The expansion of hierarchical triple star-systems

۴٫۳ MIEK-mechanism

In this section, we illustrate a dynamical outcome of mass detriment on a triple complement from a indicate of perspective of transitions in dynamical regimes, e.g. a regime though Lidov-Kozai cycles, with unchanging or with individualist Lidov-Kozai behaviour. Here, we concentration on a transition from a unchanging Lidov-Kozai regime to a individualist regime, i.e. where a octupole tenure is significant. This transition has been labelled ‘mass-loss prompted individualist Kozai’ or MIEK (Section ۲٫۳٫۳). The authorized instance of MIEK-evolution is a triple with a initial conditions as given by Table ۳ (Shappee and Thompson 2013; Michaely and Perets 2014). To imitate a examination of Shappee and Thompson (2013), we copy a expansion of this triple with TrES including three-body dynamics and breeze mass losses, however, though stellar expansion in radius, luminosity, or stellar core mass etc.

Starting from a birth of a triple system, a circuit is receptive to Lidov-Kozai cycles (Figures ۱۳ and ۱۴). The timescale of a cycles is approximately 0.1 Myr. The cycles are in a unchanging regime, i.e. (epsilon_{mathrm{oct}} = 0.002). As time passes, a stars evolve. The primary star evolves off a MS during 49 Myr, and after 55 Myr it reaches a AGB with a mass of (6.9M_{odot}) (Figure ۱۲). Subsequently, it quick loses a few solar masses in stellar winds, before it becomes an oxygen-neon white dwarf of (1.3M_{odot}) during 56 Myr. The outdoor circuit widens to about (a_{mathrm{out}}sim350~mbox{AU}) due to a breeze mass losses.

The breeze mass detriment allows a triple to transition to a individualist Lidov-Kozai regime during about 56 Myr, i.e. (epsilon_{mathrm{oct}} = 0.045) during this time. The complement is driven into intensely high eccentricities, and also a width of a Lidov-Kozai cycle in desire increases. The expansion of a complement as shown in Figures ۱۳ and ۱۴ is qualitatively identical to that found by Shappee and Thompson (2013) formed on N-body calculations and Michaely and Perets (2014) formed on a physical approach. In these studies, stellar winds are implemented ad-hoc with a consistent mass detriment rate for a bound time interlude starting during a bound time. Moreover, a complement is followed for mixed Myrs after a mass detriment eventuality in both papers, such that a desire rises above 90^∘, and a middle and outdoor circuit turn opposing to any other. In a box a make-believe is stopped before such a flip in desire develops, as RLOF is instituted in a middle binary when a middle oddity is high.

However, if we entirely embody stellar evolution, as in a customary chronicle of TrES, a triple is not driven into a octupole regime. On a AGB, a radius of a (7M_{odot})-star can strech values as vast as ({sim}1text{,}000R_{odot}) (Figure ۱۲), and therefore RLOF triggers before a MIEK-mechanism takes place. Even if a middle binary would be an private binary, RLOF would start for initial separations of (a15~mbox{AU}). For triples, RLOF can start for incomparable initial (inner) separations, as a Lidov-Kozai cycles can expostulate a middle oddity to aloft values. For wider middle binaries i.e. (a_{mathrm{in}} 16~mbox{AU}), a MIEK-mechanism does not start either, as a triple is boldly unstable. This instance indicates that a parameter space for a MIEK-mechanism to start is smaller than formerly thought, and so it might start reduction frequently. Moreover, this instance demonstrates a significance of holding into comment stellar expansion when study a expansion of triples.

For a authorized triple with (a_{mathrm{in}} =10~mbox{AU}) and (a_{mathrm {out}}=250~mbox{AU}), RLOF occurs during 55.5 Myr, only a few 0.1 Myr after a primary star arrives on a AGB. In that time, a radius of a primary increasing by a cause ∼۳, and tides can no longer be neglected. The tidal army act to circularize and synchronize a middle system, such that (e_{mathrm{in}}=0) during RLOF. The individualist Kozai-mechanism does not play a purpose during this point, i.e. (epsilon_{mathrm{oct}} = 0.0008). The mass of a core has not had adequate time to grow to a same distance as in a instance though RLOF, i.e. a core mass is (1.25M_{odot}) instead of (1.3M_{odot}). Stellar winds have reduced a mass of a primary star to (6.8M_{odot}). As a primary has a convective pouch and is some-more large than a secondary, a CE-phase develops. We prognosticate 3 scenarios formed on a opposite models for CE-evolution (Sections ۲٫۲٫۵ and ۳٫۴٫۴). First, a CE-phase leads to a partnership of a middle binary, when a middle circuit shrinks strongly, as for a α-model of CE-evolution with (alphalambda_{mathrm{ce}} = 0.25 ) (Section ۲٫۲٫۵). Second, a CE-phase leads to clever decline of a orbit, though not adequate for a middle stars to merge. In this scenario, a pouch of a donor star is totally private from a system, and a outdoor circuit widens to about 350 AU, underneath a arrogance that a mass dismissal affects a outdoor circuit as a quick wind. Assuming (alphalambda _{mathrm{ce}} = 2 ) (Eq. (۱۴), Section ۲٫۲٫۵), (a_{mathrm{in}}sim0.33~mbox{AU}) and (epsilon_{mathrm{oct}} = 0.0009) after a CE-phase. In this scenario, a triples does not enter a octupole regime, and a MIEK-mechanism does not manifest. Lastly, a CE-phase does not lead to a clever decline of a middle orbit, as for a γ-model of CE-evolution with (gamma=1.75 ) (Eq. (۱۷), Section ۲٫۲٫۵). The middle semimajor-axis even increases from 6.0 to 7.3 AU. In this scenario, (epsilon_{mathrm {oct}} = 0.02), such that a perturbations from a octupole turn turn significant. In this final scenario, a triple undergoes a MIEK mechanism, notwithstanding and since of a mass send phase.