Stellar Equator Research Articles

Nature or nurture of coplanar Tatooines: the aligned circumbinary Kuiper belt analogue around HD 131511

Abstract A key discovery of the Kepler mission is of the circumbinary planets known as ‘Tatooines’, which appear to be well aligned with their host stars’ orbits. Whether this alignment is due to initially coplanar circumbinary planet-forming discs (i.e. nature), or subsequent alignment of initially misaligned discs by warping the inner disc or torquing the binary (i.e. nurture), is not known. Tests of which scenario dominates may be possible by observing circumbinary Kuiper belt analogues (‘debris discs’), which trace the plane of the primordial disc. Here, the 140 au diameter circumbinary debris disc around HD 131511 is shown to be aligned to within 10° of the plane of the near edge-on 0.2 au binary orbit. The stellar equator is also consistent with being in this plane. If the primordial disc was massive enough to pull the binary into alignment, this outcome should be common and distinguishing nature versus nurture will be difficult. However, if only the inner disc becomes aligned with the binary, the HD 131511 system was never significantly misaligned. Given an initial misalignment, the ∼ Gyr main-sequence lifetime of the star allows secular perturbations to align the debris disc out to 100 au at the cost of an increased scaleheight. The observed debris disc scaleheight limits any misalignment to less than 25°. With only a handful known, many more such systems need to be characterized to help test whether the alignment of circumbinary planets is nature or nurture.

Detecting the spin-orbit misalignment of the super-Earth 55 Cancri e

We present time-resolved spectroscopy of transits of the super-Earth 55 Cnc e using HARPS-N observations. We devised an empirical correction for the "color effect" affecting the radial velocity residuals from the Keplerian fit, which significantly improves their dispersion with respect to the HARPS-N pipeline standard data-reduction. Using our correction, we were able to detect the smallest Rossiter-McLaughlin anomaly amplitude of an exoplanet so far (~60 cm/s). The super-Earth 55 Cnc e is also the smallest exoplanet with a Rossiter-McLaughlin anomaly detection. We measured the sky-projected obliquity lambda = 72.4 (+12.7 -11.5 deg), indicating that the planet orbit is prograde, highly misaligned and nearly polar compared to the stellar equator. The entire 55 Cancri system may have been highly tilted by the presence of a stellar companion.

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.

Multiple mean motion resonances in the HR 8799 planetary system

HR 8799 is a nearby star hosting at least four ~10 Jovian mass planets in wide orbits up to ~70au, detected through the direct, high-contrast infrared imaging. Large companions and debris disks reported interior to ~10au, and exterior to ~100au indicate massive protoplanetary disc in the past. The dynamical state of the HR 8799 system is not yet fully resolved, due to limited astrometric data covering tiny orbital arcs. We construct a new, orbital model of the HR 8799 system, assuming rapid migration of the planets after their formation in wider orbits. We found that the HR 8799 planets are likely involved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary orbits are coplanar with the stellar equator and inclined by ~25 degrees to the sky plane. This best-fit orbital configuration matches astrometry, debris disk models, and mass estimates from cooling models. The multiple MMR is stable for the age of the star ~160Myr, for at least 1 Gyr unless significant perturbations to the N-body dynamics are present. We predict four configurations with the fifth hypothetical innermost planet HR 8799f in ~9.7au, or ~7.5au orbit, extending the MMR chain to triple Laplace resonance 1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings may establish strong boundary conditions for the system formation and its early history.

Stellar scattering and the formation of hot Jupiters in binary systems

AbstractHot Jupiters (HJs) are usually defined as giant Jovian-size planets with orbital periods P⩽10 days. Although they lie close to the star, several have finite eccentricities and significant misalignment angle with respect to the stellar equator, leading to ~20% of HJs in retrograde orbits. More than half, however, seem consistent with near-circular and planar orbits. In recent years, two mechanisms have been proposed to explain the excited and misaligned subpopulation of HJs: Lidov–Kozai migration and planet–planet scattering. Although both are based on completely different dynamical phenomena, at first hand they appear to be equally effective in generating hot planets. Nevertheless, there has been no detailed analysis comparing the predictions of both mechanisms, especially with respect to the final distribution of orbital characteristics. In this paper, we present a series of numerical simulations of Lidov–Kozai trapping of single planets in compact binary systems that suffered a close fly-by of a background star. Both the planet and the binary component are initially placed in coplanar orbits, although the inclination of the impactor is assumed random. After the passage of the third star, we follow the orbital and spin evolution of the planet using analytical models based on the octupole expansion of the secular Hamiltonian. We also include tidal effects, stellar oblateness and post-Newtonian perturbations. The present work aims at the comparison of the two mechanisms (Lidov–Kozai and planet–planet scattering) as an explanation for the excited and inclined HJs in binary systems. We compare the results obtained through this paper with results in Beaugé & Nesvorný (2012), where the authors analyse how the planet–planet scattering mechanisms works in order to form this hot Jovian-size planets. We find that several of the orbital characteristics of the simulated HJs are caused by tidal trapping from quasi-parabolic orbits, independent of the driving mechanism (planet–planet scattering or Lidov–Kozai migration). These include both the 3-day pile-up and the distribution in the eccentricity versus semimajor axis plane. However, the distribution of the inclinations shows significant differences. While Lidov–Kozai trapping favours a more random distribution (or even a preference for near polar orbits), planet–planet scattering shows a large portion of bodies nearly aligned with the equator of the central star. This is more consistent with the distribution of known hot planets, perhaps indicating that scattering may be a more efficient mechanism for producing these bodies.

Star–planet–debris disc alignment in the HD 82943 system: is planetary system coplanarity actually the norm?

Recent results suggest that the two planets in the HD 82943 system are inclined to the sky plane by 20 +/- 4deg. Here, we show that the debris disk in this system is inclined by 27 +/- 4deg, thus adding strength to the derived planet inclinations and suggesting that the planets and debris disk are consistent with being aligned at a level similar to the Solar System. Further, the stellar equator is inferred to be inclined by 28 +/- 4deg, suggesting that the entire star - planet - disk system is aligned, the first time such alignment has been tested for radial velocity discovered planets on ~AU wide orbits. We show that the planet-disk alignment is primordial, and not the result of planetary secular perturbations to the disk inclination. In addition, we note three other systems with planets at >10AU discovered by direct imaging that already have good evidence of alignment, and suggest that empirical evidence of system-wide star - planet - disk alignment is therefore emerging, with the exception of systems that host hot Jupiters. While this alignment needs to be tested in a larger number of systems, and is perhaps unsurprising, it is a reminder that the system should be considered as a whole when considering the orientation of planetary orbits.

An exoplanet's response to anisotropic stellar mass loss during birth and death

The birth and death of planets may be affected by mass outflows from their parent stars during the T-Tauri or post-main-sequence phases of stellar evolution. These outflows are often modelled to be isotropic, but this assumption is not realistic for fast rotators, bipolar jets and supernovae. Here we derive the general equations of motion for the time evolution of a single planet, brown dwarf, comet or asteroid perturbed by anisotropic mass loss in terms of a complete set of planetary orbital elements, the ejecta velocity, and the parent star's co-latitude and longitude. We restrict our application of these equations to 1) rapidly rotating giant stars, and 2) arbitrarily-directed jet outflows. We conclude that the isotropic mass-loss assumption can safely be used to model planetary motion during giant branch phases of stellar evolution within distances of hundreds of au. In fact, latitudinal mass loss variations anisotropically affect planetary motion only if the mass loss is asymmetric about the stellar equator. Also, we demonstrate how constant-velocity, asymmetric bipolar outflows in young systems incite orbital inclination changes. Consequently, this phenomenon readily tilts exoplanetary orbits external to a nascent disc on the order of degrees.

Orbital and epicyclic frequencies of Maclaurin spheroids

We present analytical formulae for the orbital and epicyclic frequencies in orbits around Maclaurin spheroids in Newtonian gravity. The Laplace equation for the gravitational potential implies that the orbital frequency squared is the arithmetic mean of the squares of the epicyclic frequencies, $\omega _r^2 + \omega _z^2 = 2\Omega _{\rm o}^2$. The radial epicyclic frequency has a maximum at radius $r=\sqrt{2}ae$ for spheroid ellipticities $e>1/\sqrt{2}$, while for e = 0.834 583 18 it vanishes at the stellar equator (at r = a). For still larger ellipticities the innermost stable circular orbit (ISCO) is separated from the surface of the spheroid by a gap and has radius r ms = 1.198 203 ae. The vertical epicyclic frequency is always larger than the orbital one, and always by a factor of $\sqrt{2}$ in the marginally stable orbit. The presence of periastron motion, nodal precession (whose sense is the same as in retrograde orbits in the Kerr metric) and of the ISCO makes the properties of orbital motion around Maclaurin spheroids analogous to those in the Kerr metric. We find that the condition for the existence of circular orbits in test-particle motion is $\omega _r^2 + \omega _z^2 >0$, equally for the Maclaurin spheroid and for the Kerr metric.

Spectroscopic atlas of Hαand Hβin a sample of northern Be stars

We present Balmer lines spectroscopy for a sample of 48 Be stars. For most of them, H$\alpha$ and H$\beta$ have been observed more than two times, in a total period spanning almost two years between 2008 and 2009. Spectral synthesis of the H$\alpha$ profile was performed following two steps: photospheric contribution was computed by using Kurucz's code ATLAS9 and SYNTHE, and disk emission was derived by the approach of Hummel & Vrancken (2000, A&A, 302, 751). For 26 out of 48 stars, a modeling of the total H$\alpha$ emission has been attempted. By this modeling we derived an estimation of the disk radius, as well as the inclination angle between the rotational axis with line of sight and the base density at the stellar equator. For the stars observed more than once, we also discuss the variability of H$\alpha$ and H$\beta$ for what concerns both the equivalent width and the spectral profile. We found 16 stars with variable equivalent width and 7 stars with clear signs of profile variation. We derive effective temperature, gravity, and projected rotational velocity. We found 13 stars whose equivalent width is variable with a confidence level greater than 80% and 7 object for which spectral profiles show change with time. According to the commonly used classification scheme, we classified 16 stars as belonging to class 1, 13 to class 2, 11 are shell stars, 6 objects do not show net emission, and 2 stars display transitions from class 1 and 2. For the class 1 stars, we confirm the correlation between $v \sin i$ and peak separation. Concerning the geometry of the disk, we derived the base density at the stellar equator, the radius, and the inclination angle between rotational axis and line of sight. The maximum concentration of stars occurs for disk dimensions ranging in the interval of 6 to 8 stellar radii and for inclination angles going from 23$^\circ$ to $35^\circ$.

WASP-52b, WASP-58b, WASP-59b, and WASP-60b: Four new transiting close-in giant planets

We present the discovery of four new transiting hot jupiters, detected mainly from SuperWASP-North and SOPHIE observations. These new planets, WASP-52b, WASP-58b, WASP-59b, and WASP-60b, have orbital periods ranging from 1.7 to 7.9 days, masses between 0.46 and 0.94 M_Jup, and radii between 0.73 and 1.49 R_Jup. Their G1 to K5 dwarf host stars have V magnitudes in the range 11.7-13.0. The depths of the transits are between 0.6 and 2.7%, depending on the target. With their large radii, WASP-52b and 58b are new cases of low-density, inflated planets, whereas WASP-59b is likely to have a large, dense core. WASP-60 shows shallow transits. In the case of WASP-52 we also detected the Rossiter-McLaughlin anomaly via time-resolved spectroscopy of a transit. We measured the sky-projected obliquity lambda = 24 (+17/-9) degrees, indicating that WASP-52b orbits in the same direction as its host star is rotating and that this prograde orbit is slightly misaligned with the stellar equator. These four new planetary systems increase our statistics on hot jupiters, and provide new targets for follow-up studies.

THE DEBRIS DISK AROUND γ DORADUS RESOLVED WITHHERSCHEL

We present observations of the debris disk around gamma Doradus, an F1V star, from the Herschel Key Programme DEBRIS (Disc Emission via Bias-free Reconnaissance in the Infrared/Submillimetre). The disk is well-resolved at 70, 100 and 160 micron, resolved along its major axis at 250 micron, detected but not resolved at 350 micron, and confused with a background source at 500 micron. It is one of our best resolved targets and we find it to have a radially broad dust distribution. The modelling of the resolved images cannot distinguish between two configurations: an arrangement of a warm inner ring at several AU (best-fit 4 AU) and a cool outer belt extending from ~55 to 400 AU or an arrangement of two cool, narrow rings at ~70 AU and ~190 AU. This suggests that any configuration between these two is also possible. Both models have a total fractional luminosity of ~10^{-5} and are consistent with the disk being aligned with the stellar equator. The inner edge of either possible configuration suggests that the most likely region to find planets in this system would be within ~55 AU of the star. A transient event is not needed to explain the warm dust's fractional luminosity.

Planets on the spot

The three planets of the Kepler-30 system align closely with a starspot, indicating their common birth in a gaseous disk. Similar alignments could inform us about the origin of planets orbiting our stellar neighbours. See Letter p.449 In our Solar System, the Sun's equator and the planets' orbital planes are almost in alignment. This probably reflects the way they formed, from a single spinning disk of gas. Many exoplanet systems do not display this arrangement, however, and isolated 'hot Jupiters' are often misaligned and even have a retrograde orbit. This paper reports an exoplanet system that features alignments similar to those in the Solar System. Analysis of planetary transits across starspots on the Sun-like star Kepler-30 shows that the orbits of its three planets are aligned with the stellar equator. These findings support the suggestion that high orbital tilts (obliquities) are confined to systems that have experienced dynamic interactions of the type that produce hot Jupiters and potentially rule out star–disk misalignments as a cause.

Alignment of the stellar spin with the orbits of a three-planet system

The Sun's equator and the planets' orbital planes are nearly aligned, which is presumably a consequence of their formation from a single spinning gaseous disk. For exoplanetary systems this well-aligned configuration is not guaranteed: dynamical interactions may tilt planetary orbits, or stars may be misaligned with the protoplanetary disk through chaotic accretion , magnetic interactions or torques from neighbouring stars. Indeed, isolated 'hot Jupiters' are often misaligned and even orbiting retrograde. Here we report an analysis of transits of planets over starspots on the Sun-like star Kepler-30 (ref. 8), and show that the orbits of its three planets are aligned with the stellar equator. Furthermore, the orbits are aligned with one another to within a few degrees. This configuration is similar to that of our Solar System, and contrasts with the isolated hot Jupiters. The orderly alignment seen in the Kepler-30 system suggests that high obliquities are confined to systems that experienced disruptive dynamical interactions. Should this be corroborated by observations of other coplanar multi-planet systems, then star-disk misalignments would be ruled out as the explanation for the high obliquities of hot Jupiters, and dynamical interactions would be implicated as the origin of hot Jupiters.

GRAVITY DARKENING AND BRIGHTENING IN BINARIES

We apply a von Zeipel gravity darkening model to corotating binaries to obtain a simple, analytical expression for the emergent radiative flux from a tidally distorted primary orbiting a point-mass secondary. We adopt a simple Roche model to determine the envelope structure of the primary, assumed massive and centrally condensed, and use the results to calculate the flux. As for single rotating stars, gravity darkening reduces the flux along the stellar equator of the primary, but, unlike for rotating stars, we find that gravity brightening enhances the flux in a region around the stellar poles. We identify a critical limiting separation beyond which hydrostatic equilibrium no longer is possible, whereby the flux vanishes at the point on the stellar equator of the primary facing the companion. For equal-mass binaries, the total luminosity is reduced by about 13 % when this limiting separation is reached.

55 CANCRI: A COPLANAR PLANETARY SYSTEM THAT IS LIKELY MISALIGNED WITH ITS STAR

Although the 55 Cnc system contains multiple, closely packed planets that are presumably in a coplanar configuration, we use numerical simulations to demonstrate that they are likely to be highly inclined to their parent star's spin axis. Due to perturbations from its distant binary companion, this planetary system precesses like a rigid body about its parent star. Consequently, the parent star's spin axis and the planetary orbit normal likely diverged long ago. Because only the projected separation of the binary is known, we study this effect statistically, assuming an isotropic distribution for wide binary orbits. We find that the most likely projected spin-orbit angle is ~50 degrees, with a ~30% chance of a retrograde configuration. Transit observations of the innermost planet - 55 Cnc e - may be used to verify these findings via the Rossiter-McLaughlin effect. 55 Cancri may thus represent a new class of planetary systems with well-ordered, coplanar orbits that are inclined with respect to the stellar equator.

KEPLERAND GROUND-BASED TRANSITS OF THE EXO-NEPTUNE HAT-P-11b

We analyze 26 archival Kepler transits of the exo-Neptune HAT-P-11b, supplemented by ground-based transits observed in the blue (B-band) and near-IR (J-band). Both the planet and host star are smaller than previously believed; our analysis yields Rp=4.31 +/-0.06 Earth-radii, and Rs = 0.683 +/-0.009 solar radii, both about 3-sigma smaller than the discovery values. Our ground-based transit data at wavelengths bracketing the Kepler bandpass serve to check the wavelength dependence of stellar limb darkening, and the J-band transit provides a precise and independent constraint on the transit duration. Both the limb darkening and transit duration from our ground-based data are consistent with the new Kepler values for the system parameters. Our smaller radius for the planet implies that its gaseous envelope can be less extensive than previously believed, being very similar to the H-He envelope of GJ436b and Kepler-4b. HAT-P-11 is an active star, and signatures of star spot crossings are ubiquitous in the Kepler transit data. We develop and apply a methodology to correct the planetary radius for the presence of both crossed and uncrossed star spots. Star spot crossings are concentrated at phases -0.002 and +0.006. This is consistent with inferences from Rossiter-McLaughlin measurements that the planet transits nearly perpendicular to the stellar equator. We identify the dominant phases of star spot crossings with active latitudes on the star, and we infer that the stellar rotational pole is inclined at about 12 +/-5 degrees to the plane of the sky. We point out that precise transit measurements over long durations could in principle allow us to construct a stellar Butterfly diagram, to probe the cyclic evolution of magnetic activity on this active K-dwarf star.

Transiting exoplanets from the CoRoT space mission

We report the detection of CoRoT-18b, a massive hot Jupiter transiting in front of its host star with a period of 1.9000693 ± 0.0000028 days. This planet was discovered thanks to photometric data secured with the CoRoT satellite combined with spectroscopic and photometric ground-based follow-up observations. The planet has a mass Mp = 3.47 ± 0.38 MJup, a radius Rp = 1.31 ± 0.18 RJup, and a density ρp = 2.2 ± 0.8 g cm-3. It orbits a G9V star with a mass M⋆ = 0.95 ± 0.15 M⊙, a radius R⋆ = 1.00 ± 0.13 R⊙, and arotation period Prot = 5.4 ± 0.4 days. The age of the system remains uncertain, with stellar evolution models pointing either to a few tens Ma or several Ga, while gyrochronology and lithium abundance point towards ages of a few hundred Ma. This mismatch potentially points to a problem in our understanding of the evolution of young stars, with possibly significant implications for stellar physics and the interpretation of inferred sizes of exoplanets around young stars. We detected the Rossiter-McLaughlin anomaly in the CoRoT-18 system thanks to the spectroscopic observation of a transit. We measured the obliquity ψ = 20° ± 20° (sky-projected value λ = −10° ± 20°), indicating that the planet orbits in the same way as the star is rotating and that this prograde orbit is nearly aligned with the stellar equator.

A RADIO PULSAR SEARCH OF THE γ-RAY BINARIES LS I +61 303 AND LS 5039

LS I +61 303 and LS 5039 are exceptionally rare examples of HMXBs with MeV-TeV emission, making them two of only five known or proposed "gamma-ray binaries". There has been disagreement within the literature over whether these systems are microquasars, with stellar winds accreting onto a compact object to produce high energy emission and relativistic jets, or whether their emission properties might be better explained by a relativistic pulsar wind colliding with the stellar wind. Here we present an attempt to detect radio pulsars in both systems with the Green Bank Telescope. The upper limits of flux density are between 4.1-14.5 uJy, and we discuss the null results of the search. Our spherically symmetric model of the wind of LS 5039 demonstrates that any pulsar emission will be strongly absorbed by the dense wind unless there is an evacuated region formed by a relativistic colliding wind shock. LS I +61 303 contains a rapidly rotating Be star whose wind is concentrated near the stellar equator. As long as the pulsar is not eclipsed by the circumstellar disk or viewed through the densest wind regions, detecting pulsed emission may be possible during part of the orbit.

Constraining tidal dissipation in F-type main-sequence stars: the case of CoRoT-11

Tidal dissipation in late-type stars is presently poorly understood and the study of planetary systems hosting hot Jupiters can provide new observational constraints to test proposed theories. We focus on systems with F-type main-sequence stars and find that the recently discovered system CoRoT-11 is presently the best suited for such a kind of investigation. A classic constant tidal lag model is applied to reproduce the evolution of the system from a plausible nearly synchronous state on the ZAMS to the present state, thus putting constraints on the average modified tidal quality factor <Q'_s> of its F6V star. Initial conditions with the stellar rotation period longer than the orbital period of the planet can be excluded on the basis of the presently observed state in which the star spins faster than the planet orbit. It is found that <Q'_s> is approximately between 4.0E+06 and 2.0E+07 if the system started its evolution on the ZAMS close to synchronization with an uncertainty related to the constant tidal lag hypothesis and the estimated stellar magnetic braking within a factor of about 5-6. Moreover, we discuss how the present value of Q'_s can be measured by a timing of the mid-epoch and duration of the transits as well as of the planetary eclipses to be observed in the infrared with an accuracy of about 0.5-1 s over a time baseline of about 25 yr. CoRoT-11 is an highly interesting system potentially allowing us a direct measure of the tidal dissipation in an F-type star as well as the detection of the precession of the orbital plane of the planet that provides us with an accurate upper limit for the obliquity of the stellar equator. If the planetary orbit has a significant eccentricity (e>0.05), it will be possible to detect also the precession of the line of the apsides and derive information on the Love number of the planet and its tidal quality factor.

Time evolution and rotation of starspots on CoRoT-2 from the modelling of transit photometry

CoRoT-2, the second planet-hosting star discovered by the CoRoT satellite, is a young and active star. A total of 77 transits were observed for this system over a period of 135 days. Small modulations detected in the optical light curve of the planetary transits are used to study the position, size, intensity, and temporal evolution of the photospheric spots on the surface of the star that are occulted by the planetary disk. We apply a spot model to these variations and create a spot map of the stellar surface of CoRoT-2 within the transit band for every transit. From these maps, we estimate the stellar rotation period and obtain the longitudes of the spots in a reference frame rotating with the star. Moreover, the spots temporal evolution is determined. This model achieves a spatial resolution of 2\circ. Mapping of 392 spots vs. longitude indicates the presence of a region free of spots, close to the equator, reminiscent of the coronal holes observed on the Sun during periods of maximum activity. With this interpretation, the stellar rotation period within the transit latitudes of -14.\circ 6 \pm 10 \circ is found to be 4.48 days. This rotation period is shorter than the 4.54 days as derived from the out-of-transit light modulation. Since the transit data samples a region close to the stellar equator, while the period determined from out-of-transit data reflects the average rotation of the star, this is taken as an indication of a latitudinal differential rotation of about 3% or 0.042 rad/d.