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Renu Malhotra

Publications and source records attributed to Renu Malhotra.

At least 55 records · Page 3Linked to original sources
arXiv2020

Observational Completion Limit of Minor Planets from the Asteroid Belt to Jupiter Trojans

With the growing numbers of asteroids being discovered, identifying an observationally complete sample is essential for statistical analyses and for informing theoretical models of the dynamical evolution of the solar system. We present an easily implemented method of estimating the empirical observational completeness in absolute magnitude, H_lim, as a function of semi-major axis. Our method requires fewer assumptions and decisions to be made in its application, making results more transportable and reproducible amongst studies that implement it, as well as scalable to much larger datasets of asteroids expected in the next decade with the Vera C.~Rubin Observatory's Legacy Survey of Space and Time (LSST). Using the values of H_lim(a) determined at high resolution in semimajor axis, a, we demonstrate that the observationally complete sample size of the main belt asteroids is larger by more than a factor of 2 compared to using a conservative single value of H_lim, an approach often adopted in previous studies. Additionally, by fitting a simple, physically motivated model of H_lim(a) to 7e5 objects in the Minor Planet Database, our model reveals statistically significant deviations between the main belt and the asteroid populations beyond the main belt (Hungarias, Hildas and Trojans), suggesting potential demographic differences, such as in their size, eccentricity or inclination distributions.

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arXiv2020

The Scientific Impact of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) for Solar System Science

Vera C. Rubin Observatory will be a key facility for small body science in planetary astronomy over the next decade. It will carry out the Legacy Survey of Space and Time (LSST), observing the sky repeatedly in u, g, r, i, z, and y over the course of ten years using a 6.5 m effective diameter telescope with a 9.6 square degree field of view, reaching approximately r = 24.5 mag (5-σ depth) per visit. The resulting dataset will provide extraordinary opportunities for both discovery and characterization of large numbers (10--100 times more than currently known) of small solar system bodies, furthering studies of planetary formation and evolution. This white paper summarizes some of the expected science from the ten years of LSST, and emphasizes that the planetary astronomy community should remain invested in the path of Rubin Observatory once the LSST is complete.

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arXiv2020

A disk-driven resonance as the origin of high inclinations of close-in planets

The recent characterization of transiting close-in planets has revealed an intriguing population of sub-Neptunes with highly tilted and even polar orbits relative to their host star's equator. Any viable theory for the origin of these close-in, polar planets must explain (1) the observed stellar obliquities, (2) the substantial eccentricities, and (3) the existence of Jovian companions with large mutual inclinations. In this work, we propose a theoretical model that satisfies these requirements without invoking tidal dissipation or large primordial inclinations. Instead, tilting is facilitated by the protoplanetary disk dispersal during the late stage of planet formation, initiating a process of resonance sweeping and parametric instability. This mechanism consists of two steps. First, a nodal secular resonance excites the inclination to large values; then, once the inclination reaches a critical value, a linear eccentric instability is triggered, which detunes the resonance and ends inclination growth. The critical inclination is pushed to high values by general relativistic precession, making polar orbits an inherently post-Newtonian outcome. Our model predicts that polar, close-in sub-Neptunes coexist with cold Jupiters in low stellar obliquity orbits.

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arXiv2020

Dynamical instabilities in systems of multiple short-period planets are likely driven by secular chaos: a case study of Kepler-102

We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in $\sim20\%$ of the cases on a wide range of timescales (up to $5\times10^9$ orbits) and over an unexpectedly wide range of initial dynamical spacings. To identify the triggers of long-term instability in multi-planet systems, we investigated in detail the five-planet Kepler-102 system. Despite having several near-resonant period ratios, we find that mean motion resonances are unlikely to directly cause instability for plausible planet masses in this system. Instead, we find strong evidence that slow inward transfer of angular momentum deficit (AMD) via secular chaos excites the eccentricity of the innermost planet, Kepler-102 b, eventually leading to planet-planet collisions in $\sim80\%$ of Kepler-102 simulations. Kepler-102 b likely has a mass $>\sim0.1M_{\oplus}$, hence a bulk density exceeding about half Earth's, in order to avoid dynamical instability. To investigate the role of secular chaos in our wider set of simulations, we characterize each planetary system's AMD evolution with a "spectral fraction" calculated from the power spectrum of short integrations ($\sim5\times10^6$ orbits). We find that small spectral fractions ($\lesssim0.01$) are strongly associated with dynamical stability on long timescales ($5\times10^9$ orbits) and that the median time to instability decreases with increasing spectral fraction. Our results support the hypothesis that secular chaos is the driver of instabilities in many non-resonant multi-planet systems, and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long term (in)stability of multi-planet systems from short simulations.

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arXiv2020

On the Divergence of First Order Resonance Widths at Low Eccentricities

Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first order mean motion resonances diverge for nearly circular orbits. Here we examine the nature of this divergence with a non-perturbative analysis of a few first order resonances interior to a Jupiter-mass planet. We show that a first order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centers of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of "bridges" between adjacent first order resonances: at low eccentricities, the apocentric libration zone of a first order resonance smoothly connects with the pericentric libration zone of the neighboring first order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low eccentricity regime.

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arXiv2020

Lunar close encounters compete with the circumterrestrial Lidov-Kozai effect

Luna 3 (or Lunik 3 in Russian sources) was the first spacecraft to perform a flyby of the Moon. Launched in October 1959 on a translunar trajectory with large semi-major axis and eccentricity, it collided with the Earth in late March 1960. The short, 6-month dynamical lifetime has often been explained through an increase in eccentricity due to the Lidov-Kozai effect. However, the classical Lidov-Kozai solution is only valid in the limit of small semi-major axis ratio, a condition that is satisfied only for solar (but not for lunar) perturbations. We undertook a study of the dynamics of Luna 3 with the aim of assessing the principal mechanisms affecting its evolution. We analyze the Luna 3 trajectory by generating accurate osculating solutions, and by comparing them to integrations of singly- and doubly-averaged equations of motion in vectorial form. Lunar close encounters, which cannot be reproduced in an averaging approach, decisively affect the trajectory and break the doubly-averaged dynamics. Solar perturbations induce oscillations of intermediate period that affect the geometry of the close encounters and cause the singly-averaged and osculating inclinations to change quadrants (the orbital plane ``flips''). We find that the peculiar evolution of Luna 3 can only be explained by taking into account lunar close encounters and intermediate-period terms; such terms are averaged out in the Lidov-Kozai solution, which is not adequate to describe translunar or cislunar trajectories. Understanding the limits of the Lidov-Kozai solution is of particular significance for the motion of objects in the Earth-Moon environment and of exoplanetary systems.

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arXiv2020

Assessing and Minimizing Collisions in Satellite Mega-Constellations

We aim to provide satellite operators and researchers with an efficient means for evaluating and mitigating collision risk during the design process of mega-constellations. We first establish a baseline for evaluating various techniques for close-encounter prediction and collision-probability calculation (Hoots et al. 1984, Gronchi 2005, JeongAhn and Malhotra 2015) by carrying out brute-force numerical simulations and using a sequence of filters to greatly reduce the computational expense of the algorithm. Next, we estimate conjunction events in the orbital environment following the anticipated deployments of the OneWeb LEO and SpaceX Starlink mega-constellations. As a final step, we investigate Minimum Space Occupancy (MiSO) orbits (Bombardelli et al. 2018), a generalization of the well-known frozen orbits that account for the perturbed-Keplerian dynamics of the Earth-Moon-Sun-satellite system. We evaluate the ability of MiSO configurations of the proposed mega-constellations, as suggested by Bombardelli et al. 2018, to reduce the risk of endogenous (intra-constellation) collisions. The results indicate that the adoption of the MiSO orbital configuration can significantly reduce risk with nearly indistinguishable adjustments to the nominal orbital elements of the constellation satellites.

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arXiv2020

Search for L5 Earth Trojans with DECam

Most of the major planets in the Solar System support populations of co-orbiting bodies, known as Trojans, at their L4 and L5 Lagrange points. In contrast, Earth has only one known co-orbiting companion. This paper presents the results from a search for Earth Trojans using the DECam instrument on the Blanco Telescope at CTIO. This search found no additional Trojans in spite of greater coverage compared to previous surveys of the L5 point. Therefore, the main result of this work is to place the most stringent constraints to date on the population of Earth Trojans. These constraints depend on assumptions regarding the underlying population properties, especially the slope of the magnitude distribution (which in turn depends on the size and albedo distributions of the objects). For standard assumptions, we calculate upper limits to a 90% confidence limit on the L5 population of $N_{ET}<1$ for magnitude $H<15.5$, $N_{ET}=60-85$ for $H<19.7$, and $N_{ET}\ $= 97 for $H=20.4$. This latter magnitude limit corresponds to Trojans $\sim$300 m in size for albedo $0.15$. At H=19.7, these upper limits are consistent with previous L4 Earth Trojan constraints and significantly improve L5 constraints.

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arXiv2020

The evolution of dust-disk sizes from a homogeneous analysis of 1-10 Myr-old stars

We utilize ALMA archival data to estimate the dust disk size of 152 protoplanetary disks in Lupus (1-3 Myr), Chamaeleon I (2-3 Myr), and Upper-Sco (5-11 Myr). We combine our sample with 47 disks from Tau/Aur and Oph whose dust disk radii were estimated, as here, through fitting radial profile models to visibility data. We use these 199 homogeneously derived disk sizes to identify empirical disk-disk and disk-host property relations as well as to search for evolutionary trends. In agreement with previous studies, we find that dust disk sizes and millimeter luminosities are correlated, but show for the first time that the relationship is not universal between regions. We find that disks in the 2-3 Myr-old Cha I are not smaller than disks in other regions of similar age, and confirm the Barenfeld et al. (2017) finding that the 5-10 Myr USco disks are smaller than disks belonging to younger regions. Finally, we find that the outer edge of the Solar System, as defined by the Kuiper Belt, is consistent with a population of dust disk sizes which have not experienced significant truncation.

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arXiv2019

Resonant Kuiper Belt Objects -- a Review

Our understanding of the history of the solar system has undergone a revolution in recent years, owing to new theoretical insights into the origin of Pluto and the discovery of the Kuiper belt and its rich dynamical structure. The emerging picture of dramatic orbital migration of the planets driven by interaction with the primordial Kuiper belt is thought to have produced the final solar system architecture that we live in today. This paper gives a brief summary of this new view of our solar system's history, and reviews the astronomical evidence in the resonant populations of the Kuiper belt.

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arXiv2019

Neptune's resonances in the Scattered Disk

The Scattered Disk Objects (SDOs) are thought to be a small fraction of the ancient population of leftover planetesimals in the outer solar system that were gravitationally scattered by the giant planets and have managed to survive primarily by capture and sticking in Neptune's exterior mean motion resonances (MMRs). In order to advance understanding of the role of MMRs in the dynamics of the SDOs, we investigate the phase space structure of a large number of Neptune's MMRs in the semi-major axis range 33--140~au by use of Poincaré sections of the circular planar restricted three body model for the full range of particle eccentricity pertinent to SDOs. We find that, for eccentricities corresponding to perihelion distances near Neptune's orbit, distant MMRs have stable regions with widths that are surprisingly large and of similar size to those of the closer-in MMRs. We identify a phase-shifted second resonance zone that exists in the phase space at planet-crossing eccentricities but not at lower eccentricities; this second resonance zone plays an important role in the dynamics of SDOs in lengthening their dynamical lifetimes. Our non-perturbative measurements of the sizes of the stable resonance zones confirm previous results and provide an additional explanation for the prominence of the $N$:1 sequence of MMRs over the $N$:2, $N$:3 sequences and other MMRs in the population statistics of SDOs; our results also provide a tool to more easily identify resonant objects.

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arXiv2019

Not a simple relationship between Neptune's migration speed and Kuiper belt inclination excitation

We present numerical simulations of giant planet migration in our solar system and examine how the speed of planetary migration affects inclinations in the resulting population of small bodies (test particles) scattered outward and subsequently captured into Neptune's 3:2 mean motion resonance (the Plutinos) as well as the hot classical Kuiper belt population. We do not find a consistent relationship between the degree of test particle inclination excitation and e-folding planet migration timescales in the range 5-50 Myr. Our results present a counter-example to Nesvorny 2015's finding that the Plutino and hot classical inclinations showed a marked increase with increasing e-folding timescales for Neptune's migration. We argue that these differing results are likely due to differing secular architectures of the giant planets during and after migration. Small changes in the planets' initial conditions and differences in the numerical implementation of planet migration can result in different amplitudes of the planets' inclination secular modes, and this can lead to different final inclination distributions for test particles in the simulations. We conclude that the observed large inclination dispersion of Kuiper belt objects does not require Neptune's migration to be slow; planetary migration with e-folding timescales of 5, 10, 30, and 50 Myr can all yield inclination dispersions similar to the observed Plutino and hot classical populations, with no correlation between the degree of inclination excitation and migration speed.

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arXiv2019

Extreme Debris Disk Variability -- Exploring the Diverse Outcomes of Large Asteroid Impacts During the Era of Terrestrial Planet Formation

The most dramatic phases of terrestrial planet formation are thought to be oligarchic and chaotic growth, on timescales of up to 100-200 Myr, when violent impacts occur between large planetesimals of sizes up to proto-planets. Such events are marked by the production of large amounts of debris as has been observed in some exceptionally bright and young debris disks (termed extreme debris disks). Here we report five years of Spitzer measurements of such systems around two young solar-type stars: ID8 and P1121. The short-term (weekly to monthly) and long-term (yearly) disk variability is consistent with the aftermaths of large impacts involving large asteroid-size bodies. We demonstrate that an impact-produced clump of optically thick dust, under the influence of the dynamical and viewing geometry effects, can produce short-term modulation in the disk light curves. The long-term disk flux variation is related to the collisional evolution within the impact-produced fragments once released into a circumstellar orbit. The time-variable behavior observed in the P1121 system is consistent with a hypervelocity impact prior to 2012 that produced vapor condensates as the dominant impact product. Two distinct short-term modulations in the ID8 system argue for two violent impacts at different times and locations. Its long-term variation is consistent with the collisional evolution of two different populations of impact-produced debris dominated by either vapor condensates or escaping boulders. The bright, variable emission from the dust produced in large impacts from extreme debris disks provides a unique opportunity to study violent events during the era of terrestrial planet formation.

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arXiv2018

A near-Sun Solar System Twilight Survey with LSST

We propose a LSST Solar System near-Sun Survey, to be implemented during twilight hours, that extends the seasonal reach of LSST to its maximum as fresh sky is uncovered at about 50 square degrees per night (1500 sq. deg. per lunation) in the morning eastern sky, and surveyable sky is lost at the same rate to the western evening sky due to the Earth's synodic motion. By establishing near-horizon fence post picket lines to the far west and far east we address Solar System science use cases (including Near Earth Objects, Interior Earth Objects, Potentially Hazardous Asteroids, Earth Trojans, near-Sun asteroids, sun-grazing comets, and dormant comets) as well as provide the first look and last look that LSST will have at the transient and variable objects within each survey field. This proposed near-Sun Survey will also maximize the overlap with the field of regard of the proposed NEOCam spacecraft that will be stationed at the Earth's L1 Lagrange point and survey near quadrature with the Sun. This will allow LSST to incidently follow-up NEOCam targets and vice-versa (as well as targets from missions such as Euclid), and will roughly correspond to the Earth's L4 and L5 regions.

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arXiv2018

On the detectability of Planet X with LSST

Two planetary mass objects in the far outer Solar System --- collectively referred to here as Planet X --- have recently been hypothesized to explain the orbital distribution of distant Kuiper Belt Objects. Neither planet is thought to be exceptionally faint, but the sky locations of these putative planets are poorly constrained. Therefore, a wide area survey is needed to detect these possible planets. The Large Synoptic Survey Telescope (LSST) will carry out an unbiased, large area (around 18,000 deg$^2$), deep (limiting magnitude of individual frames of 24.5) survey (the "wide-fast-deep" survey) of the southern sky beginning in 2022, and is therefore an important tool to search for these hypothesized planets. Here we explore the effectiveness of LSST as a search platform for these possible planets. Assuming the current baseline cadence (which includes the wide-fast-deep survey plus additional coverage) we estimate that LSST will confidently detect or rule out the existence of Planet X in 61\% of the entire sky. At orbital distances up to $\sim$75 au, Planet X could simply be found in the normal nightly moving object processing; at larger distances, it will require custom data processing. We also discuss the implications of a non-detection of Planet X in LSST data.

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arXiv2018

Neptune's 5:2 Resonance in the Kuiper Belt

Observations of Kuiper belt objects (KBOs) in Neptune's 5:2 resonance present two puzzles: this third order resonance hosts a surprisingly large population, comparable to the prominent populations of Plutinos and Twotinos in the first order 3:2 and 2:1 resonances, respectively; secondly, their eccentricities are concentrated near $0.4$. To shed light on these puzzles, we investigate the phase space near this resonance with use of Poincaré sections of the circular planar restricted three body model. We find several transitions in the phase space structure with increasing eccentricity, which we explain with the properties of the resonant orbit relative to Neptune's. The resonance width is narrow for very small eccentricities, but widens dramatically for $e\gtrsim0.2$, reaching a maximum near $e\approx0.4$, where it is similar to the maximum widths of the 2:1 and 3:2 resonances. We confirm these results with N-body numerical simulations, including the effects of all four giant planets and a wide range of orbital inclinations of the KBOs. We find that the boundaries of the stable resonance zone are not strongly sensitive to inclination and remain very similar to those found with the simplified three body model, with the caveat that orbits of eccentricity above $\sim0.53$ are unstable; higher eccentricity orbits are phase-protected from destabilizing encounters with Neptune but not with Uranus. These results show that the 5:2 resonant KBOs are not more puzzling than the Plutinos and Twotinos; however, detailed understanding of the origins of eccentric, inclined resonant KBOs remains a challenge.

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arXiv2018

Ceres and the Terrestrial Planets Impact Cratering Record

Dwarf planet Ceres, the largest object in the Main Asteroid Belt, has a surface that exhibits a range of crater densities for a crater diameter range of 5-300 km. In all areas the shape of the craters' size-frequency distribution is very similar to those of the most ancient heavily cratered surfaces on the terrestrial planets. The most heavily cratered terrain on Ceres covers ~15% of its surface and has a crater density similar to the highest crater density on <1% of the lunar highlands. This region of higher crater density on Ceres probably records the high impact rate at early times and indicates that the other 85% of Ceres was partly resurfaced after the Late Heavy Bombardment (LHB) at ~4 Ga. The Ceres cratering record strongly indicates that the period of Late Heavy Bombardment originated from an impactor population whose size-frequency distribution resembles that of the Main Belt Asteroids.

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