Tidal interactions in star cluster simulations Mardling, Rosemary A.; Aarseth, Sverre J.
Monthly notices of the Royal Astronomical Society,
03/2001, Letnik:
321, Številka:
3
Journal Article
Modern applications of celestial mechanics include the study of closely packed systems of exoplanets, circumbinary planetary systems, binary-binary interactions in star clusters, and the dynamics of ...stars near the galactic centre. While developments have historically been guided by the architecture of the Solar System, the need for more general formulations with as few restrictions on the parameters as possible is obvious. Here we present clear and concise generalisations of two classic expansions of the three-body disturbing function, simplifying considerably their original form and making them accessible to the non-specialist. Governing the interaction between the inner and outer orbits of a hierarchical triple, the disturbing function in its general form is the conduit for energy and angular momentum exchange and as such, governs the secular and resonant evolution of the system and its stability characteristics. Focusing here on coplanar systems, the first expansion is one in the ratio of inner to outer semimajor axes and is valid for all eccentricities, while the second is an expansion in eccentricity and is valid for all semimajor axis ratios .... Our generalizations make both formulations valid for arbitrary mass ratios. .... We demonstrate the equivalence of the new expansions, identifying the role of the spherical harmonic order m in both and its physical significance in the three-body problem, and introducing the concept of principal resonances. Several examples of the accessibility of both expansions are given including resonance widths and the secular rates of change of the elements. Results in their final form are gathered together at the end of the paper for the reader mainly interested in their application, including a guide for the choice of expansion.
We study the effect of tidal forcing on gravitational wave signals from tidally relaxed white dwarf pairs in the LISA, DECIGO and BBO frequency band (\(0.1-100\,{\rm mHz}\)). We show that for stars ...not in hydrostatic equilibrium (in their own rotating frames), tidal forcing will result in energy and angular momentum exchange between the orbit and the stars, thereby deforming the orbit and producing gravitational wave power in harmonics not excited in perfectly circular synchronous binaries. This effect is not present in the usual orbit-averaged treatment of the equilibrium tide, and is analogous to transit timing variations in multiplanet systems. It should be present for all LISA white dwarf pairs since gravitational waves carry away angular momentum faster than tidal torques can act to synchronize the spins, and when mass transfer occurs as it does for at least eight LISA verification binaries. With the strain amplitudes of the excited harmonics depending directly on the density profiles of the stars, gravitational wave astronomy offers the possibility of studying the internal structure of white dwarfs, complimenting information obtained from asteroseismology of pulsating white dwarfs. Since the vast majority of white-dwarf pairs in this frequency band are expected to be in the quasi-circular state, we focus here on these binaries, providing general analytic expressions for the dependence of the induced eccentricity and strain amplitudes on the stellar apsidal motion constants and their radius and mass ratios. Tidal dissipation and gravitation wave damping will affect the results presented here and will be considered elsewhere.
We report the detection of a gas-giant planet in orbit around both stars of an eclipsing binary star system that also contains the smaller, inner transiting planet TOI-1338b. The new planet, called ...TOI-1338/BEBOP-1c, was discovered using radial-velocity data collected with the HARPS and ESPRESSO spectrographs. Our analysis reveals it is a \(65.2~\rm{M_{\oplus}}\) circumbinary planet with a period of \(215.5~\)days. This is the first detection of a circumbinary planet using radial-velocity observations alone, and makes TOI-1338/BEBOP-1 only the second confirmed multiplanet circumbinary system to date. We do not detect the smaller inner transiting planet with radial-velocity data, and can place an upper limit on the inner planet's mass at \(21.8~\mathrm{M}_\oplus\) with \(99\%\) confidence. The inner planet is the first circumbinary planet amenable for atmospheric characterisation, using the James Webb Space Telescope.
BEBOP is a radial-velocity survey that monitors a sample of single-lined eclipsing binaries, in search of circumbinary planets by using high-resolution spectrographs. Here, we describe and test the ...methods we use to identify planetary signals within the BEBOP data, and establish how we quantify our sensitivity to circumbinary planets by producing detection limits. This process is made easier and more robust by using a diffusive nested sampler. In the process of testing our methods, we notice that contrary to popular wisdom, assuming circular orbits in calculating detection limits for a radial velocity survey provides over-optimistic detection limits by up to \(40\%\) in semi-amplitude with implications for all radial-velocity surveys. We perform example analyses using three BEBOP targets from our Southern HARPS survey. We demonstrate for the first time a repeated ability to reach a residual root mean squared scatter of \(3~\rm m.s^{-1}\) (after removing the binary signal), and find we are sensitive to circumbinary planets with masses down to that of Neptune and Saturn, for orbital periods up to \(1000~\rm days\).
Abridged The recent discovery of a transiting planet on a non-circular orbit with a massive highly eccentric companion orbiting HAT-P-13 offers the possibility of probing the structure of the ...short-period planet. The ability to do this relies on the system being in a quasi-equilibrium state in the sense that the eccentricities are constant on the usual secular timescale, and decay on a timescale which is much longer than the age of the system. Since the equilibrium eccentricity is effectively a function only of observable system parameters and the unknown Love number of the short-period planet, the latter can be determined with accurate measurements of the planet's eccentricity and radius. However, this analysis relies on the unlikely assumption that the system is coplanar. Here we generalize our recent analysis of this fixed-point phenomenon to mutually inclined systems and show that the fixed point of coplanar systems is replaced by a limit cycle, with the average value of the eccentricity decreasing and its amplitude of variation increasing with increasing mutual inclination. This behaviour significantly reduces the ability to unambiguously determine the Love number of the short-period planet if the mutual inclination is higher than around 10^o. We show that for Q-values less than 10^6, the HAT-P-13 system cannot have a mutual inclination between 54 and 126^o because Kozai oscillations coupled with tidal dissipation would act to quickly move the inclination outside this range, and that the behaviour of retrograde systems is the mirror image of that for prograde systems. We derive a relationship between the equilibrium radius of the short-period planet, its Q-value and its core mass, and show that given current estimates of e_b and the planet radius, the HAT-P-13 system is likely to be close to coplanar ...
Explaining the origin and evolution of exoplanetary "hot Jupiters" remains a significant challenge. One possible mechanism for their production is planet-planet interactions, which produces hot ...Jupiters from planets born far from their host stars but near their dynamical stability limits. In the much more likely case of planets born far from their dynamical stability limits, can hot Jupiters can be formed in star clusters? Our N-body simulations of planetary systems inside star clusters answer this question in the affirmative, and show that hot Jupiter formation is not a rare event. We detail three case studies of the dynamics-induced births of hot Jupiters on highly eccentric orbits that can only occur inside star clusters. The hot Jupiters' orbits bear remarkable similarities to those of some of the most extreme exoplanets known: HAT-P-32 b, HAT-P-2 b, HD 80606 b and GJ 876 d. If stellar perturbations formed these hot Jupiters then our simulations predict that these very hot, inner planets are often accompanied by much more distant gas giants in highly eccentric orbits.
In order to explain the significant orbital eccentricity of the short-period transiting Neptune-mass planet GJ 436b and at the same time satisfy various observational constraints and anomalies, ...Ribas, Font-Ribera and Beaulieu have proposed the existence of an eccentric low-mass companion planet at the position of the outer 2:1 resonance. The authors demonstrate the viability of their proposal using point-mass three-body integrations, arguing that as long as the system appears to be dynamically stable, the short-term secular variations ought to dominate the long-term dissipative evolution. Here we demonstrate that if one includes tidal dissipation, both orbits circularize after a few times the circularization timescale of the inner planet. We conclude that with or without a nearby companion planet, in or out of the 2:1 resonance, the Q-value of GJ 436b must be near the upper bound estimate for Neptune if the system is as young as 1 Gyr, and an order of magnitude higher if the system is as old as 10 Gyr. We show detail of passage through resonance and conclude that even out of resonance, a companion planet should still be detectable through transit timing variations.
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