The Secular Evolution of the Primordial Kuiper Belt

A model that computes the secular evolution of a gravitating disk-planet system is developed. The disk is treated as a set of gravitating rings, with the rings'/planets' time-evolution governed by the classical Laplace-Lagrange solution for secular evolution but modified to account for the disk's finite thickness h. This system's Lagrange planetary equations yield a particular class of spiral wave solutions, usually denoted as apsidal density waves and nodal bending waves. There are two varieties of apsidal waves:long waves and short waves. Planets typically launch long density waves at the disk's nearer edge or else at a secular resonance in the disk, and these waves ultimately reflect downstream at a more distant disk edge or else at a Q-barrier in the disk, whereupon they return as short density waves. Planets also launch nodal bending waves, and these have the property that they can stall in the disk, that is, their group velocity plummets to zero upon approaching a disk region too thick to support the continued propagation of bending waves. The rings model is used to compute the secular evolution of a Kuiper Belt having a variety of masses, and it is shown that the early massive Belt was very susceptible to the propagation of low-amplitude apsidal and nodal waves launched by the giant planets.Comment: 45 pages, 6 figure

An N-body Integrator for Gravitating Planetary Rings, and the Outer Edge of Saturn's B Ring

A new symplectic N-body integrator is introduced, one designed to calculate the global 360 degree evolution of a self-gravitating planetary ring that is in orbit about an oblate planet. This freely-available code is called epi_int, and it is distinct from other such codes in its use of streamlines to calculate the effects of ring self-gravity. The great advantage of this approach is that the perturbing forces arise from smooth wires of ring matter rather than discreet particles, so there is very little gravitational scattering and so only a modest number of particles are needed to simulate, say, the scalloped edge of a resonantly confined ring or the propagation of spiral density waves. The code is applied to the outer edge of Saturn's B ring, and a comparison of Cassini measurements of the ring's forced response to simulations of Mimas' resonant perturbations reveals that the B ring's surface density at its outer edge is 195+-60 gm/cm^2 which, if the same everywhere across the ring would mean that the B ring's mass is about 90% of Mimas' mass. Cassini observations show that the B ring-edge has several free normal modes, which are long-lived disturbances of the ring-edge that are not driven by any known satellite resonances. Although the mechanism that excites or sustains these normal modes is unknown, we can plant such a disturbance at a simulated ring's edge, and find that these modes persist without any damping for more than ~10^5 orbits or ~100 yrs despite the simulated ring's viscosity of 100 cm^2/sec. These simulations also indicate that impulsive disturbances at a ring can excite long-lived normal modes, which suggests that an impact in the recent past by perhaps a cloud of cometary debris might have excited these disturbances which are quite common to many of Saturn's sharp-edged rings.Comment: 55 pages, 13 figures, accepted for publication in the Astrophysical Journa

Neptune's Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations

Nbody simulations are used to examine the consequences of Neptune's outward migration into the Kuiper Belt, with the simulated endstates being compared rigorously and quantitatively to the observations. These simulations confirm the findings of Chiang et al. (2003), who showed that Neptune's migration into a previously stirred-up Kuiper Belt can account for the Kuiper Belt Objects (KBOs) known to librate at Neptune's 5:2 resonance. We also find that capture is possible at many other weak, high-order mean motion resonances, such as the 11:6, 13:7, 13:6, 9:4, 7:3, 12:5, 8:3, 3:1, 7:2, and the 4:1. The more distant of these resonances, such as the 9:4, 7:3, 5:2, and the 3:1, can also capture particles in stable, eccentric orbits beyond 50 AU, in the region of phase space conventionally known as the Scattered Disk. Indeed, 90% of the simulated particles that persist over the age of the Solar System in the so-called Scattered Disk zone never had a close encounter with Neptune, but instead were promoted into these eccentric orbits by Neptune's resonances during the migration epoch. This indicates that the observed Scattered Disk might not be so scattered. This model also produced only a handful of Centaurs, all of which originated at Neptune's mean motion resonances in the Kuiper Belt. We also report estimates of the abundances and masses of the Belt's various subpopulations (e.g., the resonant KBOs, the Main Belt, and the so-called Scattered Disk), and also provide upper limits on the abundance of Centaurs and Neptune's Trojans, as well as upper limits on the sizes and abundances of hypothetical KBOs that might inhabit the a>50 AU zone.Comment: 60 pages, 16 figures. Accepted for publication in the Astronomical Journa

The Secular Evolution of a Close Ring-Satellite System: The Excitation of Spiral Density Waves at a Nearby Gap Edge

The Lagrange planetary equations are used to study to secular evolution of a small, eccentric satellite that orbits within a narrow gap in a broad, self-gravitating planetary ring. These equations show that the satellite's secular perturbations of the ring will excite a very long-wavelength spiral density wave that propagates away from the gap's outer edge. The amplitude of these waves, as well as their dispersion relation, are derived here. That dispersion relation reveals that a planetary ring can sustain two types of density waves: long waves that, in Saturn's A ring, would have wavelengths of order 100 km, and short waves that tend to be very nonlinear and are expected to quickly damp. The excitation of these waves also transports angular momentum from the ring to the satellite in a way that damps the satellite's eccentricity e, which also tends to reduce the amplitude of subsequent waves. The rate of eccentricity damping due to this wave action is then compared to the rates at which the satellite's Lindblad and corotation resonances alter the satellite's e. These results are then applied to the gap-embedded Saturnian satellites Pan and Daphnis, and the long-term stability of their eccentricities is assessed.Comment: Accepted for publication in the Astrophysical Journa

Impact Vaporization as a Possible Source of Mercury's Calcium Exosphere

Mercury's calcium exosphere varies in a periodic way with that planet's true anomaly. We show that this pattern can be explained by impact vaporization from interplanetary dust with variations being due to Mercury's radial and vertical excursions through an interplanetary dust disk having an inclination within 5 degrees of the plane of Mercury's orbit. Both a highly inclined dust disk and a two-disk model (where the two disks have a mutual inclination) fail to reproduce the observed variation in calcium exospheric abundance with Mercury true anomaly angle. However, an additional source of impacting dust beyond the nominal dust disk is required near Mercury's true anomaly () 25deg +/-5deg. This is close to but not coincident with Mercury's true anomaly (=45deg) when it crosses comet 2P/Encke's present day orbital plane. Interestingly, the Taurid meteor storms at Earth, which are also due to Comet Encke, are observed to occur when Earth's true anomaly is +/-20 or so degrees before and after the position where Earth and Encke orbital planes cross. The lack of exact correspondence with the present day orbit of Encke may indicate the width of the potential stream along Mercury's orbit or a previous cometary orbit. The extreme energy of the escaping calcium, estimated to have a temperature greater than 50000 K if the source is thermal, cannot be due to the impact process itself but must be imparted by an additional mechanism such as dissociation of a calcium-bearing molecule or ionization followed by recombination

Comet Shoemaker-Levy 9: An Active Comet

The important elements of the debate over the activity versus dormancy of comet Shoemaker Levy 9 (S-L 9) are reviewed. It is argued that the circularity of the isophotes in the inner comae of S-L 9 as well as the spatial dependencies of the comae brightness profiles are indicators of sustained dust production by S-L 9. It is also shown that the westward tail orientations, which were formerly interpreted as a sign of the comet's dormancy, are not a good indicator of either activity or dormancy. Rather, the tail orientations simply place constraints on the dust production rate for grains smaller than approx. equals 5(micron). All the available evidence points to S-L 9 as having been an active, dust-producing comet. Synthetic images of an active comet are fitted to Hubble Space Telescope images of the S-L 9 fragment K, and its grain size and outflow velocity distributions are extracted. These findings show that the appearance of the dust coma was dominated by large grains having radii between approx. equals 30 (micron) and approx. equals 3 mm, produced at a rate of M approx. equals 22 kg/ s, and ejected at outflow velocities of approx. equals 0.5 m/ s. Only upper limits on the production rates of smaller grains are obtained. The nucleus of fragment K was not observed directly but its size is restricted to lie within a rather narrow interval 0.4 less than or equal to Rf less than or equal to 1.2 km

Dynamics of the Sharp Edges of Broad Planetary Rings

(Abridged) The following describes a model of a broad planetary ring whose sharp edge is confined by a satellite's m^th Lindblad resonance (LR). This model uses a streamline formalism to calculate the ring's internal forces, namely, ring gravity, pressure, viscosity, as well as a hypothetical drag force. The model calculates the streamlines' forced orbit elements and surface density throughout the perturbed ring. The model is then applied to the outer edge of Saturn's B ring, which is maintained by an m=2 inner LR with the satellite Mimas. Ring models are used to illustrate how a ring's perturbed state depends on the ring's physical properties: surface density, viscosity, dispersion velocity, and the hypothetical drag force. A comparison of models to the observed outer B ring suggests that the ring's surface density there is between 10 and 280 gm/cm^2. The ring's edge also indicates where the viscous torque counterbalances the perturbing satellite's gravitational torque on the ring. But an examination of seemingly conventional viscous B ring models shows that they all fail to balance these torques at the ring's edge. This is due ring self-gravity and the fact that a viscous ring tends to be nearly peri-aligned with the satellite, which reduces the satellite's torque on the ring and makes the ring's edge more difficult to maintain. Nonetheless, the following shows that a torque balance can still be achieved in a viscous B ring, but only in an extreme case where the ratio of the ring's bulk/shear viscosities satisfy ~10^4. However, if the dissipation of the ring's forced motions is instead dominated by a weak drag force, then the satellite can exert a much stronger torque that can counterbalance the ring's viscous torque.Comment: Accepted for publication in the Astrophysical Journal on April 3, 200

Bimodal release ondansetron for acute gastroenteritis among adolescents and adults: A randomized clinical trial

Importance: Vomiting resulting from acute gastroenteritis is commonly treated with intravenous antiemetics in acute care settings. If oral treatment were beneficial, patients might not need intravenous administered hydration or medication. Furthermore, a long-acting treatment could provide sustained relief from nausea and vomiting. Objective: To determine whether an experimental long-acting bimodal release ondansetron tablet decreases gastroenteritis-related vomiting and eliminates the need for intravenous therapy for 24 hours after administration. Design, Setting, and Participants: This placebo-controlled, double-blind, randomized clinical trial included patients from 19 emergency departments and 2 urgent care centers in the United States from December 8, 2014, to February 17, 2017. Patients 12 years and older with at least 2 vomiting episodes from presumed gastroenteritis in the previous 4 hours and symptoms with less than 36 hours\u27 duration were randomized using a 3:2 active to placebo ratio. Analyses were performed on an intent-to-treat basis and conducted from June 1, 2017, to November 1, 2017. Intervention: Bimodal release ondansetron tablet containing 6 mg of immediate release ondansetron and 18 mg of a 24-hour release matrix for a total of 24 mg of ondansetron. Main Outcomes and Measures: Treatment success was defined as no further vomiting, no need for rescue medication, and no intravenous hydration for 24 hours after bimodal release ondansetron administration. Results: Analysis included 321 patients (mean [SD] age, 29.0 [11.1] years; 195 [60.7%] women), with 192 patients in the bimodal release ondansetron group and 129 patients in the placebo group. Treatment successes were observed in 126 patients in the bimodal release ondansetron group (65.6%) compared with 70 patients in the placebo group (54.3%), with an 11.4% (95% CI, 0.3%-22.4%) absolute probability difference. The proportion of treatment success was 21% higher among patients who received bimodal release ondansetron compared with those who received a placebo (relative risk, 1.21; 95% CI, 1.00-1.46; P = .04). In an analysis including only patients with a discharge diagnosis of acute gastroenteritis and no major protocol violations, there were 123 treatment successes (69.5%) in the bimodal release ondansetron group compared with 67 treatment successes (54.9%) in the placebo group (relative risk, 1.27; 95% CI, 1.05-1.53; P = .01). Adverse effects were infrequent and similar to the known safety profile of ondansetron. Conclusions and Relevance: This randomized clinical trial found that a long-acting bimodal release oral ondansetron tablet was an effective antiemetic among adolescents and adults with moderate to severe vomiting from acute gastroenteritis. The drug benefits extended to 24 hours after administration. Bimodal release ondansetron may decrease the need for intravenous access and emergency department care to manage acute gastroenteritis. Trial Registration: ClinicalTrials.gov identifier: NCT02246439

Diagnosing Circumstellar Debris Disks

(Abridged) A numerical model of a circumstellar debris disk is developed and applied to observations of the circumstellar dust orbiting beta Pictoris. The model accounts for the rates at which dust is produced by collisions among unseen planetesimals, and the rate at which dust grains are destroyed due to collisions. The model also accounts for the effects of radiation pressure, which is the dominant perturbation on the disk's smaller but abundant dust grains. Solving the resulting system of rate equations then provides the dust abundances versus grain size and over time. Those solutions also provide the dust grains' collisional lifetime versus grain size, and the debris disk's optical depth and surface brightness versus distance from the star. Comparison to observations then yields estimates of the unseen planetesimal disk's radius, and the rate at which the disk sheds mass due to planetesimal grinding. The model is then applied to optical observations of the edge-on dust disk orbiting beta Pictoris, and good agreement is achieved when the unseen planetesimal disk is broad, with 75<r<150 AU. If it is assumed that the dust grains are bright like Saturn's icy rings, then the cross section of dust in the disk is A_d~2x10^20 km^2 and its mass is M_d~11 lunar masses. In this case the planetesimal disk's dust production rate is quite heavy, dM_d/dt~9 earth-masses per Myr, implying that there is or was a substantial amount of planetesimal mass there, at least 110 earth-masses. But if the dust grains are darker than assumed, then the planetesimal disk's mass-loss rate and its total mass are heavier. In fact, the apparent dearth of any major planets in this region, plus the planetesimal disk's heavy mass-loss rate, suggests that the 75<r<150 AU zone at beta Pic might be a region of planetesimal destruction, rather than a site of ongoing planet formation.Comment: Accepted for publication in the Astrophysical Journa