Abstract
We introduce a new model to explain the modulation of the orbital period observed in close stellar binary systems based on an angular momentum exchange between the spin of the active ...component and the orbital motion. This spin-orbit coupling is not due to tides, but is produced by a non-axisymmetric component of the gravitational quadrupole moment of the active star due to a persistent non-axisymmetric internal magnetic field. The proposed mechanism easily satisfies all the energy constraints having an energy budget ∼102 − 103 times smaller than those of previously proposed models and is supported by the observations of persistent active longitudes in the active components of close binary systems. We present preliminary applications to three well-studied binary systems to illustrate the model. The case of stars with hot Jupiters is also discussed showing that no significant orbital period modulation is generally expected on the basis of the proposed model.
Since the discovery of the transiting super-Earth CoRoT-7b, several investigations have yielded different results for the number and masses of planets present in the system, mainly owing to the ...star's high level of activity. We re-observed CoRoT-7 in 2012 January with both HARPS and CoRoT, so that we now have the benefit of simultaneous radial-velocity and photometric data. This allows us to use the off-transit variations in the star's light curve to estimate the radial-velocity variations induced by the suppression of convective blueshift and the flux blocked by starspots. To account for activity-related effects in the radial velocities which do not have a photometric signature, we also include an additional activity term in the radial-velocity model, which we treat as a Gaussian process with the same covariance properties (and hence the same frequency structure) as the light curve. Our model was incorporated into a Monte Carlo Markov Chain in order to make a precise determination of the orbits of CoRoT-7b and CoRoT-7c. We measure the masses of planets b and c to be 4.73 ± 0.95 and 13.56 ± 1.08 M⊕, respectively. The density of CoRoT-7b is (6.61 ± 1.72)(R
p
/1.58 R⊕)−3 g cm−3, which is compatible with a rocky composition. We search for evidence of an additional planet d, identified by previous authors with a period close to 9 d. We are not able to confirm the existence of a planet with this orbital period, which is close to the second harmonic of the stellar rotation at ∼7.9 d. Using Bayesian model selection, we find that a model with two planets plus activity-induced variations is most favoured.
Context. Stars interact with their close-in planets through radiation, gravitation and magnetic fields. Aims. We investigate the energy input to a planetary atmosphere by reconnection between stellar ...and planetary magnetic fields and compare it to the energy input of the extreme ultraviolet (EUV) radiation field of the star. Methods. We quantify the power released by magnetic reconnection at the boundary of the planetary magnetosphere that is conveyed to the atmosphere by accelerated electrons. We introduce simple models to evaluate the energy spectrum of the accelerated electrons and the energy dissipated in the atmospheric layers in the polar region of the planet upon which they impinge. A simple transonic isothermal wind flow along field lines is considered to estimate the increase in mass loss rate in comparison with a planet irradiated only by the EUV flux of its host star. Results. We find that energetic electrons can reach levels down to column densities of 1023−1025 m-2, comparable with or deeper than EUV photons, and increase the mass loss rate up to a factor of 30−50 in close-in (< 0.10 AU), massive (≥1.5 Jupiter masses) planets. Mass loss rates up to (0.5−1.0) × 109 kg s-1 are found for atmospheres heated by electrons accelerated by magnetic reconnection at the boundary of planetary magnetospheres. On the other hand, average mass loss rates up to (0.3−1.0) × 1010 kg s-1 are found in the case of magnetic loops interconnecting the planet with the star. Conclusions. The star-planet magnetic interaction provides a remarkable source of energy for planetary atmospheres, generally comparable with or exceeding that of stellar EUV radiation for close-in planets. Therefore, it must be included in models of chemical evolution or evaporation of planetary atmospheres as well as in modelling of light curves of transiting planets at UV wavelengths.
Context.
The rotation period of some planet-hosting stars appears to be in close commensurability with the orbital period of their close-by planets. In some cases, starspots rotating with a ...commensurable period have been detected, while the star displays latitudinal differential rotation.
Aims.
A model is proposed to interpret such a phenomenon based on the excitation of resonant oscillations in the interior magnetic field of the star by a component of the tidal potential with a very low frequency in the reference frame rotating with the star.
Methods.
A magnetic flux tube located in the overshoot layer of the star is assumed in order to study the excitation of the resonant oscillations in the magnetostrophic regime. The model considers a planet on a circular oblique orbit, and the growth timescale of the oscillations is estimated. To keep the system in resonance with the exciting potential despite the variations in the magnetic field or tidal frequency, a self-regulating mechanism is proposed.
Results.
The model is applied to ten systems and proves capable of accounting for the observed close commensurability in eight of them by assuming a magnetic field between 10
2
and 10
4
G. Systems with distant low-mass planets, such as AU Mic and HAT-P-11, cannot be interpreted by the proposed model.
Conclusions.
Consequences for the spin–orbit evolution of the systems, including the dynamical tides and gyrochronology of planet-hosting stars, are discussed together with the effects on the chromospheric features produced by star–planet magnetic interactions.
Context.
Rocky planets with orbital periods shorter than ~1 day have been discovered by the method of transits and their study can provide information on Earth-like planets not available from bodies ...on longer period orbits.
Aims.
A new mechanism for the internal heating of such ultra-short-period planets is proposed based on the gravitational perturbation produced by a non-axisymmetric quadrupole moment of their host stars. Such a quadrupole is due to the magnetic flux tubes in the stellar convection zone, unevenly distributed in longitude and persisting for many stellar rotations as observed in young late-type stars.
Methods.
The rotation period of the host star evolves from its shortest value on the zero-age main sequence (ZAMS) to longer periods due to the loss of angular momentum through a magnetized wind. If the stellar rotation period comes close to twice the orbital period of the planet, the quadrupole leads to a spin-orbit resonance that excites oscillations of the star-planet separation. As a consequence, a strong tidal dissipation is produced inside the planet that converts the energy of the oscillations into internal heat. The total heat released inside the planet scales as
a
−8
, where
a
is the orbit semimajor axis, and it is largely independent of the details of the planetary internal dissipation or the lifetime of the stellar magnetic flux tubes.
Results.
We illustrate the operation of the mechanism by modeling the evolution of the stellar rotation and of the innermost planetary orbit under the action of the stellar wind and the tides in the cases of CoRoT-7, Kepler-78, and K2-141 whose present orbital periods range between 0.28 and 0.85 days. If the spin-orbit resonance occurs, the maximum power dissipated inside the planets ranges between 10
18
and 10
19
W, while the total dissipated energy is on the order of 10
30
−10
32
J over a time interval as short as (1−4.5) × 10
4
yr.
Conclusions.
Our illustrative models suggest that, if their host stars started their evolution on the ZAMS as fast rotators with periods between 0.5 and 1.0 days, the resonance occurred after about 40 Myr since the host stars settled on the ZAMS in all the three cases. This huge heating over such a short time interval produces a complete melting of the planetary interiors and may shut off their hydromagnetic dynamos. These may initiate a successive phase of intense internal heating owing to unipolar magnetic star-planet interactions and affect the composition and the escape of their atmospheres, producing effects that could be observable during the entire lifetime of the planets.
Context. The interaction between the magnetic fields of late-type stars and their close-by planets may produce stellar flares as observed in active binary systems. However, in spite of several ...claims, conclusive evidence is still lacking. Aim. We estimate the magnetic energy available in the interaction using analytical models to provide an upper bound to the expected flare energy. Methods. We investigated three different mechanisms leading to magnetic energy release. The first two can release an energy up to (0.2–1.2) B02R3/μ$(0.2\hbox{--}1.2)\, B^{2}_{0}R^{3}/\mu$ (0.2–1.2)B02R3∕μ , where B0 is the surface field of the star, R its radius, and μ the magnetic permeability of the plasma. These two mechanisms operate in young active stars whose coronae have closed magnetic field lines up to the distance of their close-by planets that can trigger the energy release. The third mechanism operates in weakly or moderately active stars with a coronal field with predominantly open field lines at the distance of their planets. The released energy is of the order of (0.002–0.1) B02R3/μ $(0.002\hbox{--}0.1)\, B^{2}_{0}R^{3}/\mu$ (0.002–0.1)B02R3∕μ and depends on the ratio of the planetary to the stellar fields, thus allowing an indirect measurement of the former when the latter is known. Results. We compute the released energy for various separations of the planet and various stellar parameters finding the conditions for the operation of the proposed mechanisms. An application to eight selected systems is presented. Conclusions. The computed energies and dissipation timescales are in agreement with flare observations in the eccentric system HD 17156 and in the circular systems HD 189733 and HD 179949. This kind of star–planet interaction can be unambiguously identified by the higher flaring frequency expected close to periastron in eccentric systems.
ABSTRACT
We introduce a model for the orbital period modulation in systems with close-by giant planets based on a spin–orbit coupling that transfers angular momentum from the orbit to the rotation of ...the planet and vice versa. The coupling is produced by a permanent non-axisymmetric gravitational quadrupole moment assumed to be present in the solid core of the planet. We investigate two regimes of internal planetary rotation, that is, when the planet rotates rigidly and when the rotation of its deep interior is time-dependent as a consequence of a vacillating or intermittent convection in its outer shell. The model is applied to a sample of very hot Jupiters predicting maximum transit-time deviations from a constant-period ephemeris of approximately 50 s in the case of rigid rotation. The transit time variations of WASP-12, currently the only system showing evidence of a non-constant period, cannot be explained by assuming rigid rotation, but can be modelled in the time-dependent internal rotation regime, thus providing an alternative to their interpretation in terms of a tidal decay of the planet orbit.
Context. Late-type stars interact with their close-in planets through their coronal magnetic fields. Aims. We introduce a theory for the interaction between the stellar and planetary fields focussing ...on the processes that release magnetic energy in the stellar coronae. Methods. We consider the energy dissipated by the reconnection between the stellar and planetary magnetic fields as well as that made available by the modulation of the magnetic helicity of the coronal field produced by the orbital motion of the planet. We estimate the powers released by both processes in the case of axisymmetric and non-axisymmetric, linear and non-linear force-free coronal fields finding that they scale as B04/3 Bp02/3 Rp2 vrel, where B0 is the mean stellar surface field, Bp0 the planetary field at the poles, Rp the radius of the planet, and vrel the relative velocity between the stellar and the planetary fields. Results. A chromospheric hot spot or a flaring activity phased to the orbital motion of the planet are found only when the stellar field is axisymmetric. In the case of a non-axisymmetric field, the time modulation of the energy release is multiperiodic and can be easily confused with the intrinsic stellar variability. We apply our theory to the systems with some reported evidence of star-planet magnetic interaction finding a dissipated power at least one order of magnitude smaller than that emitted by the chromospheric hot spots. The phase lags between the planets and the hot spots are reproduced by our models in all the cases except for υ And. Conclusions. The chromospheric hot spots rotating in phase with the planets cannot be explained by the energy dissipation produced by the interaction between stellar and planetary fields as considered by our models and require a different mechanism.
We present the results of a blind exercise to test the recoverability of stellar rotation and differential rotation in Kepler light curves. The simulated light curves lasted 1000 d and included ...activity cycles, Sun-like butterfly patterns, differential rotation and spot evolution. The range of rotation periods, activity levels and spot lifetime were chosen to be representative of the Kepler data of solar-like stars. Of the 1000 simulated light curves, 770 were injected into actual quiescent Kepler light curves to simulate Kepler noise. The test also included five 1000-d segments of the Sun's total irradiance variations at different points in the Sun's activity cycle. Five teams took part in the blind exercise, plus two teams who participated after the content of the light curves had been released. The methods used included Lomb–Scargle periodograms and variants thereof, autocorrelation function and wavelet-based analyses, plus spot modelling to search for differential rotation. The results show that the ‘overall’ period is well recovered for stars exhibiting low and moderate activity levels. Most teams reported values within 10 per cent of the true value in 70 per cent of the cases. There was, however, little correlation between the reported and simulated values of the differential rotation shear, suggesting that differential rotation studies based on full-disc light curves alone need to be treated with caution, at least for solar-type stars. The simulated light curves and associated parameters are available online for the community to test their own methods.
Context. Evidence of magnetic interaction between late-type stars and close-in giant planets is provided by the observations of stellar hot spots rotating synchronously with the planets and showing ...an enhancement of chromospheric and X-ray fluxes. Possible photospheric signatures of such an interaction have also been reported. Aims. We investigate star-planet interaction in the framework of a magnetic field model of a stellar corona, considering the interaction between the coronal field and that of a planetary magnetosphere moving through the corona. This is motivated, among other reasons, by the difficulty of accounting for the energy budgets of the interaction phenomena with previous models. Methods. A linear force-free model is applied to describe the coronal field and study the evolution of its total magnetic energy and relative helicity according to the boundary conditions at the stellar surface and the effects related to the planetary motion through the corona. Results. The energy budget of the star-planet interaction is discussed, assuming that the planet may trigger a release of the energy of the coronal field by decreasing its relative helicity. The observed intermittent character of the star-planet interaction is explained by a topological change in the stellar coronal field, induced by a variation in its relative helicity. The model predicts the formation of many prominence-like structures in the case of highly active stars owing to the accumulation of matter evaporated from the planet inside an azimuthal flux rope in the outer corona. Moreover, the model can explain why stars accompanied by close-in planets have a higher X-ray luminosity than those with distant planets. It predicts that the best conditions for detecting radio emission from the exoplanets and their host stars are achieved when the field topology is characterized by field lines connected to the surface of the star, leading to a chromospheric hot spot rotating synchronously with the planet. Conclusions. The main predictions of the model can be verified with current observational techniques, by a simultaneous monitoring of the chromospheric flux and X-ray (or radio) emission, and spectropolarimetric observations of the photospheric magnetic fields.
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