What asteroseismology can do for exoplanets

We describe three useful applications of asteroseismology in the context of exoplanet science: (1) the detailed characterisation of exoplanet host stars; (2) the measurement of stellar inclinations; and (3) the determination of orbital eccentricity from transit duration making use of asteroseismic stellar densities. We do so using the example system Kepler-410 (Van Eylen et al. 2014). This is one of the brightest (V = 9.4) Kepler exoplanet host stars, containing a small (2.8 Rearth) transiting planet in a long orbit (17.8 days), and one or more additional non-transiting planets as indicated by transit timing variations. The validation of Kepler-410 (KOI-42) was complicated due to the presence of a companion star, and the planetary nature of the system was confirmed after analyzing a Spitzer transit observation as well as ground-based follow-up observations.


Introduction
Asteroseismology can be of exceptional use in understanding and characterising planetary systems. It is well known in exoplanet science that a deep understanding of an extrasolar planet requires knowledge of the host star. We argue that in the context of exoplanets, asteroseismology can make three major contributions: 1. precise characterisation (i.e. mass, radius, age, ...) of exoplanet host stars; 2. obliquity determination of exoplanet systems by measuring stellar inclinations; 3. exoplanet eccentricity determination (without radial velocity measurements), by comparing stellar densities with measurements of transit durations.
To illustrate these points, we make use of the example system Kepler-410 [1] (formerly KOI-42), one of the brightest (V = 9.4) Kepler planet hosts. The system consists of two stars, Kepler-410A and a e-mail: vincent@phys.au.dk Kepler-410B, which are indistinguishable in Kepler photometry but have been resolved in groundbased follow-up observations [2,3]. The planet candidate (KOI-42b) was firmly established to be a planet orbiting Kepler-410A, making use of multi-color photometry, i.e. the use of Spitzer 4.5 µm observations. The data were analyzed in [1] and show a Spitzer transit depth which is essentially equal to the Kepler depth, as would be expected for a transiting planet orbiting Kepler-410A, while a planet orbiting Kepler-410B would cause a far deeper Spitzer transit because the different stellar energy distributions change the relative contributions of the two stars with different wavelengths. This principle is illustrated in Figure 1. For more details on the planetary validation, we refer to [1].
In the following we refer to the planet as Kepler-410A b. Its orbital period is 17.833648 ± 0.000054 days and its radius is 2.838 ± 0.054 R ⊕ [1]. Transit timing variations indicate Kepler-410 to be a multiplanet system, as they reveal the presence of at least one additional planet orbiting Kepler-410A.

What asteroseismology can do 2.1 Precise host star characterisation
In the context of exoplanets asteroseismology is perhaps most known for its ability to characterize stellar properties to a high level of precision. Stellar pulsations influence the brightness of stars, and the quality of Kepler time series allows for the extraction of oscillation frequencies after creating power spectra using Fourier transformation. Stellar oscillations' global patterns, such as the large frequency separation and frequency of maximum power, have been used to extract masses and radii of samples of exoplanet host stars (e.g. [4]). Detailed modeling of individual frequencies has been done for several interesting exoplanet hosts, such as Kepler-10 [5,6] and HAT-P-7 [7,8,9]. For Kepler-410, the stellar radius was measured to the percentage level [1], allowing a similar precision to be achieved for the planetary radius, a level at which systematics in the Kepler observations might become apparent [10].

Stellar inclination and obliquity
In cases with exceptionally high signal to noise photometric measurements, effects in the stellar oscillations caused by stellar rotation can be measured. Such rotational splittings provide information on   [13] (Kepler-25) and [14] (Kepler-56). Projected misalignments are measured using spot crossing events [15] (Kepler-30) and Rossiter-McLaughlin measurements [16,17] (Kepler-89 and Kepler-25). the stellar rotation rate, but the relative visibilities of the modes in triplets and quintuplets also reveal the stellar inclination [11]. This is because these visibilities are affected by geometric cancellation effects which depend on the stellar inclination. The latter is of particular use for exoplanet host stars, as it can reveal the obliquity of such systems.
The obliquities of Hot Jupiters display a wide variety [18,19], as determined from Rossiter-Mc-Laughlin observations. One possible explanation for the observed misalignments is that they have occurred during planetary migration (e.g. [20,21]), while another explanation assumes primordial stardisk misalignment (e.g. [22,23]). Observations of obliquities in multi-planet systems provide the possibility to distinguish between these scenarios. Measurements of obliquities in multi-planet systems, which typically have smaller planets, are however challenging using Rossiter-McLaughlin measurements, which are dependent on the transit depth. Asteroseismology, which directly measures stellar inclinations, is independent of the planetary size. A handful of multi-planet systems have currently been measured (see Figure 2). When compared to similar figures for Hot Jupiters (e.g. [19]), the obliquity distribution of multi-planet systems seem flatter (more aligned), consistent with [17] and [24]. However, the sample remains small.

Orbital eccentricity
Transit durations, assuming circular orbits, provide a measurement for the relative semi-major axis, a/R , which (for a known orbital period) can be converted into the stellar density using Kepler's third law [25]. If an independent measurement of the stellar density is available (e.g. from asteroseismology), then the transit duration can be used to test for circularity of the planetary orbit [26], as a non-zero eccentricity would change the transit duration. In case of disagreement in stellar density estimates, the anomalous transit duration can be related to the orbital eccentricity, which requires taking into account an (unknown) angle of periastron. Several other effects can complicate the measurement, e.g. transit timing variations, light curve blending, ... [27].
The method has been used to measure the eccentricity of Jupiter-sized planets [28,29]. For Kepler-410A b, we find a low but significantly non-zero eccentricity (0.17 +0.07 −0.06 ) [1]. We recall that Kepler-410A b, a super-Earth in a 17.8 day orbit, is beyond the range of eccentricity measurements using radial velocities, illustrating the potential of this technique.