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Register a new userA unified normal mode approach to dynamic tides and its application to rotating Sun-like stars
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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.
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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.
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
The X-ray and extreme-ultraviolet (EUV) emissions from the low-mass stars significantly affect the evolution of the planetary atmosphere. However, it is, observationally difficult to constrain the stellar high-energy emission because of the strong interstellar extinction of EUV photons. In this study, we simulate the XUV (X-ray+EUV) emission from the Sun-like stars by extending the solar coronal heating model that self-consistently solves, with sufficiently high resolution, the surface-to-coronal energy transport, turbulent coronal heating, and coronal thermal response by conduction and radiation. The simulations are performed with a range of loop lengths and magnetic filling factors at the stellar surface. With the solar parameters, the model reproduces the observed solar XUV spectrum below the Lyman edge, thus validating its capability of predicting the XUV spectra of other Sun-like stars. The model also reproduces the observed nearly-linear relation between the unsigned magnetic flux and the X-ray luminosity. From the simulation runs with various loop lengths and filling factors, we also find a scaling relation, namely $log L_{rm EUV} = 9.93 + 0.67 log L_{rm X}$, where $L_{rm EUV}$ and $L_{rm X}$ are the luminosity in the EUV and X-ray range, respectively, in cgs. By assuming a power-law relation between the Rossby number and the magnetic filling factor, we reproduce the renowned relation between the Rossby number and the X-ray luminosity. We also propose an analytical description of the energy injected into the corona, which, in combination with the conventional Rosner-Tucker-Vaiana scaling law, semi-analytically explains the simulation results. This study refines the concepts of solar and stellar coronal heating and derives a theoretical relation for estimating the hidden stellar EUV luminosity from X-ray observations.
The advent of Gaia, capable of measuring stellar wobbles caused by orbiting planets, raised an interest to the astrometric detection of exoplanets. Another source of such wobbles (often also called jitter) is stellar magnetic activity. A quantitative assessment of the stellar astrometric jitter is important for a more reliable astrometric detection and characterisation of exoplanets. We calculate the displacement of the solar photocentre due to the magnetic activity for an almost 16-year period (February 2, 1999 - August 1, 2014). We also investigate how the displacement depends on the spectral passband chosen for observations, including the wavelength range to be covered by the upcoming Small-JASMINE mission of JAXA. This is done by extending the SATIRE-S model for solar irradiance variability to calculating the displacement of the solar photocentre caused by the magnetic features on the surface of the Sun. We found that the peak to peak amplitude of the solar photocentre displacement would reach 0.5 mas if the Sun were located 10 pc away from the observer and observed in the Gaia G filter. This is by far too small to be detected by the Gaia mission. However, the Sun is a relatively inactive star so that one can expect significantly larger signals for younger, and, consequently, more active stars. The model developed in this study can be combined with the simulations of emergence and surface transport of magnetic flux which have recently became available to model the astrometric jitter over the broad range of magnetic activities.
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.
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