Roche Limit Research Articles

The β Pictoris system: Setting constraints on the planet and the disk structures at mid-IR wavelengths with NEAR

Context. β Pictoris is a young nearby system hosting a well-resolved edge-on debris disk, along with at least two exoplanets. It offers key opportunities for carrying out detailed studies of the evolution of young planetary systems and their shaping soon after the end of the planetary formation phase. Aims. We analyzed high-contrast coronagraphic images of this system, obtained in the mid-infrared, taking advantage of the NEAR experiment using the VLT/VISIR instrument, which provides access to adaptive optics, as well as phase coronagraphy. The goal of our analysis is to investigate both the detection of the planet β Pictoris b and of the disk features at mid-IR wavelengths. In addition, by combining several epochs of observation, we expect to constrain the position of the known clumps and improve our knowledge on the dynamics of the disk. Methods. We observed the β Pictoris system over two nights in December 2019 in the 10–12.5 µm coronagraphic filter. To evaluate the planet b flux contribution, we extracted the photometry at the expected position of the planet and compared it to the flux published in the literature. In addition, we used previous data from T-ReCS and VISIR in the mid-IR, updating the star's distance, to study the evolution of the position of the southwest clump that was initially observed in the planetary disk back in 2003. Results. While we did not detect the planet b, we were able to put constraints on the presence of circumplanetary material, ruling out the equivalent of a Saturn-like planetary ring around the planet. The disk presents several noticeable structures, including the known southwest clump. Using a 16-yr baseline, sampled with five epochs of observations, we were able to examine the evolution of the clump. We found that the clump orbits in a Keplerian motion with a semi-major axis of 56.1−0.3+0.4 au. In addition to the known clump, the images clearly show the presence of a second clump on the northeast side of the disk as well as possibly fainter and closer structures that are yet to be confirmed. Furthermore, we found correlations between the CO clumps detected with ALMA and the northeastern and southwestern clumps in the mid-IR images. Conclusions. If the circumplanetary material were located at the Roche radius, the maximum amount of dust determined from the flux upper limit around β Pictoris b would correspond to the mass of an asteroid of 5 km in diameter. Finally, the Keplerian motion of the southwestern clump is possibly indicative of a yet-to-be detected planet or signals the presence of a vortex.

Planetesimals drifting through dusty and gaseous white dwarf debris discs: Types I, II and III-like migration

ABSTRACT The suite of over 60 known planetary debris discs which orbit white dwarfs, along with detections of multiple minor planets in these systems, motivate investigations about the migration properties of planetesimals embedded within the discs. Here, we determine whether any of the migration regimes which are common in (pre-)main-sequence protoplanetary discs, debris discs, and ring systems could be active and important in white dwarf discs. We investigate both dust-dominated and gas-dominated regions, and quantitatively demonstrate that Type I and Type II migration, as well as their particulate disc analogues, are too slow to be relevant in white dwarf discs. However, we find that the analogue of Type III migration for particulate discs may be rapid in the dusty regions of asteroid- or moon-generated (>1018 kg) white dwarf discs, where a planetesimal exterior to its Roche radius may migrate across the entire disc within its lifetime. This result holds over a wide range of disc boundaries, both within and exterior to 1R⊙, and such that the probability of migration occurring increases with higher disc masses.

The two rings of (50000) Quaoar

Context. Quaoar is a classical trans-Neptunian object (TNO) with an area-equivalent diameter of 1100 km and an orbital semi-major axis of 43.3 astronomical units. Based on stellar occultations observed between 2018 and 2021, an inhomogeneous ring (Q1R, i.e., Quaoar’s first ring) has been detected around this body. Aims. A new stellar occultation by Quaoar was observed on August 9, 2022, with the aim of improving Quaoar’s shape models and the physical parameters of Q1R, while searching for additional material around the body. Methods. The occultation provided nine effective chords across Quaoar, pinning down its size, shape, and astrometric position. Large facilities, such as Gemini North and the Canada-France-Hawaii Telescope (CFHT), were used to obtain high acquisition rates and signal-to-noise ratios. The light curves were also used to characterize the Q1R ring (radial profiles and orbital elements). Results. Quaoar’s elliptical fit to the occultation chords yields the limb with an apparent semi-major axis of 579.5 ± 4.0 km, apparent oblateness of 0.12 ± 0.01, and area-equivalent radius of 543 ± 2 km. Quaoar’s limb orientation is consistent with Q1R and Weywot orbiting in Quaoar’s equatorial plane. The orbital radius of Q1R is refined to a value of 4057 ± 6 km. The radial opacity profile of the more opaque ring profile follows a Lorentzian shape that extends over 60 km, with a full width at half maximum (FWHM) of ∼5 km and a peak normal optical depth of 0.4. Besides the secondary events related to the already reported rings, new secondary events detected during the August 2022 occultation in three different data sets are consistent with another ring around Quaoar with a radius of 2520 ± 20 km, assuming the ring is circular and co-planar with Q1R. This new ring has a typical width of 10 km and a normal optical depth of ∼0.004. Just as Q1R, it also lies outside Quaoar’s classical Roche limit.

Exploring the Recycling Model of Phobos Formation: Rubble-pile Satellites* * Released on 2023 February 27.

Phobos is the target of the return sample mission Martian Moons eXploration by JAXA that will analyze in great detail the physical and compositional properties of the satellite from orbit, from the surface, and in terrestrial laboratories, giving clues about its formation. Some models propose that Phobos and Deimos were formed after a giant impact giving rise to an extended debris disk. Assuming that Phobos formed from a cascade of disruptions and reaccretions of several parent bodies in this disk, and that they are all characterized by a low material cohesion, Hesselbrock & Minton showed that a recycling process may happen during the assembling of Phobos, by which Phobos’s parents are destroyed into a Roche-interior ring and reaccreted several times. In this paper, we explore the recycling model in detail and pay particular attention to the characteristics of the disk using 1D models of disk/satellite interactions. In agreement with previous studies, we confirm that, if Phobos’s parent bodies are gravitational aggregates (rubble piles), then the recycling process does occur. However, Phobos should be accompanied today by a Roche-interior ring. Furthermore, the characteristics of the ring are not reconcilable with today’s observations of Mars’ environment, which put stringent constraints on the existence of a ring around Mars. The recycling mechanism may or may not have occurred at the Roche limit for an old moon population, depending on the internal cohesion. However, the Phobos we see today cannot be the outcome of such a recycling process.

A dense ring of the trans-Neptunian object Quaoar outside its Roche limit.

Planetary rings are observed not only around giant planets1, but also around small bodies such as the Centaur Chariklo2 and the dwarf planet Haumea3. Up to now, all known dense rings were located close enough to their parent bodies, being inside the Roche limit, where tidal forces prevent material with reasonable densities from aggregating into a satellite. Here we report observations of an inhomogeneous ring around the trans-Neptunian body (50000) Quaoar. This trans-Neptunian object has an estimated radius4 of 555 km and possesses a roughly 80-km satellite5 (Weywot) that orbits at 24 Quaoar radii6,7. The detected ring orbits at 7.4 radii from the central body, which is well outside Quaoar's classical Roche limit, thus indicating that this limit does not always determine where ring material can survive. Our local collisional simulations show that elastic collisions, based on laboratory experiments8, can maintain a ring far away from the body. Moreover, Quaoar's ring orbits close to the 1/3 spin-orbit resonance9 with Quaoar, a property shared by Chariklo's2,10,11 and Haumea's3 rings, suggesting that this resonance plays a key role in ring confinement for small bodies.

Unravelling the evolution of hot Jupiter systems under the effect of tidal and magnetic interactions and mass-loss

ABSTRACT Various interactions affect the population of close-in planets. Among them, the tidal and magnetic interactions drive orbital decay and star-planet angular momentum exchange, leading to stellar spin-up. As a result of the above processes, a planet may initiate the mass transfer to the host star once it encounters the Roche limit. Another mechanism providing substantial mass-loss is associated with the atmospheric escape caused by photoevaporation followed by orbital expansion, which is thought to be important for hot Neptunes and super-Earths. Thus, the fraction of the initial number of hot Jupiters may transform into lower-mass planets through the Roche lobe overflow (RLO) phase and continue secular evolution under the effect of photoevaporation. In this paper, we compile the latest prescriptions for tidal and magnetic migration and mass-loss rates to explore the dynamics of hot Jupiter systems. We study how the implemented interactions shape the orbital architecture of Jovian planets and whether their impact is enough to reproduce the observational sample. Our models suggest that the tidal interaction is able to generate the upper boundary of the hot Jupiter population in the mass–separation diagram. To recreate the sub-Jovian desert, we need to make additional assumptions regarding the RLO phase or the influence of the protoplanetary disc’s inner edge on the initial planetary location. According to our estimates, 12–15 per cent of hot Jupiters around solar-mass stars have been engulfed or become lower-mass planets. 0.20–0.25 per cent of the present-day giant planet population undergoes decay intense enough to be detected with modern facilities.

Dynamical origin of Dimorphos from fast spinning Didymos

Didymos is a binary near-Earth asteroid. It is the target of the DART and HERA space missions. The primary body, Didymos, rotates close to the spin at which it is expected to shed mass. The secondary body, Dimorphos, is a 140 meters moon that orbits the primary body in about 12 h. Here we investigate the possible origin of Dimorphos. Using 1D models of ring/satellite interactions, we study the evolution of material lost from Didymos’ surface and deposited as a ring at its equator. We find that due to viscous spreading, the ring spreads outside the Didymos’ Roche limit forming moonlets. A fraction of the mass will form Dimorphos and a set of objects near the Roche limit, while most of the ring’s mass falls back on Didymos. To match the properties of today’s Dimorphos, the total mass that must be deposited in the ring is about 25% of Didymos’ mass. It is possible that a fraction of the material travelled several times between the ring and the surface of Didymos. The models produce an orbit similar to that observed for a Didymos tidal parameter k2/Q≤10−5. If the ring deposition timescale is long (≥102 yr) (so the material flux is small) Dimorphos could be irregularly shaped as it forms from the collision of similar-sized satellitesimals. However, the top-shape of Didymos is expected to be achieved due to a fast spin-up of the asteroid, which would result in a short deposition timescale (≲yr). In that case, the satellite would form from progressively accreting material at the Roche Limit, resulting in an ellipsoidal Dimorphos constructed of small pieces with sizes of the order of meters, which is apparently in agreement with the recent images of Dimorphos obtained by DART mission.

Ye Shall Bear Witness: An Ethics of Survival in W.G. Sebald’s Rings of Saturn

In Rings of Saturn, W.G. Sebald uses the concept of the Roche limit—the nearest a satellite can come to the object it orbits without being consumed by that object’s gravity— to draw a boundary around human suffering so that in bearing witness, we shall not be destroyed.By using lists to create literary fractals—geometric designs that are self-similar at a fractional dimension—Sebald dramatizes that limit as an equilibrium that art must hold between distance from and proximity to human suffering. He asks readers not merely to bear witness but to find the proximity at which we can hold a steady gaze, unflinching, without being consumed by that suffering. At the Roche limit, we are bound by what we see but not consumed.

Two substellar survivor candidates: one found and one missing

ABSTRACT This study presents observations of two possible substellar survivors of post-main sequence engulfment, currently orbiting white dwarf stars. Infrared and optical spectroscopy of GD 1400 reveals a 9.98 h orbital period, where the benchmark brown dwarf has M2 = 68 ± 8 MJup, Teff ≈ 2100 K, and a cooling age under 1 Gyr. A substellar mass in the lower range of allowed values is favoured by the gravitational redshift of the primary. Synthetic brown dwarf spectra are able to reproduce the observed CO bands, but lines below the bandhead are notably overpredicted. The known infrared excess towards PG 0010+281 is consistent with a substellar companion, yet no radial velocity or photometric variability is found despite extensive searches. Three independent stellar mass determinations all suggest enhanced mass-loss associated with binary evolution, where the youngest total age for an isolated star is 7.5 ± 2.5 Gyr. A possible solution to this conundrum is the cannibalization of one or more giant planets, which enhanced mass-loss post-main sequence, but were ultimately destroyed. PG 0010 + 281 is likely orbited by a debris disc that is comfortably exterior to the Roche limit, adding to the growing number of non-canonical discs orbiting white dwarfs. At present, only L-type (brown) dwarfs are known to survive direct engulfment during the post-main sequence, whereas T- and Y-type substellar companions persist at wide separations. These demographics indicate that roughly 50 MJup is required to robustly avoid post-main sequence annihilation, suggesting all closely orbiting giant planets are consumed, which may contribute to mass-loss and magnetic-field generation in white dwarfs and their immediate progenitors.

High-resolution atmospheric retrievals of WASP-121b transmission spectroscopy with ESPRESSO: Consistent relative abundance constraints across multiple epochs and instruments

ABSTRACT Recent progress in high-resolution transmission spectroscopy has offered new avenues in which to characterize the atmospheres of transiting exoplanets. High-resolution cross-correlation spectroscopy allows for the unambiguous detection of molecules/atoms. It has also been used to map both atmospheric dynamics and longitudinal variations in the abundance of species across the morning and evening limbs. We present multiple Very Large Telescope (VLT)/Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO) observations of the ultrahot Jupiter WASP-121b, from which we constrain relative abundances of various neutral metals consistently across all observations, whilst accounting for the distortion of the exoplanet’s signal caused by traditional data processing techniques. We also constrain planetary orbital velocities and T–P profiles. We compare our abundance constraints with previous constraints using VLT/Ultraviolet and Visual Echelle Spectrograph (UVES) transmission spectroscopy of WASP-121b, and find our results to be consistent between observations, and also in agreement with stellar values for species previously detected in the atmosphere of WASP-121b. Our retrieval framework can also be used to identify potential exospheric species, resulting in extended absorption features beyond the transit equivalent Roche limit of WASP-121b (ReqRL ∼ 1.3 Rp). Hα, Fe ii, and Ca ii were found to extend to high altitudes (1.54 ± 0.04 Rp, 1.17 ± 0.01 Rp, and 2.52 ± 0.34 Rp, respectively), which are broadly consistent with literature values. The consistency of our constraints across multiple high-resolution observations is a strong validation of our model filtering and retrieval framework, as well as the stability of the atmosphere over the time-scales of months/years, and could allow for planet formation processes to be inferred from future ground-based observations of exoplanetary atmospheres.

Tidally Distorted Barytropes and Their Roche Limits, with Application to WASP-12b

The hot Jupiter WASP-12b has been found to be on a decaying 1.09 day orbit. The mean density of the planet inferred from transit and radial-velocity data is near its Roche limit; just how near depends on the planet’s uncertain internal structure. There is also spectroscopic evidence of mass loss. We accurately calculate the Roche density on the assumption of a synchronously rotating n = 1 polytrope, and find this to be only 15%–20% below the observational estimates for the mean density. We discuss the implied shape of the planet, its lifetime before complete disruption, and its current rate of mass loss based on our improved tidal model. The present mass-loss rate is at least as sensitive to the opacity and temperature profiles of the planet’s atmosphere as to its internal structure, however.

Numerical Simulations of Drainage Grooves in Response to Extensional Fracturing: Testing the Phobos Groove Formation Model

The long, shallow, parallel grooves that cut across the surface of the Martian moon Phobos remain enigmatic, with distinct implications for understanding the evolution of loose airless soils and the origin of Mars and its satellites. Phobos orbits deep inside the fluid Roche limit and is gradually spiraling in, creating global tidal strain, which leads to a model in which orbital decay is driving the formation of surface grooves on Phobos. Here we test this model by simulating the extension of a mildly cohesive regolith shell, driven by Phobos’s tidal strain imposed by orbital migration. Modeling Phobos as a rubble-pile interior overlaid by a cohesive layer, we find that the tidal strain could create parallel fissures with regular spacing, depending on the latitude and longitude. Fracture opening triggers drainage of upper loose material into these deep-seated valleys, which we show could lead naturally to the formation of groove-like structures. We map the prominent linear depressions on Phobos and find that some at midlatitudes correlate with the model-predicted groove orientations. Our analysis supports a layered heterogeneous structure for Phobos with possible underlying failure-induced fractures, as the precursor of the eventual demise of the de-orbiting satellite. However, we do observe significant areas showing absences and anomalies that are not consistent with the tidal fracturing model. The in situ observations on Phobos by the Mars Moons eXploration mission will conclusively determine the origin of its enigmatic striations.

Immediate Origin of the Moon as a Post-impact Satellite

The Moon is traditionally thought to have coalesced from the debris ejected by a giant impact onto the early Earth. However, such models struggle to explain the similar isotopic compositions of Earth and lunar rocks at the same time as the system’s angular momentum, and the details of potential impact scenarios are hotly debated. Above a high resolution threshold for simulations, we find that giant impacts can immediately place a satellite with similar mass and iron content to the Moon into orbit far outside Earth’s Roche limit. Even satellites that initially pass within the Roche limit can reliably and predictably survive, by being partially stripped and then torqued onto wider, stable orbits. Furthermore, the outer layers of these directly formed satellites are molten over cooler interiors and are composed of around 60% proto-Earth material. This could alleviate the tension between the Moon’s Earth-like isotopic composition and the different signature expected for the impactor. Immediate formation opens up new options for the Moon’s early orbit and evolution, including the possibility of a highly tilted orbit to explain the lunar inclination, and offers a simpler, single-stage scenario for the origin of the Moon.

Binary Interaction Dominates Mass Ejection in Classical Novae

Recent observations suggest our understanding of mass loss in classical novae is incomplete, motivating a new theoretical examination of the physical processes responsible for nova mass ejection. In this paper, we perform hydrodynamical simulations of classical nova outflows using the stellar evolution code MESA. We find that, when the binary companion is neglected, white dwarfs with masses ≳0.8 M ⊙ successfully launch radiation-pressure-driven optically thick winds that carry away most of the envelope. However, for most of the mass-loss phase, these winds are accelerated at radii beyond the white dwarf’s Roche radius assuming a typical cataclysmic variable donor. This means that, before a standard optically thick wind can be formed, mass loss will instead be initiated and shaped by binary interaction. An isotropic, optically thick wind is only successfully launched when the acceleration region recedes within the white dwarf’s Roche radius, which occurs after most of the envelope has already been ejected. The interaction between these two modes of outflow—a first phase of slow, binary-driven, equatorially focused mass loss encompassing most of the mass ejection and a second phase consisting of a fast, isotropic, optically thick wind—is consistent with observations of aspherical ejecta and signatures of multiple outflow components. We also find that isolated lower-mass white dwarfs ≲0.8 M ⊙ do not develop unbound optically thick winds at any stage, making it even more crucial to consider the effects of the binary companion on the resulting outburst.

The 2020 Eclipse of R Aquarii in the Near-infrared: Mid-eclipse Observations of Disk Distress

The Mira in the bright, dusty, symbiotic binary R Aquarii undergoes eclipses of multiyear duration every ∼44 yr by a large, opaque accretion disk. The 2020 eclipse was confirmed by I-band photometry. High-resolution M- and K-band spectra were observed near the midpoint of the eclipse, in 2020 August and September. The 4.5–5.5 μm spectrum during eclipse is a complex blend of disk and Mira features. Continuum emission from the disk region contributes to both the 2.3 μm and 4.6 μm region. The lowest energy vibration-rotation CO lines contain multiple absorption features from ∼780 K gas flowing across the disk away from the Mira. CO fundamental and overtone emission lines are also present. The eccentricity of the orbit results in significant orbital variation in the size of the Roche lobes. At periastron the Roche radius of the secondary is ∼4.0 au, smaller than both the 5 au geometric radius for the disk and estimates for the disk size from models. Fundamental band CO 2–1 emission originates from a thin, eccentric ring with inner radius ∼4.75 au and outer radius ∼6.9 au. The CO emission is identified with regions where the disk has been disrupted near the time of periastron. CO 3–2 fundamental band lines and low-excitation lines in the CO 2–0 and 3–1 overtone bands originate in a Mira-facing spot, 6.3 au from the accretion disk center, near the inner Lagrange point.

Tidally induced migration of TESS gas giants orbiting M dwarfs

ABSTRACT According to core-accretion formation models, the conditions under which gas giants will form around M dwarfs are very restrictive. Also, the correlation of the occurrence of these planets with the metallicity of host stars is still unknown due to the intrinsic faintness of M dwarfs in the optical and some intricacies in their spectra. Interestingly, NASA’s Transiting Exoplanet Survey Satellite (TESS) mission has started to create a growing sample of these systems, with 11 observed planets located in close-in orbits: contrary to what is expected for low-mass stars. Tidal interactions with the host star will play a key role in determining the fate of these planets, so by using the measured physical and orbital characteristics of these M-dwarf systems we numerically analyse the exchange of rotational and orbital angular momentum, while constraining the energy dissipation in each system to calculate whether host stars are spun up or spun down, depending on the relationship between the gain and loss of angular momentum by the stellar rotation. We also study the coupled orbital and physical evolution of their gas giant companion and calculate orbital circularization time-scales, as well as the time needed to undergo orbital decay from their current orbital position to the Roche limit. The thorough study of tidal processes occurring over short and long time-scales in star–planet systems like those studied here, can help constrain tidal dissipation rates inside the star and planet, complement tidal theories, and improve estimations of unconstrained properties of exoplanetary systems.

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor. The φ^6-model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model. The results presented in this study are intended to improve the CGLE's nonlinear dynamical characteristics, it might also assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while the hyperbolic cotangent appears in the Langevin function for magnetic polarization. The current research is frequently used to report a variety of fascinating physical phenomena, such as the Kerr law of non-linearity, which results from the fact that an external electric field causes non-harmonic motion of electrons bound in molecules, which causes nonlinear responses in a light wave in an optical fiber. The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.

The VLT-FLAMES survey of massive stars

Context. NGC 2004#115 was classified as a single lined Be spectroscopic binary in the Large Magellanic Cloud. Its Hα morphology is reminiscent of the Galactic systems LB-1 and HR 6819, both of which are proposed as either Be+BH or Be+stripped He-star systems. Aims. Multi-epoch optical spectra of NGC 2004#115 are used to determine if this binary can be explained by either of these two scenarios, and hence shed additional light on these interesting systems. Methods. VLT-FLAMES and SALT-HRS data covering a baseline of ∼20 years were analyzed to determine radial velocities and orbital parameters, while non-LTE model atmospheres were used to determine stellar parameters and the relative brightness of the system components. Archive MACHO, Gaia, and XMM-Newton data provide additional constraints on the system. Results. NGC 2004#115 is found to be a triple system consisting of an inner binary with a period P = 2.92 d, eccentricity e ∼ 0.0, and mass function f = 0.07 M⊙. The only firmly detected star in this inner binary is a B2 star, the primary, with a projected rotational velocity (ve sin i) of 10 km s−1 and a luminosity of log L/L⊙ = 3.87. It contributes ∼60% of the total V-band light, with the tertiary contributing the other ∼40% of the light, while the secondary is not detected in the optical spectrum. The possibility that the primary is a low mass inflated stripped star is excluded since its Roche radius would be smaller than its stellar radius in such a compact system. A main sequence star of mass 8.6 M⊙ is therefore inferred; however, the assumption of synchronous rotation leads to a secondary mass in excess of 25 M⊙, which would therefore be a black hole. The tertiary is detected as a fainter blended component to the hydrogen and helium lines, which is consistent with a slightly less massive B-type star, though with ve sin i ∼ 300 km s−1. The data do not permit the characterization of the outer period, though it likely exceeds 120 days and is therefore in a stable configuration. The disk-like emission is variable, but may be associated with the inner binary rather than the rapidly rotating tertiary. XMM-Newton provides an upper limit of 5 × 1033 ergs s−1 in the 0.2–12 keV band which is consistent with, though not constraining, the system hosting a quiescent B+BH binary. A number of caveats to this scenario are discussed.

Moon packing around an Earth-mass planet

ABSTRACT All four giant planets in the Solar system host systems of multiple moons, whereas the terrestrial planets only host up to two moons. The Earth can capture small asteroids as temporary satellites, which begs the question as to how many moons could stably orbit the Earth, or an Earth-mass exoplanet. We perform a series of N-body simulations of closely spaced equal-mass moons in nested orbits around an Earth-mass planet orbiting a Sun-like star. The innermost moon begins near the host planet’s Roche radius, and the system is packed until the outermost moon begins near the stability limit for single moons. The initial spacing of the moons follows an iterative scheme commonly used for studies of compact planetary systems around single stars. For the three-moon system, we generate MEGNO maps to calculate periodic and chaotic regions and to identify the destabilizing mean motion resonances. Our calculations show that the maximum number of moons depends on the assumed masses of the satellites (Ceres-, Pluto-, and Luna-mass) that could maintain stable orbits in a tightly packed environment. Through our N-body simulations, we find stable configurations for up to 7 ± 1 Ceres-mass, 4 ± 1 Pluto-mass, and 3 ± 1 Luna-mass moons. However, outward tidal migration will likely play a substantial role in the number of moons on stable orbits over the 10 Gyr stellar lifetime of a Sun-like star.

The Dynamical Viability of an Extended Jupiter Ring System

Planetary rings are often speculated as being a relatively common attribute of giant planets, partly based on their prevalence within the solar system. However, their formation and sustainability remain a topic of open discussion, and the most massive planet within our planetary system harbors a very modest ring system. Here, we present the results of an N-body simulation that explores dynamical constraints on the presence of substantial ring material for Jupiter. Our simulations extend from within the rigid satellite Roche limit to 10% of the Jupiter Hill radius, and include outcomes from 106 and 107 yr integrations. The results show possible regions of a sustained dense ring material presence around Jupiter that may comprise the foundation for moon formation. The results largely demonstrate the truncation of stable orbits imposed by the Galilean satellites, and dynamical desiccation of dense ring material within the range ∼3–29 Jupiter radii. We discuss the implications of these results for exoplanets, and the complex relationship between the simultaneous presence of rings and massive moon systems.