Assistant Professor, Yale Astronomy (Starting July 2023)
About Me
I am a 51 Pegasi b Fellow at the MIT Kavli Institute and incoming Assistant Professor of Astronomy at Yale University (starting July 2023). My research focuses on understanding the dynamical evolution of planetary systems by incorporating evidence from both exoplanet and solar system science. I am especially interested in interdisciplinary studies that break down the barriers between exoplanet-related subfields.
I completed my PhD at Yale University in February 2022, where I worked with Professor Greg Laughlin as an NSF Graduate Research Fellow and a P.E.O. Scholar. I am originally from Simi Valley, CA in the United States, and I received my Bachelor's degrees in Physics and Astrophysics from UC Berkeley. I also spent a semester abroad studying at Queen Mary University of London (QMUL), and I have conducted research at the Lawrence Berkeley National Laboratory, University College London (UCL), and the NASA Goddard Space Flight Center.
I am passionate about research, teaching, and outreach, and I am always looking for ways to support early-career astronomers in both my department and broader community. In my free time, I enjoy eating bread, playing the flute and piano, reading in coffee shops, and learning about modern and contemporary art. I also love to travel and find new ways to broaden my perspective.
My research synthesizes physical constraints from the many components of a planetary system, drawing connections between subfields to characterize the processes of planet formation and evolution. A list of my refereed publications can be found on NASA/ADS here. Read more about my specific research interests using the buttons below.
Hixenbaugh, K., Wang, X.-Y., Rice, M., & Wang, S. 2023 (in review, ApJL) - The Spin-Orbit Misalignment of [redacted]: The First Measurement of the Rossiter-McLaughlin Effect for a Warm Sub-Saturn around a Massive Star
Grunblatt, S.K., Saunders, N., Huber, D., et al. (incl Rice, M.; in review) - An Unlikely Survivor: A Low-Density Hot Neptune Orbiting a Red Giant Star
Zink, J.K., Hardegree-Ullman, K.H., Christiansen, J.L., et al. (incl Rice, M.; in review) - Scaling K2. VI. Reduced Small Planet Occurrence in High Galactic Amplitude Stars
Hon, M., Huber, D., Rui, N.Z., et al. (incl Rice, M.; in review) - A Close–in Jovian Planet Orbiting a Helium-Burning Red Giant Star
Much of my research is primarily motivated by the goal of better understanding planetary system formation and evolution. As a result, my work involves studying and characterizing the diversity of exoplanets, including the wide range of planet properties and planetary system architectures.
I have worked closely with the Twinkle Space Mission, and, as part of this collaboration, I have characterized the scientific capabilities of the Twinkle Space Telescope, a small, low-cost space mission planned for launch in 2021 for photometric and spectroscopic observations of exoplanet atmospheres. Twinkle will be capable of characterizing hundreds of exoplanet atmospheres during its lifetime, with varying SNR depending on the observed planet’s properties. For more details, see Edwards et al. 2018 below.
I also regularly observe with the Keck/HIRES instrument as a collaborator with the TESS-Keck Survey. Through these efforts, I have contributed to several observational planet detection and characterization projects.
An undiscovered ninth planet of 5-10 Earth masses has been theorized to exist within the solar system as an elegant explanation for why the observed population of extreme trans-Neptunian objects (TNOs) has periastra clustered preferentially in one direction in the sky. Planet Nine’s existence would help to explain many ongoing mysteries in the solar system. However, despite ongoing searches, it has yet to be found.
One of my research interests is the search for Planet Nine and its implications for the solar system. In a recent project, I proposed a novel method to search for Planet Nine by probing its gravitational effect on minor planets within the solar system using stellar occultation measurements. Precise positional measurements of a large (N>225) sample of Jovian Trojan asteroids would be sufficient to distinguish the signatures of Planet Nine from those of the Kuiper belt and to confirm Planet Nine’s existence (or non-existence). For a brief overview of this project, check out my first research highlight here.
I am also leading a shift-stacking survey of the outer solar system to look for Planet Nine and other distant TNOs using the Transiting Exoplanet Survey Satellite (TESS) dataset. To learn more about this project, read my fourth research highight here.
The first identified interstellar interloper, 1I/2017 U1 ('Oumuamua), was confirmed in October 2017 during the outbound of its hyperbolic orbit. The nature of this object is still under debate; however, it serves as a proof-of-concept that interstellar objects can be detected within our solar system, and it accordingly provides an impetus for further predictions of upcoming discoveries by Pan-STARRS and the Large Survey Synoptic Telescope (LSST).
I am interested in the origins of interstellar interlopers and the unique window that they provide into the properties of minor planets in extrasolar systems. I am particularly interested in the implications of ‘Oumuamua and future interstellar object detections for exoplanet occurrence rates and planet formation theory.
Debris disks are rings of rocky debris surrounding most, if not all, main sequence stars. The debris disk population provides a direct window into the composition of rocky materials in extrasolar systems, as well as the outcome of the planet formation process. Structures and asymmetries observed in debris disk systems can indicate the presence of neighboring planets, as well.
With the Gemini Planet Imager Exoplanet Survey (GPIES) debris disk team, I developed synthetic models of debris disks to better understand their geometric and compositional properties. To accomplish this, I used radiative transfer code MCFOST combined with Markov Chain Monte Carlo (MCMC) methods to solve the inverse problem of characterizing directly imaged debris disk images. By studying debris disks, I hope to improve our understanding of the late stages of planet formation.
Moons provide a fascinating window into the diversity of rocky bodies and can inform our understanding of the variety of worlds in existence. Although, to date, no moons have been confirmed in extrasolar systems, there is a plethora of such worlds to study within the solar system. Moons hint at the possible range of worlds that may exist elsewhere, and they often compose interesting dynamical systems, with several examples of moons in orbital resonance throughout the solar system.
Titan, Saturn’s largest satellite, is unique as the only moon in the solar system with a substantial atmosphere. Titan’s thick hazes, active climate, and complex geological processes ensure that the moon is rich with activity and physical processes that are not yet fully understood. As a result, studies of Titan are also used to better understand the environments of extrasolar planets. The Cassini spacecraft, which orbited Saturn from 2004-2017, observed Titan on many occasions throughout its mission lifetime. In past work, I used data from the Cassini Composite Infrared Spectrometer (CIRS) to study the water abundance in Titan’s atmosphere, and I have contributed to an observer’s guide for future users of the CIRS dataset.
Accurate measurements of stellar properties are critical to identify trends and correlations that inform our understanding of how planetary systems form. These stellar properties can be obtained with high fidelity through forward modeling with programs such as Spectroscopy Made Easy (SME), with the caveat that such programs can be computationally expensive and thus are not always tractable for use with very large datasets.
I use generative modeling code The Cannon to classify stellar spectra in order to better understand their properties and to efficiently obtain associated ''labels'' (stellar properties and abundances) using supervised learning methods. I focus on datasets that can help us to learn more about stars that have been part of planet search campaigns, with an ultimate goal of providing large, uniformly determined sets of stellar labels for use in demographic studies of exoplanet systems.
The obliquity of a star, or the angle between its spin axis and the net angular momentum vector of its surrounding planetary system, provides an important clue to understand the formation history of that system. While the Solar System planets are within a few degrees of alignment with the Sun's spin axis, exoplanets have been discovered on retrograde and polar orbits.
I am leading the Stellar Obliquities in Long-period Exoplanet Systems (SOLES) survey, through which my team measures the obliquities of systems hosting wide-separation planets using Keck/HIRES and NEID Rossiter-McLaughlin measurements. Planets with a relatively large separation from their host star have long tidal realignment timescales and can be used to better understand the primordial stellar obliquity distribution. These new measurements can also help to disentangle the effect of tidal interactions upon the distribution of hot Jupiter spin-orbit angles. Ultimately, I aim to disentangle hot and warm Jupiter formation mechanisms through population studies of exoplanet spin-orbit angles.
I also recently demonstrated that the stellar obliquity distribution provides tantalizing hints in favor of high-eccentricity migration as the key hot Jupiter formation mechanism. Read my associated research highlight here.
In my research highlight here, I show a statistically significant tendency toward alignment in warm Jupiter systems, and I describe the implications of this finding for hot and warm Jupiter formation.
The fourth result from the SOLES survey, which delves into the role of stellar binarity in the stellar obliquity distribution, is described in my research highlight here.
Teaching has been an important component of my life over the past decade, and I am continually working towards improving my abilities as an instructor and mentor. As part of these efforts, I have worked as a McDougal Graduate Teaching Fellow and McDougal/Poorvu Graduate Writing Fellow at the Yale Poorvu Center for Teaching and Learning, served as an instructor at Yale University and UC Berkeley, developed and run two student mentoring programs in astronomy, and taught extensively as a tutor in a wide range of topics.
McDougal Teaching Fellowship
From 2018-2022, I served as a McDougal Graduate Teaching Fellow at the Yale Poorvu Center for Teaching and Learning, where I developed and ran Fundamentals of Teaching workshop series and Advanced Teaching Workshops for graduate students and postdoctoral researchers. Through this position, I conducted classroom observations to provide support for Teaching Fellows at Yale, and I helped to organize and run Yale's Spring Teaching Forum and the biannual Teaching at Yale Day events for first-time graduate student instructors. Together with the community of Fellows, I also regularly discussed teaching pedagogy and related academic literature on the topic. The workshops that I have led include the following:
Fundamentals of Teaching Science (4-part series)
Fundamentals of Teaching Physics (4-part series)
Fundamentals of Evidence-Based Teaching (4-part series)
Teaching First-Generation and Non-Traditional Students
Enriching the Classroom through Multimedia
Assessing Participation Equitably
Rubrics and Grading
How We Learn (webinar)
Mentoring Undergraduates (webinar)
Preparing and Delivering Effective Lectures (webinar)
Leading Effective Discussions (webinar)
Classroom Observation (webinar)
Universal Design for Learning (webinar)
Religion in the Classroom (webinar)
Trauma-Informed Teaching (webinar)
Race, Ethnicity, and Culture in the Classroom (webinar)
I was a core coordinator for Yale's 2021 Spring Teaching Forum, with the theme "Looking Back and Looking Forward: Reflecting on Yale's Year of Online Learning." I was also the core coordinator for the Fall 2021 Teaching at Yale Day for incoming graduate students.
McDougal/Poorvu Writing Fellowship
From January 2020 through May 2021, I was a McDougal/Poorvu Writing Fellow at Yale’s Graduate Writing Lab, which supports the writing and communication endeavors of Yale graduate and professional school students. In this position, I served as a writing consultant, working with individual students to build their communication skill sets across all forms of scientific writing, grant/fellowship proposals, and oral presentations. I also collaborated with the diverse community of Writing Fellows to organize and run multidisciplinary workshops, seminars, and panels related to academic writing. The programs that I have led or co-led include the following:
Presenting Engagingly in the Sciences (4-part series)
From Paper to Publication in the Sciences (5-part series)
Writing a Prospectus in the Sciences
Scientific Research and Writing (6-part series)
Compiling a Constructive Peer-Review in the Sciences
NSF GRFP Peer-Review Groups (Summer 2020, Fall 2020)
University Teaching Experience
I have also been a student instructor for several courses at both Yale and UC Berkeley. Responsibilities in these courses have included providing lectures and tutorials in supplemental course sections, running review sessions, organizing and running planetarium/telescope visits, providing one-on-one support for students, and grading coursework. The courses that I have taught are listed below.
Yale University
Spring 2019: Astronomy 105 - Earth in its Cosmic Context
Fall 2018: Astronomy 105 - Earth in its Cosmic Context
Spring 2018: Astronomy 130 - Origins and Search for Life in the Universe
UC Berkeley
Fall 2017: Astronomy 120 - Optical and Infrared Astronomy Laboratory
Yale Young Global Scholars (YYGS)
In Summer 2021 and Summer 2022, I was an instructor for the Innovations in Science & Technology (IST) track of Yale Young Global Scholars (YYGS), an academic enrichment summer program for bright high school students from around the world. I led custom-designed seminars (listed below), discussions, simulation sessions, and mentorship groups through this program.
The Planets: Holst, Mythology, and the Solar System (2-part series)
Extrasolar Planets Across the Galaxy (2-part series)
The Chaotic Universe
The Physics of Light
The Ethics of Space Exploration
Astronomy Mentoring Programs
I have developed and run popular mentoring programs between graduate students/postdoctoral researchers and undergraduates in the astronomy departments at both UC Berkeley and Yale. Each program aims to provide resources, support, and advice for early-career scientists while fostering community in each department. Both programs included one-on-one meetings between mentors and mentees, as well as larger group social events with all program participants. I led the Berkeley mentoring program from 2016-2017 and the Yale Astro Sibs mentoring program from 2018-2021.
Tutoring
I have tutored in both paid and volunteer positions in a wide range of subjects including Physics, Math, English, and Music since 2011. A few organizations that I have taught through include the Berkeley Music Connection and the National Honor Society. I also have 600+ hours of tutoring experience through my work with the private company ScoreBeyond, through which I have worked with over 50 students in preparation for the SAT, the ACT, and the SAT Physics subject test.
From 2019-2022 (Episodes 0 through 55), I was one of the three founding members of astro[sound]bites, the podcast spinoff of Astrobites. In this podcast, astronomy graduate students discuss recent papers that have been highlighted by Astrobites. We focus on connections between papers and underlying themes across subfields, tying together these Astrobites in the broader picture of current astronomy research. Check out all of our episodes on Spotify, Apple Podcasts, Google Play, and Soundcloud.
From 2017-2021, I was also a regular volunteer with Yale's Girls' Science Investigations, a free program with the goal of motivating and empowering young women interested in science. This program holds approximately 4 events per year in which 200-300 middle school girls come to the Yale Physics Department for a day full of physics-themed activities. Through this program, I have guided participants through hands-on projects, presented background scientific explanations as an Activity Leader, run science demos, and served on panels to answer questions about careers in science.
From 2017-2021, I was a regular volunteer with Yale's Open Labs, as well, which organizes science demo events at local schools and Science Café events in which local middle schools students discuss science with Yale graduate students, complete with science talks, research poster presentations, and hands-on demos. I have provided on-site support and shared my love of science with hundreds of young students through this initiative.
From 2018-2021, I served as the head coordinator for the New Haven branch of Astronomy on Tap, for which I planned and organized events, including coordinating talks and volunteers.
Finally, I was a regular presenter at Leitner Family Observatory and Planetarium (LFOP) in New Haven from 2017-2020. I ran weekly public planetarium shows, provided support for telescope observing afterwards, and discussed astronomy with visitors during these events. I also provided support for special events taking place at LFOP, including class and school visits, special tours of the facility, and a range of additional events.
Media
Check out a few of my selected media appearances below.
Schematic of binary Jovian Trojan asteroid 617 Patroclus-Menoetius occulting the cISP network. Two possible occultation paths are shown to scale, bounded by purple lines with cyan arrows marking the central trajectories. Each white point on the map denotes a cISP network site, where the current cISP network design includes 1913 sites.
Understanding the sizes and orbits of minor planets within the solar system is crucial to characterize the origins and evolutionary pathways of the solar system. Measurements of occultations – events during which a foreground object passes in front of a background star, briefly blocking out its light – can provide this critical information with exquisite precision limited primarily by the accuracy to which the background star’s position is known. With the recent release of high-precision stellar astrometry in Gaia DR2, occultations have suddenly become an extremely powerful probe to study solar system dynamics in unprecedented detail.
In this paper, we present a novel method to study the solar system using a national network of small (16-inch) telescopes spread across the United States to continually monitor occultation events across the solar system. A map of the proposed network is shown above, where each white dot corresponds to the location of a telescope and two possible occultation tracks are bounded in purple, with binary asteroid 617 Patroclus-Menoetius shown to scale. By employing a large (N~2000) number of small telescopes, it is possible to leverage this new precision to obtain a tremendous amount of information about the solar system for less than the price of a typical small space mission.
Minimum and maximum acceleration imparted by Planet Nine.
One of the main use cases that we present for the network is the search for Planet Nine. By measuring the tidal differential acceleration across the sun for a large (N>225) number of Jovian Trojan asteroids – asteroids trapped at Jupiter’s L4 and L5 Lagrange points – we show that it is possible to observe the perturbational signatures of undiscovered solar system bodies such as Planet Nine.
In a gravitational search for Planet Nine, it is necessary to distinguish the perturbational effects of Planet Nine from those of the Kuiper belt – which, while significantly less massive than Planet Nine, is far closer to the inner solar system and can thus induce perturbations comparable to or stronger than those of Planet Nine. In this work, we show that it is possible to disentangle perturbations from each structure due to their differing mass distributions (i.e. a ring vs. a single massive planet).
Perturbations induced by Planet Nine (in color) and the Kuiper Belt (gray), with the Sun's motion subtracted from the system. Each line originates at (0, 0) and traces out perturbations over one full Trojan orbit, while the color scale provides the starting Planet Nine–Sun–Trojan orientation.
Beyond the search for Planet Nine, the proposed network has a wide range of additional use cases. One example is direct measurements of small body diameters and size distributions, which are critical to constrain the early evolution and migration of planets in the solar system. Another is dramatically improved orbital ephemerides as shown below, where we calculate the improvement in ephemerides for a medium-sized Jovian Trojan asteroid from the current constraints (in blue) after 5 occultations evenly spaced across 5 years (in black) and 5 occultations evenly spaced across 12 years (approximately a full Jovian Trojan orbit; in purple). We show a panel on the scale of the blue, current constraints in the upper right for clarity. Such precise ephemerides are highly advantageous for accurate spacecraft navigation and detailed dynamical analyses of small body systems.
Distribution of walkers after burn-in for each orbital element after five occultations evenly spaced across 5 years (black) and across 12 years (purple). In blue are the Gaussian distributions associated with the initial orbital element uncertainties prior to any occultation measurements. The original uncertainties were all improved by over an order of magnitude; as a result, the blue distributions appear flat on this scale. The top right panel shows the inclination histogram on the scale of the blue distribution.
All in all, this network would be a powerful and timely tool in the era of Gaia and LSST, which is projected to find over a million new solar system objects. While it is still theoretical in nature, it shows the enormous potential for small telescopes to teach us about the solar system in this golden era for occultations.
The October 2017 discovery of the first interstellar interloper, 'Oumuamua, sent ripples through the field of astronomy. Where did 'Oumuamua come from? How common are these objects? Will we be seeing more of them in coming years? In this Letter, we address these questions using constraints from a neighboring subfield of exoplanetary science: protoplanetary disks.
Once they have formed in a planetary system, giant planets may eject planetesimals from their circumstellar systems via gravitational interactions. In this way, planets can push material out of their systems and into interstellar space, creating a population of free-floating planetesimals such as, perhaps, 'Oumuamua.
However, not all planets are capable of efficiently conducting these gravitational assists. In particular, the most efficient planetesimal ejectors are relatively massive, long-period planets. These types of planets are heavily disfavored by the detection biases of the transit and radial velocity exoplanet detection methods; as a result, the vast majority of the 4000+ currently confirmed exoplanets cannot efficiently eject surrounding debris in their systems.
The twenty high-resolution protoplanetary disk images in the DSHARP sample, displayed in 1.25 mm continuum emission (Andrews+ 2018).
Recently, the Disk Substructures at High Angular Resolution Project (DSHARP) returned 20 high-resolution images of protoplanetary disks displaying a ubiquity of substructures. Axisymmetric rings and gaps were found to be the most common type of substructure; furthermore, the types of planets thought to carve out these gaps - Neptune+ mass planets at large semimajor axis - are exactly the kind capable of producing the interstellar object population implied by 'Oumuamua.
Radial dust distributions of the three DSHARP disks simulated in this work.
We simulated the axisymmetric dust distributions of three sample DSHARP disks (left) - AS 209, HD 143006, and HD 163296 - and their best-fitting planetary companions from Zhang+ 2018 in order to characterize the mass of rocky material ejected from each system over time.
Average mm-sized mass ejected from each of the three DSHARP disks simulated in this work.
The ejected mass of mm-sized material is shown to the right, with an exponential fit extrapolating our simulation results to a later time. Combining this result with the number density of free-floating interstellar objects implied by 'Oumuamua, we determined the corresponding power law size-frequency distributions consistent with 'Oumuamua's detection.
Using these predicted interstellar object size distributions, we then determined the expected detection rates for various size regimes of interstellar objects with the Large Survey Synoptic Telescope (LSST). Our results are provided below. Ultimately, we found that, if 'Oumuamua was representative of an isotropic background population ejected from DSHARP-like protoplanetary disks, LSST should find a few 'Oumuamua-sized interstellar objects per year, as well as up to hundreds of smaller interstellar objects with r>1 m.
Detection rates by LSST for different size regimes of ISOs, with the Do+ 2018 number density denoted by a dot-dashed line. We assumed a single-frame limiting magnitude m~24.
A comprehensive understanding of the properties of exoplanets is closely intertwined with our understanding of the formation environments of these planets. Precisely determined stellar properties are critical to appropriately interpret exoplanet observations and to discern the correlations between planetary properties and their host environments.
In this project, we applied the supervised learning code The Cannon to develop a model that extracts 18 stellar labels from continuum-normalized Keck HIRES spectra: Teff, logg, vsini, and 15 abundances (C, N, O, Na, Mg, Al, Si, Ca, Ti, V, Cr, Mn, Fe, Ni, and Y). We also applied this technique to extract 18 labels from interpolated spectra obtained by the older version of the Keck HIRES instrument before its 2004 upgrade. By interpolating spectra from the older and newer detector onto the same wavelength range, we were able to reliably recover all 18 labels from the pre-2004 spectra using a model trained on post-2004 spectra.
Distribution of properties for the 1202 pre-labeled SPOCS stars used for our model training and testing.
We trained our model using 1202 pre-labeled stars from the Spectral Properties of Cool Stars (SPOCS) dataset described in Brewer et al. 2016. The distribution of stellar properties is shown in the figure to the right. The 18 stellar labels of interest were obtained for each of these stars using the Spectroscopy Made Easy (SME) program; however, because stellar modeling with this program is relatively computationally expensive, we developed a new model to rapidly return labels for large sets of stellar spectra.
All input spectra were reduced using the CPS data reduction pipeline and further continuum-normalized using the methods described in Valenti & Fischer 2005. Beyond this initial normalization, we also used a data-driven renormalization method to further improve the continuum removal as recommended in Ness et al. 2016. Sample continuum fits implementing two different functional forms are shown below for a single echelle order; our final model implements the polynomial fit.
Sample continuum renormalization, where "continuum pixels" are selected and fit in a data-driven manner. The new fit is divided out to renormalize the spectrum.
We also masked out pixels corresponding to telluric lines, which are imprinted on all ground-based spectra from the Earth's atmosphere. The telluric mask is displayed below for all echelle orders placed side-by-side, as well as for the single echelle order that we used for initial testing. Across all echelle orders, we masked out roughly 37% of pixels.
Visualization of the telluric mask used in our model, with all 16 echelle orders displayed side-by-side and distinguished by color. A zoom-in of our primary testing echelle order is shown on the bottom.
We first verified our model's performance by testing its ability to return labels for a test set of spectra withheld from our training dataset. Our results are shown below; overall, we found that our trained model reliably returned all 18 stellar labels, with scatter provided in the figure.
Performance of our model to recover 18 known stellar labels of 240 SPOCS test set stars from their post-2004 Keck HIRES spectra.
We also verified that features picked out by the model correspond to known physical phenomena by looking at a few of the coefficients returned by The Cannon for each pixel in the vicinity of the Mg Ib triplet. Pixels with coefficients deviating further from the baseline are weighted more heavily when determining the value of that coefficient for a given spectrum. As expected, the centers of Mg lines correspond to dips in the θMg coefficients, while the wings of the lines more directly impact the code's determined surface gravity. Stellar rotational velocity relies most heavily on intermediate-depth lines that are neither saturated nor washed out by the continuum.
Relevant coefficients in the vicinity of the Mg Ib triplet. Pixels with coefficients that deviate further from their baselines are more heavily weighted when evaluating the corresponding parameter value.
Lastly, we interpolated our post-2004 spectra onto the same wavelength scale as our archival pre-2004 spectra. We re-trained our model on spectra taken with the newer, upgraded spectrograph and tested its ability to recover the correct labels from spectra obtained with the older, pre-2004 instrument. The model again reliably recovered all 18 labels, shown below. This suggests that The Cannon can be used to extract labels from spectra taken with a different spectrograph from the training set! We applied this model to extract labels for 477 stars with archival spectra, with results provided in the paper.
Performance of our model, which is trained on interpolated spectra taken after Keck's 2004 detector upgrade, to recover 18 known stellar labels of 337 SPOCS stars from their pre-2004 Keck HIRES spectra.
Download model files here for use with the keckspec program to extract 18 stellar parameters from input Keck/HIRES spectra. The models with the ending "notrainingspec" are the same as the corresponding models without that file ending, but they do not store the spectra and inverse variances upon which the model was trained. If you are concerned about storage space, these models take up much less space (100 MB instead of 1.3 GB) and should perform identically to their counterparts without the "notrainingspec" addendum.
The Transiting Exoplanet Survey Satellite (TESS) was designed to search for undiscovered extrasolar planets around bright, nearby stars. But, it turns out that its observations are also ideally suited for another purpose: searching for a proposed but as-yet undiscovered ninth planet in the solar system, dubbed "Planet Nine".
Planet Nine was hypothesized to explain the puzzling clustering of orbits observed among some of the most distant known trans-Neptunian objects. If it exists, Planet Nine would be a super-Earth sized planet located between 12-23 times as far from the Sun as Pluto. Despite its large size, this enormous distance would render its signal extremely dim, explaining why the planet would not yet have been found.
Fortunately, dim signals can be dramatically strengthened by summing over a large number of frames each containing the object of interest. The video below demonstrates how Sedna (V=20.64), a distant trans-Neptunian object (TNO) below the TESS single-frame detection limit, can be recovered by shifting and stacking reduced TESS frames along Sedna's orbit. TESS observes the vast majority of the high-inclination solar system, collecting 27 days of data at each pointing. This rich dataset can be leveraged to search for undiscovered solar system objects, including Planet Nine.
To search for undiscovered objects, we extend the idea of shift-stacking to produce "best-ever" aggregate frames in which we search for objects along all orbits of interest.
Schematic demonstrating shift-stacking (Steps 1-3) and best-ever frames (Steps 4-6).
The schematic to the right details the process of creating both shift-stacked frames to recover known objects (Steps 1-3) and best-ever frames to blindly search for undiscovered objects (Steps 4-6). We have developed a new TESS pipeline designed for both of these purposes -- we use two separate methods to subtract the baseline flux of each pixel and shift-stack the remaining frames to search for significant deviations from the baseline flux along orbital paths of interest.
We apply both of these methods to recover three known distant TNOs: Sedna, 2015 BP519, and 2007 TG422, with each recovery shown below. Because we do not recover 2007 TG422 in our blind search, we find that V~22 is roughly our magnitude limit in this parameter space.
Recoveries of each object along their known paths in the sky (Column 1) and with blind best-ever frame recoveries that incorporate no input orbital information (Columns 2 and 3). The location of each object in its orbit is provided in Column 4.
Afterwards, we apply our blind search method to look for undiscovered objects in Sectors 18 and 19, both located along the galactic plane. While our existing framework is not sensitive to Planet Nine itself, we found 17 candidate objects recovered with both of our independent baseline subtraction methods. We expect that most of these candidates are likely false positives due to the low expected number density of large, distant, and highly-inclined TNOs; however, if even one of these objects is real, it could provide important new insights to narrow down the remaining Planet Nine parameter space.
This proof-of-concept will pave the way for a much larger-scale survey of the outer solar system, which we plan to accomplish by incorporating convolutional neural networks into our pipeline framework for a more automated candidate identification process. Furthermore, we have identified several promising paths forward to push our detection limits towards dimmer and slower-moving objects such as Planet Nine, particularly as new data arrives from the ongoing TESS extended mission. Keep your eyes peeled -- the search has only just begun!
Footprints of TESS sectors 18 and 19, with 150 random Planet Nine orbits overplotted in light blue. Candidate objects identified in this work are shown in green for reference.
The ''obliquity'' of a star characterizes the offset between the stellar spin axis and the net angular momentum axis of its companion planets. This angle tells us whether the planetary system is aligned -- that is, whether the planets orbit in the same direction that the star rotates. While the Solar System planets are nearly aligned, extrasolar systems have been found with planets on sideways and upside-down orbits.
Sky-projected obliquity measurements are typically made across the transit of a planet, using either the Rossiter-McLaughlin effect or Doppler tomography. As a result, most exoplanet systems with measured obliquities host short-period planets, since these planets have a relatively high likelihood of transiting their host star. However, short-period planets experience strong tidal damping from interactions with their host star, complicating the interpretation of these measurements.
Hot stars with long-period exoplanets tentatively appear to be less misaligned than cool stars with long-period exoplanets.
Systems with longer-period planets are less heavily affected by tidal damping, so their obliquities can help us to understand how planetary systems become tilted. So far, the population of P>5 day planets has shown a very different obliquity distribution from shorter-period planet systems. Planets on very tight orbits tend to be aligned if they orbit cool stars, while they span a much wider range of obliquities around hot stars. This is potentially due to differences in the stars’ tidal and/or magnetic properties that make cool stars more effective at realigning their planetary companions. This trend is less clear for longer-period planets, as shown above; in fact, we find tentative (2.79σ) evidence that the opposite trend is present at longer orbital periods, where cool star systems are more misaligned than hot star systems.
The trend of low obliquities in these systems may suggest that protoplanetary disks are typically aligned at the time of gas dispersal. Several high-obliquity cool star systems host eccentric planets, as well, which may at least partially account for the hot/cool star discrepancy: these systems may be undergoing high-eccentricity migration or another dynamical mechanism that pumps up both their obliquity and eccentricity. The SOLES survey is designed to extend the sample of obliquity measurements for relatively wide-separation planets to disentangle which trends are robust and what they tell us about transiting planetary systems' dynamical evolution.
Exoplanets with measured host star obliquities λ. The spread in measured obliquities is larger at higher eccentricity for systems with e≠0.
In this first paper of the SOLES survey, we measured the stellar obliquity of K2-140 by observing the Rossiter-McLaughlin effect across the transit of K2-140 b, a Jupiter-mass exoplanet with period P=6.57 days and a/R*=12.88. We found that K2-140 is an aligned system, consistent with the planet's low eccentricity.
Joint fit results for the K2-140 system using new Rossiter-McLaughlin measurements (right), as well as archival photometry (left) and radial velocity (center) data.
K2-140 b is too far from its host star to have been realigned by equilibrium tides-—so, we conclude that it was likely primoridally aligned. Our ongoing survey will help to determine whether this is common around both hot and cool stars, and whether there are multiple hot and warm Jupiter formation mechanisms at play. Stay tuned!
In the 90s, the discovery of the first exoplanets came as a surprise: the first confirmed exoplanet detections were massive planets orbiting shockingly close to their host stars, known as "hot Jupiters". But how do these bizarre planets — unlike anything observed in the solar system — form? This mystery has remained at the core of exoplanet science over the past three decades.
Observations of hot Jupiters' spin-orbit angles, or their "obliquities" (the angle between the stellar spin axis and the hot Jupiter's orbit normal) provide a clue to their key formation pathway. Many hot Jupiters orbit their host stars sideways (on polar orbits), or possibly even backwards. Some mechanisms that can produce these large hot Jupiter spin-orbit misalignments are shown below.
A few potential hot Jupiter origin channels that can produce spin-orbit misalignments.
Not all hot Jupiters show these spin-orbit misalignments; in addition to the large misaligned population, many hot Jupiters have also been found at or near alignment. Previous work (Winn et al. 2010, Schlaufman et al. 2010) demonstrated that hot Jupiters orbiting hot stars span a wide range of misalignments, while those orbiting cool stars are typically aligned. This is likely due to differences in the properties of systems with host stars above and below the "Kraft break" at Teff~6100 K. Stars above the Kraft break have radiative exteriors and relatively weak tidal and magnetic interactions with their companions, while stars below the Kraft break have convective exteriors and are more capable of tidally realigning planets that had been initially misaligned.
In this paper, we add another layer to this story: that is, we show that the established discontinuity of obliquities at the Kraft break is present only for hot Jupiters on circular orbits. By contrast, hot Jupiters on eccentric orbits show no significant population-wide change in obliquities at the Kraft break, as demonstrated in the figure below.
Comparative cumulative sums demonstrating that the difference in obliquities below and above the Kraft break is not present in the population of eccentric planets.
What does this mean? Well, it takes longer to realign eccentric planets through tidal dissipation, suggesting that a large fraction of hot Jupiters may have begun with large misalignments — as would be expected in the high-eccentricity migration scenario — and that they were subsequently realigned. We demonstrate below that the hot Jupiters with the longest tidal realignment timescales also have the longest eccentricity damping timescales, as well as the largest range of measured obliquities.
Comparison of tidal realignment timescales, eccentricity damping timescales, and obliquities.
Based on these findings, we show that the obliquity distribution of hot Jupiters is consistent with being crafted by a combination of high-eccentricity migration and tidal dissipation. In this framework, most or all hot Jupiters originated further out in their host protoplanetary disks. Dynamical interactions launched these cold Jupiters to extremely high eccentricities and a wide range of misalignments, and the orbits were subsequently circularized and realigned by tidal interactions between the planet and its host star. The current obliquity distribution reflects the natural tidal realignment process that acts more effectively for planets orbiting cool stars.
Observed obliquity distributions overlaid with theoretical distributions.
The difference at the Kraft break is also visualized to the right here. Only the hot Jupiter population with circular orbits and cool host stars shows a significant excess of aligned planets, while the two eccentric populations overlap. In gray, we overplot fiducial obliquity distributions that result from several high-eccentricity migration pathways. These overlap well with all populations other than the e=0 hot Jupiters orbiting cool stars, suggesting that these planets have been realigned, while the other three populations have not been as strongly affected by tidal dissipation.
Evolution of hot Jupiter obliquities in a high-eccentricity migration mixture model.
Finally, we evolve a mixture model of the high-eccentricity migration pathways shown above to demonstrate that high-eccentricity migration, combined with tidal dissipation, can reproduce the global properties of the stellar obliquity distribution. Our analysis provides a tantalizing hint that high-eccentricity migration may be a (the?) dominant hot Jupiter formation mechanism, pushing us one step closer to answering the long-standing question of how hot Jupiters are created.
Warm Jupiters may just hold the key to understanding how hot Jupiters form. As their wider-orbiting cousins, warm Jupiters share many of the puzzling properties of hot Jupiters: they are similarly massive and close to their host stars. Yet, the differences between the two populations may offer the subtle clues necessary to delineate how both groups of planets formed.
While stellar obliquity constraints have demonstrated that hot Jupiters often show spin-orbit misalignments – that is, they often orbit sideways relative to their host star, or potentially even backwards – the distribution of warm Jupiter spin-orbit angles is not as well-constrained. Warm Jupiters are thought to form quiescently (that is, not in a dynamically violent way) due to their relatively high rate of nearby companion planets (Huang et al. 2016; Wu, Rice, & Wang 2022 in review). They also experience relatively weak star-planet interactions such that their spin-orbit angles are likely difficult to realign through tides.
As a result, stellar obliquities in warm Jupiter systems can, in some cases, serve as a proxy for the initial obliquities of their parent protoplanetary disks. This distribution can directly inform our understanding of when hot Jupiters became misaligned: that is, did they form in tilted disks, or were they thrown onto misaligned orbits later?
In this paper, we address this question by examining the population of sky-projected obliquity measurements (λ) in single-star warm Jupiter systems. We begin by presenting the third result from the SOLES survey: a measurement of the Rossiter-McLaughlin effect in the TOI-1478 warm Jupiter system, obtained using the NEID/WIYN and Keck/HIRES spectrographs. We find that the system is aligned: the warm Jupiter orbits in roughly the same direction that the host star rotates.
Rossiter-McLaughlin measurements and best-fitting models for the WIYN/NEID dataset (left), the Keck/HIRES dataset (center), and the combined dataset (right).
Combining the SOLES results with the full population of past measurements, we show that all warm Jupiters in single-star systems measured to date have been aligned with their host star within 20 degrees.
Overview of obliquity measurements in giant planet systems to date, with the three SOLES measurements highlighted.
Is this a coincidence? We conduct a series of tests to demonstrate whether single-star warm Jupiter systems are significantly more aligned than their hot Jupiter counterparts. We take random draws of measured |λ| values from three different groups of single-star hot Jupiter systems to determine the likelihood that we would have drawn zero planets with |λ| > 20 degrees from this population. We complete this test with 30,000 iterations, resulting in the figure below. 12, 12, and 10 values were drawn in the left, center, and right panels, respectively. We find that, in each case, the warm Jupiters are significantly more aligned than the hot Jupiter comparison populations.
Number of misaligned systems from random HJ draws (blue), compared with the observed zero misaligned WJs (purple line).
We also conduct a similar test with summed |λ| values, showing the distribution of summed values obtained for the single-star hot and warm Jupiters (below). The benefit of this test is that it does not assume any specific cutoff in |λ| for which planets are considered ''aligned'' vs. ''misaligned.'' Here, too, we find that single-star warm Jupiters constitute a distinctly more aligned population than their hot Jupiter counterparts.
Distribution of cumulatively summed |λ| values for hot (blue) and warm (purple) Jupiters. 12, 12, and 10 values were summed in the left, center, and right panels, respectively.
Ultimately, we conclude that warm Jupiters in single-star systems tend to be more aligned than analogous hot Jupiters. This finding implies that planets in single-star systems typically form in aligned protoplanetary disks: warm Jupiters form aligned and stay that way, while hot Jupiters are misaligned after protoplanetary disk dispersal through, for example, high-eccentricity migration.
Several outstanding questions still remain – how does eccentricity play into this picture? What happens in binary or multi-star systems? Just how rare is it to find a misaligned warm Jupiter in a single-star system? Fortunately, we can look forward to many future measurements ahead to more fully unveil the mysterious origins of hot and warm Jupiters.
Research Highlight #8
The Orbital Architecture of Qatar-6: A Fully Aligned 3-Body System?
If a planet is born in a binary star system -- that is, in a system with two stars -- how does that affect its orbital evolution? What is the role of stellar multiplicity in flipping orbits, or in pushing them back toward alignment?
These questions provide motivation for the case study examined here: the Qatar-6 AB b three-body system, which includes two stars and a warm Jupiter companion orbiting the primary star. This is the fourth result from the Stellar Obliquities in Long-period Exoplanet Systems (SOLES) survey, which is designed to constrain the evolutionary pathways that produce diverse transiting exoplanet systems.
We began by measuring the Rossiter-McLaughlin signal of the Qatar-6 A b warm Jupiter, which encodes which direction the planet orbits relative to the host star's spin. Our symmetric signal, shown in the figure below, indicates that the system is well-aligned with its host star's equator within the sky-plane.
Rossiter-McLaughlin observation and model fit for the warm Jupiter Qatar-6 A b. The system is consistent with exact alignment in the sky-plane.
Combining this result with additional constraints, we found that the true, 3D obliquity of the system is also consistent with near-exact alignment (within a few degrees). Long-term "secular" interactions with stellar companions are often quoted as a way to produce misalignments, so this was already interesting -- no evidence for misalignments here, similar to tendency toward alignment previously noted in single-star warm Jupiter systems.
Investigating the system further, we next looked at how the orientation of the stellar binary orbits might teach us about the system's past. Surprisingly, we found that the binary star system was extremely close to edge-on, just like the transiting exoplanet orbit!
Geometry of the edge-on Qatar-6 AB stellar binary system.
This means that all evidence so far points toward the 3 bodies in the system being both aligned and collinear: the planet (Qatar-6 A b) orbits in the same direction that its host star (Qatar-6 A) spins, and the orbits of the planet (Qatar-6 A b) and the binary star system (Qatar-6 AB) are both edge-on.
Selection of 1,000 accepted solutions for a binary orbit fit to Qatar-6 AB.
There are certainly caveats -- we don't know which way the planet is orbiting within the sky-plane (so it still could have a misalignment that we can't see). But, all constraints so far point toward Qatar-6 being a great example of a pristine, fully quiescent system -- the system formed with all of its components aligned (or pushed to alignment over relatively short timescales), and it stayed that way.
If the alignment is truly 3D, it likely originated at the protoplanetary disk phase: precession and dissipation of energy pushes disks towards an aligned state, and gravitational star-disk coupling and/or strong magnetic fields in the young system can keep the planet aligned with its host star.
Is this "normal" for warm Jupiters? What factors decide whether a system maintains such a distinct alignment, versus the many sideways-orbiting and otherwise misaligned systems? Case studies like the Qatar-6 system will enable us to better understand the regimes in which spin-orbit misalignment does (or doesn't!) operate, distinguishing the range of evolutionary pathways for exoplanet systems.
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i = 0;
while (!deck.isInOrder()) {
print 'Iteration ' + i;
deck.shuffle();
i++;
}
print 'It took ' + i + ' iterations to sort the deck.';
