arXiv subjects

Douglas P. Hamilton

Publications and source records attributed to Douglas P. Hamilton.

35 records · Page 2Linked to original sources

arXiv2013

Chaotic dust dynamics and implications for the hemispherical color asymmetries of the Uranian satellites

Dust grains generated by the Uranian irregular satellites will undergo chaotic large-amplitude eccentricity oscillations under the simultaneous action of radiation forces and the highly misaligned quadrupole potentials of the oblate planet and distant Sun. From a suite of orbital histories, we estimate collision proba- bilities of dust particles with the regular satellites and argue that this process may explain the observed hemispherical color asymmetries of the outermost four regular satellites of Uranus.

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arXiv2012

Dynamical Instabilities in High-Obliquity Systems

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations---large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. (2009) found that, for planets with obliquities > 68.875 degrees, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range, and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we find that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68.875 degrees. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. We find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this is occurs because radiation pressure modifies the equilibrium Laplace plane.

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arXiv2012

Long-Term Stability of Horseshoe Orbits

Unlike Trojans, horseshoe coorbitals are not generally considered to be long-term stable (Dermott and Murray, 1981; Murray and Dermott, 1999). As the lifetime of Earth's and Venus's horseshoe coorbitals is expected to be about a Gyr, we investigated the possible contribution of late-escaping inner planet coorbitals to the lunar Late Heavy Bombardment. Contrary to analytical estimates, we do not find many horseshoe objects escaping after first 100 Myr. In order to understand this behaviour, we ran a second set of simulations featuring idealized planets on circular orbits with a range of masses. We find that horseshoe coorbitals are generally long lived (and potentially stable) for systems with primary-to-secondary mass ratios larger than about 1200. This is consistent with results of Laughlin and Chambers (2002) for equal-mass pairs or coorbital planets and the instability of Jupiter's horseshoe companions (Stacey and Connors, 2008). Horseshoe orbits at smaller mass ratios are unstable because they must approach within 5 Hill radii of the secondary. In contrast, tadpole orbits are more robust and can remain stable even when approaching within 4 Hill radii of the secondary.

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arXiv2012

The Fate of Sub-micron Circumplanetary Dust Grains II: Multipolar Fields

We study the radial and vertical stability of dust grains launched with all charge-to-mass ratios at arbitrary distances from rotating planets with complex magnetic fields. We show that the aligned dipole magnetic field model analyzed by Jontof-Hutter and Hamilton (2012) is an excellent approximation in most cases, but that fundamentally new physics arises with the inclusion of non-axisymmetric magnetic field terms. In particular, large numbers of distant negatively-charged dust grains, stable in a magnetic dipole, can be driven to escape by a more complex field. We trace the origin of the instability to overlapping Lorentz resonances which are extremely powerful when the gravitational and electromagnetic forces on a dust grain are comparable. These resonances enable a dust grain to tap the spin energy of the planet to power its escape. We also explore the relatively minor influence of different launch speeds and the far more important effects of variable grain charge. Only the latter are capable of significantly affecting the micron-sized grains that dominate visible and infrared images of faint dust rings. Finally, we present full stability maps for Earth, Jupiter, Saturn, Uranus, and Neptune with magnetic fields modeled out to octupole order. Not surprisingly, dust in the tortured magnetic fields of Uranus and Neptune show the greatest instability.

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arXiv2012

The Fate of Sub-Micron Circumplanetary Dust Grains I: Aligned Dipolar Magnetic Fields

We study the stability of charged dust grains orbiting a planet and subject to gravity and the electromagnetic force. Our numerical models cover a broad range of launch distances from the planetary surface to beyond synchronous orbit, and the full range of charge-to-mass ratios from ions to rocks. Treating the spinning planetary magnetic field as an aligned dipole, we map regions of radial and vertical instability where dust grains are driven to escape or crash into the planet. We derive the boundaries between stable and unstable trajectories analytically, and apply our models to Jupiter, Saturn and the Earth, whose magnetic fields are reasonably well represented by aligned dipoles.

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arXiv2011

Finding the trigger to Iapetus' odd global albedo pattern: Dynamics of dust from Saturn's irregular satellites

The leading face of Saturn's moon Iapetus, Cassini Regio, has an albedo only one tenth that on its trailing side. The origin of this enigmatic dichotomy has been debated for over forty years, but with new data, a clearer picture is emerging. Motivated by Cassini radar and imaging observations, we investigate Soter's model of dark exogenous dust striking an originally brighter Iapetus by modeling the dynamics of the dark dust from the ring of the exterior retrograde satellite Phoebe under the relevant perturbations. In particular, we study the particles' probabilities of striking Iapetus, as well as their expected spatial distribution on the Iapetian surface. We find that, of the long-lived particles (greater than about 5 microns), most particle sizes (greater than about 10 microns) are virtually certain to strike Iapetus, and their calculated distribution on the surface matches up well with Cassini Regio's extent in its longitudinal span. The satellite's polar regions are observed to be bright, presumably because ice is deposited there. Thus, in the latitudinal direction we estimate polar dust deposition rates to help constrain models of thermal migration invoked to explain the bright poles (Spencer & Denk 2010). We also analyze dust originating from other irregular outer moons, determining that a significant fraction of that material will eventually coat Iapetus--perhaps explaining why the spectrum of Iapetus' dark material differs somewhat from that of Phoebe. Finally we track the dust particles that do not strike Iapetus, and find that most land on Titan, with a smaller fraction hitting Hyperion. As has been previously conjectured, such exogenous dust, coupled with Hyperion's chaotic rotation, could produce Hyperion's roughly isotropic, moderate-albedo surface.

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arXiv2009

Three-Body Capture of Irregular Satellites: Application to Jupiter

We investigate a new theory of the origin of the irregular satellites of the giant planets: capture of one member of a ~100-km binary asteroid after tidal disruption. The energy loss from disruption is sufficient for capture, but it cannot deliver the bodies directly to the observed orbits of the irregular satellites. Instead, the long-lived capture orbits subsequently evolve inward due to interactions with a tenuous circumplanetary gas disk. We focus on the capture by Jupiter, which, due to its large mass, provides the most stringent test of our model. We investigate the possible fates of disrupted bodies, the differences between prograde and retrograde captures, and the effects of Callisto on captured objects. We make an impulse approximation and discuss how it allows us to generalize capture results from equal-mass binaries to binaries with arbitrary mass ratios. We find that at Jupiter, binaries offer an increase of a factor of ~10 in the capture rate of 100-km objects as compared to single bodies, for objects separated by tens of radii that approach the planet on relatively low-energy trajectories. These bodies are at risk of collision with Callisto, but may be preserved by gas drag if their pericenters are raised quickly enough. We conclude that our mechanism is as capable of producing large irregular satellites as previous suggestions, and it avoids several problems faced by alternative models.

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arXiv2009

Mass Segregation in NGC 2298: limits on the presence of an Intermediate Mass Black Hole

[abridged] Theoretical investigations have suggested the presence of Intermediate Mass Black Holes (IMBHs, with masses in the 100-10000 Msun range) in the cores of some Globular Clusters (GCs). In this paper we present the first application of a new technique to determine the presence or absence of a central IMBH in globular clusters that have reached energy equipartition via two-body relaxation. The method is based on the measurement of the radial profile for the average mass of stars in the system, using the fact that a quenching of mass segregation is expected when an IMBH is present. Here we measure the radial profile of mass segregation using main-sequence stars for the globular cluster NGC 2298 from resolved source photometry based on HST-ACS data. The observations are compared to expectations from direct N-body simulations of the dynamics of star clusters with and without an IMBH. The mass segregation profile for NGC 2298 is quantitatively matched to that inferred from simulations without a central massive object over all the radial range probed by the observations, that is from the center to about two half-mass radii. Profiles from simulations containing an IMBH more massive than ~ 300-500 Msun (depending on the assumed total mass of NGC 2298) are instead inconsistent with the data at about 3 sigma confidence, irrespective of the IMF and binary fraction chosen for these runs. While providing a null result in the quest of detecting a central black hole in globular clusters, the data-model comparison carried out here demonstrates the feasibility of the method which can also be applied to other globular clusters with resolved photometry in their cores.

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arXiv2008

Galileo In-Situ Dust Measurements in Jupiter's Gossamer Rings

During its late orbital mission at Jupiter the Galileo spacecraft made two passages through the giant planet's gossamer ring system. The impact-ionization dust detector on board successfully recorded dust impacts during both ring passages and provided the first in-situ measurements from a dusty planetary ring. In all, a few thousand dust impacts were counted with the instrument accumulators during both ring passages, but only a total of 110 complete data sets of dust impacts were transmitted to Earth. Detected particle sizes range from about 0.2 to 5 micron, extending the known size distribution by an order of magnitude towards smaller particles than previously derived from optical imaging (Showalter et al. 2008). The grain size distribution increases towards smaller particles and shows an excess of these tiny motes in the Amalthea gossamer ring compared to the Thebe ring. The size distribution for the Amalthea ring derived from our in-situ measurements for the small grains agrees very well with the one obtained from images for large grains. Our analysis shows that particles contributing most to the optical cross-section are about 5 micron in radius, in agreement with imaging results. The measurements indicate a large drop in particle flux immediately interior to Thebe's orbit and some detected particles seem to be on highly-tilted orbits with inclinations up to 20 deg.

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arXiv2005

Three-Body Dynamics with Gravitational Wave Emission

We present numerical three-body experiments that include the effects of gravitational radiation reaction by using equations of motion that include the 2.5-order post-Newtonian force terms, which are the leading order terms of energy loss from gravitational waves. We simulate binary-single interactions and show that close approach cross sections for three 1 solar mass objects are unchanged from the purely Newtonian dynamics except for close approaches smaller than 1.0e-5 times the initial semimajor axis of the binary. We also present cross sections for mergers resulting from gravitational radiation during three-body encounters for a range of binary semimajor axes and mass ratios including those of interest for intermediate-mass black holes (IMBHs). Building on previous work, we simulate sequences of high-mass-ratio three-body encounters that include the effects of gravitational radiation. The simulations show that the binaries merge with extremely high eccentricity such that when the gravitational waves are detectable by LISA, most of the binaries will have eccentricities e > 0.9 though all will have circularized by the time they are detectable by LIGO. We also investigate the implications for the formation and growth of IMBHs and find that the inclusion of gravitational waves during the encounter results in roughly half as many black holes ejected from the host cluster for each black hole accreted onto the growing IMBH.

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arXiv2005

Binary Encounters With Supermassive Black Holes: Zero-Eccentricity LISA Events

Current simulations of the rate at which stellar-mass compact objects merge with supermassive black holes (called extreme mass ratio inspirals, or EMRIs) focus on two-body capture by emission of gravitational radiation. The gravitational wave signal of such events will likely involve a significant eccentricity in the sensitivity range of the Laser Interferometer Space Antenna (LISA). We show that tidal separation of stellar-mass compact object binaries by supermassive black holes will instead produce events whose eccentricity is nearly zero in the LISA band. Compared to two-body capture events, tidal separations have a high cross section and result in orbits that have a large pericenter and small apocenter. Therefore, the rate of interactions per binary is high and the resulting systems are very unlikely to be perturbed by other stars into nearly radial plunges. Depending on the fraction of compact objects that are in binaries within a few parsecs of the center, the rate of low-eccentricity LISA events could be comparable to or larger than the rate of high-eccentricity events.

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arXiv2004

Growth of Intermediate-Mass Black Holes in Globular Clusters

We present results of numerical simulations of sequences of binary-single scattering events of black holes in dense stellar environments. The simulations cover a wide range of mass ratios from equal mass objects to 1000:10:10 solar masses and compare purely Newtonian simulations to simulations in which Newtonian encounters are interspersed with gravitational wave emission from the binary. In both cases, the sequence is terminated when the binary's merger time due to gravitational radiation is less than the arrival time of the next interloper. We find that black hole binaries typically merge with a very high eccentricity (0.93 < e < 0.95 pure Newtonian; 0.85 < e < 0.90 with gravitational wave emission) and that adding gravitational wave emission decreases the time to harden a binary until merger by ~ 30% to 40%. We discuss the implications of this work for the formation of intermediate-mass black holes and gravitational wave detection.

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arXiv2003

Three-Body Encounters of Black Holes in Globular Clusters

Evidence has been mounting for the existence of black holes with masses from 10^2 to 10^4 M_Solar associated with stellar clusters. Such intermediate-mass black holes (IMBHs) will encounter other black holes in the dense cores of these clusters. The binaries produced in these interactions will be perturbed by other objects as well thus changing the orbital characteristics of the binaries. These binaries and their subsequent mergers due to gravitational radiation are important sources of gravitational waves. We present the results of numerical simulations of high mass ratio encounters, which help clarify the interactions of intermediate-mass black holes in globular clusters and help determine what types of detectable gravitational wave signatures are likely.

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arXiv2002

Four-Body Effects in Globular Cluster Black Hole Coalescence

In the high density cores of globular clusters, multibody interactions are expected to be common, with the result that black holes in binaries are hardened by interactions. It was shown by Sigurdsson & Hernquist (1993) and others that 10 solar mass black holes interacting exclusively by three-body encounters do not merge in the clusters themselves, because recoil kicks the binaries out of the clusters before the binaries are tight enough to merge. Here we consider a new mechanism, involving four-body encounters. Numerical simulations by a number of authors suggest that roughly 20-50% of binary-binary encounters will eject one star but leave behind a stable hierarchical triple. If the orbital plane of the inner binary is strongly tilted with respect to the orbital plane of the outer object, a secular Kozai resonance, first investigated in the context of asteroids in the Solar System, can increase the eccentricity of the inner body significantly. We show that in a substantial fraction of cases the eccentricity is driven to a high enough value that the inner binary will merge by gravitational radiation, without a strong accompanying kick. Thus the merged object remains in the cluster; depending on the binary fraction of black holes and the inclination distribution of newly-formed hierarchical triples, this mechanism may allow massive black holes to accumulate through successive mergers in the cores of globular clusters. It may also increase the likelihood that stellar-mass black holes in globular clusters will be detectable by their gravitational radiation.

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arXiv2001

Production of Intermediate-Mass Black Holes in Globular Clusters

The discovery of numerous non-nuclear X-ray point sources with luminosities L>10^39 erg/s in several starburst galaxies has stimulated speculation about their nature and origin. The strong variability seen in several sources points to massive black holes as the central engines. If the flux is isotropic, the luminosities range up to roughly 10^41 erg/s, implying masses of M>10^3 Msun if the luminosity is sub-Eddington. Here we explore a model for these sources. We suggest that in some tens of percent of globular clusters a very massive black hole, M>50 Msun, is formed. This black hole sinks in <10^6 yr to the center of the cluster, where in the 10^10 yr lifetime of the cluster it accretes roughly 10^3 Msun, primarily in the form of lighter black holes. Unlike less massive black holes in binaries, which are flung from clusters by recoil before they can merge gravitationally, a >50 Msun black hole has enough inertia that it remains bound to the cluster. We suggest that 10^3 Msun black holes may be common in the centers of dense globular clusters, and may therefore exist in some tens of percent of current globulars. If the cluster later merges with its host galaxy, accretion from young star clusters in molecular clouds by the black hole can generate luminosity consistent with that observed. We also consider the detectability of massive black holes in globular clusters with gravitational wave detectors such as LISA and LIGO, and speculate on future observations that may test our predictions.

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arXiv2000

Implications of the PSR 1257+12 Planetary System for Isolated Millisecond Pulsars

The first extrasolar planets were discovered in 1992 around the millisecond pulsar PSR 1257+12. We show that recent developments in the study of accretion onto magnetized stars, plus the existence of the innermost, moon-sized planet in the PSR 1257+12 system, suggest that the pulsar was born with approximately its current rotation frequency and magnetic moment. If so, this has important implications for the formation and evolution of neutron star magnetic fields as well as for the formation of planets around pulsars. In particular, it suggests that some and perhaps all isolated millisecond pulsars may have been born with high spin rates and low magnetic fields instead of having been recycled by accretion.

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arXiv2000

On the origin of the Trojan asteroids: Effects of Jupiter's mass accretion and radial migration

We present analytic and numerical results which illustrate the effects of Jupiter's accretion of nebular gas and the planet's radial migration on its Trojan companions. Initially, we approximate the system by the planar circular restricted three-body problem and assume small Trojan libration amplitudes. Employing an adiabatic invariant calculation, we show that Jupiter's thirty-fold growth from a $10 M_\oplus$ core to its present mass causes the libration amplitudes of Trojan asteroids to shrink by a factor of about 2.5 to $\sim 40%$ of their original size. The calculation also shows that Jupiter's radial migration has comparatively little effect on the Trojans; inward migration from 6.2 to 5.2 AU causes an increase in Trojan libration amplitudes of $\sim4%$. In each case, the area enclosed by small tadpole orbits, if made dimensionless by using Jupiter's semimajor axis, is approximately conserved. Similar adiabatic invariant calculations for inclined and eccentric Trojans show that Jupiter's mass growth leaves the asteroid's eccentricities and inclinations essentially unchanged, while one AU of inward migration causes an increase in both of these quantities by $\sim 4%$. Numerical integrations confirm and extend these analytic results. We demonstrate that our predictions remain valid for Trojans with small libration amplitudes even when the asteroids have low, but

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