet with 5 questions: please hand in at lecture on Fri Sep 18. I use these problems as part of the teaching process, as well as for assessment, so please do them. They require some time and effort. I encourage you to discuss the problems with others, but the work you submit should be your own. It is very obvious if people collaborate in the submitted work, and it will cost both (all) parties some marks. There will be a brief tutorial session on the assignment in class Examination: you will have a 2-hour examination for the 3 combined ATA modules. For this module, you will be asked to do two questions from a choice of three.

16. You can find the lecture notes and assignment sheet at http://www.mso.anu.edu.au/~kcf/ATA Feel free to contact me about the problems or any other aspect of the course: office ICRAR 249 phone 6488 4756 emailkcf@mso.anu.edu.au

17. References Binney & Tremaine: Galactic Dynamics (1987, 2008). The dynamical lectures are partly based on this book, which is the best book on the subject. It covers far more ground than we can cover in these lectures. Binney & Merrifield: Galactic Astronomy (1998). This is a more descriptive book and well worth reading for background. Sparke & Gallagher: Galaxies in the Universe (2007). Ditto : good book, with some theory

18. 13.7 Gyr

19. Two important timescales The dynamical time (rotation period, crossing time G  where  is a mean density. Typically 2 x 108 yr for galaxies 2) The relaxation time. In a galaxy, each star moves in the potential field  of all the other stars. Its equation of motion is where is Poisson’s equation The density (r) is the sum of 106 to 1012-functions. As the star orbits, it feels the smooth potential of distant stars and the fluctuating potential of the nearby stars

20. Question: do these fluctuations have a significant effect on the star’s orbit ? This is a classical problem - to evaluate the relaxation time TR - ie the time for encounters to affect significantly the orbit of a typical star Say v is the typical random stellar velocity in the system m mass n number density of stars Then TR = v3 / {8 G2 m2 n ln (v3 TR / 2Gm)} (see B&T I:187-190) TR / Tdyn ~ 0.1 N / ln N where N is the total number of stars in the system

21. In galactic situations, usually TR >> age eg in the solar neighborhood, m = 1 M, n = 0.1 pc-3 v = 20 km s -1 so TR = 5.10 12 yr >> age of the universe In the center of a large spiral where n = 10 4 pc -3 and v = 200 km s -1, TR = 5.10 11 yr (However, in the centers of globular clusters, the relaxation time TRranges fromabout 107 to 5.109 yr, so encounters have a slow but important effect on their dynamical evolution) Conclusion: in galaxies, stellar encounters are negligible: they are collisionless stellar systems.  is the potential of the smoothed-out mass distribution, which makes galaxy dynamics much simpler.

28. For real disk galaxies, we can calculate the potential of the stars and the gas from the observed surface density distribution of stars and gas in the disk, and then calculate the expected rotation curve from This is not usually a good fit to the observed rotation curve, because most of the mass of disk galaxies is in the form of dark matter

29. Surface Brightness HI Rotation Curve (out to 11 scale lengths) Dark matter is important here

38. If E and Lzare the only two integrals of the motion, then the orbit would visit all points within ints zero-velocity curve.

41. E L E = E max circular orbits locus of const rmax

46. A rosette orbit is the vector superposition of these two components: the epicycle + the circular guiding centre motion.

49. Now take ez