DOI: 10.5281/zenodo.15283074
title: Underlying data for the paper: Rapid formation of a very massive star $>50000 \mathrm{M}_{\odot}$ and subsequently an IMBH from runaway collisions

description: This dataset includes important input, output, and diagnostic files from both NBODY6++GPU and MOCCA simulations of a dense star cluster with 1 million stars and initial half-mass radius of 0.1 pc. The results from this simulation are presented in the paper: https://arxiv.org/abs/2505.07491
Initial N-body model and input





dat.10: file for the input model that was read by NBODY6++GPU. The same initial model was also read by MOCCA. The dat.10 file contains 10 columns, the first one is mass in N-body units. The next 6 columns are x,y,z positions and vx, vy, vz velocities. The 8th column is SSE epoch of the star (set to 0.0) and the 9th column is the metallicity of the star (Z=0.01 for all stars) and the last column is population ID (set to 1 for all stars).




 mcluster.out: Log file from the mcluster code used to generate the initial model for the N-body run



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N-body Simulation Output (files in the compressed directory: nbody-output-files.zip)

1. avmass.dat

Tracks the evolution of the average mass inside the Lagrangian radii (with the VMS/IMBH). 

Columns in order: time [NB], mass fraction(%): 0.1, 0.3, 0.5, 1, 3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99, 100.2. rlgra.dat

Tracks the evolution of the Lagrangian radii (with the VMS/IMBH). 

Columns in order: time [NB], lagragian (%): 0.1, 0.3, 0.5, 1, 3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99, 100.3. esc.datLists stars escaping from the cluster within the first 5 Myr.

Columns in order: time [Myr], Mass [M$_\odot$], Velocity [km/s], Stellar type.4. coll.dat

List of collisions within the cluster within the first 5 Myr.

Columns in order: type of collision, time [NB], ID first star, ID second star, mass first star [M$_\odot$], mass second star [M$_\odot$],  final mass [M$_\odot$].

5. pos_vel.dat

List of positions and velocities of the VMS/IMBH in each coordinate.

Columns in order: time [NB], x[pc], y[pc], z[pc], vx[km/s], vy[km/s], vz[km/s], ID6. vms.datList of stellar evolution data for the VMS/IMBH.

Columns in order: time [NB], stellar type, mass [M$_\odot$], log(radius) [R$_\odot$], age [Myr]

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 MOCCA Simulation Output (files in the compressed directory: mocca-output-files.zip)

1. history-499690.dat

The first 207 lines are header lines describing the model. Line 208 is a header line which describes the column in this file. All header lines begin with #. This file contains the complete history of events for the star which becomes the VMS and subsequently an IMBH.

Key columns:



Column 1: Linetype - String to describe the event for which the information is provided in the line (e.g., SIN_EVOL is single stellar evolution, COLLISION is a 2-body collision,  BIN_STAR is binary single interaction)



Column 4: Time [Myr]




Column 6: Star ID




Column 10: Initial stellar mass before interaction [M$_\odot$]




Column 11: Final stellar mass after interaction [M$_\odot$]




Column 13: Distance from cluster center [pc]




Column 19: Stellar type (SSE/BSE)


Column 20: Stellar type of the merging star (if there is a COLLISION event in column 1)



Column 26: Mass of the merging star (if there is a COLLISION event in column 1) [M$_\odot$]




Column 29: Final radius of the VMS [R$_\odot$]



2. evol-sin-restart-499690.datThis file contains detailed stellar evolution data for the VMS at time step.

Columns (in order):





Time [Myr]




Star ID




Stellar type (SSE/BSE)




Mass [M$_\odot$]




Radius [R$_\odot$]




Physical time [Myr]




SSE/BSE epoch




Bolometric luminosity [L$_\odot$]




Core mass [M$_\odot$]




Core radius [R$_\odot$]




Envelope mass [M$_\odot$]




Envelope radius [R$_\odot$]




Stellar age = (physical time – epoch) [Myr]



3. system.datStandard MOCCA output file containing global cluster properties over time. Column descriptions are provided in the file header that are prefixed with # and describe each column. The first 2498 lines are these header lines which describe the 572 columns that are in this output file. The physical time of the simulation in Myr is in column 2.

4. lagrangi.datTracks the evolution of Lagrangian radii (with and without the VMS/IMBH). Column descriptions are provided in the header lines which start with #. There are 47 columns which are described in the first 190 lines of this file.

5. escape-5myr.datLists stars escaping from the cluster within the first 5 Myr.

Columns in order:





 Escape time [Myr]




Mass of component 1 [M$_\odot$]




Mass of component 2 [M$_\odot$] (0.0 for single escapers)




Stellar type of component 1 (SSE/BSE)




Stellar type of component 2 (SSE/BSE)




Total escaping mass [M$_\odot$]



















The integer values for SSE/BSE stellar types are explained below:0 - Fully convective low-mass MS star (M < 0.7 M$_\odot$)1 - Main Sequence star (M > 0.7 M☉)2 - Hertzsprung Gap (subgiant star)3 - First Giant Branch4 - Core Helium Burning5 - First Asymptotic Giant Branch6 - Second Asymptotic Giant Branch7 - Main Sequence Naked Helium star8 - Hertzsprung Gap Naked Helium star9 - Giant Branch Naked Helium star10 - Helium White Dwarf11 - Carbon/Oxygen White Dwarf12 - Oxygen/Neon White Dwarf13 - Neutron Star14 - Black Hole