It is worth noting that more ECSNe are predicted for systems with a mass ratio close to unity, as the development of contact happens at longer periods for higher-q systems (see Figure 12). As the primary star starts transferring mass to the secondary, the orbit shrinks, until the mass ratio is reversed. This reversal happens earlier for mass ratios close to 1 and later for lower mass ratios, increasing the chance for contact (de Mink et al. 2013). This primarily affects the numbers of ECSNe, not so much the initial mass range (except for Case A systems). This is also true for the value of β, which controls the amount of matter that is lost from the system (i.e., 





 is conservative mass transfer, no mass that is transferred from the primary to the secondary is lost from the system; 





 is completely nonconservative mass transfer, all mass that is transferred from the primary is lost from the system, no accretion onto the secondary). For the sake of our parameter study we chose various fixed values of β, while the mass transfer efficiency in real systems varies in time and will depend on the evolutionary phase of both stars, the amount of matter already accreted onto the secondary, and how that has affected its spin rate. Several mechanisms have been suggested that control the efficiency of mass transfer, mass accretion, and mass loss, including the existence of an accretion disk that regulates the amount of mass and angular momentum that can be accreted (Paczyński 1991; Popham & Narayan 1991; Deschamps et al. 2013), the necessity of the secondary to stay below critical rotation (Packet 1981), and the effects of tides on the stellar spins and the stellar orbit (Zahn 1977; Hurley et al. 2002). Work by Deschamps et al. (2013) and van Rensbergen et al. (2008) for systems with slightly lower masses suggests periods with values of β close to 1 (i.e., very inefficient mass transfer), while simulations with a strong tidal interaction (i.e., a short spin–orbit synchronization timescale) suggest shorter periods of moderately inefficient mass transfer (Paxton et al. 2015). Although our models suggest that the efficiency of mass transfer does not really affect the mass range for ECSNe, it does, however, strongly affect the range of initial periods that can lead to an ECSN. In addition, the evolution of the secondary will be affected. It will most likely rapidly spin up after the onset of mass transfer and maintain near-critical rotation for possibly extended periods of time. This will induce strong rotational mixing (de Mink et al. 2008a, 2013; Langer 2012), causing possibly quasi-chemically homogeneous evolution (Maeder 1987; Langer 2012), and alter the evolution of the star beyond just the simple fact of mass accretion (Hirschi et al. 2004; de Mink & Mandel 2016; Marchant et al. 2016). Although it is not clear to what extent this will affect the incidence of ECSNe, the effects of tides, mass and angular momentum transfer and loss, and near-critical rotation of the secondary are possibly important and will be discussed in a forthcoming paper, in addition to the effects of additional mixing and convection criteria.
Citation: Popham & Narayan 1991
Citation function: Motivation