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The Evolution of Hierarchical Triple Star-Systems

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The Evolution of Hierarchical Triple Star-Systems Toonen et al. Computational Astrophysics and Cosmology (2016)3:6 DOI 10.1186/s40668-016-0019-0 METHODOLOGY OpenAccess The evolution of hierarchical triple star-systems Silvia Toonen* , Adrian Hamers and Simon Portegies Zwart Abstract Field stars are frequently formed in pairs, and many of these binaries are part of triples or even higher-order systems. Even though, the principles of single stellar evolution and binary evolution, have been accepted for a long time, the long-term evolution of stellar triples is poorly understood. The presence of a third star in an orbit around a binary system can significantly alter the evolution of those stars and the binary system. The rich dynamical behaviour in three-body systems can give rise to Lidov-Kozai cycles, in which the eccentricity of the inner orbit and the inclination between the inner and outer orbit vary periodically. In turn, this can lead to an enhancement of tidal effects (tidal friction), gravitational-wave emission and stellar interactions such as mass transfer and collisions. The lack of a self-consistent treatment of triple evolution, including both three-body dynamics as well as stellar evolution, hinders the systematic study and general understanding of the long-term evolution of triple systems. In this paper, we aim to address some of these hiatus, by discussing the dominant physical processes of hierarchical triple evolution, and presenting heuristic recipes for these processes. To improve our understanding on hierarchical stellar triples, these descriptions are implemented in a public source code TrES, which combines three-body dynamics (based on the secular approach) with stellar evolution and their mutual influences. Note that modelling through a phase of stable mass transfer in an eccentric orbit is currently not implemented in TrES, but can be implemented with the appropriate methodology at a later stage. Keywords: binaries (including multiple): close; stars: evolution 1 Introduction in triples (Tokovinin; , b;Raghavanetal.; The majority of stars are members of multiple systems. Moe and Di Stefano ) a fraction that gradually in- These include binaries, triples, and higher order hierar- creases (Duchêne and Kraus )to∼% for spectral chies. The evolution of single stars and binaries have been type B stars (Remage Evans ;Sanaetal.;Moeand studied extensively and there is general consensus over Di Stefano ). the dominant physical processes (Postnov and Yungel- The theoretical studies of triples can classically be di- son ;Toonenetal.). Many exotic systems, how- vided into three-body dynamics and stellar evolution, ever, cannot easily be explained by binary evolution, and whichbothareoftendiscussedseparately.Three-bodydy- these have often been attributed to the evolution of triples, namics is generally governed by the gravitational orbital for examples low-mass X-ray binaries (Eggleton and Ver- evolution, whereas the stellar evolution is governed by the bunt ) and blue stragglers (Perets and Fabrycky ). internal nuclear burning processes in the individual stars Ourlackofaclearunderstandingoftripleevolutionhin- and their mutual influence. ders the systematic exploration of these curious objects. Typical examples of studies that focused on the three- At the same time triples are fairly common; Our nearest body dynamics include Ford et al. (), Fabrycky and neighbour α Cen is a triple star system (Tokovinin a), Tremaine (), Naoz et al. (), Naoz and Fabrycky but more importantly ∼% of the low-mass stars are (), Liu et al. (a), and stellar evolution studies in- clude Eggleton and Kiseleva (), Iben and Tutukov *Correspondence: [email protected] (), Kuranov et al. (). Interdisciplinary studies, in Leiden Observatory, Leiden University, PO Box 9513, Leiden, The Netherlands which the mutual interaction between the dynamics and © The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Toonen et al. Computational Astrophysics and Cosmology (2016)3:6 Page 2 of 36 stellar aspects are taken into account are rare (Kratter and .. Timescales Perets ;PeretsandKratter;Hamersetal.; Fundamental timescales of stellar evolution are the dy- Shappee and Thompson ;MichaelyandPerets; namical (τdyn), thermal (τth), and nuclear timescale (τnucl). Naoz et al. ), but demonstrate the richness of the in- The dynamical timescale is the characteristic time that it teracting regime. The lack of a self consistent treatment would take for a star to collapse under its own gravitational hinders a systematic study of triple systems. This makes it attraction without the presence of internal pressure: hard to judge the importance of this interacting regime, or how many curious evolutionary products can be attributed R τ = ,() to triple evolution. Here we discuss triple evolution in a dyn Gm broader context in order to address some of these hiatus. In this paper we discuss the principle complexities of where R and m are the radius and mass of the star. It is triple evolution in a broader context (Section ). We start a measure of the timescale on which a star would expand by presenting an overview of the evolution of single stars or contract if the hydrostatic equilibrium of the star is dis- and binaries, and how to extend these to triple evolu- turbed. This can happen for example because of sudden mass loss. tion. In the second part of this paper we present heuristic A related timescale is the time required for the Sun to recipes for simulating their evolution (Section ). These radiate all its thermal energy content at its current lumi- recipes combine three-body dynamics with stellar evolu- nosity: tion and their mutual influences, such as tidal interactions and mass transfer. These descriptions are summarized in a GmR public source code TrES with which triple evolution can τ = ,() th L be studied. where L is the luminosity of the star. In other words, when 2 Background the thermal equilibrium of a star is disturbed, the star We will give a brief overview of isolated binary evolution will move to a new equilibrium on a thermal (or Kelvin- (Section .) and isolated triple evolution (Section .). We Helmholtz) timescale. discuss in particular under what circumstances triple evo- Finally, the nuclear timescale represents the time re- lution differs from binary evolution and what the conse- quired for the star to exhaust its supply of nuclear fuel at quences are of these differences. We start with a brief sum- its current luminosity: mary of single star evolution with a focus on those aspects cm that are relevant for binary and triple evolution. τ = nucl ,() nucl L 2.1 Single stellar evolution where is the efficiency of nuclear energy production, Hydrostatic and thermal equilibrium in a star give rise to c is the speed of light, and mnucl is the amount of mass temperatures and pressures that allow for nuclear burn- available as fuel. For core hydrogen burning, =. ing, and consequently the emission of the starlight that we and Mnucl ≈ .M. Assuming a mass-luminosity relation observe. Cycles of nuclear burning and exhaustion of fuel of L ∝ Mα, with empirically α ≈ - (e.g. Salaris and Cas- regulate the evolution of a star, and sets the various phases sisi ;Ekeretal.), it follows that massive stars live during the stellar lifetime. shorter and evolve faster than low-mass stars. The evolution of a star is predominantly determined by For the Sun, τdyn ≈ min, τth ≈ Myr, and τnucl ≈ a single parameter, namely the stellar mass (Table ). It de- Gyr. Typically, τdyn < τth < τnucl, which allows us to quan- pends only slightly on the initial chemical composition or titatively predict the structure and evolution of stars in the amount of core overshooting.a broad terms. .. Hertzsprung-Russell diagram Table 1 Necessary parameters to describe a single star system, a binary and a triple The Hertzsprung-Russell (HR) diagram in Figure shows seven evolutionary tracks for stars of different Parameters Stellar Orbital masses. The longest phase of stellar evolution is known as Single star m - the main-sequence (MS), in which nuclear burning takes Binary m1, m2 a, e place of hydrogen in the stellar core. The MS occupies the Triple m1, m2, m3 imutual, ain, ein, gin, hin, aout, eout, gout, hout region in the HR-diagram between the stellar birth on the zero-age MS (ZAMS, blue circles in Figure ) and the end For stellar parameters, age and metallicity of each star can be added. The table shows that as the multiplicity of a stellar system increases from one to three, the of the MS-phase (terminal-age MS (TAMS), blue circles in problem becomes significantly more complicated. Figure ). Stars more massive than .M contract slightly Toonen et al. Computational Astrophysics and Cosmology (2016)3:6 Page 3 of 36 Figure 2 Evolution of stellar radius. Radius as a function of stellar Figure 1 Hertzsprung-Russell diagram. Evolutionary tracks for age for two stars with masses 4 and 6.5M at solar metallicity. Specific seven stars in the HR-diagram with masses 1, 1.5, 2.5, 4, 6.5, 10, and moments in the evolution of the stars are noted by blue circles as for 15M at solar metallicity. Specific moments in the evolution of the Figure 1. The radius evolution is calculated with SeBa (Portegies stars are noted by blue circles as explained in the text. The tracks are Zwart and Verbunt 1996; Toonen et al. 2012). The figure also shows SeBa calculated with (Portegies Zwart and Verbunt 1996, Toonen that high-mass stars evolve faster and live shorter than lower-mass et al. 2012). The dashed lines show lines of constant radii by means of stars. the Stefan-Boltzmann law. at the end of the MS when the stellar core runs out of hy- the core, the outer layers of the star expand again and the drogen.
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