arXiv subjects

Alexandre C. M. Correia

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

At least 37 records · Page 2Linked to original sources

arXiv2023

Dynamics of trans-Neptunian objects near the 3/1 mean-motion resonance with Neptune

The complex classification of trans-Neptunian objects (TNOs) that are captured in mean-motion resonances (MMRs) and the constraint of their multiple origins are two significant open problems concerning the Solar System. The case-by-case study of the different MMRs and their characteristics provide information about their origin and dynamics, which helps us to understand the early stages of the Solar System evolution. In this paper, we study the dynamics of the detected TNOs close to a 3/1 MMR with Neptune. We initially use a semi-analytic three-body model to investigate the coplanar secular dynamics of these objects and find the stationary points. We then use surface sections and stability maps to analyse the non-averaged dynamics. These methods allow us to isolate the different stability regions and determine the extent of the chaotic regions. We show that stability maps are an extremely powerful tool for studying the resonant dynamics when they are computed in terms of the resonant angle. We then use these maps to study the non-planar three-body problem and the full dynamics in the presence of planetary perturbations. We confirm that TNOs near the 3/1 MMR regions can exist at very high inclinations. In the framework of the three-body problem, many of these objects can also be stable outside the 3/1 MMR owing to a Kozai secular resonance. However, when we take into account the perturbations of the four giant planets, the Kozai regions disappear and only the 3/1 MMR region remains, with eccentricities $e \lesssim 0.5$.

astro-ph.EP↗

arXiv2023

Theory of Functional Connections and Nelder-Mead optimization methods applied in satellite characterization

The growing population of man-made objects with the build up of mega-constellations not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but above all poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, we propose and analyze the application of two optimization procedures to determine the parameters associated with the dynamics of a satellite: one based on the Theory of Functional Connections (TFC) and another one based on the Nelder-Mead heuristic optimization algorithm. The TFC performs linear functional interpolation to embed the constraints of the problem into a functional. In this paper, we propose to use this functional to analytically embed the observational data of a satellite into its equations of dynamics. After that, any solution will always satisfy the observational data. The second procedure proposed in this research takes advantage of the Nealder-Mead algorithm, that does not require the gradient of the objective function, as alternative solution. The accuracy, efficiency, and dependency on the initial guess of each method is investigated, analyzed, and compared for several dynamical models. These methods can be used to obtain the physical parameters of a satellite from available observational data and for space debris characterization contributing to follow-up monitoring activities in space and astronomical observatories.

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arXiv2023

Tidal excitation of the obliquity of Earth-like planets in the habitable zone of M-dwarf stars

Close-in planets undergo strong tidal interactions with the parent star that modify their spins and orbits. In the two-body problem, the final stage for tidal evolution is the synchronisation of the rotation and orbital periods, and the alignment of the planet spin axis with the normal to the orbit (zero planet obliquity). The orbital eccentricity is also damped to zero, but over a much longer timescale, that may exceed the lifetime of the system. For non-zero eccentricities, the rotation rate can be trapped in spin-orbit resonances that delay the evolution towards the synchronous state. Here we show that capture in some spin-orbit resonances may also excite the obliquity to high values rather than damp it to zero. Depending on the system parameters, obliquities of 60 to 80 degrees can be maintained throughout the entire lifetime of the planet. This unexpected behaviour is particularly important for Earth-like planets in the habitable zone of M-dwarf stars, as it may help to sustain temperate environments and thus more favourable conditions for life.

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arXiv2023

Radial-velocity discovery of a second planet in the TOI-1338/BEBOP-1 circumbinary system

We report the detection of a gas-giant planet in orbit around both stars of an eclipsing binary star system that also contains the smaller, inner transiting planet TOI-1338b. The new planet, called TOI-1338/BEBOP-1c, was discovered using radial-velocity data collected with the HARPS and ESPRESSO spectrographs. Our analysis reveals it is a $65.2~\rm{M_{\oplus}}$ circumbinary planet with a period of $215.5~$days. This is the first detection of a circumbinary planet using radial-velocity observations alone, and makes TOI-1338/BEBOP-1 only the second confirmed multiplanet circumbinary system to date. We do not detect the smaller inner transiting planet with radial-velocity data, and can place an upper limit on the inner planet's mass at $21.8~\mathrm{M}_\oplus$ with $99\%$ confidence. The inner planet is the first circumbinary planet amenable for atmospheric characterisation, using the James Webb Space Telescope.

astro-ph.EP↗

arXiv2023

Tidal evolution for any rheological model using a vectorial approach expressed in Hansen coefficients

We revisit the two body problem, where one body can be deformed under the action of tides raised by the companion. Tidal deformation and consequent dissipation result in spin and orbital evolution of the system. In general, the equations of motion are derived from the tidal potential developed in Fourier series expressed in terms of Keplerian elliptical elements, so that the variation of dissipation with amplitude and frequency can be examined. However, this method introduces multiple index summations and some orbital elements depend on the chosen frame, which is prone to confusion and errors. Here, we develop the quadrupole tidal potential solely in a series of Hansen coefficients, which are widely used in celestial mechanics and depend just on the eccentricity. We derive the secular equations of motion in a vectorial formalism, which is frame independent and valid for any rheological model. We provide expressions for a single average over the mean anomaly and for an additional average over the argument of the pericentre. These equations are suitable to model the long-term evolution of a large variety of systems and configurations, from planet satellite to stellar binaries. We also compute the tidal energy released inside the body for an arbitrary configuration of the system.

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arXiv2023

Effect of the inclination in the passage through the 5/3 mean motion resonance between Ariel and Umbriel

The orbits of the main satellites of Uranus are expected to slowly drift away owing to tides raised in the planet. As a result, the 5/3 mean motion resonance between Ariel and Umbriel was likely encountered in the past. Previous studies have shown that, in order to prevent entrapment in this resonance, the eccentricities of the satellites must be larger than $\sim 0.01$ at the epoch, which is hard to explain. On the other hand, if the satellites experience some temporary capture and then escape, the inclinations rise to high values that are not observed today. We have revisited this problem both analytically and numerically focussing on the inclination, using a secular two-satellite model with circular orbits. We show that if the inclination of Umbriel was around $0.15^{\circ}$ at the time of the 5/3 resonance encounter, capture can be avoided in about $60\%$ of the cases. Moreover, after the resonance crossing, the inclination of Umbriel drops to a mean value around $0.08^{\circ}$, which is close to the presently observed one. The final inclination of Ariel is distributed between $0.01^{\circ}$ and $0.25^{\circ}$ with a nearly equal probability, which includes the present mean value of $0.02^{\circ}$.

astro-ph.EP↗

arXiv2023

Improving circumbinary planet detections by fitting their binary's apsidal precession

Apsidal precession in stellar binaries is the main non-Keplerian dynamical effect impacting the radial-velocities of a binary star system. Its presence can notably hide the presence of orbiting circumbinary planets because many fitting algorithms assume perfectly Keplerian motion. To first order, apsidal precession ($\dotω$) can be accounted for by adding a linear term to the usual Keplerian model. We include apsidal precession in the kima package, an orbital fitter designed to detect and characterise planets from radial velocity data. In this paper, we detail this and other additions to kima that improve fitting for stellar binaries and circumbinary planets including corrections from general relativity. We then demonstrate that fitting for $\dotω$ can improve the detection sensitivity to circumbinary exoplanets by up to an order of magnitude in some circumstances, particularly in the case of multi-planetary systems. In addition, we apply the algorithm to several real systems, producing a new measurement of aspidal precession in KOI-126 (a tight triple system), and a detection of $\dotω$ in the Kepler-16 circumbinary system. Although apsidal precession is detected for Kepler-16, it does not have a large effect on the detection limit or the planetary parameters. We also derive an expression for the precession an outer planet would induce on the inner binary and compare the value this predicts with the one we detect.

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arXiv2022

Reversible time-step adaptation for the integration of few-body systems

The time step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time step criteria commonly adopt the minimum pairwise time step, which suffers from discontinuities in the time evolution of the time step. This has a large impact on the functioning of time step symmetrisation algorithms. We provide new demonstrations of previous findings that a smooth and weighted average over all pairwise time steps in the N-body system, improves the level of energy conservation. Furthermore, we compare the performance of 27 different time step criteria, by considering 3 methods for weighting time steps and 9 symmetrisation methods. We present performance tests for strongly chaotic few-body systems, including unstable triples, giant planets in a resonant chain, and the current Solar System. We find that the harmonic symmetrisation methods (methods A3 and B3 in our notation) are the most robust, in the sense that the symmetrised time step remains close to the time step function. Furthermore, based on our Solar System experiment, we find that our new weighting method based on direct pairwise averaging (method W2 in our notation), is slightly preferred over the other methods.

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arXiv2022

Developing a data fusion concept for radar and optical ground based SST station

As part of the Portuguese Space Surveillance and Tracking (SST) program, a tracking radar and a double Wide Field of View Telescope system (4.3° x 2.3°) are being installed at the Pampilhosa da Serra Space Observatory (PASO) in the centre of continental Portugal, complementing an already installed deployable optical sensor for MEO and GEO surveillance. The tracking radar will track space debris in Low Earth Orbit (LEO) up to 1000 km and at the same time the telescope will also have LEO tracking capabilities. This article intends to discuss possible ways to take advantage of having these two sensors at the same location. Using both types of sensors takes advantage of the radar measurements which give precise radial velocity and distance to the objects, while the telescope gives better sky coordinates measurements. With the installation of radar and optical sensors, PASO can extend observation time of space debris and correlate information from optical and radar provenances in real time. During twilight periods both sensors can be used simultaneously to rapidly compute new TLEs for LEO objects, eliminating the time delays involved in data exchange between sites in a large SST network. This concept will not replace the need for a SST network with sensors in multiple locations around the globe, but will provide a more complete set of measurements from a given object passage, and therefore increase the added value for initial orbit determination, or monitoring of reentry campaigns of a given location. PASO will contribute to the development of new solutions to better characterize the objects improving the overall SST capabilities and constitute a perfect site for the development and testing of new radar and optical data fusion algorithms and techniques for space debris monitoring.

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arXiv2022

A direct N-body integrator for modelling the chaotic, tidal dynamics of multi-body extrasolar systems: TIDYMESS

Tidal dissipation plays an important role in the dynamical evolution of moons, planets, stars and compact remnants. The interesting complexity originates from the interplay between the internal structure and external tidal forcing. Recent and upcoming observing missions of exoplanets and stars in the Galaxy help to provide constraints on the physics of tidal dissipation. It is timely to develop new N-body codes, which allow for experimentation with various tidal models and numerical implementations. We present the open-source N-body code TIDYMESS, which stands for ``TIdal DYnamics of Multi-body ExtraSolar Systems''. This code implements a creep deformation law for the bodies, parametrized by their fluid Love numbers and fluid relaxation times. Due to tidal and centrifugal deformations, we approximate the general shape of a body to be an ellipsoid. We calculate the associated gravitational field to quadruple order, from which we derive the gravitational accelerations and torques. The equations of motion for the orbits, spins and deformations are integrated directly using a fourth-order integration method based on a symplectic composition. We implement a novel integration method for the deformations, which allows for a time step solely dependent on the orbits, and not on the spin periods or fluid relaxation times. This feature greatly speeds up the calculations, while also improving the consistency when comparing different tidal regimes. We demonstrate the capabilities and performance of TIDYMESS, particularly in the niche regime of parameter space where orbits are chaotic and tides become non-linear.

astro-ph.IM↗

arXiv2022

Complete determination of the orbital parameters of a system with N+1 bodies using a simple Fourier analysis of the data

Here we show how to determine the orbital parameters of a system composed of a star and N companions (that can be planets, brown-dwarfs or other stars), using a simple Fourier analysis of the radial velocity data of the star. This method supposes that all objects in the system follow keplerian orbits around the star and gives better results for a large number of observational points. The orbital parameters may present some errors, but they are an excellent starting point for the traditional minimization methods such as the Levenberg-Marquardt algorithms.

astro-ph.EP↗

arXiv2022

Dynamics of co-orbital exoplanets in a first order resonance chain with tidal dissipation

Co-orbital planets (in a $1:1$ mean motion resonance) can be formed within a Laplace resonance chain. Here, we develop a secular model to study the dynamics of the resonance chain $p:p:p+1$, where the co-orbital pair is in a first-order mean motion resonance with the outermost third planet. Our model takes into account tidal dissipation through the use of a Hamiltonian version of the constant time-lag model, which extends the Hamiltonian formalism of the point-mass case. We show the existence of several families of equilibria, and how these equilibria extend to the complete system. In one family, which we call the main branch, a secular resonance between the libration frequency of the co-orbitals and the precession frequency of the pericentres has unexpected dynamical consequences when tidal dissipation is added. We report the existence of two distinct mechanisms that make co-orbital planets much more stable within the $p:p:p+1$ resonance chain rather than outside it. The first one is due to negative real parts of the eigenvalues of the linearised system with tides, in the region of the secular resonance mentioned above. The second one comes from non-linear contributions of the vector field and it is due to eccentricity damping. These two stabilising mechanisms increase the chances of a still-to-come detection of exoplanets in the co-orbital configuration.

astro-ph.EP↗

arXiv2022

Eviction-like resonances for satellite orbits. Application to Phobos, the main satellite of Mars

The motion of a satellite can experience secular resonances between the precession frequencies of its orbit and the mean motion of the host planet around the star. Some of these resonances can significantly modify the eccentricity (evection resonance) and the inclination (eviction resonance) of the satellite. In this paper, we study in detail the secular resonances that can disturb the orbit of a satellite, in particular the eviction-like ones. Although the inclination is always disturbed while crossing one eviction-like resonance, capture can only occur when the semi-major axis is decreasing. This is, for instance, the case of Phobos, the largest satellite of Mars, that will cross some of these resonances in the future because its orbit is shrinking owing to tidal effects. We estimate the impact of resonance crossing in the orbit of the satellite, including the capture probabilities, as a function of several parameters, such as the eccentricity and the inclination of the satellite, and the obliquity of the planet. Finally, we use the method of the frequency map analysis to study the resonant dynamics based on stability maps, and we show that some of the secular resonances may overlap, which leads to chaotic motion for the inclination of the satellite.

astro-ph.EP↗

arXiv2021

Spin-orbit coupling for close-in planets

We study the spin evolution of close-in planets in multi-body systems and present a very general formulation of the spin-orbit problem. This includes a simple way to probe the spin dynamics from the orbital perturbations, a new method for computing forced librations and tidal deformation, and general expressions for the tidal torque and capture probabilities in resonance. We show that planet-planet perturbations can drive the spin of Earth-size planets into asynchronous or chaotic states, even for nearly circular orbits. We apply our results to Mercury and to the KOI-1599 system of two super-Earths in a 3/2 mean motion resonance.

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arXiv2021

BEBOP III. Observations and an independent mass measurement of Kepler-16 (AB) b -- the first circumbinary planet detected with radial velocities

The radial velocity method is amongst the most robust and most established means of detecting exoplanets. Yet, it has so far failed to detect circumbinary planets despite their relatively high occurrence rates. Here, we report velocimetric measurements of Kepler-16A, obtained with the SOPHIE spectrograph, at the Observatoire de Haute-Provence's 193cm telescope, collected during the BEBOP survey for circumbinary planets. Our measurements mark the first radial velocity detection of a circumbinary planet, independently determining the mass of Kepler-16~(AB)~b to be $0.313 \pm 0.039\,{\rm M}_{\rm Jup}$, a value in agreement with eclipse timing variations. Our observations demonstrate the capability to achieve photon-noise precision and accuracy on single-lined binaries, with our final precision reaching $\rm 1.5~m\,s^{-1}$ on the binary and planetary signals. Our analysis paves the way for more circumbinary planet detections using radial velocities which will increase the relatively small sample of currently known systems to statistically relevant numbers, using a method that also provides weaker detection biases. Our data also contain a long-term radial velocity signal, which we associate with the magnetic cycle of the primary star.

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arXiv2021

BEBOP II: Sensitivity to sub-Saturn circumbinary planets using radial-velocities

BEBOP is a radial-velocity survey that monitors a sample of single-lined eclipsing binaries, in search of circumbinary planets by using high-resolution spectrographs. Here, we describe and test the methods we use to identify planetary signals within the BEBOP data, and establish how we quantify our sensitivity to circumbinary planets by producing detection limits. This process is made easier and more robust by using a diffusive nested sampler. In the process of testing our methods, we notice that contrary to popular wisdom, assuming circular orbits in calculating detection limits for a radial velocity survey provides over-optimistic detection limits by up to $40\%$ in semi-amplitude with implications for all radial-velocity surveys. We perform example analyses using three BEBOP targets from our Southern HARPS survey. We demonstrate for the first time a repeated ability to reach a residual root mean squared scatter of $3~\rm m.s^{-1}$ (after removing the binary signal), and find we are sensitive to circumbinary planets with masses down to that of Neptune and Saturn, for orbital periods up to $1000~\rm days$.

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arXiv2021

Cyber-Cosmos: A New Citizen Science Concept in A Dark Sky Destination

Astrotourism and related citizen science activities are becoming a major trend of a sustainable, high-quality tourism segment, core elements to the protection of Dark skies in many countries. In the Summer of 2020, in the middle of COVID pandemics, we started an initiative to train young students - Cyber-Cosmos - using an Unistellar eVscope, a smart, compact and user-friendly digital telescope that offers unprecedented opportunities for deep-sky observation and citizen science campaigns. Sponsored by the Ciência Viva Summer program, this was probably the first continuous application of this equipment in a pedagogical and citizen-science context, and in a pandemic context. Pampilhosa da Serra, home to a certified Dark Sky destination (Aldeias do Xisto) in central Portugal, was the chosen location for this project, where we expect astrotourism and citizen science to flourish and contribute to space sciences education.

physics.soc-ph↗

arXiv2021

Radio astronomy and Space science in Azores: enhancing the Atlantic VLBI infrastructure cluster

Radio astronomy and Space Infrastructures in the Azores have a great scientific and industrial interest because they benefit from a unique geographical location in the middle of the North Atlantic allowing a vast improvement in the sky coverage. This fact obviously has a very high added value for: i) the establishment of space tracking and communications networks for the emergent global small satellite fleets ii) it is invaluable to connect the radio astronomy infrastructure networks in Africa, Europe and America continents using Very Large Baseline Interferometry (VLBI) techniques, iii) it allows excellent potential for monitoring space debris and Near Earth Objects (NEOs). There is in S. Miguel island a 32-metre SATCOM antenna that could be integrated in advanced VLBI networks and be capable of additional Deep Space Network ground support. This paper explores the space science opportunities offered by the upgrade of the S. Miguel 32-metre SATCOM antenna into a world-class infrastructure for radio astronomy and space exploration: it would enable a Deep Space Network mode and would constitute a key space facility for data production, promoting local digital infrastructure investments and the testing of cutting-edge information technologies. Its Atlantic location also enables improvements in angular resolution, provides many baseline in East-West and North-South directions connecting the emergent VLBI stations in America to Europe and Africa VLBI arrays therefore contributing for greater array imaging capabilities especially for sources or well studied fields close to or below the celestial equator, where ESO facilities, ALMA, SKA and its precursors do or will operate and observe in the coming decades.

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