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Showing 1-6 of about 6 results.
Refining the Transit-timing and Photometric Analysis of TRAPPIST-1: Masses, Radii, Densities, Dynamics, and EphemeridesAgol, EricDorn, CarolineGrimm, Simon L.Turbet, MartinDucrot, ElsaDelrez, LaetitiaGillon, MichaëlDemory, Brice-OlivierBurdanov, ArtemBarkaoui, KhalidBenkhaldoun, ZouhairBolmont, EmelineBurgasser, AdamCarey, Seande Wit, JulienFabrycky, DanielForeman-Mackey, DanielHaldemann, JonasHernandez, David M.Ingalls, JamesJehin, EmmanuelLangford, ZacharyLeconte, JérémyLederer, Susan M.Luger, RodrigoMalhotra, RenuMeadows, Victoria S.Morris, Brett M.Pozuelos, Francisco J.Queloz, DidierRaymond, Sean N.Selsis, FranckSestovic, MarkoTriaud, Amaury H. M. J.Van Grootel, ValerieDOI: info:10.3847/PSJ/abd022v. 21
Agol, Eric, Dorn, Caroline, Grimm, Simon L., Turbet, Martin, Ducrot, Elsa, Delrez, Laetitia, Gillon, Michaël, Demory, Brice-Olivier, Burdanov, Artem, Barkaoui, Khalid, Benkhaldoun, Zouhair, Bolmont, Emeline, Burgasser, Adam, Carey, Sean, de Wit, Julien, Fabrycky, Daniel, Foreman-Mackey, Daniel, Haldemann, Jonas, Hernandez, David M., Ingalls, James, Jehin, Emmanuel, Langford, Zachary, Leconte, Jérémy, Lederer, Susan M., Luger, Rodrigo et al. 2021. "Refining the Transit-timing and Photometric Analysis of TRAPPIST-1: Masses, Radii, Densities, Dynamics, and Ephemerides." The Planetary Science Journal 2:1.
ID: 159282
Type: article
Authors: Agol, Eric; Dorn, Caroline; Grimm, Simon L.; Turbet, Martin; Ducrot, Elsa; Delrez, Laetitia; Gillon, Michaël; Demory, Brice-Olivier; Burdanov, Artem; Barkaoui, Khalid; Benkhaldoun, Zouhair; Bolmont, Emeline; Burgasser, Adam; Carey, Sean; de Wit, Julien; Fabrycky, Daniel; Foreman-Mackey, Daniel; Haldemann, Jonas; Hernandez, David M.; Ingalls, James; Jehin, Emmanuel; Langford, Zachary; Leconte, Jérémy; Lederer, Susan M.; Luger, Rodrigo; Malhotra, Renu; Meadows, Victoria S.; Morris, Brett M.; Pozuelos, Francisco J.; Queloz, Didier; Raymond, Sean N.; Selsis, Franck; Sestovic, Marko; Triaud, Amaury H. M. J.; Van Grootel, Valerie
Abstract: We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST, and K2 transit-time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets' densities may be described with a single rocky mass-radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition but enhanced in light elements, such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses to a precision of 3%-5%, equivalent to a radial-velocity (RV) precision of 2.5 cm s-1, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small, the orbits are extremely coplanar, and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers, which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations and speculate on possible implications of the planet densities for the formation, migration, and evolution of the planet system.
Are long-term N-body simulations reliable?Hernandez, David M.Hadden, SamMakino, JunichiroDOI: info:10.1093/mnras/staa388v. 4931913–1925
Hernandez, David M., Hadden, Sam, and Makino, Junichiro. 2020. "Are long-term N-body simulations reliable?." Monthly Notices of the Royal Astronomical Society 493:1913– 1925.
ID: 156334
Type: article
Authors: Hernandez, David M.; Hadden, Sam; Makino, Junichiro
Abstract: N-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be established. We address this reliability by running a three-body planetary system over about 200 e-folding times. Using nearby initial conditions, we can construct statistics of the long-term phase-space structure and compare to rough estimates of resonant widths of the system. We compared statistics for a wide range of numerical methods, including a Runge-Kutta method, Wisdom-Holman method, symplectic corrector methods, and a method by Laskar and Robutel. `Improving' an integrator did not increase the phase-space accuracy, but simply increasing the number of initial conditions did. In fact, the statistics of a higher order symplectic corrector method were inconsistent with the other methods in one test.
REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrationsTamayo, DanielRein, HannoShi, PengshuaiHernandez, David M.DOI: info:10.1093/mnras/stz2870v. 4912885–2901
Tamayo, Daniel, Rein, Hanno, Shi, Pengshuai, and Hernandez, David M. 2020. "REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations." Monthly Notices of the Royal Astronomical Society 491:2885– 2901.
ID: 155685
Type: article
Authors: Tamayo, Daniel; Rein, Hanno; Shi, Pengshuai; Hernandez, David M.
Abstract: Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences of incorporating such forces into otherwise symplectic schemes are not always clear. We show that moving to a general framework of non-commutative operators (dissipative or not) clarifies many of these questions, and that several important properties of symplectic schemes carry over to the general case. In particular, we show that explicit splitting schemes generically exploit symmetries in the applied external forces, which often strongly suppress integration errors. Furthermore, we demonstrate that so-called 'symplectic correctors' (which reduce energy errors by orders of magnitude at fixed computational cost) apply equally well to weakly dissipative systems and can thus be more generally thought of as 'weak splitting correctors'. Finally, we show that previously advocated approaches of incorporating additional forces into symplectic methods work well for dissipative forces, but give qualitatively wrong answers for conservative but velocity-dependent forces like post-Newtonian corrections. We release REBOUNDx, an open-source C library for incorporating additional effects into REBOUND N-body integrations, together with a convenient PYTHON wrapper. All effects are machine independent and we provide a binary format that interfaces with the SimulationArchive class in REBOUND to enable the sharing and reproducibility of results. Users can add effects from a list of pre-implemented astrophysical forces, or contribute new ones.
Improving the accuracy of simulated chaotic N-body orbits using smoothnessHernandez, David M.DOI: info:10.1093/mnras/stz2662v. 4904175–4182
Hernandez, David M. 2019. "Improving the accuracy of simulated chaotic N-body orbits using smoothness." Monthly Notices of the Royal Astronomical Society 490:4175– 4182.
ID: 154534
Type: article
Authors: Hernandez, David M.
Abstract: Symplectic integrators are a foundation to the study of dynamical N-body phenomena, at scales ranging from planetary to cosmological. These integrators preserve the Poincaré invariants of Hamiltonian dynamics. The N-body Hamiltonian has another, perhaps overlooked, symmetry: it is smooth, or, in other words, it has infinite differentiability class order (DCO) for particle separations greater than 0. Popular symplectic integrators, such as hybrid methods or block adaptive stepping methods do not come from smooth Hamiltonians and it is perhaps unclear whether they should. We investigate the importance of this symmetry by considering hybrid integrators, whose DCO can be tuned easily. Hybrid methods are smooth, except at a finite number of phase space points. We study chaotic planetary orbits in a test considered by Wisdom. We find that increasing smoothness, at negligible extra computational cost in particular tests, improves the Jacobi constant error of the orbits by about 5 orders of magnitude in long-term simulations. The results from this work suggest that smoothness of the N-body Hamiltonian is a property worth preserving in simulations.
Should N-body integrators be symplectic everywhere in phase space?Hernandez, David M.DOI: info:10.1093/mnras/stz884v. 4865231–5238
Hernandez, David M. 2019. "Should N-body integrators be symplectic everywhere in phase space?." Monthly Notices of the Royal Astronomical Society 486:5231– 5238.
ID: 154174
Type: article
Authors: Hernandez, David M.
Abstract: Symplectic integrators are the preferred method of solving conservative N-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital stability. Newtonian gravity is scale free, and there is no preferred time or length-scale: this is at odds with construction of traditional symplectic integrators, in which there is an explicit time- scale in the time-step. Additional time-scales have been incorporated into symplectic integration using various techniques, such as hybrid methods and potential decompositions in planetary astrophysics, integrator sub-cycling in cosmology, and block time-stepping in stellar astrophysics, at the cost of breaking or potentially breaking symplecticity at a few points in phase space. The justification provided, if any, for this procedure is that these trouble points where the symplectic structure is broken should be rarely or never encountered in practice. We consider the case of hybrid integrators, which are used ubiquitously in astrophysics and other fields, to show that symplecticity breaks at a few points are sufficient to destroy beneficial properties of symplectic integrators, which is at odds with some statements in the literature. We show how to solve this problem in the case of hybrid integrators by requiring Lipschitz continuity of the equations of motion. For other techniques, such as time-step subdivision, consequences to this problem are not explored here, and the fact that symplectic structure is broken should be taken into account by N-body simulators, who may find an alternative non-symplectic integrator performs similarly.
Hybrid symplectic integrators for planetary dynamicsRein, HannoHernandez, David M.Tamayo, DanielBrown, GarettEckels, EmilyHolmes, EmmaLau, MichelleLeblanc, RéjeanSilburt, AriDOI: info:10.1093/mnras/stz769v. 4855490–5497
Rein, Hanno, Hernandez, David M., Tamayo, Daniel, Brown, Garett, Eckels, Emily, Holmes, Emma, Lau, Michelle, Leblanc, Réjean, and Silburt, Ari. 2019. "Hybrid symplectic integrators for planetary dynamics." Monthly Notices of the Royal Astronomical Society 485:5490– 5497.
ID: 152903
Type: article
Authors: Rein, Hanno; Hernandez, David M.; Tamayo, Daniel; Brown, Garett; Eckels, Emily; Holmes, Emma; Lau, Michelle; Leblanc, Réjean; Silburt, Ari
Abstract: Hybrid symplectic integrators such as MERCURY are widely used to simulate complex dynamical phenomena in planetary dynamics that could otherwise not be investigated. A hybrid integrator achieves high accuracy during close encounters by using a high-order integration scheme for the duration of the encounter while otherwise using a standard second-order Wisdom-Holman scheme, thereby optimizing both speed and accuracy. In this paper we reassess the criteria for choosing the switching function that determines which parts of the Hamiltonian are integrated with the high-order integrator. We show that the original motivation for choosing a polynomial switching function in MERCURY is not correct. We explain the nevertheless excellent performance of the MERCURY integrator and then explore a wide range of different switching functions including an infinitely differentiable function and a Heaviside function. We find that using a Heaviside function leads to a significantly simpler scheme compared to MERCURY , while maintaining the same accuracy in short-term simulations.