GC I []

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====== GC I ======

===== Challenge 1: Equal mass clusters in a tidal field =====

^ ^ ^  All Stars ^^^^ 1000 stars^^^^
^ Cluster ^ Method             ^$M$^$r_{\rm c}$^$r_{\rm h}$^$r_{\rm J}$ ^ $M$^$r_{\rm c}$^$r_{\rm h}$^$r_{\rm J}$^
|1 | Isotropic King (linear dens) | $0.919$ |         | $1.190$ |           | 
|  | Isotropic King (log dens)    |         | $0.046$ | $1.61$  |           | 
|  | Anisotropic Michie King      |         | $0.027$ | $1.55$  |           |  
|  | $f_\nu$              | $1.082$ |           | $1.134$ |           | 
|2 | Isotropic King (linear dens) | $0.875$ |           | $1.322$ |           | 
|  | Isotropic King (log dens)|       | $0.04$ | $1.752$ |           | 
|  | Anisotropic Michie King   |   |  $0.026$ | $1.618$ |           |  
|  | $f_\nu$              | $1.023$ |           | $1.314$ |           | 
|3 | Isotropic King (linear dens) | $0.227$ |           | $6.839$ |           | 
|  | Isotropic King (log dens) |   | $0.28$ | $7.655$ |           | 
|  | Anisotropic Michie King   |   |           |           |           |  
|  | $f_\nu$              | $0.259$ |           | $8.225$ |           | 

^ Cluster  ^ Plots ^
|1 | Isotropic King vs $f_\nu$ |{{:data:ch1_1_new.png?250}} |
|  | Anisotropic Michie King   |{{:t1c1.png?250}} |  
|2 | Isotropic King vs $f_\nu$           | {{:data:collisional_Ch1_2.png?250}} | 
|  | Anisotropic Michie King   | {{:data:t1c2.png?250}} |  
|3 | Isotropic King vs $f_\nu$ |   {{:data:collisional_Ch1_3.png?250}}| 
|  | Anisotropic Michie King   | {{:data:t1c3.png?250}} |    

  
===== Challenge 2: Isolated models with stellar evolution =====
Active participants: Alice Zocchi, Antonio Sollima, Matt Walker, ,  Laura Watkins, Glenn van de Ven, Pascal Steger?

How important is the effect of mass segregation?

  - How correct is the assumption of energy equipartition (i.e. multi-mass King models)?
  - How different are the fits when considering: 1.) all stars, 2.) only visible stars
  - Is it better to consider luminosity weighted profiles, or number density profiles?
  - How much can we do with 2 velocity components instead of 1 (i.e. with Gaia data)?


==== Description of the models: ====

(Based on simulations ran by Mark Gieles, not published)\\
Here we consider 2 clusters:

  - IC: Cored gamma/eta model, N = 1e5, Kroupa (2001) mass function between 0.1-100 Msun.
  - No primordial binaries, no central black hole, no tidal.
  - Stellar evolution and mass-loss according to Hurley et al. (2000, 2002)
  - Two values for the metallicity of the stars: [Fe/H] = -2.0 and 0.0 (solar)

Below are 2 snapshots at an age of roughly 12 Gyr. The columns are:

^ $m$    ^ $X$ ^ $Y$ ^ $Z$ ^ $V_x$ ^ $V_y$ ^ $V_z$ ^ $\log T_{EFF}$ ^ $M_{bol}$ ^ KSTAR ^
| [Msun] | [PC] |||  [km s-1]  ||| [K] |[MAG]|

KSTAR is the stellar type and can be between 0 and 22 and the meanings are given below in the Appendix.

  - {{:ETA3_SEV_N100K_ISO_FEH-0.0_T12656.gz}}
  - {{:ETA3_SEV_N100K_ISO_FEH-2.0_T12892.gz}} 

Cluster properties:

^ Cluster ^ Mass      ^ Radii ^^^^ rms velocities^^^^
|    | |$r_{\rm h}$(3D,M)|$r_{\rm h}$(2D,L)|$r_{\rm h}$(2D,M)|$r_{\rm h}$(2D,N)|$v_{\rm rms}$|$v_{\rm rms}$(Giants)|
|    |[$M_\odot$]     |      [pc]       |     [pc]        | [pc]    | [pc] |[km/s]|[km/s]|
|1   |$3.34\times10^4$| 9.73            | 3.33            | 7.27    | 10.0 | 2.39 | 2.52|
|2   |$3.33\times10^4$| 10.9            | 4.71            | 8.20    | 11.3 | 2.30 | 2.67|

Density distribution for cluster 2: {{:data:collisional_rho.png?250}}

==== (PRELIMINARY) RESULTS: ====

^ ^ ^  All Stars ND ^^^ All Stars Mass^^^ All Stars Lum^^^
^ Cluster ^ Method             ^$M$^$r_{\rm h}$^$R_{\rm h}$^$M$^$r_{\rm h}$^$R_{\rm h}$^$M$^$r_{\rm h}$^$R_{\rm h}$^$R_{\rm h}$
|1 | isotropic King            | $3.17*10^4$  | $11.76$ | $8.67$ | $3.03*10^4$ | $9.06$ | $6.66$ | $3.07*10^4$ | $8.63$ | $6.39$ | 
|  | Multi-mass King           |   |           |    |           |  
|  | $f_\nu$                   | $3.80*10^4$  | $12.88$ | $9.66$ | $3.54*10^4$ | $9.00$ | $6.73$ | $3.08*10^4$ | $3.31$ | $2.48$ |
|  | Parametric Jeans          |   |           |    |           | 
|  | Discrete Jeans            |   |           |    |           | 
|2 | Isotropic King            | $3.07*10^4$  | $14.27$ | $10.55$ | $2.72*10^4$ | $11.69$ | $8.32$ | $2.93*10^4$ | $11.13$ | $8.19$ |
|  | Multi-mass  King          |   |           |    |           |  
|  | $f_\nu$                   | $3.71*10^4$ | $14.66$ | $11.03$ | $3.66*10^4$ | $11.07$ | $8.26$ | $3.30*10^4$ | $6.08$ | $4.50$ |
|  | Parametric Jeans          |   |           |    |           | 
|  | Discrete Jeans            |   |           |    |           | 



===== Challenge 3: Clusters in tidal fields with stellar evolution =====
(Simulations ran and kindly made available by Holger Baumgardt)\\

Here we consider 2 clusters which are slightly more realistic:

  - IC: King (1966) W_0 = 5 model, N = 131072, Kroupa (2001) mass function between 0.1-15 Msun (no black-holes).
  - No primordial binaries, no central black hole, circular orbit in logarithmic halo with V = 220 km/s.
  - Z = 0.001
  - Stellar evolution and mass-loss according to Hurley et al. (2000, 2002)
  - Two Galactocentric radii: 8.5 kpc and 15 kpc.


Below are 2 snapshots at an age of roughly 10 Myr, 100 Myr, 1Gyr and 12 Gyr. The columns are the same as in Challenge 2.

  - {{:data:W05_N131K_RG8.5_FEH-0.0_T10.gz}} UPDATED! Thursday August 22
  - {{:data:W05_N131K_RG8.5_FEH-0.0_T100.gz}} UPDATED! Thursday August 22
  - {{:data:W05_N131K_RG8.5_FEH-0.0_T1000.gz}} UPDATED! Thursday August 22
  - {{:W05_N131K_RG8.5_FEH-0.0_T12000.gz}}
  - {{:data:W05-N131K_RG15_FEH-0.0.T10.gz}} NEW! Tuesday August 20
  - {{:data:W05-N131K_RG15_FEH-0.0.T100.gz}} NEW! Tuesday August 20
  - {{:data:W05-N131K_RG15_FEH-0.0.T1000.gz}} NEW! Tuesday August 20
  - {{:W05_N131K_RG15_FEH-0.0_T12000.gz}}

Questions are the same as in Challenge 2, and in addition:
  - Is the presence of the tidal field affecting the velocity anisotropy in the outer parts?
  - Can the mass segregation be reproduced by multi-mass King models? 

 Example of the velocity dispersion difference of different mass components:
{{:data:sig2ratio.png?250}}

Different models to fit:
  - $f_\nu$
  - Multi-mass King
  - Discrete "Jeans like" modelling
  - DF fitting (Mark W?)

==== Results: ====
Using all stars:
^ ^ ^ ^  All Stars ^^^^ 1000 stars^^^^
^ Cluster ^ Snapshot ^ Method             ^$M$^$r_{\rm c}$^$r_{\rm h}$^$r_{\rm J}$ ^ $M$^$r_{\rm c}$^$r_{\rm h}$^$r_{\rm J}$^
|1 | 1 | Isotropic King   |  |         | |           | 
|  | 1 | Multimass Michie King      |         | |   |           |  
|  | 1 | $f_\nu$              |  |           | |           | 
|  | 1 | Discrete modelling        |   |           |           |           | 
|1 | 2 | Isotropic King   |  |         | |           | 
|  | 2 | Multimass Michie King      |         | |   |           |  
|  | 2 | $f_\nu$              |  |           | |           | 
|  | 2 | Discrete modelling        |   |           |           |           | 
|1 | 3 | Isotropic King   |  |         | |           | 
|  | 3 | Multimass Michie King      |         | |   |           |  
|  | 3 | $f_\nu$              |  |           | |           | 
|  | 3 | Discrete modelling        |   |           |           |           | 
|1 | 4 | Isotropic King   |  |         | |           | 
|  | 4 | Multimass Michie King | $2.118$ |  | $11.353$ |  |  
|  | 4 | $f_\nu$              |  |           | |           | 
|  | 4 | Discrete modelling        |   |           |           |           | 
|2 | 1 | Isotropic King   |  |         | |           | 
|  | 1 | Multimass Michie King      |         | |   |           |  
|  | 1 | $f_\nu$              |  |           | |           | 
|  | 1 | Discrete modelling        |   |           |           |           | 
|2 | 2 | Isotropic King   |  |         | |           | 
|  | 2 | Multimass Michie King      |         | |   |           |  
|  | 2 | $f_\nu$              |  |           | |           | 
|  | 2 | Discrete modelling        |   |           |           |           | 
|2 | 3 | Isotropic King   |  |         | |           | 
|  | 3 | Multimass Michie King      |         | |   |           |  
|  | 3 | $f_\nu$              |  |           | |           | 
|  | 3 | Discrete modelling        |   |           |           |           | 
|2 | 4 | Isotropic King   |  |         | |           | 
|  | 4 | Multimass Michie King      |         | |   |           |  
|  | 4 | $f_\nu$              |  |           | |           | 
|  | 4 | Discrete modelling        |   |           |           |           | 

Plots
^ Cluster  ^ Plots ^
|1 | 1 | Isotropic King vs $f_\nu$ | |
|  | 1 | Multimass Michie King   | |  
|  | 1 | Discrete modelling        | | 
|1 | 2 | Isotropic King vs $f_\nu$ | |
|  | 2 | Multimass Michie King   | |  
|  | 2 | Discrete modelling        | | 
|1 | 3 | Isotropic King vs $f_\nu$ | |
|  | 3 | Multimass Michie King   | |  
|  | 3 | Discrete modelling        | | 
|1 | 4 | Isotropic King vs $f_\nu$ | |
|  | 4 | Multimass Michie King   |{{:data:t3c1.png?250}} |  
|  | 4 | Discrete modelling        | | 
|2 | 1 | Isotropic King vs $f_\nu$ | |
|  | 1 | Multimass Michie King   | |  
|  | 1 | Discrete modelling        | | 
|2 | 2 | Isotropic King vs $f_\nu$ | |
|  | 2 | Multimass Michie King   | |  
|  | 2 | Discrete modelling        | | 
|2 | 3 | Isotropic King vs $f_\nu$ | |
|  | 3 | Multimass Michie King   | |  
|  | 3 | Discrete modelling        | | 
|2 | 4 | Isotropic King vs $f_\nu$ | |
|  | 4 | Multimass Michie King   | |  
|  | 4 | Discrete modelling        | | 

==== Results: ====
Velocity dispersion for different mass species: the multi-mass King models assume that the product $m\sigma_K^2$= constant. The parameters $\sigma_K$ is not exactly the velocity dispersion.