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In this work, we outline a new method for estimating dayside effective temperatures of exoplanets and associated uncertainties using Gaussian process (GP) regression. By applying our method to simulated observations, we show that the GP method estimates uncertainty more robustly than other model-independent approaches. We find that unbiased estimates of effective temperatures can be made using as few as three broad-band measurements (white-light HST WFC3 and the two warm Spitzer IRAC channels), although we caution that estimates made using only IRAC can be significantly biased. We then apply our GP method to the twelve hot Jupiters in the literature whose secondary eclipse depths have been measured by WFC3 and IRAC channels 1 and 2: CoRoT-2 b; HAT-P-7 b; HD 189733 b; HD 209458 b; Kepler-13A b; TrES-3 b; WASP-4 b; WASP-12 b; WASP-18 b; WASP-33 b; WASP-43 b; and WASP-103 b. We present model-independent dayside effective temperatures for these planets, with uncertainty estimates that range from $\pm$66 K to $\pm$136 K., Comment: 11 pages, 6 figures, accepted for publication in MNRAS

The exoplanet WASP-12b is the prototype for the emerging class of ultra-hot, Jupiter-mass exoplanets. Past models have predicted---and near ultra-violet observations have shown---that this planet is losing mass. We present an analysis of two sets of 3.6 $\mu$m and 4.5 $\mu$m $\textit{Spitzer}$ phase curve observations of the system which show clear evidence of infrared radiation from gas stripped from the planet, and the gas appears to be flowing directly toward or away from the host star. This accretion signature is only seen at 4.5 $\mu$m, not at 3.6 $\mu$m, which is indicative either of CO emission at the longer wavelength or blackbody emission from cool, $\lesssim$ 600 K gas. It is unclear why WASP-12b is the only ultra-hot Jupiter to exhibit this mass loss signature, but perhaps WASP-12b's orbit is decaying as some have claimed, while the orbits of other exoplanets may be more stable; alternatively, the high energy irradiation from WASP-12A may be stronger than the other host stars. We also find evidence for phase offset variability at the level of $6.4\sigma$ ($46.2^{\circ}$) at 3.6 $\mu$m., Comment: 9 pages plus appendices and supplementary information, published in MNRAS

Launching in 2028, ESA's Atmospheric Remote-sensing Exoplanet Large-survey (ARIEL) survey of $\sim$1000 transiting exoplanets will build on the legacies of Kepler and TESS and complement JWST by placing its high precision exoplanet observations into a large, statistically-significant planetary population context. With continuous 0.5--7.8~$\mu$m coverage from both FGS (0.50--0.55, 0.8--1.0, and 1.0--1.2~$\mu$m photometry; 1.25--1.95~$\mu$m spectroscopy) and AIRS (1.95--7.80~$\mu$m spectroscopy), ARIEL will determine atmospheric compositions and probe planetary formation histories during its 3.5-year mission. NASA's proposed Contribution to ARIEL Spectroscopy of Exoplanets (CASE) would be a subsystem of ARIEL's FGS instrument consisting of two visible-to-infrared detectors, associated readout electronics, and thermal control hardware. FGS, to be built by the Polish Academy of Sciences' Space Research Centre, will provide both fine guiding and visible to near-infrared photometry and spectroscopy, providing powerful diagnostics of atmospheric aerosol contribution and planetary albedo, which play a crucial role in establishing planetary energy balance. The CASE team presents here an independent study of the capabilities of ARIEL to measure exoplanetary metallicities, which probe the conditions of planet formation, and FGS to measure scattering spectral slopes, which indicate if an exoplanet has atmospheric aerosols (clouds and hazes), and geometric albedos, which help establish planetary climate. Our design reference mission simulations show that ARIEL could measure the mass-metallicity relationship of its 1000-planet single-visit sample to $>7.5\sigma$ and that FGS could distinguish between clear, cloudy, and hazy skies and constrain an exoplanet's atmospheric aerosol composition to $>5\sigma$ for hundreds of targets, providing statistically-transformative science for exoplanet atmospheres., Comment: accepted to PASP; 23 pages, 6 figures

Here we present the analysis of multi-epoch secondary eclipse observations of HD 189733b and HD 209458b as a probe of temporal variability in the planetary climate using both Spitzer channels 1 and 2 (3.6 and 4.5 um). Constraining temporal variability will inform models and identify physical processes occurring at either length scales too small to directly observe or at pressure levels that are inaccessible to transit observations. We do not detect statistically significant variability and are able to place useful upper limits on the IR variability amplitudes in these atmospheres. There are very few planets with multi-epoch observations at the required precision to probe variability in dayside emission. The observations considered in this study span several years, providing insight into temporal variability at multiple timescales. In the case of HD 189733b, the best fit eclipse depths for the channel 2 observations exhibit a scatter of 102 ppm about a median depth of 1827 ppm and in channel 1 exhibit a scatter of 88 ppm about a median depth of 1481 ppm. For HD 209458b, the best fit eclipse depths for the channel 2 observations exhibit a scatter of 22 ppm about a median depth of 1406 ppm and in channel 1 exhibit a scatter of 131 ppm about a median depth of 1092 ppm. The precision and scatter in these observations allow us to constrain variability to less than (5.6% and 6.0%) and (12% and 1.6%) for channels (1,2) of HD 189733b and HD 209458b respectively. There is a difference in the best fit eclipse timing compared to the predicted time consistent with an offset hotspot as predicted by GCMs and confirmed in previous phase curve observations., Comment: Accepted for Publication in AJ 12/17/2019, 9 pages, 8 figures

Space-based direct imaging missions (HabEx, LUVOIR) would observe reflected light from exoplanets in the habitable zones of Sun-like stars. The ultimate---but not sole---goal of these concept missions is to characterize such planets. Knowing an exoplanet's orbit would help two-fold: (i) its semi-major axis informs whether the planet might harbour surface liquid water, making it a priority target; and (ii) predicting the planet's future location would tell us where and when to look. The science yields of HabEx and LUVOIR depend on the number, cadence, and precision of observations required to establish a planet's orbit. We produce mock observations using realistic distributions for the six Keplerian orbital parameters, experimenting with both Beta and uniform eccentricity distributions, and accounting for imperfect astrometry ($\sigma$ = 3.5 mas) and obscuration due to the inner working angle of a high-contrast imaging system (IWA = 31 mas). Using Markov chain Monte Carlo methods, we fit the orbital parameters, and retrieve their average precisions and accuracies as functions of cadence, number of epochs, and distance to target. Given the time at which it was acquired, each image provides two data: the $x$ and $y$ position of the planet with respect to its star. Parameter retrieval based on one or two images is formally under-constrained; yet the semi-major axis posterior can be obtained semi-analytically. For a planet at 1 AU around a star at a distance of 10 pc, three epochs constrain the semi-major axis to within $\lesssim$5\%, if each image is taken at least 90 days apart., Comment: 12 pages, 9 figures, accepted for publication in AJ

Directly-imaged planetary-mass companions offer unique opportunities in atmospheric studies of exoplanets. They share characteristics of both brown dwarfs and transiting exoplanets, therefore, are critical for connecting atmospheric characterizations for these objects. Rotational phase mapping is a powerful technique to constrain the condensate cloud properties in ultra-cool atmospheres. Applying this technique to directly-imaged planetary-mass companions will be extremely valuable for constraining cloud models in low mass and surface gravity atmospheres and for determining the rotation rate and angular momentum of substellar companions. Here, we present Hubble Space Telescope Wide Field Camera 3 near-infrared time-resolved photometry for three planetary-mass companions, AB Pic B, 2M0122B, and 2M1207b. Using two-roll differential imaging and hybrid point spread function modeling, we achieve sub-percent photometric precision for all three observations. We find tentative modulations ($<\!\!2\sigma$) for AB Pic B and 2M0122B but cannot reach conclusive results on 2M1207b due to strong systematics. The relatively low significance of the modulation measurements cannot rule out the hypothesis that these planetary-mass companions have the same vertical cloud structures as brown dwarfs. Our rotation rate measurements, combined with archival period measurements of planetary-mass companions and brown dwarfs do not support a universal mass-rotation relation. The high precision of our observations and the high occurrence rates of variable low-surface gravity objects encourage high-contrast time-resolved observations with the James Webb Space Telescope., Comment: Accepted for publication in AAS Journal

The exquisite photometry of Kepler has revealed reflected light from exoplanets, tidal distortion of host stars and Doppler beaming of a star's light due to its motion (Borucki 2016; Demory et al. 2012; Welsh et al. 2010; Bloemen et al. 2012). Esteves et al. (2013, 2015) and Shporer et al. (2014) reported additional odd harmonics in the light curves of two hot Jupiters: HAT-P-7b and Kepler-13Ab. They measured non-zero power at three times the orbital frequency that persisted while the planet was eclipsed and hence must originate in the star (Esteves et al. 2015). Penoyre & Sandford (2018) showed that orbital eccentricity could result in time-dependent tidal deformation of the star that manifests itself at three times the orbital frequency and suggested this could be the origin of the measured odd modes. In this Research Note, we show that the small orbital eccentricities of HAT-P-7b and Kepler-13Ab cannot generate the odd harmonics observed in these systems. Esteves et al. (2015) hypothesized that the odd modes could be due to tidal distortion of the star if its spin is misaligned with the system's orbital motion, as is the case in both of these systems (Benomar et al. 2014; Herman et al. 2018), but this mechanism has yet to be verified theoretically or numerically., Comment: 2 pages, 1 figure, RNAAS in press

Refraction can lead to a brightening just before ingress and just after egress of a transit, as light passes through the exoplanet's atmosphere and is refracted into our line of sight. Refraction just outside of transit has been seen and modeled in our own solar system during transits of Venus. For short-period planets, the model of Sidis and Sari (2010 ApJ,720,904) implies refraction peaks typically under 100 parts per million and comparable in duration to ingress and egress. Kepler photometry currently provides the best opportunity for detecting refraction. We search for the signature of refraction just outside of transit in Kepler photometry of 45 gas giants and firmly rule out the Sidis and Sari model for four candidates., Comment: 2 pages, 1 figure, accepted for publication in RNAAS

Short-period gas giants (hot Jupiters) on circular orbits are expected to be tidally locked into synchronous rotation, with permanent daysides that face their host stars, and permanent nightsides that face the darkness of space. Thermal flux from the nightside of several hot Jupiters has been measured, meaning energy is transported from day to night in some fashion. However, it is not clear exactly what the physical information from these detections reveals about the atmospheric dynamics of hot Jupiters. Here we show that the nightside effective temperatures of a sample of 12 hot Jupiters are clustered around 1100 K, with a slight upward trend as a function of stellar irradiation. The clustering is not predicted by cloud-free atmospheric circulation models. This result can be explained if most hot Jupiters have nightside clouds that are optically thick to outgoing longwave radiation and hence radiate at the cloud-top temperature, and progressively disperse for planets receiving greater incident flux. Phase curve observations at a greater range of wavelengths are crucial to determining the extent of cloud coverage, as well as the cloud composition on hot Jupiter nightsides., Comment: 18 pages, 3 figures. Submitted August 13th, 2018, accepted for publication July 5th 2019. Added a second, parallel analysis. Interpretation of results unchanged from previous version. Updated main text to reflect the published version, and removed a sentence in the Methods that misquoted Beatty+ 2019

A key legacy of the recently launched TESS mission will be to provide the astronomical community with many of the best transiting exoplanet targets for atmospheric characterization. However, time is of the essence to take full advantage of this opportunity. JWST, although delayed, will still complete its nominal five year mission on a timeline that motivates rapid identification, confirmation, and mass measurement of the top atmospheric characterization targets from TESS. Beyond JWST, future dedicated missions for atmospheric studies such as ARIEL require the discovery and confirmation of several hundred additional sub-Jovian size planets (R_p < 10 R_Earth) orbiting bright stars, beyond those known today, to ensure a successful statistical census of exoplanet atmospheres. Ground-based ELTs will also contribute to surveying the atmospheres of the transiting planets discovered by TESS. Here we present a set of two straightforward analytic metrics, quantifying the expected signal-to-noise in transmission and thermal emission spectroscopy for a given planet, that will allow the top atmospheric characterization targets to be readily identified among the TESS planet candidates. Targets that meet our proposed threshold values for these metrics would be encouraged for rapid follow-up and confirmation via radial velocity mass measurements. Based on the catalog of simulated TESS detections by Sullivan et al. (2015), we determine appropriate cutoff values of the metrics, such that the TESS mission will ultimately yield a sample of $\sim300$ high-quality atmospheric characterization targets across a range of planet size bins, extending down to Earth-size, potentially habitable worlds., Comment: accepted to PASP

Direct imaging is likely the best way to characterize the atmospheres of Earth-sized exoplanets in the habitable zone of Sun-like stars. Previously, Stark et al. (2014, 2015, 2016) estimated the Earth twin yield of future direct imaging missions, such as LUVOIR and HabEx. We extend this analysis to other types of planets, which will act as false positives for Earth twins. We define an Earth twin as any exoplanet within half an e-folding of 1 AU in semi-major axis and 1 $R_{\oplus}$ in planetary radius, orbiting a G-dwarf. Using Monte Carlo analyses, we quantify the biases and planetary false positive rates of Earth searches. That is, given a pale dot at the correct projected separation and brightness to be a candidate Earth, what are the odds that it is, in fact, an Earth twin? Our notional telescope has a diameter of 10 m, an inner working angle of 3{\lambda}/D, and an outer working angle of 10{\lambda}/D (62 mas and 206 mas at 1.0 {\mu}m). With no precursor knowledge and one visit per star, 77% of detected candidate Earths are actually un-Earths; their mean radius is 2.3 $R_{\oplus}$, a sub-Neptune. The odds improve if we image every planet at its optimal orbital phase, either by relying on precursor knowledge, or by performing multi-epoch direct imaging. In such a targeted search, 47% of detected Earth twin candidates are false positives, and they have a mean radius of 1.7 $R_{\oplus}$. The false positive rate is insensitive to stellar spectral type and the assumption of circular orbits., Comment: 15 pages, 7 figures, accepted for publication in AJ

FINESSE, a NASA MIDEX mission in Step 2, would conduct a large, uniform survey of exoplanet atmospheres and create a statistically significant sample for comparative planetology. FINESSE's technical capabilities, driven by a scientific program to study planetary formation and climate mechanisms, enable additional exoplanet science presented here., Comment: White paper submitted to The National Academies of Science, Engineering, and Medicine Exoplanet Science Strategy. 6 pages including title page, 4 figures, 1 table

A new class of exoplanets is beginning to emerge: planets whose dayside atmospheres more closely resemble stellar atmospheres as most of their molecular constituents dissociate. The effects of the dissociation of these species will be varied and must be carefully accounted for. Here we take the first steps towards understanding the consequences of dissociation and recombination of molecular hydrogen (H$_2$) on atmospheric heat recirculation. Using a simple energy balance model with eastward winds, we demonstrate that H$_2$ dissociation/recombination can significantly increase the day$-$night heat transport on ultra-hot Jupiters (UHJs): gas giant exoplanets where significant H$_2$ dissociation occurs. The atomic hydrogen from the highly irradiated daysides of UHJs will transport some of the energy deposited on the dayside towards the nightside of the planet where the H atoms recombine into H$_2$; this mechanism bears similarities to latent heat. Given a fixed wind speed, this will act to increase the heat recirculation efficiency; alternatively, a measured heat recirculation efficiency will require slower wind speeds after accounting for H$_2$ dissociation/recombination., Comment: 8 pages, 5 figures, accepted for publication in ApJL

Future space telescopes will directly image extrasolar planets at visible wavelengths. Time-resolved reflected light from an exoplanet encodes information about atmospheric and surface inhomogeneities. Previous research has shown that the light curve of an exoplanet can be inverted to obtain a low-resolution map of the planet, as well as constraints on its spin orientation. Estimating the uncertainty on 2D albedo maps has so far remained elusive. Here we present exocartographer, a flexible open-source Bayesian framework for solving the exo-cartography inverse problem. The map is parameterized with equal-area HEALPix pixels. For a fiducial map resolution of 192 pixels, a four-parameter Gaussian process describing the spatial scale of albedo variations, and two unknown planetary spin parameters, exocartographer explores a 198-dimensional parameter space. To test the code, we produce a light curve for a cloudless Earth in a face-on orbit with a 90$^\circ$ obliquity. We produce synthetic white light observations of the planet: 5 epochs of observations throughout the planet's orbit, each consisting of 24 hourly observations with a photometric uncertainty of $1\%$ (120 data). We retrieve an albedo map and$-$for the first time$-$its uncertainties, along with spin constraints. The albedo map is recognizably of Earth, with typical uncertainty of $30\%$. The retrieved characteristic length scale is 88$\pm 7 ^\circ$, or 9800 km. The obliquity is recovered with a $1-\sigma$ uncertainty of $0.8^\circ$. Despite the uncertainty in the retrieved albedo map, we robustly identify a high albedo region (the Sahara desert) and a large low-albedo region (the Pacific Ocean)., Comment: 6 pages, 3 figures

The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this paper, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points ($\delta$-maps), and spherical harmonics ($Y_l^m$-maps). In particular, we use Wigner $D$-matrices to express an harmonic lightcurve for an arbitrary viewing geometry as a non-linear combination of harmonic lightcurves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected lightcurves, as well as fast calculation of lightcurves for mapping exoplanets based on time-resolved photometry. To these ends we make available Exoplanet Analytic Reflected Lightcurves (EARL), a simple open-source code that allows rapid computation of reflected lightcurves., Comment: 8 pages, plus 6 pages of mathematical appendices, 4 figures, to be submitted

Time-resolved observations of brown dwarfs' rotational modulations provide powerful insights into the properties of condensate clouds in ultra-cool atmospheres. Multi-wavelength light curves reveal cloud vertical structures, condensate particle sizes, and cloud morphology, which directly constrain condensate cloud and atmospheric circulation models. We report results from Hubble Space Telescope/Wide Field Camera 3 near-infrared G141 taken in six consecutive orbits observations of HN Peg B, an L/T transition brown dwarf companion to a G0V type star. The best-fit sine wave to the $1.1-1.7\mu$m broadband light curve has the amplitude of $1.206\pm0.025\%$ and period of $15.4\pm0.5$ hr. The modulation amplitude has no detectable wavelength dependence except in the 1.4 $\mu$m water absorption band, indicating that the characteristic condensate particle sizes are large ($>1\mu$m). We detect significantly ($4.4\sigma$) lower modulation amplitude in the 1.4$\mu$m water absorption band, and find that HN Peg B's spectral modulation resembles those of early T type brown dwarfs. We also describe a new empirical interpolation method to remove spectral contamination from the bright host star. This method may be applied in other high-contrast time-resolved observations with WFC3., Comment: Accepted for publication in AAS Journal

Short-period planets exhibit day-night temperature contrasts of hundreds to thousands of degrees K. They also exhibit eastward hotspot offsets whereby the hottest region on the planet is east of the substellar point; this has been widely interpreted as advection of heat due to eastward winds. We present thermal phase observations of the hot Jupiter CoRoT-2b obtained with the IRAC instrument on the Spitzer Space Telescope. These measurements show the most robust detection to date of a westward hotspot offset of 23 $\pm$ 4 degrees, in contrast with the nine other planets with equivalent measurements. The peculiar infrared flux map of CoRoT-2b may result from westward winds due to non-synchronous rotation magnetic effects, or partial cloud coverage, that obscures the emergent flux from the planet's eastern hemisphere. Non-synchronous rotation and magnetic effects may also explain the planet's anomalously large radius. On the other hand, partial cloud coverage could explain the featureless dayside emission spectrum of the planet. If CoRoT-2b is not tidally locked, then it means that our understanding of star-planet tidal interaction is incomplete. If the westward offset is due to magnetic effects, our result represents an opportunity to study an exoplanet's magnetic field. If it has Eastern clouds, then it means that our understanding of large-scale circulation on tidally locked planets is incomplete., Comment: 30 pages, 4 figures, 15 supplementary figures

Multi-band phase variations in principle allow us to infer the longitudinal temperature distributions of planets as a function of height in their atmospheres. For example, 3.6 micron emission originates from deeper layers of the atmosphere than 4.5 micron due to greater water vapor absorption at the longer wavelength. Since heat transport efficiency increases with pressure, we expect thermal phase curves at 3.6 micron to exhibit smaller amplitudes and greater phase offsets than at 4.5 micron; this trend is not observed. Of the seven hot Jupiters with full-orbit phase curves at 3.6 and 4.5 micron, all have greater phase amplitude at 3.6 micron than at 4.5 micron, while four of seven exhibit a greater phase offset at 3.6 micron. We use a 3D radiative-hydrodynamic model to calculate theoretical phase curves of HD 189733b, assuming thermo-chemical equilibrium. The model exhibits temperature, pressure, and wavelength dependent opacity, primarily driven by carbon chemistry: CO is energetically favored on the dayside, while CH4 is favored on the cooler nightside. Infrared opacity therefore changes by orders of magnitude between day and night, producing dramatic vertical shifts in the wavelength-specific photospheres, which would complicate eclipse or phase mapping with spectral data. The model predicts greater relative phase amplitude and greater phase offset at 3.6 micron than at 4.5 micron, in agreement with the data. Our model qualitatively explains the observed phase curves, but is in tension with current thermo-chemical kinetics models that predict zonally uniform atmospheric composition due to transport of CO from the hot regions of the atmosphere., Comment: 9 pages, 5 figures, accepted for publications in ApJ Letters

We present new 3.6 and 4.5 $\mu m$ 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 $\mu m$ and 4.5 $\mu m$. 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.

Although the final observations of the Spitzer Warm Mission are currently scheduled for March 2019, it can continue operations through the end of the decade with no loss of photometric precision. As we will show, there is a strong science case for extending the current Warm Mission to December 2020. Spitzer has already made major impacts in the fields of exoplanets (including microlensing events), characterizing near Earth objects, enhancing our knowledge of nearby stars and brown dwarfs, understanding the properties and structure of our Milky Way galaxy, and deep wide-field extragalactic surveys to study galaxy birth and evolution. By extending Spitzer through 2020, it can continue to make ground-breaking discoveries in those fields, and provide crucial support to the NASA flagship missions JWST and WFIRST, as well as the upcoming TESS mission, and it will complement ground-based observations by LSST and the new large telescopes of the next decade. This scientific program addresses NASA's Science Mission Directive's objectives in astrophysics, which include discovering how the universe works, exploring how it began and evolved, and searching for life on planets around other stars., Comment: 75 pages. See page 3 for Table of Contents and page 4 for Executive Summary

We present an optical eclipse observation of the hot Jupiter WASP-12b using the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope. These spectra allow us to place an upper limit of $A_g < 0.064$ (97.5% confidence level) on the planet's white light geometric albedo across 290--570 nm. Using six wavelength bins across the same wavelength range also produces stringent limits on the geometric albedo for all bins. However, our uncertainties in eclipse depth are $\sim$40% greater than the Poisson limit and may be limited by the intrinsic variability of the Sun-like host star --- the solar luminosity is known to vary at the $10^{-4}$ level on a timescale of minutes. We use our eclipse depth limits to test two previously suggested atmospheric models for this planet: Mie scattering from an aluminum-oxide haze or cloud-free Rayleigh scattering. Our stringent nondetection rules out both models and is consistent with thermal emission plus weak Rayleigh scattering from atomic hydrogen and helium. Our results are in stark contrast with those for the much cooler HD 189733b, the only other hot Jupiter with spectrally resolved reflected light observations; those data showed an increase in albedo with decreasing wavelength. The fact that the first two exoplanets with optical albedo spectra exhibit significant differences demonstrates the importance of spectrally resolved reflected light observations and highlights the great diversity among hot Jupiters., Comment: 8 pages, 4 figures, 1 table, published in ApJL, in press

The large day--night temperature contrast of WASP-43b has so far eluded explanation. We revisit the energy budget of this planet by considering the impact of reflected light on dayside measurements, and the physicality of implied nightside temperatures. Previous analyses of the infrared eclipses of WASP-43b have assumed reflected light from the planet is negligible and can be ignored. We develop a phenomenological eclipse model including reflected light, thermal emission, and water absorption, and use it to fit published Hubble and Spitzer eclipse data. We infer a near-infrared geometric albedo of 27$\pm1\%$ and a cooler dayside temperature of $1527 \pm 10~$K. Additionally, we perform lightcurve inversion on the three published orbital phase curves of WASP-43b and find that each requires unphysical, negative flux on the nightside. By requiring non-negative brightnesses at all longitudes, we correct the unphysical parts of the maps and obtain a much hotter nightside effective temperature of $1076 \pm 11~$K. The cooler dayside and hotter nightside suggests a heat recirculation efficiency of $47\%$ for WASP-43b, essentially the same as for HD 209458b, another hot Jupiter with nearly the same temperature. Our analysis therefore reaffirms the trend that planets with lower irradiation temperatures have more efficient day-night heat transport. Moreover, we note that 1) reflected light may be significant for many near-IR eclipse measurements of hot Jupiters, and 2) phase curves should be fit with physically possible longitudinal brightness profiles --- it is insufficient to only require that the disk-integrated lightcurve be non-negative., Comment: Accepted for publication in ApJL. 7 pages, 4 figures

Unmixing the disk-integrated spectra of exoplanets provides hints about heterogeneous surfaces that we cannot directly resolve in the foreseeable future. It is particularly important for terrestrial planets with diverse surface compositions like Earth. Although previous work on unmixing the spectra of Earth from disk-integrated multi-band light curves appeared successful, we point out a mathematical degeneracy between the surface colors and their spatial distributions. Nevertheless, useful constraints on the spectral shape of individual surface types may be obtained from the premise that albedo is everywhere between 0 and 1. We demonstrate the degeneracy and the possible constraints using both mock data based on a toy model of Earth, as well as real observations of Earth. Despite the severe degeneracy, we are still able to recover an approximate albedo spectrum for an ocean. In general, we find that surfaces are easier to identify when they cover a large fraction of the planet and when their spectra approach zero or unity in certain bands., Comment: 11 pages, 7 figures, published in AJ. Minor text updates from previous version

Thermal phase curves of short-period planets on circular orbits provide joint constraints on the fraction of incoming energy that is reflected (Bond albedo) and the fraction of absorbed energy radiated by the night hemisphere (heat recirculation efficiency). Many empirical studies of hot Jupiters have implicitly assumed that the dayside is the hottest hemisphere and the nightside is the coldest hemisphere. For a given eclipse depth and phase amplitude, an orbital lag between a planet's peak brightness and its eclipse---a phase offset---implies that planet's nightside emits greater flux. To quantify how phase offsets impact the energy budgets of short-period planets, we compile all infrared observations of the nine planets with multi-band eclipse depths and phase curves. Accounting for phase offsets shifts planets to lower Bond albedo and greater day--night heat transport, usually by $\lesssim 1\sigma$. For WASP-12b, the published phase variations have been analyzed in two different ways, and the inferred energy budget depends sensitively on which analysis one adopts.\ Our fiducial scenario supports a Bond albedo of $0.27^{+0.12}_{-0.13}$, significantly higher than the published optical geometric albedo, and a recirculation efficiency of $0.03^{+0.07}_{-0.02}$, following the trend of larger day--night temperature contrast with greater stellar irradiation. If instead we adopt the alternative analysis, then WASP-12b has a Bond albedo consistent with zero and a much higher recirculation efficiency. To definitively determine the energy budget of WASP-12b, new observational analyses will be necessary., Comment: 11 pages, 6 figures, 2 tables; Accepted in ApJ. Minor corrections to text/references. (Improved treatment of stellar brightness temperatures and systematic uncertainties; better discussion of WASP-12b; updated Figures 2, 3, and 5, and fit parameters in Tables 1 and 2)

Using forward models for representative exoplanet atmospheres and a radiometric instrument model, we have generated synthetic observational data to explore how well the major C- and O-bearing chemical species (CO, CO2, CH4, and H2O), important for determining atmospheric opacity and radiation balance, can be constrained by transit measurements as a function of spectral wavelength coverage. This work features simulations for a notional transit spectroscopy mission and compares two cases for instrument spectral coverage (wavelength coverage from 0.5-2.5 ${\mu}$m and 0.5-5 ${\mu}$m. The simulation is conducted on a grid with a range of stellar magnitudes and incorporates a full retrieval of atmospheric model parameters. We consider a range of planets from sub-Neptunes to hot Jupiters and include both low and high mean molecular weight atmospheres. We find that including the 2.5-5 ${\mu}$m wavelength range provides a significant improvement in the degree of constraint on the retrieved molecular abundances: up to ~3 orders of magnitude for a low mean molecular weight atmosphere (${\mu}$=2.3) and up to a factor of ~6 for a high mean molecular weight atmosphere (${\mu}$=28). These decreased uncertainties imply that broad spectral coverage between the visible and the mid-infrared is an important tool for understanding the chemistry and composition of exoplanet atmospheres. This analysis suggests that the JWST/NIRSpec 0.6-5 ${\mu}$m prism spectroscopy mode, or similar wavelength coverage with possible future missions, will be an important resource for exoplanet atmospheric characterization., Comment: Accepted by PASP; 18 pages, 7 figures

The varied surfaces and atmospheres of planets make them interesting places to live, explore, and study from afar. Unfortunately, the great distance to exoplanets makes it impossible to resolve their disk with current or near-term technology. It is still possible, however, to deduce spatial inhomogeneities in exoplanets provided that different regions are visible at different times -- this can be due to rotation, orbital motion, and occultations by a star, planet, or moon. Astronomers have so far constructed maps of thermal emission and albedo for short period giant exoplanets. These maps constrain atmospheric dynamics and cloud patterns in exotic atmospheres. In the future, exo-cartography could yield surface maps of terrestrial planets, hinting at the geophysical and geochemical processes that shape them., Comment: To be published in: Handbook of Exoplanets, 2nd Edition, Hans Deeg and Juan Antonio Belmonte (Eds. in Chief), Springer International Publishing AG, part of Springer Nature. 19 pages, including 6 figures and 5 pages of references

Photometry of short-period planetary systems allows astronomers to monitor exoplanets, their host stars, and their mutual interactions. In addition to the transits of a planet in front of its star and the eclipses of the planet by its star, researchers have reported flux variations at the orbital frequency and its harmonics: planetary reflection and/or emission and Doppler beaming of starlight produce one peak per orbit, while ellipsoidal variations of a tidally distorted star and/or planet produce two maxima per orbit. Researchers have also reported significant photometric variability at three times the orbital frequency, sometimes much greater than the predictions of tidal theory. The reflected phase variations of a homogeneous planet contains power at even orbital harmonics-important for studies of ellipsoidal variations-but cannot contain odd orbital harmonics. We show that odd harmonics can, however, be produced by an edge-on planet with a time-variable map, or an inclined planet with a North-South (N-S) asymmetric map. Either of these scenarios entail weather: short-period planets are expected to have zero obliquity and hence N-S symmetric stellar forcing. North-South asymmetry in a giant planet would therefore suggest stochastic localized features, such as weather. However, we find that previous claims of large-amplitude odd modes in Kepler photometry are artifacts of removing planetary transits rather than modeling them. The only reliable claims of odd harmonics remain HAT-P-7b and Kepler-13Ab, for which the third mode amplitude is 6-8% of the planetary flux. Although time-variable albedo maps could in principle explain these odd harmonics, upper-limits on the infrared variability of hot Jupiters make this hypothesis unlikely. We urge theorists to study the effects of close-in planets on stellar atmospheres, as this remains the only plausible hypothesis., Comment: 12 pages, 10 figures, under review at MNRAS

Condensate clouds fundamentally impact the atmospheric structure and spectra of exoplanets and brown dwarfs but the connections between surface gravity, cloud structure, dust in the upper atmosphere, and the red colors of some brown dwarfs remain poorly understood. Rotational modulations enable the study of different clouds in the same atmosphere, thereby providing a method to isolate the effects of clouds. Here we present the discovery of high peak-to-peak amplitude (8%) rotational modulations in a low-gravity, extremely red (J-Ks=2.55) L6 dwarf WISEP J004701.06+680352.1 (W0047). Using the Hubble Space Telescope (HST) time-resolved grism spectroscopy we find a best-fit rotational period (13.20$\pm$0.14 hours) with a larger amplitude at 1.1 micron than at 1.7 micron. This is the third largest near-infrared variability amplitude measured in a brown dwarf, demonstrating that large-amplitude variations are not limited to the L/T transition but are present in some extremely red L-type dwarfs. We report a tentative trend between the wavelength dependence of relative amplitude, possibly proxy for small dust grains lofted in the upper atmosphere, and the likelihood of large-amplitude variability. By assuming forsterite as haze particle, we successfully explain the wavelength dependent amplitude with submicron-sized haze particles sizes of around 0.4 {\mu}m. W0047 links the earlier spectral and later spectral type brown dwarfs in which rotational modulations have been observed, the large amplitude variations in this object make this a benchmark brown dwarf for the study of cloud properties close to the L/T transition., Comment: 9 pages, 4 figures, Accepted for publication in ApJL on September 15th

Much of transiting exoplanet science relies on high-precision photometry. The current generation of instruments can exhibit sensitivity variations greater than the astrophysical signals. For the InfraRed Array Camera (IRAC) on the Spitzer Space Telescope, a popular way to handle this is BiLinearly-Interpolated Subpixel Sensitivity (BLISS) mapping. As part of a Markov Chain Monte Carlo (MCMC), BLISS mapping estimates the sensitivity at many locations (knots) on the pixel, then interpolates to the target star's centroids. We show that such embedded optimization schemes can misfit or bias parameters. Thus, we construct a model of $\textit{Spitzer}$ eclipse light curves to test the accuracy and precision of BLISS mapping. We compare standard BLISS mapping to a variant where the knots are fit during the MCMC, as well as to a polynomial model. Both types of BLISS mapping give similar eclipse depths, and we find that standard knots behave like real parameters. Standard BLISS mapping is therefore a reasonable shortcut to fitting for knots in an MCMC. BLISS maps become inaccurate when the photon noise is low, but typically approximate the real sensitivity well. We also find there is no perfect method for choosing the ideal number of BLISS knots to use on given data. BLISS mapping gives fits that are usually more accurate than precise (i.e. they are overly conservative), and the routine is more precise than polynomial models for significant eclipses or pixels with more varied sensitivities. BLISS mapping has better predictive power for most of these particular synthetic data, depending on how one treats time-correlated residuals. Overall, we conclude that BLISS mapping can be a reasonable sensitivity model for IRAC photometry., Comment: 32 pages, 13 figures; Accepted by PASP 9/26/16. Major updates: higher amplitude for main detector signals, estimating good number of BLISS knots for given data, more/better synthetic light curves, trying projected sensitivity along pixel axes, uncertainties in Figures 10-13. Most edits in Abstract, Sections 4-6. New findings but main conclusion same (i.e. BLISS Mapping can be acceptable)

The James Webb Space Telescope will revolutionize transiting exoplanet atmospheric science due to its capability for continuous, long-duration observations and its larger collecting area, spectral coverage, and spectral resolution compared to existing space-based facilities. However, it is unclear precisely how well JWST will perform and which of its myriad instruments and observing modes will be best suited for transiting exoplanet studies. In this article, we describe a prefatory JWST Early Release Science (ERS) program that focuses on testing specific observing modes to quickly give the community the data and experience it needs to plan more efficient and successful future transiting exoplanet characterization programs. We propose a multi-pronged approach wherein one aspect of the program focuses on observing transits of a single target with all of the recommended observing modes to identify and understand potential systematics, compare transmission spectra at overlapping and neighboring wavelength regions, confirm throughputs, and determine overall performances. In our search for transiting exoplanets that are well suited to achieving these goals, we identify 12 objects (dubbed "community targets") that meet our defined criteria. Currently, the most favorable target is WASP-62b because of its large predicted signal size, relatively bright host star, and location in JWST's continuous viewing zone. Since most of the community targets do not have well-characterized atmospheres, we recommend initiating preparatory observing programs to determine the presence of obscuring clouds/hazes within their atmospheres. Measurable spectroscopic features are needed to establish the optimal resolution and wavelength regions for exoplanet characterization. Other initiatives from our proposed ERS program include testing the instrument brightness limits and performing phase-curve observations.(Abridged), Comment: This is a white paper that originated from an open discussion at the Enabling Transiting Exoplanet Science with JWST workshop held November 16 - 18, 2015 at STScI (http://www.stsci.edu/jwst/science/exoplanets). Accepted for publication in PASP

Cosmology experiments at mm-wavelengths can detect Planet Nine if it is the size of Neptune, has an effective temperature of 40 K, and is 700 AU from the Sun. It would appear as a ~30 mJy source at 1 mm with an annual parallax of ~5 arcmin. The challenge is to distinguish it from the approximately 4000 foreground asteroids brighter than 30 mJy. Fortunately, these asteroids are known to the Minor Planet Center and can be identified because they move across a resolution element in a matter of hours, orders of magnitude faster than Planet Nine. If Planet Nine is smaller, colder, and/or more distant than expected, then it could be as faint as 1 mJy at 1 mm. There are roughly $10^6$ asteroids this bright and many are unknown, making current cosmology experiments confusion limited for moving sources. Nonetheless, it may still be possible to find the proverbial needle in the haystack using a matched filter. This would require mm telescopes with high angular resolution and high sensitivity in order to alleviate confusion and to enable the identification of moving sources with relatively short time baselines. Regardless of its mm flux density, searching for Planet Nine would require frequent radio measurements for large swaths of the sky, including the ecliptic and Galactic plane. Even if Planet Nine had already been detected by other means, measuring its mm-flux would constrain its internal energy budget, and therefore help resolve the mystery of Uranus and Neptune, which have vastly different internal heat., Comment: 5 pages, 1 figure, ApJL accepted

This is a joint summary of the reports from the three Astrophysics Program Analysis Groups (PAGs) in response to the "Planning for the 2020 Decadal Survey" charge given by the Astrophysics Division Director Paul Hertz. This joint executive summary contains points of consensus across all three PAGs. Additional findings specific to the individual PAGs are reported separately in the individual reports. The PAGs concur that all four large mission concepts identified in the white paper as candidates for maturation prior to the 2020 Decadal Survey should be studied in detail. These include the Far-IR Surveyor, the Habitable-Exoplanet Imaging Mission, the UV/Optical/IR Surveyor, and the X-ray Surveyor. This finding is predicated upon assumptions outlined in the white paper and subsequent charge, namely that 1) major development of future large flagship missions under consideration are to follow the implementation phases of JWST and WFIRST; 2) NASA will partner with the European Space Agency on its L3 Gravitational Wave Surveyor; 3) the Inflation Probe be classified as a probe-class mission to be developed according to the 2010 Decadal Survey report. If these key assumptions were to change, this PAG finding would need to be re-evaluated. The PAGs find that there is strong community support for the second phase of this activity - maturation of the four proposed mission concepts via Science and Technology Definition Teams (STDTs). The PAGs find that there is strong consensus that all of the STDTs contain broad and interdisciplinary representation of the science community. Finally, the PAGs find that there is community support for a line of Probe-class missions within the Astrophysics mission portfolio (condensed)., Comment: 22 pages, 2 tables, no figures

The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over most of a planet's orbit can be inverted to infer obliquity. However, few studies of more general planets with arbitrary albedo markings have been made and, in particular, a simple theoretical understanding of why it is possible to extract obliquity from light curves is missing. Reflected light seen by a distant observer is the product of a planet's albedo map, its host star's illumination, and the visibility of different regions. It is useful to treat the product of illumination and visibility as the kernel of a convolution. Time-resolved photometry constrains both the albedo map and the kernel, the latter of which sweeps over the planet due to rotational and orbital motion. The kernel's movement distinguishes prograde from retrograde rotation for planets with non-zero obliquity on inclined orbits. We demonstrate that the kernel's longitudinal width and mean latitude are distinct functions of obliquity and axial orientation. Notably, we find that a planet's spin axis affects the kernel -- and hence time-resolved photometry -- even if this planet is East-West uniform or spinning rapidly, or if it is North-South uniform. We find that perfect knowledge of the kernel at 2-4 orbital phases is usually sufficient to uniquely determine a planet's spin axis. Surprisingly, we predict that East-West albedo contrast is more useful for constraining obliquity than North-South contrast., Comment: 13 pages, 10 figures; Published in MNRAS 03/21/16. Fixed minor typos in the appendix. Related code "ReflectDirect" available on GitHub at https://github.com/joelcolinschwartz/ReflectDirect under the MIT License

Earth has a unique surface character among Solar System worlds. Not only does it harbor liquid water, but also large continents. An exoplanet with a similar appearance would remind us of home, but it is not obvious whether such a planet is more likely to bear life than an entirely ocean-covered waterworld---after all, surface liquid water defines the canonical habitable zone. In this proceeding, I argue that 1) Earth's bimodal surface character is critical to its long-term climate stability and hence is a signpost of habitability, and 2) we will be able to constrain the surface character of terrestrial exoplanets with next-generation space missions., Comment: 4 pages, 1 figure; to appear in the proceedings of the Comparative Climates of Terrestrial Planets II conference

In this work we present Spitzer 3.6 and 4.5 micron secondary eclipse observations of five new cool (<1200 K) transiting gas giant planets: HAT-P-19b, WASP-6b, WASP-10b, WASP-39b, and WASP-67b. We compare our measured eclipse depths to the predictions of a suite of atmosphere models and to eclipse depths for planets with previously published observations in order to constrain the temperature- and mass-dependent properties of gas giant planet atmospheres. We find that the dayside emission spectra of planets less massive than Jupiter require models with efficient circulation of energy to the night side and/or increased albedos, while those with masses greater than that of Jupiter are consistently best-matched by models with inefficient circulation and low albedos. At these relatively low temperatures we expect the atmospheric methane to CO ratio to vary as a function of metallicity, and we therefore use our observations of these planets to constrain their atmospheric metallicities. We find that the most massive planets have dayside emission spectra that are best-matched by solar metallicity atmosphere models, but we are not able to place strong constraints on metallicities of the smaller planets in our sample. Interestingly, we find that the ratio of the 3.6 and 4.5 micron brightness temperatures for these cool transiting planets is independent of planet temperature, and instead exhibits a tentative correlation with planet mass. If this trend can be confirmed, it would suggest that the shape of these planets' emission spectra depends primarily on their masses, consistent with the hypothesis that lower-mass planets are more likely to have metal-rich atmospheres., Comment: 16 pages, 14 figures, accepted for publication in ApJ

Kaib & Cowan (2015) recently used terrestrial planet formation simulations to conclude that the moon-forming impactor (Theia) had only a ~5% or less chance of having the same oxygen isotope composition as Earth, while Mastrobuono-Battisti et al. (2015) used seemingly similar simulations and methods to arrive at a higher value of ~20% or more. Here we derive the results of both papers from a single set of simulations. Compared to Kaib & Cowan (2015), the analysis of Mastrobuono-Battisti et al. (2015) systematically yields more massive Theia analogs and imposes flatter isotopic gradients across the original protoplanetary disk. Both of these effects diminish isotopic differences between Earth and Theia analogs. While it is notoriously difficult to produce systems resembling our actual terrestrial planets, the analysis of Kaib & Cowan (2015) more often selects and analyzes Earth and Mars analogs at orbital locations near the real planets. Given this, we conclude that the greater isotopic differences between Earth and Theia found in Kaib & Cowan (2015) better reflect the predictions of terrestrial planet formation models. Finally, although simulation uncertainties and a terrestrial contribution to Moon formation enhance the fraction of Theia analogs consistent with the canonical giant impact hypothesis, this fraction still remains in the 5-8% range., Comment: 5 pages, 4 figures, accepted to Icarus

We present full-orbit phase curve observations of the eccentric ($e\sim 0.08$) transiting hot Jupiter WASP-14b obtained in the 3.6 and 4.5 $\mu$m bands using the \textit{Spitzer Space Telescope}. We use two different methods for removing the intrapixel sensitivity effect and compare their efficacy in decoupling the instrumental noise. Our measured secondary eclipse depths of $0.1882\%\pm 0.0048\%$ and $0.2247\%\pm 0.0086\%$ at 3.6 and 4.5 $\mu$m, respectively, are both consistent with a blackbody temperature of $2402\pm 35$ K. We place a $2\sigma$ upper limit on the nightside flux at 3.6 $\mu$m and find it to be $9\%\pm 1\%$ of the dayside flux, corresponding to a brightness temperature of 1079 K. At 4.5 $\mu$m, the minimum planet flux is $30\%\pm 5\%$ of the maximum flux, corresponding to a brightness temperature of $1380\pm 65$ K. We compare our measured phase curves to the predictions of one-dimensional radiative transfer and three-dimensional general circulation models. We find that WASP-14b's measured dayside emission is consistent with a model atmosphere with equilibrium chemistry and a moderate temperature inversion. These same models tend to over-predict the nightside emission at 3.6 $\mu$m, while under-predicting the nightside emission at 4.5 $\mu$m. We propose that this discrepancy might be explained by an enhanced global C/O ratio. In addition, we find that the phase curves of WASP-14b ($7.8 M_{\mathrm{Jup}}$) are consistent with a much lower albedo than those of other Jovian mass planets with thermal phase curve measurements, suggesting that it may be emitting detectable heat from the deep atmosphere or interior processes., Comment: 17 pages, 18 figures; accepted for publication in ApJ

We consider fifty transiting short-period giant planets for which eclipse depths have been measured at multiple infrared wavelengths. The aggregate dayside emission spectrum of these planets exhibits no molecular features, nor is brightness temperature greater in the near-infrared. We combine brightness temperatures at various infrared wavelengths to estimate the dayside effective temperature of each planet. We find that dayside temperatures are proportional to irradiation temperatures, indicating modest Bond albedo and no internal energy sources, plus weak evidence that dayside temperatures of the hottest planets are disproportionately high. We place joint constraints on Bond albedo, $A_{B}$, and day-to-night transport efficiency, $\varepsilon$, for six planets by combining thermal eclipse and phase variation measurements (HD 149026b, HD 189733b, HD 209458b, WASP-12b, WASP-18b, and WASP-43b). We confirm that planets with high irradiation temperatures have low heat transport efficiency, and that WASP-43b has inexplicably poor transport; these results are statistically significant even if the precision of single-eclipse measurements has been overstated by a factor of three. Lastly, we attempt to break the $A_{B}$-$\varepsilon$ degeneracy for nine planets with both thermal and optical eclipse observations, but no thermal phase measurements. We find a systematic offset between Bond albedos inferred from thermal phase variations ($A_{B} \approx 0.35$) and geometric albedos extracted from visible light measurements ($A_{g} \approx 0.1$). These observations can be reconciled if most hot Jupiters have clouds that reflect 30-50 per cent of incident near-infrared radiation, as well as optical absorbers in the cloud particles or above the cloud deck., Comment: 12 pages, 7 figures, 4 tables; submitted to MNRAS, post-peer review

[Abridged] We present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of the stochastic late stages of planet formation. We quantify the feeding zone width, Delta a, as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet. The size of a planet's feeding zone in our simulations does not correlate with its final mass or semi-major axis, suggesting there is no systematic trend between a planet's mass and its volatile inventory. Instead, we find that the feeding zone of any planet more massive than 0.1M_Earth is roughly proportional to the radial extent of the initial disk from which it formed: Delta a~0.25(a_max-a_min), where a_min and a_max are the inner and outer edge of the initial planetesimal disk. These wide stochastic feeding zones have significant consequences for the origin of the Moon, since the canonical scenario predicts the Moon should be primarily composed of material from Earth's last major impactor (Theia), yet its isotopic composition is indistinguishable from Earth. In particular, we find that the feeding zones of Theia analogs are significantly more stochastic than the planetary analogs. Depending on our assumed initial distribution of oxygen isotopes within the planetesimal disk, we find a ~5% or less probability that the Earth and Theia will form with an isotopic difference equal to or smaller than the Earth and Moon's. In fact we predict that every planetary mass body should be expected to have a unique isotopic signature. In addition, we find paucities of massive Theia analogs and high velocity moon-forming collisions, two recently proposed explanations for the Moon's isotopic composition. Our work suggests that there is still no scenario for the Moon's origin that explains its isotopic composition with a high probability event., Comment: 16 pages, 22 figures, accepted for publication in Icarus; fixed typos