The mock data is a snapshots of large $N$-body simulation of the globular cluster M4 are available here. Full lists of data for all particles (mass, position, velocity, stellar type, stellar radius, V magnitude, B-V colour) are given at almost 400 instants in the lifetime of the model. The simulation is described in the http://arxiv.org/abs/1409.5597, which should be cited when making use of this data.

We selected the snapshot at $t = 12023.9$ Myr and assume that radial/LOS velocities are available for all stars brighter than V=15 (N=1143). A distance modulus of 11.35 mag was adopted (i.e. $D=1862.1$ pc). The cluster properties are:

1. $M = 64255.4\,M_\odot$
2. $L_{V} = 34304.8\,L_{V,\odot}$
3. $M/L_V=1.87$
4. $r_{\rm h} = 3.21\,{\rm pc}$

We do the comparison in 3 steps:

1. Surface brightness profile + RVs
2. Surface brightness profile + RVs + PMs
3. Surface brightness profile + RVs + PMs + Gaia

The data for the 3 fitting steps :

1. Step 1:
   1. Surface brightness: m4_sb.dat.gz
   2. Discrete LOS velocities: m4_rv.dat.gz
   3. LOS velocity dispersion profile: m4_rv_disp.dat.gz
2. Step 2:
   1. Discrete proper motions: m4_pm_mock.dat.gz
   2. Proper motion dispersion profiles: m4_pm_disp_mock.dat.gz

For methods that allow it, you can also use constraints from a mock observed mass function at a projected radius of 300 arcseconds from the centre: m4_mass_function.tab.gz

A number density profile for stars brighter than the main-sequence turnoff (V < 17 mag; corresponding to a turnoff mass of 0.82 solar masses) is also available (m4_number_density.dat.gz). This can be used as an alternative/complement to the surface brightness profile.

The mass profile in projection and the $M/L_V$ ratio in projection can be found here:

1. m4_sigma.dat.gz

The N-body models can be described as:

1. Initial conditions: Plummer (1911), N = 32768, all stars the same mass
2. No primordial binaries, no central black hole
3. 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.

1. 32k_logt4.tab.gz $T=10^4$
2. 32k_logt5.tab.gz $T=10^5$
3. 32k_logt6.tab.gz $T=10^6$
4. 32k_logt7.tab.gz $T=10^7$

The N-body models can be described as:

1. Initial conditions: Plummer (1911), N = 65536, all stars the same mass
2. No primordial binaries, no central black hole
3. 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 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:

1. pl_eq_n64k_rjrh100_t012102.gz : In a core minimum just after core collapse [NEW: 19 Aug, 16:15]
2. pl_eq_n64k_rjrh100_t013650.gz : In a core maximum
3. 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:

1. pl_eq_n64k_rjrh100_t050010.gz
2. pl_eq_n64k_rjrh100_t100020.gz
3. pl_eq_n64k_rjrh100_t150020.gz
4. pl_eq_n64k_rjrh100_t200020.gz
5. pl_eq_n64k_rjrh100_t250020.gz
6. pl_eq_n64k_rjrh100_t300030.gz
7. pl_eq_n64k_rjrh100_t350520.gz
8. pl_eq_n64k_rjrh100_t400020.gz
9. pl_eq_n64k_rjrh100_t450510.gz
10. pl_eq_n64k_rjrh100_t500010.gz
11. pl_eq_n64k_rjrh100_t550500.gz

Update: 29 Okt 2014: New version of the 10 snapshots above:

1. Removed the individual components of binaries, and added the binary com pos and vel in the end of the file
2. New first column with MxN = 1 for single stars and MxN = 2 for binaries
3. New column (8) = 1 if r<rt
4. New column (9) = 1 if E_Jacobi < E_crit

Update 29-Nov-2014:

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

First line: N, rt, E_crit

1. pl_eq_n64k_rjrh100_t050010.new.gz
2. pl_eq_n64k_rjrh100_t100020.new.gz
3. pl_eq_n64k_rjrh100_t150020.new.gz
4. pl_eq_n64k_rjrh100_t200020.new.gz
5. pl_eq_n64k_rjrh100_t250020.new.gz
6. pl_eq_n64k_rjrh100_t300030.new.gz
7. pl_eq_n64k_rjrh100_t350520.new.gz
8. pl_eq_n64k_rjrh100_t400020.new.gz
9. pl_eq_n64k_rjrh100_t450510.new.gz
10. pl_eq_n64k_rjrh100_t500010.new.gz
11. 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:

1. 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:

Properties of the clusters:

Data: Snapshots of simulations with a mass function.

1. N <~= $10^5$, initial half-mass radius 2.25 pc, Henon isochrone model
2. Initial half-mass relaxation time =~ 350 Myr
3. no primordial binaries
4. Galaxy = singular isothermal sphere with Vc = 220 kms/s
5. Orbit: circular orbit at RG = 4 kpc

The $10^5$ stars were evolved with SSE (Hurley et al. 2000) to an age of 12 Gyr assuming a metallicity of [Fe/H] = -2 before the N-body model was run. Then an assumption was made about the retention fraction of neutron stars (NSs) and black holes (BHs). The snapshots contain all the stars within the tidal radius.

The properties of the snapshots are:

Format of the snapshots are:

1. gc1_1gyr.gz :
2. gc1_2gyr.gz :
3. gc1_3gyr.gz :
4. gc1_4gyr.gz :
5. gc1_5gyr.gz :
6. gc1_6gyr.gz :
7. gc1_7gyr.gz :
8. gc1_8gyr.gz :
9. gc1_9gyr.gz :
10. gc1_10gyr.gz :
11. gc1_11gyr.gz :

No retention:

1. gc2_1gyr.gz :
2. gc2_2gyr.gz :
3. gc2_3gyr.gz :
4. gc2_4gyr.gz :
5. gc2_5gyr.gz :
6. gc2_6gyr.gz :
7. gc2_7gyr.gz :
8. gc2_8gyr.gz :
9. gc2_9gyr.gz :
10. gc2_10gyr.gz :
11. gc2_11gyr.gz :
12. gc2_12gyr.gz :

The definition of the stellar types (KSTAR) used in the NBODY6 snapshots can be found in the Appendix.

(Simulations ran and kindly made available by Holger Baumgardt)

Here we consider 2 clusters which are slightly more realistic:

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

1. w05_n131k_rg8.5_feh-0.0_t10.gz UPDATED! Thursday August 22
2. w05_n131k_rg8.5_feh-0.0_t100.gz UPDATED! Thursday August 22
3. w05_n131k_rg8.5_feh-0.0_t1000.gz UPDATED! Thursday August 22
4. w05_n131k_rg8.5_feh-0.0_t12000.gz
5. w05-n131k_rg15_feh-0.0.t10.gz NEW! Tuesday August 20
6. w05-n131k_rg15_feh-0.0.t100.gz NEW! Tuesday August 20
7. w05-n131k_rg15_feh-0.0.t1000.gz NEW! Tuesday August 20
8. w05_n131k_rg15_feh-0.0_t12000.gz

Final list of snapshots used in Sollima et al. in prep, columns are:

1. w5rh11.5r8.5-t0.gz
2. w5rh11.5r8.5-t10024.05.gz
3. w5rh11.5r8.5-t1019.394.gz
4. w5rh11.5r8.5-t11009.46.gz
5. w5rh11.5r8.5-t2004.809.gz
6. w5rh11.5r8.5-t3024.204.gz
7. w5rh11.5r8.5-t4009.618.gz
8. w5rh11.5r8.5-t5029.013.gz
9. w5rh11.5r8.5-t6014.427.gz
10. w5rh11.5r8.5-t7033.822.gz
11. w5rh11.5r8.5-t8019.236.gz
12. w5rh11.5r8.5-t9004.651.gz
13. w5rh1r8.5-t0.gz
14. w5rh1r8.5-t10020.gz
15. w5rh1r8.5-t1020.gz
16. w5rh1r8.5-t11010.gz
17. w5rh1r8.5-t120.gz
18. w5rh1r8.5-t12000.gz
19. w5rh1r8.5-t13020.gz
20. w5rh1r8.5-t2010.gz
21. w5rh1r8.5-t210.gz
22. w5rh1r8.5-t30.gz
23. w5rh1r8.5-t300.gz
24. w5rh1r8.5-t3000.gz
25. w5rh1r8.5-t4020.gz
26. w5rh1r8.5-t420.gz
27. w5rh1r8.5-t5010.gz
28. w5rh1r8.5-t510.gz
29. w5rh1r8.5-t60.gz
30. w5rh1r8.5-t6000.gz
31. w5rh1r8.5-t7020.gz
32. w5rh1r8.5-t8010.gz
33. w5rh1r8.5-t90.gz
34. w5rh1r8.5-t9000.gz

The definition of the stellar types (KSTAR) used in the NBODY6 snapshots can be found in the Appendix.

There 23 possible stellar types (KSTAR) in NBODY

     0       Low main sequence (M < 0.7).
     1       Main sequence.
     2       Hertzsprung gap (HG).
     3       Red giant.
     4       Core Helium burning.
     5       First AGB.
     6       Second AGB.
     7       Helium main sequence.
     8       Helium HG.
     9       Helium GB.
    10       Helium white dwarf.
    11       Carbon-Oxygen white dwarf.
    12       Oxygen-Neon white dwarf.
    13       Neutron star.
    14       Black hole.
    15       Massless supernova remnant.
    19       Circularizing binary (c.m. value).
    20       Circularized binary.
    21       First Roche stage (inactive).
    22       Second Roche stage.