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David Vokrouhlicky

Publications and source records attributed to David Vokrouhlicky.

At least 37 records · Page 2Linked to original sources

Dynamical Implantation of Blue Binaries in the Cold Classical Kuiper Belt

Colors and binarity provide important constraints on the Kuiper belt formation. The cold classical objects at radial distance r=42-47 au from the Sun are predominantly very red (spectral slope s>17%) and often exist as equal-size binaries (~30% observed binary fraction). This has been taken as evidence for the in-situ formation of cold classicals. Interestingly, a small fraction (~10%) of cold classicals is less red with s<17%, and these "blue" bodies are often found in wide binaries. Here we study the dynamical implantation of blue binaries from r<42 au. We find that they can be implanted into the cold classical belt from a wide range of initial radial distances, but the survival of the widest blue binaries -- 2001 QW322 and 2003 UN284 -- implies formation at r>30 au. This would be consistent with the hypothesized less-red to very-red transition at 30<r<40 au. For any reasonable choice of parameters (Neptune's migration history, initial disk profile, etc.), however, our model predicts a predominance of blue singles, rather than blue binaries, which contradicts existing observations. We suggest that wide blue binaries formed in situ at r=42-47 au and their color reflects early formation in a protoplanetary gas disk. The predominantly VR colors of cold classicals may be related to the production of methanol and other hydrocarbons during the late stages of the disk, when the temperature at 45 au dropped to 20 K and carbon monoxide was hydrogenated.

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Clarissa Family Age from the Yarkovsky Effect Chronology

The Clarissa family is a small collisional family composed of primitive C-type asteroids. It is located in a dynamically stable zone of the inner asteroid belt. In this work we determine the formation age of the Clarissa family by modeling planetary perturbations as well as thermal drift of family members due to the Yarkovsky effect. Simulations were carried out using the Swift-rmvs4 integrator modified to account for the Yarkovsky and Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effects. We ran multiple simulations starting with different ejection velocity fields of fragments, varying proportion of initially retrograde spins, and also tested different Yarkovsky/YORP models. Our goal was to match the observed orbital structure of the Clarissa family which is notably asymmetrical in the proper semimajor axis. The best fits were obtained with the initial ejection velocities < ~20 m/s of diameter D=2 km fragments, 4:1 preference for spin-up by YORP, and assuming that 80% of small family members initially had retrograde rotation. The age of the Clarissa family was found to be 56+/-6 Myr for the assumed asteroid density 1.5 g/cm3. Small variation of density to smaller or larger value would lead to slightly younger or older age estimates. This is the first case where the Yarkovsky effect chronology has been successfully applied to an asteroid family younger than 100 Myr.

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OSSOS XX: The Meaning of Kuiper Belt Colors

Observations show that 100-km-class Kuiper belt objects (KBOs) can be divided in (at least) two color groups, hereafter red (R, g-i<1.2) and very red (VR, g-i>1.2), reflecting a difference in their surface composition. This is thought to imply that KBOs formed over a relatively wide range of radial distance, r. The cold classicals at 42 r*, with 30<r*<40 au. The proposed transition at 30<r*<40 au would explain why the VR objects in the dynamically hot population have smaller orbital inclinations than the R objects, because the orbital excitation from Neptune weakens for orbits starting beyond 30 au. Possible causes of the R-VR color bimodality are discussed.

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Cascade disruptions in asteroid clusters

We studied asteroid clusters suggesting a possibility of at least two disruption events in their recent history (< 5 Myr). We searched for new members of known asteroid pairs and clusters and we verified their membership. We found four asteroid clusters, namely the clusters of (11842) Kap'bos, (14627) Emilkowalski, (63440) 2001 MD30 and (157123) 2004 NW5 that show at least two secondary separation events that occurred at significantly different times. We considered a possible formation mechanism for these clusters: The parent of an asteroid cluster was spun up to its critical rotation frequency, underwent a rotation fission and was slowed down by escape of the newly formed secondary/ies. Then the YORP effect spun up the primary again and it reached its critical rotation frequency and underwent another fission. We created a simple model to test whether this scenario is possible for the four clusters. We obtained a good agreement between the model and the cluster properties for the clusters of Kap'bos and (63440). For the cluster of Emilkowalski, the time needed for the primary to reach its critical frequency after the first fission event was predicted to be too long by a factor of several. We suspect, considering also its D type taxonomic classification and the existence of a dust band associated with the cluster, that the asteroid Emilkowalski may actually be a cometary nucleus. For the cluster of (157123), the final rotational frequency of the primary after the last fission event predicted by our model is in a good agreement with the observed rotation frequency of (157123). However, a separation of the older secondary is not possible in our model due to the deficiency of free energy needed for an escape of the large secondary. This could be due to an error in the H value of the secondary or the possibility that we did not find the real primary of this cluster.

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OSSOS IXX: Testing Early Solar System Dynamical Models using OSSOS Centaur Detections

We use published models of the early Solar System evolution with a slow, long-range and grainy migration of Neptune to predict the orbital element distributions and the number of modern-day Centaurs. The model distributions are biased by the OSSOS survey simulator and compared with the OSSOS Centaur detections. We find an excellent match to the observed orbital distribution, including the wide range of orbital inclinations which was the most troublesome characteristic to fit in previous models. A dynamical model, in which the original population of outer disk planetesimals was calibrated from Jupiter Trojans, is used to predict that OSSOS should detect 11+/-4 Centaurs with semimajor axis a<30 au, perihelion distance q>7.5 au and diameter D>10 km (absolute magnitude H_r<13.7 for a 6% albedo). This is consistent with 15 actual OSSOS Centaur detections with H_r<13.7. The population of Centaurs is estimated to be 21,000+/-8,000 for D>10 km. The inner scattered disk at 50 10 km bodies and the Oort cloud should contain (5.0+/-1.9)x10^8 D>10 km comets. Population estimates for different diameter cutoffs can be obtained from the size distribution of Jupiter Trojans (N(>D) proportional to D^(-2.1) for 5<D<100 km). We discuss model predictions for the Large Synoptic Survey Telescope observations of Centaurs.

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Binary Survival in the Outer Solar System

As indicated by their special characteristics, the cold classical Kuiper belt objects (KBOs) formed and survived at 42-47 au. Notably, they show a large fraction of equal-size binaries whose formation is probably related to the accretion of KBOs themselves. These binaries are uncommon in other --hot, resonant, scattered-- populations, which are thought to have been implanted from the massive disk below 30 au to >30 au during Neptune's migration. Here we highlight the possibility that equal-size binaries formed in the disk but were subsequently removed by impacts and/or dynamical effects (e.g., scattering encounters with Neptune). We determine the dependence of these processes on the size and separation of binary components. Our results indicate that tighter binaries, if they formed in the massive disk, have relatively good chances of survival (unless the disk was long-lived). In contrast, the widest binaries in the hot population, such as 2002 VF130, have a very low survival probability (<1%) even if the massive disk was short-lived. They may represent a trace of lucky survivors of a much larger population of the original disk binaries, or they formed at ~30-40~au and dodged the impact- and encounter-related perturbations that we studied here. We find that all known satellites of the largest KBOs would survive during the dynamical implantation of these bodies in the Kuiper belt. The low orbital eccentricities of Pluto's small moons may have been excited by impacts and/or encounters of the Pluto system to Neptune.

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(3200) Phaethon: Bulk density from Yarkovsky drift detection

The recent close approach of the NEA (3200) Phaethon offered a rare opportunity to obtain high-quality observational data. We used the newly obtained optical light curves to improve the spin and shape model of Phaethon and to determine its surface physical properties derived by thermophysical modeling. We also used the available astrometric observations of Phaethon, including those obtained by the Arecibo radar and the Gaia spacecraft, to constrain the secular drift of the orbital semimajor axis. This constraint allowed us to estimate the bulk density by assuming that the drift is dominated by the Yarkovsky effect. We used the convex inversion model to derive the 3D shape model of Phaethon, and a detailed numerical approach for an accurate analysis of the Yarkovsky effect. We obtained a unique solution for Phaethon's pole orientation at $(318,-47)^{\circ}$ ecliptic longitude and latitude (uncertainty of $5^{\circ}$), and confirm the previously reported thermophysical properties ($D=5.1\pm0.2$ km, $Γ=600\pm200$ SI). Phaethon has a top-like shape with possible north-south asymmetry. The characteristic size of the regolith grains is 1-2 cm. The orbit analysis reveals a secular drift of the semimajor axis of $-(6.9\pm1.9)\times 10^{-4}$ au Myr$^{-1}$. With the derived volume-equivalent size of 5.1~km, the bulk density $ρ$ is $1.67\pm0.47$ g cm$^{-3}$. If the size is slightly larger $\sim5.7$ km, as suggested by radar data, $ρ$ would decrease to $1.48\pm0.42$ g cm$^{-3}$. We further investigated the suggestion that Phaethon may be in a cluster with asteroids (155140) 2005 UD and (225416) 1999 YC that was formed by rotational fission of a critically spinning parent body. Phaethon's $ρ$ is consistent with typical values for large ($>100$ km) C-complex asteroids and supports its association with asteroid (2) Pallas. These findings render a cometary origin unlikely for Phaethon.

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Evidence for Very Early Migration of the Solar System Planets from the Patroclus-Menoetius binary Jupiter Trojan

The orbital distribution of trans-Neptunian objects provides strong evidence for the radial migration of Neptune. The outer planets' orbits are thought to have become unstable during the early stages with Jupiter having scattering encounters with a Neptune-class planet. As a consequence, Jupiter jumped inward by a fraction of an au, as required from inner solar system constraints, and obtained its current orbital eccentricity. The timing of these events is often linked to the lunar Late Heavy Bombardment that ended ~700 Myr after the dispersal of the protosolar nebula (t_0). Here we show instead that planetary migration started shortly after t_0. Such early migration is inferred from the survival of the Patroclus-Menoetius binary Jupiter Trojan. The binary formed at t <~ t_0 within a massive planetesimal disk once located beyond Neptune. The longer the binary stayed in the disk, the greater the likelihood that collisions would strip its components from one another. The simulations of its survival indicate that the disk had to have been dispersed by migrating planets within <100 Myr of t_0. This constraint implies that the planetary migration is unrelated to the formation of the youngest lunar basins.

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Debiased orbit and absolute-magnitude distributions for near-Earth objects

The debiased absolute-magnitude and orbit distributions as well as source regions for near-Earth objects (NEOs) provide a fundamental frame of reference for studies of individual NEOs and more complex population-level questions. We present a new four-dimensional model of the NEO population that describes debiased steady-state distributions of semimajor axis, eccentricity, inclination, and absolute magnitude $H$ in the range $17<H<25$. The modeling approach improves upon the methodology originally developed by Bottke et al. (2000; Science 288, 2190-2194) in that it is, for example, based on more realistic orbit distributions and uses source-specific absolute-magnitude distributions that allow for a power-law slope that varies with $H$. We divide the main asteroid belt into six different entrance routes or regions (ER) to the NEO region: the $ν_6$, 3:1J, 5:2J and 2:1J resonance complexes as well as Hungarias and Phocaeas. In addition we include the Jupiter-family comets as the primary cometary source of NEOs. We calibrate the model against NEO detections by Catalina Sky Surveys' stations 703 and G96 during 2005-2012, and utilize the complementary nature of these two systems to quantify the systematic uncertainties associated to the resulting model. The most important ERs are the $ν_6$ and 3:1J resonance complexes with JFCs contributing a few percent of NEOs on average. We predict that there are $962^{+52}_{-56}$ ($802^{+48}_{-42}\times10^3$) NEOs with $H<17.75$ ($H<25$) and these numbers are in agreement with the most recent estimates found in the literature (the uncertainty estimates only account for the random component).

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Bi-lobed Shape of Comet 67P from a Collapsed Binary

The Rosetta spacecraft observations revealed that the nucleus of comet 67P/Churyumov-Gerasimenko consists of two similarly sized lobes connected by a narrow neck. Here we evaluate the possibility that 67P is a collapsed binary. We assume that the progenitor of 67P was a binary and consider various physical mechanisms that could have brought the binary components together, including small-scale impacts and gravitational encounters with planets. We find that 67P could be a primordial body (i.e., not a collisional fragment) if the outer planetesimal disk lasted <10 Myr before it was dispersed by migrating Neptune. The probability of binary collapse by impact is 30% for tightly bound binaries. Most km-class binaries become collisionally dissolved. Roughly 10% of the surviving binaries later evolve to become contact binaries during the disk dispersal, when bodies suffer gravitational encounters to Neptune. Overall, the processes described in this work do not seem to be efficient enough to explain the large fraction (~67%) of bi-lobed cometary nuclei inferred from spacecraft imaging.

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The random walk of cars and their collision probabilities with planets

On February 6th, 2018 SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster's orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant.

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The orbital distribution of trans-Neptunian objects beyond 50 au

The dynamical structure of the Kuiper belt beyond 50 au is not well understood. Here we report results of a numerical model with long-range, slow and grainy migration of Neptune. The model implies that bodies scattered outward by Neptune to semimajor axes a>50 au often evolve into resonances which subsequently act to raise the perihelion distances of orbits to q>40 au. The implication of the model is that the orbits with 50 40 au should cluster near (but not in) the resonances with Neptune (3:1 at a=62.6 au, 4:1 at a=75.9 au, 5:1 at a=88.0 au, etc.). The recent detection of several distant Kuiper Belt Objects (KBOs) near resonances is consistent with this prediction, but it is not yet clear whether the orbits are really non-resonant as our model predicts. We estimate from the model that there should presently be ~1600-2400 bodies at the 3:1 resonance and ~1000-1400 bodies at the 4:1 resonance (for q>40 au and diameters D>100 km). These results favorably compare with the population census of distant KBOs inferred from existing observations.

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Neptune's Orbital Migration Was Grainy, Not Smooth

The Kuiper belt is a population of icy bodies beyond the orbit of Neptune. The complex orbital structure of the Kuiper belt, including several categories of objects inside and outside of resonances with Neptune, emerged as a result of Neptune's migration into an outer planetesimal disk. An outstanding problem with the existing migration models is that they invariably predict excessively large resonant populations, while observations show that the non-resonant orbits are in fact common (e.g., the main belt population is 2-4 times larger than Plutinos in the 3:2 resonance). Here we show that this problem can resolved if it is assumed that Neptune's migration was grainy, as expected from scattering encounters of Neptune with massive planetesimals. The grainy migration acts to destabilize resonant bodies with large libration amplitudes, a fraction of which ends up on stable non-resonant orbits. Thus, the non-resonant--to--resonant ratio obtained with the grainy migration is higher, up to ~10 times higher for the range of parameters investigated here, than in a model with smooth migration. The grainy migration leads to a narrower distribution of the libration amplitudes in the 3:2 resonance. The best fit to observations is obtained when it is assumed that the outer planetesimal disk below 30 AU contained 1000-4000 Plutos, or ~1000 bodies twice as massive as Pluto. We find that the probability for an outer disk object to end up on a stable orbit in the Kuiper belt is ~10^{-3}. Together, these results are consistent with having only two (known) Pluto-mass bodies in the Kuiper belt today (Pluto and Eris). The combined mass of Pluto-class objects in the original disk was ~2-8 Earth masses (M_Earth), which represents 10-40% of the estimated disk mass (M_disk ~ 20 M_Earth).

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Tilting Jupiter (a bit) and Saturn (a lot) During Planetary Migration

We study the effects of planetary late migration on the gas giants obliquities. We consider the planetary instability models from Nesvorny & Morbidelli (2012), in which the obliquities of Jupiter and Saturn can be excited when the spin-orbit resonances occur. The most notable resonances occur when the $s_7$ and $s_8$ frequencies, changing as a result of planetary migration, become commensurate with the precession frequencies of Jupiter's and Saturn's spin vectors. We show that Jupiter may have obtained its present obliquity by crossing of the $s_8$ resonance. This would set strict constrains on the character of migration during the early stage. Additional effects on Jupiter's obliquity are expected during the last gasp of migration when the $s_7$ resonance was approached. The magnitude of these effects depends on the precise value of the Jupiter's precession constant. Saturn's large obliquity was likely excited by capture into the $s_8$ resonance. This probably happened during the late stage of planetary migration when the evolution of the $s_8$ frequency was very slow, and the conditions for capture into the spin-orbit resonance with $s_8$ were satisfied. However, whether or not Saturn is in the spin-orbit resonance with $s_8$ at the present time is not clear, because the existing observations of Saturn's spin precession and internal structure models have significant uncertainties.

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Excitation of the Orbital Inclination of Iapetus during Planetary Encounters

Saturn's moon Iapetus has an orbit in a transition region where the Laplace surface is bending from the equator to the orbital plane of Saturn. The orbital inclination of Iapetus to the local Laplace plane is ~8 deg, which is unexpected, because the inclination should be ~0 if Iapetus formed from a circumplanetary disk on the Laplace surface. It thus appears that some process has pumped up Iapetus's inclination while leaving its eccentricity near zero (e=0.03 at present). Here we examined the possibility that Iapetus's inclination was excited during the early solar system instability when encounters between Saturn and ice giants occurred. We found that the dynamical effects of planetary encounters on Iapetus's orbit sensitively depend on the distance of the few closest encounters. In four out of ten instability cases studied here, the orbital perturbations were too large to be plausible. In one case, Iapetus's orbit was practically unneffected. In the remaining five cases, the perturbations of Iapetus's inclination were adequate to explain its present value. In three of these cases, however, Iapetus's eccentricity was excited to 0.1-0.25, and it is not clear whether it could have been damped to its present value (0.03) by some subsequent process (e.g., tides and dynamical friction from captured irregular satellites do not seem to be strong enough). Our results therefore imply that only 2 out of 10 instability cases (~20%) can excite Iapetus's inclination to its present value (~30% of trials lead to >5 deg) while leaving its orbital eccentricity low.

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Transit timing variations for planets coorbiting in the horseshoe regime

While not detected yet, pairs of exoplanets in the 1:1 mean motion resonance probably exist. Low eccentricity, near-planar orbits, which in the comoving frame follow the horseshoe trajectories, are one of the possible stable configurations. Here we study transit timing variations produced by mutual gravitational interaction of planets in this orbital architecture, with the goal to develop methods that can be used to recognize this case in observational data. In particular, we use a semi-analytic model to derive parametric constraints that should facilitate data analysis. We show that characteristic traits of the transit timing variations can directly constrain the (i) ratio of planetary masses, and (ii) their total mass (divided by that of the central star) as a function of the minimum angular separation as seen from the star. In an ideal case, when transits of both planets are observed and well characterized, the minimum angular separation can also be inferred from the data. As a result, parameters derived from the observed transit timing series alone can directly provide both planetary masses scaled to the central star mass.

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The Effect of Conjunctions on the Transit Timing Variations of Exoplanets

We develop an analytic model for transit timing variations produced by orbital conjunctions between gravitationally interacting planets. If the planetary orbits have tight orbital spacing, which is a common case among the Kepler planets, the effect of a single conjunction can be best described as: (1) a step-like change of the transit timing ephemeris with subsequent transits of the inner planet being delayed and those of the outer planet being sped up, and (2) a discrete change in sampling of the underlying oscillations from eccentricity-related interaction terms. In the limit of small orbital eccentricities, our analytic model gives explicit equations for these effects as a function of the mass and orbital separation of planets. We point out that a detection of the conjunction effect in real data is of crucial importance for the physical characterization of planetary systems from transit timing variations.

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Orbit and Bulk Density of the OSIRIS-REx Target Asteroid (101955) Bennu

The target asteroid of the OSIRIS-REx asteroid sample return mission, (101955) Bennu (formerly 1999 RQ$_{36}$), is a half-kilometer near-Earth asteroid with an extraordinarily well constrained orbit. An extensive data set of optical astrometry from 1999--2013 and high-quality radar delay measurements to Bennu in 1999, 2005, and 2011 reveal the action of the Yarkovsky effect, with a mean semimajor axis drift rate $da/dt = (-19.0 \pm 0.1)\times 10^{-4}$ au/Myr or $284\pm 1.5\;\rm{m/yr}$. The accuracy of this result depends critically on the fidelity of the observational and dynamical model. As an example, neglecting the relativistic perturbations of the Earth during close approaches affects the orbit with $3σ$ significance in $da/dt$. The orbital deviations from purely gravitational dynamics allow us to deduce the acceleration of the Yarkovsky effect, while the known physical characterization of Bennu allows us to independently model the force due to thermal emissions. The combination of these two analyses yields a bulk density of $ρ= 1260\pm70\,\rm{kg/m^3}$, which indicates a macroporosity in the range $40\pm10$% for the bulk densities of likely analog meteorites, suggesting a rubble-pile internal structure. The associated mass estimate is $(7.8\pm0.9)\times 10^{10}\, \rm{kg}$ and $GM = 5.2\pm0.6\,\rm{m^3/s^2}$. Bennu's Earth close approaches are deterministic over the interval 1654--2135, beyond which the predictions are statistical in nature. In particular, the 2135 close approach is likely within the lunar distance and leads to strong scattering and therefore numerous potential impacts in subsequent years, from 2175--2196. The highest individual impact probability is $9.5\times 10^{-5}$ in 2196, and the cumulative impact probability is $3.7\times 10^{-4}$, leading to a cumulative Palermo Scale of -1.70.

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