Julien Frouard

Northwestern University, Evanston, Illinois, United States

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Publications (17)36.78 Total impact

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    Valeri V. Makarov · Julien Frouard · Bryan Dorland
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    ABSTRACT: Tidal dissipation of kinetic energy, when it is strong enough, tends to synchronize the rotation of planets and moons with the mean orbital motion, or drive it into long-term stable spin-orbit resonances. As the orbital motion undergoes periodic acceleration due to a finite orbital eccentricity, the spin rate oscillates around the equilibrium mean value too, giving rise to the forced, or eccentricity-driven, librations. Both the shape and amplitude of forced librations of synchronous viscoelastic planets and moons are defined by a combination of two different types of perturbative torque, the tidal torque and the triaxial torque. Consequently, forced librations can be tidally dominated (e.g., Io and possibly Titan) or deformation-dominated (e.g., the Moon) depending on a set of orbital, rheological, and other physical parameters. With small eccentricities, for the former kind, the largest term in the libration angle can be minus cosine of the mean anomaly, whereas for the latter kind, it is minus sine of the mean anomaly. The shape and the amplitude of tidal forced librations determine the rate of orbital evolution of synchronous planets and moons, i.e., the rate of dissipative damping of semimajor axis and eccentricity. The known super-Earth exoplanets can exhibit both kinds of libration, or a mixture thereof, depending on, for example, the effective Maxwell time of their rigid mantles. Our approach can be extended to estimate the amplitudes of other libration harmonics, as well as the forced libration in non-synchronous spin-orbit resonances.
    Full-text · Article · Nov 2015 · Monthly Notices of the Royal Astronomical Society
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    ABSTRACT: We present an all-sky sample of ~ 1.4 million AGNs meeting a two color infrared photometric selection criteria for AGNs as applied to sources from the Wide-Field Infrared Survey Explorer final catalog release (AllWISE). We assess the spatial distribution and optical properties of our sample and find that the results are consistent with expectations for AGNs. These sources have a mean density of ~ 38 AGNs per square degree on the sky, and their apparent magnitude distribution peaks at g ~ 20, extending to objects as faint as g ~ 26. We test the AGN selection criteria against a large sample of optically-identified stars and determine the "leakage" (that is, the probability that a star detected in an optical survey will be misidentified as a QSO in our sample) rate to be < 4.0 x 10^-5. We conclude that our sample contains almost no optically-identified stars (< 0.041%), making this sample highly promising for future celestial reference frame work by significantly increasing the number of all-sky, compact extragalactic objects. We further compare our sample to catalogs of known AGNs/QSOs and find a completeness value of > 84% (that is, the probability of correctly identifying a known AGN/QSO is at least 84%) for AGNs brighter than a limiting magnitude of R < 19. Our sample includes approximately 1.1 million previously uncatalogued AGNs.
    Full-text · Article · Sep 2015 · The Astrophysical Journal Supplement Series
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    ABSTRACT: Proper motions are computed and collected in a catalog using the Hipparcos positions (epoch 1991.25) and URAT1 positions (epoch 2012.3 to 2014.6). The goal is to obtain a significant improvement on the proper motion accuracy of single stars in the northern hemisphere, and to identify new astrometric binaries perturbed by orbital motion. For binaries and multiple systems, the longer baseline of Tycho2 (~ 100 yr) makes it more reliable despite its larger formal uncertainties. The resulting proper motions obtained for 67,340 stars have a consequent gain in accuracy by a factor of ~ 3 compared to Hipparcos. Comparison between UrHip and Hipparcos shows that they are reasonably close, but also reveals stars with large discrepant proper motions, a fraction of which are potential binary candidates.
    Full-text · Article · Sep 2015 · The Astronomical Journal
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    Dataset: poster

    Full-text · Dataset · Aug 2015
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    ABSTRACT: The rotation of Mercury is a unique case in the Solar System since this planet is locked into a 3:2 spin-orbit resonance. We here simulate the despinning of Mercury, with or without a fluid core, and with a frequency-dependent tidal model employed. The tidal model incorporates the viscoelastic (Maxwell) rebound at low forcing frequencies and a predominantly inelastic (Andrade) creep of the mantle at higher frequencies. It is combined with a statistically relevant set of histories of Mercury's eccentricity. We show that the tidal model has a dramatic influence on the behaviour of spin histories near spin-orbit resonances. Specifically, the probabilities of capture into high-order resonances are greatly enhanced, suggesting a swift entrapment within less than 20 Myr, which was well before differentiation. Exploring several possible scenarios, we arrive at a conclusion that, most probably, the present 3:2 spin state was achieved by entrapment of an initially prograde cold Mercury.
    Full-text · Conference Paper · Jul 2015
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    Valeri Makarov · Alexei Goldin · Julien Frouard
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    ABSTRACT: Astrometric and photometric data collected with the NASA Kepler mission are heavily contaminated by Variability Induced Movement (VIM) effects and other occurrences of signal and image blending. The combination of superb relative precision in photometric and astrometric measurements with limited angular resolution of double sources, and some instrumental artifacts, make the photocenters of target stars move in complex and unpredictable fashion. We processed the entire “long cadence” collection of Kepler archival data for the ~150 000 targets searching for VIMs. We find that practically all Kepler sources are subject to VIM effects at least in one quarter of the mission, if the VIM correlation parameter is limited to a threshold value of 0.3. The presence of detrimental signal blending of distant objects is found in at least 28% of detections, caused by yet unexplained instrumental features such as CCD column illumination. The character and the high rate of VIMs drastically increase the probability of false positives in exoplanet detection and in identification of variable stars, and make astrometric applications (such as parallax determination) rather hard if not impossible.
    Full-text · Conference Paper · Jun 2015
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    ABSTRACT: Mercury's spin state is peculiar, in that it is locked into the 3:2 spin-orbit resonance. Its rotation period, 58 days, is exactly two thirds of its orbital period. It is accepted that the eccentricity of Mercury (0.206) favours the trapping into this resonance. More controversial is how the capture took place. A recent study by Makarov has shown that entrapment into this resonance is certain if the eccentricity is larger than 0.2, provided that we use a realistic tidal model, based on the Darwin-Kaula expansion of the tidal torque, including both the elastic rebound and anelastic creep of solids. We here revisit the scenario of Mercury's capture into the supersynchronous spin-orbit resonances. The study is based on a realistic model of tidal friction in solids, that takes into account the rheology and the self-gravitation of the planet. Developed in Efroimsky, it was employed by Makarov et al. to determine the likely spin state of the planet GJ581d, with its eccentricity evolution taken into account. It was also used in the afore-cited work to study the tidal spin-down and to find the likely end-state of a Mercury-like planet with its eccentricity fixed. We now go ahead by considering the evolution of Mercury's eccentricity. We find that the realistic tidal model, as opposed to the constant time lag and constant phase lag models, changes dramatically the statistics of the probable final spin-orbit states. First, after only one crossing of the 3:2 resonance this resonance becomes the most probable end-state. Second, if a capture into any resonance takes place, the capture is final, several crossings of the same state being forbidden. Third, within our model the trapping of Mercury happens much faster than previously believed. The swift capture justifies our treatment of Mercury as a homogeneous, unstratified body whose liquid core had not yet formed by the time of trapping.
    Full-text · Article · Jun 2013 · Icarus
  • A. Compère · J. Frouard · B. Carry

    No preview · Article · May 2012
  • Julien Frouard · Tadashi Yokoyama
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    ABSTRACT: An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit.
    No preview · Article · Jan 2012 · Celestial Mechanics and Dynamical Astronomy
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    Julien Frouard · Audrey Compère
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    ABSTRACT: We study the stability of the (87) Sylvia system and of the neighborhood of its two satellites. We use numerical integrations considering the non-sphericity of Sylvia, as well as the mutual perturbation of the satellites and the solar perturbation. Two numerical models have been used, which describe respectively the short and long-term evolution of the system. We show that the actual system is in a deeply stable zone, but surrounded by both fast and secular chaotic regions due to resonances. We then investigate how tidal and BYORP effects modify the location of the system over time with respect to the instability zones. Finally, we briefly generalize this study to other known triple systems and to satellites of asteroids in general, and discuss about their distance from mean-motion and evection resonances.
    Full-text · Article · Dec 2011 · Icarus
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    J. Frouard · A. Compère
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    ABSTRACT: The triple system 87 Sylvia consisting of two small satellites (Romulus and Remus) orbiting around an asteroid in nearly circular orbits is studied. We model it using a four-body system Sylvia-Romulus-Remus- Sun with a spherical harmonics expansion up to the 4th degree and order for the gravitational potential of Sylvia. We integrate the equations of motion in two ways in order to study short and long periods; a complete one with an imposed fixed rotation rate for Sylvia on its principal moment on inertia, and an averaged one over the mean longitudes. We find that the semi-major axis of the satellites are bounded by meanmotion resonances (between the mean longitudes of the satellites) and by evection resonances (between the longitude of pericenter of Romulus and the longitude of the Sun).
    Preview · Article · Oct 2011
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    J. Frouard · A. Vienne · M. Fouchard
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    ABSTRACT: Context. The dynamical region of the Jovian irregular satellites presents an interesting web of resonances that are not yet fully understood. Of particular interest is the influence of the resonances on the stochasticity of the individual orbits of the satellites, as well as on the long-term chaotic diffusion of the different families of satellites. Aims: We make a systematic numerical study of the satellite region to determine the important resonances for the dynamics, to search for the chaotic zones, and to determine their influences on the dynamics of the satellites. We also compare these numerical results to previous analytical works. Methods: Using extensive numerical integrations of the satellites along with an indicator of chaos (MEGNO), we show global and detailed views of the retrograde and prograde regions for various dynamical models of increasing complexity and indicate the appearance of the different types of resonances and the implied chaos. Results: Along with secular and mean motion resonances that shape the dynamical regions of the satellites, we report a number of resonances involving the Great Inequality, and which are present in the system thanks to the wide range of the values of frequencies of the pericenter available for the satellites. The chaotic diffusion of the satellites is also studied and shows the long-term stability of the Ananke and Carme families, in contrast to the Pasiphae family. Tables 1 and 2 are available in electronic form at http://www.aanda.org
    Preview · Article · Aug 2011 · Astronomy and Astrophysics
  • J. Frouard · M. Fouchard · A. Vienne
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    ABSTRACT: Among resonances commonly influential to the dynamics of satellites, the evection resonance introduces an important correction to the precession frequency of the satellite, as it is well known for the Moon's problem. However, the dynamic of the resonance itself, which is important for satellites stability and capture topics, including its libration and circulation regions, and its elliptic and hyperbolic points, has not been extensively studied. Here we investigate its dynamic with an improved analytic model, making comparisons with previous works, and resort to numerical methods and integrations to study and localize the different features of the resonance. This resonance is found in the outer orbital region near the orbital stability limit. However we also study and localize an other libration region that can be found much more closer to the parent planet when its oblateness is taken into account in the model.
    No preview · Article · Nov 2010
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    J. Frouard · M. Fouchard · A. Vienne
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    ABSTRACT: Context. The evection resonance appears to be the outermost region of stability for prograde satellite orbiting a planet, the critical argument of the resonance indeed being found librating in regions surrounded only by chaotic orbits. The dynamics of the resonance itself is thus of great interest for the stability of satellites, but its analysis by means of an analytical model is not straightforward because of the high perturbations acting on the dynamical region of interest. Aims: It is thus important to show the results and the limits inherent in analytical models. We use numerical methods to test the validity of the models and analyze the dynamics of the resonance. Methods: We use an analytical method based on a classical averaged expansion of the disturbing function valid for all eccentricities as well as numerical integrations of the motion and surfaces of section. Results: By comparing analytical and numerical methods, we show that aspects of the true resonant dynamic can be represented by our analytical model in a more accurate way than previous approximations, and with the help of the surfaces of section we present the exact location and dynamics of the resonance. We also show the additional region of libration of the resonance that can be found much closer to the planet due to its oblateness.
    Preview · Article · Jun 2010 · Astronomy and Astrophysics
  • Julien Frouard · M. Fouchard · A. Vienne
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    ABSTRACT: Interested in the global dynamical structure of the Jovian irregular satellites and their chaotic evolutions, we have performed numerical integrations of the satellites along with an indicator of chaos (MEGNO), to give a clear representation of the dynamical structure of the regions surrounding the satellites, and the consequences on the individual evolutions of the bodies. In particular, as the long-term integrations give indications about the chaotic diffusion of the satellites in the phase space, dynamical maps show the reasons of the detected chaos and the underlying resonant dynamics acting on the satellite system.
    No preview · Article · May 2010
  • J. Frouard · M. Fouchard · A. Vienne
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    ABSTRACT: For a long time, the estimation of the Lyapunov Characteristic Exponents (LCEs) had been used in Celestial Mechanics to caracterize the chaoticity of orbits. With the aim of gaining speed and accuracy in detecting this chaoticity, several indicators based on the theory of Lyapunov exponents have been developped. Here we present a comparison in terms of precision, CPU speed, and practicability of several of these indicators ; the FLI (Froeschlé et al, 1997) , MEGNO (Cincotta & Simó, 2000), and the GALI (Skokos et al, 2007). The GALI3 (using three tangent vectors) is the version of the GALI used here. While the FLI and MEGNO have been commonly used, the GALI has not yet been applied to Celestial Mechanics. However, this indicator has its own qualities and specificities. The final aim of the comparison of these indicators is the production of stability maps in the case of irregular satellites of giant planets, the examples and applications are shown in this sense.
    No preview · Article · Oct 2008
  • Julien Frouard · M. Fouchard · A. Vienne
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    ABSTRACT: Until now, the study of the chaoticity of the Jovian irregular satellites has been restricted to several ones and investigated on a limited integration time. We have extended these studies to the whole number of satellites and in time integration. We present the results of long-term numerical integrations of the satellites to search for chaotic behavior, giving an indication of the origin of the detected chaos.
    No preview · Article ·

Publication Stats

36 Citations
36.78 Total Impact Points

Institutions

  • 2013
    • Northwestern University
      • Department of Physics and Astronomy
      Evanston, Illinois, United States
  • 2011
    • University of Namur
      • Department of Mathematics
      Namen, Walloon, Belgium
  • 2010
    • University of Lille Nord de France
      Lille, Nord-Pas-de-Calais, France