arXiv subjects

Alexandre C. M. Correia

Publications and source records attributed to Alexandre C. M. Correia.

At least 55 records · Page 3Linked to original sources

arXiv2021

An analytical model for tidal evolution in co-orbital systems $\,$I. Application to exoplanets

Close-in co-orbital planets (in a 1:1 mean motion resonance) can experience strong tidal interactions with the central star. Here, we develop an analytical model adapted to the study of the tidal evolution of those systems. We use a Hamiltonian version of the constant time-lag tidal model, which extends the Hamiltonian formalism developed for the point-mass case. We show that co-orbital systems undergoing tidal dissipation either favour the Lagrange or the anti-Lagrange configurations, depending on the system parameters. However, for all range of parameters and initial conditions, both configurations become unstable, although the timescale for the destruction of the system can be larger than the lifetime of the star. We provide an easy-to-use criterion to determine if an already known close-in exoplanet may have an undetected co-orbital companion.

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arXiv2021

Revisiting the analysis of HW Vir eclipse timing data I. A frequentist data modeling approach and a dynamical stability analysis

HW Vir is a short-period binary that presents eclipse timing variations. Circumbinary planets have been proposed as a possible explanation, although the properties of the planets differ in each new study. Our aim is to perform robust model selection methods for eclipse timing variations (ETV) and error calculation techniques based on a frequentist approach for the case of the HW Vir system. We initially performed simultaneous light and radial velocity curve analysis to derive the masses of the binary. We then analyzed the eclipse timing variation of the system by fitting multiple models. To select the best model, we searched the confidence levels for the best model by creating an $χ^2$ surface grid and bootstrap methods for each pair of parameters. We searched for stable orbital configurations for our adopted ETV model. The masses of the binary are found as 0.413 $\pm$ 0.008 $M_\odot$ and 0.128 $\pm$ 0.004 $M_\odot$. Under the assumption of two light time effects superimposed on a secular change, the minimum masses of the circumbinary objects are calculated as $25.0_{-2.2}^{+3.5} \ M_{Jup}$ and $13.9_{-0.45}^{+0.60}\ M_{Jup}$. The projected semi-major axes are found to be $7.8_{-1.0}^{+1.4}\ au$ and $4.56_{-0.22}^{+0.27}\ au$ in respective order. We find that this configuration is unstable within a 3$σ$ range on the semi-major axis and eccentricity of the outer circumbinary object.

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arXiv2020

Tidal evolution of the Pluto-Charon binary

A giant collision is believed to be at the origin of the Pluto-Charon system. As a result, the initial orbit and spins after impact may have substantially differed from those observed today. More precisely, the distance at periapse may have been shorter, subsequently expanding to its current separation by tides raised simultaneously on the two bodies. Here we provide a general 3D model to study the tidal evolution of a binary composed of two triaxial bodies orbiting a central star. We apply this model to the Pluto-Charon binary, and notice some interesting constraints on the initial system. We observe that when the eccentricity evolves to high values, the presence of the Sun prevents Charon from escaping because of Lidov-Kozai cycles. However, for a high initial obliquity for Pluto or a spin-orbit capture of Charon's rotation, the binary eccentricity is damped very efficiently. As a result, the system can maintain a moderate eccentricity throughout its evolution, even for strong tidal dissipation on Pluto.

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arXiv2020

Portuguese SKA White Book

This white book stems from the contributions presented at the Portuguese SKA Days, held on the 6th and 7th February 2018 with the presence of the SKA Deputy Director General Alistair McPherson and the SKA Science Director Robert Braun. This initiative was held to promote the Square Kilometer Array (SKA) - the world's largest radio telescope - among the Portuguese scientific and business communities with support from the Portuguese Science and Technology Foundation (FCT) with the contribution of Portuguese policy makers and researchers. The meeting was very successful in providing a detailed overview of the SKA status, vision and goals and describes most of the Portuguese contributions to science, technology and the related industry aspirations

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arXiv2020

TOI-1338: TESS' First Transiting Circumbinary Planet

We report the detection of the first circumbinary planet found by TESS. The target, a known eclipsing binary, was observed in sectors 1 through 12 at 30-minute cadence and in sectors 4 through 12 at two-minute cadence. It consists of two stars with masses of 1.1 MSun and 0.3 MSun on a slightly eccentric (0.16), 14.6-day orbit, producing prominent primary eclipses and shallow secondary eclipses. The planet has a radius of ~6.9 REarth and was observed to make three transits across the primary star of roughly equal depths (~0.2%) but different durations -- a common signature of transiting circumbinary planets. Its orbit is nearly circular (e ~ 0.09) with an orbital period of 95.2 days. The orbital planes of the binary and the planet are aligned to within ~1 degree. To obtain a complete solution for the system, we combined the TESS photometry with existing ground-based radial-velocity observations in a numerical photometric-dynamical model. The system demonstrates the discovery potential of TESS for circumbinary planets, and provides further understanding of the formation and evolution of planets orbiting close binary stars.

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arXiv2019

Andrade rheology in time-domain. Application to Enceladus' dissipation of energy due to forced libration

The main purpose of this work is to present a time-domain implementation of the Andrade rheology, instead of the traditional expansion in terms of a Fourier series of the tidal potential. This approach can be used in any fully three dimensional numerical simulation of the dynamics of a system of many deformable bodies. In particular, it allows large eccentricities, large mutual inclinations, and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, such as chaotic motions, transient events, and resonant librations. The results are presented by means of a concrete application: the analysis of the libration of Enceladus. This is done by means of both analytic formulas in the frequency domain and direct numerical simulations. We do not a priori assume that Enceladus has a triaxial shape, the eventual triaxiality is a consequence of the satellite motion and its rheology. As a result we obtain an analytic formula for the amplitude of libration that incorporates a new correction due to the rheology. Our results provide an estimation of the amplitude of libration of the core of Enceladus as 0.6% of that of the shell. They also reproduce the observed 10 GW of tidal heat generated by Enceladus with a value of $0.17\times 10^{14}$Pa$\cdot$s for the global effective viscosity under both Maxwell and Andrade rheology.

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arXiv2019

Planets in Mean-Motion Resonances and the System Around HD45364

In some planetary systems, the orbital periods of two of its members present a commensurability, usually known by mean-motion resonance. These resonances greatly enhance the mutual gravitational influence of the planets. As a consequence, these systems present uncommon behaviors, and their motions need to be studied with specific methods. Some features are unique and allow us a better understanding and characterization of these systems. Moreover, mean-motion resonances are a result of an early migration of the orbits in an accretion disk, so it is possible to derive constraints on their formation. Here we review the dynamics of a pair of resonant planets and explain how their orbits evolve in time. We apply our results to the HD 45365 planetary system.

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arXiv2019

Nearly Polar orbit of the sub-Neptune HD3167 c: Constraints on a multi-planet system dynamical history

We present the obliquity measurement, that is, the angle between the normal angle of the orbital plane and the stellar spin axis, of the sub-Neptune planet HD3167 c, which transits a bright nearby K0 star. We study the orbital architecture of this multi-planet system to understand its dynamical history. We also place constraints on the obliquity of planet d based on the geometry of the planetary system and the dynamical study of the system. New observations obtained with HARPS-N at the Telescopio Nazionale Galileo (TNG) were employed for our analysis. The sky-projected obliquity was measured using three different methods: the Rossiter-McLaughlin anomaly, Doppler tomography, and reloaded Rossiter-McLaughlin techniques. We performed the stability analysis of the system and investigated the dynamical interactions between the planets and the star. HD3167 c is found to be nearly polar with sky-projected obliquity, $λ$ = -97$^{\circ} \pm$ 23$^{\circ}$. This misalignment of the orbit of planet c with the spin axis of the host star is detected with 97\% confidence. The analysis of the dynamics of this system yields coplanar orbits of planets c and d. It also shows that it is unlikely that the currently observed system can generate this high obliquity for planets c and d by itself. However, the polar orbits of planets c and d could be explained by the presence of an outer companion in the system. Follow-up observations of the system are required to confirm such a long-period companion.

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arXiv2018

Dynamical evolution of triple-star systems by Lidov-Kozai cycles and tidal friction

Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with tidal friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov-Kozai migration. Our framework is the secular hierarchical three-body problem (octupole order approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Both the orbital and the spin evolutions are considered. Extensive numerical simulations with uniform and non-uniform distributions of the initial orbital parameters are carried out, and unbiased initial conditions leading to Lidov-Kozai migration are revealed. Finally, we highlight the importance of the initial "Kozai constant" $h=\sqrt{(1-e^2)}\cos{i}$ in the dynamical evolution of triple-star systems, by showing that phase portraits at given $h$-values unveil different evolution paths.

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arXiv2018

Numerical Modelling of Tertiary Tides

Stellar systems consisting of multiple stars tend to undergo tidal interactions when the separations between the stars are short. While tidal phenomena have been extensively studied, a certain tidal effect exclusive to hierarchical triples (triples in which one component star has a much wider orbit than the others) has hardly received any attention, mainly due to its complexity and consequent resistance to being modelled. This tidal effect is the tidal perturbation of the tertiary by the inner binary, which in turn depletes orbital energy from the inner binary, causing the inner binary separation to shrink. In this paper, we develop a fully numerical simulation of these "tertiary tides" by modifying established tidal models. We also provide general insight as to how close a hierarchical triple needs to be in order for such an effect to take place, and demonstrate that our simulations can effectively retrieve the orbital evolution for such systems. We conclude that tertiary tides are a significant factor in the evolution of close hierarchical triples, and strongly influence at least ~ 1% of all multiple star systems.

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arXiv2018

Chaotic dynamics in the (47171) Lempo triple system

We investigate the dynamics of the (47171) Lempo triple system, also known by 1999TC$_{36}$. We derive a full 3D $N$-body model that takes into account the orbital and spin evolution of all bodies, which are assumed triaxial ellipsoids. We show that, for reasonable values of the shapes and rotational periods, the present best fitted orbital solution for the Lempo system is chaotic and unstable in short time-scales. The formation mechanism of this system is unknown, but the orbits can be stabilised when tidal dissipation is taken into account. The dynamics of the Lempo system is very rich, but depends on many parameters that are presently unknown. A better understanding of this systems thus requires more observations, which also need to be fitted with a complete model like the one presented here.

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arXiv2017

Theia: Faint objects in motion or the new astrometry frontier

In the context of the ESA M5 (medium mission) call we proposed a new satellite mission, Theia, based on relative astrometry and extreme precision to study the motion of very faint objects in the Universe. Theia is primarily designed to study the local dark matter properties, the existence of Earth-like exoplanets in our nearest star systems and the physics of compact objects. Furthermore, about 15 $\%$ of the mission time was dedicated to an open observatory for the wider community to propose complementary science cases. With its unique metrology system and "point and stare" strategy, Theia's precision would have reached the sub micro-arcsecond level. This is about 1000 times better than ESA/Gaia's accuracy for the brightest objects and represents a factor 10-30 improvement for the faintest stars (depending on the exact observational program). In the version submitted to ESA, we proposed an optical (350-1000nm) on-axis TMA telescope. Due to ESA Technology readiness level, the camera's focal plane would have been made of CCD detectors but we anticipated an upgrade with CMOS detectors. Photometric measurements would have been performed during slew time and stabilisation phases needed for reaching the required astrometric precision.

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arXiv2016

Stellar and planetary Cassini states

Cassini states correspond to equilibria of the spin axis of a body when its orbit is perturbed. They were initially described for satellites, but the spin axis of stars and planets undergoing strong dissipation can also evolve into some equilibria. For small satellites, the rotational angular momentum is usually much smaller than the total angular momentum, so classical methods for finding Cassini states rely on this approximation. Here we present a more general approach, which is valid for the secular quadrupolar non-restricted problem with spin. Our method is still valid when the precession rate and the mutual inclination of the orbits are not constant. Therefore, it can be used to study stars with close-in companions, or planets with heavy satellites, like the Earth-Moon system.

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arXiv2016

Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology

In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.

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arXiv2016

Radial Velocity Data Analysis with Compressed Sensing Techniques

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 processes 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.

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arXiv2016

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin-orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star-planet-satellite systems and triple stellar systems.

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arXiv2016

Detectability of quasi-circular co-orbital planets. Application to the radial velocity technique

Several celestial bodies in co-orbital configurations exist in the solar system. However, co-orbital exoplanets have not yet been discovered. This lack may result from a degeneracy between the signal induced by co-orbital planets and other orbital configurations. Here we determine a criterion for the detectability of quasi-circular co-orbital planets and develop a demodulation method to bring out their signature from the observational data. We show that the precision required to identify a pair of co-orbital planets depends only on the libration amplitude and on the planet's mass ratio. We apply our method to synthetic radial velocity data, and show that for tadpole orbits we are able to determine the inclination of the system to the line of sight. Our method is also valid for planets detected through the transit and astrometry techniques.

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arXiv2015

Mercury-T: A new code to study tidally evolving multi-planet systems. Applications to Kepler-62

A large proportion of observed planetary systems contain several planets in a compact orbital configuration, and often harbor at least one close-in object. These systems are then most likely tidally evolving. We investigate how the effects of planet-planet interactions influence the tidal evolution of planets. We introduce for that purpose a new open-source addition to the Mercury N-body code, Mercury-T, which takes into account tides, general relativity and the effect of rotation-induced flattening in order to simulate the dynamical and tidal evolution of multi-planet systems. It uses a standard equilibrium tidal model, the constant time lag model. Besides, the evolution of the radius of several host bodies has been implemented (brown dwarfs, M-dwarfs of mass $0.1~M_\odot$, Sun-like stars, Jupiter). We validate the new code by comparing its output for one-planet systems to the secular equations results. We find that this code does respect the conservation of total angular momentum. We applied this new tool to the planetary system Kepler-62. We find that tides influence the stability of the system in some cases. We also show that while the four inner planets of the systems are likely to have slow rotation rates and small obliquities, the fifth planet could have a fast rotation rate and a high obliquity. This means that the two habitable zone planets of this system, Kepler-62e ad f are likely to have very different climate features, and this of course would influence their potential at hosting surface liquid water.

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