arXiv subjects

David Vokrouhlicky

Publications and source records attributed to David Vokrouhlicky.

51 records · Page 3Linked to original sources

arXiv2013

Stress field and spin axis relaxation for inelastic triaxial ellipsoids

A compact formula for the stress tensor inside a self-gravitating, triaxial ellipsoid in an arbitrary rotation state is given. It contains no singularity in the incompressible medium limit. The stress tensor and the quality factor model are used to derive a solution for the energy dissipation resulting in the damping (short axis mode) or excitation (long axis) of wobbling. In the limit of an ellipsoid of revolution, we compare our solution with earlier ones and show that, with appropriate corrections, the differences in damping times estimates are much smaller than it has been claimed. This version implements corrections of misprints found in the MNRAS published text.

astro-ph.EP↗

arXiv2013

Capture of Trojans by Jumping Jupiter

Jupiter Trojans are thought to be survivors of a much larger population of planetesimals that existed in the planetary region when planets formed. They can provide important constraints on the mass and properties of the planetesimal disk, and its dispersal during planet migration. Here we tested a possibility that the Trojans were captured during the early dynamical instability among the outer planets (aka the Nice model), when the semimajor axis of Jupiter was changing as a result of scattering encounters with an ice giant. The capture occurs in this model when Jupiter's orbit and its Lagrange points become radially displaced in a scattering event and fall into a region populated by planetesimals (that previously evolved from their natal transplanetary disk to ~5 AU during the instability). Our numerical simulations of the new capture model, hereafter jump capture, satisfactorily reproduce the orbital distribution of the Trojans and their total mass. The jump capture is potentially capable of explaining the observed asymmetry in the number of leading and trailing Trojans. We find that the capture probability is (6-8)x10^-7 for each particle in the original transplanetary disk, implying that the disk contained (3-4)x10^7 planetesimals with absolute magnitude H<9 (corresponding to diameter D=80 km for a 7% albedo). The disk mass inferred from this work, M_disk=14-28 M_Earth, is consistent with the mass deduced from recent dynamical simulations of the planetary instability.

astro-ph.EP↗

arXiv2011

Spin vector and shape of (6070) Rheinland and their implications

Main belt asteroids (6070) Rheinland and (54827) 2001NQ8 belong to a small population of couples of bodies which reside on very similar heliocentric orbits. Vokrouhlicky & Nesvorny (2008, AJ 136, 280) promoted a term "asteroid pairs", pointing out their common origin within the past tens to hundreds of ky. Previous attempts to reconstruct the initial configuration of Rheinland and 2001NQ8 at the time of their separation have led to the prediction that Rheinland's rotation should be retrograde. Here we report extensive photometric observations of this asteroid and use the lightcurve inversion technique to directly determine its rotation state and shape. We confirm the retrograde sense of rotation of Rheinland, with obliquity value constrained to be >= 140 deg. The ecliptic longitude of the pole position is not well constrained as yet. The asymmetric behavior of Rheinland's lightcurve reflects a sharp, near-planar edge in our convex shape representation of this asteroid. Our calibrated observations in the red filter also allow us to determine $H_R = 13.68\pm 0.05$ and $G = 0.31\pm 0.05$ values of the H-G system. With the characteristic color index $V-R = 0.49\pm 0.05$ for the S-type asteroids, we thus obtain $H = 14.17\pm 0.07$ for the absolute magnitude of (6070) Rheinland. This a significantly larger value than previously obtained from analysis of the astrometric survey observations. We next use the obliquity constraint for Rheinland to eliminate some degree of uncertainty in the past propagation of its orbit. This is because the sign of the past secular change of its semimajor axis due to the Yarkovsky effect is now constrained. Determination of the rotation state of the secondary component, asteroid (54827) 2001NQ8, is the key element in further constraining the age of the pair and its formation process.

astro-ph.EP↗

arXiv2011

Dynamics of Dust Particles Released from Oort Cloud Comets and Their Contribution to Radar Meteors

The Oort Cloud Comets (OCCs), exemplified by the Great Comet of 1997 (Hale-Bopp), are occasional visitors from the heatless periphery of the solar system. Previous works hypothesized that a great majority of OCCs must physically disrupt after one or two passages through the inner solar system, where strong thermal gradients can cause phase transitions or volatile pressure buildup. Here we study the fate of small debris particles produced by OCC disruptions to determine whether the imprints of a hypothetical population of OCC meteoroids can be found in the existing meteor radar data. We find that OCC particles with diameters D<10 um are blown out from the solar system by radiation pressure, while those with D>1 um have a very low Earth-impact probability. The intermediate particle sizes, D=100 um, represent a sweet spot. About 1% of these particles orbitally evolve by Poynting-Robertson drag to reach orbits with semimajor axis a=1 AU. They are expected to produce meteors with radiants near the apex of the Earth's orbital motion. We find that the model distributions of their impact speeds and orbits provide a good match to radar observations of apex meteors, except for the eccentricity distribution, which is more skewed toward e=1 in our model. Finally, we propose an explanation for the long-standing problem in meteor science related to the relative strength of apex and helion/antihelion sources. As we show in detail, the observed trend, with the apex meteors being more prominent in observations of highly sensitive radars, can be related to orbital dynamics of particles released on the long-period orbits.

astro-ph.EP↗

arXiv2011

Dynamical Model for the Zodiacal Cloud and Sporadic Meteors

The solar system is dusty, and would become dustier over time as asteroids collide and comets disintegrate, except that small debris particles in interplanetary space do not last long. They can be ejected from the solar system by Jupiter, thermally destroyed near the Sun, or physically disrupted by collisions. Also, some are swept by the Earth (and other planets), producing meteors. Here we develop a dynamical model for the solar system meteoroids and use it to explain meteor radar observations. We find that the Jupiter Family Comets (JFCs) are the main source of the prominent concentrations of meteors arriving to the Earth from the helion and antihelion directions. To match the radiant and orbit distributions, as measured by the Canadian Meteor Orbit Radar (CMOR) and Advanced Meteor Orbit Radar (AMOR), our model implies that comets, and JFCs in particular, must frequently disintegrate when reaching orbits with low perihelion distance. Also, the collisional lifetimes of millimeter particles may be longer (>10^5 yr at 1 AU) than postulated in the standard collisional models (10^4 yr at 1 AU), perhaps because these chondrule-sized meteoroids are stronger than thought before. Using observations of the Infrared Astronomical Satellite (IRAS) to calibrate the model, we find that the total cross section and mass of small meteoroids in the inner solar system are (1.7-3.5)x10^11 km^2 and 4x10^19 g, respectively, in a good agreement with previous studies. The mass input required to keep the Zodiacal Cloud (ZC) in a steady state is estimated to be 10^4-10^5 kg/s. The input is up to 10 times larger than found previously, mainly because particles released closer to the Sun have shorter collisional lifetimes, and need to be supplied at a faster rate.

astro-ph.EP↗

arXiv2011

Secular theory of the orbital evolution of the young stellar disc in the Galactic Centre

We investigate the orbital evolution of a system of N mutually interacting stars on initially circular orbits around the dominating central mass. We include perturbative influence of a distant axisymmetric source and an extended spherical potential. In particular, we focus on the case when the secular evolution of orbital eccentricities is suppressed by the spherical perturbation. By means of standard perturbation methods, we derive semi-analytic formulae for the evolution of normal vectors of the individual orbits. We find its two qualitatively different modes. Either the orbits interact strongly and, under such circumstances, they become dynamically coupled, precessing synchronously in the potential of the axisymmetric perturbation. Or, if their mutual interaction is weaker, the orbits precess independently, interchanging periodically their angular momentum, which leads to oscillations of inclinations. We argue that these processes may have been fundamental for the evolution of the disc of young stars orbiting the supermassive black hole in the centre of the Milky Way.

astro-ph.GA↗

arXiv2011

Observed Binary Fraction Sets Limits on the Extent of Collisional Grinding in the Kuiper Belt

The size distribution in the cold classical Kuiper belt can be approximated by two idealized power laws: one with steep slope for radii R>R* and one with shallow slope for R<R*, where R*~25-50 km. Previous works suggested that the SFD roll-over at R* can be the result of extensive collisional grinding in the Kuiper belt that led to the catastrophic disruption of most bodies with R<R*. Here we use a new code to test the effect of collisions in the Kuiper belt. We find that the observed roll-over could indeed be explained by collisional grinding provided that the initial mass in large bodies was much larger than the one in the present Kuiper belt, and was dynamically depleted. In addition to the size distribution changes, our code also tracks the effects of collisions on binary systems. We find that it is generally easier to dissolve wide binary systems, such as the ones existing in the cold Kuiper belt today, than to catastrophically disrupt objects with R~R*. Thus, the binary survival sets important limits on the extent of collisional grinding in the Kuiper belt. We find that the extensive collisional grinding required to produce the SFD roll-over at R* would imply a strong gradient of the binary fraction with R and separation, because it is generally easier to dissolve binaries with small components and/or those with wide orbits. The expected binary fraction for R<R* is <0.1. The present observational data do not show such a gradient. Instead, they suggest a large binary fraction of ~0.4 for R=30-40 km. This may indicate that the roll-over was not produced by disruptive collisions, but is instead a fossil remnant of the KBO formation process.

astro-ph.EP↗

arXiv2010

YORP effect with anisotropic radiation

The influence of optical scattering and thermal radiation models an the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect is studied. Lambertian formulation is compared with Hapke scattering and emission laws and Lommel-Seeliger reflection. Although the form of reflectivity function strongly influences mean torques due to scattering or thermal radiation alone, their combined contribution to the rotation period YORP is not much different from the standard Lambertian values. For higher albedo values the differences between the Hapke and Lambert models become significant for the YORP in attitude.

astro-ph.EP↗

arXiv2010

Do Planetary Encounters Reset Surfaces of Near Earth Asteroids?

Processes such as the solar wind sputtering and micrometeorite impacts can modify optical properties of surfaces of airless bodies. This explains why spectra of the main belt asteroids, exposed to these `space weathering' processes over eons, do not match the laboratory spectra of ordinary chondrite (OC) meteorites. In contrast, an important fraction of Near Earth Asteroids (NEAs), defined as Q-types in the asteroid taxonomy, display spectral attributes that are a good match to OCs. Here we study the possibility that the Q-type NEAs underwent recent encounters with the terrestrial planets and that the tidal gravity (or other effects) during these encounters exposed fresh OC material on the surface (thus giving it the Q-type spectral properties). We used numerical integrations to determine the statistics of encounters of NEAs to planets. The results were used to calculate the fraction and orbital distribution of Q-type asteroids expected in the model as a function of the space weathering timescale, t_sw (see main text for definition), and maximum distance, r*, at which planetary encounters can reset the surface. We found that t_sw ~ 1e6 yr (at 1 AU) and r* ~ 5 R_pl, where R_pl is the planetary radius, best fit the data. Values t_sw < 1e5 yr would require that r* > 20 R_pl, which is probably implausible because these very distant encounters should be irrelevant. Also, the fraction of Q-type NEAs would be probably much larger than the one observed if t_sw > 1e7 yr. We found that t_sw ~ q^2, where q is the perihelion distance, expected if the solar wind sputtering controls t_sw, provides a better match to the orbital distribution of Q-type NEAs than models with fixed t_sw. We also discuss how the Earth magnetosphere and radiation effects such as YORP can influence the spectral properties of NEAs.

astro-ph.EP↗

arXiv2010

Searching for Trojan Asteroids in the HD 209458 System: Space-based MOST Photometry and Dynamical Modeling

We have searched Microvariability and Oscillations of STars (MOST) satellite photometry obtained in 2004, 2005, and 2007 of the solar-type star HD 209458 for Trojan asteroid swarms dynamically coupled with the system's transiting "hot Jupiter" HD 209458b. Observations of the presence and nature of asteroids around other stars would provide unique constraints on migration models of exoplanetary systems. Our results set an upper limit on the optical depth of Trojans in the HD 209458 system that can be used to guide current and future searches of similar systems by upcoming missions. Using cross-correlation methods with artificial signals implanted in the data, we find that our detection limit corresponds to a relative Trojan transit depth of 1\times10-4, equivalent to ~1 lunar mass of asteroids, assuming power-law Trojan size distributions similar to Jupiter's Trojans in our solar system. We confirm with dynamical interpretations that some asteroids could have migrated inward with the planet to its current orbit at 0.045 AU, and that the Yarkovsky effect is ineffective at eliminating objects of > 1 m in size. However, using numerical models of collisional evolution we find that, due to high relative speeds in this confined Trojan environment, collisions destroy the vast majority of the asteroids in <10 Myr. Our modeling indicates that the best candidates to search for exoTrojan swarms in 1:1 mean resonance orbits with "hot Jupiters" are young systems (ages of about 1 Myr or less). Years of Kepler satellite monitoring of such a system could detect an asteroid swarm with a predicted transit depth of 3\times10-7.

astro-ph.SR↗

arXiv2009

Cometary Origin of the Zodiacal Cloud and Carbonaceous Micrometeorites

The zodiacal cloud is a thick circumsolar disk of small debris particles produced by asteroid collisions and comets. Here, we present a zodiacal cloud model based on the orbital properties and lifetimes of comets and asteroids, and on the dynamical evolution of dust after ejection. The model is quantitatively constrained by IRAS observations of thermal emission, but also qualitatively consistent with other zodiacal cloud observations. We find that 85-95% of the observed mid-infrared emission is produced by particles from the Jupiter-family comets (JFCs) and $<$10% by dust from long period comets. Asteroidal dust is found to be present at $<$10%. We suggest that spontaneous disruptions of JFCs, rather than the usual cometary activity driven by sublimating volatiles, is the main mechanism that librates cometary particles into the zodiacal cloud. Our results imply that JFC particles represent $\sim$85% of the total mass influx at Earth. Since their atmospheric entry speeds are typically low ($\approx$14.5 km s$^{-1}$ mean for D=100-200 $μ$m with $\approx$12 km s$^{-1}$ being the most common case), many JFC grains should survive frictional heating and land on the Earth's surface. This explains why most micrometeorites collected in antarctic ice have primitive carbonaceous composition. The present mass of the inner zodiacal cloud at $<$5 AU is estimated to be 1-$2\times10^{19}$ g, mainly in D=100-200 $μ$m particles. The inner zodiacal cloud should have been $>10^4$ times brighter during the Late Heavy Bombardment (LHB) epoch $\approx$3.8 Gyr ago, when the outer planets scattered numerous comets into the inner solar system. The bright debris disks with a large 24-$μ$m excess observed around mature stars may be an indication of massive cometary populations existing in those systems.

astro-ph.EP↗

arXiv2008

On a Scattered-Disk Origin for the 2003 El61 Collisional Family - an Example of the Importance of Collisions on the Dynamics of Small Bodies

The recent discovery of the 2003EL61 collisional family in the Kuiper belt (Brown et al., 2007) is surprising because the formation of such a family is a highly improbable event in today's belt. Assuming Brown et al.'s estimate of the size of progenitors, we find that the probability that a Kuiper belt object was involved in such a collision since primordial times is less than roughly 0.001. In addition, it is not possible for the collision to have occurred in a massive primordial Kuiper belt because the dynamical coherence of the family would not have survived whatever event produced the currently observed orbital excitation. Here we suggest that the family is the result of a collision between two scattered disk objects. We show that the probability that a collision occurred between two such objects with sizes similar to those advocated in Brown et al. (2007) and that the center of mass of the resulting family is on an orbit typical of the Kuiper belt can be as large as 47%. Given the large uncertainties involved in this estimate, this result is consistent with the existence of one such family. If true, this result has implications far beyond the origin of a single collisional family, because it shows that collisions played an important role in shaping the dynamical structure of the small body populations that we see today.

astro-ph↗

arXiv1996

Testing for gravitationally preferred directions using the lunar orbit

As gravity is a long-range force, it is {\it a priori} conceivable that the Universe's global matter distribution select a preferred rest frame for local gravitational physics. At the post-Newtonian approximation, the phenomenology of preferred-frame effects is described by two parameters, $α_1$ and $α_2$, the second of which is already very tightly constrained. Confirming previous suggestions, we show through a detailed Hill-Brown type calculation of a perturbed lunar orbit that lunar laser ranging data have the potential of constraining $α_1$ at the $10^{-4}$ level. It is found that certain retrograde planar orbits exhibit a resonant sensitivity to external perturbations linked to a fixed direction in space. The lunar orbit being quite far from such a resonance exhibits no significant enhancement due to solar tides. Our Hill-Brown analysis is extended to the perturbation linked to a possible differential acceleration toward the galactic center. It is, however, argued that there are strong {\it a priori} theoretical constraints on the conceivable magnitude of such an effect.

gr-qc↗

arXiv1995

The Equivalence Principle and the Moon

The perturbation of the lunar motion caused by a hypothetical violation of the equivalence principle is analytically worked out in terms of power series à la Hill-Brown. The interaction with the quadrupolar tide is found to amplify the leading order term in the synodic range oscillation by more than 62\%. Confirming a recent suggestion of Nordtvedt, we find that this amplification has a pole singularity for an orbit beyond the lunar orbit. This singularity is shown to correspond to the critical prograde orbit beyond which, as found by Hénon, Hill's periodic orbit becomes exponentially unstable. It is suggested that ranging between prograde and retrograde orbits around outer planets might provide future high precision orbital tests of the equivalence principle. It is argued that, within the context of string-derived non-Einsteinian theories, the theoretical significance of orbital tests of the universality of free fall is to measure the basic coupling strength of some scalar field through composition-dependent effects. Present Lunar Laser Ranging data yield the value $\barγ = (-1.2\pm 1.7) \times 10^{-7}$ for the effective Eddington parameter $\barγ \equiv γ-1$ measuring this coupling strength.

gr-qc↗

arXiv1995

Conservation laws for systems of extended bodies in the first post-Newtonian approximation.

The general form of the global conservation laws for $N$-body systems in the first post-Newtonian approximation of general relativity is considered. Our approach applies to the motion of an isolated system of $N$ arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies and uses a framework recently introduced by Damour, Soffel and Xu (DSX). We succeed in showing that seven of the first integrals of the system (total mass-energy, total dipole mass moment and total linear momentum) can be broken up into a sum of contributions which can be entirely expressed in terms of the basic quantities entering the DSX framework: namely, the relativistic individual multipole moments of the bodies, the relativistic tidal moments experienced by each body, and the positions and orientations with respect to the global coordinate system of the local reference frames attached to each body. On the other hand, the total angular momentum of the system does not seem to be expressible in such a form due to the unavoidable presence of irreducible nonlinear gravitational effects.

gr-qc↗