Spin-orbit Angle Research Articles

THE DYNAMICS OF THE MULTI-PLANET SYSTEM ORBITING KEPLER-56

Kepler-56 is a multi-planet system containing two coplanar inner planets that are in orbits misaligned with respect to the spin axis of the host star, and an outer planet. Various mechanisms have been proposed to explain the broad distribution of spin-orbit angles among exoplanets, and these theories fall under two broad categories. The first is based on dynamical interactions in a multi-body system, while the other assumes that disk migration is the driving mechanism in planetary configuration and that the star (or disk) is titled with respect to the planetary plane. Here we show that the large observed obliquity of Kepler-56 system is consistent with a dynamical origin. In addition, we use observations by Huber et al. (2013) to derive the obliquity's probability distribution function, thus improving the constrained lower limit. The outer planet may be the cause of the inner planets' large obliquities, and we give the probability distribution function of its inclination, which depends on the initial orbital configuration of the planetary system. We show that even in the presence of precise measurement of the true obliquity, one cannot distinguish the initial configurations. Finally we consider the fate of the system as the star continues to evolve beyond the main sequence, and we find that the obliquity of the system will not undergo major variations as the star climbs the red giant branch. We follow the evolution of the system and find that the innermost planet will be engulfed in ~129 Myr. Furthermore we put an upper limit of ~155 Myr for the engulfment of the second planet. This corresponds to ~ 3% of the current age of the star.

MERGERS AND OBLIQUITIES IN STELLAR TRIPLES

Many close stellar binaries are accompanied by a far-away star. The "eccentric Kozai-Lidov" (EKL) mechanism can cause dramatic inclination and eccentricity fluctuations, resulting in tidal tightening of inner binaries of triple stars. We run a large set of Monte-Carlo simulations including the secular evolution of the orbits, general relativistic precession and tides, and we determine the semimajor axis, eccentricity, inclination and spin-orbit angle distributions of the final configurations. We find that the efficiency of forming tight binaries (<~16 d) when taking the EKL mechanism into account is ~ 21%, and about 4% of all simulated systems ended up in a merger event. These merger events can lead to the formation of blue-stragglers. Furthermore, we find that the spin-orbit angle distribution of the inner binaries carries a signature of the initial setup of the system, thus observations can be used to disentangle close binaries' birth configuration. The resulting inner and outer final orbits' period distributions, and their estimated fraction, suggests secular dynamics may be a significant channel for the formation of close binaries in triples and even blue stragglers.

ROSSITER-MCLAUGHLIN OBSERVATIONS OF 55 Cnc e

We present Rossiter-McLaughlin observations of the transiting super-Earth 55 Cnc e collected during six transit events between January 2012 and November 2013 with HARPS and HARPS-N. We detect no radial-velocity signal above 35 cm/s (3-sigma) and confine the stellar v sin i to 0.2 +/- 0.5 km/s. The star appears to be a very slow rotator, producing a very low amplitude Rossiter-McLaughlin effect. Given such a low amplitude, the Rossiter-McLaughlin effect of 55 Cnc e is undetected in our data, and any spin-orbit angle of the system remains possible. We also performed Doppler tomography and reach a similar conclusion. Our results offer a glimpse of the capacity of future instrumentation to study low amplitude Rossiter-McLaughlin effects produced by super-Earths.

A SPIN-ORBIT ALIGNMENT FOR THE HOT JUPITER HATS-3b

We have measured the alignment between the orbit of HATS-3b (a recently discovered, slightly inflated Hot Jupiter) and the spin-axis of its host star. Data were obtained using the CYCLOPS2 optical-fiber bundle and its simultaneous calibration system feeding the UCLES spectrograph on the Anglo-Australian Telescope. The sky-projected spin-orbit angle of $\lambda = 3\pm25^{\circ}$ was determined from spectroscopic measurements of Rossiter-McLaughlin effect. This is the first exoplanet discovered through the HATSouth transit survey to have its spin-orbit angle measured. Our results indicate that the orbital plane of HATS-3b is consistent with being aligned to the spin axis of its host star. The low obliquity of the HATS-3 system, which has a relatively hot mid F-type host star, agrees with the general trend observed for Hot Jupiter host stars with effective temperatures $>6250$K to have randomly distributed spin-orbit angles.

Spin-orbit angle distribution and the origin of (mis)aligned hot Jupiters

For 61 transiting hot Jupiters, the projection of the angle between the orbital plane and the stellar equator (called the spin-orbit angle) has been measured. For about half of them, a significant misalignment is detected, and retrograde planets have been observed. This challenges scenarios of the formation of hot Jupiters. In order to better constrain formation models, we relate the distribution of the real spin-orbit angle $\Psi$ to the projected one $\beta$. Then, a comparison with the observations is relevant. We analyse the geometry of the problem to link analytically the projected angle $\beta$ to the real spin-orbit angle $\Psi$. The distribution of $\Psi$ expected in various models is taken from the literature, or derived with a simplified model and Monte-Carlo simulations in the case of the disk-torquing mechanism. An easy formula to compute the probability density function (PDF) of $\beta$ knowing the PDF of $\Psi$ is provided. All models tested here look compatible with the observed distribution beyond 40 degrees, which is so far poorly constrained by only 18 observations. But only the disk-torquing mechanism can account for the excess of aligned hot Jupiters, provided that the torquing is not always efficient. This is the case if the exciting binaries have semi-major axes as large as 10000 AU. Based on comparison with the set of observations available today, scattering models and the Kozai cycle with tidal friction models can not be solely responsible for the production of all hot Jupiters. Conversely, the presently observed distribution of the spin-orbit angles is compatible with most hot Jupiters having been transported by smooth migration inside a proto-planetary disk, itself possibly torqued by a companion.

Spin-orbit angle in compact planetary systems perturbed by an inclined companion. Application to the 55 Cancri system

AbstractThe stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. For example, 55 Cancri is a system composed of 5 planets orbiting a member of a stellar binary for which a projected obliquity of 72±12 ° relative to the orbit of the innermost planet has been reported (Bourrier &amp; Hébrard 2014). This large obliquity has been attributed to the perturbation induced by the binary. Here we describe the secular evolution of similar systems and we discuss the case of the 55 Cancri system more deeply. We provide two different orbital configurations compatible with the currently available observations.

COMPACT PLANETARY SYSTEMS PERTURBED BY AN INCLINED COMPANION. II. STELLAR SPIN-ORBIT EVOLUTION

The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an inclined outer companion. Our study is based on classical secular theory, using a vectorial approach developed in a separate paper. When planet-planet perturbations are truncated at the second order in eccentricity and mutual inclination, and the planet-companion perturbations are developed at the quadrupole order, the problem becomes integrable. The motion is composed of a uniform precession of the whole system around the total angular momentum, and in the rotating frame, the evolution is periodic. Here, we focus on the relative motion associated to the oscillations of the inclination between the planet system and the outer orbit, and of the obliquities of the star with respect to the two orbital planes. The solution is obtained using a powerful geometric method. With this technique, we identify four different regimes characterized by the nutation amplitude of the stellar spin-axis relative to the orbital plane of the planets. In particular, the obliquity of the star reaches its maximum when the system is in the Cassini regime where planets have more angular momentum than the star, and where the precession rate of the star is similar to that of the planets induced by the companion. In that case, spin-orbit oscillations exceed twice the inclination between the planets and the companion. Even if mutual inclination is only ~ 20 deg, this resonant case can cause the spin-orbit angle to oscillate between perfectly aligned and retrograde values.

THE BANANA PROJECT. V. MISALIGNED AND PRECESSING STELLAR ROTATION AXES IN CV VELORUM

As part of the BANANA project (Binaries Are Not Always Neatly Aligned), we have found that the eclipsing binary CV Velorum has misaligned rotation axes. Based on our analysis of the Rossiter-McLaughlin effect, we find sky-projected spin-orbit angles of $\beta_{\rm p} = -52\pm6^{\circ}$ and $\beta_{\rm s}= 3\pm7^{\circ}$ for the primary and secondary stars (B2.5V $+$ B2.5V, $P=6.9$ d). We combine this information with several measurements of changing projected stellar rotation speeds ($v \sin i_{\star}$) over the last $30$ years, leading to a model in which the primary star's obliquity is $\approx65^{\circ}$, and its spin axis precesses around the total angular momentum vector with a period of about $140$ years. The geometry of the secondary star is less clear, although a significant obliquity is also implicated by the observed time variations in the $v \sin i_{\star}$. By integrating the secular tidal evolution equations backward in time, we find that the system could have evolved from a state of even stronger misalignment similar to DI Herculis, a younger but otherwise comparable binary.

TIDAL EVOLUTION OF THE SPIN-ORBIT ANGLE IN EXOPLANETARY SYSTEMS

The angle between the stellar spin and the planetary orbit axes (spin-orbit angle) is supposed to carry valuable information on the initial condition of the planet formation and the subsequent migration history. Indeed current observations of the Rossiter- McLaughlin effect have revealed a wide range of spin-orbit misalignments for transiting exoplanets. We examine in detail the tidal evolution of a simple system comprising a Sun-like star and a hot Jupiter adopting the equilibrium tide and the inertial wave dissipation effects simultaneously. We find that the combined tidal model works as a very efficient realignment mechanism; it predicts three distinct states of the spin-orbit angle (i.e., parallel, polar, and anti-parallel orbits) for a while, but the latter two states eventually approach the parallel spin-orbit configuration. The intermediate spin-orbit angles as measured in recent observations are difficult to be achieved. Therefore the current model cannot reproduce the observed broad distribution of the spin-orbit angles, at least in its simple form. This indicates that the observed diversity of the spin-orbit angles may emerge from more complicated interactions with outer planets and/or may be the consequence of the primordial misalignment between the proto-planetary disk and the stellar spin, which requires future detailed studies.

A NEARLY POLAR ORBIT FOR THE EXTRASOLAR HOT JUPITER WASP-79b

We report the measurement of a spin-orbit misalignment for WASP-79b, a recently discovered, bloated transiting hot Jupiter from the WASP survey. Data were obtained using the CYCLOPS2 optical-fiber bundle and its simultaneous calibration system feeding the UCLES spectrograph on the Anglo-Australian Telescope. We have used the Rossiter-McLaughlin effect to determine the sky-projected spin-orbit angle to be lambda = -106+19-13 degrees. This result indicates a significant misalignment between the spin axis of the host star and the orbital plane of the planet -- the planet being in a nearly polar orbit. WASP-79 is consistent with other stars that have Teff > 6250K and host hot Jupiters in spin-orbit misalignment.

Spin-Orbit Angles as a Probe to Orbital Evolution

AbstractWe observed with HARPS, the Rossiter-McLaughlin effect for 40 of the 75 transiting hot Jupiters discovered in the Southern Hemisphere by WASP. Our observations reveal a wide distribution in orbital inclinations indicative of past dynamical interactions. Our data also demonstrate the important effect produced by tidal interactions in shaping the spin–orbit (β) angle distribution. We briefly present and interpret the data we collected in a series of graphs.

ANALYSIS OF SPIN-ORBIT MISALIGNMENT IN THE ECLIPSING BINARY DI HERCULIS

Eclipsing binary DI Herculis (DI Her) is known to exhibit anomalously slow apsidal precession, below the rate predicted by the general relativity. Recent measurements of the Rossiter-McLauglin effect indicate that stellar spins in DI Her are almost orthogonal to the orbital angular momentum, which explains the anomalous precession in agreement with the earlier theoretical suggestion by Shakura. However, these measurements yield only the projections of the spin-orbit angles onto the sky plane, leaving the spin projection onto our line of sight unconstrained. Here we describe a method of determining the full three-dimensional spin orientation of the binary components relying on the use of the gravity darkening effect, which is significant for the rapidly rotating stars in DI Her. Gravity darkening gives rise to nonuniform brightness distribution over the stellar surface, the pattern of which depends on the stellar spin orientation. Using archival photometric data obtained during multiple eclipses spread over several decades we are able to constrain the unknown spin angles in DI Her with this method, finding that spin axes of both stars lie close to the plane of the sky. Our procedure fully accounts for the precession of stellar spins over the long time span of observations.

THE BANANA PROJECT. IV. TWO ALIGNED STELLAR ROTATION AXES IN THE YOUNG ECCENTRIC BINARY SYSTEM EP CRUCIS: PRIMORDIAL ORIENTATION AND TIDAL ALIGNMENT

With observations of the EP Cru system, we continue our series of measurements of spin-orbit angles in eclipsing binary star systems, the BANANA project (Binaries Are Not Always Neatly Aligned). We find a close alignment between the sky projections of the rotational and orbital angular momentum vectors for both stars (beta_p = -1.8+-1.6 deg and |beta_s|<17 deg). We also derive precise absolute dimensions and stellar ages for this system. The EP Cru and DI Her systems provide an interesting comparison: they have similar stellar types and orbital properties, but DI Her is younger and has major spin-orbit misalignments, raising the question of whether EP Cru also had a large misalignment at an earlier phase of evolution. We show that tidal dissipation is an unlikely explanation for the good alignment observed today, because realignment happens on the same timescale as spin-orbit synchronization, and the stars in EP Cru are far from syncrhonization (they are spinning 9 times too quickly). Therefore it seems that some binaries form with aligned axes, while other superficially similar binaries are formed with misaligned axes.

New analytical expressions of the Rossiter-McLaughlin effect adapted to different observation techniques

The Rossiter-McLaughlin (hereafter RM) effect is a key tool for measuring the projected spin-orbit angle between stellar spin axes and orbits of transiting planets. However, the measured radial velocity (RV) anomalies produced by this effect are not intrinsic and depend on both instrumental resolution and data reduction routines. Using inappropriate formulas to model the RM effect introduces biases, at least in the projected velocity Vsin(i) compared to the spectroscopic value. Currently, only the iodine cell technique has been modeled, which corresponds to observations done by, e.g., the HIRES spectrograph of the Keck telescope. In this paper, we provide a simple expression of the RM effect specially designed to model observations done by the Gaussian fit of a cross-correlation function (CCF) as in the routines performed by the HARPS team. We derived also a new analytical formulation of the RV anomaly associated to the iodine cell technique. For both formulas, we modeled the subplanet mean velocity v_p and dispersion beta_p accurately taking the rotational broadening on the subplanet profile into account. We compare our formulas adapted to the CCF technique with simulated data generated with the numerical software SOAP-T and find good agreement up to Vsin(i) < 20 km/s. In contrast, the analytical models simulating the two different observation techniques can disagree by about 10 sigma in Vsin(i) for large spin-orbit misalignments. It is thus important to apply the adapted model when fitting data.

The EBLM project

This paper introduces a series of papers aiming to study the dozens of low mass eclipsing binaries (EBLM), with F, G, K primaries, that have been discovered in the course of the WASP survey. Our objects are mostly single-line binaries whose eclipses have been detected by WASP and were initially followed up as potential planetary transit candidates. These have bright primaries, which facilitates spectroscopic observations during transit and allows the study of the spin-orbit distribution of F, G, K+M eclipsing binaries through the Rossiter-McLaughlin effect. Here we report on the spin-orbit angle of WASP-30b, a transiting brown dwarf, and improve its orbital parameters. We also present the mass, radius, spin-orbit angle and orbital parameters of a new eclipsing binary, J1219-39b (1SWAPJ121921.03-395125.6, TYC 7760-484-1), which, with a mass of 95 +/- 2 Mjup, is close to the limit between brown dwarfs and stars. We find that both objects orbit in planes that appear aligned with their primaries' equatorial planes. Neither primaries are synchronous. J1219-39b has a modestly eccentric orbit and is in agreement with the theoretical mass--radius relationship, whereas WASP-30b lies above it.

PLANET-PLANET ECLIPSE AND THE ROSSITER-McLAUGHLIN EFFECT OF A MULTIPLE TRANSITING SYSTEM: JOINT ANALYSIS OF THE SUBARU SPECTROSCOPY AND THE KEPLER PHOTOMETRY

We report a joint analysis of the Rossiter-McLaughlin (RM) effect with Subaru and the Kepler photometry for Kepler Object of Interest (KOI) 94 system. The system comprises four transiting planet candidates with orbital periods of 22.3 (KOI-94.01), 10.4 (KOI-94.02), 54.3 (KOI-94.03), and 3.7 (KOI-94.04) days from the Kepler photometry. We performed the radial velocity (RV) measurement of the system with the Subaru 8.2 m telescope on August 10, 2012 (UT), covering a complete transit of KOI-94.01 for $\sim 6.7$ hours. The resulting RV variation due to the RM effect spectroscopically confirms that KOI-94.01 is indeed the transiting planet, and implies that its orbital axis is well aligned with the stellar spin axis; the projected spin-orbit angle $\lambda$ is estimated as $-6_{-11}^{+13}$ deg. This is the first measurement of the RM effect for a multiple transiting system. Remarkably, the archived Kepler lightcurve around BJD=2455211.5 (date in UT January 14/15, 2010) indicates a "ouble transit" event of KOI-94.01 and KOI-94.03, in which the two planets transit the stellar disk simultaneously. Moreover, the two planets partially overlap each other, and exhibit a "planet-planet eclipse" around the transit center. This provides a rare opportunity to put tight constraints on the configuration of the two transiting planets by joint analysis with our Subaru RM measurement. Indeed, we find that the projected mutual inclination of KOI-94.01 and KOI-94.03 is estimated to be $\delta = -1.15 \pm 0.55$ deg. Implications for the migration model of multiple planet systems are also discussed.

MEASUREMENTS OF STELLAR INCLINATIONS FOR KEPLER PLANET CANDIDATES

We present an investigation of spin-orbit angles for planetary system candidates reported by Kepler. By combining the rotational period $P_s$ inferred from the flux variation due to starspots and the projected rotational velocity $V\sin I_s$ and stellar radius obtained by a high resolution spectroscopy, we attempt to estimate the inclination $I_s$ of the stellar spin axis with respect to the line-of-sight. For transiting planetary systems, in which planetary orbits are edge-on seen from us, the stellar inclination $I_s$ can be a useful indicator of a spin-orbit alignment/misalignment. We newly conducted spectroscopic observations with Subaru/HDS for 15 KOI systems, whose lightcurves show periodic flux variations. After detailed analyses of their lightcurves and spectra, it turned out that some of them are binaries, or the flux variations are too coherent to be caused by starspots, probably representing ellipsoidal variations, and consequently we could constrain stellar inclinations $I_s$ for eight systems. Among them, KOI-262 and 280 are in good agreement with $I_s=90^\circ$ suggesting a spin-orbit alignment, while at least one system, KOI-261, shows a possible spin-orbit misalignment. We also obtain a small $I_s$ for KOI-1463, but the transiting companion seems to be a star rather than a planet. The results for KOI-257, 269, 367, and 974 are ambiguous, and can be explained with either misalignments or moderate differential rotation. Since our method can be applied to any system having starspots regardless of the planet size, future observations will allow for the expansion of the parameter space in which the spin-orbit relations are investigated.

Detection and Characterization of Transiting Systems with Smaller Exoplanets

AbstractWe present our effort to detect and characterize transiting systems with small exoplanets. First we present our on-going project to detect transiting exoplanets around late-type stars. As many authors point out, late-type stars can host potentially habitable rocky planets, whose transits are detectable with 2-meter class telescopes. We aim at detecting (small-sized) transiting exoplanets around M-type stars and are conducting a survey using the Okayama 1.88m telescope. We introduce our campaign at Okayama. Next we discuss the characterization of small-sized exoplanets. We focus on the measurement of the spin-orbit angle, the angle between the stellar spin axis and planetary orbital axis. The spin-orbit relations are of great importance in discussing planetary formations, evolutions, and migrations. To this point, the Rossiter-McLaughlin (RM) effect, an apparent radial velocity anomaly during a planetary transit, has been mainly investigated to measure the projected spin-orbit angles. However, as the size of the transiting planet becomes smaller, the detection of the RM effect becomes challenging because of the small RM signal. We have newly developed a technique to investigate spin-orbit relations for smaller planets by combining Kepler's ultra-precise photometry and spectroscopic measurements. We show that, contrary to planetary systems with close-in giant planets, most of the systems with small-sized planets (including Earth-sized ones) have smaller spin-orbit angles, which implies a different evolutional history of the planetary systems. We also discuss future prospects on the detection and characterization of smaller transiting exoplanets.

ON THE FORMATION OF HOT JUPITERS IN STELLAR BINARIES

We study the production of Hot Jupiters (HJs) in stellar binaries. We show that the "eccentric Kozai-Lidov" (EKL) mechanism can play a key role in the dynamical evolution of a star-planet-star triple system. We run a large set of Monte Carlo simulations including the secular evolution of the orbits, general relativistic precession, and tides, and we determine the semi-major axis, eccentricity, inclination and spin-orbit angle distributions of the HJs that are produced. We explore the effect of different tidal friction parameters on the results. We find that the efficiency of forming HJs when taking the EKL mechanism into account is higher then previously estimated. Accounting for the frequency of stellar binaries, we find that this production mechanism can account for about 30% of the observed HJ population. Current observations of spin-orbit angles are consistent with this mechanism producing \sim 30% of all HJs, and up to 100% of the misaligned systems. Based on the properties of binaries without a HJ in our simulations, we predict the existence of many Jupiter-like planets with moderately eccentric and inclined orbits and semi-major axes of several AU.

Doppler tomography of transiting exoplanets: a prograde, low-inclined orbit for the hot Jupiter CoRoT-11b

We report the detection of the Doppler shadow of the transiting hot Jupiter CoRoT-11b. Our analysis is based on line-profile tomography of time-series, Keck/HIRES high-resolution spectra acquired during the transit of the planet. We measured a sky-projected, spin-orbit angle of 0.1 +/- 2.6 degrees, which is consistent with a very low-inclined orbit with respect to the stellar rotation axis. We refined the physical parameters of the system using a Markov chain Monte Carlo simultaneous fitting of the available photometric and spectroscopic data. An analysis of the tidal evolution of the system shows how the currently measured obliquity and its uncertainty translate into an initial absolute value of less than about 10 degrees on the zero-age main sequence, for an expected average modified tidal quality factor of the star Q'* > 4 x 10^6. This is indicative of an inward migration scenario that would not have perturbed the primordial low obliquity of CoRoT-11b. Taking into account the effective temperature and mass of the planet host star (Teff=6440 K, M*=1.23 MSun), the system can be considered a new telling exception to the recently proposed trend, according to which relatively hot and massive stars (Teff>6250 K, M*>1.2 MSun) seem to be preferentially orbited by hot Jupiters with high obliquity.