1. 1 KIAA Lectures Beijing, July 2010 Ken Freeman, RSAA, ANU Lecture 2: dynamical processes which lose information

2. 2 Accretion of satellites Resonances Disk Heating Orbit swapping Dynamical processes which lose information or generate potentially misleading information for Galactic archaeology

3. 3 Accretion and destruction of satellites This is an important part of CDM theory: merging of smaller objects of the hierarchy to form larger objects. Small galaxies are accreted and destroyed by larger galaxies: the debris of the small ones becomes part of the halo, bulge or disk of the larger one. The orbital energy and angular momentum of the smaller galaxy is absorbed by the dark halo and disk of the larger one. The existence of thin disks constrains the merger history since the disk formed, because disks can be destroyed by major mergers. Goal here is to describe some of the essential dynamics of merging, accretion and disruption

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5. 5 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.

6. 6 r(t) AB vv

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8. 8 NGC 5907: debris of a small accreted galaxy Our Galaxy has a similar structure from the disrupting Sgr dwarf APOD

9. 9 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.

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16. 16 Accretion of small satellites

17. 17 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 1996

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19. 19 Abadi et al 2003 analysed an SPH simulation of the formation of a disk galaxy assembled hierarchically in  CDM. They identified a large spheroid and two disk components: thin and thick. The spheroid stars are old (> 8 Gyr). The disk stars cover a wide range of age, but most of the older (> 10 Gyr) disk stars did not form in the disk but came from accreted satellites whose orbits were circularized before disruption. The computations show that the satellite typically sinks into the plane of the parent in less than a Gyr. The disk provides about 75% of the integrated torque on the satellite (resonances are important): dynamical friction against the halo provides the rest.

20. 20 Abadi et al 2003 The 3 components: spheroid, thick and thin disks

21. 21 Abadi et al 2003 Only a small fraction of the old disk stars formed in the disk: most of it comes from circularized satellite debris In the simulation, the thick disk is mostly old; the thin disk is mostly younger

22. 22 How could we test whether much of the old disk stars came from outside ? Kinematically this would be difficult, because their kinematics would be much like those of in- situ disk stars. Chemical techniques look promising … The overall metal abundance of the satellites depends on their stellar luminosity. Disk stars have abundances [Fe/H] > -1 so the absolute magnitudes of the infalling satellites must have been brighter than -15. That is consistent with the Abadi et al (2003) satellites which fell into the disk: they were typically more massive than 10 9 M . That makes sense too from dynamical friction theory: dynamical friction affects only the more massive satellites.

23. 23 Dwarf Galaxies: chemical signatures and abundance range Ultra-faint dSphs contain individual stars with [Fe/H] < -3 Large range of abundance in individual dwarfs [Fe/H] - L relation  internal chemical evolution. Mateo 2008 globular clusters satellites Mean abundance - luminosity relation

24. 24 Chemical studies of the old disk stars in the Galaxy might help to identify disk stars which came in from outside in satellites which then disrupted. The chemical properties of surviving satellites (the dwarf spheroidal galaxies) vary from satellite to satellite, and are different in detail from the more homogeneous overall properties of the disk stars. We can think of a chemical space of abundances of elements O, Na, Mg, Al, Ca, Mn, Fe, Cu, Sr, Ba, Eu for example. The dimensionality of this space is between about 7 and 9. Most disk stars inhabit a sub-region of this space. Stars which came in from satellites may be different enough to stand out from the rest of the disk stars. With this chemical tagging approach (more later), we may be able to detect or put observational limits on the satellite accretion history of the galactic disk

25. 25 Each galaxy has had a different evolutionary track The position of the knee forms a sequence following SFH-timescales (and somewhat the galaxy total luminosity) s- process (AGB product) very efficient in galaxies with strong SFR at younger ages ( LMC > Sgr > Scl r/s-process elements can be used as another clock (or even 2 clocks: r/s transition knee, and start of rise in s ) AGB lifetimes + s-process yields are metallicity-dependent (seeds) Abundance pattern in the metal-poor stars everywhere undistinguishable ? Seems to be the case for stars in the exended low- metallicity populations. SNII +SNIa rise in s-process LMC Pompeia, Hill et al. 2008 Sgr Sbordone et al. 2007 Fornax Letarte PhD 2007 Sculptor Hill et al. 2008 in prep + Geisler et al. 2005 Carina Koch et al. 2008 + Shetrone et al. 2003 Milky-Way Venn et al. 2004 Abundance ratios reflect different star formation histories Venn 2008

26. 26 Hercules dSph : M * = 4 x 10 4 M , large abundance spread low Ca/Fe but … and undetected Ba, Sr, Eu very large [Mg/Ca] The high Mg/Ca suggests enrichment by just 1 or 2 high mass SNII (M ~ 35 M  ) Koch et al 2008 galactic stars other dSph stars Hercules

27. 27 The metal-poor stellar halo abundance range [Fe/H] = -1 to -5 overlaps with the metal-poor tail of the thin disk Density distribution  ~ r -3.5, extends out to ~100 kpc mass of stellar halo ~ 1 x 10 9 M  (total stellar mass of the Galaxy is about 6 x 10 10 M  ) Probably made up at least partly from debris of lower-mass accreted satellites

28. 28 Tidal Streams in the Galactic Halo (simulation of accretion of 100 satellite galaxies) x (kpc) y (kpc) R GC (kpc) RV GC (km s -1 ) (Spaghetti: Harding)

29. 29 Input - different colors represent different satellites Output after 12 Gyr -stars within 6 kpc of -the sun - convolved with GAIA errors Helmi & de Zeeuw Accretion in integral space (E,L z )

30. 30 Helmi & de Zeeuw adopted a time-independent gravitational field for their simulation Cosmological simulations (eg Gill et al, Gao & White) indicate that the dark halo has doubled its mass since z =1 Gill et al showed that satellite debris retains its identity in the (E, L z ) plane, although its average (E, L z ) does change Dynamically reconstructing at least some of the objects that formed at high redshift and then became part of the Galactic halo seems feasible: GAIA will contribute greatly.

31. 31 Now look at some nasty stellar dynamical effects First need briefly to discuss stellar orbits in galaxies Got to here

32. 32 L z is the z-component of the angular momentum Stellar Orbits

33. 33 A typical near-circular rosette orbit in an axisymmetric potential, bounded by its energy and L z values: see the effect of the third integral: this is also an isolating integral but cannot be written down in analytical form. Galactic disks are made up of such orbits. Galactic plane projection Side-on projection

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35. 35 In real galaxies

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37. 37 A rosette orbit is the vector superposition of these two components: the epicycle + the circular guiding centre motion.  

38. 38 Now look at the motions of stars near the sun, in the light of the orbit theory. This defines the UVW system of stellar motions relative to the Local Standard of Rest (a coordinate System at the solar radius, going around the Galaxy at the circular velocity of 220 km/s. V is in the sense of Galactic rotation. We will see that the distribution of stars in the (U,V) plane is lumpy: are these lumps the remains of star forming events which would be interesting archaeologically ?

39. 39 (Hipparcos data for nearby stars) The Hercules group is probably associated with local resonant kinematic disturbance by the inner bar (Dehnen 1999) Sirius and Hyades streams - mainly earlier-type stars Dehnen 1999 U V Hercules disturb- ance from OLR -mainly late-type stars

40. 40 Hercules group o field stars Bensby et al 2007 Chemically, the Hercules group looks just like a random sample of disk stars. No hint that its stars may be related by birth. The Hercules group is believed to be a resonance or dynamical group

41. 41   pp Outer Lindblad Resonance occurs where  p =  (R) +  (R) /2 : stars with such values of  see same bar potential on each  -oscillation. They are locked into the resonance instead of drifting off on their orbits. For the Galactic bar and disk, OLR lies near the Sun. Stars in OLR have guiding center radius lying inside solar radius, so their angular momentum is a bit lower than the LSR’s and their V ~ -50 km/s, like the Hercules group Resonant Groups Some stars are in resonance with a rotating gravitational pattern: bar or spiral structure Guiding center frequency  and epicyclic frequency  depend on R. The bar frequency  p is a constant.

42. 42 Resonances can occur not only from the bar but also from any azimuthally propagating disturbance like a transient spiral structure that has a well- defined pattern speed. Many (most ?) groups of stars observed to be moving together are probably resonant phenomena. There are  p =    /2 resonances and also  p =    /4,  p =    /6 etc resonances, all of which can generate bogus (ie dynamical) moving stellar groups Fuchs 2007  +  /2  Real coeval chemically homogeneous moving groups do exist. They are good but rare. The dynamical groups are a nuisance for archaeology. The  /6 resonances lie between the 4:1 resonances and corotation

43. 43 Histograms of J z for Gratton's (2003) sample of nearby metal- poor stars with well-measured chemical abundances The retrograde  Cen feature is thought to be associated with the accretion event that brought  Cen into the MW. Its stars have the same chemical peculiarities as  Cen (Wylie et al 2010) - Na, Mg, s-process over-abundances. The Arcturus feature was also thought to be the debris of an accretion event associated with the thick disk (Navarro et al 2004). Williams et al (2008) believe it is from a 6:1 resonance, because it shows no chemical identity. Meza et al 2006 Some potential metal-poor moving groups

44. 44 Omega Centauri Omega Cen is the most massive globular cluster in the Galaxy. It is the only cluster which is very inhomogeneous in its heavy element abundances, and it has some unusual element abundance ratios. The chemical properties and very bound retrograde orbit of  Cen suggest that it is the nucleus of a satellite of mass ~ 10 8 M  which was dragged in to the Galaxy by dynamical friction and then tidally disrupted This may have been the event that thickened the thick disk (Bekki & Freeman 2003) Finding the debris of the  Cen satellite galaxy is an interesting archaeological goal : see Wylie et al 2010

45. 45 For small epicyclic amplitudes, resonances occur at a particular guiding center radius, eg where  p =  (R) +  (R) /2 When the epicyclic amplitude A is larger than a few hundred pc, the linear theory breaks down. Orbit can still be represented as guiding center + epicycle, but  is no longer just a function of R: now  =  (R,A). The resonant condition is still  p =    /2 and  is still  (R) but the non-linearity in  broadens the resonance in R, so resonances become yet more widespread. Identity of Sirius and Hyades moving groups is still undecided: They could be real or dynamical (I think real) Sirius and Hyades streams - mainly earlier-type stars

46. 46 Nonlinear epicycle Rosette orbit as seen from nonrotating frame Orbit as seen from frame rotating at angular velocity   

47. 47 Radial Mixing: orbit swapping An azimuthally propagating disturbance with pattern frequency  p affects stars near corotation (where  p =  ). Depending on the relative phase of the star and the disturbance, the star can be flipped from a near-circular orbit at one radius to another near-circular orbit at a different radius (Sellwood & Binney 2002). The amplitude and sign of the radius change depends on the strength and phase of the disturbance This adds to the difficulties of Galactic archaeology: we have always believed that stars in near-circular orbits are at radii close to where they were born. This need not be true. eg recent simulations by Roskar et al (2008), aimed at understanding the outer truncation that is seen in many galactic disks. See also Schoenich & Binney papers (2009) for application to evolution of the Galactic disk.

48. 48 pp Corotation  =  p AB Star A gains angular momentum and is flipped to larger radius Star B loses angular momentum and is flipped to smaller radius Transient disturbances have different corotation radii so as time goes on, different parts of the disk are affected

49. 49 Disk Truncation M33 - outer disk truncated, very smooth structure NGC 300 - exponential disk goes for at least 10 scale- lengths without truncation Bland-Hawthorn et al 2005Ferguson et al 2003

50. 50 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) - SPH 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 via spiral arm interactions (Sellwood & Binney 2002) so its stars are relatively old.

51. 51 Roskar et al (2008) stellar surface density gas surface density star formation rate mean stellar age

52. 52 Roskar et al (2008) Secular radial distribution of stars via spiral arm interaction into outer (break) region of truncated disk break

53. 53 Very important now to assess how well radial mixing works for orbits with large epicyclic amplitudes. Does radial mixing significantly affect the old stars in the disk, or is it mainly a young disk effect ? My guess is that it should work, but will be diluted by the z-motion: orbits with large z-amplitudes will spend much of their time away from the Galactic plane where the spiral disturbance is greatest.

54. 54 Radial mixing may explain the reversal in the abundance gradient seen in NGC 300, and its lack of disk truncation Is the outermost disk of NGC 300 populated by stars scattered out from the more metal-rich inner regions ? Vlajic et al 2008 NGC 300

55. 55 The point of all this is that kinematics alone cannot reliably show whether a moving group is a resonance effect or the debris of an ancient accretion event or star formation event. We cannot assume that stars are near their birth radius, not even for stars in near-circular orbits. Chemical signatures are essential for Galactic archaeology

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57. 57 Meza et al (2006): evolution of disrupting satellite in V R - R plane Curves show a few loci of constant (E, L z )

58. 58 Meza et al (2006): the Chiba-Beers metal poor stars - histogram of V rot : see a few substructure peaks including possible retrograde omega Cen galaxy debris Arcturus peak is a thick disk feature: maybe debris of an accreted galaxy Histogram of V rot for metal-poor stars

59. 59 Meza et al 2006 Gratton's (2003) sample of metal-poor stars with well-measured chemical abundances see the omega Cen and Arcturus features again Histogram of J z

60. 60 The red points are potential omega Cen debris candidates. Less  -enriched than other halo stars : implies a longer history of chemical evolution, as observed in omega Cen itself Element abundances [  /Fe] vs [Fe/H] (Meza et al 2006)

61. 61 simulation of Can Maj accretion event, seen from N pole. Cold system,  ~ 11 km/s S Martin et al 2005 +

62. 62 Also the Monoceros/Canis Majoris feature in the outer half of the Galaxy, near plane : probably remains of an accreted dwarf but may just be a feature in the galactic disk. Not easy to visualize - look at current best-fit simulation of accretion of dwarf (Martin et al 2005)