Cosmic Rates of Black Hole Mergers and Pair-Instability Supernovae from Chemically Homogeneous Binary Evolution

Data products and files to reproduce the results from du Buisson et al. (2020).

MESA Calculations

This work included the calculation of large grids of binary models with the MESA code version 11701. The template used for these calculations is included (template.tar.xz), to model any specific system the files inlist_extra and inlist_extra_sj must be updated with the necessary initial parameters.

The resulting data from all simulations is also included in the files named Z*.tar.xz, where the "*" should be replaced for the specific value of log10(Z) for that set of simulations. Data is included in folders with a naming format of logM1_massratio_periodindays, so for instance the folder named 2.100_1.000_2.800 contains a simulation performed for a primary of mass 10^(2.1) Msun, a mass ratio of unity, and an initial orbital period of 2.8 days (note that all simulations are done for a mass ratio of unity). Each folder is a full MESA work directory, including the necessary input files and source code to rerun the simulation. The data files included in each folder are:

1. LOGS1/history.data.s: A MESA history file containing information of the primary every 5 steps of the simulation. This file has been processed from the original MESA output to reduce its size.
2. binary_history.data.s: Similar to the previous one but containing information of the binary system itself
3. last_profile_1.data.s: MESA profile file containing the interior structure of the star at the end of the simulation. These files are only stored for systems that deplete central carbon, or become pair unstable. This file has also been post-processed to reduce its size, mostly by removing redundant columns and reducing the reported precision.
4. out.txt.s: The last 100 lines of the terminal output from the simulation, useful to quickly glance the outcome.

Summary data tables for the MESA simulations

Data tables summarizing the outcome of all simulations are included in the file data_tables.tar.xz. Each of the files contained in that archive have the results from one metallicity, with the name indicating the value of log10(Z). Each row in the files represents one simulation, and the data provided in the different columns is:

1. "log10(M_1i)(Msun)", "qratio(M_2i/M_1i)", "P_i(days)", "metallicity": The initial parameters of the simulation.
2. "result": A string indicating the outcome of the system (see the header of the data files for a list of outcomes). In particular when the outcome is "double_BH", "PISN", "PPISN", the following columns indicate information at the terminal point of the simulation. For all other outcomes, most of the following columns are empty.
3. had_contact: Specifies whether the system undergoes a contact phase (see header in the data files for allowed values).
4. "M_1f(Msun)", "M_2f(Msun)", "P_f(days)": Final orbital parameters.
5. "merge_time(Gyr)": Time to merge from the system assuming the system forms a binary black hole with masses and period given by the M_1f, M_2f and P_f values.
6. "Kerr_param_1", "Kerr_param_2": Black hole spin assuming all angular momentum and mass is conserved at collapse.
7. For the values listed in 4,5 and 6, we also provide values with an added "wpi" description, these indicate the expected results when including pair and pulsational pair instability supernovae, as described in the paper.
8. "he_core_mass_1": Mass coordinate in Msun of the uppermost layer of the star with a mass fraction of hydrogen < 0.01. Any other arbitrary cut can be computed using the profile data.
9. "c_core_mass_1": Mass coordinate in Msun of the uppermost layer of the star with a mass fraction of helium < 0.01.
10. "total_mass_h1_1", "total_mass_he4_1": Total mass of hydrogen and helium at the end of the simulation
11. The remaining columns contain the same information as points 8,9,10 for the secondary. Since all our simulations have q=1 they're actually redundant.

Montecarlo Simulations

Using the results of the MESA calculations, Montecarlo simulations were performed that sample the relevant distribution functions and the cosmic star formation history. The code used to perform these calculations is included in the archive montecarlo_code.tar.xz, and it includes a readme.txt file with instructions on how to use it. The outcome of these Montecarlo simulations is included in the files:

1. fiducial.tar.xz
2. sfr_c1.tar.xz
3. sfr_c2.tar.xz
4. sfr_c3.tar.xz
5. sfr_c4.tar.xz

The first file contains the information on our standard choice of SFR history, including simulations with no kicks, and with and without PPISN. The other four files correspond to each of the cases of SFR variations that we considered in the paper. Each of these archives contain three files:

1. direct.txt: Information for systems that form BHs through direct collapse
2. PISN.txt: Sampled systems which undergo PISN.
3. PPISN.txt: Systems that fall in the range where we expect PPISN to occur. Information is provided assuming both direct collapse and PPISN mass loss, so the effect of PPISNe can be distinguished.
4. volume.txt: Comoving value for the simulation. All the formed BHs and PISN listed can be assumed to be a complete sample of a box of this size through cosmic time (formed by the CHE channel of course, we don't include our evolutionary channels here).

The data contained for these systems is

1. "M1i[Msun]", "Pi[days]", "Z", "z_b": Initial primary mass (same as secondary), orbital period in days, metallicity and birth redshift. We assume the time between birth and formation of the binary black hole or PISN event is negligible.
2. "M1f[Msun]", "Pf[days]": For the case of BH formation, these indicate the mass of the black hole formed by the primary (which is equal to the secondary) and the orbital period at BBH formation. For the case of systems undergoing PISN, they represent instead the properties at the onset of the PISN.
3. "spin": Spin of each BH. We assume the spin is aligned with the orbit. Not included for PISN systems.
4. "z_m": Redshift at which the BBH would merge from GW emission. Not included for PISN systems.
5. "t_d[Gyr]": The delay time between BBH formation and merger due to GW emission. Not included for PISN systems.
6. "p_*": Detection probability for the source assuming a random orientation of the source in the sky with respect to the detector. This includes "O1", "O2" and "O3" for LIGO's first observing runs, as well as "F" for LIGO's design sensitivity. "ET" is used for the detection probability for the Einstein telescope. Not included for PISN systems. Also, for the different studies of SFR variations we only considered LIGO at full design sensitivity and ET.
7. All quantities denoted with "_pp" indicate variations to the previous values in the case we consider pulsational pair instability supernovae, as described in the paper.

The Montecarlo simulations with kicks are not included, but can be recomputed using the source code provided.