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--- collision [2013/08/22 16:53] – gieles
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-====== Collisional systems / star clusters ======
-These mock data are designed to mimic collisional systems like star/globular clusters.
-**Key working group coordinator:** Mark Gieles
-Below are details of 5 challenges based on data from collisional N-body models.
-===== Challenge 1: Equal mass cluster in a tidal field ====
-Active participants: Alice Zocchi, Antonio Sollima, Mark Gieles
-Questions we will address here:
-  - What is a suitable model to describe post-collapse clusters? We here consider 3 models:
-        - Isotropic King (1966) [Alice]
-        - Anisotropic Michie King [Antonio]
-        - $f_\nu$ [[http://adsabs.harvard.edu/abs/2003ApJ...584..729B|Bertin & Trenti (2003)]]; [[http://adsabs.harvard.edu/abs/2012A%26A...539A..65Z|Zocchi et al. (2012)]] [Alice]
-  - How much does tangential anisotropy/retrograde rotation due to the tides matter? [Mark, Anna Lisa?]
-==== Description of the models: ====
-The N-body models can be described as:
-  - Initial conditions: Plummer (1911), N = 65536, all stars the same mass
-  - No primordial binaries, no central black hole
-  - Circular orbit in a weak tidal field due to a point-mass galaxy with initially r_jacobi/r_h = 100
-The model was ran until complete dissolution (roughly 6e5 N-body times) with Sverre Aarseth's ''NBODY6''. Two-body relaxation drives the evolution: core collapse occurs at roughly T = 1.2e4 and the cluster expands until it fills the Roche-volume roughly half-mass the evolution (T = 3e5). More details about this run can be found [[http://adsabs.harvard.edu/abs/2012MNRAS.422.3415A|Alexander & Gieles (2012)]].
-Below are 3 snapshots at interesting moments of the evolution. The Heggie & Mathieu (1986) N-body units are used: G=M=r_vir=1 (i.e. the mass of individual stars is m=1/65536). The 6 columns contain:
-^ $X$ ^ $Y$ ^ $Z$ ^ $V_x$ ^ $V_y$ ^ $V_z$ ^
-|  [NBODY]  |||    [NBODY]   |||
-  - {{:data:PL_EQ_N64K_RJRH100_T012102.gz}} : In a core minimum just after core collapse [NEW: 19 Aug, 16:15]
-  - {{:PL_EQ_N64K_RJRH100_T013650.gz}} : In a core maximum
-  - {{:PL_EQ_N64K_RJRH100_T323790.gz}} : When ~75% of the stars is lost and the cluster is Roche-filling
-For the last snapshot a table with specific energy and the z-component of the specific angular momentum vector can be found here:
-  - {{:data:PL_EQ_N64K_RJRH100_T323790.EJZ.gz}} : When ~75% of the stars is lost and the cluster is Roche-filling
-Note: the initial Jacobi radius of this model was $r_{\rm J}= 78.17$, such that the angular frequency of the orbit is $\Omega = 8.354\times 10^{-4}$ and the critical energy $E_{\rm crit} = -7.469\times 10^{-3}$ at T=323790 .
-Illustration of the model evolution, moments of the snapshots are marked with dashed lines:
-{{:data:collisional_singlemass_radii.png?300}}
-Properties of the clusters:
-^ Cluster ^ Mass ^ $r_{\rm c}$ ^ $r_{\rm h}$ ^ $r_{\rm J}$ ^
-|1        | 0.975|$5.25\times 10^{-3}$ |1.143| 77.3|
-|2        | 0.953|$8.61\times 10^{-3}$ |1.334| 76.6|
-|3        | 0.238|$0.199$              |6.871| 48.3|
-==== Results: ====
-Using all stars:
-^ ^ ^  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      |         | $0.027$ | $1.55$  |           |
-|  | $f_\nu$              | $1.082$ |           | $1.134$ |           |
-|  | Discrete modelling        |   |           |           |           |
-|2 | Isotropic King (linear dens) | $0.875$ |           | $1.322$ |           |
-|  | Isotropic King (log dens)|       | $0.04$ | $1.752$ |           |
-|  | Anisotropic Michie King   |   |  $0.026$ | $1.618$ |           |
-|  | $f_\nu$              | $1.023$ |           | $1.314$ |           |
-|  | Discrete modelling        |   |           |           |           |
-|3 | Isotropic King (linear dens) | $0.227$ |           | $6.839$ |           |
-|  | Isotropic King (log dens) |   | $0.28$ | $7.655$ |           |
-|  | Anisotropic Michie King   |   |           |           |           |
-|  | $f_\nu$              | $0.259$ |           | $8.225$ |           |
-|  | Discrete modelling        |   |           |           |           |
-Plots
-^ Cluster  ^ Plots ^
-|1 | Isotropic King vs $f_\nu$ |{{:data:ch1_1_new.png?250}} |
-|  | Anisotropic Michie King   |{{:t1c1.png?250}} |
-|  | Discrete modelling        |  |
-|2 | Isotropic King vs $f_\nu$           | {{:data:collisional_Ch1_2.png?250}} |
-|  | Anisotropic Michie King   | {{:data:t1c2.png?250}} |
-|  | Discrete modelling        |  |
-|3 | Isotropic King vs $f_\nu$ |   {{:data:collisional_Ch1_3.png?250}}|
-|  | Anisotropic Michie King   | {{:data:t1c3.png?250}} |
-|  | Discrete modelling        |  |
-===== 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 0.1-100 Msun.
-  - No primordial binaries, no central black hole, circular orbit in logarithmic halo with V = 220 km/s.
-  - [Fe/H] = 0.0 (solar)
-  - 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   | |
-|  | 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.
-===== Challenge 4: Pal 5 model from Andreas Kuepper in streams section =====
-Same analyses as in Challenge 2 and 3, but with cluster on eccentric orbit and "polluting" stars from tidal tails. The models posted in the streams section were not evolved with stellar evolution and for a Hubble time, but Andreas sent me files for that. Will upload them if there is interest.
-===== Challenge 5: Model with initial rotation =====
-Different models with angular momentum are within the group: collapsing spheres, cold fractal collapse, cluster mergers.
-=== Collapse of homogeneous spheres with angular momentum ===
-Below snapshots of 3 cold(ish) collapses of homogeneous spheres with angular momentum. Initial virial ratios and angular momentum were taken from the 3 models described in Gott (1972). The models contain 2e5 stars, a Kroupa IMF between 0.1 and 100 Msun and snapshots are at t=30 [NBODY]. The amount of rotation is quantified with Peebles $\lambda$ parameter in the title:
-  - {{:data:rot_collapse_lam0.127.gz}} NEW! Tuesday August 20
-  - {{:data:rot_collapse_lam0.168.gz}} NEW! Tuesday August 20
-  - {{:data:rot_collapse_lam0.212.gz}} NEW! Tuesday August 20
-[[http://personal.ph.surrey.ac.uk/~mg0033/movies/lam212.avi|visualisation]]
-=== Mergers ===
-Merger between 2 clusters of equal mass, equal containing 1e5 stars, a Kroupa IMF between 0.1 and 100 Msun. The initial orbit of the cluster pair had zero energy and different angular momentum. The
-  - {{:data:rot_merger_lam0.128.gz}} NEW! Tuesday August 20
-For both collapse and mergers collapse contain:
-^ $M$ ^ $X$ ^ $Y$ ^ $Z$ ^ $V_x$ ^ $V_y$ ^ $V_z$ ^
-| [$M_\odot$]  | [NBODY] |||    [NBODY]   |||
-=== Collapse of non-homogeneous spheres with angular momentum ===
-(Based on simulations ran by Anna Lisa Varri, see [[http://adsabs.harvard.edu/abs/2013AAS...22211703G|Ref1 ]] [[http://adsabs.harvard.edu/abs/2013AAS...22211702T|Ref2]])
-Below snapshots of two cold(ish) collapses of isolated spheres with N=64k, equal mass stars, non-homogeneous initial density distribution (fractal dimension D = 2.8, 2.4, as in the file name), and approximate solid-body rotation. The configurations are characterized by the same **initial** values of virial ratio and global angular momentum as in the homogeneous case #3 (with  $\lambda=0.212$). The simulations have been performed with [[http://www.sns.ias.edu/~starlab/|STARLAB]] and the snapshots are taken at T=20 [NBODY].
-   - {{:data:rot_collapse_fracd2.4.gz}} NEW! Tuesday August 20
-   - {{:data:rot_collapse_fracd2.8.gz}} NEW! Tuesday August 20
-The file header contains: N, T, coordinates and velocities of the center of mass. The file format is as follow:
-^ $ID$ ^ $M$ ^ $X$ ^ $Y$ ^ $Z$ ^ $V_x$ ^ $V_y$ ^ $V_z$ ^
-|  | [NBODY]  | [NBODY] |||    [NBODY]   |||
-===== Other challenges =====
-No data is available yet for the following problems:
-  - what is the effect of binary stars?
-  - Is there a dynamical "smoking gun" for an intermediate mass black hole?
-===== Appendix =====
-There 23 possible stellar types (KSTAR) in ''NBODY'' (given in Challenge 2 and 3 above)
-       Low main sequence (M < 0.7).
-       Main sequence.
-       Hertzsprung gap (HG).
-       Red giant.
-       Core Helium burning.
-       First AGB.
-       Second AGB.
-       Helium main sequence.
-       Helium HG.
-       Helium GB.
-       Helium white dwarf.
-       Carbon-Oxygen white dwarf.
-       Oxygen-Neon white dwarf.
-       Neutron star.
-       Black hole.
-       Massless supernova remnant.
-       Circularizing binary (c.m. value).
-       Circularized binary.
-       First Roche stage (inactive).
-       Second Roche stage.
-If posting new tests, please try to approximately follow the template set out for the "spherical collisionless tests" [[:sphtri|here]].