The role of mass transfer efficiency in stability criteria: A Study with SEVN
Abstract
The fate of binary systems is largely determined by whether mass transfer proceeds stably or leads to a dynamical disruption. A standard approach to evaluate this stability compares how the donor star’s radius and its Roche lobe respond to mass loss. In reality, most population synthesis codes, including those based on Hurley’s prescriptions, assume fully efficient mass transfer, meaning that all the transferred mass is accreted by the companion, and no mass or angular momentum is lost from the system. In this work, we improve this prescription by introducing a new one that incorporates non-conservative mass transfer—allowing for mass and angular momentum loss—to calculate the Roche lobe’s response more realistically. This leads to a more physically consistent criterion for determining the stability of Roche lobe overflow. We implement this improved stability criterion in the SEVN population synthesis code and explore its impact on two distinct types of systems: blue straggler stars and binary black holes.
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The role of mass transfer efficiency in stability criteria: A Study with SEVN M. Echeveste1, G. J. Escobar2,3, E. Pancino1,4 1 INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy. e-mail: [email protected] 2 Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain 3 Universidad de La Laguna, Dpto. Astrofísica, E-38206 La Laguna, Tenerife, Spain 4 Space Science Data Center, Via del Politecnico SNC, I-00133 Roma, Italy Procedure Hertzsprung-Russell diagram of BSS (secondary) and their companions (primary). Each quartet refers to a value of β. The left column corresponds to the β dependent criterion and the right column to the Hurley-Webbink one. The formation of BSS is explored at two ages: 4 and 8 Gyr. 1 Tout C. A., Aarseth S. J., Pols O. R., Eggleton P. P 1997, MNRAS, 291, 732 4 Iorio, G., Mapelli, M., Costa, G. et al. 2023, MNRAS, 524, 426 5 Leiner E. & Geller A., 2021, ApJ, 908,229 2 Spera M., Mapelli M., Bressan A. et al. 2015, MNRAS, 451, 4086 3 Spera M., Mapelli M., Giacobbo N. et al., 2019, MNRAS, 485, 889 Mass transfer (MT) in interacting binary stars plays a central role in shaping a wide range of astrophysical phenomena. A key step in modeling MT is determining whether it proceeds in a stable or unstable way, as this distinction profoundly affects the outcome of the interaction. The stability of MT depends on how the donor star radius responds to mass loss compared to the response of its Roche lobe radius. These quantities are characterized by: ●The donor's adiabatic response, ξad = (d log Rad / d log M), which depends on the stellar structure, in particular, on the energy transport mechanism that dominates in the envelope. ●The Roche lobe response, ξL = (d log RL / d log M), which depends on the binary's configuration and on the total mass and angular momentum evolution. ξL > ξad implies instability and ξL ≤ ξad implies stability at the onset of a Roche lobe overflow phase. Context Population synthesis codes often use the expression for ξL derived by Tout et al. (1997)1 under conservative assumptions—i.e., neither mass nor angular momentum are lost from the system. However, this expression is still widely applied in non-conservative cases. Here, we derive a generalized expression for ξL that includes non-conservative MT and implement it in the population-synthesis code SEVN (Spera et al. 20152, 20193, Iorio et al. 20234). We explore its implications in the formation of blue straggler stars (BSS) and binary compact objects (BCO). We follow the same steps that lead to Tout’s expression for ξL , now dropping the conservation assumptions and using We find the expression where q = M1/M2 (i.e. the donor-to-accretor mass-ratio) and A, B, and c are constants. We implement this expression in SEVN. Here, we assume the angular momentum is lost from the vicinity of the accretor. We explore three values for the parameter β (0.1, 0.5, and 0.9). We compare the number of BSS and BCO formed with the Hurley-Webbink stability criterion (named QCBSE in Iorio et al. 2023) and with the new β-dependent one. Results: binary compact objects Histograms of the delay times for binaries composed by two black holes (BBH), a black hole and a neutron star (BHNS) and two neutron stars (BNS). Each column refers to a value of β. The teal histograms refer to the Hurley-Webbink prescription while white, diagonal-hatched histograms refer to the β-dependent one. The vertical brown line shows the value of Hubble time employed in this work, 13.8 Gyr. Results: blue stragglers Although the distribution of BCO under the β-dependent criterion is broadly consistent with that obtained using the Hurley-Webbink prescription, a deeper investigation is warranted. In particular, it would be valuable to explore whether the relative contribution of different formation channels changes depending on the adopted MT stability criterion. Such an analysis could provide new insights into the evolutionary pathways leading to BCO formation and help refine current binary evolution models. On the other hand, our results show that the β-dependent stability criterion produces more BSS than the Hurley-Webbink model. As noted by Leiner and Geller (2021)5, ‘population synthesis assumptions dramatically under-produce the number of BSS in old open clusters. This suggests that adopting more realistic physically motivated stability criteria may help address this discrepancy. Conclusions HW BD