====== Challenge 1: single mass clusters ======

==== Isolated models: ====

The N-body models can be described as: 

  - Initial conditions: Plummer (1911), N = 32768, all stars the same mass
  - No primordial binaries, no central black hole
  - Isolation
 
The data has the following format. Note that the first column can be used to recognise binaries (MN=2). The single components of the binaries are not given.
^ $M\times N$ ^ $X$ ^ $Y$ ^ $Z$ ^ $V_x$ ^ $V_y$ ^ $V_z$ ^ 
|  [NBODY] |  [NBODY]  |||    [NBODY]   |||      

  - {{:data:32k_logt4.tab.gz}} $T=10^4$
  - {{:data:32k_logt5.tab.gz}} $T=10^5$
  - {{:data:32k_logt6.tab.gz}} $T=10^6$
  - {{:data:32k_logt7.tab.gz}} $T=10^7$

==== Tidally limited 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

Update 14-Oct-2014: More snapshots for this model (roughly) equally spaced by $5\times10^4$ $N$-body times covering the entire life-cycle:

  - {{:data:PL_EQ_N64K_RJRH100_T050010.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T100020.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T150020.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T200020.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T250020.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T300030.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T350520.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T400020.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T450510.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T500010.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T550500.gz}} 

Update: 29 Okt 2014: New version of the 10 snapshots above:
  - Removed the individual components of binaries, and added the binary com pos and vel in the end of the file
  - New first column with MxN = 1 for single stars and MxN = 2 for binaries
  - New column (8) = 1 if r<rt 
  - New column (9) = 1 if E_Jacobi < E_crit 

Update 29-Nov-2014: 
   - Fixed bug in energy computation
   - New column (8): phi (= specific potential)
   - New column (9); E_J = jacobi energy (see e.g. Fukushige & Heggie (2000), below equation 3)
   - Added top line with: N, rt, E_crit 

First line: N, rt, E_crit
^ $M\timesN$ | $X$ ^ $Y$ ^ $Z$ ^ $V_x$ ^ $V_y$ ^ $V_z$ ^ $\phi$ ^ $E_J$ ^ r < rt ^ E<Ecrit ^ 
| [NBODY] |  [NBODY]  |||    [NBODY]   |||[NBODY]|[NBODY]|0 or 1 | 0 or 1 |      

  - {{:data:PL_EQ_N64K_RJRH100_T050010.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T100020.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T150020.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T200020.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T250020.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T300030.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T350520.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T400020.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T450510.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T500010.new.gz}} 
  - {{:data:PL_EQ_N64K_RJRH100_T550500.new.gz}} 


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?600}}


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|