arXiv subjects

Tobias C. Hinse

Publications and source records attributed to Tobias C. Hinse.

At least 19 recordsLinked to original sources

arXiv2026

Long-term monitoring of WASP-19 b: Signs of apsidal precession and molecular signatures

With more than 6000 exoplanets discovered so far, about 12 percent are hot Jupiters. Their large sizes and short orbital periods make them valuable targets for studying planetary formation, atmospheres, and orbital evolution. We present a homogeneous analysis of the WASP-19 b system using a 15 year dataset to investigate both its orbital dynamics and atmospheric properties. We test whether the transit times show evidence for tidal orbital decay, apsidal precession, or periodic perturbations from an additional body, and we also construct a photometric transmission spectrum. Multi-wavelength light curves are modeled with PRISM to account for starspots, and linear, quadratic, and cubic ephemeris models are fitted to the transit timing residuals. Our dataset includes 27 new transits and reveals no statistically significant periodic signal. Although none of the tested models fully reproduces the timing scatter, the transit times show systematic deviations from a constant period and are best described by the cubic ephemeris, indicating a slow long-term trend over the full baseline. This behavior is more consistent with gradual apsidal precession than with monotonic tidal decay. A precession model yields a rate of 1.00 +/- 0.12 x 10^-4 rad per orbit and a planetary Love number k2p = 0.107 +/- 0.08. The transmission spectrum shows signatures of Na, K, and H2O, with no strong evidence for TiO or VO. These results suggest that apsidal precession may dominate the long-term orbital evolution of WASP-19 b. Continued high-precision timing and spectroscopic observations are needed to further test this scenario.

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arXiv2025

SPECTRUMMATE: A Low-cost Spectrometer for Small Telescopes

This project presents the development and implementation of a compact spectrometer, named SPECTRUMMATE, tailored for small telescopes. Small telescopes offer several advantages: they are cost-effective, occupy less space, and are simpler to set up than larger instruments. This makes them particularly suitable for amateur astronomers and educational institutions with limited resources. Moreover, small telescopes can effectively observe bright celestial objects, enabling valuable contributions to astronomical projects. Based on the Sol'EX design, SPECTRUMMATE was constructed using optical components available at the Space and Applications Laboratory (SpaceLAB), University of Science and Technology of Hanoi, Vietnam. The instrument is designed to meet the specific needs of astronomers who require detailed analysis within the visible spectrum (SPECTRUMMATE can capture a waveband of 368 angstrom/image, spectral coverage from 4000 to 6600 angstrom, and resolving power R = 2546 at 5500 angstrom). To achieve optimal performance, the design process involved selecting and configuring optical elements, including a collimator, diffraction grating, and objective lens. Experimental setups were tested to minimize spectral dispersion while ensuring the system's compactness and ease of alignment. Spectra obtained by SPECTRUMMATE demonstrated efficient spectral calibration and the capability to capture high-resolution spectra of bright light sources, such as the Sun, making it a valuable tool for specialised spectroscopic observations. The modular design of SPECTRUMMATE also allows users to change its components easily to achieve the desired spectral range and resolution.

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arXiv2025

Broadband Low-Resolution Spectrograph - SpectrumMate LR

This paper presents the development and application of SpectrumMate LR, a broadband, low-resolution spectrograph for small telescope use. SpectrumMate LR is designed to offer affordable, accessible spectroscopic capabilities for amateur astronomers and educators, inspired by the need for versatile instruments in amateur and educational settings. Utilising a 300 grooves/mm grating, 80 mm collimator and objective lenses, SpectrumMate LR is optimised to perform analyses across the visible spectrum, enabling users to classify stars by spectral type, measure stellar temperatures, and test filter transmission ranges. Tests demonstrate SpectrumMate LR's ability to capture accurate spectral data, validating its efficacy in observing both celestial and terrestrial light sources. This instrument fills a niche for cost-effective spectroscopy, empowering a broader audience to engage in detailed observational astronomy.

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arXiv2025

Shape and spin state model of contact binary (388188) 2006 DP14 using combined radar and optical observations

Contact binaries are found throughout the solar system. The recent discovery of Selam, the satellite of MBA (152830) Dinkinesh, by the NASA LUCY mission has made it clear that the term `contact binary' covers a variety of different types of bi-modal mass distributions and formation mechanisms. Only by modelling more contact binaries can this population be properly understood. We determined a spin state and shape model for the Apollo group contact binary asteroid (388188) 2006 DP14 using ground-based optical and radar observations collected between 2014 and 2023. Radar delay-Doppler images and continuous wave spectra were collected over two days in February 2014, while 16 lightcurves in the Cousins R and SDSS-r filters were collected in 2014, 2022 and 2023. We modelled the spin state using convex inversion before using the SHAPE modelling software to include the radar observations in modelling concavities and the distinctive neck structure connecting the two lobes. We find a spin state with a period of $(5.7860\pm0.0001)$ hours and pole solution of $λ= (180\pm121)^\circ$ and $β= (-80\pm7)^\circ$ with morphology indicating a 520 m long bi-lobed shape. The model's asymmetrical bi-modal mass distribution resembles other small NEA contact binaries such as (85990) 1999 JV6 or (8567) 1996 HW1, which also feature a smaller `head' attached to a larger `body'. The final model features a crater on the larger lobe, similar to several other modelled contact binaries. The model's resolution is 25 m, comparable to that of the radar images used.

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arXiv2024

Unveiling hidden companions in post-common-envelope binaries: A robust strategy and uncertainty exploration

Some post-common-envelope binaries are binary stars with short periods that exhibit significant period variations over long observational time spans. These eclipse timing variations (ETVs) are most likely to be accounted for by the presence of an unseen massive companion, potentially of planetary or substellar nature, and the light-travel time (LTT) effect. In this study, our main objective is to describe the diversity of compatible nontransit companions around PCEBs and explore the robustness of the solutions by employing tools for uncertainty estimation. We select the controversial data of the QS Vir binary star, which previous studies have suggested hosts a planet. We employ a minimizing strategy, using genetic algorithms to explore the global parameter space followed by refinement of the solution using the simplex method. We evaluate errors through the classical MCMC approach and discuss the error range for parameters. Our results highlight the strong dependence of ETV models for close binaries on the dataset used, which leads to relatively loose constraints on the parameters of the unseen companion. We find that the shape of the $O-C$ curve is influenced by the dataset employed. We propose an alternative method to evaluate errors on the orbital fits based on a grid search surrounding the best-fit values, obtaining a wider range of plausible solutions that are compatible with goodness-of-fit statistics. We also analyze how the parameter solutions are affected by the choice of the dataset, and find that this system continuously changes the compatible solutions as new data are obtained from eclipses. The best-fit parameters for QS Vir correspond to a low-mass stellar companion (57.71 $M_{jup}$ ranging from 40 to 64 $M_{jup}$) on an eccentric orbit ($e=0.91^{+0.07}_{-0.17}$) with a variety of potential periods ($P = 16.69 ^{+0.47}_{-0.42}$ yr.)

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arXiv2023

Optical monitoring of the Didymos-Dimorphos asteroid system with the Danish telescope around the DART mission impact

The NASA's Double-Asteroid Redirection Test (DART) was a unique planetary defence and technology test mission, the first of its kind. The main spacecraft of the DART mission impacted the target asteroid Dimorphos, a small moon orbiting asteroid (65803) Didymos, on 2022 September 26. The impact brought up a mass of ejecta which, together with the direct momentum transfer from the collision, caused an orbital period change of 33 +/- 1 minutes, as measured by ground-based observations. We report here the outcome of the optical monitoring campaign of the Didymos system from the Danish 1.54 m telescope at La Silla around the time of impact. The observations contributed to the determination of the changes in the orbital parameters of the Didymos-Dimorphos system, as reported by arXiv:2303.02077, but in this paper we focus on the ejecta produced by the DART impact. We present photometric measurements from which we remove the contribution from the Didymos-Dimorphos system using a H-G photometric model. Using two photometric apertures we determine the fading rate of the ejecta to be 0.115 +/- 0.003 mag/d (in a 2" aperture) and 0.086 +/- 0.003 mag/d (5") over the first week post-impact. After about 8 days post-impact we note the fading slows down to 0.057 +/- 0.003 mag/d (2" aperture) and 0.068 +/- 0.002 mag/d (5"). We include deep-stacked images of the system to illustrate the ejecta evolution during the first 18 days, noting the emergence of dust tails formed from ejecta pushed in the anti-solar direction, and measuring the extent of the particles ejected sunward to be at least 4000 km.

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arXiv2022

An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing

We report the first unambiguous detection and mass measurement of an isolated stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry out precise astrometry of the source star of the long-duration (t_E~270 days), high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462 (hereafter designated as MOA-11-191/OGLE-11-462), in the direction of the Galactic bulge. HST imaging, conducted at eight epochs over an interval of six years, reveals a clear relativistic astrometric deflection of the background star's apparent position. Ground-based photometry of MOA-11-191/OGLE-11-462 shows a parallactic signature of the effect of the Earth's motion on the microlensing light curve. Combining the HST astrometry with the ground-based light curve and the derived parallax, we obtain a lens mass of 7.1 +/- 1.3 Msun and a distance of 1.58 +/- 0.18 kpc. We show that the lens emits no detectable light, which, along with having a mass higher than is possible for a white dwarf or neutron star, confirms its BH nature. Our analysis also provides an absolute proper motion for the BH. The proper motion is offset from the mean motion of Galactic-disk stars at similar distances by an amount corresponding to a transverse space velocity of ~45 km/s, suggesting that the BH received a 'natal kick' from its supernova explosion. Previous mass determinations for stellar-mass BHs have come from radial-velocity measurements of Galactic X-ray binaries, and from gravitational radiation emitted by merging BHs in binary systems in external galaxies. Our mass measurement is the first for an isolated stellar-mass BH using any technique.

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arXiv2022

Physical properties of near-Earth asteroid (2102) Tantalus from multi-wavelength observations

Between 2010 and 2017 we have collected new optical and radar observations of the potentially hazardous asteroid (2102)~Tantalus from the ESO NTT and Danish telescopes at the La Silla Observatory and from the Arecibo planetary radar. The object appears to be nearly spherical, showing a low amplitude light-curve variation and limited large-scale features in the radar images. The spin-state is difficult to constrain with the available data; including a certain light-curve subset significantly changes the spin-state estimates, and the uncertainties on period determination are significant. Constraining any change in rotation rate was not possible, despite decades of observations. The convex lightcurve-inversion model, with rotational pole at $λ=210{\pm}41$° and $β=-30{\pm}35$°, is more flattened than the two models reconstructed by including radar observations: with prograde ($λ=36{\pm}23$°, $β=30{\pm}15$°), and with retrograde rotation mode ($λ=180{\pm}24$°, $β=-30{\pm}16$°). Using data from WISE we were able to determine that the prograde model produces the best agreement in size determination between radar and thermophysical modelling. Radar measurements indicate possible variation in surface properties, suggesting one side might have lower radar albedo and be rougher at centimetre-to-decimetre scale than the other. However, further observations are needed to confirm this. Thermophysical analysis indicates a surface covered in fine-grained regolith, consistent with radar albedo and polarisation ratio measurements. Finally, geophysical investigation of the spin-stability of Tantalus shows that it could be exceeding its critical spin-rate via cohesive forces.

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arXiv2021

Transiting Exoplanet Monitoring Project (TEMP). VI. The Homogeneous Refinement of System Parameters for 39 Transiting Hot Jupiters with 127 New Light Curves

We present 127 new transit light curves for 39 hot Jupiter systems, obtained over the span of five years by two ground-based telescopes. A homogeneous analysis of these newly collected light curves together with archived spectroscopic, photometric, and Doppler velocimetric data using EXOFASTv2 leads to a significant improvement in the physical and orbital parameters of each system. All of our stellar radii are constrained to accuracies of better than 3\%. The planetary radii for 37 of our 39 targets are determined to accuracies of better than $5\%$. Compared to our results, the literature eccentricities are preferentially overestimated due to the Lucy-Sweeney bias. Our new photometric observations therefore allow for significant improvement in the orbital ephemerides of each system. Our correction of the future transit window amounts to a change exceeding $10\,{\rm min}$ for ten targets at the time of JWST's launch, including a $72\,{\rm min}$ change for WASP-56. The measured transit mid-times for both literature light curves and our new photometry show no significant deviations from the updated linear ephemerides, ruling out in each system the presence of companion planets with masses greater than $0.39 - 5.0\, rm M_{\oplus}$, $1.23 - 14.36\, \rm M_{\oplus}$, $1.65 - 21.18\, \rm M_{\oplus}$, and $0.69 - 6.75\, \rm M_{\oplus}$ near the 1:2, 2:3, 3:2, and 2:1 resonances with the hot Jupiters , respectively, at a confidence level of $\pm 1\,σ$. The absence of resonant companion planets in the hot Jupiter systems is inconsistent with the conventional expectation from disk migration.

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arXiv2021

Revisiting the analysis of HW Vir eclipse timing data I. A frequentist data modeling approach and a dynamical stability analysis

HW Vir is a short-period binary that presents eclipse timing variations. Circumbinary planets have been proposed as a possible explanation, although the properties of the planets differ in each new study. Our aim is to perform robust model selection methods for eclipse timing variations (ETV) and error calculation techniques based on a frequentist approach for the case of the HW Vir system. We initially performed simultaneous light and radial velocity curve analysis to derive the masses of the binary. We then analyzed the eclipse timing variation of the system by fitting multiple models. To select the best model, we searched the confidence levels for the best model by creating an $χ^2$ surface grid and bootstrap methods for each pair of parameters. We searched for stable orbital configurations for our adopted ETV model. The masses of the binary are found as 0.413 $\pm$ 0.008 $M_\odot$ and 0.128 $\pm$ 0.004 $M_\odot$. Under the assumption of two light time effects superimposed on a secular change, the minimum masses of the circumbinary objects are calculated as $25.0_{-2.2}^{+3.5} \ M_{Jup}$ and $13.9_{-0.45}^{+0.60}\ M_{Jup}$. The projected semi-major axes are found to be $7.8_{-1.0}^{+1.4}\ au$ and $4.56_{-0.22}^{+0.27}\ au$ in respective order. We find that this configuration is unstable within a 3$σ$ range on the semi-major axis and eccentricity of the outer circumbinary object.

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arXiv2020

TraMoS V. Updated ephemeris and multi-epoch monitoring of the hot Jupiters WASP-18Ab, WASP-19b, and WASP-77Ab

We present 22 new transit observations of the exoplanets WASP-18Ab, WASP-19b, and WASP-77Ab, from the Transit Monitoring in the South (TraMoS) project. We simultaneously model our newly collected transit light curves with archival photometry and radial velocity data, to obtain refined physical and orbital parameters. We include TESS light curves of the three exoplanets to perform an extended analysis of the variations in their transit mid-time (TTV) and to refine their planetary orbital ephemeris. We did not find significant $\rm TTV_{RMS}$ variations larger than 47, 65, and 86 seconds for WASP-18Ab, WASP-19b, and WASP-77Ab, respectively. Dynamical simulations were carried out to constrain the masses of a possible perturber. The observed RMS could be produced by a perturber body with an upper limit mass of 9, 2.5, 11 and $4~M_{\oplus}$ in 1:2, 1:3, 2:1, and 3:1 resonances in the WASP-18Ab system. In the case of WASP-19b, companions with masses up to 0.26, 0.65, 1 and $2.8~M_{\oplus}$, in 1:2, 2:1, 3:1, and 5:3 resonances, produce the RMS. And for the WASP-77Ab system, a planet with mass between $1.5-9~M_{\oplus}$ in 1:2, 1:3, 2:1, 2:3, 3:1, 3:5, 5:3 resonances. Comparing our results with RV variations, we discard massive companions with $350~M_{\oplus}$ in 17:5 resonance for WASP-18Ab, $95~M_{\oplus}$ in 4:1 resonance for WASP-19b and $105~M_{\oplus}$ in 5:2 resonance for WASP-77Ab. Finally, using a Lomb-Scargle period search we find no evidence of a periodic trend on our TTV data for the three exoplanets.

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arXiv2019

OGLE-2017-BLG-1186: first application of asteroseismology and Gaussian processes to microlensing

We present the analysis of the event OGLE-2017-BLG-1186 from the 2017 Spitzer microlensing campaign. This is a remarkable microlensing event because its source is photometrically bright and variable, which makes it possible to perform an asteroseismic analysis using ground-based data. We find that the source star is an oscillating red giant with average timescale of $\sim 9$ d. The asteroseismic analysis also provides us source properties including the source angular size ($\sim 27~μ{\rm as}$) and distance ($\sim 11.5$ kpc), which are essential for inferring the properties of the lens. When fitting the light curve, we test the feasibility of Gaussian Processes (GPs) in handling the correlated noise caused by the variable source. We find that the parameters from the GP model are generally more loosely constrained than those from the traditional $χ^2$ minimization method. We note that this event is the first microlensing system for which asteroseismology and GPs have been used to account for the variable source. With both finite-source effect and microlens parallax measured, we find that the lens is likely a $\sim 0.045~M_{\odot}$ brown dwarf at distance $\sim 9.0$ kpc, or a $\sim 0.073~M_{\odot}$ ultracool dwarf at distance $\sim 9.8$ kpc. Combining the estimated lens properties with a Bayesian analysis using a Galactic model, we find a $\sim 35$ per cent probability for the lens to be a bulge object and $\sim 65$ per cent to be a background disc object.

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arXiv2019

Discovery of a Third Transiting Planet in the Kepler-47 Circumbinary System

Of the nine confirmed transiting circumbinary planet systems, only Kepler-47 is known to contain more than one planet. Kepler-47 b (the "inner planet") has an orbital period of 49.5 days and a radius of about $3\,R_{\oplus}$. Kepler-47 c (the "outer planet") has an orbital period of 303.2 days and a radius of about $4.7\,R_{\oplus}$. Here we report the discovery of a third planet, Kepler-47 d (the "middle planet"), which has an orbital period of 187.4 days and a radius of about $7\,R_{\oplus}$. The presence of the middle planet allows us to place much better constraints on the masses of all three planets, where the $1σ$ ranges are less than $26\,M_{\oplus}$, between $7-43\,M_{\oplus}$, and between $2-5\,M_{\oplus}$ for the inner, middle, and outer planets, respectively. The middle and outer planets have low bulk densities, with $ρ_{\rm middle} < 0.68$ g cm$^{-3}$ and $ρ_{\rm outer} < 0.26$ g cm$^{-3}$ at the $1σ$ level. The two outer planets are "tightly packed," assuming the nominal masses, meaning no other planet could stably orbit between them. All of the orbits have low eccentricities and are nearly coplanar, disfavoring violent scattering scenarios and suggesting gentle migration in the protoplanetary disk.

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arXiv2019

$Spitzer$ Microlensing Parallax for OGLE-2017-BLG-0896 Reveals a Counter-Rotating Low-Mass Brown Dwarf

The kinematics of isolated brown dwarfs in the Galaxy, beyond the solar neighborhood, is virtually unknown. Microlensing has the potential to probe this hidden population, as it can measure both the mass and five of the six phase-space coordinates (all except the radial velocity) even of a dark isolated lens. However, the measurements of both the microlens parallax and finite-source effects are needed in order to recover the full information. Here, we combine $Spitzer$ satellite parallax measurement with the ground-based light curve, which exhibits strong finite-source effects, of event OGLE-2017-BLG-0896. We find two degenerate solutions for the lens (due to the known satellite-parallax degeneracy), which are consistent with each other except for their proper motion. The lens is an isolated brown dwarf with a mass of either $18\pm1M_J$ or $20\pm1M_J$. This is the lowest isolated-object mass measurement to date, only $\sim$45\% more massive than the theoretical deuterium-fusion boundary at solar metallicity, which is the common definition of a free-floating planet. The brown dwarf is located at either $3.9\pm0.1$ kpc or $4.1\pm0.1$ kpc toward the Galactic bulge, but with proper motion in the opposite direction of disk stars, with one solution suggesting it is moving within the Galactic plane. While it is possibly a halo brown dwarf, it might also represent a different, unknown population.

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arXiv2018

Transiting Exoplanet Monitoring Project (TEMP). I. Refined System Parameters and Transit Timing Variations of HAT-P-29b

We report the photometry of six transits of the hot Jupiter HAT-P-29b obtained from 2013 October to 2015 January. We analyze the new light curves, in combination with the published photometric, and Doppler velocimetric, and spectroscopic measurements, finding an updated orbital ephemeris for the HAT-P-29 system, $T_{\rm C}[0]= 2456170.5494(15)\,[\rm{BJD_{TDB}}]$ and $P=5.723390(13) \,{\rm days}$. It is $17.63\,{\rm s}$ ($4.0\,σ$) longer than the previously published value, amounting to errors exceeding $2.5\,\rm{hrs}$ at the time of writing (on UTC 2018 June 1). The measured transit mid-times for HAT-P-29b show no compelling evidence of timing anomalies from a linear model, which rules out the presence of a perturbers with masses greater than $0.6$, $0.7$, $0.5$, and $0.4\,{\rm M_\oplus}$ near the $1:2$, $2:3$, $3:2$, and $2:1$ resonances with HAT-P-29b, respectively.

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arXiv2018

Transiting Exoplanet Monitoring Project (TEMP). IV. Refined System Parameters, Transit Timing Variations and Orbital Stability of the Transiting Planetary System HAT-P-25

We present eight new light curves of the transiting extra-solar planet HAT-P-25b obtained from 2013 to 2016 with three telescopes at two observatories. We use the new light curves, along with recent literature material, to estimate the physical and orbital parameters of the transiting planet. Specifically, we determine the mid-transit times (T$_{C}$) and update the linear ephemeris, T$_{C[0]}$=2456418.80996$\pm$0.00025 [$\mathrm{BJD}_\mathrm{TDB}$] and P=3.65281572$\pm$0.00000095 days. We carry out a search for transit timing variations (TTVs), and find no significant TTV signal at the $ΔT=$80 s-level, placing a limit on the possible strength of planet-planet interactions ($\mathrm{TTV_{G}}$). In the course of our analysis, we calculate the upper mass-limits of the potential nearby perturbers. Near the 1:2, 2:1, and 3:1 resonances with HAT-P-25b, perturbers with masses greater than 0.5, 0.3, and 0.5 $\mathrm{M_{\oplus}}$ respectively, can be excluded. Furthermore, based on the analysis of TTVs caused by light travel time effect (LTTE) we also eliminate the possibility that a long-period perturber exists with $M_{\rm p}> 3000 \,\mathrm{M_{J}}$ within $a=11.2\,{\rm AU}$ of the parent star.

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arXiv2017

The Dynamical History Of 2060 Chiron And Its Proposed Ring System

The surprising discovery of a ring system around the Centaur 10199 Chariklo in 2013 led to a reanalysis of archival stellar occultation data for the Centaur 2060 Chiron by Ortiz et al. One possible interpretation of that data is that a system of rings exists around Chiron. In this work, we study the dynamical history of the proposed Chiron ring system by integrating nearly 36,000 clones of the Centaur backward in time for 100 Myr under the influence of the Sun and the four giant planets. The severity of all close encounters between the clones and planets while the clones are in the Centaur region is recorded, along with the mean time between close encounters. We find that severe and extreme close encounters are very rare, making it possible that the Chiron ring system has remained intact since its injection into the Centaur region, which we find likely occurred within the past 8.5 Myr. Our simulations yield a backward dynamical half-life for Chiron of 0.7 Myr. The dynamical classes of a sample of clones are found. It is found that, on average, the Centaur lifetimes of resonance hopping clones are twice those of random-walk clones because of resonance sticking in mean motion resonances. In addition, we present MEGNO and chaotic lifetime maps of the region bound by 13 au $\le a \le$14 au and e $\le$0.5. We confirm that the current mean orbital parameters of Chiron are located in a highly chaotic region of a-e phase space.

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arXiv2017

The Dynamical History of Chariklo and its Rings

Chariklo is the only small Solar system body confirmed to have rings. Given the instability of its orbit, the presence of rings is surprising, and their origin remains poorly understood. In this work, we study the dynamical history of the Chariklo system by integrating almost 36,000 Chariklo clones backwards in time for one Gyr under the influence of the Sun and the four giant planets. By recording all close encounters between the clones and planets, we investigate the likelihood that Chariklo's rings could have survived since its capture to the Centaur population. Our results reveal that Chariklo's orbit occupies a region of stable chaos, resulting in its orbit being marginally more stable than those of the other Centaurs. Despite this, we find that it was most likely captured to the Centaur population within the last 20 Myr, and that its orbital evolution has been continually punctuated by regular close encounters with the giant planets. The great majority (> 99%) of those encounters within one Hill radius of the planet have only a small effect on the rings. We conclude that close encounters with giant planets have not had a significant effect on the ring structure. Encounters within the Roche limit of the giant planets are rare, making ring creation through tidal disruption unlikely.

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