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Fathi Namouni

Publications and source records attributed to Fathi Namouni.

At least 19 recordsLinked to original sources
arXiv2025

High-inclination Centaur reservoirs beyond Neptune

(Abridged) Numerical simulations of the past evolution of high-inclination Centaurs showed they originated from orbits beyond Neptune that were perpendicular to the Solar System's invariable plane in a region called the polar corridor. Recently, a study of Centaur injection in the three-body problem showed that Neptune-crossing TNOs in the polar corridor in the range [40:160] au have dynamical times that exceed the Solar System's age suggesting the presence of long-lived Centaur-producing reservoirs. We demonstrate the existence of such reservoirs in the Solar System by simulating the TNOs' time-forward evolution in the presence of the giant planets, the Galactic tide and passing stars using the IAS15 integrator of the REBOUND and REBOUNDx packages. We also assess the efficiency of Centaur injection as a function of the initial inclination and determine if high-inclination Centaurs may be produced by low inclination reservoirs. We find that TNO reservoirs in the semi-major axis range [50:140] au are long-lived and their populations peak at the Tisserand parameters T=0.5 and T=-1.5. Saturn is found to induce secondary structures in the polar corridor by holding the perihelia of a fraction of high-inclination reservoir material. We find that the Centaur inclination at minimum semi-major axis depends linearly on the Tisserand parameter regardless of the initial semi-major axis. Its amplitude shows that low inclination reservoirs such as the early protoplanetary disk are unlikely to produce high-inclination Centaurs in contrast to reservoirs in the polar corridor. We identified the likely location of the closest reservoirs to Neptune populated by TNOs captured in the early Solar System that produce high-inclination Centaurs. The Legacy Survey of Space and Time will be able to constrain the reservoirs' extent and population size

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arXiv2023

Orbit injection of planet-crossing asteroids

Solar system Centaurs originate in transneptunian space from where planet orbit crossing events inject their orbits inside the giant planets' domain. Here, we examine this injection process in the three-body problem by studying the orbital evolution of transneptunian asteroids located at Neptune's collision singularity as a function of the Tisserand invariant, T. Two injection modes are found, one for T>0.1, or equivalently prograde inclinations far from the planet, where unstable motion dominates injection, and another for T<= 0.1, or equivalently polar and retrograde inclinations far from the planet, where stable motion dominates injection. The injection modes are independent of the initial semi-major axis and the dynamical time at the collision singularity. The simulations uncovered a region in the polar corridor where the dynamical time exceeds the solar system's age suggesting the possibility of long-lived primordial polar transneptunian reservoirs that supply Centaurs to the giant planets' domain.

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arXiv2020

On the interstellar origin of high-inclination Centaurs

Following our identification of the probable interstellar origin of high-inclination Centaurs, Morbidelli et al. (2020) issued a rebuttal criticizing our methods and conclusions. Here, we show that the criticism is unfounded. Entropy's increase in the past is not an obstacle to accessing the statistical properties of Centaur past orbits as entropic expansion occurs around a time-independent conserved quantity that explains the probable orbits' clustering in parameter space, known as the polar corridor. The Copernican principle does not imply that unstable motion does not exist in the solar system. It clarifies the meaning of the dynamical lifetime ensuring that Centaurs originating in the planetesimal disc are able to return to it in the time-backward simulation. Our conclusions are supported by published independent research that shows conventional disc relaxation models do not explain the abundance of high inclination Centaurs and that enrichment from the interstellar medium is required. Future physical observations of the identified Centaurs and TNOs are likely to reveal the similarities and differences between solar system-born and interstellar origin Centaurs.

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arXiv2020

An interstellar origin for high-inclination Centaurs

We investigate the possible origins of real high-inclination Centaurs and trans-neptunian objects using a high-resolution statistical search for stable orbits that simulates their evolution back in time to the epoch when planet formation ended 4.5 billion years in the past. The simulation is a precise orbit determination method that does not involve ad hoc initial conditions or assumptions such as those found in planetesimal disk relaxation models upon which their conclusions depend. It can therefore be used to independently test origin theories based on relaxation models by examining the past orbits of specific real objects. Here, we examined 17 multiple-opposition high-inclination Centaurs and the two polar trans-neptunian objects 2008 KV42 and (471325) 2011 KT19. The statistical distributions show that their orbits were nearly polar 4.5 Gyr in the past, and were located in the scattered disk and inner Oort cloud regions. Early polar inclinations cannot be accounted for by current Solar system formation theory as the early planetesimal system must have been nearly flat in order to explain the low-inclination asteroid and Kuiper belts. Furthermore, the early scattered disk and inner Oort cloud regions are believed to have been devoid of Solar system material as the planetesimal disk could not have extended far beyond Neptune's current orbit in order to halt the planet's outward migration. The nearly polar orbits of high-inclination Centaurs 4.5 Gyr in the past therefore indicate their probable early capture from the interstellar medium.

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arXiv2020

Resonance libration and width at arbitrary inclination

We apply the analytical disturbing function for arbitrary inclination derived in our previous work to characterize resonant width and libration of mean motion resonances at arbitrary inclination obtained from direct numerical simulations of the three-body problem. We examine the 2:1 and 3:1 inner Jupiter and 1:2 and 1:3 outer Neptune resonances and their possible asymmetric librations using a new analytical pendulum model of resonance that includes the simultaneous libration of multiple arguments and their second harmonics. The numerically-derived resonance separatrices are obtained using the Mean Exponential Growth factor of Nearby Orbits (MEGNO chaos indicator). We find that the analytical and numerical estimates are in agreement and that resonance width is determined by the first few fundamental resonance modes that librate simultaneously on the resonant timescale. Our results demonstrate that the new pendulum model may be used to ascertain resonance width analytically, and more generally, that the disturbing function for arbitrary inclination is a powerful analytical tool that describes resonance dynamics of low as well as high inclination asteroids in the solar system.

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arXiv2018

An interstellar origin for Jupiter's retrograde co-orbital asteroid

Asteroid (514107) 2015 BZ509 was discovered recently in Jupiter's co-orbital region with a retrograde motion around the Sun. The known chaotic dynamics of the outer Solar System have so far precluded the identification of its origin. Here, we perform a high-resolution statistical search for stable orbits and show that asteroid (514107) 2015 BZ509 has been in its current orbital state since the formation of the Solar System. This result indicates that (514107) 2015 BZ509 was captured from the interstellar medium 4.5 billion years in the past as planet formation models cannot produce such a primordial large-inclination orbit with the planets on nearly-coplanar orbits interacting with a coplanar debris disk that must produce the low-inclination small-body reservoirs of the Solar System such as the asteroid and Kuiper belts. This result also implies that more extrasolar asteroids are currently present in the Solar System on nearly-polar orbits.

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arXiv2017

The disturbing function for asteroids with arbitrary inclinations

The classical disturbing function of the three-body problem widely used in planetary dynamics studies is an expansion of the gravitational interaction of the three-body problem with respect to zero eccentricity and zero inclination. This restricts its validity to nearly coplanar orbits. Motivated by the dynamical study of asteroids, Centaurs and transneptunian objects with arbitrary inclinations, we derive a series expansion of the gravitational interaction with respect to an arbitrary reference inclination that generalises our work on the polar and retrograde disturbing functions. The new disturbing function, like the polar one, may model any resonance as expansion order is unrelated to resonance order. The powers of eccentricity and inclination of the force amplitude of a $p$:$q$ resonance depend only on the parity of the resonance order $|p-q|$. Disturbing functions with non zero reference inclinations are thus physically different from the classical disturbing function as the former are based on the three-dimensional three-body problem and the latter on the two-dimensional one. We illustrate the use of the new disturbing function by showing that what is known as pure eccentricity resonances are intrinsically dependent on inclination contrary to the prediction of the classical disturbing function. We determine the inclination dependence of the resonance widths of the 2:1 and 3:1 prograde and retrograde inner resonances with Jupiter as well as those of the asymmetric librations of the 1:2 and 1:3 prograde outer resonances with Neptune.

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arXiv2017

The disturbing function for polar Centaurs and transneptunian objects

The classical disturbing function of the three-body problem is based on an expansion of the gravitational interaction in the vicinity of nearly coplanar orbits. Consequently, it is not suitable for the identification and study of resonances of the Centaurs and transneptunian objects on nearly polar orbits with the solar system planets. Here, we provide a series expansion algorithm of the gravitational interaction in the vicinity of polar orbits and produce explicitly the disturbing function to fourth order in eccentricity and inclination cosine. The properties of the polar series differ significantly from those of the classical disturbing function: the polar series can model any resonance as the expansion order is not related to the resonance order. The powers of eccentricity and inclination of the force amplitude of a $p$:$q$ resonance do not depend on the value of the resonance order $|p-q|$ but only on its parity. Thus all even resonance order eccentricity amplitudes are $\propto e^2$ and odd ones $\propto e$ to lowest order in eccentricity $e$. With the new findings on the structure of the polar disturbing function and the possible resonant critical arguments, we illustrate the dynamics of the polar resonances 1:3, 3:1, 2:9 and 7:9 where transneptunian object 471325 could currently be locked.

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arXiv2017

Coorbital capture at arbitrary inclination

The process of capture in the coorbital region of a solar system planet is studied. Absolute capture likelihood in the 1:1 resonance is determined by randomly constructed statistical ensembles numbering $7.24\times 10^5$ of massless asteroids that are set to migrate radially from the outer to the inner boundaries of the coorbital region of a Jupiter-mass planet. Orbital states include coorbital capture, ejection, collisions with the Sun and the planet and free-crossing of the coorbital region. The relative efficiency of retrograde capture with respect to prograde capture is confirmed as an intrinsic property of the coorbital resonance. Half the asteroids cross the coorbital region regardless of eccentricity and for any inclination less than $120^\circ$. We also find that the recently discovered retrograde coorbital of Jupiter, asteroid 2015 BZ509, lies almost exactly at the capture efficiency peak associated with its orbital parameters.

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arXiv2017

Resonance capture at arbitrary inclination: II. Effect of the radial drift rate

The effect of radial drift rate on mean motion resonance capture is studied for prograde, polar and retrograde orbits. We employ the numerical framework of our earlier exploration of resonance capture at arbitrary inclination. Randomly constructed samples of massless particles are set to migrate radially from outside the orbit of a Jupiter-mass planet at different drift rates totalling more than $1.6\times 10^6$ numerical simulations. Slower drift rates reduce overall capture probability especially for prograde orbits and enhance capture at specific initial inclinations of high order resonances such as the outer 1:5, 1:4, 1:3, 2:5, 3:7 and 5:7. Global capture is reduced with increasing eccentricity at all inclinations as high order resonances capture more particles that are subsequently lost by disruptive close encounters with the planet. The relative efficiency of retrograde resonances at long-lived capture with respect to prograde resonances is explained by the reduced effect of planet encounters as such events occur with a shorter duration and a higher relative velocity for retrograde motion. Capture in the coorbital 1:1 resonance is marginally affected by the radial drift rate except for nearly coplanar retrograde eccentric orbits whose capture likelihood is increased significantly with slower drift rates. An unexpected finding is the presence of a dynamical corridor for capture in high order inner prograde resonances with initial inclinations in the range [50$^\circ$,80$^\circ$] especially at the inner 5:2 resonance whose capture likelihood peaks at 80% to 90% depending on initial eccentricity.

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arXiv2016

A numerical investigation of coorbital stability and libration in three dimensions

Motivated by the dynamics of resonance capture, we study numerically the coorbital resonance for inclination180 >=I>=0 in the circular restricted three-body problem. We examine the similarities and differences between planar and three dimensional coorbital resonance capture and seek their origin in the stability of coorbital motion at arbitrary inclination. After we present stability maps of the planar prograde and retrograde coorbital resonances, we characterize the new coorbital modes in three dimensions. We see that retrograde mode I (R1) and mode II (R2) persist as we change the relative inclination, while retrograde mode III (R3) seems to exist only in the planar problem. A new coorbital mode (R4) appears in 3D which is a retrograde analogue to an horseshoe-orbit. The Kozai-Lidov resonance is active for retrograde orbits as well as prograde orbits and plays a key role in coorbital resonance capture. Stable coorbital modes exist at all inclinations, including retrograde and polar obits. This result confirms the robustness the coorbital resonance at large inclination and encourages the search for retrograde coorbital companions of the solar system's planets.

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arXiv2015

Towards an interpretation of MOND as a modification of inertia

We explore the possibility that Milgrom's Modified Newtonian Dynamics (MOND) is a manifestation of the modification of inertia at small accelerations. Consistent with the Tully-Fisher relation, dynamics in the small acceleration domain may originate from a quartic (cubic) velocity-dependence of energy (momentum) whereas gravitational potentials remain linear with respect to mass. The natural framework for this interpretation is Finsler geometry. The simplest static isotropic Finsler metric of a gravitating mass that incorporates the Tully-Fisher relation at small acceleration is associated with a spacetime interval that is either a homogeneous quartic root of polynomials of local displacements or a simple root of a rational fraction thereof. We determine the low energy gravitational equation and find that Finsler spacetimes that produce a Tully-Fisher relation require that the gravitational potential be modified. For an isolated mass, Newton's potential $Mr^{-1}$ is replaced by $Ma_0\log (r/r_0)$ where $a_0$ is MOND's acceleration scale and $r_0$ is a yet undetermined distance scale. Orbital energy is linear with respect to mass but angular momentum is proportional to $ M^{3/4}$. Asymptotic light deflection resulting from time curvature is similar to that of a singular isothermal sphere implying that space curvature must be the main source of deflection in static Finsler spacetimes possibly through the presence of the distance scale $r_0$ that appears in the asymptotic form of the gravitational potential. The quartic nature of the Finsler metric hints at the existence of an underlying area-metric that describes the effective structure of spacetime.

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arXiv2014

Resonance capture at arbitrary inclination

Resonance capture is studied numerically in the three-body problem for arbitrary inclinations. Massless particles are set to drift from outside the 1:5 resonance with a Jupiter-mass planet thereby encountering the web of the planet's diverse mean motion resonances. Randomly constructed samples explore parameter space for inclinations from 0 to 180 deg with 5deg increments totalling nearly 6x10^5 numerical simulations. Thirty resonances internal and external to the planet's location are monitored. We find that retrograde resonances are unexpectedly more efficient at capture than prograde resonances and that resonance order is not necessarily a good indicator of capture efficiency at arbitrary inclination. Capture probability drops significantly at moderate sample eccentricity for initial inclinations in the range [10deg,110deg]. Orbit inversion is possible for initially circular orbits with inclinations in the range [60deg,130deg]. Capture in the 1:1 coorbital resonance occurs with great likelihood at large retrograde inclinations. The planet's orbital eccentricity, if larger than 0.1, reduces the capture probabilities through the action of the eccentric Kozai-Lidov mechanism. A capture asymmetry appears between inner and outer resonances as prograde orbits are preferentially trapped in inner resonances. The relative capture efficiency of retrograde resonance suggests that the dynamical lifetimes of Damocloids and Centaurs on retrograde orbits must be significantly larger than those on prograde orbits implying that the recently identified asteroids in retrograde resonance, 2006 BZ8, 2008 SO218, 2009 QY6 and 1999 LE31(Morais and Namouni, 2013, MNRAS 436, L30) may be among the oldest small bodies that wander between the outer giant planets.

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arXiv2012

The excitation of planetary orbits by stellar jet variability and polarity reversal

Planets form in active protoplanetary disks that sustain stellar jets. Momentum loss from the jet system may excite the planets' orbital eccentricity and inclination (Namouni 2005, AJ 130, 280). Evaluating quantitatively the effects of such excitation requires a realistic modeling of the momentum loss profiles associated with stellar jets. In this work, we model linear momentum loss as a time-variable stochastic process that results in a zero mean stellar acceleration. Momentum loss may involve periodic or random polarity reversals. We characterize orbital excitation as a function of the variability timescale and identify a novel excitation resonance between a planet's orbital period and the jet's variability timescale where the former equals twice the latter. For constant variability timescales, resonance is efficient for both periodic and random polarity reversals, the latter being stronger than the former. For a time variable variability timescale, resonance crossing is a more efficient excitation mechanism when polarity reversals are periodic. Each polarity reversal type has distinct features that may help constrain the magnetic history of the star through the observation of its planetary companions. For instance, outward planet migration to large distances from parent stars is one of the natural outcomes of periodic polarity reversal excitation if resonance crossing is sufficiently slow. Applying the excitation mechanism to the solar system, we find that the planet-jet variability resonance with periodic polarity reversal momentum loss is a possible origin for the hitherto unexplained inclination of Jupiter's orbit by 6 deg. with respect to the Sun's equator.

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arXiv2010

On dynamical friction in a gaseous medium with a boundary

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. We study the effects of the presence of a boundary on dynamical friction by studying analytically the interaction of perturber with uniform rectilinear motion in a uniform homogeneous medium with a reflecting planar boundary. Wake reflection at a medium's boundary may occur at the edges of truncated disks perturbed by planetary or stellar companions as well as in numerical simulations of planet-disk interaction with no-outflow boundary conditions. In this paper, we show that the presence of the boundary modifies the behaviour of dynamical friction significantly. We find that perturbers are invariably pushed away from the boundary and reach a terminal subsonic velocity near Mach 0.37 regardless of initial velocity. Dynamical friction may even be reversed for Mach numbers less than 0.37 thereby accelerating instead of decelerating the perturber. Perturbers moving parallel to the boundary feel additional friction orthogonal to the direction of motion that is much stronger than the standard friction along the direction of motion. These results indicate that the common use of the standard Chandrasekhar formula as a short hand estimate of dynamical friction may be inadequate as observed in various numerical simulations.

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arXiv2010

The fate of moons of close-in giant exoplanets

We show that the fate of moons of a close-in giant planet is mainly determined by the migration history of the planet in the protoplanetary disk. As the planet migrates in the disk from beyond the snow line towards a multi-day period orbit, the formed and forming moons become unstable as the planet's sphere of influence shrinks. Disk-driven migration is faster than the moons' tidal orbital evolution. Moons are eventually ejected from around close-in exoplanets or forced into collision with them before tides from the star affect their orbits. If moons are detected around close-in exoplanets, they are unlikely to have been formed in situ, instead they were captured from the protoplanetary disk on retrograde orbits around the planets.

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arXiv2009

Dynamical friction for accelerated motion in a gaseous medium

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that its amplitude may depend on the perturber's initial velocity. The force on an accelerating perturber is maximal between Mach 1 and Mach 2, where it is smaller than the corresponding uniform motion friction. In the limit where the perturber's size is much smaller than the distance needed to change the Mach number by unity through acceleration, a subsonic perturber feels a force similar to uniform motion friction only if its past history does not include supersonic episodes. Once an accelerating perturber reaches large supersonic speeds, accelerated motion friction is marginally stronger than uniform motion friction. The force on a decelerating supersonic perturber is weaker than uniform motion friction as the velocity decreases to a few times the sound speed. Dynamical friction on a decelerating subsonic perturber with an initial Mach number larger than 2 is much larger than uniform motion friction and tends to a finite value as the velocity vanishes in contrast to uniform motion friction.

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