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The presented population synthesis models
are from Belczynski et al. (2020), A&A accepted
available at: https://ui.adsabs.harvard.edu/abs/2017arXiv170607053B/abstract
M10
standard assumptions from Belczynski et al. (2016):
- rapid SNa BH masses Fryer et al. (2012a)
- strong pair-instability pulsation supernovae (PPSN)
and pair-instability supernovae (PSN) -
described in: (Belczynski et al. 2016a), (Leung et al. 2019)
- 10% neutrino mass loss at BH/NS formation
- low-to-no BH natal kicks (set by fallback)
- high NS natal kicks (Hobbs et al. (2005);
Maxwellian distribution with sigma = 265 km s^-1)
- 50% non-conservative RLOF
- 10% Bondi-Hoyle rate accretion onto NS/BH in CE
- efficient accretion onto BH in stable MT/winds
- no effects of rotation on stellar evolution
- initial binary parameters from Sana et al. (2012)
- massive star winds Vink et al. (2001) + LBV winds from (Belczynski et al. 2010a)
- BH spins: Geneva models, Belczynski et al. (2020)
- SFRD(z) and Z(z) from Madau & Dickinson (2014)
- solar metallicity: Zsun = 0.02
Other assumptions (not mentioned here) are described in Belczynski et al. (2020)
CE evolution as described in Dominik et al. (2012)
M13
as in M10, but with:
- high natal kicks for both NS & BH (Hobbs et al. (2005):
Maxwellian distribution with sigma = 265 km s^-1),
not lowered by fallback
M20
as in M10, but with:
- 80% non-conservative RLOF
- 5% Bondi-Hoyle rate accretion onto BH in CE
- 20% higher CO core mass (expected effect of rotation)
M26
as in M20, but with:
- small BH/NS natal kicks
(Maxwellian distribution with sigma = 70 km s^-1)
M25
as in M20, but with:
- intermediate BH/NS natal kicks
(Maxwellian distribution with sigma = 130 km s^-1)
M23
as in M20, but with:
- high BH/NS natal kicks
(Maxwellian distribution with sigma = 265 km s^-1)
M30
- rapid SNa BH masses Fryer et al. (2012a)
- weak pair-instability pulsation supernova
and pair-instability supernova
- 1% neutrino mass loss at BH formation
- 10% neutrino mass loss at NS formation
- low-to-no BH natal kicks (set by fallback)
- high NS kicks
(Maxwellian distribution with sigma = 265 km s^-1)
- 50% non-conservative RLOF
- 5% Bondi-Hoyle rate accretion onto BH in CE
- inefficient accretion onto BH in stable MT/winds
- no effects of rotation on stellar evolution
- initial binary parameters Sana et al. (2012)
- massive star winds
Vink et al. (2001)
+ LBV (Luminous Blue Variable winds: 1.5e-4 M_sun yr^-1)
- BH spins: MESA models (Belczynski et al. 2020, eq. 4)
- SFRD(z) and Z(z) from Madau & Fragos (2017)
- solar metallicity: Zsun = 0.014
HG donors do not survive CE phase in this model (pesymistic scenario).
M33
as in M30, but with:
- high BH/NS natal kicks
(sigma = 265 km s^-1)
M35
as in M30, but with:
- intermediate BH/NS natal kicks
(sigma = 130 km s^-1)
M40
as in M30, but with:
- BH spins: Fuller model, Belczynski et al. (2020)
(aspin=0.01) (spin [cJ/(G Mbh^2)] of the BH: set to -1.0 if not a BH)
M43
as in M40, but with:
- high BH/NS natal kicks (sigma = 265 km s^-1)
M50
as in M30, but:
-stellar wind mass loss reduced to 30%
of usually assumed values from other models
M60
as in M30, but with:
- 'strong' pair-instability pulsation supernova,
10% neutrino mass loss for BH/NS at formation
M70
as in M30, but with:
- 'moderate' pair-instability pulsation supernova
The data for each model is divided into 3 parts,
provided in separate archives:
-compact.[model].tar
-[model].[sfr].dat.gz
-IMRPhenomDAdLIGOMidHigh.dat_[model].[sfr].dat.gz file
where [model]=M10, M30 etc.
and [sfr] marks the employed SFRD:
sfrd0 - SFRD from Madau&Dickinsom 2014 (sfr=1)
sfrdL - low SFRD from Madau&Fragos 2017 (sfr=2)
sfrdH - high SFRD from Madau&Fragos 2017 (sfr=3)
For sfr=1 average Z evolution
from modified Madau&Dickinsom (2014) is used,
while for sfr1,2 average Z evolution from Madau&Fragos 2017 is used.
General information not mentioned above:
--Simulated metallicities count per model: 32
--Simulated systems number per metallicity: 2,000,000
--Initial mass function (IMF) - (Kroupa et al. 2013).
--Files contain systems: BH-BH, BH-NS and NS-NS,
without common envelope HG donors only.
--Used formulas assume both rapid and delayed supernova engines.
--Minimum BH mass: 2.5 M_sun (delayed model), 5 M_sun (rapid model)
--PPSN mass loss: strong PPSN (Belczynski et al. 2016a),
moderate and weak PPSN (Leung et al. 2019)
--Maximum initial stars masses: M_ZAMS<150 M_sun
--Initial BH spin magnitudes adopted from given stellar model
Compact files are in .tar.gz, to unpack run:
tar -zxvf [file.tar.gz]
IMRP* and m* files are in gz format, to unpack run:
gunzip [file.gz]
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compact.[model].tar catalog:
Each file within the archive contains the original output
from our population synthesis calculations (StarTrack).
There are 32 files per one model, each of them for different
metallicity at which the stars were formed.
Filenames are: compact.[model].[metallicity].dat.
Value 0250 corresponds to metallicity Z=0.025 etc.
Each file consists of the chunks of data
grouped in 10-line blocks, separated by blank lines.
Each of the 10-line blocks describes one system.
The format of the data is:
t,Ka,Kb,Ma,Mb,a,e,tA_end,tB_end,inbin
a0,e0,Mzamsa,Mzamsb,idum_run,iidd_old
Tms,Tmr,Vsm0[0],Vsm0[1],Vsm0[2],Vsm[0],Vsm[1],Vsm[2]
MpgaA,MpgbA,KpgaA,KpgbA,apgA,epgA,tpgA,MendaA,dMcea,ecssna
MpgaB,MpgbB,KpgaB,KpgbB,apgB,epgB,tpgB,MendbB,dMceb,ecssnb
aspina,aspinb,aspina0,aspinb0,i0,iA,iB,Mcoa,Mcob
twra,awra,ewra,Mwra,Mcoma,twrb,awrb,ewrb,Mwrb,Mcomb
a_0,e_0,i_0,Om_0,om_0,tau_0,a_0a,e_0a,i_0a,Om_0a,om_0a,tau_0a,a_1,e_1,i_1,Om_1,om_1,tau_1,a_2,e_2,i_2,Om_2,om_2,tau_2,jx_0,jy_0,jz_0,jx_1,jy_1,jz_1,jx_2,jy_2,jz_2
ttms1a,tthg1a,ttrgb1a,ttcheb1a,ttagb1a,tthems1a,tthehg1a,tthergb1a,ttms1b,tthg1b,ttrgb1b,ttcheb1b,ttagb1b,tthems1b,tthehg1b,tthergb1b(*)
nevroute,evroute
(*) this line is present in the output from
the newest StarTrack version only (i.e. the models: M30, M33 and newer)
"final" - values just after second remnant formation
1st line:
t - time [Myr] at the formation of double compact object
(current time at output)
Ka, Kb - final remnant type of star A, B respectively
(the details under the format description)
Ma, Mb - final remnant mass [Msun] of star A, B respectively
a - final orbital semi-major axis [Rsun]
e - final orbital eccentricity
tA_end, tB_end - end time [Myr] of the nuclear evolution
of star A, B respectively
inbin - bound (1) or disrupted (0) double compact object binary
(at the moment we include only bound binaries)
2nd line:
a0 - initial (ZAMS) orbital semi-major axis [Rsun]
e0 - initial (ZAMS) eccentricity
Mzamsa, Mzamsb - ZAMS mass [Msun] of the star A,B respectively
idum_run - random number generator seed used for a given run
iidd_old - this number tells how many times random number generator
was used prior to evolution of the given binary
3rd line:
Tms - time interval [Myr] between formation of two compact objects
Tmr - gravitational merger time [Myr] of the two compact objects
(counted from double compact object time formation)
Vsm0[0], Vsm0[1], Vsm0[2] - the three components (X,Y,Z)
of the center of mass velocity [Rsun/day] gained at the 1st supernova
Vsm[0], Vsm[1], Vsm[2] - the three components (X,Y,Z)
of the center of mass velocity [Rsun/day] gained at the 2nd supernova
4th line:
MpgaA, MpgbA - mass [Msun] of the component A, B just prior to the component A supernova respectively
KpgaA, KpgbA - type of the component A, B just prior to the component A supernova respectively
apgA - orbital semi-major axis [Rsun] just prior to component A supernova
epgA - orbital eccentricity just prior to component A supernova
tpgA - time [Myr] of component A supernova
MendaA - mass [Msun] of component A just after component A supernova
dMcea - mass [Msun] accreated in CE by NS/BH formed out of A
ecssna - 0: regular core-collapse supernova of A,
1: electron capture supernova of A
5th line:
MpgaB, MpgbB - mass [Msun] of component A, B respectively
just prior to component B supernova
KpgaB, KpgbB - type of component A, B respectively
just prior to component B supernova
apgB - orbital semi-major axis [Rsun]
just prior to component B supernova
epgB - orbital eccentricity just prior to component B supernova
tpgB - time [Myr] of component B supernova
MendbB - mass [Msun] of component B just after component B supernova
dMceb - mass [Msun] accreated in CE by NS/BH formed out of B
ecssnb - 0: regular core-collapse supernova of B,
1: electron capture supernova of B
6th line:
aspina, aspinb - spin [cJ/(G Mbh^2)]
of the BH from star A, B respectively: set to -1.0 if A/B not a BH
aspina0, aspinb0 - spin magnitude [cJ/(G Mbh^2)]
of A and B at BH formation, respectively
i0 - initial tilt [rad] of binary orbit
iA, iB - tilt [rad] of binary orbit
after supernova of star A and star B, respectively
Mcoa, Mcob [Msun] - CO core mass of star A and B, respectively
7th line:
When A becomes a naked helium (possibly WR) star:
twra - time [Myr]
awra - orbital semi-major axis [Rsun]
ewra - eccentricity
Mwra - mass [Msun]
Mcoma - companion mass [Msun]
When B becomes a naked helium (possibly WR) star:
twrb - time [Myr]
awrb - orbital semi-major axis [Rsun]
ewrb - eccentricity
Mwrb - mass [Msun]
Mcomb - companion mass [Msun]
8th line:
Orbital parameters just prior to A component supernova:
a_0 - semi-major axis [Rsun]
e_0 - eccentricity
i_0 - tilt [rad] of binary orbit
Om_0 - longitude [rad] of ascending node
om_0 - argument of periapsis [rad]
tau_0 - time [d] of perihelion passage
Orbital parameters just after A component supernova:
a_0a - semi-major axis [Rsun]
e_0a - eccentricity
i_0a - tilt [rad] of binary orbit
Om_0a - longitude [rad] of ascending node
om_0a - argument of periapsis [rad]
tau_0a - time [d] of perihelion passage
Orbital parameters just prior to B component supernova:
a_1 - semi-major axis [Rsun]
e_1 - eccentricity
i_1 - tilt [rad] of binary orbit
Om_1 - longitude [rad] of ascending node
om_1 - argument of periapsis [rad]
tau_1 - time [d] of perihelion passage
Orbital parameters just after B component supernova:
a_2 - semi-major axis [Rsun]
e_2 - eccentricity
i_2 - tilt [rad] of binary orbit
Om_2 - longitude [rad] of ascending node
om_2 - argument of periapsis [rad]
tau_2 - time [d] of perihelion passage
jx_0, jy_0, jz_0 - three components (X,Y,Z)
of initial (ZAMS) binary angular momentum vector
jx_1, jy_1, jz_1 - three components (X,Y,Z)
of binary angular momentum vector after A component supernova
jx_2, jy_2, jz_2 - three components (X,Y,Z)
of binary angular momentum vector after B component supernova
9th line:
ttms1a, tthg1a, ttrgb1a, ttcheb1a, ttagb1a, tthems1a, tthehg1a, tthergb1a - times [Myr] of A component type change
ttms1b, tthg1b, ttrgb1b, ttcheb1b, ttagb1b, tthems1b, tthehg1b, tthergb1b - times [Myr] of B component type change
Acronyms used here:
ms - main sequence, hg - hertzsprung gap,
rgb - red giant branch, cheb - core helium burning,
agb - asymptotic giant branch, hems - helium ms,
hehg - helium hg, hergb - helium rgb
10th line:
nevroute - number of evolutionary history strings
evroute - evolutionary history
(details under the stellar types description)
Star types:
Star types K (adopted mostly from Hurley et al. 2000):
0 - main sequence star with M<=0.7 Msun (deeply or fully convective)
1 - main sequence star with M>0.7 Msun
2 - Hertzsprung gap star
3 - first giant branch star
4 - core helium burning star
5 - early asymptotic giant branch star
6 - thermally pulsing asymptotic giant branch star
7 - main sequence naked helium star
8 - Hertzsprung gap naked helium star
9 - giant branch naked helium star
10 - helium white dwarf
11 - carbon/oxygen white dwarf
12 - oxygen/neon white dwarf
13 - neutron star
14 - black hole
15 - massless remnant
16 - hydrogen WD (formed from low mass MS star)
17 - hybrid (He envelope/CO core) WD
-1 - naked carbon/oxygen core
Evolutionary history:
CE - common envelope (unstable Roche Lobe Overflow)
MT - mass transfer (stable Roche Lobe Overflow)
SNA, SNB - supernova A/B explosion respectively
CE(Kai-Kbi;Kaf-Kbf) with:
Kai, Kbi - A/B star type before an event(initial) respectively
Kai, Kbi - A/B star type after an event(final) respectively
MT(Ka-Kb) with:
Ka - component A type at MT step
Kb - component B type at MT step
New entry is created if any of the componets has changed its type.
AIC with:
NS - collapse of a ONeMg white dwarf (K=12) to a neutron star (K=13)
BH - collapse of a neutron star (K=13) to a black hole (K=14)
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[model].[sfr].dat file:
This file contains the simulated data for a given model
used in the calculations of the cosmological merger rates
and the properties of the populations of merging double compact objects
(it includes e.g. redshift of formation and merger of a given system).
It includes all mergers from the Population I and II stars out to redshift z=15.
The format is (one system per line):
Ma,Mb,zmer,s_i,ri,rdi,zbirth,Z,idum_run,iidd_old,aspina,aspinb,aspina0,aspinb0,i0,iA,iB,Mcoa,Mcob,MendaA,MendbB,tA_end,tB_end,a,e,twra,awra,ewra,Mwra,Mcoma,twrb,awrb,ewrb,Mwrb,Mcomb,hece,jx_0,jy_0,jz_0,jx_1,jy_1,jz_1,jx_2,jy_2,jz_2,thetaA,thetaB,Xeff
Where:
Ma - final remnant mass [Msun] of component A
Mb - final remnant mass [Msun] of component B
zmer- redshift of merger
s_i [yr^-1 Mpc^-3] - rate (number per dt dV) for one event
(http://adsabs.harvard.edu/abs/2016ApJ...819..108B ->eq.7)
ri - source frame merger rate of a given event [yr^-1]:
ri=4pi*s_i*(dV_c/dz)*(dz/dt)*Delta_t,
where dV_c/dz is a comoving volume derivative,
z is a redshift and Delta_t is simulation time bin size
rdi - source frame merger rate density for a given event [Gpc^-3 yr^-1]:
rdi=ri/V_12, V12=4pi/3 * (Dc(z2)^3-Dc(z1)^3)
where z1, z2 are redshift bin limits in which given merger takes place,
and V12 is comoving volume between z1 and z2.
Dc is comoving distance (see eq.5 of Belczynski et al. 2016).
zbirth - redshift of the formation of the progenitor binary
Z - metallicity
idum_run - random number generator seed used for a given run
iidd_old - this number tells how many times random number generator
was used prior to evolution of the given binary
aspina, aspinb - spin [cJ/(G Mbh^2)] of BH from star A, B respectively: -1.0 if A/B not BHs
aspina0, aspinb0 - spin magnitude [cJ/(G Mbh^2)]
of A and B at BH formation, respectively
i0 - initial tilt [rad] of binary orbit
iA, iB - tilt [rad] of binary orbit after supernova
of star A and star B, respectively
Mcoa, Mcob [Msun] - CO core mass
of star A and B, respectively
MendaA - mass [Msun] of component A just after component A supernova
MendbB - mass [Msun] of component B just after component B supernova
tA_end, tB_end - star a,b end time [Myr] of nuclear evolution respectively
a - orbital semi-major axis [Rsun]
e - orbital eccentricity
When A becomes a naked helium (possibly WR) star:
twra - time [Myr]
awra - orbital semi-major axis [Rsun]
ewra - eccentricity
Mwra - mass [Msun]
Mcoma - companion mass [Msun]
When B becomes a naked helium (possibly WR) star:
twrb - time [Myr]
awrb - orbital semi-major axis [Rsun]
ewrb - eccentricity
Mwrb - mass [Msun]
Mcomb - companion mass [Msun]
hece - common envelope with Hertzsprung gap star as a donor (0- no, 1-yes)
jx_0, jy_0, jz_0 - three components (X,Y,Z)
of initial (ZAMS) binary angular momentum vector
jx_1, jy_1, jz_1 - three components (X,Y,Z)
of binary angular momentum vector after A component supernova
jx_2, jy_2, jz_2 - three components (X,Y,Z)
of binary angular momentum vector after B component supernova
thetaA - inclination of BH A spin
from binary angular momentum vector [rad]
thetaB - inclination of BH B spin
from binary angular momentum vector [rad]
Xeff - effective spin of BH-BH merger event
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IMRPhenomDAdLIGOMidHigh.dat_[model].[sfr].dat file:
Data only for mergers that are detectable by LIGO/Virgo,
assuming MidHigh LIGO sensitivity (O3 proxy) - it corresponds
to the current LIGO sensitivity - (Belczynski et al. 2019).
The format is(each line is one system):
Ma,Mb,zmer,s_i,ri,rdi,zbirth,Z,idum_run,iidd_old,aspina,aspinb,aspina0,aspinb0,i0,iA,iB,Mcoa,Mcob,MendaA,MendbB,tA_end,tB_end,a,e,twra,awra,ewra,Mwra,Mcoma,twrb,awrb,ewrb,Mwrb,Mcomb,hece,jx_0,jy_0,jz_0,jx_1,jy_1,jz_1,jx_2,jy_2,jz_2,thetaA,thetaB,Xeff,SNR,zhor,drate
Where:
Ma - final remnant mass [Msun] of component A
Mb - final remnant mass [Msun] of component B
zmer - redshift of merger
s_i [yr^-1 Mpc^-3] - rate (number per dt dV) for one event
(http://adsabs.harvard.edu/abs/2016ApJ...819..108B ->eq.7)
ri - source frame merger rate of a given event [yr^-1]:
ri=4pi*s_i*(dV_c/dz)*(dz/dt)*Delta_t,
where dV_c/dz is a comoving volume derivative,
z is a redshift and Delta_t is simulation time bin size
rdi - source frame merger rate density for a given event [Gpc^-3 yr^-1]:
rdi=ri/V_12, V12=4pi/3 * (Dc(z2)^3-Dc(z1)^3)
where z1, z2 are redshift bin limits in which given merger takes place,
and V12 is comoving volume between z1 and z2.
Dc is comoving distance (see eq.5 of Belczynski et al. 2016).
zbirth - redshift of the formation of the progenitor binary
Z - metallicity
idum_run - random number generator seed used for a given run
iidd_old - this number tells how many times random number generator
was used prior to evolution of the given binary
aspina, aspinb - spin [cJ/(G Mbh^2)] of BH from star A, B respectively: -1.0 if A/B not BHs
aspina0, aspinb0 - spin magnitude [cJ/(G Mbh^2)]
of A and B at BH formation, respectively
i0 - initial tilt [rad] of binary orbit
iA, iB - tilt [rad] of binary orbit after supernova
of star A and star B, respectively
Mcoa, Mcob [Msun] - CO core mass
of star A and B, respectively
MendaA - mass [Msun] of component A just after component A supernova
MendbB - mass [Msun] of component B just after component B supernova
tA_end, tB_end - star a,b end time [Myr] of nuclear evolution respectively
a - orbital semi-major axis [Rsun]
e - orbital eccentricity
When A becomes a naked helium (possibly WR) star:
twra - time [Myr]
awra - orbital semi-major axis [Rsun]
ewra - eccentricity
Mwra - mass [Msun]
Mcoma - companion mass [Msun]
When B becomes a naked helium (possibly WR) star:
twrb - time [Myr]
awrb - orbital semi-major axis [Rsun]
ewrb - eccentricity
Mwrb - mass [Msun]
Mcomb - companion mass [Msun]
hece - common envelope with Hertzsprung gap star as a donor (0- no, 1-yes)
jx_0, jy_0, jz_0 - three components (X,Y,Z)
of initial (ZAMS) binary angular momentum vector
jx_1, jy_1, jz_1 - three components (X,Y,Z)
of binary angular momentum vector after A component supernova
jx_2, jy_2, jz_2 - three components (X,Y,Z)
of binary angular momentum vector after B component supernova
thetaA - inclination of BH A spin
from binary angular momentum vector [rad]
thetaB - inclination of BH B spin
from binary angular momentum vector [rad]
Xeff - effective spin of BH-BH merger event
SNR - LIGO single detector signal to noise ratio:
only systems with SNR>8.0 reported
zhor - horizon redshift for best located and oriented source
(overhead and orbital plane perpendicular to direction of sight)
drate [yr^-1] - detection rate for LIGO MidHigh sensitivity