arXiv subjects

Tiger Lu

Publications and source records attributed to Tiger Lu.

At least 19 recordsLinked to original sources

arXiv2026

Understanding eccentric temperate giants: an in-depth study of the architecture and stellar obliquity of the TOI-2134 system

We revisit the TOI-2134 planetary system with three new high-cadence TESS sectors and 98 more spectra. This new analysis confirms the two orbiting planets by simultaneously modelling a total of eight sectors of corrected TESS photometry and 280 HARPS-N and SOPHIE radial velocities: an inner mini-Neptune in a near-circular $9.229198\pm0.000003$ days orbit, and an outer temperate sub-Saturn orbiting with a $95.852840\pm0.000042$ days period and eccentricity of $0.31\pm0.01$. The masses and radii of the planets were computed to be $9.37\pm0.54$ Me and $2.735\pm0.068$ Re for planet b, and $58.3\pm1.9$ Me and $7.35\pm0.18$ Re for planet c. The new data not only improves the detection significance and precisions on the planetary orbits, but also breaks the original multimodality in the eccentricity solution for the outer planet. We also detect a long-term trend in the radial velocity data, which we attribute to a stellar magnetic cycle. We investigate the spin-orbit alignment of the system via observations of the Rossiter-McLaughlin effect for TOI-2134~b with EXPRES and TOI-2134~c with PARAS-2. No RM effect was detected for planet b, but we find a 4.7$\sigma$ detection of a $59\pm31^{\circ}$ obliquity for planet c. Finally, we examine the architecture of the system, assess its completeness, investigate the planetary interior, and their suitability for follow-up atmospheric analysis.

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arXiv2026

A Massive Hot-Jupiter Companion that Disfavors Giant Planet Formation Beyond the Water-Ice Line

We report evidence for a brown-dwarf companion with mass $34^{+30}_{-11}~M_{\rm J}$ in the KELT-20 system, in which an ultra-hot Jupiter transits an A2-type star. The companion's properties are inferred from a joint analysis of astrometric accelerations and transit timing variations, and its present-day orbit imposes dynamical limits on where the hot Jupiter could have formed. Given the star's current luminosity, the water-ice line is expected at $\sim$8-15 au, but the companion's inferred pericenter distance of a few au would lead to orbit crossing or long-term instability for any planet formed at such distances. If the companion formed early and remained near its current orbit over the system's lifetime, the proto-hot Jupiter must have formed within $\sim$3.7 au to avoid orbit crossing, and within $\sim$1.5 au to remain dynamically stable over the system's lifetime. These results disfavor formation beyond the ice line and point instead to formation at smaller orbital distances followed by inward migration.

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arXiv2026

The Architecture of the 14 Herculis System Suggests Primordial Ejection of a Massive Planet

The 14 Herculis system hosts two super-Jupiters on eccentric, significantly misaligned orbits. This orbital architecture represents a dynamical puzzle that demands explanation. In this work, we reproduce the system's dynamical history and current architecture using a large suite of N-body simulations of planet-planet scattering. Our results demonstrate that planet-planet scattering is able to reproduce 14 Her's peculiar orbital architecture, but only if additional massive bodies were initially present in the system that were subsequently ejected. The mass of any such ejected planet can in turn constrain the system's initial configuration. We also analyze the present-day secular evolution of the system and conclude that while there are most likely nontrivial eccentricity and inclination oscillations currently occurring, the magnitudes of these oscillations are not strong enough to allow tidal forces to meaningfully alter the system's architecture. Finally, we discuss how forthcoming observations from future Gaia data releases and the Roman mission may situate 14 Her's dynamical history within a broader, population-level framework.

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arXiv2026

A Coordinate System for Dynamical Instabilities in Hierarchical Systems in REBOUND

We implement coordinates suitable for studying wide binary systems in TRACE, a hybrid integrator in the widely used open-source N-body integration package REBOUND. This is a regime in which traditional hybrid integrators perform poorly. The coordinate system supports close encounters between any pair of bodies in the system. We describe the implementation of this coordinate system and benchmark its performance against other integrators in the REBOUND ecosystem. In tests of planet-planet scattering, stellar flybys, and ZLK oscillations. TRACE in wide binary coordinates is qualitatively correct when other hybrid methods fail, and in many cases returns statistically similar results to the high-precision IAS15 integrator with up to 9x speedups. We also provide some guidelines for when use of these coordinates are appropriate.

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arXiv2026

Observational and Dynamical Constraints on an Unseen Outer Perturber in the GJ 436 Hot Neptune System

Hot Neptunes in the sub-Jovian desert offer unique insights into planetary system evolution, retaining signatures of dynamical processes that shaped their present-day architectures. Many of these planets exhibit polar orbits, yet the mechanisms responsible for these misalignments between the stellar spin axis and planet orbit normal remain under debate. GJ 436 b stands among the very few hot Neptunes with both a polar and an eccentric orbit, thereby preserving dynamical signatures that may have otherwise been erased by tidal circularization. We investigate the unusual orbital architecture of GJ 436, exploring von Zeipel-Lidov-Kozai migration induced by a distant companion as a mechanism to explain the present-day orbit of GJ 436 b. Using $\sim$20 years of archival radial velocity measurements and astrometric data from the Hipparcos-Gaia Catalog of Accelerations, we constrain a potential companion to $a_{c}<5.4$ AU for $m_{c}>0.05$ $M_{Jup}$ and $a_{c}<64$ AU for $m_{c}>24$ $M_{Jup}$ in the GJ 436 system at the $2\sigma$ confidence level, providing the most stringent constraints to date. We further perform three-body hierarchical secular simulations to determine which companion configurations could reproduce GJ 436 b's present-day orbit within the observationally constrained parameter space. Our dynamical modeling favors sub-Jovian masses on orbits with $a_\mathrm{c} \gtrsim 6.8$ AU, suggesting a substellar perturber. These observational and dynamical constraints can guide future companion searches and illuminate formation mechanisms for hot Neptune desert planets on polar orbits.

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arXiv2025

Double Hot Jupiter Formation through Mirrored ZLK Migration in Binary Star Systems: The Case of WASP-94

To date, only a handful of binary star systems are known with at least one confirmed planet orbiting each star. Such systems, however, offer a unique perspective on the stochasticity intrinsic to planet formation and evolution -- particularly in twin binary star systems, which consist of near-equal-mass stars formed contemporaneously in the same birth environment. The WASP-94 system, which includes twin F-type stars, is a striking exemplar of such systems, containing two hot Jupiters: WASP-94 Ab is a transiting, spin-orbit misaligned giant planet with a 4-day orbital period, while WASP-94 Bb is non-transiting and has a tighter 2-day orbital period. In this work, we leverage N-body simulations to show that the current double hot Jupiter configuration of the WASP-94 system can be reproduced through mirrored von Zeipel-Lidov-Kozai migration. The upcoming Gaia astrometric data releases offer the potential to search for additional twin planetary systems, including double cold Jupiter systems that may serve as the progenitors for WASP-94-like configurations.

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arXiv2025

The Astrometric Resoeccentric Degeneracy: Eccentric Single Planets Mimic 2:1 Resonant Planet Pairs in Astrometry

Detections of long-period giant exoplanets will expand dramatically with Gaia Data Release 4 (DR4), but interpreting these signals will require care. We derive the astrometric resoeccentric degeneracy: an astrometric analogue of the well-known radial velocity degeneracy in which a single eccentric planet can mimic two circular planets near a 2:1 period ratio. To first order in eccentricity, the sky-projected motion of a single eccentric orbit decomposes into a fundamental mode and first harmonic with an amplitude proportional to that eccentricity. A pair of coplanar, circular planets in a 2:1 orbital resonance produces the same harmonic structure: the outer planet sets the fundamental mode, while the inner planet supplies an apparent first harmonic. We present a mapping between the harmonic amplitudes and effective eccentricity ($e_\mathrm{eff}$) of a single planet that mimics a 2:1 configuration, demonstrating that $e_\mathrm{eff} = \, 2^{1/3}(M_{p,2}/M_{p,1})$, the masses of the inner and outer planets, respectively. Using simulated Gaia data we show that (1) coplanar 2:1 systems are statistically indistinguishable from a single eccentric planet and (2) mutual inclination can break this degeneracy. This bias favors detecting mutually inclined systems, often fingerprints of a dynamically hot history -- traces for processes such as planet-planet scattering or secular chaos. Determining the planetary architectures in which this degeneracy holds will be essential for measuring cool-giant occurrence rates with Gaia and for inferring their dynamical evolution histories.

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arXiv2025

Origins of Mercury's Big Heart of Iron: Exploring Pathways to Form High Core Mass Fraction (CMF) Planets via N-body Simulations

Mercury's core mass fraction (CMF) is ~0.7, more than double that of the other rocky planets in the solar system, which have CMFs of ~0.3. The origin of Mercury's large, iron-rich core remains unknown. Adding to this mystery, an elusive population of "Exo-Mercuries" with high densities is emerging. Therefore, understanding the formation of Mercury and its exoplanetary analogs is essential to developing a comprehensive planet formation theory. Two hypotheses have been proposed to explain the high CMF of Mercury: (1) giant impacts during the latest stages of planet formation strip away mantle layers, leaving Mercury with a large core; and (2) earlier-stage iron enrichment of planetesimals closer to the Sun leads to the formation of an iron-rich planet. In this work, we conduct N-body simulations to test these two possibilities. Our simulations are focused on the solar system, however, we aim to provide a framework that can later be applied to the formation of high-CMF exoplanets. To investigate the giant impact scenario, we employ uniform initial CMF distributions. To address the other hypothesis, we use a step function with higher CMFs in the inner region. For a uniform initial CMF distribution, our results indicate that although erosive impacts produce iron-rich particles, without mechanisms that deplete stripped mantle material, these particles merge with lower-CMF objects and do not lead to Mercury's elevated CMF. However, a step function initial CMF distribution leads to the formation of a high-CMF planet alongside Earth-like planets, resembling the architecture of the terrestrial solar system.

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arXiv2025

A High-Precision, Differentiable Code for Solar System Ephemerides

We present jorbit, a python/JAX library designed to enable modern data-driven numerical studies of the solar system. Written entirely in JAX, an auto-differentiable and optionally GPU accelerated language behind many current large-scale machine learning efforts, jorbit includes an independent implementation of REBOUND's IAS15 integrator and the ability to parse precomputed ephemerides such as the JPL DE series. In its default behavior, jorbit maintains ~1 mas agreement with JPL Horizons on ~decade timescales for typical main-belt asteroids, enabling it to fully capitalize on high-precision astrometry and ranging data. We include details of the code's implementation and several worked examples, including illustrations of jorbit's ability to simulate N-body systems, forward model astrometric data, fit orbits, replicate the Minor Planet Center's "MPChecker" service, and contribute to modeling the effect of minor planets on stellar light curves.

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arXiv2025

JWST Coronagraphic Images of 14 Her c: a Cold Giant Planet in a Dynamically Hot, Multi-planet System

Most observed multi-planet systems are coplanar, in a dynamically "cold" configuration of concentric orbits like our own Solar System. With the James Webb Space Telescope (JWST) we have detected 14 Her c, the first mature and cold exoplanet directly imaged in a dynamically "hot", multi-planet system. With large eccentricities and a nonzero mutual inclination, the present-day architecture of this system points to a turbulent past and ongoing angular momentum exchange between the planetary orbits of 14 Her b and c. The temperature of 14 Her c rivals both the coldest imaged exoplanet and the coldest known brown dwarf. Moreover, its photometry at 4.4 mu is consistent with the presence of carbon disequilibrium chemistry and water ice clouds in its atmosphere. 14 Her c presents a unique laboratory to study giant planet formation, dynamical evolution of multi-planet system architectures, and atmospheric composition and dynamics in extremely cold worlds.

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arXiv2025

Collisional Fragmentation Support in TRACE

We present improved collision support for TRACE, a state-of-the-art hybrid integrator in REBOUND. TRACE now supports collisional fragmentation and can handle both removing and adding particles mid-timestep. We describe the back-end logic implemented for robust collision support, and compare TRACE's performance to other integrators including MERCURIUS on a large-N protoplanetary disk simulation with various collision prescriptions, a system which TRACE previously could not handle. TRACE matches the behavior of these integrators, while offering potentially vast speedups of over 70x. All updates described in this Note are available with the most recent public release of REBOUND.

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arXiv2025

The Formation of Double Hot Jupiter Systems through von Zeipel-Lidov-Kozai Migration

The von Zeipel-Lidov-Kozai (ZLK) mechanism with tidal friction has been demonstrated as a promising avenue to generate hot Jupiters in stellar binary systems. Previous population studies of hot Jupiter formation have largely examined this mechanism in systems comprised of three bodies: two stars and one planet. However, because stars in a binary system form in similar environments with comparable metallicities, the formation of a single hot Jupiter in such a system may imply that the conditions are more likely met for the companion star, as well. We investigate the ZLK mechanism with tidal friction as a potential mechanism to produce double hot Jupiter systems in stellar binaries. Using N-body simulations, we characterize the evolution of two cold Jupiters, each orbiting one star in a binary system, undergoing mirrored ZLK migration. We then examine the robustness of this mechanism to asymmetries in stellar masses, planet masses, and planet orbital inclinations relative to the binary plane. We predict that, under the assumptions that (1) most hot Jupiters in binary star systems form through ZLK migration of primordially formed cold Jupiters and (2) if one star in a binary system forms a cold Jupiter, the second does as well, a comprehensive search could identify double hot Jupiters in up to ~9% of the close- to moderate- separation $a<2000$ AU) binary systems that already host a known hot Jupiter. We also argue that a blind search for ZLK-migrated double hot Jupiters should prioritize twin stellar binaries with pericenter approaches of a few hundred AU.

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arXiv2024

The Dynamical History of HIP-41378 f -- Oblique Exorings Masquerading as a Puffy Planet

The super-puff HIP-41378 f represents a fascinating puzzle due to its anomalously low density on a far-out orbit in contrast with other known super-puffs. In this work, we explore the hypothesis that HIP-41378 f is not in fact a low-density planet, but rather hosts an opaque ring system. We analyze the dynamical history of the system, and show that convergent migration is necessary to explain the system's long-term stability. We then show that this same migration process plausibly captures HIP-41378 f into spin-orbit resonance and excites the planetary obliquity to high values. This tilts the surrounding ring and is a plausible explanation for the large transit depth. In the end, we also briefly comment on the likelihood of other super-puff planets being in high-obliquity states. We show that the existence of a tilted extensive ring around a high obliquity planet can serve as an explanation for puffy planets, particularly in multi-planetary systems at far distances from their host stars.

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arXiv2024

squishyplanet: Modeling Transits of Non-spherical Exoplanets in JAX

While astronomers often assume that exoplanets are perfect spheres when analyzing observations, the subset of these distant worlds that are subject to strong tidal forces and/or rapid rotations are expected to be distinctly ellipsoidal or even triaxial. Since a planet's response to these forces is determined in part by its interior structure, measurements of an exoplanet's deviations from spherical symmetry can lead to powerful insights into its composition and surrounding environment. These shape deformations will imprint themselves on a planet's phase curve and transit lightcurve and cause small (1s-100s of parts per million) deviations from their spherical-planet counterparts. Until recently, these deviations were undetectable in typical real-world datasets due to limitations in photometric precision. Now, however, current and soon-to-come-online facilities such as JWST will routinely deliver observations that warrant the consideration of more complex models. To this end we present squishyplanet, a JAX-based Python package that implements an extension of the polynomial limb-darkened transit model presented in Agol et al. 2020 to non-spherical (triaxial) planets, as well as routines for modeling reflection and emission phase curves.

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arXiv2024

Planet-Planet Scattering and ZLK Migration -- The Dynamical History of HAT-P-11

The two planets of the HAT-P-11 system represent fascinating dynamical puzzles due to their significant eccentricities and orbital misalignments. In particular, HAT-P-11 b is on a close-in orbit that tides should have circularized well within the age of the system. Here we propose a two-step dynamical process that can reproduce all intriguing aspects of the system. We first invoke planet-planet scattering to generate significant eccentricities and mutual inclinations between the planets. We then propose that this misalignment initiated von-Zeipel-Lidov-Kozai cycles and high-eccentricity migration that ultimately brought HAT-P-11 b to its present-day orbit. We find that this scenario is fully consistent only when significant tidally-driven radius inflation is accounted for during the tidal migration. We present a suite of N-body simulations exploring each phase of evolution and show that this scenario is consistent with all observational posteriors and the reported age of the system.

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arXiv2024

Significant mutual inclinations between the stellar spin and the orbits of both planets in the HAT-P-11 system

Planet-star obliquity and planet-planet ]mutual inclination encode a planetary system's dynamical history, but both of their values are hard to measure for misaligned systems with close-in companions. HAT-P-11 is a K4 star with two known planets: a close-in, misaligned super-Neptune with a $\approx$5-day orbit, and an outer super-Jupiter with a $\approx$10-year orbit. In this work we present a joint orbit fit of the HAT-P-11 system with astrometry and S-index corrected RV data. By combining our results with previous constraints on the orientation of the star and the inner planet, we find that all three angular momenta -- those of the star, planet b, and planet c -- are significantly misaligned. We confirm the status of planet c as a super-Jupiter, with $2.68\pm0.41\, \mathrm{M_{\rm Jup}}$ at a semimajor axis of $4.10\pm0.06\,$AU, and planet b's mass of $\mathrm{M_b\sin{i_b}}=0.074\pm0.004\, \mathrm{M_{\rm Jup}}$. We present the posterior probability distribution of obliquity between star A and planet c, and mutual inclination between planet b and planet c.

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arXiv2024

TRACE: a code for Time-Reversible Astrophysical Close Encounters

We present TRACE, an almost time-reversible hybrid integrator for the planetary N-body problem. Like hybrid symplectic integrators, TRACE can resolve close encounters between particles while retaining many of the accuracy and speed advantages of a fixed time-step symplectic method such the Wisdom-Holman map. TRACE switches methods time-reversibly during close encounters following the prescription of Hernandez & Dehnen. In this paper we describe the derivation and implementation of TRACE and study its performance for a variety of astrophysical systems. In all our test cases, TRACE is at least as accurate and fast as the hybrid symplectic integrator MERCURIUS. In many cases, TRACE's performance is vastly superior to that of MERCURIUS. In test cases with planet-planet close encounters, TRACE is as accurate as MECURIUS with a 12x speed-up. If close encounters with the central star are considered, TRACE achieves good error performance while MERCURIUS fails to give qualitatively correct results. In ensemble tests of violent scattering systems, TRACE matches the high-accuracy IAS15 while providing a 15x speed-up. In large N systems simulating lunar accretion, TRACE qualitatively gives the same results as IAS15 but at a 41x speed-up. We also discuss some cases such as von Zeipel-Lidov-Kozai cycles where hybrid integrators perform poorly and provide some guidance on which integrator to use for which system. TRACE is freely available within the REBOUND package.

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arXiv2024

Emerging Researchers in Exoplanetary Science (ERES): Lessons Learned in Conference Organization for Early-Career Researchers

Since 2015, the Emerging Researchers in Exoplanetary Science (ERES) conference has provided a venue for early-career researchers in exoplanetary astronomy, astrophysics, and planetary science to share their research, network, and build new collaborations. ERES stands out in that it is spearheaded by early-career researchers, providing a unique attendance experience for the participants and a professional experience for the organizers. In this Bulletin, we share experiences and lessons learned from the perspective of the organizing committee for the 2023 edition of ERES. For this eighth ERES conference, we hosted over 100 participants in New Haven, CT, for a three-day program. This manuscript is aimed primarily toward groups of early-career scientists who are planning a conference for their fields of study. We anticipate that this Bulletin will continue dialogue within the academic community about best practices for equitable event organization.

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