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Register a new userA new general normal mode approach to dynamic tides in rotating stars with realistic structure and its applications
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We review our recent results on a unified normal mode approach to dynamic tides proposed in Ivanov, Papaloizou $&$ Chernov (2013) and Chernov, Papaloizou $&$ Ivanov (2013). Our formalism can be used whenever the tidal interactions are mainly determined by normal modes of a star with identifiable regular spectrum of low frequency modes. We provide in the text basic expressions for tidal energy and angular momentum transfer valid both for periodic and parabolic orbits, and different assumptions about efficiency of normal mode damping due to viscosity and/or non-linear effects and discuss applications to binary stars and close orbiting extrasolar planets.
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We determine the response of a uniformly rotating star to tidal perturbations due to a companion. General periodic orbits and parabolic flybys are considered. We evaluate energy and angular momentum exchange rates as a sum of contributions from normal modes allowing for dissipative processes. We consider the case when the response is dominated by the contribution of an identifiable regular spectrum of low frequency modes, such as gravity modes and evaluate it in the limit of very weak dissipation. Our formalism may be applied both to Sun-like stars with radiative cores and convective envelopes and to more massive stars with convective cores and radiative envelopes. We provide general expressions for transfer of energy and angular momentum valid for an orbit with any eccentricity. Detailed calculations are made for Sun-like stars in the slow rotation regime where centrifugal distortion is neglected in the equilibrium and the traditional approximation is made for the normal modes. We use both a WKBJ procedure and direct numerical evaluation which are found to be in good agreement for regimes of interest. Finally we use our formalism to determine the evolution time scales for an object, in an orbit of small eccentricity, around a Sun-like star in which the tidal response is assumed to occur. Systems with either no rotation or synchronous rotation are considered. Only rotationally modified gravity modes are taken into account under the assumption that wave dissipation occurs close to the stellar centre.
All the studies of the interaction between tides and a convective flow assume that the large scale tides can be described as a mean shear flow which is damped by small scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover timescale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late-type binaries or the tidal dissipation factor of giant planets. Here, we argue that the above description is inconsistent, because fluctuations and mean flow should be identified based on the timescale, not on the spatial scale, on which they vary. Therefore, the standard picture should be reversed, with the fluctuations being the tidal oscillations and the mean shear flow provided by the largest convective eddies. We assume that energy is locally transferred from the tides to the convective flow. Using this assumption, we obtain values for the tidal $Q$ factor of Jupiter and Saturn and for the circularization periods of PMS binaries in good agreement with observations. The timescales obtained with the equilibrium tide approximation are however still 40 times too large to account for the circularization periods of late-type binaries. For these systems, shear in the tachocline or at the base of the convective zone may be the main cause of tidal dissipation.
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
Apsidal motion is a gradual shift in the position of periastron. The impact of dynamic tides on apsidal motion has long been debated, because the contribution could not be quantified due to the lack of high quality observations. KIC 4544587 with tidally excited oscillations has been observed by textit{Kepler} high-precision photometric data based on long time baseline and short-cadence schema. In this paper, we compute the rate of apsidal motion that arises from the dynamic tides as $19.05pm 1.70$ mrad yr$^{-1}$ via tracking the orbital phase shifts of tidally excited oscillations. We also calculate the procession rate of the orbit due to the Newtonian and general relativistic contribution as $21.49 pm 2.8$ and $2.4 pm 0.06$ mrad yr$^{-1}$, respectively. The sum of these three factors is in excellent agreement with the total observational rate of apsidal motion $42.97 pm 0.18$ mrad yr$^{-1}$ measured by eclipse timing variations. The tidal effect accounts for about 44% of the overall observed apsidal motion and is comparable to that of the Newtonian term. Dynamic tides have a significant contribution to the apsidal motion. The analysis method mentioned in this paper presents an alternative approach to measuring the contribution of the dynamic tides quantitatively.
We developed a code that estimates distances to stars using measured spectroscopic and photometric quantities. We employ a Bayesian approach to build the probability distribution function over stellar evolutionary models given these data, delivering estimates of model parameters for each star individually. The code was first tested on simulations, successfully recovering input distances to mock stars with <1% bias.The method-intrinsic random distance uncertainties for typical spectroscopic survey measurements amount to around 10% for dwarf stars and 20% for giants, and are most sensitive to the quality of $log g$ measurements. The code was validated by comparing our distance estimates to parallax measurements from the Hipparcos mission for nearby stars (< 300 pc), to asteroseismic distances of CoRoT red giant stars, and to known distances of well-studied open and globular clusters. The external comparisons confirm that our distances are subject to very small systematic biases with respect to the fundamental Hipparcos scale (+0.4 % for dwarfs, and +1.6% for giants). The typical random distance scatter is 18% for dwarfs, and 26% for giants. For the CoRoT-APOGEE sample, the typical random distance scatter is ~15%, both for the nearby and farther data. Our distances are systematically larger than the CoRoT ones by about +9%, which can mostly be attributed to the different choice of priors. The comparison to known distances of star clusters from SEGUE and APOGEE has led to significant systematic differences for many cluster stars, but with opposite signs, and with substantial scatter. Finally, we tested our distances against those previously determined for a high-quality sample of giant stars from the RAVE survey, again finding a small systematic trend of +5% and an rms scatter of 30%.
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