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On the orbital velocity
anisotropy of cluster galaxies
Francesca Iannuzzi
MPA
How does the anisotropy profile
evolve in time for different
galaxy populations?
Anisotropy
β = 1 −
σ2
t
σ2
r
Anisotropy
Circular orbits
β = 1 −
σ2
t
σ2
r
β = −∞ β = 1
Radial orbits
Anisotropy
Circular orbits
β = 1 −
σ2
t
σ2
r
β = −∞ β = 1
Radial orbits
β 0
“Isotropy”
Observational evidences
From Biviano&Poggianti (2009)
2 cluster sets
z 0
(59 ENACS clusters)
z 0.6
(15 EDisCS + 4 MORPHS c...
Observational evidences
From Biviano&Poggianti (2009)
2 cluster sets
z 0
(59 ENACS clusters)
z 0.6
(15 EDisCS + 4 MORPHS c...
The anisotropy profile
low-zt high-zt
The anisotropy profile
2566
low-zt high-zt
Isotropy
Isotropy
0.6
radial
anisotropy
radial anisotropy
radial anisotropy (?)
Their explanation
• Non-emission-line galaxies have been
around the cluster environment for longer
• Emission-line galaxie...
Cautionary remarks
• Large uncertainties
• Jeans analysis
(Spherical symmetry, dynamical equilibrium, collisionless dynami...
Millennium + SAMs
Millennium + SAMs
1000 clusters with M200 > 2 x 1014 Msun
1 million galaxies
Colour
Star formation
Age
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 /...
Member galaxies
of the high-z clusters
Progenitors of z=0 galaxies
at high z
Anisotropy at z>0
Anisotropy at z>0
Galaxies surviving till z=0 are characterised by a much lower β at
high z with respect to the full popul...
Anisotropy at infall
Member galaxies
of the high-z clusters
Progenitors of z=0 galaxies at high z
Progenitors of blue gals...
Anisotropy at infall
Progenitors of blue gals at z=0
Progenitors that are blue at infall
Galaxies surviving till z=0 enter...
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 ...
Anisotropy vs. infall time
Infall
(see previous plot)
The anisotropy of
galaxies increases
after entering the
cluster
(esp...
Why does the anisotropy
increase in time?
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
what about ...
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
CASE A
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
CASE A
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
CASE A
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
CASE A CASE...
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
CASE A CASE...
Individual orbits
500 galaxies and their full history
integrate the orbits given initial position and velocity
CASE A CASE...
Individual orbits - examples
Mass inside rsatellite vs. time_________ orbit
____ bound orbit
original orbit
CASE A - fixed ...
Individual orbits - examples
_________ orbit
____ bound orbit
Mass inside rsatellite vs. time
3.4 · 1014
M
5.2 · 1014
M
Individual orbits - examples
_________ orbit
____ bound orbit
Mass inside rsatellite vs. time
7 · 1013
M
2.7 · 1014
M
Individual orbits - examples
Mass inside rsatellite vs. time
_________ orbit
____ bound orbit 1.6 · 1014
M
9.8 · 1013
M
Individual orbits - examples
Mass inside rsatellite vs. time
_________ orbit
____ bound orbit
8 · 1013
M
1.4 · 1014
M
Evolution of circularityN(η)dη
Circularity (η)
initial distribution
final distribution
Te
η = 1 − e2
Evolution of circularityN(η)dη
Circularity (η)
initial distribution
final distribution
Temedianinit 0.48
medianfinal 0.26
me...
Summary
• At z=0, blue galaxies have lower β than red galaxies
• Galaxies that are blue at z=0 entered the cluster
with a ...
θ
θ
θ
ν
¯v
¯v
¯v
true anomaly
angle between the state vectors
Miscellaneous
Maybe a hint from Rocha et al. (2011)?
Figure 5. Tangential velocity as a function of infall time for subsamples of subhal...
Simulations
Simulations
• Very similar anisotropy profiles at z=0
(both shape and global β)
• No evidence of evolution at higher z
• N...
Jeans analysis & BP09
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...
Jeans analysis
Assume models for
NFW - concentration c
Mamon-Lokas or Osipkov-Merritt - anisotropy radius a
M(rn), β(rn)
Mamon-Lokas or Osipkov-Merritt - anisotropy radius a
Assume models for
Jeans analysis
NFW - concentration c
M(rn), β(rn)
f...
Jeans analysis
Use 2 independent tracers of the cluster potential
(Battaglia et al. 2008)
ELG & nELG
Solve the equations s...
In practice
2566
low-zt high-zt
N(Rn)
NFW, c = 2.4 NFW, c = 7.5
core model
NFW, c = 2.7
In practice
2566
low-zt high-zt
σlos(Rn)
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 Je...
anisotropy
anisotropy
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  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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