Orbital Evolution in Binary and Triple Stars, with an Application to SS Lacertae

By P. Eggleton, L. Kiseleva-Eggleton. 2001

329 citations recorded by the source corpus.

We present equations governing the way in which both the orbit and the intrinsic spins of stars in a close binary should evolve subject to a number of perturbing forces, including the effect of a third body in a possibly inclined wider orbit. We illustrate the solutions in some binary star and triple star situations: tidal friction in a wide but eccentric orbit of a radio pulsar about a B star (0045-7319), the Darwin and eccentricity instabilities in a more massive but shorter period massive X-ray binary, and the interaction of tidal friction with Kozai cycles in a triple star, such as β Per at an early stage in that star's life, when all three components were zero-age main sequence stars. We also attempt to model in some detail the interesting triple system SS Lac, which stopped eclipsing in about 1950. We find that our model of SS Lac is quite constrained by the relatively good observational data of this system and leads to a specific inclination (29°) of the outer orbit relative to the inner orbit at epoch zero (1912). We make some predictions about changes to system parameters in the short term (20-40 yr) and also in the medium term (up to ~3000 yr). Although the intrinsic spins of the stars have little effect on the orbit, the converse is not true: the spin axes can vary their orientation relative to the close binary by up to 120° on a timescale of about a century.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/3bcba89597728c36312eecec3585095fa43dbab7

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Citations in the corpus

• Common envelope evolution: where we stand and how we can move forward (2012, background): “An instability such as the Darwin instability (Darwin 1879), or a secular tidal instability (Hut 1980; Lai et al. 1993; Eggleton and Kiseleva-Eggleton 2001).”
• Contact Binaries with Additional Components. I. The Extant Data (2006, background): “The close periastron interactions may then lead to a rapid angular momentum loss (Kiseleva et al. 1998; Eggleton & Kiseleva-Eggleton 2001).”
• THE ECCENTRIC KOZAI MECHANISM FOR A TEST PARTICLE (2011, background): “For example, in triple star systems, if the outer star is inclined it can force Kozai oscillations in the inner binary, increasing the inner binary’s eccentricity until tidal dissipation circularizes it into a very tight orbit (e.g., Eggleton & Kiseleva-Eggleton 2001; Fabrycky & Tremaine 2007).”
• SECULAR EVOLUTION OF COMPACT BINARIES NEAR MASSIVE BLACK HOLES: GRAVITATIONAL WAVE SOURCES AND OTHER EXOTICA (2012, unknown): “The time scale of periapsis precession due to non dissipative tides is (Kiseleva et al. 1998; Eggleton & Kiseleva-Eggleton 2001): TTide= 8a 13/2 1 15(GMb)1/2 (1 − e21)5 8 + 12e21 + e 4 1 × [ m1 m0 k0R 5 0 + m0 m1 k1R 5 1 ]−1 , (5) with R0 and R1 the stellar radii and k0 and k1 the tidal Love…”
• On the tidal evolution of Hot Jupiters on inclined orbits (2009, methodology): “Here we present the orbit-averaged tidal evolution equations (Eggleton et al. 1998; Eggleton & Kiseleva-Eggleton 2001; Mardling & Lin 2002) used in this work.”
• ACCELERATING COMPACT OBJECT MERGERS IN TRIPLE SYSTEMS WITH THE KOZAI RESONANCE: A MECHANISM FOR “PROMPT” TYPE Ia SUPERNOVAE, GAMMA-RAY BURSTS, AND OTHER EXOTICA (2010, background): “…action of tidal friction and Kozai oscillations on the period distrbution of solar-type binaries in triple systems has been considered in detail by FT07 (see also Mazeh & Shaham 1979; Kiseleva et al. 1998; Eggleton & Kiseleva-Eggleton 2001; Wu & Murray 2003; Wu et al. 2007; Perets & Fabrycky 2009).”
• The Eccentric Kozai-Lidov Effect and Its Applications (2016, background): “abrycky and Tremaine (2007), up to the gravitational in uence of the third body which they described by the tensor S. In our formalism its redundant. The functional form of W;V;X;Y and Zwere given in Eggleton and Kiseleva-Eggleton (2001) and are simply: V 1 = 9 t F1 1 + 15e2 1=4 + 15e 4 1=8 + 5e 6 ”
• ON THE FORMATION OF HOT JUPITERS IN STELLAR BINARIES (2012, methodology): “We include an octupole-level approximation to the perturbing potential and the tidal interactions between the star and the planet (following Eggleton & Kiseleva-Eggleton 2001), as well as GR precession.”
• The ASAS-SN catalogue of variable stars I: The Serendipitous Survey (2018, background): “The Lidov-Kozai mechanism (Lidov 1962; Kozai 1962) is likely to have created these systems from short period detached binaries (Mazeh & Shaham 1979; Kiseleva et al. 1998; Eggleton & Kiseleva-Eggleton 2001; Paczyński et al. 2006; Eggleton 2012).”
• KEPLER-413B: A SLIGHTLY MISALIGNED, NEPTUNE-SIZE TRANSITING CIRCUMBINARY PLANET (2014, background): “A tertiary companion on a wide orbit can be responsible for complex dynamical history of the binary system involving Kozai cycles with tidal friction (Kozai 1962; Fabrycky and Tremaine 2007b; Kiseleva et al. 1998; Eggleton and Kiseleva-Eggleton 2001; Pejcha et al. 2013).”
• SECULAR CHAOS AND THE PRODUCTION OF HOT JUPITERS (2010, background): “First proposed by Wu & Murray (2003), it asserts that a highly inclined companion star can induce Kozai oscillations (Kozai 1962; Eggleton & Kiseleva-Eggleton 2001) in the planet, gradually exciting the planet to a high enough eccentricity that it approaches the central star, whereupon tidal…”
• Secular Dynamics in Hierarchical Three-Body Systems (2011, methodology): “…results (e.g., Mazeh and Shaham 1979; Quinn et al. 1990; Bailey et al. 1992; Innanen et al. 1997; Eggleton et al. 1998; Mikkola and Tanikawa 1998; Eggleton and Kiseleva-Eggleton 2001; Valtonen and Karttunen 2006; Fabrycky and Tremaine 2007; Wu et al. 2007; Zdziarski et al. 2007; Takeda et al.…”
• Formation and evolution of compact binaries in globular clusters – II. Binaries with neutron stars (2007, background): “Ifτcirc/2e2i τcoll, the inner binary will shrink until one of the components overfills its Roche lobe or its separation will small enough to cause the Darwin instability resulting in a merger (Eggleton & Kiseleva-Eggleton 2001).”