Precise estimates of fundamental parameters of exoplanet host stars impact the characteri-zation of the planet. From photometric planetary transits the ratio of the radii of the planet and the star can be deduced, i.e.∆F/F = (Rp/R)2, where∆F/F is the transit depth in the photometric signal. Here and below, the index (p) denotes the properties of the planet, quantities without index correspond to the host star. When the inclinationipof the normal
Figure 6.2: Asteroseismic constraint on the mass of the companion of HD 52265. The filled circlerepresents the estimate on the stellar angular velocity, Ω, in units of the Car-rington value (Ω/2π =0.424µHz) and the inclination angle, sini, of the rotation axis of HD 52265 (Fit A). These values are derived from a global fit of the HD 52265 oscillation power spectrum. Thered areaindicates the uncertainty onΩandideduced from the like-lihood function and contains 68% (dark-red) and 85% (light-red) of all fits from the Monte Carlo simulation. Thediamondsrepresent the results for Ω andi obtained by the other groups of the DAT. The horizontal green lines correspond to the low-frequency peaks in the power spectrum which are attributed to stellar surface rotation (see Section 3.3.2, Figure 3.5). Theblue linesrepresent an alternative estimate onΩsini' vsini/R, where vsini is constrained by spectroscopy and R is derived from seismic modeling (see also Section 3.7.4). A lower limit for the mass of the companion HD 52265b was determined with radial velocity measurements, i.e. Mpsinip = 1.09±0.11 MJup(Butler et al. 2006).
Hereip is the inclination of the normal to the orbital plane of HD 52265b with respect to the line of sight. The mass is given in units of the Jupiter mass MJup. Thus, the in-clination angle of the rotation axis, i.e. the x-axis, may be interpreted as the mass, Mp
of the HD 52265b in units of MJupsini/sinip. Assuming i = ip, the upper x-axis gives the absolute mass of HD 52265b, suggesting that it is a planet and not a brown dwarf as indicated by thegrey shaded regions.
to the orbital plane with respect to the line of sight is known from the transit measure-ment, spectroscopic follow-up observations allow one to solve Kepler’s laws, such that the mass function, (Mp/M)2/3, can be determined with a precision of a few percent. The two relations demonstrate that the precision of the mass and radius of the planet crucially depends on the precision of the mass and radius estimates of the host star. Furthermore, the modeling of the evolution of exoplanetary systems require precise constraints on the age of the system, i.e. the age of the host star. In Section 6.2, I showed that asteroseismol-ogy provides improved estimates on these parameters compared to classical methods, in particular considering the stellar mass and age.
The assumption of the spin-orbit alignment, i = ip, to determine the mass of HD 52265b in the previous section is a very strong assumption which does not neces-sarily has to apply in the case of HD 52265. In fact, the measurement of the spin-orbit angle has become an important topic in the field of exoplanet research. According to the current state of the evolution of exoplanetary systems, giant gas planets are believed to form in the outer regions (∼ 5 AU) of the circumstellar disc of the central star and later migrate towards it and become a "hot Jupiter". There are several scenarios describing the migration process which try to model the actual distribution of of eccentricities and semi-major axis of the orbits of hot Jupiters. The "classical" disc-migration scenario proposed by Lin et al. (1996) results in planet orbits which are co-aligned with the stellar equator.
On the other hand scenarios like the Kozai cycles (Kozai 1962, Wu and Murray 2003) and planet scattering (Rasio and Ford 1996) allow for a misalignment of the stellar spin axis and the normal to the planetary orbit. The measurement of the spin-orbit angle may favor one of these scenarios and may help to constrain the theoretical modeling of the evolution of exoplanetary systems. Thetruespin-orbit angle,ψ, is given by (see e.g. Fabrycky and Winn 2009, Winn et al. 2009b)
cosψ=cosicosip+sinisinipcosλ, (6.3) whereλis thesky-projectedspin-orbit angle. The measurement of the spin-orbit angleψ requires an estimate of the inclination angle of the rotation axis of the host star. It was shown in this work, that the analysis of the time series of solar-like oscillations may in principle provide such an estimate oni. The inclination,ip, of the normal to the planet’s orbit and the sky-projected spin-orbit angle,λ, can be derived from planetary transits. The parameterλcan be measured with the Rossiter-McLaughlin (RM) effect (Rossiter 1924, McLaughlin 1924), i.e. the apparent shift of a spectral line while the planet transits its host star. When the planet occults a part of the star that forms, for example, the blue wing of the spectral line, this components is partially removed and the spectral line appears to be red-shifted and vice versa. For a detailed description of the measurement of λ, see for instance Gaudi and Winn (2007). In recent years, the sky-projected spin-orbit angle was measured for several systems. The first successful measurement ofλfor HD 20958 suggested a fairly co-aligned system (Queloz et al. 2000, Winn et al. 2005). Recent stud-ies reported on several transit systems which show a significant spin-orbit misalignment, e.g. HD 80606 (Moutou et al. 2009, Winn et al. 2009a), XO-3 (Hébrard et al. 2008, Winn et al. 2009c), CoRoT-3b (Triaud et al. 2009), and WASP 14b (Johnson et al. 2009). Winn et al. (2009b) even found that the planet HAT-P-7 is in a retrograde orbit around its host star, i.e. the orbital motion of the planet is opposite to the stellar rotation. Based on mea-surements ofλand reasonable assumptions on the distribution of the inclination angle of
study of Triaud et al. (2010) comprises all 26 known planetary systems where λ could be measured so far. Assuming a uniform distribution for cosi, i.e. the inclination of the stellar rotation axis, they conclude thatψ >20◦for 80% of the "hot Jupiters". I note again that these results are based on assumptions on the distribution of the stellar spin axis. As shown in this work, asteroseismology is in principle able to provide real measurements of the inclination of the stellar rotation axis such that true measurements of the spin-orbit angle,ψ, are feasible.
There is no transit measurement for HD 52265. Thus, a measurement of ψ for this system is not possible. However, the analysis of the CoRoT time series of HD 52265 reveals the potential of asteroseismology to supplement the characterization of planetary systems. The primary objective of the Kepler mission is the detection of planets with the transit method (e.g. Borucki et al. 2010). At the same time, the data may be used for an asteroseismic investigation of the observed stars (e.g. Christensen-Dalsgaard et al. 2008, Gilliland et al. 2010). Combined with spectroscopic follow-up observations this will im-prove constraints on the fundamental parameters of the observed planets, in particular their mass and age. The first seismic studies of planet host stars among the Kepler tar-gets presented by Christensen-Dalsgaard et al. (2010) look very promising. In particular, the object HAT-P-7 provides both the planetary transit and a clear spectrum of solar-like oscillations.
The possibility of combining planetary transit measurements with asteroseismic in-vestigations of their host stars will be taken to the next level if PLATO (e.g. Catala 2009) will be selected as an ESA M-class mission in late 2011 (the planned launch would be around 2018). The objective of PLATO is the characterization of planetary systems and the study of their evolution. For this purpose PLATO will observe 30000 cool dwarfs with V ≤ 11 for which a detailed asteroseismic analysis will be feasible. Combining the precise results on the stellar mass and age from seismology with the information ob-tained from the transits and the follow-up observations (e.g. ground-based spectroscopy and GAIA astrometry), mass and radius estimates of the planets with a precision of∼2%
and an age within a few hundred million years will become feasible.