arXiv subjects

Chris Stockdale

Publications and source records attributed to Chris Stockdale.

At least 19 recordsLinked to original sources

arXiv2026

Assessing the Impact of High-Resolution Imaging on Statistical Validation of TESS Planet Candidates

High-resolution imaging is widely used to constrain false-positive scenarios in exoplanet validation, but it is a finite follow-up resource that reaches only a subset of candidates, and its population-level impact on validation outcomes has not been quantified through controlled removal experiments. Using an automated pipeline built on TRICERATOPS, we compute the false-positive probability (FPP) of 443 TESS planet candidates. For the 264 planet candidates with high-resolution imaging observations, we compute FPP with and without the corresponding contrast curves, allowing us to quantify the impact of the additional data. We find that 72% of 68 contrast-curve bearing validated planets would fail validation without their adopted contrast curves. The fraction requiring imaging decreases with increasing planet size, from 100% below $1.7~R_\oplus$ to $33\%$ above $4~R_\oplus$: within our sample and TRICERATOPS-based analysis, the availability of high-resolution imaging directly limits the yield of small-planet validation and the supply of validated targets for atmospheric characterization. Our analysis statistically validates 64 new TESS planets with sizes spanning 0.94 to 7.83 $R_\oplus$ across hosts of spectral type M through F. Four of these are highly amenable to JWST observations based on the transmission and emission spectroscopy metrics, and each achieves validation only with its imaging constraint.

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arXiv2026

A Pair of Warm Saturn-mass Planets near the 2:1 Mean Motion Resonance around TOI-3850

Warm Jupiters, with orbital periods of $10$--$200~\rm{days}$ and radii exceeding $8~R_{\oplus}$, are a relatively understudied class of exoplanets occupying the parameter space between hot Jupiters and more widely separated, colder Jupiter analogs. In this work, we report the detection of a multi-planet warm Jupiter system around TOI-3850 (TIC-143008050), a moderately active, near-solar metallicity G0 dwarf star observed by TESS in Sectors 15, 21, 41, 48 and 75. Initially, a single candidate planet was discovered by TESS, displaying transit timing variations (TTVs) with an amplitude of $\sim 1~\rm hr$ and a super-period of $513~\rm days$. Through a combination of transit photometry, radial velocity observations with MAROON-X, and TTV modeling, we identify two planets: TOI-3850 b $(P_b=14.484\pm0.002~\mathrm{days},~ M_b =112\pm20~M_{\oplus},~e_b = 0.018\pm0.008, R_b = 12.07\pm0.09~R_{\oplus}, ~T_{\rm{eq}}=841\pm10~\rm{K})$, a transiting warm Jupiter, and TOI-3850 c $(P_c=29.85\pm0.01~\mathrm{days},~ M_c =90\pm15~M_{\oplus},~e_c < 0.015, ~T_{\rm{eq}}=661\pm7~\rm{K})$, a non-transiting, Saturn-mass companion. The two planets lie wide of the 2:1 mean motion resonance $(P_c/P_b \approx 2.06)$, consistent with a formation history involving disk-driven migration. $N$-body integrations indicate that TOI-3850 c may begin to transit on decadal timescales, while TOI-3850 b remains a promising target for follow-up atmospheric characterization.

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arXiv2026

ASTEP confirmation of a pair of long-period Jupiter-sized planets with extremely low densities transiting TOI-791

Gas giant planets with periods $20~<~P~<~300~\rm days$ orbiting Sun-like stars are a relatively uncommon outcome of planetary formation, and key questions about the nature and formation of this sub-population remain unanswered. Theoretical models for the location of their formation (in- or ex-situ) and for their subsequent migration predict different outcomes in terms of planet masses and eccentricities, indicating that observations have a key role to play in disentangling their histories. In this work we present the discovery and confirmation of a pair of long-period Jupiter-sized planets transiting an F7 star: TOI-791 b is a $0.993\pm0.033\rm~R_{Jup}$ planet on a $139.29931_{-0.00012}^{+0.00011}~\rm day$ orbit, and TOI-791 c, a $1.155\pm0.040\rm ~R_{Jup}$ planet on a $232.01570_{-0.00071}^{+0.00067}~\rm day$ orbit. The two planets are within 0.07% of a second-order 5:3 period commensurability leading to transit timing variations (TTVs) of up to 50 minutes. We confirm their planetary nature using ground-based photometry, including multiple full detections of the $>11~\rm hr$ transits of both TOI-791 b and c from Antarctica with ASTEP, making these the longest-duration transits ever observed in their entirety from the ground. Our detailed analysis of the TTV signal allows us to measure dynamical masses for both planets, which yield densities of $ρ_{\rm b}=0.038\pm0.008 \rm ~g~cm^{-3}$ and $ρ_{\rm c}=0.047\pm0.006 \rm ~g~cm^{-3}$, indicating that TOI-791~b and c are two of the lowest density giant planets ever detected. While these measurements are robust, further follow-up is needed to fully characterise the TTV signal and the architecture of the system.

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arXiv2026

Stellar Obliquities of Young Systems, Atmospheres Undergoing Contraction and Escape (SOYSAUCE) II: a 135 Myr planet on an aligned orbit with transit timing variations

Young planets (<1 Gyr) provide opportunities to directly probe planet formation and evolution processes in action. However, due to heightened stellar activity, there is a lack of known transiting planets in adolescence (~100-500 Myr). Here we present the validation of TIC 150070085 b, a 3.6 R_E planet on a 10.47 day orbit, and report the candidate TIC 150070085 c, a 3.0 R_E planet on a 15.90 day orbit. While we are unable to validate the second signal, the proximity to mean motion resonance (3:2) and transit timing variations observed in the transits of TIC 150070085 b strongly suggest the signal is planetary. We confirm the host star as a member of Alessi 84 and combine the group's CMD, rotation, and variability properties to update the age to 135 +/- 10 Myr. We additionally use MAROON-X to observe the Rossiter-McLaughlin signal of TIC 150070085 b and measure the sky projected obliquity angle ($λ$). We find TIC 150070085 b is consistent with a near-aligned orbit with its host star (|$λ$| = 18 +/- 12$^\circ$), in line with similarly aged transiting planets with measured $λ$ values. Continued discovery and characterization of planets in this age regime are vital to link planetary infancy (<50 Myr) and maturity (>1 Gyr).

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arXiv2026

Uncovering the Rapidly Evolving Orbits of the Dynamic TOI-201 System

Studying planetary interactions in exoplanet systems informs theories of planet formation and evolution, providing essential context for understanding our own solar system. We combine spectroscopy, transit photometry, transit timing variations, and astrometry to characterize the TOI-201 system. The co-transiting system consists of a super-Earth, warm Jupiter, and massive companion at 5.8, 53, and 2900 day orbital periods, respectively. We perform dynamical simulations to study the past and future of the system. von-Zeipel-Kozai-Lidov oscillations emerge as the most plausible scenario to explain the outer companion's high orbital eccentricity, with planet-planet scattering a possible but less likely contender. Due to non-zero mutual inclinations between the planets, the system is visibly evolving on very short timescales, with the current co-transiting configuration ending in 200 years.

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arXiv2026

A Warm Massive Pair of Planets around TOI-1232 Revealed with Transit-timing Variations and Doppler Spectroscopy

TOI-1232 is a G-dwarf star with a mass of $1.06_{-0.06}^{+0.07} M_\odot$, a radius of $1.07\pm 0.05 R_\odot$, and slightly higher metallicity than solar of Fe/H = $0.18 \pm 0.05$. The star hosts a transiting warm Jovian-mass planet, TOI-1232 b, with an orbital period of $P_{b} = 14.256_{-0.001}^{+0.001}$ days, identified with data from multiple sectors of the $\textit{TESS}$ space telescope. The $\textit{TESS}$ light curve of TOI-1232 is complex, as it is contaminated by a background eclipsing binary with a period of $1.37$ days. The TOI-1232 b was firmly confirmed by ground-based transit follow-up campaigns from Las Cumbres, Hazelwood, Brierfield, and ASTEP observatories.Additionally, the $\textit{TESS}$ transits of TOI-1232 b exhibit strong transit timing variations (TTVs) with a super-period of $235.5 \pm 0.7$ days and a semi-amplitude of 27 minutes. Radial velocity (RV) follow-up with the FEROS spectrograph confirms the planetary nature of the transiting candidate, while a self-consistent $N$-body analysis of RVs and TTVs pinpoints the presence of a second outer Saturn-mass companion, TOI-1232 c with a period of $P_{c} = 30.356_{-0.012}^{+0.010}$ days. The TOI-1232 warm-giant system is particularly important due to the evidence of two massive planets that reside near the 2:1 commensurability but are not locked in a mean motion resonance (MMR). Thanks to $\textit{TESS}$, we have revealed a handful of these rare systems. Hence, TOI-1232 is an important addition to understanding the formation and dynamical evolution of such compact, massive, warm giant planets.

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arXiv2026

A Ground-Based Transit Observation of the Long-Period Extremely Low-Density Planet HIP 41378 f

We present a ground-based transit detection of HIP 41378 f, a long-period ($P = 542$ days), extremely low-density ($0.09 \pm 0.02$ g cm$^{-3}$) giant exoplanet in a dynamically complex system. Using photometry from Tierras, TRAPPIST-North, and multiple LCOGT sites, we constrain the transit center time to $T_{C,6} = 2460438.891 \pm 0.052$ BJD TDB. This marks only the second ground-based detection of HIP 41378 f, currently the longest-period and longest-duration transiting exoplanet observed from the ground. We use this new detection, along with a recently published transit time from Rossiter-McLaughlin observations, to update the TTV solution for HIP 41378 f. We predict the next two transits will occur at $T_{C,7} = 2460980.793^{+0.098}_{-0.129}$ BJD TDB (2025 November 1) and $T_{C,8} = 2461522.653^{+0.213}_{-0.238}$ BJD TDB (2027 April 27). Incorporating new TESS Sector 88 data, we also rule out the 101-day orbital period alias for HIP 41378 d, and find that the remaining viable solutions are centered on the 278, 371, and 1113-day aliases. The latter two imply dynamical configurations that challenge the canonical view of planet e as the dominant perturber of planet f. Our results suggest that HIP 41378 d may instead play the leading role in shaping the TTV of HIP 41378 f.

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arXiv2026

The Occurrence Rate of Nearby Planetary Companions to Hot Jupiters

Of the > 500 confirmed transiting hot jupiters and approximately 2000 additional candidates today, only ten are known to have nearby companion planets. The survival of nearby companions means that these hot jupiters cannot have migrated to their present location via dynamically disruptive high-eccentricity migration but instead have undergone disk migration or formed in situ. The occurrence rate for these nearby companions, therefore, constrains the relative efficiency of different hot jupiter formation pathways. Here, we perform a uniform box least-squares search for nearby transiting companions to hot jupiters in the first five years of TESS data. Accounting for observational completeness and detection efficiency, we arrive at an occurrence rate of $(7.6^{+5.5}_{-3.8})\%$, which is a lower limit on the fraction of hot jupiters that underwent disk migration or in situ formation. Comparing this rate with that derived from transit-timing variation searches suggests that hot jupiters are likely mostly aligned with their nearby companions, but their apparently higher incidence of grazing transits may point to a slight preferential misalignment. We also synthesize evidence that hot jupiters with nearby companions may have cold companions at a rate similar to that of other hot jupiters. Comprehensive transit, radial velocity, and stellar obliquity measurements in hot jupiter systems with nearby companions will be necessary to fully account for the relative prevalence of proposed hot jupiter formation pathways.

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arXiv2025

From Earths to Super-Earths: Five New Small Planets Transiting M Dwarf Stars

Earth-sized planets transiting M dwarf stars present one of the best opportunities with current facilities for studying the atmospheric and bulk compositions of terrestrial worlds. Here, we statistically validate five new transiting Earth and super-Earth sized planets orbiting M dwarf stars using a combination of light curves from the Transiting Exoplanet Survey Satellite, multi-color observations from Palomar and Las Cumbres Observatory, high-resolution imaging, and stellar spectroscopy. The sample includes: TOI-5716 b, an Earth-sized planet (R_p = 0.96 $\pm$ 0.05 Rearth) with a 6.766-day orbit around a metal-poor thin-disk star ([Fe/H] = -0.54 $\pm$ 0.10); TOI-5728 b, a super-Earth (R_p = 1.31 $\pm$ 0.05 Rearth) on an 11.497-day orbit; and TOI-5736 b, a larger planet (R_p = 1.56 $\pm$ 0.07 Rearth) with an ultra-short period of just 0.649 days. We also statistically validate a multi-planet system, TOI-5489, hosting two similarly-sized super-Earths: TOI-5489 b (R_p = 1.40 $\pm$ 0.05 R_earth) and TOI-5489 c (R_p = 1.28 $\pm$ 0.07 R_earth) with orbital periods of 3.152 and 4.921 days, respectively. Due to their longer orbital periods, TOI-5716 b and TOI-5728 b both have equilibrium temperatures $\leq$ 400 K, making them useful test cases for studies of atmospheric mass loss. If TOI-5728 b is confirmed to have an Earth-like bulk composition, it would join the very small sample of rocky planets orbiting mid- to late-M dwarfs that lie below the cosmic shoreline and therefore may have retained high mean molecular weight atmospheres.

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arXiv2025

THYME XIII: Two young Neptunes orbiting a 75-Myr star in the Alpha Persei Cluster

Young planets with mass measurements are particularly valuable in studying atmospheric mass-loss processes, but these planets are rare and their masses difficult to measure due to stellar activity. We report the discovery of a planetary system around TOI-6109, a young, 75 Myr-old Sun-like star in the Alpha Persei cluster. It hosts at least two transiting Neptune-like planets. Using three TESS sectors, 30 CHEOPS orbits, and photometric follow-up observations from the ground, we confirm the signals of the two planets. TOI-6109 b has an orbital period of P=$5.6904^{+0.0004}_{-0.0004}$ days and a radius of R=$4.87^{+0.16}_{-0.12}$ R$_\oplus$. The outer planet, TOI-6109 c has an orbital period of P=$8.5388^{+0.0006}_{-0.0005}$ days and a radius of R=$4.83^{+0.07}_{-0.06}$ R$_\oplus$. These planets orbit just outside a 3:2 mean motion resonance. The near-resonant configuration presents the opportunity to measure the planet's mass via TTV measurements and to bypass difficult RV measurements. Measuring the masses of the planets in this system will allow us to test theoretical models of atmospheric mass loss.

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arXiv2025

Migration and Evolution of giant ExoPlanets (MEEP) II: Super-Jupiters and Lithium-rich Host Stars

Although hot Jupiters were the first exoplanets discovered orbiting main sequence stars, the dominant mechanisms through which they form and evolve are not known. To address the questions surrounding their origins, the Migration and Evolution of giant ExoPlanets (MEEP) survey aims to create a complete, magnitude-limited ($G<$12.5) sample of hot Jupiters that can be used to constrain the frequency of different migration pathways. NASA's Transiting Exoplanet Survey Satellite provides the unique combination of sky-coverage and photometric precision to achieve this goal, which will likely be a key result of the mission. In this second installment of the MEEP survey, we reanalyze one benchmark hot Jupiter system, TOI-4138, and discover four additional super-Jupiters which are each more than five times as massive as Jupiter: TOI-4773 b, TOI-5261 b, TOI-5350 b, and TOI-6420 b. One of these planets, TOI-5261 b, is 11.49 times the mass of Jupiter, nearly massive enough to ignite deuterium fusion, and has an eccentric ($e = 0.1585$) orbit. TOI-4138, TOI-4773, TOI-5350, and TOI-6420 each have lithium absorption features in their spectra. TOI-4138 is an F-type subgiant with a lithium equivalent width of $120. \pm 13$ mÅ, which is $\sim 4.5σ$ larger than the median lithium equivalent width of a control sample of 1381 similar stars, making TOI-4138 a compelling candidate for planetary engulfment.

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arXiv2025

Validation of TESS Planet Candidates with Multi-Color Transit Photometry and TRICERATOPS+

We present an upgraded version of TRICERATOPS, a software package designed to calculate false positive probabilities for planet candidates identified by the Transiting Exoplanet Survey Satellite (TESS). This enhanced framework now incorporates ground-based light curves in separate bandpasses, which are routinely obtained as part of the candidate vetting process. We apply this upgraded framework to explore the planetary nature of 14 TESS planet candidates, combining primarily J band light curves acquired with the 200-inch Hale Telescope at Palomar Observatory with complementary archival observations from the Las Cumbres Observatory Global Telescope (LCOGT), the Fred Lawrence Whipple Observatory (FLWO), and the Teide Observatory, along with existing TESS data and contrast curves from high-resolution imaging. As a result of this analysis we statistically validate (False Positive Probability < 1.5% and Nearby False Positive Probability < 0.1%) six new planets in five systems: TOI-1346 b, TOI-1346 c, TOI-2719 b, TOI-4155 b, TOI-6000 b, and TOI-6324 b. For these systems, we provide updated estimates of their stellar and planetary properties derived from the TESS and ground-based observations. These new systems contain planets with radii between 0.9-6 Re and orbital periods between 0.3-5.5 days. Finally, we use our upgraded version of TRICERATOPS to quantify the relative importance of multi-wavelength transit photometry and high-resolution imaging for exoplanet candidate validation, and discuss which kinds of candidates typically benefit the most from ground-based multi-color transit observations.

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arXiv2025

Updated Masses for the Gas Giants in the Eight-Planet Kepler-90 System Via Transit-Timing Variation and Radial Velocity Observations

The eight-planet Kepler-90 system exhibits the greatest multiplicity of planets found to date. All eight planets are transiting and were discovered in photometry from the NASA Kepler primary mission. The two outermost planets, g ($P_g$ = 211 d) and h ($P_h$ = 332 d) exhibit significant transit-timing variations (TTVs), but were only observed 6 and 3 times respectively by Kepler. These TTVs allow for the determination of planetary masses through dynamical modeling of the pair's gravitational interactions, but the paucity of transits allows a broad range of solutions for the masses and orbital ephemerides. To determine accurate masses and orbital parameters for planets g and h, we combined 34 radial velocities (RVs) of Kepler-90, collected over a decade, with the Kepler transit data. We jointly modeled the transit times of the outer two planets and the RV time series, then used our two-planet model to predict their future times of transit. These predictions led us to recover a transit of Kepler-90 g with ground-based observatories in May 2024. We then combined the 2024 transit and several previously unpublished transit times of planets g and h with the Kepler photometry and RV data to update the masses and linear ephemerides of the planets, finding masses for g and h of $15.0 \pm 1.3\, M_\oplus$, and $203 \pm 16\, M_\oplus$ respectively from a Markov Chain Monte Carlo analysis. These results enable further insights into the architecturally rich Kepler-90 system and pave the way for atmospheric characterization with space-based facilities.

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arXiv2025

Giant Outer Transiting Exoplanet Mass (GOT 'EM) Survey. VI: Confirmation of a Long-Period Giant Planet Discovered with a Single TESS Transit

We report the discovery and confirmation of TOI-4465 b, a $1.25^{+0.08}_{-0.07}~R_{J}$, $5.89\pm0.26~M_{J}$ giant planet orbiting a G dwarf star at $d\simeq$ 122 pc. The planet was detected as a single-transit event in data from Sector 40 of the Transiting Exoplanet Survey Satellite (TESS) mission. Radial velocity (RV) observations of TOI-4465 showed a planetary signal with an orbital period of $\sim$102 days, and an orbital eccentricity of $e=0.24\pm0.01$. TESS re-observed TOI-4465 in Sector 53 and Sector 80, but did not detect another transit of TOI-4465 b, as the planet was not expected to transit during these observations based on the RV period. A global ground-based photometry campaign was initiated to observe another transit of TOI-4465 b after the RV period determination. The $\sim$12 hour-long transit event was captured from multiple sites around the world, and included observations from 24 citizen scientists, confirming the orbital period as $\sim$102 days. TOI-4465 b is a relatively dense ($3.73\pm0.53~\rm{g/cm^3}$), temperate (375-478 K) giant planet. Based on giant planet structure models, TOI-4465 b appears to be enriched in heavy elements at a level consistent with late-stage accretion of icy planetesimals. Additionally, we explore TOI-4465 b's potential for atmospheric characterization, and obliquity measurement. Increasing the number of long-period planets by confirming single-transit events is crucial for understanding the frequency and demographics of planet populations in the outer regions of planetary systems.

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arXiv2025

ExoMiner++: Enhanced Transit Classification and a New Vetting Catalog for 2-Minute TESS Data

We present ExoMiner++, an enhanced deep learning model that builds on the success of ExoMiner to improve transit signal classification in 2-minute TESS data. ExoMiner++ incorporates additional diagnostic inputs, including periodogram, flux trend, difference image, unfolded flux, and spacecraft attitude control data, all of which are crucial for effectively distinguishing transit signals from more challenging sources of false positives. To further enhance performance, we leverage multi-source training by combining high-quality labeled data from the Kepler space telescope with TESS data. This approach mitigates the impact of TESS's noisier and more ambiguous labels. ExoMiner++ achieves high accuracy across various classification and ranking metrics, significantly narrowing the search space for follow-up investigations to confirm new planets. To serve the exoplanet community, we introduce new TESS catalog containing ExoMiner++ classifications and confidence scores for each transit signal. Among the 147,568 unlabeled TCEs, ExoMiner++ identifies 7,330 as planet candidates, with the remainder classified as false positives. These 7,330 planet candidates correspond to 1,868 existing TESS Objects of Interest (TOIs), 69 Community TESS Objects of Interest (CTOIs), and 50 newly introduced CTOIs. 1,797 out of the 2,506 TOIs previously labeled as planet candidates in ExoFOP are classified as planet candidates by ExoMiner++. This reduction in plausible candidates combined with the excellent ranking quality of ExoMiner++ allows the follow-up efforts to be focused on the most likely candidates, increasing the overall planet yield.

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arXiv2025

The Eccentricity Distribution of Warm Sub-Saturns in TESS

We present the eccentricity distribution of warm sub-Saturns (4-8 Re, 8-200 day periods) as derived from an analysis of transit light curves from NASA's Transiting Exoplanet Survey Satellite (TESS) mission. We use the "photoeccentric" effect to constrain the eccentricities of 76 planets, comprising 60 and 16 from single- and multi-transiting systems, respectively. We employ Hierarchical Bayesian Modelling to infer the eccentricity distribution of the population, testing both a Beta and Mixture Beta distribution. We identify a few highly eccentric (e ~ 0.7-0.8) warm sub-Saturns with eccentricities that appear too high to be explained by disk migration or planet-planet scattering alone, suggesting high-eccentricity migration may play a role in their formation. The majority of the population have a mean eccentricity of e = 0.103+0.047-0.045, consistent with both planet-disk and planet-planet interactions. Notably, we find that the highly eccentric sub-Saturns occur in single-transiting systems. This study presents the first evidence at the population level that the eccentricities of sub-Saturns may be sculpted by dynamical processes.

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arXiv2025

Confirmation of four hot Jupiters detected by TESS using follow-up spectroscopy from MaHPS at Wendelstein together with NEID and TRES

We report the confirmation and characterization of four hot Jupiter-type exoplanets initially detected by TESS: TOI-1295 b, TOI-2580 b, TOI-6016 b, and TOI-6130 b. Using observations with the high-resolution echelle spectrograph MaHPS on the 2.1m telescope at Wendelstein Observatory, together with NEID at Kitt Peak National Observatory and TRES at the Fred Lawrence Whipple Observatory, we confirmed the planetary nature of these four planet candidates. We also performed precise mass measurements. All four planets are found to be hot Jupiters with orbital periods between 2.4 and 4.0 days. The sizes of these planets range from 1.29 to 1.64 Jupiter radii, while their masses range from 0.6 to 1.5 Jupiter masses. Additionally, we investigated whether there are signs of other planets in the systems but have found none. Lastly, we compared the radii of our four objects to the results of an empirical study of radius inflation and see that all four demonstrate a good fit with the current models. These four planets belong to the first array of planets confirmed with MaHPS data, supporting the ability of the spectrograph to detect planets around fainter stars as faint as V=12.

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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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