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Understanding the physics of planetary magma oceans has been the subject of growing efforts, in light of the increasing abundance of Solar system samples and extrasolar surveys. A rocky planet harboring such an ocean is likely to interact tidally with its host star, planetary companions, or satellites. To date, however, models of the tidal response and heat generation of magma oceans have been restricted to the framework of weakly viscous solids, ignoring the dynamical fluid behavior of the ocean beyond a critical melt fraction. Here we provide a handy analytical model that accommodates this phase transition, allowing for a physical estimation of the tidal response of lava worlds. We apply the model in two settings: The tidal history of the early Earth-Moon system in the aftermath of the giant impact; and the tidal interplay between short-period exoplanets and their host stars. For the former, we show that the fluid behavior of the Earth's molten surface drives efficient early Lunar recession to ${\sim} 25$ Earth radii within $10^4{-} 10^5$ years, in contrast with earlier predictions. For close-in exoplanets, we report on how their molten surfaces significantly change their spin-orbit dynamics, allowing them to evade spin-orbit resonances and accelerating their track towards tidal synchronization from a Gyr to Myr timescale. Moreover, we re-evaluate the energy budgets of detected close-in exoplanets, highlighting how the surface thermodynamics of these planets are likely controlled by enhanced, fluid-driven tidal heating, rather than vigorous insolation, and how this regime change substantially alters predictions for their surface temperatures., Comment: 32 pages, 12 figures, accepted for publication in ApJ

Thermal tides are atmospheric tides caused by variations in day-night insolation, similar to gravitational tides but with key differences. While both result in delayed mass redistribution, energy dissipation, and angular momentum exchanges between the planet and its host star, thermal tides can drive a planet's dynamics away from the rotational equilibrium states predicted by classical tidal theory. In this work, we present a novel closed-form solution for the thermotidal response of rocky planets. This general solution is derived from first principles, assuming either dry or moist adiabatic temperature profiles for the planet's atmosphere, and can be readily applied to study the long-term evolution of exoplanets in the habitable zones of their host stars. Despite relying on a small number of parameters, the model successfully captures the key features of the thermotidal torque predicted by General Circulation Models (GCMs). It also accurately predicts Earth's current semidiurnal thermotidal response and provides new insights into the evolution of the length of day during the Precambrian era., Comment: 5 pages, 2 figures, proceedings of the SF2A annual meeting

One of the most critical tasks of Microsoft sellers is to meticulously track and nurture potential business opportunities through proactive engagement and tailored solutions. Recommender systems play a central role to help sellers achieve their goals. In this paper, we present a content recommendation model which surfaces various types of content (technical documentation, comparison with competitor products, customer success stories etc.) that sellers can share with their customers or use for their own self-learning. The model operates at the opportunity level which is the lowest possible granularity and the most relevant one for sellers. It is based on semantic matching between metadata from the contents and carefully selected attributes of the opportunities. Considering the volume of seller-managed opportunities in organizations such as Microsoft, we show how to perform efficient semantic matching over a very large number of opportunity-content combinations. The main challenge is to ensure that the top-5 relevant contents for each opportunity are recommended out of a total of $\approx 40,000$ published contents. We achieve this target through an extensive comparison of different model architectures and feature selection. Finally, we further examine the quality of the recommendations in a quantitative manner using a combination of human domain experts as well as by using the recently proposed "LLM as a judge" framework.

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

Azure Core workload insights have time-series data with different metric units. Faults or Anomalies are observed in these time-series data owing to faults observed with respect to metric name, resources region, dimensions, and its dimension value associated with the data. For Azure Core, an important task is to highlight faults or anomalies to the user on a dashboard that they can perceive easily. The number of anomalies reported should be highly significant and in a limited number, e.g., 5-20 anomalies reported per hour. The reported anomalies will have significant user perception and high reconstruction error in any time-series forecasting model. Hence, our task is to automatically identify 'high significant anomalies' and their associated information for user perception., Comment: Published in IAAI 2024, which is the Industrial track of AAAI 2024

Ultra-hot Jupiters present a unique opportunity to understand the physics and chemistry of planets at extreme conditions. WASP-12b stands out as an archetype of this class of exoplanets. We performed comprehensive analyses of the transits, occultations, and phase curves of WASP-12b by combining new CHEOPS observations with previous TESS and Spitzer data to measure the planet's tidal deformation, atmospheric properties, and orbital decay rate. The planet was modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number, $h_2$, which quantifies its radial deformation and provides insight into the interior structure. We measured the tidal deformation of WASP-12b and estimated a Love number of $h_2=1.55_{-0.49}^{+0.45}$ (at 3.2$\sigma$) from its phase curve. We measured occultation depths of $333\pm24$ppm and $493\pm29$ppm in the CHEOPS and TESS bands, respectively, while the dayside emission spectrum indicates that CHEOPS and TESS probe similar pressure levels in the atmosphere at a temperature of 2900K. We also estimated low geometric albedos of $0.086\pm0.017$ and $0.01\pm0.023$ in the CHEOPS and TESS passbands, respectively, suggesting the absence of reflective clouds in the dayside of the WASP-12b. The CHEOPS occultations do not show strong evidence for variability in the dayside atmosphere of the planet. Finally, we refine the orbital decay rate by 12% to a value of -30.23$\pm$0.82 ms/yr. WASP-12b becomes the second exoplanet, after WASP-103b, for which the Love number has been measured (at 3$sigma$) from the effect of tidal deformation in the light curve. However, constraining the core mass fraction of the planet requires measuring $h_2$ with a higher precision. This can be achieved with high signal-to-noise observations with JWST since the phase curve amplitude, and consequently the induced tidal deformation effect, is higher in the infrared., Comment: accepted for publication in A&A

In this paper, we design a real-time question-answering system specifically targeted for helping sellers get relevant material/documentation they can share live with their customers or refer to during a call. Taking the Seismic content repository as a relatively large scale example of a diverse dataset of sales material, we demonstrate how LLM embeddings of sellers' queries can be matched with the relevant content. We achieve this by engineering prompts in an elaborate fashion that makes use of the rich set of meta-features available for documents and sellers. Using a bi-encoder with cross-encoder re-ranker architecture, we show how the solution returns the most relevant content recommendations in just a few seconds even for large datasets. Our recommender system is deployed as an AML endpoint for real-time inferencing and has been integrated into a Copilot interface that is now deployed in the production version of the Dynamics CRM, known as MSX, used daily by Microsoft sellers.

String matching algorithms in the presence of abbreviations, such as in Stock Keeping Unit (SKU) product catalogs, remains a relatively unexplored topic. In this paper, we present a unified architecture for SKU search that provides both a real-time suggestion system (based on a Trie data structure) as well as a lower latency search system (making use of character level TF-IDF in combination with language model vector embeddings) where users initiate the search process explicitly. We carry out ablation studies that justify designing a complex search system composed of multiple components to address the delicate trade-off between speed and accuracy. Using SKU search in the Dynamics CRM as an example, we show how our system vastly outperforms, in all aspects, the results provided by the default search engine. Finally, we show how SKU descriptions may be enhanced via generative text models (using gpt-3.5-turbo) so that the consumers of the search results may get more context and a generally better experience when presented with the results of their SKU search.

Azure Cognitive Search (ACS) has emerged as a major contender in "Search as a Service" cloud products in recent years. However, one of the major challenges for ACS users is to improve the relevance of the search results for their specific usecases. In this paper, we propose a novel method to find the optimal ACS configuration that maximizes search relevance for a specific usecase (product search, document search...) The proposed solution improves key online marketplace metrics such as click through rates (CTR) by formulating the search relevance problem as hyperparameter tuning. We have observed significant improvements in real-world search call to action (CTA) rate in multiple marketplaces by introducing optimized weights generated from the proposed approach.

We address the issue of structure changes of a canola protein gel (as a solid food model) during gastrointestinal digestion. We present a method for synchrotron Small-Angle X-ray Scattering analysis of the digestion of a gel in a capillary. Scanning the capillary allows tracking the digestion under diffusion of enzymatic juices. The fitting parameters characterizing the sizes, scattering intensities and structures allow to distinguish the compact, unfolded or aggregated states of proteins. The evolutions of these parameters enable to detail the complex changes of proteins during gel digestion, involving back-and-forth evolutions with proteins unfolding (1 st and 3 rd steps), re-compaction (2 nd step) due to gastrointestinal pH and enzyme actions, before final protein scissions (4 th step) resulting in small peptides. This complexity is related to the wide ranges of successive pH and enzyme activity acting on large and charged protein assemblies. Digestion is therefore impacted by the conditions of food preparation.

Recent observations and theoretical progress made about the history of the Earth-Moon system suggest that tidal dissipation in oceans primarily drives the long term evolution of orbital systems hosting ocean planets. Particularly, they emphasise the key role played by the geometry of land-ocean distributions in this mechanism. However, the complex way continents affect oceanic tides still remains to be elucidated. In the present study, we investigate the impact of a single supercontinent on the tidal response of an ocean planet and the induced tidally dissipated energy. The adopted approach is based on the linear tidal theory. By simplifying the continent to a spherical cap of given angular radius and position on the globe, we proceed to a harmonic analysis of the whole planet's tidal response including the coupling with the solid part due to ocean loading and self-attraction variations. In this framework, tidal flows are formulated analytically in terms of explicitly defined oceanic eigenmodes, as well as the resulting tidal Love numbers, dissipated power, and torque. The analysis highlights the symmetry breaking effect of the continent, which makes the dependence of tidal quantities on the tidal frequency become highly irregular. The metric introduced to quantify this continentality effect reveals abrupt transitions between polar and non-polar configurations, and between small-sized and medium-sized continents. Additionally, it predicts that a continent similar to South America or smaller (30{\deg}-angular radius) does not alter qualitatively the tidal response of a global ocean whatever its position on the planet., Comment: 35 pages, 13 figures, 5 tables. Accepted for publication in Astronomy & Astrophysics

With the continuous improvement in the precision of exoplanet observations, it has become feasible to probe for subtle effects that can enable a more comprehensive characterization of exoplanets. A notable example is the tidal deformation of ultra-hot Jupiters by their host stars, whose detection can provide valuable insights into the planetary interior structure. In this work, we extend previous research on modeling deformation in transit light curves by proposing a simple approach to account for tidal deformation in phase curves. The planetary shape is modeled as a function of the second fluid Love number for radial deformation $h_{2f}$. We show that the effect of tidal deformation manifests across the full orbit of the planet as its projected area varies with phase, thereby allowing us to better probe the planet's shape in phase curves than in transits. Comparing the effects and detectability of deformation by different space-based instruments, we find that the effect of deformation is more prominent in infrared observations where the phase curve amplitude is the largest. A single JWST phase curve observation of a deformed planet, such as WASP-12b, can allow up to 17$\sigma$ measurement of $h_{2f}$ compared to 4$\sigma$ from transit-only observation. Such high precision $h_{2f}$ measurement can constrain the core mass of the planet to within 19\% of the total mass, thus providing unprecedented constraints on the interior structure. Due to the lower phase curve amplitudes in the optical, the other instruments provide $\leq4\sigma$ precision on $h_{2f}$ depending on the number of phase curves observed. We also find that detecting deformation from infrared phase curves is less affected by uncertainty in limb darkening, unlike detection in transits. Finally, the assumption of sphericity when analyzing the phase curve of deformed planets can lead to biases in several system parameters, Comment: 15 pages, 14 figures, Accepted for publication in Astronomy and Astrophysics

Rotational dynamics of the Earth, over geological timescales, have profoundly affected local and global climatic evolution, probably contributing to the evolution of life. To better retrieve the Earth's rotational history, and motivated by the published hypothesis of a stabilized length of day during the Precambrian, we examine the effect of thermal tides on the evolution of planetary rotational motion. The hypothesized scenario is contingent upon encountering a resonance in atmospheric Lamb waves, whereby an amplified thermotidal torque cancels the opposing torque of the oceans and solid interior, driving the Earth into a rotational equilibrium. With this scenario in mind, we construct an ab initio model of thermal tides on rocky planets describing a neutrally stratified atmosphere. The model takes into account dissipative processes with Newtonian cooling and diffusive processes in the planetary boundary layer. We retrieve from this model a closed-form solution for the frequency-dependent tidal torque which captures the main spectral features previously computed using 3D general circulation models. In particular, under longwave heating, diffusive processes near the surface and the delayed thermal response of the ground prove to be responsible for attenuating, and possibly annihilating, the accelerating effect of the thermotidal torque at the resonance. When applied to the Earth, our model prediction suggests the occurrence of the Lamb resonance in the Phanerozoic, but with an amplitude that is insufficient for the rotational equilibrium. Interestingly, though our study was motivated by the Earth's history, the generic tidal solution can be straightforwardly and efficiently applied in exoplanetary settings., Comment: 20 pages (+14 for appendices), 6 figures

After the initial suggestion by Zahnle and Walker (1987) that the torque accelerating the spin rate of the Earth and produced by the heating of the atmosphere by the Sun could counteract the braking lunir-solar gravitational torque in the Precambrian, several authors have recently revisited this hypothesis. In these studies, it is argued that the geological evidences of the past spin state of the Earth play in favor of this atmospheric tidal locking of the length of the day (LOD). In the present review of the recent literature, we show that the drawn conclusions depend crucially on the consideration of the stromatolite geological LOD estimates obtained by Pannella at 1.88 and 2.0 Ga, which are subject to large uncertainties. When only the most robust cyclostatigraphic estimates of the LOD are retained, the LOD locking hypothesis is not supported. Moreover, the consideration of the published General Circulation Model numerical simulations and of new analytical models for the thermal atmospheric tides suggest that the atmospheric tidal resonance, which is the crucial ingredient for the LOD locking in the Precambrian, was never of sufficiently large amplitude to allow for this tidal LOD lock., Comment: 16 pages, 9 figures

The low-voltage ride-through service is carried out in this paper according to the voltage profile described by the IEC 61400-21 European normative when short-duration voltage sags happen, and some instantaneous reactive power is delivered to the grid in accordance with the Spanish grid code; the mandatory limitation of the amplitude of the three-phase inverter currents to its nominal value is carried out with a novel control strategy, in which a certain amount of instantaneous constant active power can also be delivered to the grid when small or moderate voltage sags happen. A Multiple second order generalized integrator frequency-locked loop synchronization algorithm is employed in order to estimate the system frequency without harmonic distortions, as well as to output the positive- and the negative- sequence of the {\alpha}\b{eta} quantities of the three-phase grid voltages when balanced and unbalanced voltage sags happen in a frequency-adaptive scheme. The current control is carried out in the stationary reference frame, which guarantees the cancellation of the harmonic distortions in the utility grid currents using a Harmonic compensation structure, and the implementation of a constant active power control in order to protect the DC link capacitor from thermal stresses avoiding the appearance of large harmonic distortions at twice the fundamental frequency in the DC link voltage. A case study of a three-phase single-stage grid-connected PV system with a maximum apparent power about 500 kVA is tested with several simulations using MATLAB/SIMULINK firstly, and secondly, with some experiments using the Controller hardware-in-the-loop (CHIL) simulation technique for several types of voltage sags in order to do the final validation of the control algorithms.

Typographical errors are a major source of frustration for visitors of online marketplaces. Because of the domain-specific nature of these marketplaces and the very short queries users tend to search for, traditional spell cheking solutions do not perform well in correcting typos. We present a data augmentation method to address the lack of annotated typo data and train a recurrent neural network to learn context-limited domain-specific embeddings. Those embeddings are deployed in a real-time inferencing API for the Microsoft AppSource marketplace to find the closest match between a misspelled user query and the available product names. Our data efficient solution shows that controlled high quality synthetic data may be a powerful tool especially considering the current climate of large language models which rely on prohibitively huge and often uncontrolled datasets.

We report the discovery and characterisation of a giant transiting planet orbiting a nearby M3.5V dwarf (d = 80.4 pc, $G$ = 15.1 mag, $K$=11.2 mag, R$_\star$ = 0.358 $\pm$ 0.015 R$_\odot$, M$_\star$ = 0.340 $\pm$ 0.009 M$_\odot$). Using the photometric time series from TESS sectors 10, 36, 46, and 63 and near-infrared spectrophotometry from ExTrA, we measured a planetary radius of 0.77 $\pm$ 0.03 R$_J$ and an orbital period of 1.52 days. With high-resolution spectroscopy taken by the CFHT/SPIRou and ESO/ESPRESSO spectrographs, we refined the host star parameters ([Fe/H] = 0.27 $\pm$ 0.12) and measured the mass of the planet (0.273 $\pm$ 0.006 M$_J$). Based on these measurements, TOI-4860 b joins the small set of massive planets ($>$80 M$_E$) found around mid to late M dwarfs ($<$0.4 R$_\odot$), providing both an interesting challenge to planet formation theory and a favourable target for further atmospheric studies with transmission spectroscopy. We identified an additional signal in the radial velocity data that we attribute to an eccentric planet candidate ($e=0.66\pm0.09$) with an orbital period of $427\pm7$~days and a minimum mass of $1.66\pm 0.26$ M$_J$, but additional data would be needed to confirm this., Comment: 16 pages, 14 figures, accepted for publication in A&A

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 timescale of months under differential rotation and intrinsic variability. The small-scale field, estimated from the broadening of spectral lines, reaches $2.61\pm0.05$ 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 $550\pm30$ G. We also find that surface differential rotation, as derived from the large-scale field, is $\simeq$30% 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 $33.39\pm0.10$ d, i.e., near the 4:1 resonance with b. The RV signature of e is detected at 6.5$\sigma$ while those of b and c show up at $\simeq$4$\sigma$, yielding masses of $10.2^{+3.9}_{-2.7}$ and $14.2^{+4.8}_{-3.5}$ Earth masses for b and c, and a minimum mass of $35.2^{+6.7}_{-5.4}$ Earth masses for e., Comment: MNRAS, in press (20 pages and 12 figures + 9 pages of supplementary material)

Dependency hell is a well-known pain point in the development of large software projects and machine learning (ML) code bases are not immune from it. In fact, ML applications suffer from an additional form, namely, "data source dependency hell". This term refers to the central role played by data and its unique quirks that often lead to unexpected failures of ML models which cannot be explained by code changes. In this paper, we present an automated dependency mapping framework that allows MLOps engineers to monitor the whole dependency map of their models in a fast paced engineering environment and thus mitigate ahead of time the consequences of any data source changes (e.g., re-train model, ignore data, set default data etc.). Our system is based on a unified and generic approach, employing techniques from static analysis, from which data sources can be identified reliably for any type of dependency on a wide range of source languages and artefacts. The dependency mapping framework is exposed as a REST web API where the only input is the path to the Git repository hosting the code base. Currently used by MLOps engineers at Microsoft, we expect such dependency map APIs to be adopted more widely by MLOps engineers in the future.

Tidal orbital decay is suspected to occur especially for hot Jupiters, with the only observationally confirmed case of this being WASP-12 b. By examining this effect, information on the properties of the host star can be obtained using the so-called stellar modified tidal quality factor $Q_*'$, which describes the efficiency with which kinetic energy of the planet is dissipated within the star. This can help to get information about the interior of the star. In this study, we aim to improve constraints on the tidal decay of the KELT-9, KELT-16 and WASP-4 systems, to find evidence for or against the presence of this particular effect. With this, we want to constrain each star's respective $Q_*'$ value. In addition to that, we also aim to test the existence of the transit timing variations (TTVs) in the HD 97658 system, which previously favoured a quadratic trend with increasing orbital period. Making use of newly acquired photometric observations from CHEOPS and TESS, combined with archival transit and occultation data, we use Markov chain Monte Carlo (MCMC) algorithms to fit three models, a constant period model, an orbital decay model, and an apsidal precession model, to the data. We find that the KELT-9 system is best described by an apsidal precession model for now, with an orbital decay trend at over 2 $\sigma$ being a possible solution as well. A Keplerian orbit model with a constant orbital period fits the transit timings of KELT-16 b the best due to the scatter and scale of their error bars. The WASP-4 system is represented the best by an orbital decay model at a 5 $\sigma$ significance, although apsidal precession cannot be ruled out with the present data. For HD 97658 b, using recently acquired transit observations, we find no conclusive evidence for a previously suspected strong quadratic trend in the data., Comment: 19 pages, 11 figures, 9 tables, accepted for publication in A&A

Context. The 98{\deg}-obliquity of Uranus is commonly attributed to giant impacts that occurred at the end of the planetary formation. This picture, however, is not devoid of weaknesses. Aims. On a billion-year timescale, the tidal migration of the satellites of Jupiter and Saturn has been shown to strongly affect their spin-axis dynamics. We aim to revisit the scenario of tilting Uranus in light of this mechanism. Methods. We analyse the precession spectrum of Uranus and identify the candidate secular spin-orbit resonances that could be responsible for the tilting. We determine the properties of the hypothetical ancient satellite required for a capture and explore the dynamics numerically. Results. If it migrates over 10 Uranus' radii, a single satellite with minimum mass 4e-4 Uranus' mass is able to tilt Uranus from a small obliquity and make it converge towards 90{\deg}. In order to achieve the tilting in less than the age of the Solar System, the mean drift rate of the satellite must be comparable to the Moon's current orbital expansion. Under these conditions, simulations show that Uranus is readily tilted over 80{\deg}. Beyond this point, the satellite is strongly destabilised and triggers a phase of chaotic motion for the planet's spin axis. The chaotic phase ends when the satellite collides into the planet, ultimately freezing the planet's obliquity in either a prograde, or plainly retrograde state (as Uranus today). Spin states resembling that of Uranus can be obtained with probabilities as large as 80%, but a bigger satellite is favoured, with mass 1.7e-3 Uranus' mass or more. Yet, a smaller ancient satellite is not categorically ruled out, and there is room for improving this basic scenario in future studies. Interactions among several pre-existing satellites is a promising possibility., Comment: Accepted for publication in Astronomy and Astrophysics

Due to tidal interactions in the Earth-Moon system, the spin of the Earth slows down and the Moon drifts away. This recession of the Moon is now measured with great precision, but it has been realized, more than fifty years ago, that simple tidal models extrapolated back in time lead to an age of the Moon that is by far incompatible with the geochronological and geochemical evidence. In order to evade this problem, more elaborate models have been proposed, taking into account the oceanic tidal dissipation. However, these models did not fit both the estimated lunar age and the present rate of lunar recession simultaneously. Here we present a physical model that reconciles these two constraints and yields a unique solution of the tidal history. This solution fits well the available geological proxies for the history of the Earth-Moon system and consolidates the cyclostratigraphic method. The resulting evolution involves multiple crossings of resonances in the oceanic dissipation that are associated with significant and rapid variations in the lunar orbital distance, the Earth's length of the day, and the Earth's obliquity.

WASP-103b is the exoplanet with the highest expected deformation signature in its transit light curve and one of the shortest expected spiral-in times. Measuring the tidal deformation of the planet would allow us to estimate the second degree fluid Love number and gain insight into the planet's internal structure. Moreover, measuring the tidal decay timescale would allow us to estimate the stellar tidal quality factor, which is key to constraining stellar physics. We obtained 12 transit light curves of WASP-103b with the CHEOPS to estimate the tidal deformation and tidal decay of this extreme system. We modelled the high-precision CHEOPS transit light curves together with systematic instrumental noise using multi-dimensional Gaussian process regression informed by a set of instrumental parameters. To model the tidal deformation, we used a parametrisation model which allowed us to determine the second degree fluid Love number of the planet. We combined our light curves with previously observed transits of WASP-103b with HST and Spitzer. We estimate the radial Love number of WASP-103b to be $h_f = 1.59^{+0.45}_{-0.53}$. This is the first time that the tidal deformation is directly detected (at $3\, \sigma$) from the transit light curve of an exoplanet. Combining the transit times derived from CHEOPS, with the other transit times available in the literature, we find no significant orbital period variation for WASP-103b. However, the data show a hint of an orbital period increase instead of a decrease, as is expected for tidal decay. This could be either due to a visual companion star if this star is bound, the Applegate effect, or a statistical artefact. The estimated Love number of WASP-103b is similar to Jupiter's. This will allow us to constrain the internal structure and composition of WASP-103b, which could provide clues on the inflation of hot Jupiters. (Abridged), Comment: 21 pages, 9 figures, 11 tables, CHEOPS light curves available online, Published A&A

The equilibrium figure of an inviscid tidally deformed body is the starting point for the construction of many tidal theories such as Darwinian tidal theories or the hydrodynamical Creep tide theory. This paper presents the ellipsoidal equilibrium figure when the spin rate vector of the deformed body is not perpendicular to the plane of motion of the companion. We obtain the equatorial and the polar flattenings as functions of the Jeans and the Maclaurin flattenings, and of the angle $\theta$ between the spin rate vector and the radius vector. The equatorial vertex of the equilibrium ellipsoid does not point toward the companion, which produces a torque perpendicular to the rotation vector, which introduces terms of precession and nutation. We find that the direction of spin may differ significantly from the direction of the principal axis of inertia $C$, so the classical approximation $\mathsf{I}\vec{\omega}\approx C\vec{\omega}$ only makes sense in the neighborhood of the planar problem. We also study the so-called Cassini states. Neglecting the short-period terms in the differential equation for the spin direction and assuming a uniform precession of the line of the orbital ascending node, we obtain the same differential equation as that found by Colombo (1966). That is, a tidally deformed inviscid body has exactly the same Cassini states as a rotating axisymmetric rigid body, the tidal bulge having no secular effect at first order., Comment: 17 pages, 7 figures

The obliquity of a planet is the tilt between its equator and its orbital plane. Giant planets are expected to form with near-zero obliquities. After its formation, some dynamical mechanism must therefore have tilted Saturn up to its current obliquity of 26.7{\deg}. This event is traditionally thought to have happened more than 4 Gyrs ago during the late planetary migration because of the crossing of a resonance between the spin-axis precession of Saturn and the nodal orbital precession mode of Neptune. Here, we show that the fast tidal migration of Titan measured by Lainey et al. (2020) is incompatible with this scenario, and that it offers a new explanation for Saturn's current obliquity. A significant migration of Titan would prevent any early resonance, invalidating previous constraints on the late planetary migration set by the tilting of Saturn. We propose instead that the resonance was encountered recently, about 1 Gyr ago, forcing Saturn's obliquity to increase from a small value (possibly less than 3{\deg}), up to its current state. This scenario suggests that Saturn's normalised polar moment of inertia lies between 0.224 and 0.237. Our findings bring out a new paradigm for the spin-axis evolution of Saturn, Jupiter, and possibly giant exoplanets in multiple systems, whereby obliquities are not settled once for all, but continuously evolve as a result of the migration of their satellites., Comment: Author's manuscript of the letter published in Nature Astronomy on 18-01-2021. The published version can be found at https://www.nature.com/articles/s41550-020-01284-x