arXiv subjects
Publications and source records attributed to Eric Agol.
Presently, the Galactic plane receives relatively few observations compared to most of the LSST footprint. While this may address static science, the plane will also represent the highest density of variable Galactic sources. The proper characterization of variability of these sources will benefit greatly from observations at a higher cadence.
LHS 1140 is a nearby mid-M dwarf known to host a temperate rocky super-Earth (LHS 1140 b) on a 24.737-day orbit. Based on photometric observations by MEarth and Spitzer as well as Doppler spectroscopy from HARPS, we report the discovery of an additional transiting rocky companion (LHS 1140 c) with a mass of $1.81\pm0.39~{\rm M_{Earth}}$ and a radius of $1.282\pm0.024~{\rm R_{Earth}}$ on a tighter, 3.77795-day orbit. We also obtain more precise estimates of the mass and radius of LHS 1140 b to be $6.98\pm0.89~{\rm M_{Earth}}$ and $1.727\pm0.032~{\rm R_{Earth}}$. The mean densities of planets b and c are $7.5\pm1.0~\rm{g/cm^3}$ and $4.7\pm1.1~\rm{g/cm^3}$, respectively, both consistent with the Earth's ratio of iron to magnesium silicate. The orbital eccentricities of LHS 1140 b and c are consistent with circular orbits and constrained to be below 0.06 and 0.31, respectively, with 90% confidence. Because the orbits of the two planets are co-planar and because we know from previous analyses of Kepler data that compact systems of small planets orbiting M dwarfs are commonplace, a search for more transiting planets in the LHS 1140 system could be fruitful. LHS 1140 c is one of the few known nearby terrestrial planets whose atmosphere could be studied with the upcoming James Webb Space Telescope.
We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon or star during an occultation if the specific intensity map of the body is expressed as a sum of spherical harmonics. Our expressions are valid to arbitrary degree and may be computed recursively for speed. The formalism we develop here applies to the computation of stellar transit light curves, planetary secondary eclipse light curves, and planet-planet/planet-moon occultation light curves, as well as thermal (rotational) phase curves. In this paper we also introduce STARRY, an open-source package written in C++ and wrapped in Python that computes these light curves. The algorithm in STARRY is six orders of magnitude faster than direct numerical integration and several orders of magnitude more precise. STARRY also computes analytic derivatives of the light curves with respect to all input parameters for use in gradient-based optimization and inference, such as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit observed light curves to infer properties of a celestial body's surface map.
We explore the connection between starspots and plages of three main-sequence stars by studying the chromospheric and photospheric activity over several rotation periods. We present simultaneous photometry and high-resolution ($R\sim 31,500$) spectroscopy of KIC 9652680, a young, superflare-producing G1 star with a rotation period of 1.4 days. Its Kepler light curve shows rotational modulation consistent with a bright hemisphere followed by a relatively dark hemisphere, generating photometric variability with a semi-amplitude of 4%. We find that KIC 9652680 is darkest when its $S$-index of Ca II H & K emission is at its maximum. We interpret this anti-correlation between flux and $S$ to indicate that dark starspots in the photosphere are co-located with the bright plages in the chromosphere, as they are on the Sun. Moving to lower masses and slower rotators, we present K2 observations with simultaneous spectroscopy of EPIC 211928486 (K5V) and EPIC 211966629 (K4V), two active stars in the 650 Myr-old open cluster Praesepe. The K2 photometry reveals that both stars have rotation periods of 11.7 days; while their flux varies by 1 and 2% respectively, their Ca II H & K $S$-indices seem to hold relatively constant as a function of rotational phase. This suggests that extended chromospheric networks of plages are not concentrated into regions of emission centered on the starspots that drive rotational modulation, unlike KIC 9652680. We also note that the Ca II emission of EPIC 211928486 dipped and recovered suddenly over the duration of one rotation, suggesting that the evolution timescale of plages may be of order the rotation period.
We apply the transit light curve self-contamination technique of Morris et al. (2018) to search for the effect of stellar activity on the transits of the ultracool dwarf TRAPPIST-1 with 2018 Spitzer photometry. The self-contamination method fits the transit light curves of planets orbiting spotted stars, allowing the host star to be a source of contaminating positive or negative flux which influences the transit depths but not the ingress/egress durations. We find that none of the planets show statistically significant evidence for self-contamination by bright or dark regions of the stellar photosphere. However, we show that small-scale magnetic activity, analogous in size to the smallest sunspots, could still be lurking in the transit photometry undetected.
We typically measure the radii of transiting exoplanets from the transit depth, which is given by the ratio of cross-sectional areas of the planet and star. However, if a star has dark starspots (or bright regions) distributed throughout the transit chord, the transit depth will be biased towards smaller (larger) values, and thus the inferred planet radius will be smaller (larger) if unaccounted for. We reparameterize the transit light curve to account for "self-contamination" by photospheric inhomogeneities by splitting the parameter $R_p/R_\star$ into two parameters: one for the radius ratio -- which controls the duration of ingress and egress -- and another which measures the possibly contaminated transit depth. We show that this is equivalent to the formulation for contamination by a second star (with positive or negative flux), and that it is sensitive to time-steady inhomogeneity of the stellar photosphere. We use synthetic light curves of spotted stars at high signal-to-noise to show that the radius recovered from measurement of the ingress/egress duration can recover the true radii of planets transiting spotted stars with axisymmetric spot distributions if the limb-darkening parameters are precisely known. We fit time-averaged high signal-to-noise transit light curves from Kepler and Spitzer of ten planets to measure the planet radii and search for evidence of spot distributions. We find that this sample has a range of measured depths and ingress durations which are self-consistent, providing no strong evidence for contamination by spots. However, there is suggestive evidence for occultation of starspots on Kepler-17, and that relatively bright regions are occulted by the planets of Kepler-412 and HD 80606. Future observations with the James Webb Space Telescope may enable this technique to yield accurate planetary radii in the presence of stellar inhomogeneities.
The Origins Space Telescope (OST) is one of four mission concepts currently being studied by NASA in preparation for the Astrophysics 2020 Decadal Survey. With active cooling (~4 K), OST will be sensitive in mid- to far-IR wavelengths, using imaging and spectroscopy to probe the furthest reaches of our galaxies, trace the path of water through star and planet formation, and place thermochemical constraints on the atmospheres of exoplanets ranging in size from Jupiter to Earth. This contribution to the Exoplanet Science Strategy committee discusses the significant advancements that the OST Mid-Infrared Imager, Spectrometer, and Coronagraph (MISC) instrument can make in studying cool planetary atmospheres. We particularly focus on the atmospheres of transiting rocky planets in the habitable zones of mid-to-late M stars. We discuss how OST thermal infrared observations can significantly enhance our understanding of the temperature structure and molecular abundances of biologically interesting gases on these worlds, including O3, CH4, H2O, and CO2.
The M8V star TRAPPIST-1 hosts seven roughly Earth-sized planets and is a promising target for exoplanet characterization. Kepler/K2 Campaign 12 observations of TRAPPIST-1 in the optical show an apparent rotational modulation with a 3.3 day period, though that rotational signal is not readily detected in the Spitzer light curve at 4.5 $μ$m. If the rotational modulation is due to starspots, persistent dark spots can be excluded from the lack of photometric variability in the Spitzer light curve. We construct a photometric model for rotational modulation due to photospheric bright spots on TRAPPIST-1 which is consistent with both the Kepler and Spitzer light curves. The maximum-likelihood model with three spots has typical spot sizes of $R_\mathrm{spot}/R_\star \approx 0.004$ at temperature $T_\mathrm{spot} \gtrsim 5300 \pm 200$ K. We also find that large flares are observed more often when the brightest spot is facing the observer, suggesting a correlation between the position of the bright spots and flare events. In addition, these flares may occur preferentially when the spots are increasing in brightness, which suggests that the 3.3 d periodicity may not be a rotational signal, but rather a characteristic timescale of active regions.
Metal pollution in white dwarf atmospheres may be the accreted remnants of planetary objects. After the discovery of disintegrating planetary objects transiting WD 1145+017 (Vanderburg et al. 2015), undergraduates in the University of Washington's Pre- Major in Astronomy Program (Pre-MAP) were inspired to collect photometry of the brightest white dwarfs to hunt for similar transiting objects around other metal-polluted white dwarfs. Prior surveys have yet to make a detection of a transiting planet orbiting a white dwarf, yet white dwarfs are still an attractive target for searches of small, rocky planetary material. Since a typical white dwarf is Earth-sized, transits of Earth-sized planets could have depths >50%, so even low S/N photometry has a chance at discovering transiting material. We identified bright, northern, metal-polluted white dwarfs in the SDSS DR10 white dwarf catalog, and observed five targets with the Astrophysical Research Consortium Small Aperture Telescope (ARCSAT) 0.5-meter telescope at Apache Point Observatory. The ARCSAT photometry had sufficient precision to detect Moon-sized objects or larger at short orbital periods, though no such planets were detected for these targets. We look forward to surveys which may find planets orbiting white dwarfs, such as NASA's TESS, ESA's PLATO, and the Evryscope.
Astrometry from Gaia will measure the positions of stellar photometric centroids to unprecedented precision. We show that the precision of Gaia astrometry is sufficient to detect starspot-induced centroid jitter for nearby stars in the Tycho-Gaia Astrometric Solution (TGAS) sample with magnetic activity similar to the young G-star KIC 7174505 or the active M4 dwarf GJ 1243, but is insufficient to measure centroid jitter for stars with Sun-like spot distributions. We simulate Gaia observations of stars with 10 year activity cycles to search for evidence of activity cycles, and find that Gaia astrometry alone likely can not detect activity cycles for stars in the TGAS sample, even if they have spot distributions like KIC 7174505. We review the activity of the nearby low-mass stars in the TGAS sample for which we anticipate significant detections of spot-induced jitter.
Context. The TRAPPIST-1 system hosts seven Earth-sized, temperate exoplanets orbiting an ultra-cool dwarf star. As such, it represents a remarkable setting to study the formation and evolution of terrestrial planets that formed in the same protoplanetary disk. While the sizes of the TRAPPIST-1 planets are all known to better than 5% precision, their densities have significant uncertainties (between 28% and 95%) because of poor constraints on the planet's masses. Aims.The goal of this paper is to improve our knowledge of the TRAPPIST-1 planetary masses and densities using transit-timing variations (TTV). The complexity of the TTV inversion problem is known to be particularly acute in multi-planetary systems (convergence issues, degeneracies and size of the parameter space), especially for resonant chain systems such as TRAPPIST-1. Methods. To overcome these challenges, we have used a novel method that employs a genetic algorithm coupled to a full N-body integrator that we applied to a set of 284 individual transit timings. This approach enables us to efficiently explore the parameter space and to derive reliable masses and densities from TTVs for all seven planets. Results. Our new masses result in a five- to eight-fold improvement on the planetary density uncertainties, with precisions ranging from 5% to 12%. These updated values provide new insights into the bulk structure of the TRAPPIST-1 planets. We find that TRAPPIST-1\,c and e likely have largely rocky interiors, while planets b, d, f, g, and h require envelopes of volatiles in the form of thick atmospheres, oceans, or ice, in most cases with water mass fractions less than 5%.
Recent Kepler photometry has revealed that about half of white dwarfs (WDs) have periodic, low-level (~ 1e-4 - 1e-3), optical variations. Hubble Space Telescope (HST) ultraviolet spectroscopy has shown that up to about one half of WDs are actively accreting rocky planetary debris, as evidenced by the presence of photospheric metal absorption lines. We have obtained HST ultraviolet spectra of seven WDs that have been monitored for periodic variations, to test the hypothesis that these two phenomena are causally connected, i.e. that the optical periodic modulation is caused by WD rotation coupled with an inhomogeneous surface distribution of accreted metals. We detect photospheric metals in four out of the seven WDs. However, we find no significant correspondence between the existence of optical periodic variability and the detection of photospheric ultraviolet absorption lines. Thus the null hypothesis stands, that the two phenomena are not directly related. Some other source of WD surface inhomogeneity, perhaps related to magnetic field strength, combined with the WD rotation, or alternatively effects due to close binary companions, may be behind the observed optical modulation. We report the marginal detection of molecular hydrogen in WD J1949+4734, only the fourth known WD with detected H_2 lines. We also re-classify J1926+4219 as a carbon-rich He-sdO subdwarf.
TRAPPIST-1 hosts seven Earth-sized planets transiting an M8 star. We observed mid-transit times of each of the inner two planets with the Astrophysical Research Consortium (ARC) 3.5 m Telescope at Apache Point Observatory (APO) to help constrain the planet masses with transit timing variations, and we outline a procedure for analyzing transit observations of late-M stars with APO. The transit times of TRAPPIST-1 b and c are $\mathrm{BJD}_{\mathrm{TDB}} = 2457580.87634^{+0.00034}_{-0.00034}$ and $2457558.89477^{+0.00080}_{-0.00085}$, respectively, which will help constrain the planet masses.
The recently detected TRAPPIST-1 planetary system, with its seven planets transiting a nearby ultracool dwarf star, offers the first opportunity to perform comparative exoplanetology of temperate Earth-sized worlds. To further advance our understanding of these planets' compositions, energy budgets, and dynamics, we are carrying out an intensive photometric monitoring campaign of their transits with the $\textit{Spitzer Space Telescope}$. In this context, we present 60 new transits of the TRAPPIST-1 planets observed with $\textit{Spitzer}$/IRAC in February and March 2017. We combine these observations with previously published $\textit{Spitzer}$ transit photometry and perform a global analysis of the resulting extensive dataset. This analysis refines the transit parameters and provides revised values for the planets' physical parameters, notably their radii, using updated properties for the star. As part of our study, we also measure precise transit timings that will be used in a companion paper to refine the planets' masses and compositions using the transit timing variations method. TRAPPIST-1 shows a very low level of low-frequency variability in the IRAC 4.5-$μ$m band, with a photometric RMS of only 0.11$\%$ at a 123-s cadence. We do not detect any evidence of a (quasi-)periodic signal related to stellar rotation. We also analyze the transit light curves individually, to search for possible variations in the transit parameters of each planet due to stellar variability, and find that the $\textit{Spitzer}$ transits of the planets are mostly immune to the effects of stellar variations. These results are encouraging for forthcoming transmission spectroscopy observations of the TRAPPIST-1 planets with the $\textit{James Webb Space Telescope}$.
We present new 3.6 and 4.5 $μm$ Spitzer phase curves for the highly irradiated hot Jupiter WASP-33b and the unusually dense Saturn-mass planet HD 149026b. As part of this analysis, we develop a new variant of pixel level decorrelation that is effective at removing intrapixel sensitivity variations for long observations (>10 hours) where the position of the star can vary by a significant fraction of a pixel. Using this algorithm, we measure eclipse depths, phase amplitudes, and phase offsets for both planets at 3.6 $μm$ and 4.5 $μm$. We use a simple toy model to show that WASP-33b's phase offset, albedo, and heat recirculation efficiency are largely similar to those of other hot Jupiters despite its very high irradiation. On the other hand, our fits for HD 149026b prefer a very high albedo and an unusually high recirculation efficiency. We also compare our results to predictions from general circulation models, and find that while neither are a good match to the data, the discrepancies for HD 149026b are especially large. We speculate that this may be related to its high bulk metallicity, which could lead to enhanced atmospheric opacities and the formation of reflective cloud layers in localized regions of the atmosphere. We then place these two planets in a broader context by exploring relationships between the temperatures, albedos, heat transport efficiencies, and phase offsets of all planets with published thermal phase curves. We find a striking relationship between phase offset and irradiation temperature--the former drops with increasing temperature until around 3400 K, and rises thereafter. Although some aspects of this trend are mirrored in the circulation models, there are notable differences that provide important clues for future modeling efforts.
We explore the occurrence and detectability of planet-planet occultations (PPOs) in exoplanet systems. These are events during which a planet occults the disk of another planet in the same system, imparting a small photometric signal as its thermal or reflected light is blocked. We focus on the planets in TRAPPIST-1, whose orbital planes we show are aligned to within 0.3 degrees at 90% confidence. We present a photodynamical model for predicting and computing PPOs in TRAPPIST-1 and other systems for various assumptions of the planets' atmospheric states. When marginalizing over the uncertainties on all orbital parameters, we find that the rate of PPOs in TRAPPIST-1 is about 1.4 per day. We investigate the prospects for detection of these events with the James Webb Space Telescope, finding that ~10-20 occultations per year of b and c should be above the noise level at 12-15 microns. Joint modeling of several of these PPOs could lead to a robust detection. Alternatively, observations with the proposed Origins Space Telescope should be able to detect individual PPOs at high signal-to-noise. We show how PPOs can be used to break transit timing variation degeneracies, imposing strong constraints on the eccentricities and masses of the planets, as well as to constrain the longitudes of nodes and thus the complete three-dimensional structure of the system. We further show how modeling of these events can be used to reveal a planet's day/night temperature contrast and construct crude surface maps. We make our photodynamical code available on github.
Kepler photometry of the hot Neptune host star HAT-P-11 suggests that its spot latitude distribution is comparable to the Sun's near solar maximum. We search for evidence of an activity cycle in the CaII H & K chromospheric emission $S$-index with archival Keck/HIRES spectra and observations from the echelle spectrograph on the ARC 3.5 m Telescope at APO. The chromospheric emission of HAT-P-11 is consistent with a $\gtrsim 10$ year activity cycle, which plateaued near maximum during the Kepler mission. In the cycle that we observed, the star seemed to spend more time near active maximum than minimum. We compare the $\log R^\prime_{HK}$ normalized chromospheric emission index of HAT-P-11 with other stars. HAT-P-11 has unusually strong chromospheric emission compared to planet-hosting stars of similar effective temperature and rotation period, perhaps due to tides raised by its planet.
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose but, since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small datasets. In this paper, we present a novel method for Gaussian Process modeling in one-dimension where the computational requirements scale linearly with the size of the dataset. We demonstrate the method by applying it to simulated and real astronomical time series datasets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically-driven damped harmonic oscillators -- providing a physical motivation for and interpretation of this choice -- but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable Gaussian Process methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.