arXiv subjects

Andrew Vanderburg

Publications and source records attributed to Andrew Vanderburg.

At least 73 records · Page 4Linked to original sources

arXiv2025

A long spin period for a sub-Neptune-mass exoplanet

HIP 41378 f is a sub-Neptune exoplanet with an anomalously low density. Its long orbital period and deep transit make it an ideal candidate for detecting oblateness photometrically. We present a new cross-platform, GPU-enabled code greenlantern, suitable for computing transit light curves of oblate planets at arbitrary orientations. We then use Markov Chain Monte Carlo to fit K2 data of HIP 41378 f, specifically examining its transit for possible oblateness and obliquity. We find that the flattening of HIP 41378 f is $f \leq 0.889$ at the 95% confidence level, consistent with a rotation period of $P_\text{rot} \geq 15.3$ hr. In the future, high-precision data from JWST has the potential to tighten such a constraint and can differentiate between spherical and flattened planets.

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arXiv2025

Long-lived Habitable Zones around White Dwarfs undergoing Neon-22 Distillation

White dwarf stars have attracted considerable attention in the past 15 years as hosts for potentially habitable planets, but their low luminosity and continuous cooling are major challenges for habitability. Recently, astronomers have found that about 6% of massive white dwarfs seem to have "paused" their cooling for up to ~10 Gyr. The leading explanation for this cooling delay is the distillation of neutron-rich isotopes such as $^{22}$Ne in the white dwarf's interior, which releases a considerable amount of gravitational energy as the star's internal structure rearranges. Here, we consider the impact of $^{22}$Ne distillation on the evolution of white dwarf habitable zones. We find that $^{22}$Ne distillation in the white dwarf host dramatically increases the time that a planet can continuously reside within the habitable zone (giving more time for life to arise) and that long-lasting habitable zones are located farther from the star (decreasing the impact of tidal forces). These properties may make white dwarfs undergoing $^{22}$Ne distillation more promising locations for habitability than white dwarfs undergoing standard cooling.

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arXiv2025

LensNet: Enhancing Real-time Microlensing Event Discovery with Recurrent Neural Networks in the Korea Microlensing Telescope Network

Traditional microlensing event vetting methods require highly trained human experts, and the process is both complex and time-consuming. This reliance on manual inspection often leads to inefficiencies and constrains the ability to scale for widespread exoplanet detection, ultimately hindering discovery rates. To address the limits of traditional microlensing event vetting, we have developed LensNet, a machine learning pipeline specifically designed to distinguish legitimate microlensing events from false positives caused by instrumental artifacts, such as pixel bleed trails and diffraction spikes. Our system operates in conjunction with a preliminary algorithm that detects increasing trends in flux. These flagged instances are then passed to LensNet for further classification, allowing for timely alerts and follow-up observations. Tailored for the multi-observatory setup of the Korea Microlensing Telescope Network (KMTNet) and trained on a rich dataset of manually classified events, LensNet is optimized for early detection and warning of microlensing occurrences, enabling astronomers to organize follow-up observations promptly. The internal model of the pipeline employs a multi-branch Recurrent Neural Network (RNN) architecture that evaluates time-series flux data with contextual information, including sky background, the full width at half maximum of the target star, flux errors, PSF quality flags, and air mass for each observation. We demonstrate a classification accuracy above 87.5%, and anticipate further improvements as we expand our training set and continue to refine the algorithm.

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arXiv2024

Planets Around Solar Twins/Analogs (PASTA) I.: High precision stellar chemical abundance for 17 planet-hosting stars and the condensation temperature trend

The Sun is depleted in refractory elements compared to nearby solar twins, which may be linked to the formation of giant or terrestrial planets. Here we present high-resolution, high signal-to-noise spectroscopic data for 17 solar-like stars hosting planets, obtained with Magellan II/MIKE, to investigate whether this depletion is related to planet formation. We derive stellar parameters, including stellar atmosphere, age, radius, mass, and chemical abundances for 22 elements from carbon to europium through line-by-line differential analysis. Our uncertainties range from 0.01 dex for Fe and Si to 0.08 dex for Sr, Y, and Eu. By comparing the solar abundances to those of the 17 stars, we investigate the differential abundance ([X/Fe]$_{\rm solar}$ - [X/Fe]$_{\rm star}$) versus condensation temperature ($T_c$) trend. In particular, we apply Galactic chemical evolution corrections to five solar twins within the full sample. Our results conform to previous studies that the Sun is relatively depleted in refractory compared to volatile elements. For both five solar twins and the rest of solar-like stars, we find that all stars hosting known gas giant planets exhibit negative $T_c$ trend slopes, suggesting that the Sun is relatively depleted in refractory elements compared to similar giant-planet-host stars. Additionally, we find no correlation between $T_c$ trend slopes and the total mass of detected terrestrial planets in each system, suggesting that terrestrial planet formation may not be the cause of refractory element depletion in the Sun.

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arXiv2024

Two Earth-size Planets and an Earth-size Candidate Transiting the Nearby Star HD 101581

We report the validation of multiple planets transiting the nearby ($d = 12.8$ pc) K5V dwarf HD 101581 (GJ 435, TOI-6276, TIC 397362481). The system consists of at least two Earth-size planets whose orbits are near a mutual 4:3 mean-motion resonance, HD 101581 b ($R_{p} = 0.956_{-0.061}^{+0.063}~R_{\oplus}$, $P = 4.47$ days) and HD 101581 c ($R_{p} = 0.990_{-0.070}^{+0.070}~R_{\oplus}$, $P = 6.21$ days). Both planets were discovered in Sectors 63 and 64 TESS observations and statistically validated with supporting ground-based follow-up. We also identify a signal that probably originates from a third transiting planet, TOI-6276.03 ($R_{p} = 0.982_{-0.098}^{+0.114}~R_{\oplus}$, $P = 7.87$ days). These planets are remarkably uniform in size and their orbits are evenly spaced, representing a prime example of the "peas-in-a-pod" architecture seen in other compact multi-planet systems. At $V = 7.77$, HD 101581 is the brightest star known to host multiple transiting planets smaller than $1.5~R_{\oplus}$. HD 101581 is a promising system for atmospheric characterization and comparative planetology of small planets.

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arXiv2024

TOI-4504: Exceptionally large Transit Timing Variations induced by two resonant warm gas giants in a three planet system

We present a joint analysis of TTVs and Doppler data for the transiting exoplanet system TOI-4504. TOI-4504 c is a warm Jupiter-mass planet that exhibits the largest known transit timing variations (TTVs), with a peak-to-node amplitude of $\sim$ 2 days, the largest value ever observed, and a super-period of $\sim$ 930 d. TOI-4504 b and c were identified in public TESS data, while the TTVs observed in TOI-4504 c, together with radial velocity (RV) data collected with FEROS, allowed us to uncover a third, non-transiting planet in this system, TOI-4504 d. We were able to detect transits of TOI-4504 b in the TESS data with a period of 2.4261$\pm 0.0001$ days and derive a radius of 2.69$\pm 0.19$ R$_{\oplus}$. The RV scatter of TOI-4504 was too large to constrain the mass of TOI-4504 b, but the RV signals of TOI-4504 c \& d were sufficiently large to measure their masses. The TTV+RV dynamical model we apply confirms TOI-4504 c as a warm Jupiter planet with an osculating period of 82.54$\pm 0.02$ d, mass of 3.77$\pm 0.18$ M$_{\rm J}$ and a radius of 0.99$\pm 0.05$ R$_{\rm J}$, while the non-transiting planet TOI-4504 d, has an orbital period of 40.56$\pm 0.04$ days and mass of 1.42$_{-0.06}^{+0.07}$ M$_{\rm J}$. We present the discovery of a system with three exoplanets: a hot sub-Neptune and two warm Jupiter planets. The gas giant pair is stable and likely locked in a first-order 2:1 mean-motion resonance (MMR). The TOI-4504 system is an important addition to MMR pairs, whose increasing occurrence supports a smooth migration into a resonant configuration during the protoplanetary disk phase.

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arXiv2024

A gravitational wave detectable candidate Type Ia supernova progenitor

Type Ia supernovae, critical for studying cosmic expansion, arise from thermonuclear explosions of white dwarfs, but their precise progenitor pathways remain unclear. Growing evidence supports the ``double-degenerate'' scenario, where two white dwarfs interact. The absence of other companion types capable of explaining the observed Ia rate, along with observations of hyper-velocity white dwarfs interpreted as surviving companions of such systems provide compelling evidence in favor of this scenario. Upcoming millihertz gravitational wave observatories like the Laser Interferometer Space Antenna (LISA) are expected to detect thousands of double-degenerate systems, though the most compact known candidate Ia progenitors produce only marginally detectable gravitational wave signals. Here, we report observations of ATLAS J1138-5139, a binary white dwarf system with an orbital period of 28 minutes. Our analysis reveals a 1 solar mass carbon-oxygen white dwarf accreting from a helium-core white dwarf. Given its mass, the accreting carbon-oxygen white dwarf is poised to trigger a typical-luminosity Type Ia supernova within a few million years, or to evolve into a stably mass-transferring AM CVn system. ATLAS J1138-5139 provides a rare opportunity to calibrate binary evolution models by directly comparing observed orbital parameters and mass transfer rates closer to merger than any previously identified candidate Type Ia progenitor. Its compact orbit ensures detectability by LISA, demonstrating the potential of millihertz gravitational wave observatories to reveal a population of Type Ia progenitors on a Galactic scale, paving the way for multi-messenger studies offering insights into the origins of these cosmologically significant explosions.

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arXiv2024

A giant planet transiting a 3-Myr protostar with a misaligned disk

Astronomers have found more than a dozen planets transiting 10-40 million year old stars, but even younger transiting planets have remained elusive. A possible reason for the lack of such discoveries is that newly formed planets are not yet in a configuration that would be recognized as a transiting planet or cannot exhibit transits because our view is blocked by a protoplanetary disk. However, we now know that many outer disks are warped; provided the inner disk is depleted, transiting planets may thus be visible. Here we report the observations of the transiting planet IRAS 04125+2902 b orbiting a 3 Myr, 0.7 M$_\odot$, pre-main sequence star in the Taurus Molecular Cloud. IRAS 04125+2902 hosts a nearly face-on (i $\sim$ 30$^\circ$) transitional disk and a wide binary companion. The planet has a period of 8.83 days, a radius of 10.9 R$_\oplus$ (0.97R$_J$), and a 95%-confidence upper limit on its mass of 90M$_\oplus$ (0.3M$_J$) from radial velocity measurements, making it a possible precursor of the super-Earths and sub-Neptunes that are commonly found around main-sequence stars. The rotational broadening of the star and the orbit of the wide (4", 635 AU) companion are both consistent with edge-on orientations. Thus, all components of the system appear to be aligned except the outer disk; the origin of this misalignment is unclear. Given the rare set of circumstances required to detect a transiting planet at ages when the disk is still present, IRAS 04125+2902 b likely provides a unique window into sub-Neptunes immediately following formation.

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arXiv2024

HD 28185 Revisited: An Outer Planet, Instead of a Brown Dwarf, On a Saturn-like Orbit

As exoplanet surveys reach ever-higher sensitivities and durations, planets analogous to the solar system giant planets are increasingly within reach. HD 28185 is a Sun-like star known to host a $m\sin i=6 M_J$ planet on an Earth-like orbit; more recently, a brown dwarf with a more distant orbit has been claimed. In this work we present a comprehensive reanalysis of the HD 28185 system, based on 22 years of radial velocity observations and precision Hipparcos-Gaia astrometry. We confirm the previous characterisation of HD 28185 b as a temperate giant planet, with its $385.92^{+0.06}_{-0.07}$ day orbital period giving it an Earth-like incident flux. In contrast, we substantially revise the parameters of HD 28185 c; with a new mass of $m=6.0\pm0.6 M_J$ we reclassify this companion as a super-jovian planet. HD 28185 c has an orbital period of $24.9^{+1.3}_{-1.1}$ years, a semi-major axis of $8.50^{+0.29}_{-0.26}$ AU, and a modest eccentricity of $0.15\pm0.04$, resulting in one of the most Saturn-like orbits of any known exoplanet. HD 28185 c lies at the current intersection of detection limits for RVs and direct imaging, and highlights how the discovery of giant planets at $\approx$10 AU separations is becoming increasingly routine.

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arXiv2024

TESS Hunt for Young and Maturing Exoplanets (THYME) XII: A Young Mini-Neptune on the Upper Edge of the Radius Valley in the Hyades Cluster

We present the discovery and characterization of TOI-4364\,b, a young mini-Neptune in the tidal tails of the Hyades cluster, identified through TESS transit observations and ground-based follow-up photometry. The planet orbits a bright M dwarf ($K=9.1$\,mag) at a distance of 44\,pc, with an orbital period of 5.42\,days and an equilibrium temperature of $488^{+4}_{-4}$\,K. The host star's well-constrained age of 710\,Myr makes TOI-4364\,b an exceptional target for studying early planetary evolution around low-mass stars. We determined a planetary radius of $2.01^{+0.1}_{-0.08}$\,Earth radii, indicating that this planet is situated near the upper edge of the radius valley. This suggests that the planet retains a modest H/He envelope. As a result, TOI-4364\,b provides a unique opportunity to explore the transition between rocky super-Earths and gas-rich mini-Neptunes at the early stages of evolution. Its radius, which may still evolve as a result of ongoing atmospheric cooling, contraction, and photoevaporation, further enhances its significance for understanding planetary development. Furthermore, TOI-4364\,b possesses a moderately high Transmission Spectroscopy Metric of 44.2, positioning it as a viable candidate for atmospheric characterization with instruments such as JWST. This target has the potential to offer crucial insights into atmospheric retention and loss in young planetary systems.

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arXiv2024

TIC 290061484: A Triply Eclipsing Triple System with the Shortest Known Outer Period of 24.5 Days

We have discovered a triply eclipsing triple-star system, TIC 290061484, with the shortest known outer period, Pout, of only 24.5 days. This "eclipses" the previous record set by lambda Tauri at 33.02 days, which held for 68 yr. The inner binary, with an orbital period of Pin = 1.8 days, produces primary and secondary eclipses and exhibits prominent eclipse timing variations with the same periodicity as the outer orbit. The tertiary star eclipses, and is eclipsed by, the inner binary with pronounced asymmetric profiles. The inclinations of both orbits evolve on observable timescales such that the third-body eclipses exhibit dramatic depth variations in TESS data. A photodynamical model provides a complete solution for all orbital and physical parameters of the triple system, showing that the three stars have masses of 6.85, 6.11, and 7.90 MSun, radii near those corresponding to the main sequence, and Teff in the range of 21,000-23,700 K. Remarkably, the model shows that the triple is in fact a subsystem of a hierarchical 2+1+1 quadruple with a distant fourth star. The outermost star has a period of ~3200 days and a mass comparable to the stars in the inner triple. In ~20 Myr, all three components of the triple subsystem will merge, undergo a Type II supernova explosion, and leave a single remnant neutron star. At the time of writing, TIC 290061484 is the most compact triple system and one of the tighter known compact triples (i.e., Pout/Pin = 13.7).

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arXiv2024

The Featherweight Giant: Unraveling the Atmosphere of a 17 Myr Planet with JWST

The characterization of young planets (< 300 Myr) is pivotal for understanding planet formation and evolution. We present the 3-5$μ$m transmission spectrum of the 17 Myr, Jupiter-size ($R$ $\sim$10$R_{\oplus}$) planet, HIP 67522 b, observed with JWST/NIRSpec/G395H. To check for spot contamination, we obtain a simultaneous $g$-band transit with SOAR. The spectrum exhibits absorption features 30-50% deeper than the overall depth, far larger than expected from an equivalent mature planet, and suggests that HIP 67522 b's mass is $<$20 $M_{\oplus}$ irrespective of cloud cover and stellar contamination. A Bayesian retrieval analysis returns a mass constraint of $13.8\pm1.0M_{\oplus}$. This challenges the previous classification of HIP 67522 b as a hot Jupiter and instead, positions it as a precursor to the more common sub-Neptunes. With a density of $<$0.10g/cm$^{3}$, HIP 67522 b is one of the lowest density planets known. We find strong absorption from H$_{2}$O and CO$_{2}$ ($\ge7σ$), a modest detection of CO (3.5$σ$), and weak detections of H$_2$S and SO$_2$ ($\simeq2σ$). Comparisons with radiative-convective equilibrium models suggest supersolar atmospheric metallicities and solar-to-subsolar C/O ratios, with photochemistry further constraining the inferred atmospheric metallicity to 3$\times$10 Solar due to the amplitude of the SO$_2$ feature. These results point to the formation of HIP 67522 b beyond the water snowline, where its envelope was polluted by icy pebbles and planetesimals. The planet is likely experiencing substantial mass loss (0.01-0.03 M$_{\oplus}$ Myr$^{-1}$), sufficient for envelope destruction within a Gyr. This highlights the dramatic evolution occurring within the first 100 Myr of its existence.

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arXiv2024

TESS Investigation -- Demographics of Young Exoplanets (TI-DYE) II: a second giant planet in the 17-Myr system HIP 67522

The youngest ($<$50 Myr) planets are vital to understand planet formation and early evolution. The 17 Myr system HIP 67522 is already known to host a giant ($\simeq$10$R_\oplus$) planet on a tight orbit. In the discovery paper, Rizzuto et al. 2020 reported a tentative single transit detection of an additional planet in the system using TESS. Here, we report the discovery of HIP 67522 c which matches with that single transit event. We confirm the signal with ground-based multi-wavelength photometry from Sinistro and MuSCAT4. At a period of 14.33 days, planet c is close to a 2:1 mean motion resonance with b (6.96 days or 2.06:1). The light curve shows distortions during many of the transits, which are consistent with spot crossing events and/or flares. Fewer stellar activity events are seen in the transits of planet b, suggesting that planet c is crossing a more active latitude. Such distortions, combined with systematics in the TESS light curve extraction, likely explain why planet c was previously missed.

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arXiv2024

The K2 and TESS Synergy III: search and rescue of the lost ephemeris for K2's first planet

K2-2 b/HIP 116454 b, the first exoplanet discovery by K2 during its Two-Wheeled Concept Engineering Test, is a sub-Neptune (2.5 $\pm$ 0.1 $R_\oplus$, 9.7 $\pm$ 1.2 $M_\oplus$) orbiting a relatively bright (KS = 8.03) K-dwarf on a 9.1 day period. Unfortunately, due to a spurious follow-up transit detection and ephemeris degradation, the transit ephemeris for this planet was lost. In this work, we recover and refine the transit ephemeris for K2-2 b, showing a $\sim40σ$ discrepancy from the discovery results. To accurately measure the transit ephemeris and update the parameters of the system, we jointly fit space-based photometric observations from NASA's K2, TESS, and Spitzer missions with new photometric observations from the ground, as well as radial velocities from HARPS-N that are corrected for stellar activity using a new modeling technique. Ephemerides becoming lost or significantly degraded, as is the case for most transiting planets, highlights the importance of systematically updating transit ephemerides with upcoming large efforts expected to characterize hundreds of exoplanet atmospheres. K2-2 b sits at the high-mass peak of the known radius valley for sub-Neptunes, and is now well-suited for transmission spectroscopy with current and future facilities. Our updated transit ephemeris will ensure no more than a 13-minute uncertainty through 2030.

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arXiv2024

The MIRI Exoplanets Orbiting White Dwarfs (MEOW) Survey: Mid-Infrared Excess Reveals a Giant Planet Candidate around a Nearby White Dwarf

The MIRI Exoplanets Orbiting White dwarfs (MEOW) Survey is a cycle 2 JWST program to search for exoplanets around dozens of nearby white dwarfs via infrared excess and direct imaging. In this paper, we present the detection of mid-infrared excess at 18 and 21 microns towards the bright (V = 11.4) metal-polluted white dwarf WD 0310-688. The source of the IR excess is almost certainly within the system; the probability of background contamination is $<0.1\%$. While the IR excess could be due to an unprecedentedly small and cold debris disk, it is best explained by a $3.0^{+5.5}_{-1.9}$ M$_{\rm Jup}$ cold (248$^{+84}_{-61}$ K) giant planet orbiting the white dwarf within the forbidden zone (the region where planets are expected to be destroyed during the star's red giant phase). We constrain the source of the IR excess to an orbital separation of 0.1-2 AU, marking the first discovery of a white dwarf planet candidate within this range of separations. WD 0310-688 is a young remnant of an A or late B-type star, and at just 10.4 pc it is now the closest white dwarf with a known planet candidate. Future JWST observations could distinguish the two scenarios by either detecting or ruling out spectral features indicative of a planet atmosphere.

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arXiv2024

Searching for GEMS: Characterizing Six Giant Planets around Cool Dwarfs

Transiting giant exoplanets around M-dwarf stars (GEMS) are rare, owing to the low-mass host stars. However, the all-sky coverage of TESS has enabled the detection of an increasingly large number of them to enable statistical surveys like the \textit{Searching for GEMS} survey. As part of this endeavour, we describe the observations of six transiting giant planets, which includes precise mass measurements for two GEMS (K2-419Ab, TOI-6034b) and statistical validation for four systems, which includes validation and mass upper limits for three of them (TOI-5218b, TOI-5616b, TOI-5634Ab), while the fourth one -- TOI-5414b is classified as a `likely planet'. Our observations include radial velocities from the Habitable-zone Planet Finder on the Hobby-Eberly Telescope, and MAROON-X on Gemini-North, along with photometry and high-contrast imaging from multiple ground-based facilities. In addition to TESS photometry, K2-419Ab was also observed and statistically validated as part of the K2 mission in Campaigns 5 and 18, which provides precise orbital and planetary constraints despite the faint host star and long orbital period of $\sim 20.4$ days. With an equilibrium temperature of only 380 K, K2-419Ab is one of the coolest known well-characterized transiting planets. TOI-6034 has a late F-type companion about 40\arcsec~away, making it the first GEMS host star to have an earlier main-sequence binary companion. These confirmations add to the existing small sample of confirmed transiting GEMS.

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arXiv2024

TESS Giants Transiting Giants. VI. Newly Discovered Hot Jupiters Provide Evidence for Efficient Obliquity Damping after the Main Sequence

The degree of alignment between a star's spin axis and the orbital plane of its planets (the stellar obliquity) is related to interesting and poorly understood processes that occur during planet formation and evolution. Hot Jupiters orbiting hot stars ($\gtrsim$6250 K) display a wide range of obliquities, while similar planets orbiting cool stars are preferentially aligned. Tidal dissipation is expected to be more rapid in stars with thick convective envelopes, potentially explaining this trend. Evolved stars provide an opportunity to test the damping hypothesis, particularly stars that were hot on the main sequence and have since cooled and developed deep convective envelopes. We present the first systematic study of the obliquities of hot Jupiters orbiting subgiants that recently developed convective envelopes using Rossiter-McLaughlin observations. Our sample includes two newly discovered systems in the Giants Transiting Giants Survey (TOI-6029 b, TOI-4379 b). We find that the orbits of hot Jupiters orbiting subgiants that have cooled below $\sim$6250 K are aligned or nearly aligned with the spin-axis of their host stars, indicating rapid tidal realignment after the emergence of a stellar convective envelope. We place an upper limit for the timescale of realignment for hot Jupiters orbiting subgiants at $\sim$500 Myr. Comparison with a simplified tidal evolution model shows that obliquity damping needs to be $\sim$4 orders of magnitude more efficient than orbital period decay to damp the obliquity without destroying the planet, which is consistent with recent predictions for tidal dissipation from inertial waves excited by hot Jupiters on misaligned orbits.

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arXiv2024

Aligning Planet-Hosting Binaries via Dissipative Precession in Circumstellar Disks

Recent observations have demonstrated that some subset of even moderately wide-separation planet-hosting binaries are preferentially configured such that planetary and binary orbits appear to lie within the same plane. In this work, we explore dissipation during the protoplanetary disk phase, induced by disk warping as the system is forced into nodal recession by an inclined binary companion as a possible avenue of achieving orbit-orbit alignment. We analytically model the coupled evolution of the disk angular momentum vector and stellar spin vector under the influence of a distant binary companion. We find that a population of systems with random initial orientations can appear detectably more aligned after undergoing dissipative precession, and that this process can simultaneously produce an obliquity distribution that is consistent with observations. While dissipative precession proceeds efficiently in close binaries, favorable system properties (e.g., $r_{out} \gtrsim 100$ AU, $α\gtrsim 0.05$, and/or $M_b/M_{*} \gtrsim 1$) are required to reproduce observed alignment trends at wider binary separations $a_\mathrm{b} \gtrsim450$ AU. Our framework further predicts that circum-primary planets in systems with high stellar mass ratios should be preferentially less aligned than planets in equal-mass stellar binary systems. We discover tentative evidence for this trend in \textit{Gaia} DR3 and TESS data. Our findings suggest that dissipative precession may play a significant role in sculpting orbital configurations in a sub-set of moderately-wide planet-hosting binaries, but is likely not solely responsible for their observed population-level alignment.

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