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A. C. M. Correia - One of the best experts on this subject based on the ideXlab platform.

  • dynamical evolution of triple star systems by lidov kozai cycles and Tidal Friction
    Monthly Notices of the Royal Astronomical Society, 2018
    Co-Authors: M Bataille, A-s Libert, A. C. M. Correia
    Abstract:

    Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with Tidal Friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov-Kozai migration. Our framework is the secular hierarchical three-body problem (octupole order approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Both the orbital and the spin evolutions are considered. Extensive numerical simulations with uniform and non-uniform distributions of the initial orbital parameters are carried out, and unbiased initial conditions leading to Lidov-Kozai migration are revealed. Finally, we highlight the importance of the initial "Kozai constant" $h=\sqrt{(1-e^2)}\cos{i}$ in the dynamical evolution of triple-star systems, by showing that phase portraits at given $h$-values unveil different evolution paths.

  • Dynamical evolution of triple-star systems by Lidov–Kozai cycles and Tidal Friction
    Monthly Notices of the Royal Astronomical Society, 2018
    Co-Authors: M Bataille, A-s Libert, A. C. M. Correia
    Abstract:

    Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with Tidal Friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov-Kozai migration. Our framework is the secular hierarchical three-body problem (octupole order approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Both the orbital and the spin evolutions are considered. Extensive numerical simulations with uniform and non-uniform distributions of the initial orbital parameters are carried out, and unbiased initial conditions leading to Lidov-Kozai migration are revealed. Finally, we highlight the importance of the initial "Kozai constant" $h=\sqrt{(1-e^2)}\cos{i}$ in the dynamical evolution of triple-star systems, by showing that phase portraits at given $h$-values unveil different evolution paths.

P. P. Eggleton - One of the best experts on this subject based on the ideXlab platform.

  • Formation and Evolution of Contact Binaries
    Journal of Astronomy and Space Sciences, 2012
    Co-Authors: P. P. Eggleton
    Abstract:

    I describe a series of processes, including hierarchical fragmentation, gravitational scattering, Kozai cycles within triple systems, Tidal Friction and magnetic braking, that I believe are responsible for producing the modest but significant fraction of stars that are observed as contact binaries. I also discuss further processes, namely heat transport, mass transport, nuclear evolution, thermal relaxation oscillations, and further magnetic braking with Tidal Friction, that influence the evolution during contact. The endpoint, for contact, is that the two components merge into a single star, as recently was observed in the remarkable system V1309 Sco. The single star probably throws off some mass and rotates rapidly at first, and then slows by magnetic braking to become a rather inconspicuous but normal dwarf or subgiant. If however the contact binary was part of a triple system originally-as I suggested above was rather likely-then the result could be a binary with apparently non-coeval components. There are several such known.

  • The Formation of Contact and Very Close Binaries
    Proceedings of the International Astronomical Union, 2007
    Co-Authors: P. P. Eggleton, Ludmila Kisseleva-eggleton
    Abstract:

    We explore the possibility that all close binaries, i.e. those with periods {approx}< 3 d, including contact (W UMa) binaries, are produced from initially wider binaries (periods of say 10's of days) by the action of a triple companion through the medium of Kozai Cycles with Tidal Friction (KCTF).

  • The Evolution of Cool Algols
    The Astrophysical Journal, 2002
    Co-Authors: P. P. Eggleton, Ludmila Kiseleva-eggleton
    Abstract:

    We apply a model of dynamo-driven mass loss, magnetic braking and Tidal Friction to the evolution of stars with cool convective envelopes; in particular we apply it to binary stars where the combination of magnetic braking and Tidal Friction can cause angular-momentum loss from the {\it orbit}. For the present we consider the simplification that only one component of a binary is subject to these non-conservative effects, but we emphasise the need in some circumstances to permit such effects in {\it both} components. The model is applied to examples of (i) the Sun, (ii) BY Dra binaries, (iii) Am binaries, (iv) RS CVn binaries, (v) Algols, (vi) post-Algols. A number of problems regarding some of these systems appear to find a natural explanation in our model. There are indications from other systems that some coefficients in our model may vary by a factor of 2 or so from system to system; this may be a result of the chaotic nature of dynamo activity.

  • Can Combination of ‘Kozai Effect’ and Tidal Friction Produce Close Stellar and Planetary Orbits?
    International Astronomical Union Colloquium, 1999
    Co-Authors: L. G. Kiseleva, P. P. Eggleton
    Abstract:

    In binary stars, Tidal Friction dissipates a fraction of the orbital energy at constant angular momentum and will circularise binary orbits on a rather short rimescale compared with the nuclear rimescale, provided that at least one star of the binary has a radius comparable to the separation between binary components. This dissipation effectively ceases once the orbit is circularised. In a hierarchical triple system such dissipation cannot cease entirely, as neither inner nor outer orbit can become exactly circular because of the perturbation of the third distant body. Thus in such systems Tidal Friction can lead to a steady secular decrease of the inner semimajor axis, accompanied by transfer of angular momentum from the inner to the outer pair, persisting over the whole nuclear lifetime of the system. The situation can be even more dramatic if two orbits have high relative inclination i > 40° It can be shown analytically and numerically (see e.g., Kozai 1962, Marchal 1990, Kiseleva 1996 and references therein) that for triple systems with high relative inclination there is a quasi-periodic change of the inner eccentricity (on a timescale ) during which it reaches a maximum value . This value only depends on the inclination i between the two orbital planes; other parameters affect only the timescale. For example, if we approximate a triple stellar system like β Per (Algol) (m1 = 0.8M⊙, m2 = 3.7M⊙, Pin = 2.87 days; m3 = 1.7M⊙, Pout = 1.86 yr, eout = 0.23; i = 100°) as three point masses, then the inner eccentricity ein cycles rather smoothly between 0 and 0.985, while i fluctuates between 100° and 140°. We call these fluctuations ‘Kozai cycles’. Such ‘Kozai cycles’ do not actually occur in this semi-detached system: they can be damped to a small value by Tidal Friction, but in fact they are also strongly reduced by the non-dissipative effect of the quadrupole moments of the two stars in the inner pair. This effect produces apsidal motion which is much more rapid than the apsidal motion due to the third star, and so prevents the Kozai cycles from operating.

  • Tidal Friction in triple stars
    Monthly Notices of the Royal Astronomical Society, 1998
    Co-Authors: L. G. Kiseleva, P. P. Eggleton, Seppo Mikkola
    Abstract:

    Tidal Friction in close binaries, with periods of a few days, is expected to circularize the orbit on a time-scale long compared with human observation but shorter than, or comparable to, the lifetimes of main-sequence stars. In a hierarchical triple star, however, the perturbing effect of the distant third star may decircularize the inner orbit significantly on a time-scale of the order of days (as in λ Tau) or centuries (as in β Per). If the inner pair is observed to be semidetached, however, it is plausible to assume that the eccentricity is small. This may be because Tidal Friction is operating on a comparably short time-scale, and so it is in principle amenable to observation. We attempt to determine a lower limit to the strength of Tidal Friction in λ Tau and β Per, on the basis of this consideration. Tidal Friction will also lead to a secular transfer of angular momentum from the inner orbit to the outer orbit. Too rapid a transfer may lead to orbital shrinkage that is fast compared with the nuclear time-scales of the inner systems, and this can also be ruled out on observational grounds. Thus we may be able to set an upper as well as a lower limit to the strength of Tidal Friction, on the basis of observations. In a young hierarchical triple, provided that the orbits are fairly nearly orthogonal, Tidal Friction can serve to reduce the inner orbital period from months to days within a fairly short period of time, of order P2out/Pin. This may be a significant mechanism for producing young short-period binaries.

Scott Tremaine - One of the best experts on this subject based on the ideXlab platform.

  • shrinking binary and planetary orbits by kozai cycles with Tidal Friction
    The Astrophysical Journal, 2007
    Co-Authors: Daniel C Fabrycky, Scott Tremaine
    Abstract:

    At least two arguments suggest that the orbits of a large fraction of binary stars and extrasolar planets shrank by 1-2 orders of magnitude after formation: (1) the physical radius of a star shrinks by a large factor from birth to the main sequence, yet many main-sequence stars have companions orbiting only a few stellar radii away, and (2) in current theories of planet formation, the region within ~0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass planet to form, yet many hot Jupiters are observed at such distances. We investigate orbital shrinkage by the combined effects of secular perturbations from a distant companion star (Kozai oscillations) and Tidal Friction. We integrate the relevant equations of motion to predict the distribution of orbital elements produced by this process. Binary stars with orbital periods of 0.1-10 days, with a median of ~2 days, are produced from binaries with much longer periods (10 to ~105 days), consistent with observations indicating that most or all short-period binaries have distant companions (tertiaries). We also make two new testable predictions: (1) For periods between 3 and 10 days, the distribution of the mutual inclination between the inner binary and the tertiary orbit should peak strongly near 40? and 140?. (2) Extrasolar planets whose host stars have a distant binary companion may also undergo this process, in which case the orbit of the resulting hot Jupiter will typically be misaligned with the equator of its host star.

  • Shrinking binary and planetary orbits by Kozai cycles with Tidal Friction
    The Astrophysical Journal, 2007
    Co-Authors: Daniel C Fabrycky, Scott Tremaine
    Abstract:

    At least two arguments suggest that the orbits of a large fraction of binary stars and extrasolar planets shrank by 1-2 orders of magnitude after formation: (i) the physical radius of a star shrinks by a large factor from birth to the main sequence, yet many main-sequence stars have companions orbiting only a few stellar radii away, and (ii) in current theories of planet formation, the region within ~0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass planet to form, yet many "hot Jupiters" are observed at such distances. We investigate orbital shrinkage by the combined effects of secular perturbations from a distant companion star (Kozai oscillations) and Tidal Friction. We integrate the relevant equations of motion to predict the distribution of orbital elements produced by this process. Binary stars with orbital periods of 0.1 to 10 days, with a median of ~2 d, are produced from binaries with much longer periods (10 d to 10^5 d), consistent with observations indicating that most or all short-period binaries have distant companions (tertiaries). We also make two new testable predictions: (1) For periods between 3 and 10 d, the distribution of the mutual inclination between the inner binary and the tertiary orbit should peak strongly near 40 deg and 140 deg. (2) Extrasolar planets whose host stars have a distant binary companion may also undergo this process, in which case the orbit of the resulting hot Jupiter will typically be misaligned with the equator of its host star.

L. G. Kiseleva - One of the best experts on this subject based on the ideXlab platform.

  • Can Combination of ‘Kozai Effect’ and Tidal Friction Produce Close Stellar and Planetary Orbits?
    Impact of Modern Dynamics in Astronomy, 1999
    Co-Authors: L. G. Kiseleva, P. P. Eggleton
    Abstract:

    In binary stars, Tidal Friction dissipates a fraction of the orbital energy at constant angular momentum and will circularise binary orbits on a rather short timescale compared with the nuclear timescale, provided that at least one star of the binary has a radius comparable to the separation between binary components. This dissipation effectively ceases once the orbit is circularised. In a hierarchical triple system such dissipation cannot cease entirely, as neither inner nor outer orbit can become exactly circular because of the perturbation of the third distant body. Thus in such systems Tidal Friction can lead to a steady secular decrease of the inner semimajor axis, accompanied by transfer of angular momentum from the inner to the outer pair, persisting over the whole nuclear lifetime of the system. The situation can be even more dramatic if two orbits have high relative inclination i > 40° It can be shown analytically and numerically (see e.g., Kozai 1962, Marchal 1990, Kiseleva 1996 and references therein) that for triple systems with high relative inclination there is a quasi-periodic change of the inner eccentricity (on a timescale ∼ P out 2 /P in) during which it reaches a maximum value e in max . This value only depends on the inclination i between the two orbital planes; other parameters affect only the timescale. For example, if we approximate a triple stellar system like β Per (Algol) (m 1 = 0.8M ⊙, m 2 = 3.7M ⊙, P in = 2.87 days; m 3 = 1.7M ⊙, P out = 1.86 yr, e out = 0.23; i = 100°) as three point masses, then the inner eccentricity e in cycles rather smoothly between 0 and 0.985, while i fluctuates between 100° and 140°.

  • Can Combination of ‘Kozai Effect’ and Tidal Friction Produce Close Stellar and Planetary Orbits?
    International Astronomical Union Colloquium, 1999
    Co-Authors: L. G. Kiseleva, P. P. Eggleton
    Abstract:

    In binary stars, Tidal Friction dissipates a fraction of the orbital energy at constant angular momentum and will circularise binary orbits on a rather short rimescale compared with the nuclear rimescale, provided that at least one star of the binary has a radius comparable to the separation between binary components. This dissipation effectively ceases once the orbit is circularised. In a hierarchical triple system such dissipation cannot cease entirely, as neither inner nor outer orbit can become exactly circular because of the perturbation of the third distant body. Thus in such systems Tidal Friction can lead to a steady secular decrease of the inner semimajor axis, accompanied by transfer of angular momentum from the inner to the outer pair, persisting over the whole nuclear lifetime of the system. The situation can be even more dramatic if two orbits have high relative inclination i > 40° It can be shown analytically and numerically (see e.g., Kozai 1962, Marchal 1990, Kiseleva 1996 and references therein) that for triple systems with high relative inclination there is a quasi-periodic change of the inner eccentricity (on a timescale ) during which it reaches a maximum value . This value only depends on the inclination i between the two orbital planes; other parameters affect only the timescale. For example, if we approximate a triple stellar system like β Per (Algol) (m1 = 0.8M⊙, m2 = 3.7M⊙, Pin = 2.87 days; m3 = 1.7M⊙, Pout = 1.86 yr, eout = 0.23; i = 100°) as three point masses, then the inner eccentricity ein cycles rather smoothly between 0 and 0.985, while i fluctuates between 100° and 140°. We call these fluctuations ‘Kozai cycles’. Such ‘Kozai cycles’ do not actually occur in this semi-detached system: they can be damped to a small value by Tidal Friction, but in fact they are also strongly reduced by the non-dissipative effect of the quadrupole moments of the two stars in the inner pair. This effect produces apsidal motion which is much more rapid than the apsidal motion due to the third star, and so prevents the Kozai cycles from operating.

  • Tidal Friction in Triple Systems: A Means of Producing Close Stellar and Planetary Orbits
    The Dynamics of Small Bodies in the Solar System, 1999
    Co-Authors: L. G. Kiseleva, P. P. Eggleton
    Abstract:

    In hierarchical triple systems the combination of Tidal Friction (TF) with fluctuations of eccentricity due to the third body can lead to potentially large but slow changes in the inner orbit, especially if the two orbits have high (40° or more) relative inclination. We model the dynamical evolution of triple systems using a force law which includes a combination of point-mass gravity, quadrupolar distortion (QD) of each body by the other two, and a dissipative TF term. In hypothetical cases of triple systems with relative orbital inclination i = 100° (as in the well-known triple stellar system β Per), the effect of the third star is periodically to increase the inner eccentricity up to nearly unity, provided we neglect the effects of QD and TF. The combined effect of QD and TF may reduce the fluctuations of the inner eccentricity, and in some cases the binary orbit may shrink quite drastically after a suitably long interval of time. These results can be applied to systems where all three components are of stellar mass, and also to triple systems with one binary component, or even two components including the distant one, being Jupiter-like planets. This is potentially important for the long-term evolution of such systems and can probably explain the origin of very short-period orbits for some recently discovered extra-Solar planets, such as τ Boo — which has both a Jupiter-like companion in a 3d orbit and an M2V companion in a ~2000 yr orbit.

  • Tidal Friction in triple stars
    Monthly Notices of the Royal Astronomical Society, 1998
    Co-Authors: L. G. Kiseleva, P. P. Eggleton, Seppo Mikkola
    Abstract:

    Tidal Friction in close binaries, with periods of a few days, is expected to circularize the orbit on a time-scale long compared with human observation but shorter than, or comparable to, the lifetimes of main-sequence stars. In a hierarchical triple star, however, the perturbing effect of the distant third star may decircularize the inner orbit significantly on a time-scale of the order of days (as in λ Tau) or centuries (as in β Per). If the inner pair is observed to be semidetached, however, it is plausible to assume that the eccentricity is small. This may be because Tidal Friction is operating on a comparably short time-scale, and so it is in principle amenable to observation. We attempt to determine a lower limit to the strength of Tidal Friction in λ Tau and β Per, on the basis of this consideration. Tidal Friction will also lead to a secular transfer of angular momentum from the inner orbit to the outer orbit. Too rapid a transfer may lead to orbital shrinkage that is fast compared with the nuclear time-scales of the inner systems, and this can also be ruled out on observational grounds. Thus we may be able to set an upper as well as a lower limit to the strength of Tidal Friction, on the basis of observations. In a young hierarchical triple, provided that the orbits are fairly nearly orthogonal, Tidal Friction can serve to reduce the inner orbital period from months to days within a fairly short period of time, of order P2out/Pin. This may be a significant mechanism for producing young short-period binaries.

M Bataille - One of the best experts on this subject based on the ideXlab platform.

  • dynamical evolution of triple star systems by lidov kozai cycles and Tidal Friction
    Monthly Notices of the Royal Astronomical Society, 2018
    Co-Authors: M Bataille, A-s Libert, A. C. M. Correia
    Abstract:

    Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with Tidal Friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov-Kozai migration. Our framework is the secular hierarchical three-body problem (octupole order approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Both the orbital and the spin evolutions are considered. Extensive numerical simulations with uniform and non-uniform distributions of the initial orbital parameters are carried out, and unbiased initial conditions leading to Lidov-Kozai migration are revealed. Finally, we highlight the importance of the initial "Kozai constant" $h=\sqrt{(1-e^2)}\cos{i}$ in the dynamical evolution of triple-star systems, by showing that phase portraits at given $h$-values unveil different evolution paths.

  • Dynamical evolution of triple-star systems by Lidov–Kozai cycles and Tidal Friction
    Monthly Notices of the Royal Astronomical Society, 2018
    Co-Authors: M Bataille, A-s Libert, A. C. M. Correia
    Abstract:

    Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with Tidal Friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov-Kozai migration. Our framework is the secular hierarchical three-body problem (octupole order approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Both the orbital and the spin evolutions are considered. Extensive numerical simulations with uniform and non-uniform distributions of the initial orbital parameters are carried out, and unbiased initial conditions leading to Lidov-Kozai migration are revealed. Finally, we highlight the importance of the initial "Kozai constant" $h=\sqrt{(1-e^2)}\cos{i}$ in the dynamical evolution of triple-star systems, by showing that phase portraits at given $h$-values unveil different evolution paths.