ABSTRACT Eccentricity is a parameter of particular interest as it is an informative indicator of the past of planetary systems. It is however not always clear whether the eccentricity fitted on ...radial velocity data is real or if it is an artefact of an inappropriate modelling. In this work, we address this question in two steps: we first assume that the model used for inference is correct and present interesting features of classical estimators. Secondly, we study whether the eccentricity estimates are to be trusted when the data contain incorrectly modelled signals, such as missed planetary companions, non-Gaussian noises, correlated noises with unknown covariance, etc. Our main conclusion is that data analysis via posterior distributions, with a model including a free error term gives reliable results provided two conditions. First, convergence of the numerical methods needs to be ascertained. Secondly, the noise power spectrum should not have a particularly strong peak at the semiperiod of the planet of interest. As a consequence, it is difficult to determine if the signal of an apparently eccentric planet might be due to another inner companion in 2:1 mean motion resonance. We study the use of Bayes factors to disentangle these cases. Finally, we suggest methods to check if there are hints of an incorrect model in the residuals. We show on simulated data the performance of our methods and comment on the eccentricities of Proxima b and 55 Cnc f.
We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed ...sensing techniques, which are modified to be compatible with the Gaussian process framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick Observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen.
The angular momentum deficit (AMD)-stability criterion allows to discriminate between a priori stable planetary systems and systems for which the stability is not granted and needs further ...investigations. AMD-stability is based on the conservation of the AMD in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first-order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first-order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first-order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopædia.
Since the original work of Hansen and Tisserand in the XIXth century, there have been many variations in the analytical expansion of the three-body disturbing function in series of the semi-major ...axis ratio. With the increasing number of planetary systems of large eccentricity, these expansions are even more interesting as they allow us to obtain for the secular systems finite expressions that are valid for all eccentricities and inclinations. We revisited the derivation of the disturbing function in Legendre polynomial, with a special focus on the secular system. We provide here expressions of the disturbing function for the planar and spatial case at any order with respect to the ratio of the semi-major axes. Moreover, for orders in the ratio of semi-major axis up to ten in the planar case and five in the spatial case, we provide explicit expansions of the secular system, and simple algorithms with minimal computation to extend this to higher order, as well as the algorithms for the computation of non secular terms.
Stellar-activity features such as spots can complicate the determination of planetary parameters through spectroscopic and photometric observations. The overlap of a transiting planet and a stellar ...spot, for instance, can produce anomalies in the transit light-curves that may lead to an inaccurate estimation of the transit duration, depth, and timing. These inaccuracies can for instance affect the precise derivation of the planet radius. We present the results of a quantitative study on the effects of stellar spots on high-precision transit light-curves. We show that spot anomalies can lead to an estimate of a planet radius that is 4% smaller than the real value. Likewise, the transit duration may be estimated about 4%, longer or shorter. Depending on the size and distribution of spots, anomalies can also produce transit-timing variations (TTVs) with significant amplitudes. For instance, TTVs with signal amplitudes of 200 s can be produced when the spot is completely dark and has the size of the largest Sun spot. Our study also indicates that the smallest size of a stellar spot that still has detectable effects on a high-precision transit light-curve is around 0.03 time the stellar radius for typical Kepler Telescope precision. We also show that the strategy of including more free parameters (such as transit depth and duration) in the fitting procedure to measure the transit time of each individual transit will not produce accurate results for active stars.
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 Vsini⋆ 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 a new analytical formulation of the RV anomaly associated to the iodine cell technique. For both formulas, we modeled the subplanet mean velocity vp and dispersion βp 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 Vsini⋆ ≲ 20 km s-1. In contrast, the analytical models simulating the two different observation techniques can disagree by about 10σ in Vsini⋆ for large spin-orbit misalignments. It is thus important to apply the adapted model when fitting data.
Context. Short-period planets are influenced by the extreme tidal forces of their parent stars. These forces deform the planets causing them to attain nonspherical shapes. The nonspherical shapes, ...modeled here as triaxial ellipsoids, can have an impact on the observed transit light-curves and the parameters derived for these planets. Aims. We investigate the detectability of tidal deformation in short-period planets from their transit light curves and the instrumental precision needed. We also aim to show how detecting planet deformation allows us to obtain an observational estimate of the second fluid Love number from the light curve, which provides valuable information about the internal structure of the planet. Methods. We adopted a model to calculate the shape of a planet due to the external potentials acting on it and used this model to modify the ellc transit tool. We used the modified ellc to generate the transit light curve for a deformed planet. Our model is parameterized by the Love number; therefore, for a given light curve we can derive the value of the Love number that best matches the observations. Results. We simulated the known cases of WASP-103b and WASP-121b which are expected to be highly deformed. Our analyses show that instrumental precision ≤50 ppm min−1 is required to reliably estimate the Love number and detect tidal deformation. This precision can be achieved for WASP-103b in ∼40 transits using the Hubble Space Telescope and in ∼300 transits using the forthcoming CHEOPS instrument. However, fewer transits will be required for short-period planets that may be found around bright stars in the TESS and PLATO survey missions. The unprecedented precisions expected from PLATO and JWST will permit the detection of shape deformation with a single transit observation. However, the effects of instrumental and astrophysical noise must be considered as they can increase the number of transits required to reach the 50 ppm min−1 detection limit. We also show that improper modeling of limb darkening can act to bury signals related to the shape of the planet, thereby leading us to infer sphericity for a deformed planet. Accurate determination of the limb darkening coefficients is therefore required to confirm planet deformation.
The hot-Jupiter WASP-10b was reported by Maciejewski et al. to show transit timing variations (TTVs) with an amplitude of ∼3.5 min. These authors proposed that the observed TTVs were caused by a 0.1M
...Jup perturbing companion with an orbital period of ∼5.23 d, and hence, close to the outer 5:3 mean-motion resonance with WASP-10b. To test this scenario, we present eight new transit light curves of WASP-10b obtained with the Faulkes Telescope North and the Liverpool Telescope. The new light curves, together with 22 previously published ones, were modelled with a Markov Chain Monte Carlo transit fitting code. Transit depth differences reported for WASP-10b are thought to be due to starspot-induced brightness modulation of the host star. Assuming the star is brighter at the activity minimum, we favour a small planetary radius. We find
in agreement with Johnson et al. and Maciejewski et al. Recent studies find no evidence for a significant eccentricity in this system. We present consistent system parameters for a circular orbit and refine the orbital ephemeris of WASP-10b. Our homogeneously derived transit times do not support the previous claimed TTV signal, which was strongly dependent on two previously published transits that have been incorrectly normalized. Nevertheless, a linear ephemeris is not a statistically good fit to the transit times of WASP-10b. We show that the observed transit time variations are due to spot occultation features or systematics. We discuss and exemplify the effects of occultation spot features in the measured transit times and show that despite spot occultation during egress and ingress being difficult to distinguish in the transit light curves, they have a significant effect in the measured transit times. We conclude that if we account for spot features, the transit times of WASP-10b are consistent with a linear ephemeris with the exception of one transit (epoch 143) which is a partial transit. Therefore, there is currently no evidence for the existence of a companion to WASP-10b. Our results support the lack of TTVs of hot-Jupiters reported for the Kepler sample.
ABSTRACT
In this paper, we present an analysis of near-infrared spectropolarimetric and velocimetric data of the young M dwarf AU Mic, collected with SPIRou at the Canada–France–Hawaii telescope from ...2019 to 2022, mostly within the SPIRou Legacy Survey. With these data, we study the large- and small-scale magnetic field of AU Mic, detected through the unpolarized and circularly polarized Zeeman signatures of spectral lines. We find that both are modulated with the stellar rotation period (4.86 d), and evolve on a time-scale of months under differential rotation and intrinsic variability. The small-scale field, estimated from the broadening of spectral lines, reaches 2.61 ± 0.05 kG. The large-scale field, inferred with Zeeman–Doppler imaging from Least-Squares Deconvolved profiles of circularly polarized and unpolarized spectral lines, is mostly poloidal and axisymmetric, with an average intensity of 550 ± 30 G. We also find that surface differential rotation, as derived from the large-scale field, is ≃30 per cent weaker than that of the Sun. We detect the radial velocity (RV) signatures of transiting planets b and c, although dwarfed by activity, and put an upper limit on that of candidate planet d, putatively causing the transit-timing variations of b and c. We also report the detection of the RV signature of a new candidate planet (e) orbiting further out with a period of 33.39 ± 0.10 d, i.e. near the 4:1 resonance with b. The RV signature of e is detected at 6.5σ while those of b and c show up at ≃4σ, yielding masses of $10.2^{+3.9}_{-2.7}$ and $14.2^{+4.8}_{-3.5}$ M⊕ for b and c, and a minimum mass of $35.2^{+6.7}_{-5.4}$ M⊕ for e.
In this work, we present the solution of the stellar spot problem using the Kelvin–Stokes theorem. Our result is applicable for any given location and dimension of the spots on the stellar surface. ...We present explicitly the result up to the second degree in the limb-darkening law. This technique can be used to calculate very efficiently mutual photometric effects produced by eclipsing bodies occulting stellar spots and to construct complex spot shapes.
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