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Table of Contents
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, Laura Watkins?
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]
- $f_\nu$ Bertin & Trenti (2003); 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 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] | ||||
- 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:
- 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:
| 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 $f_\nu$ |  |
| Anisotropic Michie King |  |
|
| Discrete modelling | ||
| 2 | Isotropic King vs $f_\nu$ |  |
| Anisotropic Michie King |  |
|
| Discrete modelling | ||
| 3 | Isotropic King vs $f_\nu$ |  |
| Anisotropic Michie King |  |
|
| Discrete modelling |
Challenge 2: Isolated models with stellar evolution
Active participants: Alice Zocchi, Antonio Sollima, Matt Walker, 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.
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: 
(PRELIMINARY) RESULTS:
| All Stars ND | All Stars Mass | All Stars Lum | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cluster | Method | $M$ | $r_{\rm h}$ | $R_{\rm h}$ | $M$ | $r_{\rm h}$ | $R_{\rm h}$ | $M$ | $r_{\rm h}$ | $R_{\rm h}$ | |||
| 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.
- w05_n131k_rg8.5_feh-0.0_t10.gz UPDATED! Thursday August 22
- w05_n131k_rg8.5_feh-0.0_t100.gz UPDATED! Thursday August 22
- w05_n131k_rg8.5_feh-0.0_t1000.gz UPDATED! Thursday August 22
- w05-n131k_rg15_feh-0.0.t10.gz NEW! Tuesday August 20
- w05-n131k_rg15_feh-0.0.t100.gz NEW! Tuesday August 20
- w05-n131k_rg15_feh-0.0.t1000.gz NEW! Tuesday August 20
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?
Different models to fit:
- $f_\nu$
- Multi-mass King
- Discrete “Jeans like” modelling
- DF fitting (Mark W?)
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:
- rot_collapse_lam0.127.gz NEW! Tuesday August 20
- rot_collapse_lam0.168.gz NEW! Tuesday August 20
- rot_collapse_lam0.212.gz NEW! Tuesday August 20
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
- 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 Ref1 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 STARLAB and the snapshots are taken at T=20 [NBODY].
- rot_collapse_fracd2.4.gz NEW! Tuesday August 20
- 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)
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.
If posting new tests, please try to approximately follow the template set out for the “spherical collisionless tests” here.