arXiv subjects

Jacques Laskar

Publications and source records attributed to Jacques Laskar.

At least 37 records · Page 2Linked to original sources

arXiv2023

Timescales of Chaos in the Inner Solar System: Lyapunov Spectrum and Quasi-integrals of Motion

Numerical integrations of the Solar System reveal a remarkable stability of the orbits of the inner planets over billions of years, in spite of their chaotic variations characterized by a Lyapunov time of only 5 million years and the lack of integrals of motion able to constrain their dynamics. To open a window on such long-term behavior, we compute the entire Lyapunov spectrum of a forced secular model of the inner planets. We uncover a hierarchy of characteristic exponents that spans two orders of magnitude, manifesting a slow-fast dynamics with a broad separation of timescales. A systematic analysis of the Fourier harmonics of the Hamiltonian, based on computer algebra, reveals three symmetries that characterize the strongest resonances responsible for the orbital chaos. These symmetries are broken only by weak resonances, leading to the existence of quasi-integrals of motion that are shown to relate to the smallest Lyapunov exponents. A principal component analysis of the orbital solutions independently confirms that the quasi-integrals are among the slowest degrees of freedom of the dynamics. Strong evidence emerges that they effectively constrain the chaotic diffusion of the orbits, playing a crucial role in the statistical stability over the Solar System lifetime.

astro-ph.EP↗

arXiv2023

Chaotic diffusion of the fundamental frequencies in the Solar System

The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the determination of the geological timescales. However, the orbital variations beyond 60 Myr cannot be reliably predicted because of the chaotic dynamics of the planetary orbits in the Solar System. Taking this dynamical uncertainty into account is necessary for a complete astronomical calibration of geological records. Our work addresses this problem with a statistical analysis of 120 000 orbital solutions of the secular model of the Solar System ranging from 500 Myr to 5 Gyr. We obtain the marginal probability density functions of the fundamental secular frequencies using kernel density estimation. The uncertainty of the density estimation is also obtained here in the form of confidence intervals determined by the moving block bootstrap method. The results of the secular model are shown to be in good agreement with those of the direct integrations of a comprehensive model of the Solar System. Application of our work is illustrated on two geological data sets: the Newark-Hartford records and the Libsack core.

astro-ph.EP↗

arXiv2022

TOI-836: A super-Earth and mini-Neptune transiting a nearby K-dwarf

We present the discovery of two exoplanets transiting TOI-836 (TIC 440887364) using data from TESS Sector 11 and Sector 38. TOI-836 is a bright ($T = 8.5$ mag), high proper motion ($\sim\,200$ mas yr$^{-1}$), low metallicity ([Fe/H]$\approx\,-0.28$) K-dwarf with a mass of $0.68\pm0.05$ M$_{\odot}$ and a radius of $0.67\pm0.01$ R$_{\odot}$. We obtain photometric follow-up observations with a variety of facilities, and we use these data-sets to determine that the inner planet, TOI-836 b, is a $1.70\pm0.07$ R$_{\oplus}$ super-Earth in a 3.82 day orbit, placing it directly within the so-called 'radius valley'. The outer planet, TOI-836 c, is a $2.59\pm0.09$ R$_{\oplus}$ mini-Neptune in an 8.60 day orbit. Radial velocity measurements reveal that TOI-836 b has a mass of $4.5\pm0.9$ M$_{\oplus}$ , while TOI-836 c has a mass of $9.6\pm2.6$ M$_{\oplus}$. Photometric observations show Transit Timing Variations (TTVs) on the order of 20 minutes for TOI-836 c, although there are no detectable TTVs for TOI-836 b. The TTVs of planet TOI-836 c may be caused by an undetected exterior planet.

astro-ph.EP↗

arXiv2022

The Resonant Tidal Evolution of the Earth-Moon Distance

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.

astro-ph.EP↗

arXiv2022

Long-term instability of the inner Solar System: numerical experiments

Apart from being chaotic, the inner planets in the Solar System constitute an open system, as they are forced by the regular long-term motion of the outer ones. No integrals of motion can bound a priori the stochastic wanderings in their high-dimensional phase space. Still, the probability of a dynamical instability is remarkably low over the next 5 billion years, a timescale thousand times longer than the Lyapunov time. The dynamical half-life of Mercury has indeed been estimated recently at 40 billion years. By means of the computer algebra system TRIP, we consider a set of dynamical models resulting from truncation of the forced secular dynamics recently proposed for the inner planets at different degrees in eccentricities and inclinations. Through ensembles of $10^3$ to $10^5$ numerical integrations spanning 5 to 100 Gyr, we find that the Hamiltonian truncated at degree 4 practically does not allow any instability over 5 Gyr. The destabilisation is mainly due to terms of degree 6. This surprising result suggests an analogy to the Fermi-Pasta-Ulam-Tsingou problem, in which tangency to Toda Hamiltonian explains the very long timescale of thermalisation, which Fermi unsuccessfully looked for.

astro-ph.EP↗

arXiv2022

The origin of chaos in the Solar System through computer algebra

The discovery of the chaotic motion of the planets in the Solar System dates back more than 30 years. Still, no analytical theory has satisfactorily addressed the origin of chaos so far. Implementing canonical perturbation theory in the computer algebra system TRIP, we systematically retrieve the secular resonances at work along the orbital solution of a forced long-term dynamics of the inner planets. We compare the time statistic of their half-widths to the ensemble distribution of the maximum Lyapunov exponent and establish dynamical sources of chaos in an unbiased way. New resonances are predicted by the theory and checked against direct integrations of the Solar System. The image of an entangled dynamics of the inner planets emerges.

astro-ph.EP↗

arXiv2022

Uncovering the true periods of the young sub-Neptunes orbiting TOI-2076

Context: TOI-2076 is a transiting three-planet system of sub-Neptunes orbiting a bright (G = 8.9 mag), young ($340\pm80$ Myr) K-type star. Although a validated planetary system, the orbits of the two outer planets were unconstrained as only two non-consecutive transits were seen in TESS photometry. This left 11 and 7 possible period aliases for each. Aims: To reveal the true orbits of these two long-period planets, precise photometry targeted on the highest-probability period aliases is required. Long-term monitoring of transits in multi-planet systems can also help constrain planetary masses through TTV measurements. Methods: We used the MonoTools package to determine which aliases to follow, and then performed space-based and ground-based photometric follow-up of TOI-2076 c and d with CHEOPS, SAINT-EX, and LCO telescopes. Results: CHEOPS observations revealed a clear detection for TOI-2076 c at $P=21.01538^{+0.00084}_{-0.00074}$ d, and allowed us to rule out three of the most likely period aliases for TOI-2076 d. Ground-based photometry further enabled us to rule out remaining aliases and confirm the $P=35.12537\pm0.00067$ d alias. These observations also improved the radius precision of all three sub-Neptunes to $2.518\pm0.036$, $3.497\pm0.043$, and $3.232\pm0.063$ $R_\oplus$. Our observations also revealed a clear anti-correlated TTV signal between planets b and c likely caused by their proximity to the 2:1 resonance, while planets c and d appear close to a 5:3 period commensurability, although model degeneracy meant we were unable to retrieve robust TTV masses. Their inflated radii, likely due to extended H-He atmospheres, combined with low insolation makes all three planets excellent candidates for future comparative transmission spectroscopy with JWST.

astro-ph.EP↗

arXiv2022

A pair of Sub-Neptunes transiting the bright K-dwarf TOI-1064 characterised with CHEOPS

We report the discovery and characterisation of a pair of sub-Neptunes transiting the bright K-dwarf TOI-1064 (TIC 79748331), initially detected in TESS photometry. To characterise the system, we performed and retrieved CHEOPS, TESS, and ground-based photometry, HARPS high-resolution spectroscopy, and Gemini speckle imaging. We characterise the host star and determine $T_{\rm eff, \star}=4734\pm67$ K, $R_{\star}=0.726\pm0.007$ $R_{\odot}$, and $M_{\star}=0.748\pm0.032$ $M_{\odot}$. We present a novel detrending method based on PSF shape-change modelling and demonstrate its suitability to correct flux variations in CHEOPS data. We confirm the planetary nature of both bodies and find that TOI-1064 b has an orbital period of $P_{\rm b}=6.44387\pm0.00003$ d, a radius of $R_{\rm b}=2.59\pm0.04$ $R_{\oplus}$, and a mass of $M_{\rm b}=13.5_{-1.8}^{+1.7}$ $M_{\oplus}$, whilst TOI-1064 c has an orbital period of $P_{\rm c}=12.22657^{+0.00005}_{-0.00004}$ d, a radius of $R_{\rm c}=2.65\pm0.04$ $R_{\oplus}$, and a 3$σ$ upper mass limit of 8.5 ${\rm M_{\oplus}}$. From the high-precision photometry we obtain radius uncertainties of $\sim$1.6%, allowing us to conduct internal structure and atmospheric escape modelling. TOI-1064 b is one of the densest, well-characterised sub-Neptunes, with a tenuous atmosphere that can be explained by the loss of a primordial envelope following migration through the protoplanetary disc. It is likely that TOI-1064 c has an extended atmosphere due to the tentative low density, however further RVs are needed to confirm this scenario and the similar radii, different masses nature of this system. The high-precision data and modelling of TOI-1064 b are important for planets in this region of mass-radius space, and it allows us to identify a trend in bulk density-stellar metallicity for massive sub-Neptunes that may hint at the formation of this population of planets.

astro-ph.EP↗

arXiv2021

Faint objects in motion: the new frontier of high precision astrometry

Sky survey telescopes and powerful targeted telescopes play complementary roles in astronomy. In order to investigate the nature and characteristics of the motions of very faint objects, a flexibly-pointed instrument capable of high astrometric accuracy is an ideal complement to current astrometric surveys and a unique tool for precision astrophysics. Such a space-based mission will push the frontier of precision astrometry from evidence of Earth-mass habitable worlds around the nearest stars, to distant Milky Way objects, and out to the Local Group of galaxies. As we enter the era of the James Webb Space Telescope and the new ground-based, adaptive-optics-enabled giant telescopes, by obtaining these high precision measurements on key objects that Gaia could not reach, a mission that focuses on high precision astrometry science can consolidate our theoretical understanding of the local Universe, enable extrapolation of physical processes to remote redshifts, and derive a much more consistent picture of cosmological evolution and the likely fate of our cosmos. Already several missions have been proposed to address the science case of faint objects in motion using high precision astrometry missions: NEAT proposed for the ESA M3 opportunity, micro-NEAT for the S1 opportunity, and Theia for the M4 and M5 opportunities. Additional new mission configurations adapted with technological innovations could be envisioned to pursue accurate measurements of these extremely small motions. The goal of this White Paper is to address the fundamental science questions that are at stake when we focus on the motions of faint sky objects and to briefly review instrumentation and mission profiles.

astro-ph.IM↗

arXiv2021

Transit detection of the long-period volatile-rich super-Earth $ν^2$ Lupi d with $CHEOPS$

Exoplanets transiting bright nearby stars are key objects for advancing our knowledge of planetary formation and evolution. The wealth of photons from the host star gives detailed access to the atmospheric, interior, and orbital properties of the planetary companions. $ν^2$ Lupi (HD 136352) is a naked-eye ($V = 5.78$) Sun-like star that was discovered to host three low-mass planets with orbital periods of 11.6, 27.6, and 107.6 days via radial velocity monitoring (Udry et al. 2019). The two inner planets (b and c) were recently found to transit (Kane et al. 2020), prompting a photometric follow-up by the brand-new $CHaracterising\:ExOPlanets\:Satellite\:(CHEOPS)$. Here, we report that the outer planet d is also transiting, and measure its radius and mass to be $2.56\pm0.09$ $R_{\oplus}$ and $8.82\pm0.94$ $M_{\oplus}$, respectively. With its bright Sun-like star, long period, and mild irradiation ($\sim$5.7 times the irradiation of Earth), $ν^2$ Lupi d unlocks a completely new region in the parameter space of exoplanets amenable to detailed characterization. We refine the properties of all three planets: planet b likely has a rocky mostly dry composition, while planets c and d seem to have retained small hydrogen-helium envelopes and a possibly large water fraction. This diversity of planetary compositions makes the $ν^2$ Lupi system an excellent laboratory for testing formation and evolution models of low-mass planets.

astro-ph.EP↗

arXiv2021

Long-term dynamics of the solar system inner planets

Although the discovery of the chaotic motion of the inner planets in the solar system dates back to more than thirty years ago, the secular chaos of their orbits still dares more analytical analyses. Apart from the high-dimensional structure of the motion, this is probably related to the lack of an adequately simple dynamical model. Here, we consider a new secular dynamics for the inner planets, with the aim of retaining a fundamental set of interactions responsible for their chaotic behaviour, while being consistent with the predictions of the most precise orbital solutions currently available. We exploit the regularity in the secular motion of the outer planets, to predetermine a quasi-periodic solution for their orbits. This reduces the secular phase space to the degrees of freedom dominated by the inner planets. On top of that, the smallness of the inner planet masses and the absence of strong mean-motion resonances permits to restrict ourselves to first-order secular averaging. The resulting dynamics can be integrated numerically in a very efficient way through Gauss's method, while computer algebra allows for analytical inspection of planet interactions, once the Hamiltonian is truncated at a given total degree in eccentricities and inclinations. The new model matches very satisfactorily reference orbital solutions of the solar system over timescales shorter than or comparable to the Lyapunov time. It correctly reproduces the maximum Lyapunov exponent of the inner system and the statistics of the high eccentricities of Mercury over the next five billion years. The destabilizing role of the $g_1-g_5$ secular resonance also arises. A numerical experiment, consisting of a thousand orbital solutions over one hundred billion years, reveals the essential properties of the stochastic process driving the destabilization of the inner solar system and clarifies its current metastable state.

astro-ph.EP↗

arXiv2021

Constraining the Earth's Dynamical Ellipticity from Ice Age Dynamics

The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In the case of the Earth, uncertainties in this quantity's history produce an uncertainty in the solutions for the past evolution of the Earth-Moon system. Constraining this history has been a target of interdisciplinary efforts as it represents an astro-geodetic parameter whose variation is shaped by geophysical processes, and whose imprints can be found in the geological signal. We revisit the classical problem of its variation during ice ages, where glacial cycles exerted a varying surface loading that had altered the shape of the geoid. In the framework of glacial isostatic adjustment, and with the help of a recent paleoclimatic proxy of ice volume, we present the evolution of the dynamical ellipticity over the Cenozoic ice ages. We map out the problem in full generality identifying major sensitivities to surface loading and internal variations in parameter space. This constrained evolution is aimed to be used in future astronomical computations of the orbital and insolation quantities of the Earth.

astro-ph.EP↗

arXiv2020

The CHEOPS mission

The CHaracterising ExOPlanet Satellite (CHEOPS) was selected in 2012, as the first small mission in the ESA Science Programme and successfully launched in December 2019. CHEOPS is a partnership between ESA and Switzerland with important contributions by ten additional ESA Member States. CHEOPS is the first mission dedicated to search for transits of exoplanets using ultrahigh precision photometry on bright stars already known to host planets. As a follow-up mission, CHEOPS is mainly dedicated to improving, whenever possible, existing radii measurements or provide first accurate measurements for a subset of those planets for which the mass has already been estimated from ground-based spectroscopic surveys and to following phase curves. CHEOPS will provide prime targets for future spectroscopic atmospheric characterisation. Requirements on the photometric precision and stability have been derived for stars with magnitudes ranging from 6 to 12 in the V band. In particular, CHEOPS shall be able to detect Earth-size planets transiting G5 dwarf stars in the magnitude range between 6 and 9 by achieving a photometric precision of 20 ppm in 6 hours of integration. For K stars in the magnitude range between 9 and 12, CHEOPS shall be able to detect transiting Neptune-size planets achieving a photometric precision of 85 ppm in 3 hours of integration. This is achieved by using a single, frame-transfer, back-illuminated CCD detector at the focal plane assembly of a 33.5 cm diameter telescope. The 280 kg spacecraft has a pointing accuracy of about 1 arcsec rms and orbits on a sun-synchronous dusk-dawn orbit at 700 km altitude. The nominal mission lifetime is 3.5 years. During this period, 20% of the observing time is available to the community through a yearly call and a discretionary time programme managed by ESA.

astro-ph.IM↗

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.

astro-ph.EP↗

arXiv2019

High order regularised symplectic integrator for collisional planetary systems

We present a new mixed variable symplectic (MVS) integrator for planetary systems, that fully resolve close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators, while also reducing the effective step size whenever two planets encounter. We use a high order MVS scheme such that it is possible to integrate with large time steps far away from close encounters. We show that this algorithm is able to resolve almost exact collisions (i.e with a mutual separation of a fraction of the physical radius) while using the same time-step as in weakly perturbed problem such as the Solar System. We demonstrate the long term behaviour on systems of six super-Earths experiencing strong scattering for 50 kyr. We compare our algorithm to hybrid methods such as MERCURY and show that for an equivalent cost we obtain much better energy conservation.

astro-ph.EP↗

arXiv2019

Observational constraint on the radius and oblateness of the lunar core-mantle boundary

Lunar laser ranging (LLR) data and Apollo seismic data analyses, revealed independent evidence for the presence of a fluid lunar core. However, the size of the lunar fluid core remained uncertain by $\pm55$ km (encompassing two contrasting 2011 Apollo seismic data analyses). Here we show that a new description of the lunar interior's dynamical model provides a determination of the radius and geometry of the lunar core-mantle boundary (CMB) from the LLR observations. We compare the present-day lunar core oblateness obtained from LLR analysis with the expected hydrostatic model values, over a range of previously expected CMB radii. The findings suggest a core oblateness ($f_c=(2.2\pm0.6)\times10^{-4}$) that satisfies the assumption of hydrostatic equilibrium over a tight range of lunar CMB radii ($\mathcal{R}_{CMB}=381\pm12$ km). Our estimates of a presently-relaxed lunar CMB translates to a core mass fraction in the range of $1.59-1.77\%$ with a present-day Free Core Nutation (FCN) within $(367\pm100)$ years.

physics.geo-ph↗

arXiv2019

Refined betatron tune measurements by mixing beam position data

The measurement of the betatron tunes in a circular accelerator is of paramount importance due to their impact on beam dynamics. The resolution of the these measurements, when using turn by turn (TbT) data from beam position monitors (BPMs), is greatly limited by the available number of turns in the signal. Due to decoherence from finite chromaticity and/or amplitude detuning, the transverse betatron oscillations appear to be damped in the TbT signal. On the other hand, an adequate number of samples is needed, if precise and accurate tune measurements are desired. In this paper, a method is presented that allows for very precise tune measurements within a very small number of turns. The theoretical foundation of this method is presented with results from numerical and tracking simulations but also from experimental TbT data which are recorded at electron and proton circular accelerators.

physics.acc-ph↗