An upper limit on the spins of merging binary black holes formed through isolated binary evolution

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Volume 691 (November 2024)

A&A, 691 (2024) A339

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Table 1.

Overview of the steps in the semi-analytic model presented in Sect. 3.

Evolutionary phase	Component mass	Orbital period	Angular momentum
TAMS	M_TAMS	P_TAMS > P_contact(R_TAMS)	$J_{TAMS} = \frac{2 π}{P_{TAMS}} I_{TAMS}$ $\displaystyle J_{\mathrm{TAMS}}=\frac{2\pi}{ P_{\mathrm{TAMS}}}{I_{\mathrm{TAMS}}}$

He-ZAMS	M_{He − ZAMS} = M_TAMS	P_{He − ZAMS} = P_TAMS	J_{He-ZAMS, max} = I_{He − ZAMS}Ω_{crit, He − ZAMS}
			J_{He − ZAMS} = min(J_TAMS, J_{He-ZAMS, max})

He-TAMS	M_{He − TAMS} = f_WRM_{He − ZAMS}	P_{He − TAMS} = f_WR⁻²P_{He − ZAMS}	J_{He − TAMS} = f_WR^2/(3k)J_{He − ZAMS}

C. dep	M_C. dep = M_{He − TAMS}	P_C. dep = P_{He − TAMS}	$J_{C.} dep, max = I_{C dep} Ω_{crit, C . dep}$ $J_\text{C. dep, max}={I_{\mathrm{C\,dep}} \Omega_{\mathrm{crit,C.\,dep}}}$
			J_{He − ZAMS} = min(J_{He − TAMS}, J_{He-ZAMS, max})

Notes. This covers the evolution of a CHE from TAMS to carbon depletion, taking as free parameters the mass of each star M_TAMS and their orbital period P_TAMS at the TAMS, as well as the fraction of mass lost via winds (parametrized by f_WR). The model makes use of metallicity-dependent structure properties that we take from our single star calculations. For clarity, the free model parameters are marked in orange, while the structure information taken from the stellar models is marked in teal.

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