Evolving a single binary¶
Initial conditions¶
Below is the process to initialize and evolve a binary that could have formed a GW150914-like binary. First, import the modules in COSMIC that initialize and evolve the binary.
In [1]: from cosmic.sample.initialbinarytable import InitialBinaryTable
In [2]: from cosmic.evolve import Evolve
To initialize a single binary, populate the InitialBinaries method in the InitialBinaryTable class. Each initialized binary requires the following parameters:
m1 : ZAMS mass of the primary star in \(M_{\odot}\)
m2 : ZAMS mass of the secondary star in \(M_{\odot}\)
porb : initial orbital period in days
ecc : initial eccentricity
tphysf : total evolution time of the binary in Myr
kstar1 : initial primary stellar type, following the BSE convention
kstar2 : initial secondary stellar type, following the BSE convention
metallicity : metallicity of the population (e.g. \(Z_{\odot}=0.014\))
In [3]: single_binary = InitialBinaryTable.InitialBinaries(m1=85.543645, m2=84.99784, porb=446.795757,
...: ecc=0.448872, tphysf=13700.0,
...: kstar1=1, kstar2=1, metallicity=0.002)
...:
In [4]: print(single_binary)
kstar_1 kstar_2 mass_1 mass_2 ... bhspin_1 bhspin_2 tphys binfrac
0 1.0 1.0 85.543645 84.99784 ... 0.0 0.0 0.0 1.0
[1 rows x 38 columns]
(Binary) stellar physics assumptions¶
The flags for the various binary evolution prescriptions used in BSE also need to be set. Each flag is saved in the BSEDict dictionary. Note that the BSEDict only needs to be specified the first time a binary is evolved with COSMIC or if you need to change the binary evolution prescriptions.
If you are unfamiliar with these prescriptions, it is highly advised to run the defaults from the COSMIC install which are consistent with Breivik+2020
In [5]: BSEDict = {
...: "pts1": 0.001, "pts2": 0.01, "pts3": 0.02, "zsun": 0.014, "windflag": 3,
...: "eddlimflag": 0, "neta": 0.5, "bwind": 0.0, "hewind": 0.5, "beta": 0.125,
...: "xi": 0.5, "acc2": 1.5, "LBV_flag": 1, "alpha1": 1.0, "lambdaf": 0.0,
...: "ceflag": 1, "cekickflag": 2, "cemergeflag": 1, "cehestarflag": 0,
...: "qcflag": 5,
...: "qcrit_array": [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
...: "kickflag": 5, "sigma": 265.0, "bhflag": 1, "bhsigmafrac": 1.0,
...: "sigmadiv": -20.0, "ecsn": 2.25, "ecsn_mlow": 1.6, "aic": 1, "ussn": 1,
...: "polar_kick_angle": 90.0,
...: "natal_kick_array": [[-100.0, -100.0, -100.0, -100.0, 0.0], [-100.0, -100.0, -100.0, -100.0, 0.0]],
...: "mm_mu_ns": 400.0, "mm_mu_bh": 200.0, "remnantflag": 4,
...: "fryer_mass_limit": 0, "mxns": 3.0, "rembar_massloss": 0.5,
...: "wd_mass_lim": 1, "maltsev_mode": 0, "maltsev_fallback": 0.5,
...: "maltsev_pf_prob": 0.1, "pisn": -2, "ppi_co_shift": 0.0,
...: "ppi_extra_ml": 0.0, "bhspinflag": 0, "bhspinmag": 0.0, "grflag": 1,
...: "eddfac": 10, "gamma": -2, "don_lim": -1, "acc_lim": -1, "tflag": 1,
...: "ST_tide": 1,
...: "fprimc_array": [2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0,2.0/21.0],
...: "ifflag": 1, "wdflag": 1, "epsnov": 0.001, "bdecayfac": 1,
...: "bconst": 3000, "ck": 1000, "rejuv_fac": 1.0, "rejuvflag": 0,
...: "bhms_coll_flag": 0, "htpmb": 1, "ST_cr": 1, "rtmsflag": 0
...: }
...:
Running a binary¶
Once the binary is initialized and the BSE model is set, the system is evolved with the the Evolve class, which calls the evolv2.f subroutine in the BSE source code.
In [6]: bpp, bcm, initC, kick_info = Evolve.evolve(initialbinarytable=single_binary, BSEDict=BSEDict)
Output¶
For every evolved binary system, BSE generates two arrays, which are stored as pandas DataFrames in COSMIC:
bpp - contains binary parameters at important stages in the binary’s evolution, including stellar evolutionary phase changes or mass transfer episodes.
bcm - contains several binary parameters at user specified time steps during the binary’s evolution. The default setting in COSMIC is to output the final stage of the binary at the evolution time specified by the user.
You can see the different parameters included in each DataFrame using the columns attribute of the DataFrame:
In [7]: print(bpp.columns)
Index(['tphys', 'mass_1', 'mass_2', 'kstar_1', 'kstar_2', 'sep', 'porb', 'ecc',
'RRLO_1', 'RRLO_2', 'evol_type', 'aj_1', 'aj_2', 'tms_1', 'tms_2',
'massc_he_layer_1', 'massc_he_layer_2', 'massc_co_layer_1',
'massc_co_layer_2', 'rad_1', 'rad_2', 'mass0_1', 'mass0_2', 'lum_1',
'lum_2', 'teff_1', 'teff_2', 'radc_1', 'radc_2', 'menv_1', 'menv_2',
'renv_1', 'renv_2', 'omega_spin_1', 'omega_spin_2', 'B_1', 'B_2',
'bacc_1', 'bacc_2', 'tacc_1', 'tacc_2', 'epoch_1', 'epoch_2',
'bhspin_1', 'bhspin_2', 'bin_num'],
dtype='object')
In [8]: print(bcm.columns)
Index(['tphys', 'kstar_1', 'mass0_1', 'mass_1', 'lum_1', 'rad_1', 'teff_1',
'massc_he_layer_1', 'massc_co_layer_1', 'radc_1', 'menv_1', 'renv_1',
'epoch_1', 'omega_spin_1', 'deltam_1', 'RRLO_1', 'kstar_2', 'mass0_2',
'mass_2', 'lum_2', 'rad_2', 'teff_2', 'massc_he_layer_2',
'massc_co_layer_2', 'radc_2', 'menv_2', 'renv_2', 'epoch_2',
'omega_spin_2', 'deltam_2', 'RRLO_2', 'porb', 'sep', 'ecc', 'B_1',
'B_2', 'SN_1', 'SN_2', 'bin_state', 'merger_type', 'bin_num'],
dtype='object')
The units are broadly consistent with BSE and are described in Understanding COSMIC outputs.
The evol_type column in bpp indicates the evolutionary change that occurred for each line. The meaning of each number is described here, Evolve Type.
Each of the parameters in bpp or bcm can be accessed in the usual way for DataFrames:
In [9]: print(bpp.mass_1)
0 85.543645
0 72.740518
0 31.876188
0 31.784608
0 32.229916
0 25.623264
0 25.623264
0 25.597151
0 25.097151
0 25.097151
Name: mass_1, dtype: float64
In [10]: print(bpp[['mass_1', 'mass_2', 'kstar_1', 'kstar_2', 'sep', 'evol_type']])
mass_1 mass_2 kstar_1 kstar_2 sep evol_type
0 85.543645 84.997840 1 1 1363.435508 1
0 72.740518 72.399424 2 1 1598.929105 2
0 31.876188 76.067471 7 1 1898.319594 2
0 31.784608 76.034872 7 2 1900.501225 2
0 32.229916 33.831229 7 7 2993.944619 2
0 25.623264 26.598448 7 7 3787.361254 16
0 25.623264 26.098448 7 14 3861.356624 2
0 25.597151 26.098448 7 14 3862.446573 15
0 25.097151 26.098448 14 14 3891.511099 2
0 25.097151 26.098448 14 14 3890.644221 10
You can use the utils.convert_kstar_evol_type function to convert the
kstar_1, kstar_2, and evol_type columns from integers to strings
that describe each int:
In [11]: from cosmic.utils import convert_kstar_evol_type
In [12]: convert_kstar_evol_type(bpp)
Out[12]:
tphys mass_1 mass_2 ... bhspin_1 bhspin_2 bin_num
0 0.000000 85.543645 84.997840 ... 0.0 0.0 0
0 3.716919 72.740518 72.399424 ... 0.0 0.0 0
0 3.719160 31.876188 76.067471 ... 0.0 0.0 0
0 3.724093 31.784608 76.034872 ... 0.0 0.0 0
0 3.726205 32.229916 33.831229 ... 0.0 0.0 0
0 4.055902 25.623264 26.598448 ... 0.0 0.0 0
0 4.055902 25.623264 26.098448 ... 0.0 0.0 0
0 4.057240 25.597151 26.098448 ... 0.0 0.0 0
0 4.057240 25.097151 26.098448 ... 0.0 0.0 0
0 13700.000000 25.097151 26.098448 ... 0.0 0.0 0
[10 rows x 46 columns]
Note that utils.convert_kstar_evol_type is only applicable to the bpp
array.
Modifying the columns in each table¶
The columns in each table can be modified by passing in a list of desired columns to the
bpp_columns or bcm_columns keyword arguments in the Evolve.evolve method.
This is useful if you only want a subset of the available columns to reduce memory usage, or if you
want columns from bcm in the bpp table or vice versa.
For example, to only get the time, masses, stellar types, separation, and evolution type, you can do:
In [13]: bpp, bcm, initC, kick_info = Evolve.evolve(
....: initialbinarytable=single_binary,
....: BSEDict=BSEDict,
....: bpp_columns=['tphys', 'mass_1', 'mass_2', 'kstar_1', 'kstar_2', 'sep', 'evol_type']
....: )
....:
In [14]: print(bpp)
tphys mass_1 mass_2 ... sep evol_type bin_num
0 0.000000 85.543645 84.997840 ... 1363.435508 1 0
0 3.716919 72.740518 72.399424 ... 1598.929105 2 0
0 3.719160 31.876188 76.067471 ... 1898.319594 2 0
0 3.724093 31.784608 76.034872 ... 1900.501225 2 0
0 3.726205 32.229916 33.831229 ... 2993.944619 2 0
0 4.055902 25.623264 26.598448 ... 3787.361254 16 0
0 4.055902 25.623264 26.098448 ... 3808.001363 2 0
0 4.057240 25.597151 26.098448 ... 3809.076251 15 0
0 4.057240 25.097151 26.098448 ... 3831.763930 2 0
0 13700.000000 25.097151 26.098448 ... 3830.910362 10 0
[10 rows x 8 columns]
Note
Whichever columns are specified in bpp_columns or bcm_columns, there will always be a bin_num
column included in the output tables to identify each binary uniquely.
Plotting the evolution¶
You can also use the built-in plotting function to see how the system evolves:
In [15]: from cosmic.plotting import evolve_and_plot
In [16]: fig = evolve_and_plot(single_binary, t_min=None, t_max=None, BSEDict=BSEDict, sys_obs={})
(Source code, png, hires.png, pdf)
In this case, all the action happens in the first few Myr, so let’s specify a t_max:
In [17]: fig = evolve_and_plot(initC, t_min=None, t_max=6.0, BSEDict=BSEDict, sys_obs={})
(Source code, png, hires.png, pdf)
