DOI: 10.5281/zenodo.15858711
title: Data for Escaping Binary Black Holes That Will Merge within 14 Gyr from 268 MOCCA models simulated between 2023-2025

description: Each line in the file escaping-merging-BBH-new-MOCCA-models.dat contains information for an escaping binary black hole (BBH) from a diverse set of new MOCCA models simulated between 2023 to 2025. Additionally, we also include the file: escaping-BBH-by-model.dat which provides more information about the star cluster properties and the number of escaping merging binary black holes they produce. This dataset has been used for a manuscript currently in preparation by Yuetong, Askar et al.

The 60 columns in the file escaping-merging-BBH-new-MOCCA-models.dat are described below:

-----------Escaping binary properties------------- * 1 - identifier  - Integer number to indicate that escaping binary comes from a particular model* 2 - t_escp      - Time that the binary escaped in Myrs* 3 - idd1        - MOCCA ID of the first BH component of the binary* 4 - idd2        - MOCCA ID of the second BH (if idd1 and idd2 differ by 1 then binary is primordial otherwise it formed dynamically)* 5 - ik1         - BSE star type binary component 1 (should be 14 for BH)* 6 - ik2         - BSE star type binary component 2 (should be 14 for BH)* 7 - sm1         - Mass of binary component: BH1 (Msun)* 8 - sm2        - Mass of binary component BH2 (Msun)* 9 - ap         -  Semi-major axis at the time of escape (in units of Solar radii)* 10 - ecc        - Eccentricity of the binary at the time of escape

* 11 - escape_vel - Velocity of escaping object in km/s * 12 - escape_dis - Radial Distance inside the cluster before escape (pc)* 13 - escape_ene - Energy of escaping binary [physical units]* 14 - escang     - total angular momentum of the escaping object [pc*km/s*Msun]* 15 - iekind     - kind of escaping object* 16 - ietype     - reason for escaper ("0 - if some velocity is assigned in relax.f,                         "1 - relaxation case of escape, "2 - twobody case of escape,                         "3 - binsin case of escape", ", 4 - binbin case of escape)* 17 - esctime      - escape time in Myr reported in escape.dat (should be similar/equal to t_escp)* 18 -  mass_ratio    - mass ratio of binary components (q = m_small/m_large)* 19 - chirp_mass      - chirp mass calculated from masses of binary components* 20 -  t_GW_approx    - merger time due to GW radiation in Myr (approximate calculation from Peters formula)* 21 - t_delay_approx - delay time in [Myr] = escape time + t_GW_approx* 22 - hist1 - compact history of binary component 1* 23 - hist2 - compact history of binary component 2* 24 - outputID - output ID of the escaping binary* 25 - nkick - flag for object (NS/BH) which recieved natal kick because of supernovae explosion: (0: no kick 1: kick single star 2: binary cm 3: binary merger 4: binary first component 5: binary second component 6: wd kick 7: GR kick)

-----------Initial cluster properties (T=0)------------- 

* 26 - smt0  - Initial mass of the cluster in units of solar mass* 27 - rh0   - Initial half-mass radius of the cluster model in pc* 28 - rc0   - Initial core radius of the cluster model in pc* 29 - rho0  - Initial central density of the cluster (in units of Solar mass/pc^3)* 30 - u1_0  - Initial central potential of the cluster (scaled to (km/s)^2)* 31 - vc_0  - Initial central velocity of the cluster model in units of km/s (mass weighted)* 32 - rtid_0   - Initial tidal radius of the cluster model in pc* 33 - num_0    - Initial number of objects in the cluster (single+binary) - binary is counted as 1* 34 - nbb_0  - Initial number of binaries in the cluster

-----------Cluster properties at the time the binary escaped------------- 

* 35 - smt_esc  - Mass of the cluster in units of solar mass at escape time* 36 - rh_esc   - Half-mass radius of the cluster model in pc  at escape time* 37 - rc_esc   - Core radius of the cluster model in pc  at escape time* 38 - rho_esc  - Central density of the cluster (in units of Solar mass/pc^3)  at escape time* 39 - u1__esc  - Central potential of the cluster (scaled to (km/s)^2)  at escape time* 40 - vc_esc   - Central velocity of the cluster model in units of km/s (mass weighted)  at escape time* 41 - rt_esc   - Tidal radius of the cluster model in pc at escape time* 42 - num_esc   - Numebr of objects in the cluster at escape time* 43 - nbb_esc   - Numebr of binaries in the cluster at escape time* 44 - max_sbh  - Maximum mass of a single BH in the cluster at escape time (Msun)* 45 - max_bbh  - Maximum mass of a BH in a binary system in the cluster at escape time (Msun)* 46 - max_bbh  - Central surface brightness of the cluster at escape time (in units of Lsun/pc^2)

-----------Cluster properties at 100 Myr ------------- * 47 - time_100  - system.dat time at or just larger than 100 Myr* 48 - smt_100  - Cluster mass at 100 Myr in units of solar mass* 49 - rh_100   - Half-mass radius of the cluster at 100 Myr model in pc* 50 - rc_100   - Core radius of the cluster at 100 Myr model in pc* 51 - rho_100  -  Central density of the cluster at 100 Myr(in units of Solar mass/pc^3)* 52 - u1_100  - Central potential of the cluster at at 100 Myr (scaled to (km/s)^2)* 53 - vc_100  - Central velocity of the cluster model at 100 Myr in units of km/s (mass weighted)* 54 - rtid_100 - Tidal radius of the cluster model at 100 Myr in pc* 55 - num_100  - Number of objects in the cluster (single+binary) at 100 Myr - binary is counted as 1* 56 - nbb_100  - Number of binaries in the cluster at at 100 Myr

* 57 - metallicity - Absolute metallicity of the cluster in Z 

-----------Merger and Delay Time------------- * 58 - t_merge - Merger time due to GW radiation in Myr (full integration of Peters equations; more accurate than column 20)* 59 - t_delay - Actual merger time Escape time + t_merge (in column 47)

* 60 - path to cluster model  - Simulation/workspace path containing the simulated cluster data

------------------------------------------------------------------------------------------------------------------The description of the 32 columns in the file escaping-BBH-by-model.dat are provided below:

# Description of columns in escaping-BBH-by-model.dat

* 1.  identifier         - Integer model identifier. Unique number for each star cluster model.* 2.  n_esc_BBH          - Total number of escaping binary black holes (BBHs) from this model.* 3.  n_dynamic_BBH      - Number of escaping BBHs formed dynamically (exchanged binaries: |idd1 - idd2| > 1).* 4.  n_primordial_BBH   - Number of escaping primordial BBHs (|idd1 - idd2| == 1).

----Initial cluster properties at t = 0---* 5.  smt0               - Initial total mass of the cluster [Msun]* 6.  rh0                - Initial half-mass radius of the cluster [pc]* 7.  rc0                - Initial core radius of the cluster [pc]* 8.  rho0               - Initial central density [Msun/pc^3]* 9.  u1_0               - Initial central potential (scaled to (km/s)^2)* 10. vc_0               - Initial central velocity dispersion [km/s]* 11. rtid_0             - Initial tidal radius [pc]* 12. num_0              - Initial number of objects (single+binary) in the cluster (binary counted as 1)* 13. nbb_0              - Initial number of binaries in the cluster

---Cluster properties at 100 Myr---* 14. time_100           - Time (system.dat) at or just after 100 Myr* 15. smt_100            - Total mass of the cluster at 100 Myr [Msun]* 16. rh_100             - Half-mass radius of the cluster at 100 Myr [pc]* 17. rc_100             - Core radius at 100 Myr [pc]* 18. rho_100            - Central density at 100 Myr [Msun/pc^3]* 19. u1_100             - Central potential at 100 Myr (scaled to (km/s)^2)* 20. vc_100             - Central velocity dispersion at 100 Myr [km/s]* 21. rtid_100           - Tidal radius at 100 Myr [pc]*22. num_100            - Number of objects (single+binary) at 100 Myr (binary counted as 1)* 23. nbb_100            - Number of binaries at 100 Myr

* 24. metallicity        - Absolute metallicity (Z) of the cluster

* 25. path               - Filesystem path to the simulated cluster model

* 26. Rgc                - Galactocentric distance of the cluster [kpc]

* 27. pop_flag           - Population flag: 1 = single-population (no pop2 stars at t=0 or t~100); 2 = two-population, no time delay (pop2 present at t=0); 3 = two-population, with time delay (pop2 appears after t=0); * 28. core_dens_0        - Initial core density of the cluster at t = 0 [Msun/pc^3], calculated as core_mass_0 / ((4/3) * π * rc_0^3)* 29. core_dens_100      - Core density of the cluster at t ≈ 100 Myr [Msun/pc^3], calculated as core_mass_100 / ((4/3) * π * rc_100^3)* 30. halfmass_dens_0    - Initial half-mass density at t = 0 [Msun/pc^3], calculated as 3 × cluster_mass_0 / (8 × π × rh_0^3)* 31. halfmass_dens_100  - Half-mass density at t ≈ 100 Myr [Msun/pc^3], calculated as 3 × cluster_mass_100 / (8 × π × rh_100^3)* 32. imbh_mass          - Maximum black hole mass in the cluster found at t ≈ 100, 1000, or 10,000 Myr [Msun]; set to the largest BH mass at these times if ≥ 500 Msun, otherwise 0