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

2. Galaxies are collections of stars, gas, dust and dark matter Masses are between about 10 6 and 10 12 M . The Milky Way is a disk galaxy and is near the upper end of the mass range. Introduction

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 Surface brightness distribution I(R) = I o exp(-R / h) I o 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. Flat rotating disk-like systems, often with spiral structure 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 right is 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. Our Galaxy Believed to be much like NGC 891, with weak bar like M83. Rotational velocity ~ 220 km/s Our Galaxy at 2.4  Schematic picture of our Galaxy, showing bulge, thin disk, thick disk, stellar halo and dark halo

10. 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. MOVIE 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. 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 Movie synopsis

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

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 1)The dynamical time (rotation period, crossing time   G     where  is a mean density. Typically 2 x 10 8 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 10 6 to 10 12  -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 T R - 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 T R = v 3 / {8  G 2 m 2 n ln (v 3 T R / 2Gm)} (see B&T I:187-190) T R / T dyn ~ 0.1 N / ln N where N is the total number of stars in the system

21. In galactic situations, usually T R >> age eg in the solar neighborhood, m = 1 M , n = 0.1 pc -3 v = 20 km s -1 so T R = 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, T R = 5.10 11 yr (However, in the centers of globular clusters, the relaxation time T R ranges from about 10 7 to 5.10 9 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 L z are the only two integrals of the motion, then the orbit would visit all points within ints zero-velocity curve.

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

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

49. Now take  e z

51. NGC 1300

54. Define the convective derivative in phase space Then we can show that for a collisionless system. This is the collisionless Boltzmann equation: the convective derivative of the phase space density is zero.

55. These two equations are coupled:

64. Merrifield (1992) Rotation of the Galaxy

66. 25001250  RR 2 (km s -1 ) 2 -30 -20 -10 (km s -1 ) Stromberg’s asymmetric drift

74. absorbs

75. Merging stimulates star formation and disrupts the galaxies. This is NGC 4038/ 9 : note the long tidal arms. The end product of the merger is often an elliptical galaxy. Disk galaxies interact tidally and merge.

76. NGC 5907: debris of small accreted galaxy Our Galaxy has a similar structure from the disrupting Sgr dwarf APOD

77. The “field of streams” seen in SDSS star counts in the halo of our Galaxy north galactic pole l = 180, b = 25 Accretion of small galaxies is more important than major mergers for the evolution of the Milky Way: look now at the two main processes involved in accretion.

80. Recent HST proper motion measurements for the LMC indicate that the LMC is not in a circular orbit around the Galaxy and may not even be bound to the Galaxy. The HI Magellanic Stream (Putman 2002), believed to come from interaction of the Galaxy and the Magellanic Clouds. Seen only in HI, not in stars.

87. The pioneering work on this problem was done by Quinn & Goodman 1986)

89. Decay of a prograde satellite orbit The satellite sinks into the plane of the galaxy in < 1 Gyr. The disk provides about 75% of the torque on the satellite: dynamical friction against the dark halo Provides the rest

91. Some background to the paper “Panoramic High Resolution Spectroscopy” and galactic archaeology Chemical Evolution Elements lighter than ~ Be are built in the hot universe, shortly after the big bang Elements heaver than Be are built in stars, and ejected back into the interstellar gas by supernovae and AGB stars - many cycles of enrichment give chemical evolution up to the present level of chemical abundance - SN and AGB stars Two main kinds of supernovae: SNII (progenitor M > 8M  ) produce  -elements (O, Mg, Si, Ca,Ti), some Fe-peak elements (V … Zn), and r-process elements (eg Eu) all on timescales ~ 10 7 years SNIa (lower mass progenitors, probably white dwarf binaries) produce mainly Fe-peak elements but on longer timescales ~ 10 9 years AGB stars over wide range of mass produce s-process elements (Sr, Zr,Ba), again on longer timescales ~ 10 9 years If we see stars which are rich in  -elements relative to iron, this means that the chemical evolution of the gas from which they formed happened quickly (~ 10 8 yr), before there was time for the SNIa to generate a lot of iron etc To measure the abundances of chemical elements accurately, we need high resolution spectra with R > 30,000. Until now, high resolution spectrographs can measure only one star at a time. In the near future, we will be able to measure hundreds a a time.

92. The galactic disk shows kinematical substructure in the solar neighborhood: groups of stars moving together, usually called moving stellar groups (Kapteyn, Eggen) Some are associated with dynamical resonances (eg Hercules group): don't expect chemical homogeneity Some are debris of star-forming aggregates in the disk (eg HR1614 group). Might expect chemical homogeneity; these could be useful for reconstructing the history of the galactic disk. Others may be debris of infalling objects, as seen in  CDM simulations: eg Abadi et al 2003 (Arcturus Group, Navarro et al 2004) Stellar Moving Groups in the Disk

93. The Hercules group is associated with local resonant kinematic disturbances by the inner bar : OLR is near solar radius (Hipparcos data) : Dehnen (1999), Fux (2001), Feast (2002) Sirius and Hyades streams - mainly earlier-type stars Hercules disturb- ance from OLR -mainly later-type stars Dehnen 1999 (U,V are relative to the LSR) U V

94. The abundances of Hercules Group stars cannot be distinguished from the field stars. This is a dynamical group, not the relic of a star forming event. Hercules group o field stars Bensby et al 2007

95. Now look at the HR1614 group (age ~ 2 Gyr, [Fe/H] = +0.2). Studied by Feltzing & Holmberg (2000) who argued for its reality as a relic group. De Silva et al (2007) measured very precise chemical abundances for many elements in HR1614 stars, and finds a very small spread in abundances. The Wolf 630 group was recently found to be similarly homogeneous in its element abundances

96. HR 1614 o field stars The HR 1614 stars (age 2 Gyr) are chemically homogeneous. They are probably the dispersed relic of an old star forming event. De Silva et al 2007

97. NGC 4762 - a disk galaxy with a bright thick disk (Tsikoudi 1980) M ost spirals (including our Galaxy) have a second thicker disk component. In some galaxies, it is easily seen The thin diskThe thick disk

98. Our Galaxy has a significant thick disk its scaleheight is about 1000 pc, compared to 300 pc for the thin disk its surface brightness is about 10% of the thin disk’s. it rotates almost as rapidly as the thin disk its stars are older than 12 Gyr, and are significantly more metal poor than the thin disk (-0.5 > [Fe/H] > -2.2) and alpha-enriched

99. The galactic thick disk its mass is about 10% of the thin disk’s it is old (> 12 Gyr) and significantly more metal poor than the thin disk: mean [Fe/H] ~ -0.7 and  -enhanced its rotation lags the thin disk by only ~ 50 km/s thick disk thin disk higher [  /Fe]  more rapid formation

100. Most disk galaxies have thick disks: (eg Yoachim & Dalcanton 2006) The Galactic element abundance data are consistent with a time delay between formation of thick disk stars and the onset of star formation in the current thin disk. The fraction of baryons in the thick disk is typically small (~ 10-15%) in large galaxies like the MW but rises to ~ 50% in smaller disk systems

101. Yoachim & Dalcanton 2006 Baryonic mass ratio: thick disk/thin disk

102. How do thick disks form ? a normal part of early disk settling (Samland et al 2003, Brook et al 2004) accretion debris (Abadi et al 2003, Walker et al 1996) early thin disk, heated by accretion events - eg the  Cen accretion event (Bekki & KF 2003): Thin disk formation begins early, at z = 2 to 3. Partly disrupted during merger epoch which heats it into thick disk observed now, The rest of the gas then gradually settles to form the present thin disk

103. Disks have a roughly exponential light distribution in R and z: I(R,z) = I o exp (-R/h R ) exp (-z/h z ) out to R = (3 to 5) h R, then often truncated M33 (Ferguson et al)

104. The truncations are not understood: may be associated with the star formation threshold angular momentum redistribution by bars and spiral waves the hierarchical accretion process bombardment by dark matter subhalos (de Jong et al 2007) Roskar et al (2008) - SPG simulation of disk formation from cooling gas in an isolated dark halo : includes star formation and feedback. The break is seeded by rapid radial decrease in surface density of cool gas : break forms within 1 Gyr and gradually moves outwards as the disk grows. The outer exponential is fed by secularly redistributed stars from inner regions (Sellwood & Binney 2002) so its stars are relatively old.

105. Roskar et al (2008) stellar surface density gas surface density star formation rate mean stellar age

106. Roskar et al (2008) Secular radial distribution of stars via spiral arm interaction into outer (break) region of truncated disk Redistribution of stars by orbit swapping will affect the galactic abundance gradient break

107. The galactic disk shows an abundance gradient (eg galactic cepheids: Luck et al 2006)....

108. Background to the final section …. Using dispersed star clusters for galactic archaeology: finding fossil remains of the star forming events which built up our Galaxy Galaxies like the Milky Way are believed to form by the infall of gas which then turns gradually to stars (most of which form in the disk of the Galaxy, in open star clusters which quickly dissolve), and also by the accretion of smaller galaxies which become absorbed in the larger system. A major goal is to determine how important these accretion events were in building up the Galactic disk and the bulge. Our current galaxy formation theory based on Cold Dark Matter predicts a very high level of accretion activity which conflicts with many observed properties of disk galaxies.

109. By now, the star clusters and the small accreted galaxies have broken up and be unrecognisable: their debris will be dispersed right around the Galaxy. But … We can use their chemical signatures over many chemical elements to identify their debris: stars from a common cluster have similar chemical signatures, and their chemical properties vary from cluster to cluster stars from a small accreted galaxy have chemical patterns that are very different from those we see in the open clusters which formed in the disk. Using chemical signatures to identify stars having a common origin is called chemical tagging This will be one of the big things of the next decade in galactic astronomy

110. Cluster abundance patterns Hyades Coll 261 HR1614 De Silva 2007 Zr Ba Mn Ca Si Mg Na

111. Clusters vs nearby field stars Hyades Coll 261 HR1614 De Silva 2007 Clusters have small abundance spread: The mean is different from cluster to cluster

112. Galactic Archaeology with HERMES Simulations show that a chemical tagging program to reconstruct the fossils of the star forming aggregates that built up our Galaxy needs high resolution spectra of about a million stars We are building a large multi-object spectrometer (HERMES) for the AAT to do this survey. It will acquire high resolution spectra of about 400 stars at a time, and the survey will take about 400 clear nights. Expect to start work in 2012