Stellar Inclination Research Articles

A Relationship between Stellar Age and Spot Coverage

Abstract We investigate starspot distributions consistent with space-based photometry of F, G, and K stars in six stellar associations ranging in age from 10 Myr to 4 Gyr. We show that a simple light-curve statistic called the “smoothed amplitude” is proportional to stellar age as t −1/2, following a Skumanich-like spin-down relation. We marginalize over the unknown stellar inclinations by forward modeling the ensemble of light curves for direct comparison with the Kepler, K2, and TESS photometry. We sample the posterior distributions for spot coverage with approximate Bayesian computation. We find typical spot coverages in the range 1%–10%, which decrease with increasing stellar age. The spot coverage is proportional to t n where n = −0.37 ± 0.16, also statistically consistent with a Skumanich-like t −1/2 decay of starspot coverage with age. We apply two techniques to estimate the spot coverage of young exoplanet-hosting stars likely to be targeted for transmission spectroscopy with the James Webb Space Telescope, and estimate the bias in exoplanet radius measurements due to varying starspot coverage.

Activity time series of old stars from late F to early K

Context. The effect of stellar activity on radial velocity (RV) measurements appears to be a limiting factor in detecting Earth-mass planets in the habitable zone of a star that is similar to the Sun in spectral type and activity level. It is crucial to estimate whether this conclusion remain true for other stars with current correction methods. Aims. We built realistic time series in radial velocity and chromospheric emission for old main-sequence F6-K4 stars. We studied the effect of the stellar parameters we investigate on exoplanet detectability. The stellar parameters are spectral type, activity level, rotation period, cycle period and amplitude, latitude coverage, and spot constrast, which we chose to be in ranges that are compatible with our current knowledge of stellar activity. Methods. This very large set of synthetic time series allowed us to study the effect of the parameters on the RV jitter and how the different contributions to the RV are affected in this first analysis of the data set. The RV jitter was used to provide a first-order detection limit for each time series and different temporal samplings. Results. We find that the coverage in latitude of the activity pattern and the cycle amplitudes have a strong effect on the RV jitter, as has stellar inclination. RV jitter trends with B–V and Log R′HK are similar to observations, but activity cannot be responsible for RV jitter larger than 2–3 m s−1 for very quiet stars: this observed jitter is therefore likely to be due to other causes (instrumental noise or stellar or planetary companions, e.g.). Finally, we show that based on the RV jitter that is associated with each time series and using a simple criterion, a planet with one Earth mass and a period of one to two years probably cannot be detected with current analysis techniques, except for the lower mass stars in our sample, but very many observations would be required. The effect of inclination is critical. Conclusions. The results are very important in the context of future RV follow-ups of transit detections of such planets. We conclude that a significant improvement of analysis techniques and/or observing strategies must be made to reach such low detection limits.

Bayesian hierarchical inference of asteroseismic inclination angles

Abstract The stellar inclination angle – the angle between the rotation axis of a star and our line of sight – provides valuable information in many different areas, from the characterization of the geometry of exoplanetary and eclipsing binary systems to the formation and evolution of those systems. We propose a method based on asteroseismology and a Bayesian hierarchical scheme for extracting the inclination angle of a single star. This hierarchical method therefore provides a means to both accurately and robustly extract inclination angles from red giant stars. We successfully apply this technique to an artificial data set with an underlying isotropic inclination angle distribution to verify the method. We also apply this technique to 123 red giant stars observed with Kepler. We also show the need for a selection function to account for possible population-level biases, which are not present in individual star-by-star cases, in order to extend the hierarchical method towards inferring underlying population inclination angle distributions.

The Misaligned Orbit of the Earth-sized Planet Kepler-408b

Abstract Kepler-408 is one of the 33 planet-hosting Kepler stars for which asteroseismology has been used to investigate the orientation of the stellar rotation axis relative to the planetary orbital plane. The transiting hot Earth, Kepler-408b, has an orbital period of 2.5 days and a radius of 0.86 R ⊕, making it much smaller than the planets for which spin–orbit alignment has been studied using the Rossiter–McLaughlin effect. Because conflicting asteroseismic results have been reported in the literature, we undertake a thorough re-appraisal of this system and perform numerous checks for consistency and robustness. We find that the conflicting results are due to the different models for the low-frequency noise in the power spectrum. A careful treatment of the background noise resolves these conflicts, and shows that the stellar inclination is degrees. Kepler-408b is, by far, the smallest planet known to have a significantly misaligned orbit.

Star–disc (mis-)alignment in Rho Oph and Upper Sco: insights from spatially resolved disc systems with K2 rotation periods

The discovery of close in, giant planets (hot Jupiters) with orbital angular momentum vectors misaligned with respect to the rotation axis of their host stars presents problems for planet formation theories in which planets form in discs with angular momentum vectors aligned with that of the star. Violent, high eccentricity migration mechanisms purported to elevate planetary orbits above the natal disc plane predict populations of proto-hot Jupiters which have not been observed with Kepler. Alternative theories invoking primordial star-disc misalignments have recently received more attention. Here, the relative alignment between stars and their protoplanetary discs is assessed for the first time for a sample of 20 pre-main-sequence stars. Recently published rotation periods derived from high quality, long duration, high cadence K2 light curves for members of the $\rho$ Ophiuchus and Upper Scorpius star forming regions are matched with high angular resolution observations of spatially resolved discs and projected rotational velocities to determine stellar rotation axis inclination angles which are then compared to the disc inclinations. Ten of the fifteen systems for which the stellar inclination could be estimated are consistent with star-disc alignment while five systems indicate potential misalignments between the star and its disc. The potential for chance misalignment of aligned systems due to projection effects and characteristic measurement uncertainties is also investigated. While the observed frequency of apparent star-disc misalignments could be reproduced by a simulated test population in which 100% of systems are truly aligned, the distribution of the scale of inferred misalignment angles could not.

Observing the simulations: applying ZDI to 3D non-potential magnetic field simulations

The large-scale magnetic fields of stars can be obtained with the Zeeman-Doppler-Imaging (ZDI) technique, but their interpretation is still challenging as the contribution of the small-scale field or the reliability of the reconstructed field properties is still not fully understood. To quantify this, we use 3D non-potential magnetic field simulations for slowly rotating solar-like stars as inputs to test the capabilities of ZDI. These simulations are based on a flux transport model connected to a non-potential coronal evolution model using the observed solar flux emergence pattern. We first compare four field prescriptions regarding their reconstruction capabilities and investigate the influence of the spatial resolution of the input maps on the corresponding circularly polarised profiles. We then generate circularly polarised spectra based on our high resolution simulations of three stellar models with different activity levels, and reconstruct their large-scale magnetic fields using a non-potential ZDI code assuming two different stellar inclination angles. Our results show that the ZDI technique reconstructs the main features of slowly rotating solar-like stars but with $\sim\,$one order of magnitude less magnetic energy. The large-scale field morphologies are recovered up to harmonic modes $\ell \sim 5$, especially after averaging over several maps for each stellar model. While ZDI is not able to reproduce the input magnetic energy distributions across individual harmonic modes, the fractional energies across the modes are generally within $20\,\%$ agreement. The fraction of axisymmetric and toroidal field tends to be overestimated for stars with solar flux emergence patterns for more pole-on inclination angles.

Period spacings in red giants

Context. Oscillation modes with a mixed character, as observed in evolved low-mass stars, are highly sensitive to the physical properties of the innermost regions. Measuring their properties is therefore extremely important to probe the core, but requires some care, due to the complexity of the mixed-mode pattern. Aims. The aim of this work is to provide a consistent description of the mixed-mode pattern of low-mass stars, based on the asymptotic expansion. We also study the variation of the gravity offset εg with stellar evolution. Methods. We revisit previous works about mixed modes in red giants and empirically test how period spacings, rotational splittings, mixed-mode widths, and heights can be estimated in a consistent view, based on the properties of the mode inertia ratios. Results. From the asymptotic fit of the mixed-mode pattern of a large set of red giants at various evolutionary stages, we derive unbiased and precise asymptotic parameters. As the asymptotic expansion of gravity modes is verified with a precision close to the frequency resolution for stars on the red giant branch (10−4 in relative values), we can derive accurate values of the asymptotic parameters. We decipher the complex pattern in a rapidly rotating star, and explain how asymmetrical splittings can be inferred. We also revisit the stellar inclinations in two open clusters, NGC 6819 and NGC 6791: our results show that the stellar inclinations in these clusters do not have privileged orientation in the sky. The variation of the asymptotic gravity offset with stellar evolution is investigated in detail. We also derive generic properties that explain under which conditions mixed modes can be observed.

The GJ 504 system revisited

Context. The G-type star GJ504A is known to host a 3–35 MJup companion whose temperature, mass, and projected separation all contribute to making it a test case for planet formation theories and atmospheric models of giant planets and light brown dwarfs. Aims. We aim at revisiting the system age, architecture, and companion physical and chemical properties using new complementary interferometric, radial-velocity, and high-contrast imaging data. Methods. We used the CHARA interferometer to measure GJ504A’s angular diameter and obtained an estimation of its radius in combinationwith the HIPPARCOS parallax. The radius was compared to evolutionary tracks to infer a new independent age range for the system. We collected dual imaging data with IRDIS on VLT/SPHERE to sample the near-infrared (1.02–2.25 μm) spectral energy distribution (SED) of the companion. The SED was compared to five independent grids of atmospheric models (petitCODE,Exo-REM, BT-SETTL, Morley et al., and ATMO) to infer the atmospheric parameters of GJ 504b and evaluate model-to-model systematic errors. In addition, we used a specific model grid exploring the effect of different C/O ratios. Contrast limits from 2011 to 2017 were combined with radial velocity data of the host star through the MESS2 tool to define upper limits on the mass of additional companions in the system from 0.01 to 100 au. We used an MCMC fitting tool to constrain the companion’sorbital parameters based on the measured astrometry, and dedicated formation models to investigate its origin. Results. We report a radius of 1.35 ± 0.04 R⊙ for GJ504A. The radius yields isochronal ages of 21 ± 2 Myr or 4.0 ± 1.8 Gyr for the system and line-of-sight stellar rotation axis inclination of 162.4−4.3+3.8 degrees or 186.6−3.8+4.3 degrees. We re-detect the companion in the Y2, Y3, J3, H2, and K1 dual-band images. The complete 1–4 μm SED shape of GJ504b is best reproduced by T8-T9.5 objects with intermediate ages (≤ 1.5Gyr), and/or unusual dusty atmospheres and/or super-solar metallicities. All atmospheric models yield Teff = 550 ± 50 K for GJ504b and point toward a low surface gravity (3.5–4.0 dex). The accuracy on the metallicity value is limited by model-to-model systematics; it is not degenerate with the C/O ratio. We derive log L∕L⊙ = −6.15 ± 0.15 dex for the companion from the empirical analysis and spectral synthesis. The luminosity and Teff yield masses of M = 1.3−0.3+0.6 MJup and M = 23−9+10 MJup for the young and old age ranges, respectively. The semi-major axis (sma) is above 27.8 au and the eccentricity is lower than 0.55. The posterior on GJ 504b’s orbital inclination suggests a misalignment with the rotation axis of GJ 504A. We exclude additional objects (90% prob.) more massive than 2.5 and 30 MJup with semi-major axes in the range 0.01–80 au for the young and old isochronal ages, respectively. Conclusions. The mass and semi-major axis of GJ 504b are marginally compatible with a formation by disk-instability if the system is 4 Gyr old. The companion is in the envelope of the population of planets synthesized with our core-accretion model. Additional deep imaging and spectroscopic data with SPHERE and JWST should help to confirm the possible spin-orbit misalignment and refine the estimates on the companion temperature, luminosity, and atmospheric composition.

Characterization of the HD 219134 multiplanet system I. Observations of stellar magnetism, wind, and high-energy flux★

HD 219134 hosts several planets, with seven candidates reported, and the two shortest period planets are rocky (4-5 $M_{\oplus}$) and transit the star. Here we present contemporaneous multi-wavelength observations of the star HD 219134. We observed HD 219134 with the Narval spectropolarimeter at the Observatoire du Pic du Midi, and used Zeeman Doppler Imaging to characterise its large-scale stellar magnetic field. We found a weak poloidal magnetic field with an average unsigned strength of 2.5 G. From these data we confidently confirm the rotation period of 42 days, measure a stellar inclination of 77$\pm$8 degrees, and find evidence for differential rotation. The projected obliquity of the two transiting super-Earths is therefore between 0 and 20 degrees. We employed HST STIS observations of the Ly$\alpha$ line to derive a stellar wind mass-loss rate of half the solar value ($10^{-14} M_{\odot} {\rm yr}^{-1}$). We further collected photometric transit observations of the closest planet at near-UV wavelengths centred on the Mg II h&k lines with AstroSat. We found no detectable absorption, setting an upper limit on the transit depth of about 3%, which rules out the presence of a giant magnesium cloud larger than 9 planet radii. Finally, we estimated the high-energy flux distribution of HD 219134 as seen by planets b and c. These results present a detailed contemporaneous characterisation of HD 219134, and provide the ingredients necessary for accurately modelling the high-energy stellar flux, the stellar wind, and their impact on the two shortest-period planets, which will be presented in the second paper of this series.

HD 89345: a bright oscillating star hosting a transiting warm Saturn-sized planet observed by K2

We report the discovery and characterization of HD 89345b (K2-234b; EPIC 248777106b), a Saturn-sized planet orbiting a slightly evolved star. HD 89345 is a bright star ($V = 9.3$ mag) observed by the K2 mission with one-minute time sampling. It exhibits solar-like oscillations. We conducted asteroseismology to determine the parameters of the star, finding the mass and radius to be $1.12^{+0.04}_{-0.01}~M_\odot$ and $1.657^{+0.020}_{-0.004}~R_\odot$, respectively. The star appears to have recently left the main sequence, based on the inferred age, $9.4^{+0.4}_{-1.3}~\mathrm{Gyr}$, and the non-detection of mixed modes. The star hosts a "warm Saturn" ($P = 11.8$~days, $R_p = 6.86 \pm 0.14~R_\oplus$). Radial-velocity follow-up observations performed with the FIES, HARPS, and HARPS-N spectrographs show that the planet has a mass of $35.7 \pm 3.3~M_\oplus$. The data also show that the planet's orbit is eccentric ($e\approx 0.2$). An investigation of the rotational splitting of the oscillation frequencies of the star yields no conclusive evidence on the stellar inclination angle. We further obtained Rossiter-McLaughlin observations, which result in a broad posterior of the stellar obliquity. The planet seems to conform to the same patterns that have been observed for other sub-Saturns regarding planet mass and multiplicity, orbital eccentricity, and stellar metallicity.

Reliability of stellar inclination estimated from asteroseismology: analytical criteria, mock simulations and Kepler data analysis

Advances in asteroseismology of solar-like stars, now provide a unique method to estimate the stellar inclination $i_{\star}$. This enables to evaluate the spin-orbit angle of transiting planetary systems, in a complementary fashion to the Rossiter-McLaughlin effect, a well-established method to estimate the projected spin-orbit angle $\lambda$. Although the asteroseismic method has been broadly applied to the Kepler data, its reliability has yet to be assessed intensively. In this work, we evaluate the accuracy of $i_{\star}$ from asteroseismology of solar-like stars using 3000 simulated power spectra. We find that the low signal-to-noise ratio of the power spectra induces a systematic under-estimate (over-estimate) bias for stars with high (low) inclinations. We derive analytical criteria for the reliable asteroseismic estimate, which indicates that reliable measurements are possible in the range of $20^\circ \lesssim i_{\star} \lesssim 80^\circ$ only for stars with high signal-to-noise ratio. We also analyse and measure the stellar inclination of 94 Kepler main-sequence solar-like stars, among which 33 are planetary hosts. According to our reliability criteria, a third of them (9 with planets, 22 without) have accurate stellar inclination. Comparison of our asteroseismic estimate of $v\sin{i_{\star}}$ against spectroscopic measurements indicates that the latter suffers from a large uncertainty possibly due to the modeling of macro-turbulence, especially for stars with projected rotation speed $v\sin{i_{\star}} \lesssim 5$ km/s. This reinforces earlier claims, and the stellar inclination estimated from the combination of measurements from spectroscopy and photometric variation for slowly rotating stars needs to be interpreted with caution.

The first 62 AGNs observed with SDSS-IV MaNGA – I. Their characterization and definition of a control sample

We report the characterization of the first $62$ MaNGA Active Galactic Nuclei (AGN) hosts in the Fifth Product Launch (MPL-5) and the definition of a control sample of non-active galaxies. This control sample - comprising two galaxies for each AGN - was selected in order to match the AGN hosts in terms of stellar mass, redshift, visual morphology and inclination. The stellar masses are in the range $9.4<\log(M/M_\odot)<11.5$, and most objects have redshifts $\leq 0.08$. The AGN sample is mostly comprised of low-luminosity AGN, with only 17 nuclei with $L([OIII]\lambda 5007)\geq 3.8\times 10^{40}$ erg s$^{-1}$ (that we call "strong AGN"). The stellar population of the control sample galaxies within the inner $1$-$3$ kpc is dominated by the old ($\sim$ $4$ - $13$ Gyr) age component, with a small contribution of intermediate age ($\sim 640$-$940$ Myr) and young stars ($\leq 40$ Myr) to the total light at $5700\AA$. While the weaker AGN show a similar age distribution to that of the control galaxies, the strong AGN show an increased contribution of younger stars and a decreased contribution of older stars. Examining the relationship between the AGN stellar population properties and $L([OIII])$, we find that with increasing $L([OIII])$, the AGN exhibit a decreasing contribution from the oldest ($>4$ Gyr) stellar population relative to control galaxies, but have an increasing contribution from the younger components with ages $\sim 40$ Myr. We also find a correlation of the mean age differences (AGN - control) with $L([OIII])$, in the sense that more luminous AGN are younger than the control objects, while the low-luminosity AGN seem to be older. These results support a connection between the growth of the galaxy bulge via formation of new stars and the growth of the Supermassive Black Hole via matter accretion in the AGN phase.

An investigation of the rotational properties of magnetic chemically peculiar stars

The magnetic chemically peculiar (mCP) stars of the upper main sequence exhibit strong, globally-organised magnetic fields which are inclined to the rotational axis and facilitate the development of surface abundance inhomogeneities resulting in photometric and spectroscopic variability. Therefore, mCP stars are perfectly suited for a direct measurement of the rotational period without the need for any additional calibrations. We have investigated the rotational properties of mCP stars based on an unprecedentedly large sample consisting of more than 500 objects with known rotational periods. Using precise parallaxes from the Hipparcos and Gaia satellite missions, well-established photometric calibrations and state-of-the-art evolutionary models, we have determined the location of our sample stars in the Hertzsprung-Russell diagram and derived astrophysical parameters such as stellar masses, effective temperature, radii, inclinations and critical rotational velocities. We have confirmed the conservation of angular momentum during the main sequence evolution; no signs of additional magnetic braking were found. The inclination angles of the rotational axes are randomly distributed, although an apparent excess of fast rotators with comparable inclination angles has been observed. We have found a rotation rate of $\upsilon/\upsilon_{\rm crit} \geq 0.5$ for several stars, whose characteristics cannot be explained by current models. For the first time, we have derived the relationship between mass and rotation rate of mCP stars, and provide an analysis that links mass and rotation with magnetic field strength. Our sample is unique and offers crucial input for forthcoming evolutionary models that include the effects of magnetic fields for upper main sequence stars.

Starspot signature on the light curve

Quasi-periodic modulations of the stellar light curve may result from dark spots crossing the visible stellar disc. Due to differential rotation, spots at different latitudes generally have different rotation periods. Hence, by studying spot-induced modulations, one can learn about stellar surface (differential) rotation and magnetic activity. Recently, Reinhold & Arlt (2015) proposed a method based on the Lomb-Scargle periodogram of light curves to identify the sign of the differential rotation at the stellar surface. Our goal is to understand how the modulation of the stellar light curve due to the presence of spots and the corresponding periodogram are affected by both the stellar and spot properties. We generate synthetic light curves of stars with different properties (inclination angle, limb darkening, and rotation rate) and spot configurations (number of spots, latitude, intensity contrast, and size). By analysing their Lomb-Scargle periodograms, we compute the ratio between the heights of the second and first harmonics of the rotation period (peak-height-ratio). We find that the peak-height ratios are essentially a function of a single parameter, the fraction of time the spot is visible, which is related to the sinusoidality of the spot modulation. We identify the conditions under which the periodogram analysis can actually provide an estimate of the spot latitudes and/or the stellar inclination angle. We also identify possible sources of error in the identification of the sign of the differential rotation.

First Results from the Hertzsprung SONG Telescope: Asteroseismology of the G5 Subgiant Star μ Herculis*

Abstract We report the first asteroseismic results obtained with the Hertzsprung Stellar Observations Network Group Telescope from an extensive high-precision radial-velocity observing campaign of the subgiant μ Herculis. The data set was collected during 215 nights in 2014 and 2015. We detected a total of 49 oscillation modes with l values from zero to three, including some l = 1 mixed modes. Based on the rotational splitting observed in l = 1 modes, we determine a rotational period of 52 days and a stellar inclination angle of 63°. The parameters obtained through modeling of the observed oscillation frequencies agree very well with independent observations and imply a stellar mass between 1.11 and 1.15 M ⊙ and an age of Gyr. Furthermore, the high-quality data allowed us to determine the acoustic depths of the He ii ionization layer and the base of the convection zone.

Learning about the latitudinal distribution of starspots through the periodogram analysis of photometric data

Starspots are cooler and darker than the stellar surface. Therefore, the emitted flux of a star changes when spots are visible on its surface. The presence of spots together with the stellar rotation leads to a periodic modulation on the light curve. By studying that modulation one can then learn about the stellar rotation and also magnetic activity. Recently, Reinhold & Arlt (2015) proposed a method based on the analysis of the Lomb Scargle periodogram of the light curve to identify the sign of the differential rotation, i.e. whether the equator rotates faster than the poles or the opposite. We have been studying in detail the spots' impact on the light curve and on the resulting periodogram. We find that, under some conditions, the periodogram can actually provide an estimate of the true spot latitudes and/or the stellar inclination angle. Moreover, we find that the impact of the spot on the ratio between the heights of the second and first harmonics of the main peaks in the periodogram can be described by a single parameter, the visibility time of the spot. Finally, we also identify possible sources of false positives/negatives for the sign of the differential rotation.

OBLIQUITIES OF EXOPLANET HOST STARS FROM PRECISE DISTANCES AND STELLAR ANGULAR DIAMETERS

ABSTRACT The next generation of exoplanet space photometry missions proposed by both NASA and ESA promise to discover small transiting planets around the nearest and brightest main-sequence stars. The physical and rotational properties of these stars, in conjunction with Gaia-precision distances, can be used to determine the inclination of the stellar rotation axis. Given edge-on orbital paths for transiting planets, stellar inclinations can be interpreted as obliquities projected into the line of sight, which can be used to more clearly reveal the system architectures of small planets and the factors that drive their orbital evolution. To demonstrate the method, we use a sample of simulated target stars for the NASA Transiting Exoplanet Survey Satellite (TESS) mission. Based on predicted characteristics of these stars and likely measurement uncertainties, we show that the expected TESS discoveries will allow us to finely differentiate the true underlying obliquity distribution. Under conservative assumptions in our illustrative example—in which the true distribution is assumed to contain systems drawn from both well-aligned and isotropic distributions (e.g., due to multiple migration channels)—the correct fractions can be determined to within 0.15, thus enabling constraints on the evolutionary processes that shape system architectures. Moreover, because of the excellent astrometric precision expected from Gaia, this technique will also be applicable to the large number of planets already discovered by Kepler orbiting much more distant stars.

Recovering planet radial velocity signals in the presence of starspot activity in fully convective stars

Accounting for stellar activity is a crucial component of the search for ever-smaller planets orbiting stars of all spectral types. We use Doppler imaging methods to demonstrate that starspot induced radial velocity variability can be effectively reduced for moderately rotating, fully convective stars. Using starspot distributions extrapolated from sunspot observations, we adopt typical M dwarf starspot distributions with low contrast spots to synthesise line profile distortions. The distortions are recovered using maximum entropy regularised fitting and the corresponding stellar radial velocities are measured. The procedure is demonstrated for a late-M star harbouring an orbiting planet in the habitable zone. The technique is effective for stars with vsini = 1-10 km/s, reducing the stellar noise contribution by factors of nearly an order of magnitude. With a carefully chosen observing strategy, the technique can be used to determine the stellar rotation period and is robust to uncertainties such as unknown stellar inclination. While demonstrated for late-type M stars, the procedure is applicable to all spectral types.

The Rossiter-McLaughlin effect reloaded: Probing the 3D spin-orbit geometry, differential stellar rotation, and the spatially-resolved stellar spectrum of star-planet systems

When a planet transits its host star, it blocks regions of the stellar surface from view; this causes a distortion of the spectral lines and a change in the line-of-sight (LOS) velocities, known as the Rossiter-McLaughlin (RM) effect. Since the LOS velocities depend, in part, on the stellar rotation, the RM waveform is sensitive to the star-planet alignment (which provides information on the system's dynamical history). We present a new RM modelling technique that directly measures the spatially-resolved stellar spectrum behind the planet. This is done by scaling the continuum flux of the (HARPS) spectra by the transit light curve, and then subtracting the in- from the out-of-transit spectra to isolate the starlight behind the planet. This technique does not assume any shape for the intrinsic local profiles. In it, we also allow for differential stellar rotation and centre-to-limb variations in the convective blueshift. We apply this technique to HD189733 and compare to 3D magnetohydrodynamic (MHD) simulations. We reject rigid body rotation with high confidence (> 99% probability), which allows us to determine the occulted stellar latitudes and measure the stellar inclination. In turn, we determine both the sky-projected (lambda ~ -0.4 +/- 0.2 degrees) and true 3D obliquity (psi ~ 7^+12_-4 degrees). We also find good agreement with the MHD simulations, with no significant centre-to-limb variations detectable in the local profiles. Hence, this technique provides a new powerful tool that can probe stellar photospheres, differential rotation, determine 3D obliquities, and remove sky-projection biases in planet migration theories. This technique can be implemented with existing instrumentation, but will become even more powerful with the next generation of high-precision radial velocity spectrographs.

SPIN–ORBIT ALIGNMENT OF EXOPLANET SYSTEMS: ENSEMBLE ANALYSIS USING ASTEROSEISMOLOGY

ABSTRACT The angle ψ between a planet’s orbital axis and the spin axis of its parent star is an important diagnostic of planet formation, migration, and tidal evolution. We seek empirical constraints on ψ by measuring the stellar inclination i s via asteroseismology for an ensemble of 25 solar-type hosts observed with NASA’s Kepler satellite. Our results for i s are consistent with alignment at the 2σ level for all stars in the sample, meaning that the system surrounding the red-giant star Kepler-56 remains as the only unambiguous misaligned multiple-planet system detected to date. The availability of a measurement of the projected spin–orbit angle λ for two of the systems allows us to estimate ψ. We find that the orbit of the hot Jupiter HAT-P-7b is likely to be retrograde ( &psgr; = 116 &fdg; 4 &minus; 14.7 &plus; 30.2 ?> ), whereas that of Kepler-25c seems to be well aligned with the stellar spin axis ( &psgr; = 12 &fdg; 6 &minus; 11.0 &plus; 6.7 ?> ). While the latter result is in apparent contradiction with a statement made previously in the literature that the multi-transiting system Kepler-25 is misaligned, we show that the results are consistent, given the large associated uncertainties. Finally, we perform a hierarchical Bayesian analysis based on the asteroseismic sample in order to recover the underlying distribution of ψ. The ensemble analysis suggests that the directions of the stellar spin and planetary orbital axes are correlated, as conveyed by a tendency of the host stars to display large values of inclination.