Binary physics

Settings that control the binary physics in the simulation

Timesteps


pts1

Sets the timestep modifier for main sequence stars (dtp *= pts1)

Default: 0.001

Option details

  • positive values: Timestep modifier
  • 0.001: Recommended value from Bannerjee+2019 for NS/BH progenitors
  • 0.05: Recommended value from Hurley+2000

pts2

Sets the timestep modifier for Giant Branch (GB, CHeB, AGB, HeGB) stars (dtp *= pts2)

Default: 0.01

Option details

  • positive values: Timestep modifier
  • 0.01: Recommended value from Hurley+2000

pts3

Sets the timestep modifier for HG, HeMS stars (dtp *= pts3)

Default: 0.02

Option details

  • positive values: Timestep modifier
  • 0.02: Recommended value from Hurley+2000

Metallicity


zsun

Sets the metallicity of the Sun which primarily affects stellar winds.

Default: 0.014

Option details

Note that the wind prescriptions for OB stars are calibrated to zsun = 0.019 as described in Vink+2001.

  • positive values: Set the solar metallicity
  • 0.014: Following Asplund+2009

Stellar Winds


windflag

Selects the model for wind mass loss for each star

Default: 3

Option details

  • 0: Standard SSE/BSE (Hurley+2000)
  • 1: StarTrack (Belczynski+2008)
  • 2: Metallicity dependence for O/B stars and Wolf Rayet stars (Vink+2001, Vink+2005)
  • 3: Same as 2, but LBV-like mass loss for giants and non-degenerate stars beyond the Humphreys-Davidson limit

eddlimflag

Adjusts the dependence of mass loss on metallicity for stars near the Eddington limit (see Grafener+2011, Giacobbo+2018).

Default: 0

Option details

  • 0: does not adjust metallicity dependence for stars near the Eddington limit
  • 1: adjusts metallicity dependence for stars near the Eddington limit as in Giacobbo+2018.

neta

Reimers mass-loss coefficient (Equation 106 of SSE).

Default: 0.5

Option details

Note: this equation has a typo. There is an extra \(\eta\) out front; the correct rate is directly proportional to \(\eta\). See also Kurdritzki+1978, Section Vb for discussion.

  • positive values: Set \(\eta\) value
  • 0.5: Sets \(\eta\) for Reimers mass loss to 0.5

bwind

Binary enhanced mass loss parameter

Default: 0.0

Option details

This parameter is used to enhance mass loss in binaries. See Hurley+2000, Eq. 12 for more information.

  • positive values: Sets the binary enhanced mass loss parameter, \(B_w\), from Hurley+2000, Eq. 12
  • 0.0: Default value (no effect on single stars)

hewind

Helium star mass loss parameter

Default: 0.5

Option details

\( 10^{-13} {\rm \ \texttt{hewind} \ } L^{2/3}\) gives He star mass-loss. Equivalent to \(1 - \mu\) in the last equation on Hurley+2000, page 19.

  • positive values: Sets the helium star mass loss parameter
  • 0.5: Default value

beta

Wind velocity factor. \( v_{\rm wind}^2 \propto \beta\), see Hurley+2002, Eq. 9.

Default: 0.125

Option details

  • -1: Follow StarTrack prescription for wind velocity factor, \(\beta_w\), from Belczynski+2008
  • positive values: Sets the wind velocity factor, \(\beta_w\)
  • 0.125: Default value

xi

Wind accretion efficiency factor, which gives the fraction of angular momentum lost via winds from the primary that transfers to the spin angular momentum of the companion.

Default: 0.5

Option details

Corresponds to \(\mu_w\) in Hurley+2002, Eq. 11

  • positive values: Sets the wind accretion efficiency factor
  • 0.5: Default value

acc2

Bondi-Hoyle wind accretion factor where the mean wind accretion rate onto the secondary is proportional to acc2. See Hurley+2002, Eq. 6.

Default: 1.5

Option details

This value is equivalent to \(\alpha_w\) in Hurley+2002, Eq. 6.

  • positive values: Sets the Bondi-Hoyle wind accretion factor, \(\alpha_w\)
  • 1.5: Default value

Common-envelope


Note: there are cases where a common envelope is forced regardless of the critical mass ratio for unstable mass transfer. In the following cases, a common envelope occurs regardless of the choices below:
  • contact: the stellar radii go into contact (common for similar ZAMS systems)
  • periapse contact: the periapse distance is smaller than either of the stellar radii (common for highly eccentric systems)
  • core Roche overflow: either of the stellar radii overflow their component's Roche radius (in this case, mass transfer from the convective core is always dynamically unstable)

alpha1

Common-envelope efficiency parameter which scales the efficiency of transferring orbital energy to the envelope. See Hurley+2002, Eq. 71.

Default: 1.0

Option details

This value is equivalent to \(\alpha\) in Hurley+2002, Eq. 71.

  • positive values: Sets the common-envelope efficiency parameter, \(\alpha\)
  • 1.0: Default value

lambdaf

Binding energy factor for common envelope evolution. The initial binding energy of the stellar envelope is proportional to \(1 / \lambda\). See Hurley+2002, Eq. 69.

Default: 0.0

Option details

  • positive values: uses variable lambda prescription detailed in appendix of Claeys+2014 where lambdaf is the fraction of the ionization energy that can go into ejecting the envelope; to use this prescription without extra ionization energy, set lambdaf = 0
  • 0.0: As above, this is the default choice
  • -1.0: Uses a fixed value (i.e. fixes \( \lambda \) to a value of -lambdaf)

ceflag

Selects the model to set the initial orbital energy (choose whether to use total mass of the stars instead of the core masses)

Default: 1

Option details

  • 0: Use the core masses of the stars to set the initial orbital energy (as in Hurley+2002 Eq. 70)
  • 1: Use the total mass of the stars to set the initial orbital energy (as in de Kool 1990)

cekickflag

Selects which mass and separation values to use when a supernova occurs during the CE and a kick needs to be applied.

Default: 2

Option details

  • 0: uses pre-CE mass and post-CE sep (BSE default)
  • 1: uses pre-CE mass and sep values
  • 2: uses post-CE mass and sep

cemergeflag

Determines whether stars that begin a CE without a distinct core-envelope boundary automatically lead to merger in a CE. These systems include: kstars = [0,1,2,7,8,10,11,12].

Default: 1

Option details

Note that while the optimal choice is cemergeflag=1 according to Belczynski+2008, cemergeflag=0 allows for both options to be explored, since it is trivial to remove these systems from a population in post processing.

  • 0: allows the CE to proceed (optimistic CE)
  • 1: forces the stars to merge in the CE (pessimistic CE)

cehestarflag

Uses fitting formulae from Tauris+2015 for evolving RLO systems with a helium star donor and compact object accretor. NOTE: this flag will override cekickflag if set

Default: 0

Option details

  • 0: Do not use the fitting formulae from Tauris+2015
  • 1: Use the fitting formulae from Tauris+2015 for final period only
  • 2: Use the fitting formulae from Tauris+2015 for both final mass and final period

qcflag

Selects model to determine critical mass ratios for the onset of unstable mass transfer and/or a common envelope during RLO. NOTE: this is overridden by qcrit_array if any of its values are non-zero.

Default: 1

Option details

The table below shows the values for qcflag across the choices of this flag and the kstar type. The equations in the table correspond to:
- Eq.1: qc = 0.362 + 1.0/(3.0*(1.0 - massc(j1)/mass(j1))) (from Hjellming & Webbink 1983)
- Eq 2: qc = (1.67d0-zpars(7)+2.d0*(massc(j1)/mass(j1))**5)/2.13d0 (from Claeys+ 2014)

kstar qc=0 qc=1 qc=2 qc=3 qc=4 qc=5
0 0.695 0.695 0.695 / 1.0 0.695 / 1.0 3.000 1.717
1 3 3 1.6 / 1.0 1.6 / 1.0 3.000 1.717
2 4 4 4.0 / 4.7619 4.0 / 4.7619 3.000 3.825
3 Eq.2 Eq.1 Eq.2 / 1.15 Eq.1 / 1.15 3.000 Eq.1
4 3 3 3.0 / 3.0 3.0 / 3.0 3.000 3
5 Eq.2 Eq.1 Eq.2 / 1.15 Eq.1 / 1.15 3.000 Eq.1
6 Eq.2 Eq.1 Eq.2 / 1.15 Eq.1 / 1.15 3.000 Eq.1
7 3 3 3.0 / 3.0 3.0 / 3.0 1.700 inf
8 0.784 0.784 4.0 / 4.7619 4.0 / 4.7619 3.500 inf
9 0.784 0.784 0.784 / 1.15 0.784 / 1.15 3.500 inf
10-14 0.628 0.628 3.0 / 0.625 3.0 / 0.625 0.628 0.628
Comparison of qcrit Values (Donor Mass/Accretor Mass) For Each Donor Kstar Type Across Flag Options

qcrit_array

User-defined values for critical mass ratios for the onset of unstable mass transfer and a common envelope during RLOF.

Default: [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]

Option details

Array of dimensions (1,16) specifying user-input values for the critical mass ratios that govern the onset of unstable mass transfer and a common envelope. Each item is set individually for its associated kstar, and a value of 0.0 will apply the prescription specified qcflag for that kstar.
NOTE: Recall from the start of this section that there are cases where a common envelope is forced regardless of the critical mass ratio for unstable mass transfer.

  • [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]: Default value, which applies the prescription specified by qcrit for each kstar type

Natal kicks


kickflag

Sets the particular natal kick prescription to use. Note that sigmadiv, bhflag, bhsigmafrac, aic, and ussn, which are described below, are only used when abs(kickflag)=1. Positive values use the Pfahl+2002 prescription for handling natal kicks.

Default: 1

Option details

  • 1: The standard COSMIC kick prescription, where kicks are drawn from a bimodal distribution with standard FeCCSN getting a kick drawn from a Maxwellian distribution with dispersion parameter sigma and ECSN/USSN are drawn according to sigmadiv. This setting has additional possible options for bhflag, bhsigmafrac, aic and ussn.
  • 2: Natal kicks are drawn according to sigma and scaled by the ejecta mass and remnant mass following Eq. 1 of Giacobbo & Mapelli 2020 with their default parameters (\(m_{\rm NS = 1.2 {\rm M_\odot}\), \(m_{\rm ej = 9 {\rm M_\odot}\))
  • 3: Natal kicks are drawn according to sigma and scaled by just the ejecta mass following Eq. 2 of Giacobbo & Mapelli 2020, which does not scale the kick by (\(m_{\rm NS\)
  • 4: Natal kicks are drawn according to Eq. 1 of Bray & Eldridge 2016, with their default parameters (\(\alpha=70 \, {\rm km/s}, \beta = 120 \, {\rm km/s)}
  • negative values: Same as above settings but using the old Kiel & Hurley 2009 prescription for changing the orbital configuration of the binary, available for reproducibility purposes but not recommended for new work

sigma

Sets the dispersion in the Maxwellian for the SN kick velocity in km/s

Default: 265.0

Option details

  • positive values: Sets the dispersion in the Maxwellian for the SN kick velocity in km/s
  • 265.0: Default choice

bhflag

Sets the model for how SN kicks are applied to BHs, where bhflag != 0 allows for velocity kick at BH formation

Default: 1

Option details

  • 0: No BH kick
  • 1: fallback-modulated kicks following Fryer+2012
  • 2: kicks decreased by ratio of BH mass to NS mass (1.44 Msun); conserves linear momentum
  • 3: BH natal kicks are not decreased compared to NS kicks and are drawn from the same Maxwellian distribution with dispersion = sigma set above

bhsigmafrac

Sets a fractional modification which scales down sigma for BHs. This works in addition to whatever is chosen for bhflag, and is applied to sigma before the bhflag prescriptions are applied

Default: 1.0

Option details

  • values between [0, 1]: reduces sigma by bhsigmafrac for BHs
  • 1.0: Default choice

sigmadiv

Sets the modified ECSN kick strength

Default: -20.0

Option details

  • positive values: divide sigma (defined above) by sigmadiv
  • negative values: sets ECSN kicks to be drawn from a Maxwellian distribution with dispersion given by sigmadiv
  • -20.0: Default choice

ecsn

Allows for electron capture SNe and sets the maximum He-star mass (at core helium depletion) that will result in an ECSN

Default: 2.25

Option details

ecsn_low

Sets the low end of the ECSN mass range

Default: 1.6

Option details

aic

Sets the model for accretion induced collapse SN natal kicks

Default: 1

Option details

Applies even if ecsn = 0<.code>

  • 0: AIC SN receive kicks drawn from Maxwellian with dispersion = sigma defined above
  • 1: sets AIC SN kick strength according to sigmadiv; NOTE that this will apply even if ecsn = 0.0

ussn

Reduces kicks according to the sigmadiv selection for ultra-stripped supernovae, assumed to happen if a He-star undergoes a CE with a compact companion

Default: 1

Option details

  • 0: USSN receive kicks drawn from Maxwellian with dispersion = sigma defined above
  • 1: sets USSN kick strength according to sigmadiv

pisn

Allows for (pulsational) pair instability supernovae and sets either the model to use or the maximum mass of the remnant.

Default: -2

Option details

  • 0: no pulsational pair instability SN
  • -1: uses the formulae from Spera & Mapelli 2017
  • -2: uses a polynomial fit to Table 1 in Marchant+2018
  • -3: uses a polynomial fit to Table 5 in Woosley 2019
  • positive values: turns on pulsational pair instability and pair instability SNe, and sets the maximum mass of the allowed remnant (i.e., the bottom of the pair instability mass gap). He core masses between pisn and 65 Msun are assumed to go through pulsational pair instability and limit the He core mass to pisn, while He core masses from 65-135 Msun are assumed have a pair instability SN and leave no remnant.

polar_kick_angle

Sets the opening angle of the SN kick relative to the pole of the exploding star

Default: 90.0

Option details

  • values between [0, 90]: Sets the opening angle of the SN kick relative to the pole of the exploding star
  • 0.0: Strictly polar kicks
  • 90.0: Fully isotropic kicks (default choice)

natal_kick_array

Array of dimensions (2,5) which takes user input values for the SN natal kick, where the first row corresponds to the first star and the second row corresponds to the second star and columns are: [vk, phi, theta, mean_anomaly, rand_seed].

Default: [[-100.0, -100.0, -100.0, -100.0, 0.0], [-100.0, -100.0, -100.0, -100.0, 0.0]]

Option details

NOTE: any numbers outside the ranges below will be sampled in the standard ways detailed above.

  • vk: SN kick velocity in km/s, valid on the range [0, inf]
  • phi: SN kick co-lateral polar angle in degrees, valid on the range [-90, 90]
  • theta: SN kick azimuthal angle in degrees, valid on the range [0, 360]
  • mean_anomaly: SN kick mean anomaly in degrees, valid on the range [0, 360]
  • rand_seed: supplied if restarting evolution after a supernova has already occurred
  • [[-100.0, -100.0, -100.0, -100.0, 0.0], [-100.0, -100.0, -100.0, -100.0, 0.0]]: Default choice, which applies the standard natal kick prescription

Remnant mass


remnantflag

Determines the remnant mass prescription used for NSs and BHs.

Default: 4

Option details

mxns

Sets the boundary between the maximum NS mass and the minimum BH mass

Default: 3.0

Option details

  • positive values: Sets the boundary between the maximum NS mass and the minimum BH mass
  • 3.0: Default choice

rembar_massloss

Determines the prescriptions for mass conversion due to neutrino emission during the collapse of the proto-compact object

Default: 0.5

Option details

  • positive values: sets the maximum amount of mass loss, which should be about 10% of the maximum mass of an iron core (\({\sim 5 \mathrm{M}_\odot}\) Fryer, private communication)
  • values in [-1, 0): assumes that proto-compact objects lose a constant fraction of their baryonic mass when collapsing to a black hole, such that \(M_{\rm rem} = (1 + \texttt{rembar\_massloss}) M_{\rm rem}\) (e.g., rembar_massloss = -0.1 gives the black hole a gravitational mass that is 90% of the proto-compact object's baryonic mass)
  • 0.5: Default choice

wd_mass_lim

Determines if the maximum white dwarf mass is limited to the chandraekhar mass during merger induced collapse

Default: 1

Option details

  • 0: Do not apply the limit
  • 1: Apply the limit

Remnant spin


bhspinflag

Uses different prescriptions for BH spin after formation

Default: 0

Option details

  • 0: sets all BH spins to bhspinmag
  • 1: draws a random BH spin between 0 and bhspinmag for every BH
  • 2: core-mass dependent BH spin (based on Belczynski+2017 v1)

bhspinmag

Sets either the spin of all BHs or the upper limit of the uniform distribution for BH spins (see bhspinflag)

Default: 0.0

Option details

  • positive values: Sets either the spin of all BHs or the upper limit of the uniform distribution for BH spins (see bhspinflag)
  • 0.0: Default choice

GR Orbital Decay


grflag

Turns on or off orbital decay due to gravitational wave emission

Default: 1

Option details

  • 0: No orbital decay due to gravitational wave emission
  • 1: Orbital decay due to gravitational wave emission is turned on

Mass transfer


eddfac

Eddington limit factor for mass transfer.

Default: 1

Option details

  • 1: mass transfer rate is limited by the Eddington rate following Equation 67 in Hurley+2002
  • values > 1: permit super-Eddington accretion up to value eddfac
  • values in [0, 1]: restrict accretion limit to fraction of Eddington (sub-Eddington accretion)

gamma

Angular momentum prescriptions for mass lost during Roche-lobe overflow at super-Eddington mass transfer rates

Default: -2

Option details

  • -1: assumes the lost material carries away the specific angular momentum of the primary
  • -2: assumes material is lost from the system as if it is a wind from the secondary
  • -3: assumes mass is lost through the outer Lagrangian point, forming a circumbinary disk. See Zapartas+17 Eq. 9 and Artymowicz & Lubow (1994).
  • positive values: assumes that the lost material takes away a fraction gamma of the orbital angular momentum

don_lim

Determines the rate of mass loss through Roche-lobe overflow mass transfer from the donor star

Default: -1

Option details

  • -1: donor mass loss rate is calculated following Hurley+2002
  • -2: donor mass loss rate is calculated following Claeys+2014

acc_lim

Limits the amount of mass accreted during Roche-lobe overflow

Default: -1

Option details

  • -1: limited to 10x the thermal rate of the accretor for MS/HG/CHeB and unlimited for GB/EAGB/AGB stars
  • -2: limited to 1x the thermal rate of the accretor for MS/HG/CHeB and unlimited for GB/EAGB/AGB stars
  • -3: limited to 10x the thermal rate of the accretor for all stars
  • -4: limited to 1x the thermal rate of the accretor for all stars
  • >= 0: sets overall fraction of donor material that is accreted, with the rest being lost from the system (acc_lim = 0.5 assumes 50% accretion efficiency as in Belczynski+2008)

Tides


tflag

Activates tidal circularization following Hurley+2002

Default: 1

Option details

  • 0: No tidal circularization
  • 1: Tidal circularization is turned on

ST_tide

Activates StarTrack setup for tides following Belczynski+2008

Default: 1

Option details

  • 0: Follows BSE (Hurley+2002)
  • 1: Follow StarTrack (Belczynski+2008). Note StarTrack method does not use a better integration scheme (yet) but simply ; follows similar set up to startrack (including initial vrot, using roche-lobe check ; at periastron, and circularisation and synchronisation at start of MT).

fprimc_array

Controls the scaling factor for convective tides. Each value in the array is set individually for its associated kstar. The relevant equation is Hurley+2002 Eq. 21.

Default: [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]

Option details

  • positive values: sets scaling factor of Equation 21 referenced above
  • [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]: Default choice, which applies the standard scaling factor

White dwarfs


ifflag

Activates the initial-final white dwarf mass relation from Han+1995 Equations 3, 4, and 5.

Default: 1

Option details

  • 0: No modifications to BSE
  • 1: Initial-final white dwarf mass relation is turned on

wdflag

Activates an alternate cooling law found in the description immediately following Equation 1 in Hurley & Shara 2003. Equation 1 gives the BSE default Mestel cooling law.

Default: 1

Option details

  • 0: No modifications to BSE
  • 1: Alternate cooling law is turned on

epsnov

Fraction of accreted matter retained in a nova eruption. This is relevant for accretion onto degenerate objects; see Section 2.6.6.2 in Hurley+2002.

Default: 0.001

Option details

  • positive values: Retains epsnov fraction of accreted matter
  • 0.001: Default choice

Pulsars


bdecayfac

Activates different models for accretion induced field decay; see Kiel+2008.

Default: 1

Option details

  • 0: uses an exponential decay
  • 1: uses an inverse decay

bconst

Sets the magnetic field decay timescale for pulsars following Section 3 of Kiel+2008.

Default: 3000

Option details

  • positive values: sets \(k\) in Myr from Equation 8 to bconst
  • 3000: Default choice

ck

Sets the magnetic field decay timescale for pulsars following Section 3 of Kiel+2008.

Default: 1000

Option details

  • positive values: sets \(\tau_b\) in Myr from Equation 2 to ck
  • 1000: Default choice

Mixing variables


rejuv_fac

Sets the mixing factor in main sequence star collisions. This is hard coded to 0.1 in the original BSE release and in Equation 80 of Hurley+2002 but can lead to extended main sequence lifetimes in some cases.

Default: 1.0

Option details

  • positive values: sets the mixing factor in main sequence star collisions
  • 1.0: Default choice

rejuvflag

Sets whether to use the orginal prescription for mixing of main-sequence stars (based on equation 80 of Hurley+2002) or whether to use the ratio of the pre-merger He core mass at the base of the giant branch to the merger product's He core mass at the base of the giant branch

Default: 0

Option details

  • 0: No modifications to BSE
  • 1: modified mixing times

bhms_coll_flag

If set to 1, then the star is not destroyed in a BH+star collision if \(M_{\rm star} > M_{\rm BH}\)

Default: 0

Option details

  • 0: Star is destroyed in a BH+star collision even if \(M_{\rm star} > M_{\rm BH}\)
  • 1: Star is not destroyed in a BH+star collision if \(M_{\rm star} > M_{\rm BH}\)

Magnetic Braking


htpmb

Activates different models for magnetic braking

Default: 1

Option details

Miscellaneous


ST_cr

Activates different convective vs radiative boundaries

Default: 1

Option details

rtmsflag

Flag for calculating the radius at the end of the main sequence.

Default: 0

Option details

  • 0: Use the original SSE calculation except if M>200Msun and Z<0.0008 (~0.04 Zsun). For the exception, an extrapolation is used. This ad hoc extrapolation works well for stars with M < 4000 Msun for Z >= 0.01 Zsun. For lower metallicities, you may still run into issues of negative radii for very massive stars - use at your own risk.
  • 1: Calculate using BoOST simulation data. BoOST metallicities = [1.1e-4, 2.1e-4, 1e-3, 2e-3] corresponding to [dwarfD, IZw18, dwarfA, SMC] models (Szecsi et al. (2022))
  • 2: Calculating using BPASS simulation data. BPASS metallicities = [1e-4, *2e-4*, 1e-3, 2e-3]. NOTE : For BPASS, we used a power law to fit the rtms v/s mzams values for each metallicity. We have coded the best fit power-laws for the above BPASS metallicities here. Since, Z = 2e-4 model is not available in the BPASS tracks, we assume the same rtms v/s mzams power law as Z=1e-4 for Z=2e-4.