Star-planet interactions

Stars interact with their planets through gravitation, radiation, and magnetic fields. I shall focus on the interactions between late-type stars with an outer convection zone and close-in planets, i.e., with an orbital semimajor axis smaller than approximately 0.15 AU. I shall review the roles of tides and magnetic fields considering some key observations and discussing theoretical scenarios for their interpretation with an emphasis on open questions.Comment: 20 pages, 5 figures, invited talk at the 18th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, Proceedings of Lowell Observatory, edited by G. van Belle & H. Harri

Star-planet magnetic interaction and evaporation of planetary atmospheres

Stars interact with their close-in planets through radiation, gravitation, and magnetic fields. 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. 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 regions 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. We find that energetic electrons can reach levels down to column densities of 10^{23}-10^{25} 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)x10^{9} kg/s 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)x10^{10} kg/s are found in the case of magnetic loops interconnecting the planet with the star. 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.Comment: 13 pages, 8 figures, accepted by Astronomy and Astrophysic

On the correlation between stellar chromospheric flux and the surface gravity of close-in planets

The chromospheric emission of stars with close-in transiting planets has been found to correlate with the surface gravity of their planets. Stars with low-gravity planets have on average a lower chromospheric flux. We propose that this correlation is due to the absorption by circumstellar matter that comes from the evaporation of the planets. Planets with a lower gravity have a greater mass-loss rate which leads to a higher column density of circumstellar absorption and this in turn explains the lower level of chromospheric emission observed in their host stars. We estimated the required column density and found that planetary evaporation can account for it. We derived a theoretical relationship between the chromospheric emission as measured in the core of the Ca II H&K lines and the planet gravity. We applied this relationship to a sample of transiting systems for which both the stellar Ca II H&K emission and the planetary surface gravity are known and found a good agreement, given the various sources of uncertainties and the intrinsic variability of the stellar emissions and planetary evaporation rates. We consider implications for the radial velocity jitter applied to fit the spectroscopic orbits and for the age estimates of planetary systems based on the chromospheric activity level of their host stars.Comment: 5 pages, 2 figures, accepted as a Letter to the Editor of Astronomy and Astrophysic

Stellar activity, differential rotation, and exoplanets

The photospheric spot activity of some of the stars with transiting planets discovered by the CoRoT space experiment is reviewed. Their out-of-transit light modulations are fitted by a spot model previously tested with the total solar irradiance variations. This approach allows us to study the longitude distribution of the spotted area and its variations versus time during the five months of a typical CoRoT time series. The migration of the spots in longitude provides a lower limit for the surface differential rotation, while the variation of the total spotted area can be used to search for short-term cycles akin the solar Rieger cycles. The possible impact of a close-in giant planet on stellar activity is also discussed.Comment: 6 pages, 1 figure, 1 table; invited talk at the IAU Symposium 273 "Physics of Sun and Star Spots", Eds. D. P. Choudhary and K. G. Strassmeier, Cambridge Univ. Pres

Close-by planets and flares in their host stars

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. We estimate the magnetic energy available in the interaction using analytical models to provide an upper bound to the expected flare energy. We investigate three different mechanisms leading to magnetic energy release. The first two can release an energy up to $(0.2-1.2) B^{2}_{0} R^{3}/\mu$, where $B_{0}$ is the surface field of the star, $R$ its radius, and $\mu$ the magnetic permeability of the plasma. They 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 having a coronal field with predominantly open field lines at the distance of their planets. The released energy is of the order of $(0.002-0.1) B^{2}_{0} R^{3}/\mu$ 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. We compute the released energy for different separations of the planet and different stellar parameters finding the conditions for the operation of the proposed mechanisms. An application to eight selected systems is presented. 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.Comment: 17 pages, 9 figures, 5 tables; accepted to Astronomy and Astrophysic

Current state of the modelling of photospheric activity

I briefly review the current state of the modelling of photospheric activity based on the high-precision optical light curves obtained with MOST, CoRoT, and Kepler. These models can be used to search for active longitudes where activity is preferentially concentrated, estimate the amplitude of stellar differential rotation, and look for short-term activity cycles as, e.g., in the case of CoRoT-2. In the case of a late-type star accompanied by a transiting hot Jupiter, the small light modulations observed during transits when a dark spot is occulted by the disc of the planet are also briefly considered. They can be used to derive information on individual active regions as well as on stellar rotation and the spin-orbit alignment of the system.Comment: 6 pages, invited review at the 20th Stellar Pulsation Conference "Impact of new instrumentation and new insights in stellar pulsation" held in Granada, Spain, 5-9 September 2011 - L. A. Balona, J. Christensen-Dalsgaard, R. Garrido and J. C. Suarez (Eds.) to appear in Astrophysics and Space Science Proceeding

Comparing the performance of stellar variability filters for the detection of planetary transits

We have developed a new method to improve the transit detection of Earth-sized planets in front of solar-like stars by fitting stellar microvariability by means of a spot model. A large Monte Carlo numerical experiment has been designed to test the performance of our approach in comparison with other variability filters and fitting techniques for stars of different magnitudes and planets of different radius and orbital period, as observed by the space missions CoRoT and Kepler. Here we report on the results of this experiment.Comment: 4 pages, 3 postscript figures, Transiting Planets Proceeding IAU Symposium No.253, 200

Measurement of the radial velocity of the Sun as a star by means of a reflecting solar system body. The effect of the body rotation

Minor bodies of the solar system can be used to measure the spectrum of the Sun as a star by observing sunlight reflected by their surfaces. To perform an accurate measurement of the radial velocity of the Sun as a star by this method, it is necessary to take into account the Doppler shifts introduced by the motion of the reflecting body. Here we discuss the effect of its rotation. It gives a vanishing contribution only when the inclinations of the body rotation axis to the directions of the Sun and of the Earth observer are the same. When this is not the case, the perturbation of the radial velocity does not vanish and can reach up to about 2.4 m/s for an asteroid such as 2 Pallas that has an inclination of the spin axis to the plane of the ecliptic of about 30 degrees. We introduce a geometric model to compute the perturbation in the case of a uniformly reflecting body of spherical or triaxial ellipsoidal shape and provide general results to easily estimate the magnitude of the effect.Comment: 14 pages, 5 figures, 3 tables, accepted by Experimental Astronom

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.Comment: 32 pages, 10 figures, one table; accepted to Celestial Mechanics and Dynamical Astronomy, special issue on tide

Time evolution and rotation of starspots on CoRoT-2 from the modelling of transit photometry

CoRoT-2, the second planet-hosting star discovered by the CoRoT satellite, is a young and active star. A total of 77 transits were observed for this system over a period of 135 days. Small modulations detected in the optical light curve of the planetary transits are used to study the position, size, intensity, and temporal evolution of the photospheric spots on the surface of the star that are occulted by the planetary disk. We apply a spot model to these variations and create a spot map of the stellar surface of CoRoT-2 within the transit band for every transit. From these maps, we estimate the stellar rotation period and obtain the longitudes of the spots in a reference frame rotating with the star. Moreover, the spots temporal evolution is determined. This model achieves a spatial resolution of 2\circ. Mapping of 392 spots vs. longitude indicates the presence of a region free of spots, close to the equator, reminiscent of the coronal holes observed on the Sun during periods of maximum activity. With this interpretation, the stellar rotation period within the transit latitudes of -14.\circ 6 \pm 10 \circ is found to be 4.48 days. This rotation period is shorter than the 4.54 days as derived from the out-of-transit light modulation. Since the transit data samples a region close to the stellar equator, while the period determined from out-of-transit data reflects the average rotation of the star, this is taken as an indication of a latitudinal differential rotation of about 3% or 0.042 rad/d.Comment: 8 pages, 12 figure