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anisotropy

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anisotropy

  1. 1. On the orbital velocity anisotropy of cluster galaxies Francesca Iannuzzi MPA
  2. 2. How does the anisotropy profile evolve in time for different galaxy populations?
  3. 3. Anisotropy β = 1 − σ2 t σ2 r
  4. 4. Anisotropy Circular orbits β = 1 − σ2 t σ2 r β = −∞ β = 1 Radial orbits
  5. 5. Anisotropy Circular orbits β = 1 − σ2 t σ2 r β = −∞ β = 1 Radial orbits β 0 “Isotropy”
  6. 6. Observational evidences From Biviano&Poggianti (2009) 2 cluster sets z 0 (59 ENACS clusters) z 0.6 (15 EDisCS + 4 MORPHS clusters) 2566 galaxies 556 galaxies
  7. 7. Observational evidences From Biviano&Poggianti (2009) 2 cluster sets z 0 (59 ENACS clusters) z 0.6 (15 EDisCS + 4 MORPHS clusters) 2566 galaxies 556 galaxies 2 populations Emission lines No emission lines
  8. 8. The anisotropy profile low-zt high-zt
  9. 9. The anisotropy profile 2566 low-zt high-zt Isotropy Isotropy 0.6 radial anisotropy radial anisotropy radial anisotropy (?)
  10. 10. Their explanation • Non-emission-line galaxies have been around the cluster environment for longer • Emission-line galaxies have only recently entered and retain memory of their infall
  11. 11. Cautionary remarks • Large uncertainties • Jeans analysis (Spherical symmetry, dynamical equilibrium, collisionless dynamics)
  12. 12. Millennium + SAMs
  13. 13. Millennium + SAMs 1000 clusters with M200 > 2 x 1014 Msun 1 million galaxies Colour Star formation Age
  14. 14. Anisotropy at z=0 Global values: β = 0.257± 0.03 β = 0.352± 0.04 β = 0.191± 0.03 Populations selected by colour: u-i>2.5 / u-i<2.5
  15. 15. Member galaxies of the high-z clusters Progenitors of z=0 galaxies at high z Anisotropy at z>0
  16. 16. Anisotropy at z>0 Galaxies surviving till z=0 are characterised by a much lower β at high z with respect to the full population (particularly evident for galaxies that are blue at z=0)
  17. 17. Anisotropy at infall Member galaxies of the high-z clusters Progenitors of z=0 galaxies at high z Progenitors of blue gals at z=0 Progenitors that are blue at infall
  18. 18. Anisotropy at infall Progenitors of blue gals at z=0 Progenitors that are blue at infall Galaxies surviving till z=0 enter the clusters with a much lower β The anisotropy at infall grows going towards z=0
  19. 19. Anisotropy vs. infall time Infall (see previous plot) z = 0.7 (6.1 Gyrs) z = 0.5 (5 Gyrs) z = 0.3 (3.5 Gyrs) z = 0.2 (2.4 Gyrs) z = 0.1 (1.4 Gyrs) z = 0 Anisotropy of galaxies grouped by zinfall
  20. 20. Anisotropy vs. infall time Infall (see previous plot) The anisotropy of galaxies increases after entering the cluster (especially in the first 2 Gyrs)
  21. 21. Why does the anisotropy increase in time?
  22. 22. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity
  23. 23. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity what about the mass of the cluster?
  24. 24. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity
  25. 25. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity
  26. 26. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity CASE A
  27. 27. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity CASE A
  28. 28. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity CASE A
  29. 29. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity CASE A CASE B
  30. 30. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity CASE A CASE B
  31. 31. Individual orbits 500 galaxies and their full history integrate the orbits given initial position and velocity CASE A CASE B
  32. 32. Individual orbits - examples Mass inside rsatellite vs. time_________ orbit ____ bound orbit original orbit CASE A - fixed mass CASE B - varying mass 1.5 · 1014 M 4.9 · 1014 M
  33. 33. Individual orbits - examples _________ orbit ____ bound orbit Mass inside rsatellite vs. time 3.4 · 1014 M 5.2 · 1014 M
  34. 34. Individual orbits - examples _________ orbit ____ bound orbit Mass inside rsatellite vs. time 7 · 1013 M 2.7 · 1014 M
  35. 35. Individual orbits - examples Mass inside rsatellite vs. time _________ orbit ____ bound orbit 1.6 · 1014 M 9.8 · 1013 M
  36. 36. Individual orbits - examples Mass inside rsatellite vs. time _________ orbit ____ bound orbit 8 · 1013 M 1.4 · 1014 M
  37. 37. Evolution of circularityN(η)dη Circularity (η) initial distribution final distribution Te η = 1 − e2
  38. 38. Evolution of circularityN(η)dη Circularity (η) initial distribution final distribution Temedianinit 0.48 medianfinal 0.26 medianinit 0.31 medianfinal 0.5 η = 1 − e2
  39. 39. Summary • At z=0, blue galaxies have lower β than red galaxies • Galaxies that are blue at z=0 entered the cluster with a much lower β than average • The anisotropy of member galaxies increases once these enter the cluster environment (It could be a natural evolution of the orbits when sgalaxies move in an ever-deeper potential well)
  40. 40. θ θ θ ν ¯v ¯v ¯v true anomaly angle between the state vectors
  41. 41. Miscellaneous
  42. 42. Maybe a hint from Rocha et al. (2011)? Figure 5. Tangential velocity as a function of infall time for subsamples of subhalos with similar radial velocities and galactocentric distances to those of the given dwarf galaxies. The subsample selection criterion is the same as in Fig. 4. The 1-sigma uncertainties in the proper motions are represented by the shaded regions. The addition of proper motion constraints provides a better estimate of the infall time than radial velocity alone.
  43. 43. Simulations
  44. 44. Simulations • Very similar anisotropy profiles at z=0 (both shape and global β) • No evidence of evolution at higher z • No evidence of progenitors having higher β than their z=0 descendants
  45. 45. Jeans analysis & BP09
  46. 46. Jeans analysis Observables N(Rn) σlos(Rn) N(Rn) 2D 3D Abel inversion equation ν(rn) σlos(Rn) = f(N(Rn), ν(rn), M(rn), β(rn)) Mass-anisotropy degeneracy Binney & Mamon 1982 Binney &Tremaine 1987 van der Marel 1994
  47. 47. Jeans analysis Assume models for NFW - concentration c Mamon-Lokas or Osipkov-Merritt - anisotropy radius a M(rn), β(rn)
  48. 48. Mamon-Lokas or Osipkov-Merritt - anisotropy radius a Assume models for Jeans analysis NFW - concentration c M(rn), β(rn) from Mamon&Lokas (2005) Mamon-Lokas Osipkov-Merritt
  49. 49. Jeans analysis Use 2 independent tracers of the cluster potential (Battaglia et al. 2008) ELG & nELG Solve the equations separately for each component Minimise χ2 = χ2 nELG + χ2 ELG c Use c and do it again a and a
  50. 50. In practice 2566 low-zt high-zt N(Rn) NFW, c = 2.4 NFW, c = 7.5 core model NFW, c = 2.7
  51. 51. In practice 2566 low-zt high-zt σlos(Rn)
  52. 52. In practice 2566 low-zt high-zt σlos(Rn) c = 4 OM, a = 3.6 OM, a = 1.3 c = 3.2 ML, a = 0.01 ML, a = 0.01 Results of the Jeans analysis

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