Data for Escaping Binary Black Holes That Will Merge within 14 Gyr from 268 MOCCA models simulated between 2023-2025

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

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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