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Register a new userDynamical tides in exoplanetary systems containing Hot Jupiters: confronting theory and observations
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We study the effect of dynamical tides associated with the excitation of gravity waves in an interior radiative region of the central star on orbital evolution in observed systems containing Hot Jupiters. We consider WASP-43, Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence (MS). For these systems there are observational estimates regarding the rate of change of the orbital period. We also investigate Kepler-91 which contains an evolved giant star. We adopt the formalism of Ivanov et al. for calculating the orbital evolution. For the MS stars we determine expected rates of orbital evolution under different assumptions about the amount of dissipation acting on the tides, estimate the effect of stellar rotation for the two most rapidly rotating stars and compare results with observations. All cases apart from possibly WASP-43 are consistent with a regime in which gravity waves are damped during their propagation over the star. However, at present this is not definitive as observational errors are large. We find that although it is expected to apply to Kepler-91, linear radiative damping cannot explain this dis- sipation regime applying to MS stars. Thus, a nonlinear mechanism may be needed. Kepler-91 is found to be such that the time scale for evolution of the star is comparable to that for the orbit. This implies that significant orbital circularisation may have occurred through tides acting on the star. Quasi-static tides, stellar winds, hydrodynamic drag and tides acting on the planet have likely played a minor role.
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We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions and nonlinear excitation of modes by the time-varying gravitational potential of the companion. This paper presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism is applicable to binaries containing stars, planets, or compact objects, we focus on solar type stars with stellar or planetary companions. Our primary results include: (1) The linear tidal solution often used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited gravity waves are unstable to parametric resonance for companion masses M > 10-100 M_Earth at orbital periods P = 1-10 days. The nearly static equilibrium tide is, however, parametrically stable except for solar binaries with P < 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes waves to grow so rapidly that they must be treated as traveling waves rather than standing waves. (3) We find a novel form of parametric instability in which a single parent wave excites a very large number of daughter waves (N = 10^3[P / 10 days]) and drives them as a single coherent unit with growth rates that are ~N times faster than the standard three wave parametric instability. (4) Independent of the parametric instability, tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.
Binary stars are places of complex stellar interactions. While all binaries are in principle converging towards a state of circularization, many eccentric systems are found even in advanced stellar phases. In this work we discuss the sample of binaries with a red-giant component, discovered from observations of the NASA Kepler space mission. We first discuss which effects and features of tidal interactions are detectable in photometry, spectroscopy and the seismic analysis. In a second step, the sample of binary systems observed with Kepler, is compared to the well studied sample of Verbunt & Phinney (1995, hereafter VP95). We find that this study of circularization of systems hosting evolving red-giant stars with deep convective envelopes is also well applicable to the red-giant binaries in the sample of Kepler stars.
Zahns theory of dynamical tides is analyzed critically. We compare the results of this theory with our numerical calculations for stars with a convective core and a radiative envelope and with masses of one and a half and two solar masses. We show that for a binary system consisting of stars of one and a half or two solar masses and a point object with a mass equal to the solar mass and with an orbital period of one day under the assumption of a dense spectrum and moderately rapid dissipation, the evolution time scales of the semimajor axis will be shorter than those in Zahns theory by several orders of magnitude
Zahn (1975) first put forward and calculated in detail the torque experienced by stars in a close binary systems due to dynamical tides. His widely used formula for stars with radiative envelopes and convective cores is expressed in terms of the stellar radius, even though the torque is actually being applied to the convective core at the core radius. This results in a large prefactor, which is very sensitive to the global properties of the star, that multiplies the torque. This large factor is compensated by a very small multiplicative factor, $E_{2}$. Although this is mathematically accurate, depending on the application this can lead to significant errors. The problem is even more severe, since the calculation of $E_{2}$ itself is non-trivial, and different authors have obtained inconsistent values of $E_{2}$. Moreover, many codes (e.g. BSE, StarTrack, MESA) interpolate (and sometimes extrapolate) a fit of $E_{2}$ values to the stellar mass, often in regimes where this is not sound practice. We express the torque in an alternate form, cast in terms of parameters at the envelope-core boundary and a dimensionless coefficient, $beta_{2}$. Previous attempts to express the torque in such a form are either missing an important factor, which depends on the density profile of the star, or are not easy to implement. We show that $beta_{2}$ is almost independent of the properties of the star and its value is approximately unity. Our formula for the torque is simple to implement and avoids the difficulties associated with the classic expression.
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.
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