Hill Sphere Research Articles

Eccentricities and the stability of closely-spaced five-planet systems

Observations of exoplanets have revealed that systems with planets on closely-spaced orbits are common, which motivates the question “How closely can planets orbit to one another and still be dynamically-stable for very long times?”. To address this question, we investigate the stability of idealized planetary systems consisting of five planets, each equal in mass to the Earth, orbiting a one solar mass star. All planets orbit in the same plane and in the same direction, and the planets are uniformly spaced in units of mutual Hill Sphere radii. Most of the systems that we integrate begin with one or more planets on eccentric orbits, with eccentricities e as large as e=0.05 being considered. For a given initial orbital separation, larger initial eccentricity of a single planet generally leads to shorter system lifetime, with little systematic dependence of which planet is initially on an eccentric orbit. The approximate trend of instability times increasing exponentially with initial orbital separation of the planets found previously for planets with initially circular orbits is also present for systems with initially eccentric orbits. Mean motion resonances also tend to destabilize these systems, although the reductions in system lifetimes are not as large as for initially circular orbits. Systems with all planets having initial e=0.05 and aligned periapse angles typically survive far longer than systems with the same spacing in initial semi-major axis and one planet with e=0.05, but they have slightly shorter lifetimes than those with planets initially on circular orbits.

Application of Orbital Stability and Tidal Migration Constraints for Exomoon Candidates

Abstract Satellites of extrasolar planets, or exomoons, are on the frontier of detectability using current technologies and theoretical constraints should be considered in their search. In this Letter, we apply theoretical constraints of orbital stability and tidal migration to the six candidate Kepler Object of Interest (KOI) systems proposed by Fox & Wiegert to identify whether these systems can potentially host exomoons. The host planets orbit close to their respective stars and the orbital stability extent of exomoons is limited to only ∼40% of the host planet's Hill radius (∼20 R p). Using plausible tidal parameters from the solar system, we find that four out of six systems would either tidally disrupt their exomoons or lose them to outward migration within the system lifetimes. The remaining two systems (KOI 268.01 and KOI 1888.01) could host exomoons that are within 25 R p and less than ∼3% of the host planet's mass. However, a recent independent transit timing analysis by Kipping found that these systems fail rigorous statistical tests to validate them as candidates. Overall, we find the presence of exomoons in these systems that are large enough for transit timing variation signatures to be unlikely given the combined constraints of observational modeling, tidal migration, and orbital stability. Software to reproduce our results is available in the GitHub repository: Multiversario/satcand.

Black hole, neutron star, and white dwarf merger rates in AGN discs

ABSTRACT Advanced LIGO and Advanced Virgo are detecting a large number of binary stellar origin black hole (BH) mergers. A promising channel for accelerated BH merger lies in active galactic nucleus (AGN) discs of gas around supermasssive BHs. Here, we investigate the relative number of compact object (CO) mergers in AGN disc models, including BH, neutron stars (NS), and white dwarfs, via Monte Carlo simulations. We find the number of all merger types in the bulk disc grows ∝ t1/3 which is driven by the Hill sphere of the more massive merger component. Median mass ratios of NS–BH mergers in AGN discs are $\tilde{q}=0.07\pm 0.06(0.14\pm 0.07)$ for mass functions (MF) M−1(− 2). If a fraction fAGN of the observed rate of BH–BH mergers (RBH–BH) come from AGN, the rate of NS–BH (NS–NS) mergers in the AGN channel is ${R}_{\mathrm{ BH}\!-\!\mathrm{ NS}} \sim f_{\mathrm{ AGN}}[10,300]\, \rm {Gpc}^{-3}\, \rm {yr}^{-1},({\mathit{ R}}_{NS\!-\!NS} \le \mathit{ f}_{AGN}400\, \rm {Gpc}^{-3}\, \rm {yr}^{-1}$). Given the ratio of NS–NS/BH–BH LIGO search volumes, from preliminary O3 results the AGN channel is not the dominant contribution to observed NS–NS mergers. The number of lower mass gap events expected is a strong function of the nuclear MF and mass segregation efficiency. CO merger ratios derived from LIGO can restrict models of MF, mass segregation, and populations embedded in AGN discs. The expected number of electromagnetic (EM) counterparts to NS–BH mergers in AGN discs at z < 1 is $\sim [30,900]\, {\rm {yr}}^{-1}(f_{\mathrm{ AGN}}/0.1)$. EM searches for flaring events in large AGN surveys will complement LIGO constraints on AGN models and the embedded populations that must live in them.

Non-coplanar interplanetary flight simulation considering motion relative to the center of mass peculiarities of solar sail spacecraft

The paper is devoted to the non-coplanar interplanetary Earth–Venus flight of a spacecraft equipped with a non-perfectly reflecting solar sail, the magnitude and direction of acceleration from which is calculated taking into account specular and diffuse reflections, absorption and transmission of photons by the surface of the solar sail. The goal of the heliocentric motion is to transfer the solar sail spacecraft into the Hill sphere of Venus with zero hyperbolic excess of speed. A feature of the paper is the study of the motion of a non-perfectly reflecting solar sail spacecraft taking into account the motion relative to the center of mass. The problem is divided into three stages. At the first stage, a nominal program for controlling the motion of the spacecraft center of mass is formed. At the second stage, sufficient angular velocities are determined to ensure the obtained nominal control program and the parameters of the spacecraft controls – thin-film controls located along the perimeter of the solar sail – are calculated. The operating principle of the thin-film controls is quite simple. When the voltage applied to the thin-film controls changes, they become transparent or opaque, there is a difference in the normal components of the light pressure forces, which provides a control torque for changing the orientation of the spacecraft in space. At the third stage, the joint motion of the center of mass and relative to the center of mass of the spacecraft is simulated to demonstrate the feasibility of the obtained control program. As a result, a comparison is made of non-coplanar interplanetary Earth–Venus flights with and without thin-film control elements.

On the Evolution of Balloon Satellite Motions in a Plane Restricted Planetary Four-Body Problem with Light Pressure

In this paper, we consider the plane restricted four-body problem taking into account the light pressure forces when the Earth’s orbit is a Keplerian ellipse with a focus at the Sun, the Moon’s orbit is a Keplerian ellipse with a focus at the Earth, and the balloon satellite is a passively gravitating body. The averaged perturbing function of the problem in osculating elements is obtained in the nonresonant case, when the unperturbed orbit of the Earth satellite lies in the outer sphere of the Earth’s gravitational influence, located beyond the lunar Hill sphere. It is found that the integrals of averaged equations in the osculating elements are the semimajor axis of the satellite orbit as well as the average value of the force function. The stationary modes of oscillations and their bifurcation depending on the light pressure coefficient and the semimajor axis are investigated. Phase oscillation portraits are constructed for different values of the light pressure coefficient. The librational and rotational orbits of the satellite in the ecliptic plane are calculated.

Retention of Long-period Gas Giant Planets: Type II Migration Revisited

Abstract During their formation, emerging protoplanets tidally interact with their natal disks. Proto–gas giant planets, with Hill radii larger than the disk thickness, open gaps and quench gas flow in the vicinity of their orbits. It is usually assumed that their type II migration is coupled to the viscous evolution of the disk. Although this hypothesis provides an explanation for the origin of close-in planets, it also encounters a predicament on the retention of long-period orbits for most gas giant planets. Moreover, numerical simulations indicate that the planets’ migrations are not solely determined by the viscous diffusion of their natal disk. Here we carry out a series of hydrodynamic simulations combined with analytic studies to examine the transition between different paradigms of type II migration. We find a range of planetary mass for which gas continues to flow through a severely depleted gap so that the surface density distribution in the disk region beyond the gap is maintained in a quasi-steady state. The associated gap profile modifies the location of corotation and Lindblad resonances. In the proximity of the planet’s orbit, high-order Lindblad and corotation torque are weakened by the gas depletion in the gap, while low-order Lindblad torques near the gap walls preserve their magnitude. Consequently, the intrinsic surface density distribution of the disk delicately determines both the pace and direction of the planets’ type II migration. We show that this effect might stall the inward migration of giant planets and preserve them in disk regions where the surface density is steep.

The Erratic Path to Coalescence of LISA Massive Black Hole Binaries in Subparsec-resolution Simulations of Smooth Circumnuclear Gas Disks

Abstract We perform high-resolution simulations to follow the orbital decay of 5 × 105 and 107 M ⊙ massive black hole (MBH) pairs embedded in a circumnuclear gas disk (CND), from the CND scale (100 pc) down to 0.1–0.01 pc, the scale at which a circumbinary disk (CBD) could form. The MBHs’ erratic orbital evolution is characterized by three stages: (i) a slow initial decay that leads to some circularization; (ii) a fast-migration phase, analogous to type III migration for massive planets in protoplanetary disks, in which angular momentum is efficiently drained by disk-driven torques arising from the co-orbital region of the secondary MBH, at a distance of 1–3 Hill radii; and (iii) a very slow decay phase, in which orbital angular momentum can even increase. In this last stage, a CBD forms when the parsec-scale decay rate becomes small enough to allow sufficient time for a cavity to be carved. When this happens, the MBH separation nearly stalls in our higher-resolution run. We suggest an empirically modified gap-opening criterion that takes into account such timescale effects, as well as other deviations from standard assumptions. Interestingly, a CBD does not form in the lower-resolution runs, resulting in a faster subparsec decay. Our findings show that the subparsec MBH pairing in gaseous disks is a stochastic and fragile process. Additional mechanisms, such as the stellar-driven hardening, may be necessary to guarantee that the gravitational wave emission phase is entered and the MBHs become accessible to future detectors such as the Laser Interferometer Space Antenna.

Dynamical Packing in the Habitable Zone: The Case of Beta CVn

Abstract Uncovering the occurrence rate of terrestrial planets within the habitable zone (HZ) of their host stars has been a particular focus of exoplanetary science in recent years. The statistics of these occurrence rates have largely been derived from transiting planet discoveries, and have uncovered numerous HZ planets in compact systems around M-dwarf host stars. Here we explore the width of the HZ as a function of spectral type, and the dynamical constraints on the number of stable orbits within the HZ for a given star. We show that, although the Hill radius for a given planetary mass increases with larger semimajor axis, the width of the HZ for earlier-type stars allows for more terrestrial planets in the HZ than late-type stars. In general, dynamical constraints allow ∼6 HZ Earth-mass planets for stellar masses ≳0.7M ⊙, depending on the presence of farther out giant planets. As an example, we consider the case of Beta CVn, a nearby bright solar-type star. We present 20 yr of radial velocities (RV) from the Keck/High Resolution Echelle Spectrometer (HIRES) and Automated Planet Finder (APF) instruments and conduct an injection-recovery analysis of planetary signatures in the data. Our analysis of these RV data rule out planets more massive than Saturn within 10 au of the star. These system properties are used to calculate the potential dynamical packing of terrestrial planets in the HZ and show that such nearby stellar targets could be particularly lucrative for HZ planet detection by direct imaging exoplanet missions.

Limits on the orbits of possible exomoons around Kepler giant planets in the habitable zone

Regions of Hill stability were determined using the full three-body theory for the planetary candidates that were found by the Kepler mission to lie in the Habitable Zone of the host star with radii larger than 3 Earth radii. The values obtained give a more accurate assessment of the sphere of influence of a planet than does the Hill radius using the restricted three-body expression. The values given by the two estimates for circular orbits are compared. The variation in the full three-body Hill regions were examined for a variety of possible moon masses and orbital eccentricities and inclinations. It was found that the critical moon planet separation decreased with increased moon orbital eccentricity and inclination but to a far greater extent when the planetary orbital eccentricity increased suggesting they would lie inside the Roche limit and are unlikely to have formed or exist now. The angular separation of the moon and planet and the radial velocity amplitudes of the planets likely to be observed are also affected. This is important for future observations and missions. It was also found that the giant planets in the habitable zone lie in a narrow band that can be fitted by a linear regression relation between log10(Planet luminosity) and log10 (Planet temperature) with a slope of 3.34.

On the local and global properties of gravitational spheres of influence

ABSTRACT We revisit the concept of spheres of gravitational activity, to which we give both a geometrical and a physical meaning. This study aims to refine this concept in a much broader context that could, for instance, be applied to exo-planetary problems (in a Galactic stellar disc–star–planets system) in order to define a first-order ‘boundary’ of a planetary system. The methods used in this paper rely on classical Celestial Mechanics and develop the equations of motion in the framework of the three-body problem (e.g. Star-Planet-Satellite System). We start with the basic definition of a planet’s sphere of activity as the region of space in which it is feasible to assume the planet as the central body and the Sun as the perturbing body when computing perturbations of the satellite’s motion. We then investigate the geometrical properties and physical meaning of the ratios of solar accelerations (central and perturbing) and planetary accelerations (central and perturbing), and the boundaries they define. Throughout the paper, we clearly distinguish amongst the sphere of activity, the Chebotarev sphere (a particular case of the sphere of activity), the Laplace sphere, and the Hill sphere. The last two are often wrongfully thought to be one and the same. Furthermore, by taking a closer look at and comparing the ratio of the star’s accelerations (central/perturbing) with that of the planetary accelerations (central/perturbing) as a function of the planeto-centric distance, we have identified different dynamical regimes, which are presented in the semi-analytical analysis.

Orbital Stability of Exomoons and Submoons with Applications to Kepler 1625b-I

Abstract An intriguing question in the context of dynamics arises: could a moon possess a moon itself? Such a configuration does not exist in the solar system, although this may be possible in theory. Kollmeier & Raymond determined the critical size of a satellite necessary to host a long-lived subsatellite, or submoon. However, the orbital constraints for these submoons to exist are still undetermined. Domingos et al. indicated that moons are stable out to a fraction of the host planet's Hill radius R H,p, which in turn depend on the eccentricity of its host’s orbit. Motivated by this, we simulate systems of exomoons and submoons for 105 planetary orbits, while considering many initial orbital phases to obtain the critical semimajor axis in terms of R H,p or the host satellite’s Hill radius R H,sat, respectively. We find that, assuming circular coplanar orbits, the stability limit for an exomoon is 0.40 R H,p and for a submoon is 0.33 R H,sat. Additionally, we discuss the observational feasibility of detecting these subsatellites through photometric, radial velocity, or direct imaging observations using the Neptune-sized exomoon candidate Kepler 1625b-I and identify how stability can shape the identification of future candidates.

Formation of Giant Planet Satellites

Abstract Recent analyses have shown that the concluding stages of giant planet formation are accompanied by the development of a large-scale meridional flow of gas inside the planetary Hill sphere. This circulation feeds a circumplanetary disk that viscously expels gaseous material back into the parent nebula, maintaining the system in a quasi-steady state. Here, we investigate the formation of natural satellites of Jupiter and Saturn within the framework of this newly outlined picture. We begin by considering the long-term evolution of solid material, and demonstrate that the circumplanetary disk can act as a global dust trap, where s • ∼ 0.1–10 mm grains achieve a hydrodynamical equilibrium, facilitated by a balance between radial updraft and aerodynamic drag. This process leads to a gradual increase in the system’s metallicity, and eventually culminates in the gravitational fragmentation of the outer regions of the solid subdisk into km satellitesimals. Subsequently, satellite conglomeration ensues via pair-wise collisions but is terminated when disk-driven orbital migration removes the growing objects from the satellitesimal feeding zone. The resulting satellite formation cycle can repeat multiple times, until it is brought to an end by photoevaporation of the parent nebula. Numerical simulations of the envisioned formation scenario yield satisfactory agreement between our model and the known properties of the Jovian and Saturnian moons.

Large eddy simulations of slope effects on flow fields over isolated hills and ridges

The slope of a hill could affect the flow patterns significantly. In the present study, three smooth three dimensional (3D) hills (H2, H4, and H8) and three smooth two dimensional (2D) ridges (R2, R4, and R8), with the hill heights increased by factors of 2.0 while the hill radii are kept constant to achieve different slopes, are examined systematically using large eddy simulations (LES). The reattachment of the flow is found to become difficult as the slope increases or as the shape changes from 3D hill to 2D ridge. In addition, the differences of the flow fields between the 3D hills and the 2D ridges will become more evident as the slope increases. Moreover, the mean velocities and the fluctuations for H2 and R2 are almost the same, whereas as the hill slope increases, the differences between the 3D hills and 2D ridges become stronger, and the similarities between the 3D hills and 2D ridges almost disappear for H8 and R8. Based on information available from LES, an analytical model to predict the fractional speed-up ratio is proposed. As for the turbulence structures over the 3D hills, a spiral structure is identified, and the pitch of the spiral becomes narrow as the hill slope increases. When the hill slope further increases to H8, the spiral structures are broken into separated circular tubes. For R4, a hairpin structure is identified, whereas for R8, the hairpin structure disappears, and a vortex with a long spanwise size occurs periodically.

The imprint of the protoplanetary disc in the accretion of super-Earth envelopes

ABSTRACT Super-Earths are by far the most dominant type of exoplanet, yet their formation is still not well understood. In particular, planet formation models predict that many of them should have accreted enough gas to become gas giants. Here, we examine the role of the protoplanetary disc in the cooling and contraction of the protoplanetary envelope. In particular, we investigate the effects of (1) the thermal state of the disc as set by the relative size of heating by accretion or irradiation, and whether its energy is transported by radiation or convection, and (2) advection of entropy into the outer envelope by disc flows that penetrate the Hill sphere, as found in 3D global simulations. We find that, at 5 and 1 au, this flow at the level reported in the non-isothermal simulations where it penetrates only to ∼0.3 times the Hill radius has little effect on the cooling rate since most of the envelope mass is concentrated close to the core, and far from the flow. On the other hand, at 0.1 au, the envelope quickly becomes fully radiative, nearly isothermal, and thus cannot cool down, stalling gas accretion. This effect is significantly more pronounced in convective discs, leading to envelope mass orders of magnitude lower. Entropy advection at 0.1 au in either radiative or convective discs could therefore explain why super-Earths failed to undergo runaway accretion. These results highlight the importance of the conditions and energy transport in the protoplanetary disc for the accretion of planetary envelopes.

The white dwarf planet WD J0914+1914 b: barricading potential rocky pollutants?

Abstract An ice giant planet was recently reported orbiting white dwarf WD J0914+1914 at an approximate distance of 0.07 au. The striking non-detection of rocky pollutants in this white dwarf’s photosphere contrasts with the observations of nearly every other known white dwarf planetary system. Here, I analyse the prospects for exterior extant rocky asteroids, boulders, cobbles, and pebbles to radiatively drift inward past the planet due to the relatively high luminosity ($0.1 \, \mathrm{L}_{\odot }$) of this particularly young (13 Myr) white dwarf. Pebbles and cobbles drift too slowly from Poynting–Robertson drag to bypass the planet, but boulders and asteroids are subject to the much stronger Yarkovsky effect. In this paper, I (i) place lower limits on the time-scales for these objects to reach the planet’s orbit, (ii) establish 3 m as the approximate limiting radius above which a boulder drifts too slowly to avoid colliding with the planet, and (iii) compute bounds on the fraction of boulders that succeed in traversing mean motion resonances and the planet’s Hill sphere to eventually pollute the star. Overall, I find that the planet acts as a barrier against rather than a facilitator for radiatively driven rocky pollution, suggesting that future rocky pollutants would most likely originate from distant scattering events.

The Gemini Planet Imager Exoplanet Survey: Dynamical Mass of the Exoplanet β Pictoris b from Combined Direct Imaging and Astrometry

Abstract We present new observations of the planet β Pictoris b from 2018 with the Gemini Planet Imager (GPI), the first GPI observations following conjunction. Based on these new measurements, we perform a joint orbit fit to the available relative astrometry from ground-based imaging, the Hipparcos Intermediate Astrometric Data (IAD), and the Gaia DR2 position, and demonstrate how to incorporate the IAD into direct imaging orbit fits. We find a mass consistent with predictions of hot-start evolutionary models and previous works following similar methods, though with larger uncertainties: 12.8+5.3 −3.2 M Jup. Our eccentricity determination of disfavors circular orbits. We consider orbit fits to several different imaging data sets, and find generally similar posteriors on the mass for each combination of imaging data. Our analysis underscores the importance of performing joint fits to the absolute and relative astrometry simultaneously, given the strong covariance between orbital elements. Time of conjunction is well-constrained within 2.8 days of 2017 September 13, with the star behind the planet’s Hill sphere between 2017 April 11 and 2018 February 16 (±18 days). Following the recent radial velocity detection of a second planet in the system, β Pic c, we perform additional two-planet fits combining relative astrometry, absolute astrometry, and stellar radial velocities. These joint fits find a significantly smaller mass (8.0 ± 2.6 M Jup) for the imaged planet β Pic b, in a somewhat more circular orbit. We expect future ground-based observations to further constrain the visual orbit and mass of the planet in advance of the release of Gaia DR4.

A survey for variable young stars with small telescopes: II – mapping a protoplanetary disc with stable structures at 0.15 au

ABSTRACT The HOYS citizen science project conducts long-term, multifilter, high-cadence monitoring of large YSO samples with a wide variety of professional and amateur telescopes. We present the analysis of the light curve of V1490 Cyg in the Pelican Nebula. We show that colour terms in the diverse photometric data can be calibrated out to achieve a median photometric accuracy of 0.02 mag in broad-band filters, allowing detailed investigations into a variety of variability amplitudes over time-scales from hours to several years. Using Gaia DR2, we estimate the distance to the Pelican Nebula to be 870 $^{+70}_{-55}$ pc. V1490 Cyg is a quasi-periodic dipper with a period of 31.447 ± 0.011 d. The obscuring dust has homogeneous properties, and grains larger than those typical in the ISM. Larger variability on short time-scales is observed in U and Rc−H α, with U amplitudes reaching 3 mag on time-scales of hours, indicating that the source is accreting. The H α equivalent width and NIR/MIR colours place V1490 Cyg between CTTS/WTTS and transition disc objects. The material responsible for the dipping is located in a warped inner disc, about 0.15 au from the star. This mass reservoir can be filled and emptied on time-scales shorter than the period at a rate of up to 10−10 M⊙ yr−1, consistent with low levels of accretion in other T Tauri stars. Most likely, the warp at this separation from the star is induced by a protoplanet in the inner accretion disc. However, we cannot fully rule out the possibility of an AA Tau-like warp, or occultations by the Hill sphere around a forming planet.

Control program for noncoplanar heliocentric flight to Venus of non-perfectly reflecting solar sail spacecraft

A noncoplanar controlled heliocentric flight to Venus of a spacecraft with a non-perfectly reflecting solar sail is considered. The aim of the heliocentric flight is to get a spacecraft into Hill sphere of Venus with zero hyperbolic excess velocity. An algorithm has been developed for applying the locally optimal control laws for the fastest change of the osculating elements. Solar sail orientation is controlled by thin-film control elements arranged along the solar sail surface perimeter. The flight trajectory, the control program and the required width and area of thin-film control elements are obtained as a result of motion simulation.

Saturn's C ring and Cassini division: Particle sizes from Cassini UVIS, VIMS, and RSS occultations

Abstract Saturn's C ring and Cassini Division share many morphological traits: both contain numerous opaque, sharp–edged ringlets and gaps, broader low optical depth “background” regions, larger-optical depth regions that rise abruptly from the background (known as the C ring's plateaus and the Cassini Division's triple band feature), and linear ramps in optical depth up to the abrupt inner edges of the B ring and A ring, respectively. Throughout the majority of both regions, the surface mass density of the rings is small enough that the Toomre critical wavelength (most unstable wavelength for gravitational collapse) is comparable in size to, or smaller than, the largest individual ring particles. Thus, self-gravity wakes do not form in these regions, unlike the A and B rings where the critical wavelength is tens of meters and the self-gravity wakes introduce strong dependence of the observed optical depth on viewing geometry. In the absence of self-gravity wakes, we model the ring particle size distribution with a simple power-law, where the number of particles per unit area of the rings in the size range [a, a + da] is given by n(a)da = Ca-qda between amin and amax. We fit normal optical depths derived from the power-law size distribution parameters and the thin-layers ring model of Zebker et al. (1985) to the wavelength-dependent optical depth profiles obtained by 3 Cassini Instruments: UVIS at λ = 0.15 μm, VIMS at λ = 2.9 μm, and RSS Ka-band (λ = 9.4 mm), X-band at (λ = 3.4 cm), and S-band (λ = 13.0 cm). We find that the C ring is best characterized by five or more thin layers of particles with a mean power-law index of q ~ 3.16 in the C ring background and q ~ 3.05 in the C ring plateaus, in the rings. We find a minimum particle radius of amin ~ 4.1 mm in the background C ring and plateaus and amin ~ 6 mm in the plateaus. The cross-section-weighted effective particle radius determined using the excess variance of UVIS signal beyond Poisson counting statistics by Colwell et al. (2018) constrains the size of the largest particles in the rings. We find the largest particles contributing to the power-law size distribution, and thus to the optical depth, are amax ~ 10–15 m in the background C ring and amax ~ 5–6 m in the C ring plateaus. This substantial difference in the sizes of the largest ring particles together with the overall shallower power law index in the plateaus explains their optical depth difference relative to the background C ring. Additionally, Baillie et al. (2013) used UVIS stellar occultations to find a distribution of small-scale, low optical depth gaps in the plateaus. These regions, with radial widths of We constrain the particle densities by dividing the surface mass densities determined from the dispersion of spiral density waves by the total particle volume integrated over a square meter of the ring slab. We derive low bulk particle densities of ρ ~ 0.1–0.3 g/cm3 except in the central background C ring where we find ρ ~ 0.9 g/cm3. These low derived densities may be due to inter-particle spaces within 1–20 m particle aggregates that contribute to the measured optical depth and thus to the upper end of the size distribution. Our results are consistent with Zhang et al. (2017) who reported particles with porosities >75% made of water ice with up to 11% silicate contaminate in the central background C ring.

Breaking the centrifugal barrier to giant planet contraction by magnetic disc braking

ABSTRACT During the runaway phase of their formation, gas giants fill their gravitational spheres of influence out to Bondi or Hill radii. When runaway ends, planets shrink several orders of magnitude in radius until they are comparable in size to present-day Jupiter; in 1D models, the contraction occurs on the Kelvin–Helmholtz time-scale tKH, which is initially a few thousand years. However, if angular momentum is conserved, contraction cannot complete, as planets are inevitably spun up to their breakup periods Pbreak. We consider how a circumplanetary disc (CPD) can de-spin a primordially magnetized gas giant and remove the centrifugal barrier, provided the disc is hot enough to couple to the magnetic field, a condition that is easier to satisfy at later times. By inferring the planet’s magnetic field from its convective cooling luminosity, we show that magnetic spin-down times are shorter than contraction times throughout post-runaway contraction: tmag/tKH ∼ (Pbreak/tKH)1/21 ≲ 1. Planets can spin-down until they corotate with the CPD’s magnetospheric truncation radius, at a period Pmax/Pbreak ∼ (tKH/Pbreak)1/7. By the time the disc disperses, Pmax/Pbreak ∼ 20–30; further contraction at fixed angular momentum can spin planets back up to ∼10Pbreak, potentially explaining observed rotation periods of giant planets and brown dwarfs.