arXiv subjects

Erik Petigura

Publications and source records attributed to Erik Petigura.

At least 19 recordsLinked to original sources

arXiv2026

Does HD 3167 Have Planets with Perpendicular Orbits?

The two transiting planets of HD 3167 were reported to follow nearly perpendicular paths, with the inner orbit aligned with the stellar equator and the outer orbit nearly polar. This interpretation depends critically on a challenging single-transit detection of the Rossiter-McLaughlin effect of the inner planet. We observed three additional transits of the inner planet with the Keck Planet Finder and analyzed the new data together with two archival ESPRESSO transit datasets. We do not confirm the previously reported low obliquity. Our analysis favors a projected obliquity of $-66^{+14}_{-12}$ degrees, consistent with coplanar orbits. However, because the best-fit projected rotation velocity is higher than expected, and because the obliquity uncertainty grows substantially when the most discrepant of the five transit datasets is omitted, we regard the geometry of the HD 3167 system as still unsettled.

astro-ph.EP↗

arXiv2026

Predicting Macroturbulence in F/G/K Dwarfs to 100 m/s Precision

We leverage the high resolution and spectral stability of the Keck Planet Finder (KPF) spectrograph to investigate macroturbulence broadening via the stellar cross-correlation function (CCF). As our calibration sample, we use main sequence benchmark slow-rotators v$\sin$i < 4 km/s where rotation rates were derived from the most robust asteroseismic mode splitting measurements, independent from spectral line broadening. We fit a linear relationship for macroturbulence as a function of derived $ν_{max}$, the frequency of maximum power due to stellar oscillations, with an RMS scatter of 90 m/s. Previous studies have calibrated macroturbulence against T$_{eff}$, but we find $ν_{max}$ to be a lower dispersion predictor by a factor of 4 indicating a deeper relationship between $ν_{max}$and convective motions.

astro-ph.SR↗

arXiv2026

A Smooth Transition from Giant Planets to Brown Dwarfs from the Radial Occurrence Distribution

Measuring the occurrence rates of celestial objects is a valuable way to study their origins and evolution. Giant planets and brown dwarfs produce large Doppler signatures that are easily detectable by modern instrumentation, and legacy radial velocity (RV) surveys have now achieved full orbital coverage for periods $\lesssim$30 years. However, the Doppler method's sensitivity to companion minimum mass $M_c \sin i$ -- as opposed to true mass $M_c$ -- prevents unambiguous characterization using RVs alone, as purported giant planets may be brown dwarfs or stars on inclined orbits. Here we combined legacy RVs with absolute astrometry to re-fit the orbits of 195 companions from the California Legacy Survey. Nearly 50% (8/18) of the ``brown dwarfs" ($M_c \sin i$=13--80 $M_{Jup}$) we refit had true masses above 80 $M_{Jup}$. We incorporated our orbital posteriors and target sensitivity maps into a Poisson likelihood model to calculate occurrence as a function of true companion mass $M_c$ (0.8--80 $M_{Jup}$) and separation $a$ (0.3--30 AU). The semi-major axis distributions of objects in this range vary smoothly with mass, with Jupiter analogs favoring an abrupt increase in occurrence near 1 AU and brown dwarfs exhibiting a gradual enhancement at wider separations. Marginalized companion occurrence between 1--10 AU decreases smoothly with mass, with brown dwarfs having the lowest occurrence rate: $0.9^{+0.5}_{-0.4}$%. Jupiter analogs are 10 times as common as brown dwarfs per mass interval in this range, demonstrating that the brown dwarf desert extends to 10 AU. The smooth variation in these distributions disfavors a sharp transition mass between ``bottom-up" core accretion and ``top-down" gravitational instability formation mechanisms, and rather suggests that these processes may produce companions in overlapping mass ranges.

astro-ph.EP↗

arXiv2026

Gaia Exoplanet Orbits, Demographics, and Evolution Survey (GEODES): Characteristics of Three Long-Period Companions Accelerating their Host Stars

The upcoming release of $Gaia$ DR4 will yield thousands of giant planet candidates, eventually enabling studies of giant planet eccentricities, masses, and occurrence rates across a broad range of stellar host masses, metallicities, and ages. However, some of these planet candidates are expected to be false positives, and even genuine detections will require additional observations to precisely determine their orbits and masses. We present here the first results of the $Gaia$ Exoplanet Orbits, Demographics, and Evolution Survey (GEODES), an observational campaign to identify the most promising planet candidate hosts for pre-DR4 vetting and post-DR4 validation and characterization. In this paper we showcase three systems from our broader sample exhibiting both tangential and radial accelerations, each representing a distinct outcome of our survey strategy. We combine $Hipparcos$, $Hipparcos$-$Gaia$, $Gaia$ DR2, and $Gaia$ DR3 absolute astrometry with adaptive optics (AO) imaging and precision RVs to constrain companion masses and orbits. HIP 18512, a nearby (15.3 pc) K4V dwarf, hosts a low-mass stellar companion at 10.87" $\pm$ 0.07" (166 AU) which produces significant RV and astrometric accelerations on its host star. The RV trend and astrometric acceleration of the nearby (24.2 pc) K4V star HIP 45839, together with an AO imaging non-detection, constrain the companion to $a$ = 17.9^{+4.8}_{-2.7} AU ($P$ = 70--127 years) and $M$ = 45.2^{+10.5}_{-12.7} $M_{Jup}$. In the case of HIP 81991 (43.8 pc, G5V), the astrometric and RV data indicate that the companion has a separation of 6.4^{+0.6}_{-0.3} AU ($P$ = 14.4--17.7 years) and a mass of 9.5^{+5.4}_{-2.2} $M_{Jup}$, and is more likely a planet (65%) than a brown dwarf (35%).

astro-ph.EP↗

arXiv2026

Photochemical CS$_2$ Gas Detected on a 20-Myr-old Exoplanet

Probing the atmospheres of young exoplanets offers a powerful window into how planetary systems evolve and the physical and chemical processes that drive those early evolutions. We present JWST/NIRSpec transmission spectroscopy of V1298 Tau e, a $\sim$20-Myr-old, $\sim$15-$M_\oplus$ planet with a Jupiter-like radius orbiting a young Sun-like star. We identified carbon disulfide (CS$_2$) in its atmosphere at $>$8$σ$ significance based on spectral features between 4.3 and 4.7~$μ$m. Photochemical forward models show that the inferred CS$_2$ abundance is physically plausible in an H/He-dominated atmosphere exposed to intense ultraviolet irradiation. The atmosphere of V1298 Tau e is strikingly different from its nearest neighboring planet b, whose atmosphere shows SO$_2$ rather than CS$_2$. These observations demonstrate that even planets within the same system can occupy distinct photochemical regimes. Our results further provide empirical evidence for complex sulfur photochemistry in exoplanet atmospheres in general and may also point to divergent formation or evolutionary pathways within the same planetary system.

astro-ph.EP↗

arXiv2026

Extracting Astrophysical Information of Highly-Eccentric Binaries in the Millihertz Gravitational Wave Band

Wide, highly eccentric ($e>0.9$) compact binaries can naturally arise as progenitors of gravitational wave (GW) mergers. These systems are expected to have a significant population in the mHz band (e.g., $\sim 3-45$ detectable stellar-mass binary black holes with $e>0.9$ in the Milky Way), with their GW signals characterized by "repeated bursts" emitted upon each pericenter passage. In this study, we show that the detection of mHz GW signals from highly eccentric stellar mass binaries in the local universe can strongly constrain their orbital parameters. Specifically, it can achieve a relative measurement error of $\sim 10^{-6}$ for orbital frequency and $\sim 1\%$ for eccentricity (as $1-e$) in most of the detectable cases. On the other hand, the binary's mass ratio, distance, and intrinsic orbital orientation may be less precisely determined due to degeneracies in the GW waveform. We also perform mock LISA data analysis to evaluate the realistic detectability of highly eccentric compact binaries. Our results show that highly eccentric systems could be efficiently identified when multiple GW sources and stationary Gaussian instrumental noise are present in the detector output. This work highlights the potential of extracting the signal of "bursting'' LISA sources to provide valuable insights into their orbital evolution, surrounding environment, and formation channels.

astro-ph.HE↗

arXiv2026

An Adolescent and Near-Resonant Planetary System Near the End of Photoevaporation

Young exoplanets provide vital insights into the early dynamical and atmospheric evolution of planetary systems. Many multi-planet systems younger than 100 Myr exhibit mean-motion resonances, likely established through convergent disk migration. Over time, however, these resonant chains are often disrupted, mirroring the Nice model proposed for the Solar System. We present a detailed characterization of the ~200-Myr-old TOI-2076 system, which contains four sub-Neptune planets between 1.4 and 3.5 Earth radii. We demonstrate that its planets are near but not locked in mean-motion resonances, making the system dynamically fragile. The four planets have comparable core masses but display a monotonic increase in hydrogen and helium (H/He) envelope mass fractions (stripped-1%-5%-5%) with decreasing stellar insolation. This trend is consistent with atmospheric mass-loss due to photoevaporation, which predicts that the envelopes of irradiated planets either erode completely or stabilize at a residual level of ~1% by mass within the first few hundred million years, with more distant, less-irradiated planets retaining most of primordial envelopes. Additionally, previous detections of metastable helium outflows rule out a pure water-world scenario for TOI-2076 planets. Our finding provides direct observational evidence that the dynamical and atmospheric reshaping of compact planetary systems begin early, offering an empirical anchor for models of their long-term evolution.

astro-ph.EP↗

arXiv2026

Seeking Spectroscopic Binaries with Data-Driven Models

Data-driven stellar classification has a long and important history in astronomy, dating as far back as Annie Jump Cannon's "by eye" classifications of stars into spectral types still used today. In recent years, data-driven spectroscopy has proven to be an effective means of deriving stellar properties for large samples of stars, sidestepping issues with computational efficiency, incomplete line lists, and radiative transfer calculations associated with physical stellar models. A logical application of these algorithms is the detection of unresolved stellar binaries, which requires accurate spectroscopic models to resolve flux contributions from a fainter secondary star in the spectrum. Here we use The Cannon to train a data-driven model on spectra from the Keck High Resolution Echelle Spectrometer. We show that our model is competitive with existing data-driven models in its ability to predict stellar properties Teff, stellar radius, [Fe/H], vsin(i), and instrumental PSF, particularly when we apply a novel wavelet-based processing step to spectra before training. We find that even with accurate estimates of star properties, our model's ability to detect unresolved binaries is limited by its approx. 3% accuracy in per-pixel flux predictions, illuminating possible limitations of data-driven model applications.

astro-ph.SR↗

arXiv2024

No evidence for a metallicity-dependent enhancement of distant giant companions to close-in small planets in the California Legacy Survey

Understanding the relationship between close-in small planets (CS) and distant giants (DG) is central to understanding the formation of planetary systems like our own. Most studies of this connection have found evidence for a positive correlation, though significant statistical and systematic uncertainties remain due to differences in sample size, target selection bias, and even the definitions of `close-in small' and `distant giant' planets. Recently, Bryan & Lee (2024) conducted a study of 184 stars hosting super-Earths ($M \sin i = 1-20 \, M_{E}$ or $R = 1-4 \, R_{E}$) to determine the effect of stellar metallicity on the prevalence of distant giant companions ($M \sin i = 0.5-20 \, M_{Jup}$, $a = 1-10$ AU). They found that such giants are twice as common in the presence of inner planets, but \textit{only} in metal-rich systems: P(DG|CS, [Fe/H]>0) = $28^{+4.9}_{-4.6}\%$ vs. P(DG|[Fe/H]>0) = $14.3 ^{+2.0}_{-1.8}\%$. Further, they found that this correlation disappears for metal-poor stars: P(DG|CS, [Fe/H]$\leq$0) = $4.5^{+2.6}_{-1.9}\%$ vs. P(DG|[Fe/H]$\leq$0) = $5.0^{+1.6}_{-1.3}\%$. We conducted an analogous study to test whether this effect was present in the California Legacy Survey sample. Using the same planet definitions, we did not find evidence for an enhancement in metal-rich systems: P(DG|CS, [Fe/H]>0) = $14^{+12}_{-8}\%$ vs. P(DG|[Fe/H]>0) = $16.4^{+2.5}_{-2.4}\%$. We also found a $2σ$ tension between our conditional rate and a 2x enhancement. The discrepancy between our findings and theirs may arise from a variety of sources, underscoring the need for large exoplanet surveys to overcome both small number statistics and sample inhomogeneities.

astro-ph.EP↗

arXiv2024

A Data-driven Spectral Model of Main Sequence Stars in Gaia DR3

Precise spectroscopic classification of planet hosts is an important tool of exoplanet research at both the population and individual system level. In the era of large-scale surveys, data-driven methods offer an efficient approach to spectroscopic classification that leverages the fact that a subset of stars in any given survey has stellar properties that are known with high fidelity. Here, we use The Cannon, a data-driven framework for modeling stellar spectra, to train a generative model of spectra from the Gaia Data Release 3 Radial Velocity Spectrometer. Our model derives stellar labels with precisions of 72 K in Teff , 0.09 dex in log g, 0.06 dex in [Fe/H], 0.05 dex in [α/Fe] and 1.9 km/s in vbroad for main-sequence stars observed by Gaia DR3 by transferring GALAH labels, and is publicly available at https://github.com/isabelangelo/gaiaspec. We validate our model performance on planet hosts with available Gaia RVS spectra at SNR>50 by showing that our model is able to recover stellar parameters at {\geq}20% improved accuracy over the existing Gaia stellar parameter catalogs, measured by the agreement with high-fidelity labels from the Spectroscopic Observations of Cool Stars (SPOCS) survey. We also provide metrics to test for stellar activity, binarity, and reliability of our model outputs and provide instructions for interpreting these metrics. Finally, we publish updated stellar labels and metrics that flag suspected binaries and active stars for Kepler Input Catalog objects with published Gaia RVS spectra.

astro-ph.SR↗

arXiv2024

The SN 2023ixf Progenitor in M101: II. Properties

We follow our first paper with an analysis of the ensemble of the extensive pre-explosion ground- and space-based infrared observations of the red supergiant (RSG) progenitor candidate for the nearby core-collapse supernova SN 2023ixf in Messier 101, together with optical data prior to explosion obtained with the Hubble Space Telescope (HST). We have confirmed the association of the progenitor candidate with the SN, as well as constrained the metallicity at the SN site, based on SN observations with instruments at Gemini-North. The internal host extinction to the SN has also been confirmed from a high-resolution Keck spectrum. We fit the observed spectral energy distribution (SED) for the star, accounting for its intrinsic variability, with dust radiative-transfer modeling, which assume a silicate-rich dust shell ahead of the underlying stellar photosphere. The star is heavily dust-obscured, likely the dustiest progenitor candidate yet encountered. We found median estimates of the star's effective temperature and luminosity of 2770 K and 9.0e4 L_Sun, with 68% credible intervals of 2340--3150 K and (7.5--10.9)e4 L_sun. The candidate may have a Galactic RSG analog, IRC -10414, with a strikingly similar SED and luminosity. Via comparison with single-star evolutionary models we have constrained the initial mass of the progenitor candidate from 12 M_sun to as high as 14 M_sun. We have had available to us an extraordinary view of the SN 2023ixf progenitor candidate, which should be further followed up in future years with HST and the James Webb Space Telescope.

astro-ph.SR↗

arXiv2024

ethraid: A simple method for characterizing long-period companions using Doppler, astrometric, and imaging constraints

We present \texttt{ethraid}, an open source Python package designed to measure the mass ($m_c$) and separation ($a$) of a bound companion from measurements covering a fraction of the orbital period. \texttt{ethraid} constrains $m_c$ and $a$ by jointly modeling radial velocity (RV), astrometric, and/or direct imaging data in a Bayesian framework. Partial orbit data sets, especially those with highly limited phase coverage, are well-represented by a few method-specific summary statistics. By modeling these statistics rather than the original data, \texttt{ethraid} optimizes computational efficiency with minimal reduction in accuracy. \texttt{ethraid} uses importance sampling to efficiently explore the often broad posteriors that arise from partial orbits. The core computations of \texttt{ethraid} are implemented in Cython for speed. We validate \texttt{ethraid}'s performance by using it to constrain the masses and separations of the planetary companions to HD 117207 and TOI-1694. We designed \texttt{ethraid} to be both fast and simple, and to give broad, "quick look" constraints on companion parameters using minimal data. \texttt{ethraid} is pip installable and available on Github.

astro-ph.EP↗

arXiv2024

Planet Occurrence from Doppler and transit surveys, 2nd ed

Prior to the 1990s, speculations about the occurrence of planets around other stars were based only on planet formation theory, observations of circumstellar disks, and the knowledge that at least one seemingly ordinary star is the host of four terrestrial planets, two gas giants, and two ice giants. Since then, Doppler and transit surveys have been exploring the population of planets around other Sun-like stars, especially those with orbital periods shorter than a few years. Over the last decade, these surveys have risen to new heights with Doppler spectrographs with a precision better than 1 m/s precision, and space telescopes capable of detecting the transits of Earth-sized planets. This article is a brief introductory review of the knowledge of planet occurrence that has been gained from these surveys.

astro-ph.EP↗

arXiv2023

Signs of Similar Stellar Obliquity Distributions for Hot and Warm Jupiters Orbiting Cool Stars

Transiting giant planets provide a natural opportunity to examine stellar obliquities, which offer clues about the origin and dynamical histories of close-in planets. Hot Jupiters orbiting Sun-like stars show a tendency for obliquity alignment, which suggests that obliquities are rarely excited or that tidal realignment is common. However, the stellar obliquity distribution is less clear for giant planets at wider separations where realignment mechanisms are not expected to operate. In this work, we uniformly derive line-of-sight inclinations for 47 cool stars ($T_\mathrm{eff}$ $<$ 6200 K) harboring transiting hot and warm giant planets by combining rotation periods, stellar radii, and $v \sin i$ measurements. Among the systems that show signs of spin-orbit misalignment in our sample, three are identified as being misaligned here for the first time. Of particular interest are Kepler-1654, one of the longest-period (1047 d; 2.0 AU) giant planets in a misaligned system, and Kepler-30, a multi-planet misaligned system. By comparing the reconstructed underlying inclination distributions, we find that the inferred minimum misalignment distributions of hot Jupiters spanning $a/R_{*}$ = 3-20 ($\approx$ 0.01-0.1 AU) and warm Jupiters spanning $a/R_{*}$ = 20-400 ($\approx$ 0.1-1.9 AU) are in good agreement. With 90$\%$ confidence, at least 24$^{+9}_{-7}\%$ of warm Jupiters and 14$^{+7}_{-5}\%$ of hot Jupiters around cool stars are misaligned by at least 10$^\circ$. Most stars harboring warm Jupiters are therefore consistent with spin-orbit alignment. The similarity of hot and warm Jupiter misalignment rates suggests that either the occasional misalignments are primordial and originate in misaligned disks, or the same underlying processes that create misaligned hot Jupiters also lead to misaligned warm Jupiters.

astro-ph.EP↗

arXiv2022

Report on Community Cadence Observing to Maximize the Scientific Output of the Keck Planet Finder

The arrival of the Keck Planet Finder (KPF) in 2022 represents a major advance in the precision radial velocity (PRV) capabilities of the W. M. Keck Observatory. In preparation for KPF science, our committee of PRV experts and WMKO staff studied the current implementation of cadence observing at Keck and other PRV facilities. We find that many of KPF's major science cases are not feasible through Keck's standard allocations of full or half nights to individual PIs. Pooling time among several PIs as is currently done by the California Planet Search (CPS) collaboration with HIRES results in lower quality science results than is possible when KPF is available at higher observational cadence. This strategy also creates barriers to entry, particularly for researchers wishing to lead small proposals. This report makes recommendations for optimizing PRV cadence at Keck subject to the following constraints: preservation of clear boundaries between cadence observations and classically scheduled time; and ensuring fairness and scientific independence of different Keck TACs and different KPF PIs. We recommend establishing a new category of Keck time allocation, "KPF Community Cadence" (KPF-CC). In many ways, KPF-CC will formalize observing strategies provided by CPS, but with higher observational cadence appropriate for KPF science and with universal access to the program for all Keck users. We recommend that KPF-CC time be scheduled classically into blocks as small as a quarter night subject to considerations of bright/dark time, variations in proposal pressure with the seasons, and the needs of non-KPF observing programs. Within KPF-CC time, the Keck Observing Assistants would execute observations generated by a dynamic scheduler. We recommend that Keck staff and a board of PRV experts design and maintain the scheduling software.

astro-ph.IM↗

arXiv2022

Kepler-1656b's Extreme Eccentricity: Signature of a Gentle Giant

Highly eccentric orbits are one of the major surprises of exoplanets relative to the Solar System and indicate rich and tumultuous dynamical histories. One system of particular interest is Kepler-1656, which hosts a sub-Jovian planet with an eccentricity of 0.8. Sufficiently eccentric orbits will shrink in semi-major axis due to tidal dissipation of orbital energy during periastron passage. Here our goal was to assess whether Kepler-1656b is currently undergoing such high-eccentricity migration, and to further understand the system's origins and architecture. We confirm a second planet in the system with $M_{\rm c}= 0.40 \pm 0.09M_{\rm jup}$ and P$_{\rm c}= 1919\pm 27\,$days. We simulated the dynamical evolution of planet b in the presence of planet c and find a variety of possible outcomes for the system, such as tidal migration and engulfment. The system is consistent with an in situ dynamical origin of planet b followed by subsequent Eccentric Kozai Lidov (EKL) perturbations that excite Kepler-1656b's eccentricity gently, i.e. without initiating tidal migration. Thus, despite its high eccentricity, we find no evidence that planet b is or has migrated through the high-eccentricity channel. Finally, we predict the outer orbit to be mutually inclined in a nearly perpendicular configuration with respect to the inner planet orbit based on the outcomes of our simulations, and make observable predictions for the inner planet's spin-orbit angle. Our methodology can be applied to other eccentric or tidally locked planets to constrain their origins, orbital configurations and properties of a potential companion.

astro-ph.EP↗

arXiv2020

Tidal Inflation Reconciles Low-Density Sub-Saturns with Core Accretion

While the Solar System contains no planets between the sizes of Uranus and Saturn, our current exoplanet census includes several dozen such planets with well-measured masses and radii. These sub-Saturns exhibit a diversity of bulk densities, ranging from ~$0.1-3\ \rm{g\ cm}^{-3}$. When modeled simply as hydrogen/helium envelopes atop rocky cores, this diversity in densities translates to a diversity in planetary envelope fractions, $f_\rm{env}=M_\rm{env}/M_p$ ranging from ~$10\%$ to ~$50\%$. Planets with $f_\rm{env}\sim50\%$ pose a challenge to traditional models of giant planet formation by core-nucleated accretion, which predict the onset of runaway gas accretion when $M_\rm{env}\sim M_\rm{core}$. Here we show that many of these apparent $f_\rm{env}\sim50\%$ planets are less envelope rich than they seem, after accounting for tidal heating. We present a new framework for modeling sub-Saturn interiors that incorporates envelope inflation due to tides, which are driven by the observed non-zero eccentricities, as well as potential obliquities. Consequently, when we apply our models to known sub-Saturns, we infer lower $f_\rm{env}$ than tides-free estimates. We present a case study of K2-19 b, a moderately eccentric sub-Saturn. Neglecting tides, K2-19 b appears to have $f_\rm{env}\sim50\%$, poised precariously near the runaway threshold; by including tides, we find $f_\rm{env}\sim10\%$, resolving the tension. Through a systematic analysis of $4-8\ R_{\oplus}$ planets, we find that most (but not all) of the similarly envelope-rich planets have more modest envelopes of $f_\rm{env}\sim10\%-20\%$. Thus, many sub-Saturns may be understood as sub-Neptunes that have undergone significant radius inflation, rather than a separate class of objects. Tidal radius inflation likely plays an important role in other size classes of planets including ultra-low-density Jupiter-size planets like WASP-107 b.

astro-ph.EP↗

arXiv2019

Revisiting the HIP41378 system with K2 and Spitzer

We present new observations of the multi-planet system HIP~41378, a bright star ($V$ = 8.9, $K_s$ = 7.7) with five known transiting planets. Observations in Campaign 5 of the K2 mission showed multiple transits of two Neptune-sized bodies and single transits of three larger planets ($R_P= 0.33R_J, 0.47R_J, 0.88 R_J$). K2 recently observed the system again in Campaign 18. We observe one new transit each of two of the larger planets, HIP41378~d and~f, giving maximal possible orbital periods of 1114 and 1084 days, respectively. Other possible periods include integer divisions of these maximum values down to a lower limit of about 50 days. We use all available photometry to determine the eccentricity distributions of HIP41378~d \& f, finding that periods $\lesssim$300 days require non-zero eccentricity. We also perform a stability analysis on the orbits of planets d and f to assess the likelihood of their different possible periods, finding that short periods (P $<$ 300 days) are disfavored. In addition, we observe transits of the inner two planets b and c with Spitzer/IRAC, which we combine with the new K2 observations of these planets to search for transit timing variations (TTVs). We find a linear ephemeris for planet b, but see a significant TTV signal for planet c that could be induced by planet d, e, or f. The ability to recover the two smaller planets with Spitzer shows that the several planets in this fascinating system will continue to be detectable with Spitzer, CHEOPS, TESS, and other observatories. This will allow us to precisely determine the periods of d and f, characterize the TTVs of planet~c, recover the transits of planet~e, and further enhance our view of this remarkable dynamical laboratory.

astro-ph.EP↗