What Asteroseismology Can Do for Exoplanets: KOI-42Ab Is a Small Neptune in an Eccentric Orbit Consistent with Low Obliquity
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What asteroseismology can do for exoplanets: KOI-42Ab is a Small Neptune in an eccentric orbit consistent with low obliquity V. Van Eylen1;2?, M. N. Lund1;4, V. Silva Aguirre1, T. Arentoft1, H. Kjeldsen1, S. Albrecht3, W. J. Chaplin5, H. Isaacson6, M. G. Pedersen1, J. Jessen-Hansen1, B. Tingley1, J. Christensen-Dalsgaard1, C. Aerts2 and T. Campante5 1 Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark 2 Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium 3 Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 4Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia 5School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK 6Department of Astronomy, University of California, Berkeley, CA 94820, USA [email protected] ABSTRACT We confirm the Kepler planet candidate KOI-42b as a Neptune sized exoplanet on a 17:8 day, eccentric, orbit around the bright (Kp = 9:4) star KOI-42A. KOI-42 consists of a blend between the fast rotating planet host star (KOI-42A) and a fainter star (KOI-42B), which has complicated the confirmation of the planetary candidate. Employing asteroseismology, using constraints from the transit light curve, adaptive optics and speckle images, and Spitzer transit observations, we demonstrate that the candidate can only be an exoplanet orbiting KOI-42A. Via asteroseismology we determine the following stellar and planetary parameters with high precision; M? = 1:214 ± 0:033 M ,R? = 1:352 ± 0:010 R , Age = 2:76 ± 0:54 Gyr, planetary radius (2:838 ± 0:054 R⊕), and +0:10 orbital eccentricity (0:17−0:05). In addition, rotational splitting of the pulsation modes allows for a measurement of KOI-42A's inclination and rotation rate. Our measurement of an inclination +5:0 ◦ of 82:5−5:2 [ ] indicates a low obliquity in this system. Subject headings: stars: individual (KOI-42; KIC 8866102; HD 175289) – stars: oscillations – planetary systems – stars: fundamental parameters 1. Introduction illustrates the intrinsic difficulty of exoplanet confir- mation. Launched March 2009, the Kepler mission has con- Stars showing transit-like features are termed tinuously observed a field in the sky centered on the Kepler Objects of Interest (KOIs). Here we study Cygnus-Lyra region with the primary goal of detect- KOI-42 (KIC 8866102, HD 175289), which shows ing (small) exoplanets, by photometrically measuring transit light features consistent with a small planet planetary transits to a high level of precision (Borucki (R ≈ 2:6 R ) on a relatively long orbit (17.83 d; et al. 2008). Apart from a growing list of confirmed p ⊕ Borucki et al. 2011). Apart from the bright host star planets (currently 152), the Kepler catalogue contains (Kepler magnitude K = 9.4) KOI-42 also consists of 3548 planetary candidates (Batalha et al. 2013). The p a fainter blended object (K = 12.2, Adams et al. order of magnitude difference between those numbers p 2012). We refer to this object as KOI-42B, while we 1 use KOI-42A for the bright host star. The brightness 2.1. Asteroseismic frequency analysis of the system would make it a prime target for follow- The extraction of mode parameters for the aster- up studies, if it can be confirmed that the transits are oseismic analysis was performed by Peak-bagging indeed occurring around KOI-42A. Unfortunately the the power spectrum (see, e. g., Appourchaux 2003). added complexity due to the presence of KOI-42B, This was done by making a global optimisation of and the presumably small mass of the planet candi- the power spectrum using an Markov Chain Monte date, has so far prevented the planetary candidate to be Carlo (MCMC) routine2, including a parallel temper- confirmed as planet, or shown to be a false positive. ing scheme to better search the full parameter space In this paper we will show that the transit like (see Handberg & Campante 2011). In the fit the fol- features are indeed caused by a planet orbiting KOI- lowing model was used for the power spectrum: 42A. For this we combine information from the well- determined transit shape with additional (ground- based) observations and Spitzer measurements. We nb 2 ` ˜ 2 X X X E`m(i)V` αn` also take advantage of KOI-42 being almost exclu- P(ν j; Θ) = +B(ν); (1) 4 − 2 n=n `=0 m=−` 1 + 2 (ν νn`m) sively observed in Kepler’s short-cadence mode (sam- a Γn` pling it every 58.8 s, Borucki et al. 2008), which allows for the detection of solar-like oscillations. Analyzing here na and nb represent respectively the first and last the stellar pulsations aids the confirmation of KOI-42A radial order included from the power spectrum. We as planet host and leads to accurate determination of include modes of degree ` = 0 − 2. Each mode is the stellar parameters. We further measure the stellar described by a Lorentzian profile (see, e. g., Anderson rotation and its inclination by analyzing the pulsation et al. 1990; Gizon & Solanki 2003) due to the way in modes. Such an analysis was recently carried out for which the p-modes are excited, namely stochastically Kepler-50 and Kepler-65 by (Chaplin et al. 2013). by the turbulent convection in the outer envelope upon which they are intrinsically damped (Goldreich et al. In §2, we describe the asteroseismic modeling be- 1994). In this description ν is the frequency of the fore we present the various arguments that validate n`m mode while Γ is a measure for the damping3 rate of KOI-42Ab as a planet in §3. The planetary and or- n` the mode and equals the full width at half maximum of bital parameters are presented in §4. We discuss the the Lorentzian. E (i) is a function that sets the relative characteristics of the the system in §5 and our conclu- `m heights between the azimuthal m-components in a split sions are presented in §6. multiplet as a function of the stellar inclination (see, e. g., Dziembowski 1977; Gizon & Solanki 2003). The 2. Stellar properties from asteroseismology ˜ 2 factor V` is the relative visibility (in power) of a mode KOI-42 was observed in short-cadence mode for relative to the radial and non-split ` = 0 modes. The the entire duration of the Kepler mission, except dur- factor αn` represents an amplitude modulation which ing the second quarter of observations (Q2) where the mainly depends on frequency and is generally well ap- long cadence mode was used. The latter observations proximated with a Gaussian. are not included in the asteroseismic analysis. Before In this work we do not fix the relative visibilities, using the data as input for asteroseismology, it is de- as recent studies (see e. g., Deheuvels et al. 2010; Sal- trended and normalised using a specifically designed abert et al. 2011; Lund et al. 2013) have suggested median filter to remove all transit features from the that the theoretical computed values are generally not time series. The resulting time series is then used to in good agreement with observations (see, e. g., Ballot derive a power spectrum1, which is shown in Figure1. et al. 2011). We describe the granulation background signal 1The power spectrum was calculated using a sine-wave fitting method given by B(ν) by power laws (Harvey 1985), specifi- (see, e. g., Kjeldsen 1992; Frandsen et al. 1995) which is normal- ized according to the amplitude-scaled version of Parseval’s theorem 2 (see, e. g., Kjeldsen & Frandsen 1992), in which a sine wave of peak The program StellarMC was used, which was written and is main- amplitude, A, will have a corresponding peak in the power spectrum tained by Rasmus Handberg. 3 of A2. The mode life time is given by τ = 1/πΓn`. 2 0.5 0.4 ] 2 0.3 Power [ppm 0.2 0.1 1200 1400 1600 1800 2000 2200 2400 2600 2800 Frequency [µHz] Fig. 1.— Power spectrum of KOI-42 (grey). Overlain are the model fits (Eq.1) obtained from the MCMC peak-bagging. The black curve gives the model when including modes from the range 1370 − 2630 µHz - all mode frequencies in this range were included in the stellar modelling. The red curve gives the model obtained when excluding the five outermost modes obtained in the first fit (black curve) in each end of the frequency scale. From this fit we get the estimates of the stellar inclination and frequency splitting. cally in the version proposed by Karoff (2008): will be split as (Ledoux 1951): 2 2 Ω X 4σ τi B(ν) = B + i : (2) νn`m = νn` + m (1 − Cn`) ≈ νn` + mνs; (3) n 1 + (2πντ )2 + (2πντ )4 2π i=1 i i with νn`m being the frequency entering into Eq.1, In this equation σ and τ gives, respectively, the rms i i while νn` gives the unperturbed resonance frequency. variation in the time domain and the characteristic time The azimuthal order of the mode is given by m, Ω is scale for the granulation and the faculae components. the angular rotation rate of the star and Cn` is a so- The constant Bn is a measure for the photon shot-noise. called Ledoux constant; here a dimensionless quantity The frequencies of the individual modes in the in- that describes the effect of the Coriolis force. For high- terval 1370−2630 µHz found from this optimisation is order, low-degree solar oscillations, as the ones seen −2 used in the stellar modelling, see § 2.2 and Figure1.