The coupled effect of tides and stellar winds on the evolution of compact binaries

Abstract

We follow the evolution of compact binaries under the coupled effect of tides and stellar winds until the onset of Roche-lobe overflow. These binaries contain a compact object (either a black-hole, a neutron-star, or a planet) and a stellar component. We integrate the full set of tidal equations, which are based on Hut's model for tidal evolution, and we couple them with the angular momentum loss in a stellar wind. Our aim is twofold. Firstly, we wish to highlight some interesting evolutionary outcomes of the coupling. When tides are coupled with a non-massive stellar wind, one interesting outcome is that in certain types of binaries, the stellar spin tends to reach a quasi-equilibrium state, where the effect of tides and wind are counteracting each other. When tides are coupled with a massive wind, we parametrize the evolution in terms of the decoupling radius, at which the wind decouples from the star. Even for small decoupling radii this wind braking can drive systems on the main sequence to Roche-lobe overflow that otherwise would fail to do so. Our second aim is to inspect whether simple timescale considerations are a good description of the evolution of the systems. We find that simple timescale considerations, which rely on neglecting the coupling between tides and stellar winds, do not accurately represent the true evolution of compact binaries. The outcome of the coupled evolution of the rotational and orbital elements can strongly differ from simple timescale considerations, as already pointed out by Barker & Ogilvie 2009 in the case of short-period planetary systems.

On the Lack of Circumbinary Planets Orbiting Isolated Binary Stars

“…For simplicity, we model a star as a solid body with a given density profile parameterized by the radius of gyration, r g , where the moment of inertia is given by I = mr 2 g R 2 for mass m and radius R. We assume solid body rotation for stars as the surface rotation evolution of low-mass ( < ∼ 1M ) stars can be reasonably approximated by assuming stellar solid-body rotation (Bouvier et al 1997) and since adopting stellar solid-body rotation is common amongst studies examining stellar-tidal interactions (e.g. Dobbs-Dixon et al 2004;Heller et al 2011;Barnes et al 2013;Repetto & Nelemans 2014;Bolmont & Mathis 2016;Bolmont et al 2017). We neglect effects such as differential rotation and changes in r g but perform sensitivity tests on r g in § 4.3.…”

“…The second magnetic braking model we consider is presented in Repetto & Nelemans (2014) and is derived from the empirical relation for stellar spin-down of Sunlike stars empirically derived by Skumanich (1972). The change in angular momentum due to this spin-down law is given by…”

“…where γ = 5 × 10 −25 s m −2 (Repetto & Nelemans 2014). Assuming one of the magnetic braking laws forJ , the change in stellar rotation rate due to magnetic braking isω…”

“…These magnetic braking laws, however, have successfully been used to model the evolution of short-period binary systems ranging from compact object-stellar binaries (e.g. Verbunt & Zwaan 1981;Repetto & Nelemans 2014), the formation of main sequence stellar contact binaries (e.g. Stepien 1995;Andronov et al 2006), and cataclysmic variable evolution (e.g.…”

Effect of Reimpacting Debris on the Solidification of the Lunar Magma Ocean

“…Furthermore, the Moon formed at approximately the Roche limit (Canup, 2004). Thus, any initial atmosphere would have been highly susceptible to Roche lobe overflow (e.g., Repetto & Nelemans, 2014), especially considering the large-scale height a hot early lunar atmosphere would have had. There are also other depletion mechanisms to consider including hydrodynamic escape (e.g., Pepin, 1991), impact removal (e.g., Melosh & Vickery, 1989), and charged particle interactions (e.g., Luhmann et al, 1992).…”