arXiv subjects

Casey L. Brinkman

Publications and source records attributed to Casey L. Brinkman.

At least 19 recordsLinked to original sources

arXiv2026

Revisiting the Exo-Mercury Candidate GJ 367 b with ESPRESSO and a Self-Consistent Tidal Distortion Model

We report revised mass and radius measurements for GJ 367 b, an ultra-short-period (7.7 hr) sub-Earth in a multi-planet system orbiting a nearby (~9 pc) M dwarf host. Previous mass and radius measurements have suggested GJ 367 b has an anomalously high bulk density, close to that of solid iron. The existence of such an iron-rich planet is in tension with established planet formation scenarios. We utilized newly available TESS short-cadence photometry to constrain the radius of GJ 367 b to 0.736 +/- 0.035 R_Earth. We consider observational and modeling effects such as photometric dilution, stellar activity, and tidal distortion to account for possible inaccuracies in the star and planet radius measurements. From our radial velocity (RV) analysis using VLT/ESPRESSO data covering nearly the full orbit in a single night, we find a mass of 0.503 +/- 0.078 M_Earth, corresponding to a bulk density of 6.9 +1.6/-1.4 g cm-1. We present a new tidal distortion and interior composition modeling framework to assess the iron mass fraction of GJ 367 b. Considering several different interior composition assumptions and radial aspect ratios, we find an iron fraction of ~50-70%, which is broadly consistent with that of Mercury and not as iron rich as previously suggested.

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arXiv2025

A Link Between Rocky Planet Density and Host Star Chemistry

Planets and their host stars form from the same cloud of gas and dust, so we assume that their chemical compositions are linked. However, a clear correlation between rocky planet interior properties and host star chemistry remains elusive for planets around FGK dwarfs, and non-existent for planets around M dwarfs because cool stars frequently lack detailed chemical information. Here, we investigate the relationship between small (R$_{P}$ $\leq$ 1.8 R$_{\oplus}$) planet densities and host star elemental abundances. We use the Sloan Digital Sky Survey-V/Milky Way Mapper and an accompanying data-driven framework to obtain abundances for FGK and M dwarf hosts of 22 rocky planets. We find that planet densities exhibit a strong, inverse relationship to [Mg/Fe] abundances of FGK hosts (p = 0.001). This correlation becomes more significant with the addition of M dwarf hosts (p = 0.0005). If we assume that rocky planets have terrestrial-like compositions, this suggests that low [Mg/Fe] environments form planets with larger Fe-rich cores and thus higher densities. The thick disk planets in our sample help anchor this trend, illustrating the importance of sampling exoplanet properties across a range of host star populations. This finding highlights the connection between Galactic chemical evolution and rocky planet formation, and indicates that Earth-like planet compositions may vary significantly across different regions of the Galaxy.

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arXiv2025

TOI-6324b: An Earth-Mass Ultra-Short-Period Planet Transiting a Nearby M Dwarf

We report the confirmation of TOI-6324 b, an Earth-sized (1.059 $\pm$ 0.041 R$_\oplus$) ultra-short-period (USP) planet orbiting a nearby ($\sim$20 pc) M dwarf. Using the newly commissioned Keck Planet Finder (KPF) spectrograph, we have measured the mass of TOI-6324 b 1.17 $\pm$ 0.22 M$_\oplus$. Because of its extremely short orbit of just $\sim$6.7 hours, TOI-6324 b is intensely irradiated by its M dwarf host, and is expected to be stripped of any thick, H/He envelope. We were able to constrain its interior composition and found an iron core mass fraction (CMF = 27$\pm$37%) consistent with that of Earth ($\sim$33%) and other confirmed USPs. TOI-6324 b is the closest to Earth-sized USP confirmed to date. TOI-6324 b is a promising target for JWST phase curve and secondary eclipse observations (Emission Spectroscopy Metric = 25) which may reveal its surface mineralogy, day-night temperature contrast, and possible tidal deformation. From 7 sectors of TESS data, we report a tentative detection of the optical phase curve variation with an amplitude of 42$\pm$28 ppm.

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arXiv2025

Planet Masses, Radii, and Orbits from NASA's K2 Mission

We report the masses, sizes, and orbital properties of 86 planets orbiting 55 stars observed by NASA's K2 Mission with follow-up Doppler measurements by the HIRES spectrometer at the W. M. Keck Observatory and the Automated Planet Finder at Lick Observatory. Eighty-one of the planets were discovered from their transits in the K2 photometry, while five were found based on subsequent Doppler measurements of transiting planet host stars. The sizes of the transiting planets range from Earth-size to larger than Jupiter (1-3 REarth is typical), while the orbital periods range from less than a day to a few months. For 32 of the planets, the Doppler signal was detected with significance greater than 5-sigma (51 were detected with >3-sigma significance). An important characteristic of this catalog is the use of uniform analysis procedures to determine stellar and planetary properties. This includes the transit search and fitting procedures applied to the K2 photometry, the Doppler fitting techniques applied to the radial velocities, and the spectral modeling to determine bulk stellar parameters. Such a uniform treatment will make the catalog useful for statistical studies of the masses, densities, and system architectures of exoplanetary systems. This work also serves as a data release for all previously unpublished RVs and associated stellar activity indicators obtained by our team for these systems, along with derived stellar and planet parameters.

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arXiv2024

The Compositions of Rocky Planets in Close-in Orbits Tend to be Earth-Like

Hundreds of exoplanets between 1-1.8 times the size of the Earth have been discovered on close in orbits. However, these planets show such a diversity in densities that some appear to be made entirely of iron, while others appear to host gaseous envelopes. To test this diversity in composition, we update the masses of 5 rocky exoplanets (HD 93963 A b, Kepler-10 b, Kepler-100 b, Kepler-407 b, and TOI-1444 b) and present the confirmation of a new planet (TOI-1011) using 187 high precision RVs from Gemini/MAROON-X and Keck/KPF. Our updated planet masses suggest compositions closer to that of the Earth than previous literature values for all planets in our sample. In particular, we report that two previously identified ``super-Mercuries'' (Kepler-100 b and HD 93963 A b) have lower masses that suggest less iron-rich compositions. We then compare the ratio of iron to rock-building species to the abundance ratios of those elements in their host stars. These updated planet compositions do not suggest a steep relationship between planet and host star compositions, contradictory to previous results, and suggest that planets and host stars have similar abundance ratios.

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arXiv2024

Revisiting the Relationship Between Rocky Exoplanet and Stellar Compositions: Reduced Evidence for a Super-Mercury Population

Planets and the stars they orbit are born from the same cloud of gas and dust, and the primordial compositions of rocky exoplanets have been assumed to have iron and refractory abundance ratios consistent with their host star. To test this assumption, we modeled the interior iron-to-rock ratio of 20 super-Earth sized (1-1.8R$_{\oplus}$) exoplanets around stars with homogeneously measured stellar parameters. We computed the core mass fraction for each planet and an equivalent ``core mass fraction'' for each host star based on its Fe and Mg abundances. We then fit a linear correlation using two methods (Ordinary Least Squares and Orthogonal Distance Regression) between planetary and stellar core mass fraction, obtaining substantially different slopes between these two methods (m=1.3 $\pm$ 1.0 and m=5.6 $\pm$ 1.6, respectively). Additionally, we find that 75$\%$ of planets have a core mass fraction consistent with their host star to within 1$σ$, and do not identify a distinct population of high-density super-Mercuries. Overall, we conclude that current uncertainties in observational data and differences in modeling methods prevent definitive conclusions about the relationship between between planet and host star chemical compositions.

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arXiv2024

The TESS-Keck Survey. XXII. A sub-Neptune Orbiting TOI-1437

Exoplanet discoveries have revealed a dramatic diversity of planet sizes across a vast array of orbital architectures. Sub-Neptunes are of particular interest; due to their absence in our own solar system, we rely on demographics of exoplanets to better understand their bulk composition and formation scenarios. Here, we present the discovery and characterization of TOI-1437 b, a sub-Neptune with a 18.84 day orbit around a near-Solar analog (Mstar = 1.10 +/- 0.10 Msun, Rstar = 1.17 +/- 0.12 Rsun). The planet was detected using photometric data from the Transiting Exoplanet Survey Satellite (TESS) mission and radial velocity follow-up observations were carried out as a part of the TESS-Keck Survey (TKS) using both the HIRES instrument at Keck Observatory and the Levy Spectrograph on the Automated Planet Finder (APF) telescope. A combined analysis of these data reveal a planet radius of Rp = 2.24 +/- 0.23 Rearth and a mass measurement of Mp = 9.6 +/- 3.9 Mearth). TOI-1437 b is one of few (~50) known transiting sub-Neptunes orbiting a solar-mass star that has a radial velocity mass measurement. As the formation pathway of these worlds remains an unanswered question, the precise mass characterization of TOI-1437 b may provide further insight into this class of planet.

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arXiv2024

An Earth-sized Planet on the Verge of Tidal Disruption

TOI-6255~b (GJ 4256) is an Earth-sized planet (1.079$\pm0.065$ $R_\oplus$) with an orbital period of only 5.7 hours. With the newly commissioned Keck Planet Finder (KPF) and CARMENES spectrographs, we determined the planet's mass to be 1.44$\pm$0.14 $M_{\oplus}$. The planet is just outside the Roche limit, with $P_{\rm orb}/P_{\rm Roche}$ = 1.13 $\pm0.10$. The strong tidal force likely deforms the planet into a triaxial ellipsoid with a long axis that is $\sim$10\% longer than the short axis. Assuming a reduced stellar tidal quality factor $Q_\star^\prime \approx10^7$, we predict that tidal orbital decay will cause TOI-6255 to reach the Roche limit in roughly 400 Myr. Such tidal disruptions may produce the possible signatures of planet engulfment that have been on stars with anomalously high refractory elemental abundances compared to its conatal binary companion. TOI-6255 b is also a favorable target for searching for star-planet magnetic interactions, which might cause interior melting and hasten orbital decay. TOI-6255 b is a top target (Emission Spectroscopy Metric of about 24) for phase curve observations with the James Webb Space Telescope.

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arXiv2024

The TESS-Keck Survey XX: 15 New TESS Planets and a Uniform RV Analysis of all Survey Targets

The Transiting Exoplanet Survey Satellite (TESS) has discovered hundreds of new worlds, with TESS planet candidates now outnumbering the total number of confirmed planets from $\textit{Kepler}$. Owing to differences in survey design, TESS continues to provide planets that are better suited for subsequent follow-up studies, including mass measurement through radial velocity (RV) observations, compared to Kepler targets. In this work, we present the TESS-Keck Survey's (TKS) Mass Catalog: a uniform analysis of all TKS RV survey data which has resulted in mass constraints for 126 planets and candidate signals. This includes 58 mass measurements that have reached $\geq5σ$ precision. We confirm or validate 32 new planets from the TESS mission either by significant mass measurement (15) or statistical validation (17), and we find no evidence of likely false positives among our entire sample. This work also serves as a data release for all previously unpublished TKS survey data, including 9,204 RV measurements and associated activity indicators over our three year survey. We took the opportunity to assess the performance of our survey, and found that we achieved many of our goals including measuring the mass of 38 small ($<4R_{\oplus}$) planets, nearly achieving the TESS mission's basic science requirement. In addition, we evaluated the performance of the Automated Planet Finder (APF) as survey support and observed meaningful constraints on system parameters due to its more uniform phase coverage. Finally, we compared our measured masses to those predicted by commonly used mass-radius relations and investigated evidence of systematic bias.

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arXiv2024

Planet Hunters TESS V: a planetary system around a binary star, including a mini-Neptune in the habitable zone

We report on the discovery and validation of a transiting long-period mini-Neptune orbiting a bright (V = 9.0 mag) G dwarf (TOI 4633; R = 1.05 RSun, M = 1.10 MSun). The planet was identified in data from the Transiting Exoplanet Survey Satellite by citizen scientists taking part in the Planet Hunters TESS project. Modeling of the transit events yields an orbital period of 271.9445 +/- 0.0040 days and radius of 3.2 +/- 0.20 REarth. The Earth-like orbital period and an incident flux of 1.56 +/- 0.2 places it in the optimistic habitable zone around the star. Doppler spectroscopy of the system allowed us to place an upper mass limit on the transiting planet and revealed a non-transiting planet candidate in the system with a period of 34.15 +/- 0.15 days. Furthermore, the combination of archival data dating back to 1905 with new high angular resolution imaging revealed a stellar companion orbiting the primary star with an orbital period of around 230 years and an eccentricity of about 0.9. The long period of the transiting planet, combined with the high eccentricity and close approach of the companion star makes this a valuable system for testing the formation and stability of planets in binary systems.

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arXiv2024

A Tale of Two Peas-In-A-Pod: The Kepler-323 and Kepler-104 Systems

In order to understand the relationship between planet multiplicity, mass, and composition, we present newly measured masses of five planets in two planetary systems: Kepler-323 and Kepler-104. We used the HIRES instrument at the W.M. Keck Observatory to collect 79 new radial velocity measurements (RVs) for Kepler-323, which we combined with 48 literature RVs from TNG/HARPS-N. We also conducted a reanalysis of the Kepler-104 system, using 44 previously published RV measurements. Kepler-323 b and c have masses of $2.0^{+1.2}_{-1.1}$ M$_\oplus$ and 6.5$\pm1.6$ M$_\oplus$, respectively, whereas the three Kepler-104 planets are more massive (10.0$\pm2.8$ M$_\oplus$, $7.1^{+3.8}_{-3.5}$ M$_\oplus$, and $5.5^{+4.6}_{-3.5}$ M$_\oplus$ for planets b, c, and d, respectively). The Kepler-104 planets have densities consistent with rocky cores overlaid with gaseous envelopes ($4.1^{+1.2}_{-1.1}$ g/cc, $2.9^{+1.7}_{-1.5}$ g/cc, and $1.6^{+1.5}_{-1.1}$ g/cc respectively), whereas the Kepler-323 planets are consistent with having rocky compositions ($4.5^{+2.8}_{-2.4}$ g/cc and $9.9^{+2.7}_{-2.5}$ g/cc). The Kepler-104 system has among the lowest values for gap complexity ($\mathcal{C}$ = 0.004) and mass partitioning ($\mathcal{Q}$ = 0.03); whereas, the Kepler-323 planets have a mass partitioning similar to that of the Inner Solar System ($\mathcal{Q}$ = 0.28 and $\mathcal{Q}$ = 0.24, respectively). For both exoplanet systems, the uncertainty in the mass partitioning is affected equally by (1) individual mass errors of the planets and (2) the possible existence of undetected low-mass planets, meaning that both improved mass characterization and improved sensitivity to low-mass planets in these systems would better elucidate the mass distribution among the planets.

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arXiv2024

The TESS-Keck Survey. XVIII. A sub-Neptune and spurious long-period signal in the TOI-1751 system

We present and confirm TOI-1751 b, a transiting sub-Neptune orbiting a slightly evolved, solar-type, metal-poor star ($T_{eff} = 5996 \pm 110$ K, $log(g) = 4.2 \pm 0.1$, V = 9.3 mag, [Fe/H] = $-0.40 \pm 0.06$ dex) every 37.47 d. We use TESS photometry to measure a planet radius of $2.77_{-0.07}^{+0.15}~\rm{R_\oplus}$. We also use both Keck/HIRES and APF/Levy radial velocities (RV) to derive a planet mass of $14.5_{-3.14}^{+3.15} ~\rm{M_\oplus}$, and thus a planet density of $3.6 \pm 0.9 \, {\rm g}\,{\rm cm}^{-3}$. There is also a long-period ($\sim400~\rm{d}$) signal that is observed in only the Keck/HIRES data. We conclude that this long-period signal is not planetary in nature, and is likely due to the window function of the Keck/HIRES observations. This highlights the role of complementary observations from multiple observatories to identify and exclude aliases in RV data. Finally, we investigate potential compositions of this planet, including rocky and water-rich solutions, as well as theoretical irradiated ocean models. TOI-1751 b is a warm sub-Neptune, with an equilibrium temperature of $\sim 820$ K. As TOI-1751 is a metal-poor star, TOI-1751 b may have formed in a water-enriched formation environment. We thus favor a volatile-rich interior composition for this planet.

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arXiv2024

Giant Outer Transiting Exoplanet Mass (GOT 'EM) Survey. IV. Long-term Doppler Spectroscopy for 11 Stars Thought to Host Cool Giant Exoplanets

Discovering and characterizing exoplanets at the outer edge of the transit method's sensitivity has proven challenging owing to geometric biases and the practical difficulties associated with acquiring long observational baselines. Nonetheless, a sample of giant exoplanets on orbits longer than 100 days has been identified by transit hunting missions. We present long-term Doppler spectroscopy for 11 such systems with observation baselines spanning a few years to a decade. We model these radial velocity observations jointly with transit photometry to provide initial characterizations of these objects and the systems in which they exist. Specifically, we make new precise mass measurements for four long-period giant exoplanets (Kepler-111 c, Kepler-553 c, Kepler-849 b, and PH-2 b), we place new upper limits on mass for four others (Kepler-421 b, KOI-1431.01, Kepler-1513 b, and Kepler-952 b), and we show that several "confirmed" planets are in fact not planetary at all. We present these findings to complement similar efforts focused on closer-in short-period giant planets, and with the hope of inspiring future dedicated studies of cool giant exoplanets.

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arXiv2024

The Kepler Giant Planet Search. I: A Decade of Kepler Planet-host Radial Velocities from W. M. Keck Observatory

Despite the importance of Jupiter and Saturn to Earth's formation and habitability, there has not yet been a comprehensive observational study of how giant exoplanets correlate with the architectural properties of close-in, sub-Neptune-sized exoplanets. This is largely because transit surveys are particularly insensitive to planets at orbital separations >1 au, and so their census of Jupiter-like planets is incomplete, inhibiting our study of the relationship between Jupiter-like planets and the small planets that do transit. To investigate the relationship between close-in, small and distant, giant planets, we conducted the Kepler Giant Planet Survey (KGPS). Using the W. M. Keck Observatory High Resolution Echelle Spectrometer, we spent over a decade collecting 2844 radial velocities (RVs; 2167 of which are presented here for the first time) of 63 Sunlike stars that host 157 transiting planets. We had no prior knowledge of which systems would contain giant planets beyond 1 au, making this survey unbiased with respect to previously detected Jovians. We announce RV-detected companions to 20 stars from our sample. These include 13 Jovians (0.3 MJ < M sin i < 13 MJ, 1 au < a < 10 au), eight nontransiting sub-Saturns, and three stellar-mass companions. We also present updated masses and densities of 84 transiting planets. The KGPS project leverages one of the longest-running and most data-rich collections of RVs of the NASA Kepler systems yet, and it will provide a basis for addressing whether giant planets help or hinder the growth of sub-Neptune-sized and terrestrial planets. Future KGPS papers will examine the relationship between small, transiting planets and their long-period companions.

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arXiv2023

The TESS-Keck Survey XVII: Precise Mass Measurements in a Young, High Multiplicity Transiting Planet System using Radial Velocities and Transit Timing Variations

We present a radial velocity (RV) analysis of TOI-1136, a bright TESS system with six confirmed transiting planets, and a seventh single-transiting planet candidate. All planets in the system are amenable to transmission spectroscopy, making TOI-1136 one of the best targets for intra-system comparison of exoplanet atmospheres. TOI-1136 is young ($\sim$ 700 Myr), and the system exhibits transit timing variations (TTVs). The youth of the system contributes to high stellar variability on the order of 50 m s$^{-1}$, much larger than the likely RV amplitude of any of the transiting exoplanets. Utilizing 359 HIRES and APF RVs collected as a part of the TESS-Keck Survey (TKS), and 51 HARPS-N RVs, we experiment with a joint TTV-RV fit. With seven possible transiting planets, TTVs, more than 400 RVs, and a stellar activity model, we posit that we may be presenting the most complex mass recovery of an exoplanet system in the literature to date. By combining TTVs and RVs, we minimized GP overfitting and retrieved new masses for this system: (m$_{b-g}$ = 3.50$^{+0.8}_{-0.7}$, 6.32$^{+1.1}_{-1.3}$, 8.35$^{+1.8}_{-1.6}$, 6.07$^{+1.09}_{-1.01}$, 9.7$^{+3.9}_{-3.7}$, 5.6$^{+4.1}_{-3.2}$ M$_{\oplus}$). We are unable to significantly detect the mass of the seventh planet candidate in the RVs, but we are able to loosely constrain a possible orbital period near 80 days. Future TESS observations might confirm the existence of a seventh planet in the system, better constrain the masses and orbital properties of the known exoplanets, and generally shine light on this scientifically interesting system.

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arXiv2023

TESS Giants Transiting Giants V -- Two hot Jupiters orbiting red-giant hosts

In this work we present the discovery and confirmation of two hot Jupiters orbiting red-giant stars, TOI-4377 b and TOI-4551 b, observed by TESS in the southern ecliptic hemisphere and later followed-up with radial-velocity (RV) observations. For TOI-4377 b we report a mass of $0.957^{+0.089}_{-0.087} \ M_\mathrm{J}$ and a inflated radius of $1.348 \pm 0.081 \ R_\mathrm{J}$ orbiting an evolved intermediate-mass star ($1.36 \ \mathrm{M}_\odot$, $3.52 \ \mathrm{R}_\odot$; TIC 394918211) on a period of of $4.378$ days. For TOI-4551 b we report a mass of $1.49 \pm 0.13 \ M_\mathrm{J}$ and a radius that is not obviously inflated of $1.058^{+0.110}_{-0.062} \ R_\mathrm{J}$, also orbiting an evolved intermediate-mass star ($1.31 \ \mathrm{M}_\odot$, $3.55 \ \mathrm{R}_\odot$; TIC 204650483) on a period of $9.956$ days. We place both planets in context of known systems with hot Jupiters orbiting evolved hosts, and note that both planets follow the observed trend of the known stellar incident flux-planetary radius relation observed for these short-period giants. Additionally, we produce planetary interior models to estimate the heating efficiency with which stellar incident flux is deposited in the planet's interior, estimating values of $1.91 \pm 0.48\%$ and $2.19 \pm 0.45\%$ for TOI-4377 b and TOI-4551 b respectively. These values are in line with the known population of hot Jupiters, including hot Jupiters orbiting main sequence hosts, which suggests that the radii of our planets have reinflated in step with their parent star's brightening as they evolved into the post-main-sequence. Finally, we evaluate the potential to observe orbital decay in both systems.

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arXiv2023

The TESS-Keck Survey. XVI. Mass Measurements for 12 Planets in Eight Systems

With JWST's successful deployment and unexpectedly high fuel reserves, measuring the masses of sub-Neptunes transiting bright, nearby stars will soon become the bottleneck for characterizing the atmospheres of small exoplanets via transmission spectroscopy. Using a carefully curated target list and more than two years' worth of APF-Levy and Keck-HIRES Doppler monitoring, the TESS-Keck Survey is working toward alleviating this pressure. Here we present mass measurements for 11 transiting planets in eight systems that are particularly suited to atmospheric follow-up with JWST. We also report the discovery and confirmation of a temperate super-Jovian-mass planet on a moderately eccentric orbit. The sample of eight host stars, which includes one subgiant, spans early-K to late-F spectral types ($T_\mathrm{eff} =$ 5200--6200 K). We homogeneously derive planet parameters using a joint photometry and radial velocity modeling framework, discuss the planets' possible bulk compositions, and comment on their prospects for atmospheric characterization.

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arXiv2022

TOI-1136 is a Young, Coplanar, Aligned Planetary System in a Pristine Resonant Chain

Convergent disk migration has long been suspected to be responsible for forming planetary systems with a chain of mean-motion resonances (MMR). Dynamical evolution over time could disrupt the delicate resonant configuration. We present TOI-1136, a 700-Myr-old G star hosting at least 6 transiting planets between $\sim$2 and 5 $R_\oplus$. The orbital period ratios deviate from exact commensurability by only $10^{-4}$, smaller than the $\sim$\,$10^{-2}$ deviations seen in typical Kepler near-resonant systems. A transit-timing analysis measured the masses of the planets (3-8$M_\oplus$) and demonstrated that the planets in TOI-1136 are in true resonances with librating resonant angles. Based on a Rossiter-McLaughlin measurement of planet d, the star's rotation appears to be aligned with the planetary orbital planes. The well-aligned planetary system and the lack of detected binary companion together suggest that TOI-1136's resonant chain formed in an isolated, quiescent disk with no stellar fly-by, disk warp, or significant axial asymmetry. With period ratios near 3:2, 2:1, 3:2, 7:5, and 3:2, TOI-1136 is the first known resonant chain involving a second-order MMR (7:5) between two first-order MMR. The formation of the delicate 7:5 resonance places strong constraints on the system's migration history. Short-scale (starting from $\sim$0.1 AU) Type-I migration with an inner disk edge is most consistent with the formation of TOI-1136. A low disk surface density ($Σ_{\rm 1AU}\lesssim10^3$g~cm$^{-2}$; lower than the minimum-mass solar nebula) and the resultant slower migration rate likely facilitated the formation of the 7:5 second-order MMR. TOI-1136's deep resonance suggests that it has not undergone much resonant repulsion during its 700-Myr lifetime. One can rule out rapid tidal dissipation within a rocky planet b or obliquity tides within the largest planets d and f.

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