Stellar Obliquity Research Articles

Starspots and spin‐orbit alignment for Kepler cool host stars

AbstractThe angle between the spin axis of the host star and the orbit of its planets (i.e., the stellar obliquity) is precious information about the formation and evolution of exoplanetary systems. Measurements of the Rossiter‐McLaughlin effect revealed that many stars that host a hot‐Jupiter have high obliquities, suggesting that hot‐Jupiter formation involves excitation of orbital inclinations. In this contribution we show how the passage of the planet over starspots can be used to measure the obliquity of exoplanetary systems. This technique is used to obtain – for the first time – the obliquity of a system with several planets that lie in a disk, Kepler‐30, with the result that the star has an obliquity smaller than 10 degrees. The implications for the formation of exoplanetary systems, in particular the hot‐Jupiter population, are also discussed. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

KELT-1b: A STRONGLY IRRADIATED, HIGHLY INFLATED, SHORT PERIOD, 27 JUPITER-MASS COMPANION TRANSITING A MID-F STAR

We present the discovery of KELT-1b, the first transiting low-mass companion from the wide-field Kilodegree Extremely Little Telescope-North (KELT-North) survey. The V=10.7 primary is a mildly evolved, solar-metallicity, mid-F star. The companion is a low-mass brown dwarf or super-massive planet with mass of 27.23+/-0.50 MJ and radius of 1.110+0.037-0.024 RJ, on a very short period (P=1.21750007) circular orbit. KELT-1b receives a large amount of stellar insolation, with an equilibrium temperature assuming zero albedo and perfect redistribution of 2422 K. Upper limits on the secondary eclipse depth indicate that either the companion must have a non-zero albedo, or it must experience some energy redistribution. Comparison with standard evolutionary models for brown dwarfs suggests that the radius of KELT-1b is significantly inflated. Adaptive optics imaging reveals a candidate stellar companion to KELT-1, which is consistent with an M dwarf if bound. The projected spin-orbit alignment angle is consistent with zero stellar obliquity, and the vsini of the primary is consistent with tidal synchronization. Given the extreme parameters of the KELT-1 system, we expect it to provide an important testbed for theories of the emplacement and evolution of short-period companions, and theories of tidal dissipation and irradiated brown dwarf atmospheres.

COUPLED EVOLUTIONS OF THE STELLAR OBLIQUITY, ORBITAL DISTANCE, AND PLANET'S RADIUS DUE TO THE OHMIC DISSIPATION INDUCED IN A DIAMAGNETIC HOT JUPITER AROUND A MAGNETIC T TAURI STAR

We revisit the calculation of the Ohmic dissipation in a hot Jupiter presented in Laine et al. (2008) by considering more realistic interior structures, stellar obliquity, and the resulting orbital evolution. In this simplified approach, the young hot Jupiter of one Jupiter mass is modelled as a diamagnetic sphere with a finite resistivity, orbiting across tilted stellar magnetic dipole fields in vacuum. Since the induced Ohmic dissipation occurs mostly near the planet's surface, we find that the dissipation is unable to significantly expand the young hot Jupiter. Nevertheless, the planet inside a small co-rotation orbital radius can undergo orbital decay by the dissipation torque and finally overfill its Roche lobe during the T Tauri star phase. The stellar obliquity can evolve significantly if the magnetic dipole is parallel/anti-parallel to the stellar spin. Our results are validated by the general torque-dissipation relation in the presence of the stellar obliquity. We also run the fiducial model in Laine et al. (2008) and find that the planet's radius is sustained at a nearly constant value by the Ohmic heating, rather than being thermally expanded to the Roche radius as suggested by the authors.

Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters

Observations of hot Jupiters around solar-type stars with very short orbital periods (~day) suggest that tidal dissipation in such stars is not too efficient so that these planets can survive against rapid orbital decay. This is consistent with recent theoretical works, which indicate that the tidal Q of planet-hosting stars can indeed be much larger than the values inferred from stellar binaries. On the other hand, recent measurements of Rossiter-McLaughlin effects in transiting hot Jupiter systems not only reveal that many such systems have misaligned stellar spin with respect to the orbital axis, but also show that systems with cooler host stars tend to have aligned spin and orbital axes. Winn et al. suggested that this obliquity - temperature correlation may be explained by efficient damping of stellar obliquity due to tidal dissipation in the star. This explanation, however, is in apparent contradiction with the survival of these short-period hot Jupiters. We show that in the solar-type parent stars of close-in exoplanetary systems, the effective tidal Q governing the damping of stellar obliquity can be much smaller than that governing orbital decay. This is because for misaligned systems, the tidal potential contains a Fourier component with frequency equal to the stellar spin frequency (in the rotating frame of the star). This component can excite inertial waves in the convective envelope of the star, and the dissipation of inertial waves then leads to a spin-orbit alignment torque, but not orbital decay. By contrast, for aligned systems, such inertial wave excitation is forbidden since the tidal forcing frequency is much larger than the stellar spin frequency. We derive a general effective tidal evolution theory for misaligned binaries, taking account of different tidal responses and dissipation rates for different tidal forcing components.

Spin–orbit resonance, transit duration variation and possible secular perturbations in KOI-13

ABSTRACT KOI-13 is the first known transiting system exhibiting light-curve distortions due to gravity darkening of the rapidly rotating host star. In this Letter, we analyse publicly available Kepler Q2–Q3 short-cadence observations, revealing a continuous light variation with a period of Prot= 25.43 ± 0.05 h and a half-amplitude of 21 ppm, which is linked to stellar rotation. This period is in exact 5:3 resonance with the orbit of KOI-13.01, which is the first detection of a spin–orbit resonance in a host of a substellar companion. The stellar rotation leads to stellar oblateness, which is expected to cause secular variations in the orbital elements. We indeed detect the gradual increment of the transit duration with a rate of (1.14 ± 0.30) × 10−6 d cycle−1. The confidence of this trend is 3.85σ, and the two-sided false alarm probability is 0.012 per cent. We suggest that the reason for this variation is the expected change of the impact parameter, with a rate of d b/d t=−0.016 ± 0.004 yr−1. Assuming b≈ 0.25, KOI-13.01 may become a non-transiting object in 75–100 years. The observed rate is compatible with the expected secular perturbations due to the stellar oblateness yielded by the fast rotation.

ROTATIONAL DOPPLER BEAMING IN ECLIPSING BINARIES

In eclipsing binaries the stellar rotation of the two components will cause a rotational Doppler beaming during eclipse ingress and egress when only part of the eclipsed component is covered. For eclipsing binaries with fast spinning components this photometric analogue of the well-known spectroscopic Rossiter-McLaughlin effect can exceed the strength of the orbital effect. Example light curves are shown for a detached double white dwarf binary, a massive O-star binary and a transiting exoplanet case, similar to WASP-33b. Inclusion of the rotational Doppler beaming in eclipsing systems is a prerequisite for deriving the correct stellar parameters from fitting high quality photometric light curves and can be used to determine stellar obliquities as well as e.g. an independent measure of the rotational velocity in those systems that may be expected to be fully synchronized.

STARSPOTS, SPIN-ORBIT MISALIGNMENT, AND ACTIVE LATITUDES IN THE HAT-P-11 EXOPLANETARY SYSTEM

We present the analysis of 4 months of Kepler photometry of the K4V star HAT-P-11, including 26 transits of its "super-Neptune" planet. The transit data exhibit numerous anomalies that we interpret as passages of the planet over dark starspots. These spot-crossing anomalies preferentially occur at two specific phases of the transit. These phases can be understood as the intersection points between the transit chord and the active latitudes of the host star, where starspots are most abundant. Based on the measured characteristics of spot-crossing anomalies, and previous observations of the Rossiter-McLaughlin effect, we find two solutions for the stellar obliquity (psi) and active latitude (l): either psi = 106 and l = 19.7, or psi = 97 and l = 67 (all in degrees). If the active latitude changes with time in analogy with the "butterfly diagram" of the Sun's activity cycle, future observations should reveal changes in the preferred phases of spot-crossing anomalies.

MEASUREMENT OF THE SPIN-ORBIT MISALIGNMENT OF KOI-13.01 FROM ITS GRAVITY-DARKENED KEPLER TRANSIT LIGHTCURVE

We model the asymmetry of the KOI-13.01 transit lightcurve assuming a gravity-darkened rapidly-rotating host star in order to constrain the system's spin-orbit alignment and transit parameters. We find that our model can reproduce the Kepler lightcurve for KOI-13.01 with a sky-projected alignment of {\lambda} = $23 \pm 4$ degrees and with the star's north pole tilted away from the observer by $48 \pm 4$ degrees (assuming $M_* = 2.05 M_\odot$). With both these determinations, we calculate that the net misalignment between this planet's orbit normal and its star's rotational pole is $56 \pm 4$ degrees. Degeneracies in our geometric interpretation also allow a retrograde spin-orbit angle of $124 \pm 4$ degrees. This is the first spin-orbit measurement to come from gravity darkening, and is one of only a few measurements of the full (not just the sky-projected) spin-orbit misalignment of an extrasolar planet. We also measure accurate transit parameters incorporating stellar oblateness and gravity darkening: $R_* = 1.756 \pm 0.014 R_\odot$, $R_p = 1.445 \pm 0.016 R_{Jup}$, and $i = 85.9 \pm 0.4$ degrees. The new lower planetary radius falls within the planetary mass regime for plausible interior models for the transiting body. A simple initial calculation shows that KOI-13.01's circular orbit is apparently inconsistent with the Kozai mechanism having driven its spin-orbit misalignment; planet-planet scattering and stellar spin migration remain viable mechanisms. Future Kepler data will improve the precision of the KOI-13.01 transit lightcurve, allowing more precise determination of transit parameters and the opportunity to use the Photometric Rossiter-McLaughlin effect to resolve the prograde/retrograde orbit determination degeneracy.

WASP-50 b: a hot Jupiter transiting a moderately active solar-type star

We report the discovery by the WASP transit survey of a giant planet in a close orbit (0.0295+-0.0009 AU) around a moderately bright (V=11.6, K=10) G9 dwarf (0.89+-0.08 M_sun, 0.84+-0.03 R_sun) in the Southern constellation Eridanus. Thanks to high-precision follow-up photometry and spectroscopy obtained by the telescopes TRAPPIST and Euler, the mass and size of this planet, WASP-50b, are well constrained to 1.47+-0.09 M_jup and 1.15+-0.05 R_jup, respectively. The transit ephemeris is 2455558.6120 (+-0.0002) + N x 1.955096 (+-0.000005) HJD_UTC. The size of the planet is consistent with basic models of irradiated giant planets. The chromospheric activity (log R'_HK = -4.67) and rotational period (P_rot = 16.3+-0.5 days) of the host star suggest an age of 0.8+-0.4 Gy that is discrepant with a stellar-evolution estimate based on the measured stellar parameters (rho_star = 1.48+-0.10 rho_sun, Teff = 5400+-100 K, [Fe/H]= -0.12+-0.08) which favours an age of 7+-3.5 Gy. This discrepancy could be explained by the tidal and magnetic influence of the planet on the star, in good agreement with the observations that stars hosting hot Jupiters tend to show faster rotation and magnetic activity (Pont 2009; Hartman 2010). We measure a stellar inclination of 84 (-31,+6) deg, disfavouring a high stellar obliquity. Thanks to its large irradiation and the relatively small size of its host star, WASP-50b is a good target for occultation spectrophotometry, making it able to constrain the relationship between hot Jupiters' atmospheric thermal profiles and the chromospheric activity of their host stars proposed by Knutson et al. (2010).

TWO UPPER LIMITS ON THE ROSSITER-MCLAUGHLIN EFFECT, WITH DIFFERING IMPLICATIONS: WASP-1 HAS A HIGH OBLIQUITY AND WASP-2 IS INDETERMINATE

We present precise radial-velocity measurements of WASP-1 and WASP-2 throughout transits of their giant planets. Our goal was to detect the Rossiter-McLaughlin (RM) effect, the anomalous radial velocity observed during eclipses of rotating stars, which can be used to study the obliquities of planet-hosting stars. For WASP-1 a weak signal of a prograde orbit was detected with ~2sigma confidence, and for WASP-2 no signal was detected. The resulting upper bounds on the RM amplitude have different implications for these two systems, because of the contrasting transit geometries and the stellar types. Because WASP-1 is an F7V star, and such stars are typically rapid rotators, the most probable reason for the suppression of the RM effect is that the star is viewed nearly pole-on. This implies the WASP-1 star has a high obliquity with respect to the edge-on planetary orbit. Because WASP-2 is a K1V star, and is expected to be a slow rotator, no firm conclusion can be drawn about the stellar obliquity. Our data and our analysis contradict an earlier claim that WASP-2b has a retrograde orbit, thereby revoking this system's status as an exception to the pattern that cool stars have low obliquities.

STARSPOTS AND SPIN-ORBIT ALIGNMENT IN THE WASP-4 EXOPLANETARY SYSTEM

We present photometry of 4 transits of the exoplanet WASP-4b, each with a precision of approximately 500 ppm and a time sampling of 40-60s. We have used the data to refine the estimates of the system parameters and ephemerides. During two of the transits we observed a short-lived, low-amplitude anomaly that we interpret as the occultation of a starspot by the planet. We also find evidence for a pair of similar anomalies in previously published photometry. The recurrence of these anomalies suggests that the stellar rotation axis is nearly aligned with the orbital axis, or else the star spot would not have remained on the transit chord. By analyzing the timings of the anomalies we find the sky-projected stellar obliquity to be -1_{-12}^{+14} degrees. This result is consistent with (and more constraining than) a recent observation of the Rossiter-McLaughlin effect. It suggests that the planet migration mechanism preserved the initially low obliquity, or else that tidal evolution has realigned the system. Future applications of this method using data from the Corot and Kepler missions will allow spin-orbit alignment to be probed for many other exoplanets.

The radius anomaly in the planet/brown dwarf overlapping mass regime

The recent detection of the transit of very massive substellar companions (CoRoT-3b, Deleuil et al. 2008; CoRoT-15b, Bouchy et al. 2010; WASP-30b, Anderson et al. 2010; Hat-P-20b, Bakos et al. 2010) provides a strong constraint to planet and brown dwarf formation and migration mechanisms. Whether these objects are brown dwarfs originating from the gravitational collapse of a dense molecular cloud that, at the same time, gave birth to the more massive stellar companion, or whether they are planets that formed through core accretion of solids in the protoplanetary disk can not always been determined unambiguously and the mechanisms responsible for their short orbital distances are not yet fully understood. In this contribution, we examine the possibility to constrain the nature of a massive substellar object from the various observables provided by the combination of Radial Velocity and Photometry measurements (e.g. M_p, R_p, M_s, Age, a, e...). In a second part, developments in the modeling of tidal evolution at high eccentricity and inclination - as measured for HD 80 606 with e=0.9337 (Naef et al. 2001), XO-3 with a stellar obliquity >37.3+-3.7 deg (H\'ebrard et al. 2008; Winn et al. 2009) and several other exoplanets - are discussed along with their implication in the understanding of the radius anomaly problem of extrasolar giant planets.

The Rossiter-McLaughlin effect for exoplanets

There are now more than 30 stars with transiting planets for which the stellar obliquity—or more precisely its sky projection—has been measured, via the eponymous effect of Rossiter and McLaughlin. The history of these measurements is intriguing. For 8 years a case was gradually building that the orbits of hot Jupiters are always well-aligned with the rotation of their parent stars. Then in a sudden reversal, many misaligned systems were found, and it now seems that even retrograde systems are not uncommon. I review the measurement technique underlying these discoveries, the patterns that have emerged from the data, and the implications for theories of planet formation and migration.

TIDAL EVOLUTION OF CLOSE-IN PLANETS

Recent discoveries of several transiting planets with clearly non-zero eccentricities and some large obliquities started changing the simple picture of close-in planets having circular and well-aligned orbits. The two major scenarios that form such close-in planets are planet migration in a disk and planet–planet interactions combined with tidal dissipation. The former scenario can naturally produce a circular and low-obliquity orbit, while the latter implicitly assumes an initially highly eccentric and possibly high-obliquity orbit, which are then circularized and aligned via tidal dissipation. Most of these close-in planets experience orbital decay all the way to the Roche limit as previous studies showed. We investigate the tidal evolution of transiting planets on eccentric orbits, and find that there are two characteristic evolution paths for them, depending on the relative efficiency of tidal dissipation inside the star and the planet. Our study shows that each of these paths may correspond to migration and scattering scenarios. We further point out that the current observations may be consistent with the scattering scenario, where the circularization of an initially eccentric orbit occurs before the orbital decay primarily due to tidal dissipation in the planet, while the alignment of the stellar spin and orbit normal occurs on a similar timescale to the orbital decay largely due to dissipation in the star. We also find that even when the stellar spin–orbit misalignment is observed to be small at present, some systems could have had a highly misaligned orbit in the past, if their evolution is dominated by tidal dissipation in the star. Finally, we also re-examine the recent claim by Levrard et al. that all orbital and spin parameters, including eccentricity and stellar obliquity, evolve on a similar timescale to orbital decay. This counterintuitive result turns out to have been caused by a typo in their numerical code. Solving the correct set of tidal equations, we find that the eccentricity behaves as expected, with orbits usually circularizing rapidly compared to the orbital decay rate.

The Rossiter-McLaughlin effect for exoplanets

AbstractThere are now more than 35 stars with transiting planets for which the stellar obliquity—or more precisely its sky projection—has been measured, via the eponymous effect of Rossiter and McLaughlin. The history of these measurements is intriguing. For 8 years a case was gradually building that the orbits of hot Jupiters are always well-aligned with the rotation of their parent stars. Then in a sudden reversal, many misaligned systems were found, and it now seems that even retrograde systems are not uncommon. I review the measurement technique underlying these discoveries, the patterns that have emerged from the data, and the implications for theories of planet formation and migration.

Starspots and spin-orbit alignment in the WASP-4 exoplanetary system

AbstractWe present the photometric analysis of 4 transits of the exoplanet WASP-4b, obtained with the Baade 6.5m telescope, one of the two Magellan telescopes at Las Campanas. The light curves have a photometric precision of 0.5 mmag and a time sampling of 30s. This high precision has allowed us to detect several “spot anomalies”: temporary brightenings due to the occultation of a starspot on the transit chord. By analyzing these anomalies we find the sky-projected stellar obliquity to be λ = 1°+12°−14°. The small value suggests that the planet migration mechanism preserved the initially low obliquity, or that tidal evolution has realigned the system.

HOT STARS WITH HOT JUPITERS HAVE HIGH OBLIQUITIES

We show that stars with transiting planets for which the stellar obliquity is large are preferentially hot (T_eff > 6250 K). This could explain why small obliquities were observed in the earliest measurements, which focused on relatively cool stars drawn from Doppler surveys, as opposed to hotter stars that emerged later from transit surveys. The observed trend could be due to differences in planet formation and migration around stars of varying mass. Alternatively, we speculate that hot-Jupiter systems begin with a wide range of obliquities, but the photospheres of cool stars realign with the orbits due to tidal dissipation in their convective zones, while hot stars cannot realign because of their thinner convective zones. This in turn would suggest that hot Jupiters originate from few-body gravitational dynamics, and that disk migration plays at most a supporting role.

Misaligned spin and orbital axes cause the anomalous precession of DI Herculis

The orbits of binary stars precess as a result of general relativistic effects, forces arising from the asphericity of the stars, and forces from any additional stars or planets in the system. For most binaries, the theoretical and observed precession rates are in agreement. One system, however-DI Herculis-has resisted explanation for 30 years. The observed precession rate is a factor of four slower than the theoretical rate, a disagreement that once was interpreted as evidence for a failure of general relativity. Among the contemporary explanations are the existence of a circumbinary planet and a large tilt of the stellar spin axes with respect to the orbit. Here we report that both stars of DI Herculis rotate with their spin axes nearly perpendicular to the orbital axis (contrary to the usual assumption for close binary stars). The rotationally induced stellar oblateness causes precession in the direction opposite to that of relativistic precession, thereby reconciling the theoretical and observed rates.

ON THE SPIN-ORBIT MISALIGNMENT OF THE XO-3 EXOPLANETARY SYSTEM

We present photometric and spectroscopic observations of the 2009 Feb. 2 transit of the exoplanet XO-3b. The new data show that the planetary orbital axis and stellar rotation axis are misaligned, as reported earlier by Hebrard and coworkers. We find the angle between the sky projections of the two axes to be 37.3 +/- 3.7 deg, as compared to the previously reported value of 70 +/- 15 deg. The significance of this discrepancy is unclear because there are indications of systematic effects. XO-3b is the first exoplanet known to have a highly inclined orbit relative to the equatorial plane of its parent star, and as such it may fulfill the predictions of some scenarios for the migration of massive planets into close-in orbits. We revisit the statistical analysis of spin-orbit alignment in hot-Jupiter systems. Assuming the stellar obliquities to be drawn from a single Rayleigh distribution, we find the mode of the distribution to be 13^{+5}_{-2} deg. However, it remains the case that a model representing two different migration channels--in which some planets are drawn from a perfectly-aligned distribution and the rest are drawn from an isotropic distribution--is favored over a single Rayleigh distribution.

FALLING TRANSITING EXTRASOLAR GIANT PLANETS

We revisit the tidal stability of extrasolar systems harboring a transiting planet and demonstrate that, independently of any tidal model, none, but one (HAT-P-2b) of these planets has a tidal equilibrium state, which implies ultimately a collision of these objects with their host star. Consequently, conventional circularization and synchronization timescales cannot be defined because the corresponding states do not represent the endpoint of the tidal evolution. Using numerical simulations of the coupled tidal equations for the spin and orbital parameters of each transiting planetary system, we confirm these predictions and show that the orbital eccentricity and the stellar obliquity do not follow the usually assumed exponential relaxation but instead decrease significantly, eventually reaching a zero value only during the final runaway merging of the planet with the star. The only characteristic evolution timescale of all rotational and orbital parameters is the lifetime of the system, which crucially depends on the magnitude of tidal dissipation within the star. These results imply that the nearly circular orbits of transiting planets and the alignment between the stellar spin axis and the planetary orbit are unlikely to be due to tidal dissipation. Other dissipative mechanisms, for instance interactions with the protoplanetary disk, must be invoked to explain these properties.