Pixel Level Decorrelation Research Articles

A Comparative Study of TESS Light-curve Extraction Methods Applied to Blazars

Blazars are characterized by largely aperiodic variability on timescales ranging from minutes to decades across the electromagnetic spectrum. The Transiting Exoplanet Survey Satellite (TESS) mission provides continuous sampling of blazar variability on timescales ranging from tens of minutes to 27 days for a single sector observation. Proper removal of the background, thermal ramping, and onboard systematic effects are crucial to the extraction of a reliable blazar light curve. Multiple publicly available procedures have been created to correct for these effects. Using ground-based observations from the Zwicky Transit Facility (ZTF) and the Asteroid Terrestrial-impact Last Alert System (ATLAS) as “ground truth” observations, we compare six different methods (regression, cotrending basis vectors, pixel-level decorrelation, eleanor, quaver, and simple differential photometry) to each other, and to our “ground truth” observations, to identify which methods properly correct light curves of a sample of 11 bright blazars, including the suspected neutrino source TXS 0506+056. In addition to comparing the resulting light curves, we compare the slopes of the power spectral densities, perform least-square fitting to simultaneous ZTF data, and quantify other statistical qualities generated from the light curves of each method. We find that only three of the six methods compared (simple differential photometry, eleanor, and quaver) produce TESS light curves consistent with the ground-based ZTF and ATLAS observations.

Spitzer Dayside Emission of WASP-34b

We analyzed two eclipse observations of the low-density transiting, likely grazing, exoplanet WASP-34b with the Spitzer Space Telescope’s InfraRed Array Camera using two techniques to correct for intrapixel sensitivity variation: Pixel-Level Decorrelation and BiLinearly Interpolated Subpixel Sensitivity. When jointly fitting both light curves, timing results are consistent within 0.7σ between the two models and eclipse depths are consistent within 1.1σ, where the difference is due to photometry methods, not the models themselves. By combining published radial velocity data, amateur and professional transit observations, and our eclipse timings, we improved on measurements of orbital parameters and found an eccentricity consistent with zero (0.0). Atmospheric retrieval, using our Bayesian Atmospheric Radiative Transfer code, shows that the planetary spectrum most resembles a blackbody, with no constraint on molecular abundances or vertical temperature variation. WASP-34b is redder than other warm Jupiters with a similar temperature, hinting at unique chemistry, although further observations are necessary to confirm this.

K2, Spitzer, and TESS Transits of Four Sub-Neptune Exoplanets

Abstract We present new Spitzer transit observations of four K2 transiting sub-Neptunes: K2-36 c, K2-79b, K2-167b, and K2-212b. We derive updated orbital ephemerides and radii for these planets based on a joint analysis of the Spitzer, TESS, and K2 photometry. We use the EVEREST pipeline to provide improved K2 photometry, by detrending instrumental noise and K2's pointing jitter. We used a pixel-level decorrelation method on the Spitzer observations to reduce instrumental systematic effects. We modeled the effect of possible blended eclipsing binaries, seeking to validate these planets via the achromaticity of the transits (K2 versus Spitzer). However, we find that Spitzer’s signal-to-noise ratio for these small planets is insufficient to validate them via achromaticity. Nevertheless, by jointly fitting radii between K2 and Spitzer observations, we were able to independently confirm the K2 radius measurements. Due to the long time baseline between the K2 and Spitzer observations, we were also able to increase the precision of the orbital periods compared to K2 observations alone. The improvement is a factor of 3 for K2-36 c, and more than an order of magnitude for the remaining planets. Considering possible JWST observations in 1/2023, previous 1σ uncertainties in transit times for these planets range from 74–434 minutes, but we have reduced them to the range of 8–23 minutes.

Evidence for disequilibrium chemistry from vertical mixing in hot Jupiter atmospheres

Aims. We present a large atmospheric study of 49 gas giant exoplanets using infrared transmission photometry with Spitzer/IRAC at 3.6 and 4.5 μm. Methods. We uniformly analyze 70 photometric light curves of 33 transiting planets using our custom pipeline, which implements pixel level decorrelation. Augmenting our sample with 16 previously published exoplanets leads to a total of 49. We use this survey to understand how infrared photometry traces changes in atmospheric chemical properties as a function of planetary temperature. We compare our measurements to a grid of 1D radiative-convective equilibrium forward atmospheric models which include disequilibrium chemistry. We explore various strengths of vertical mixing (Kzz = 0–1012 cm2 s−1) as well as two chemical compositions (1x and 30x solar). Results. We find that, on average, Spitzer probes a difference of 0.5 atmospheric scale heights between 3.6 and 4.5 μm, which is measured at 7.5σ level of significance. Changes in the opacities in the two Spitzer bandpasses are expected with increasing temperature due to the transition from methane-dominated to carbon-monoxide-dominated atmospheres at chemical equilibrium. Comparing the data with our model grids, we find that the coolest planets show a lack of methane compared to expectations, which has also been reported by previous studies of individual objects. We show that the sample of coolest planets rule out 1x solar composition with >3σ confidence while supporting low vertical mixing (Kzz = 108 cm2 s−1). On the other hand, we find that the hot planets are best explained by models with 1x solar metallicity and high vertical mixing (Kzz = 1012 cm2 s−1). We interpret this as the lofting of CH4 to the upper atmospheric layers. Changing the interior temperature changes the expectation for equilibrium chemistry in deep layers, hence the expectation of disequilibrium chemistry higher up. We also find a significant scatter in the transmission signatures of the mid-temperate and ultra-hot planets, likely due to increased atmospheric diversity, without the need to invoke higher metallicities. Additionally, we compare Spitzer transmission with emission in the same bandpasses for the same planets and find no evidence for any correlation. Although more advanced modelling would test our conclusions further, our simple generic model grid points towards different amounts of vertical mixing occurring across the temperature range of hot Jupiters. This finding also agrees with the observed scatter with increasing planetary magnitude seen in Spitzer/IRAC color-magnitude diagrams for planets and brown dwarfs.

Identification and Mitigation of a Vibrational Telescope Systematic with Application to Spitzer

Abstract We observed Proxima Centauri with the Spitzer Space Telescope Infrared Array Camera five times in 2016 and 2017 to search for transits of Proxima Centauri b. Following standard analysis procedures, we found three asymmetric, transit-like events that are now understood to be vibrational systematics. This systematic is correlated with the width of the point-response function (PRF), which we measure with rotated and nonrotated-Gaussian fits with respect to the detector array. We show that the systematic can be removed with a novel application of an adaptive elliptical-aperture photometry technique, and compare the performance of this technique with fixed and variable circular-aperture photometry, using both BiLinearly Interpolated Subpixel Sensitivity (BLISS) maps and nonbinned Pixel-Level Decorrelation (PLD). With BLISS maps, elliptical photometry results in a lower standard deviation of normalized residuals, and reduced or similar correlated noise when compared to circular apertures. PLD prefers variable, circular apertures, but generally results in more correlated noise than BLISS. This vibrational effect is likely present in other telescopes and Spitzer observations, where correction could improve results. Our elliptical apertures can be applied to any photometry observations, and may be even more effective when applied to more circular PRFs than Spitzer’s.

Pixel level decorrelation in service of the Spitzer microlens parallax survey

ABSTRACT Microlens parallax measurements combining space-based and ground-based observatories can be used to study planetary demographics. In recent years, the Spitzer Space Telescope was used as a microlens parallax satellite. Meanwhile, Spitzer IRAC has been employed to study short-period exoplanets and their atmospheres. As these investigations require exquisite photometry, they motivated the development of numerous self-calibration techniques now widely used in the exoplanet atmosphere community. Specifically, pixel level decorrelation (PLD) was developed for starring-mode observations in uncrowded fields. We adapt and extend PLD to make it suitable for observations obtained as part of the Spitzer Microlens Parallax Campaign. We apply our method to two previously published microlensing events, OGLE-2017-BLG-1140 and OGLE-2015-BLG-0448, and compare its performance to the state-of-the-art pipeline used to analyses Spitzer microlensing observation. We find that our method yields photometry 1.5–6 times as precise as previously published. In addition to being useful for Spitzer, a similar approach could improve microlensing photometry with the forthcoming Nancy Grace Roman Space Telescope.

Wōtan: Comprehensive Time-series Detrending in Python

The detection of transiting exoplanets in time-series photometry requires the removal or modeling of instrumental and stellar noise. While instrumental systematics can be reduced using methods such as pixel level decorrelation, removing stellar trends while preserving transit signals proves challenging. Due to vast archives of light curves from recent transit surveys, there is a strong need for accurate automatic detrending, without human intervention. A large variety of detrending algorithms are in active use, but their comparative performance for transit discovery is unexplored. We benchmark all commonly used detrending methods against hundreds of Kepler, K2, and TESS planets, selected to represent the most difficult cases for systems with small planet-to-star radius ratios. The full parameter range is explored for each method to determine the best choices for planet discovery. We conclude that the ideal method is a time-windowed slider with an iterative robust location estimator based on Tukey's biweight. This method recovers 99% and 94% of the shallowest Kepler and K2 planets, respectively. We include an additional analysis for young stars with extreme variability and conclude they are best treated using a spline-based method with a robust Huber estimator. All stellar detrending methods explored are available for public use in wotan, an open-source Python package on GitHub (see https://github.com/hippke/wotan).

The Pointing Limits of Transiting Exoplanet Light Curve Characterization with Pixel Level Decorrelation

Abstract We present scope (simulated CCD observations for photometric experimentation), a Python package to create a forward model of telescope detectors and simulate stellar targets with motion relative to the CCD. The primary application of this package is the simulation of the Kepler Space Telescope detector to predict and characterize increased instrumental noise in the spacecraft’s final campaigns of observation. As the fuel powering the spacecraft’s stabilizing thrusters ran out and thruster fires began to sputter and fail, stellar point-spread functions experienced more extreme and less predictable motion relative to regions of varied sensitivity on the spacecraft detector, generating more noise in transiting exoplanet light curves. Using our simulations, we demonstrate that current de-trending techniques effectively capture and remove systematics caused by sensitivity variation for spacecraft motion as high as about 10 times that typically experienced by K2. The scope package is open source and has been generalized to allow custom detector and stellar target parameters. Future applications include simulating observations made by the Transiting Exoplanet Survey Satellite and ground-based observations with synthetic atmospheric interference as testbeds for noise removal techniques.

Killing Planet Candidates with EVEREST

Abstract We exploit high-quality photometry from the EVEREST pipeline to evaluate false-positive exoplanet candidates from the K2 mission. We compare the practical capabilities of EVEREST’s pixel-level decorrelation scheme to the data analysis pipelines widely used at the time of these planet candidates’ discovery. Removing stellar variability from the EVEREST-corrected light curves, we search for potential secondary eclipses. For each object exhibiting a secondary eclipse, we compare the implied brightness temperature of the planet candidate to its calculated equilibrium temperature. We thereby identify objects whose brightness temperature is too high to be consistent with a planet. We identify seven systems previously flagged as planetary candidates in preliminary vetting pipelines, and use EVEREST to instead identify six of them as eclipsing binaries. We also project the importance of optimal photometric vetting for TESS data. We find that the majority of blended eclipsing binaries could be identified using TESS photometry, and a systematic study of that kind could in principle also yield valuable information on the mass ratio distribution in stellar eclipsing binaries.

An Update to the EVEREST K2 Pipeline: Short Cadence, Saturated Stars, and Kepler-like Photometry Down to Kp = 15

Abstract We present an update to the EVEREST K2 pipeline that addresses various limitations in the previous version and improves the photometric precision of the light curves. We develop a fast regularization scheme for pixel-level decorrelation (PLD) and adapt the algorithm to include the PLD vectors of other stars to enhance the predictive power of the model and minimize overfitting, particularly for faint stars. We also modify PLD to work for saturated stars and improve its performance on variable stars, although some high-frequency variables may still suffer from overfitting. On average, EVEREST 2.0 light curves have 10–20% higher photometric precision than those in version 1, yielding the highest-precision light curves at all magnitudes of any publicly available K2 catalog. For most K2 campaigns, we recover the original Kepler precision to at least = 14, and to at least = 15 for campaigns 1, 5, 6, and 13. We also detrend most short-cadence targets observed by K2, obtaining even higher photometric precision for these stars. Like all aggressive, flexible models, EVEREST is prone to overfitting, and may cause a decrease in transit depths by ∼10%; we urge users to mask signals of interest using our open-source software, which we show removes this bias. Light curves for campaigns 0–8 and 10–13 are available online in the EVEREST catalog, which will be updated with future campaigns. EVEREST 2.0 is open source and is coded in a framework that can be adapted to other photometric surveys, including Kepler and the upcoming TESS mission.

Confirming Variability in the Secondary Eclipse Depth of the Super-Earth 55 Cancri e

Abstract We present a reanalysis of five transit and eight eclipse observations of the ultrashort-period super-Earth 55 Cancri e observed using the Spitzer Space Telescope during 2011–2013. We use pixel-level decorrelation to derive accurate transit and eclipse depths from the Spitzer data, and we perform an extensive error analysis. We focus on determining possible variability in the eclipse data, as was reported in Demory et al. From the transit data, we determine updated orbital parameters, yielding T 0 = 2,455,733.0037 ± 0.0002, P = 0.7365454 ± 0.0000003 days, i = 83.5 ± 1.°3, and R p = 1.89 ± 0.05 R ⊕. Our transit results are consistent with a constant depth, and we conclude that they are not variable. We find a significant amount of variability between the eight eclipse observations and confirm agreement with Demory et al. through a correlation analysis. We convert the eclipse measurements to brightness temperatures, and generate and discuss several heuristic models that explain the evolution of the planet’s eclipse depth versus time. The eclipses are best modeled by a year-to-year variability model, but variability on shorter timescales cannot be ruled out. The derived range of brightness temperatures can be achieved by a dark planet with inefficient heat redistribution intermittently covered over a large fraction of the substellar hemisphere by reflective grains, possibly indicating volcanic activity or cloud variability. This time-variable system should be observable with future space missions, both planned (JWST) and proposed (i.e., ARIEL).

Spitzer secondary eclipses of Qatar-1b

Aims. Previous secondary eclipse observations of the hot Jupiter Qatar-1b in the Ks band suggest that it may have an unusually high day side temperature, indicative of minimal heat redistribution. There have also been indications that the orbit may be slightly eccentric, possibly forced by another planet in the system. We investigate the day side temperature and orbital eccentricity using secondary eclipse observations with Spitzer. Methods. We observed the secondary eclipse with Spitzer/IRAC in subarray mode, in both 3.6 and 4.5 μm wavelengths. We used pixel-level decorrelation to correct for Spitzer’s intra-pixel sensitivity variations and thereby obtain accurate eclipse depths and central phases. Results. Our 3.6 μm eclipse depth is 0.149 ± 0.051% and the 4.5 μm depth is 0.273 ± 0.049%. Fitting a blackbody planet to our data and two recent Ks band eclipse depths indicates a brightness temperature of 1506 ± 71 K. Comparison to model atmospheres for the planet indicates that its degree of longitudinal heat redistribution is intermediate between fully uniform and day-side only. The day side temperature of the planet is unlikely to be as high (1885 K) as indicated by the ground-based eclipses in the Ks band, unless the planet’s emergent spectrum deviates strongly from model atmosphere predictions. The average central phase for our Spitzer eclipses is 0.4984 ± 0.0017, yielding e cos ω = −0.0028 ± 0.0027. Our results are consistent with a circular orbit, and we constrain e cos ω much more strongly than has been possible with previous observations.

Phase Curves of WASP-33b and HD 149026b and a New Correlation between Phase Curve Offset and Irradiation Temperature

Abstract 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 hr) 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 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. We also compare our results to predictions from general circulation models, and we find that while neither planet matches the models well, 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.

SPITZER SECONDARY ECLIPSE DEPTHS WITH MULTIPLE INTRAPIXEL SENSITIVITY CORRECTION METHODS OBSERVATIONS OF WASP-13b, WASP-15b, WASP-16b, WASP-62b, AND HAT-P-22b

ABSTRACT We measure the 4.5 μm thermal emission of five transiting hot Jupiters, WASP-13b, WASP-15b, WASP-16b, WASP-62b, and HAT-P-22b using channel 2 of the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. Significant intrapixel sensitivity variations in Spitzer IRAC data require careful correction in order to achieve precision on the order of several hundred parts per million (ppm) for the measurement of exoplanet secondary eclipses. We determine eclipse depths by first correcting the raw data using three independent data reduction methods. The Pixel Gain Map (PMAP), Nearest Neighbors (NNBR), and Pixel Level Decorrelation (PLD) each correct for the intrapixel sensitivity effect in Spitzer photometric time-series observations. The results from each methodology are compared against each other to establish if they reach a statistically equivalent result in every case and to evaluate their ability to minimize uncertainty in the measurement. We find that all three methods produce reliable results. For every planet examined here NNBR and PLD produce results that are in statistical agreement. However, the PMAP method appears to produce results in slight disagreement in cases where the stellar centroid is not kept consistently on the most well characterized area of the detector. We evaluate the ability of each method to reduce the scatter in the residuals as well as in the correlated noise in the corrected data. The NNBR and PLD methods consistently minimize both white and red noise levels and should be considered reliable and consistent. The planets in this study span equilibrium temperatures from 1100 to 2000 K and have brightness temperatures that require either high albedo or efficient recirculation. However, it is possible that other processes such as clouds or disequilibrium chemistry may also be responsible for producing these brightness temperatures.

EVEREST: PIXEL LEVEL DECORRELATION OF K2 LIGHT CURVES

ABSTRACT We present EPIC Variability Extraction and Removal for Exoplanet Science Targets (EVEREST), an open-source pipeline for removing instrumental noise from K2 light curves. EVEREST employs a variant of pixel level decorrelation to remove systematics introduced by the spacecraft’s pointing error and a Gaussian process to capture astrophysical variability. We apply EVEREST to all K2 targets in campaigns 0–7, yielding light curves with precision comparable to that of the original Kepler mission for stars brighter than , and within a factor of two of the Kepler precision for fainter targets. We perform cross-validation and transit injection and recovery tests to validate the pipeline, and compare our light curves to the other de-trended light curves available for download at the MAST High Level Science Products archive. We find that EVEREST achieves the highest average precision of any of these pipelines for unsaturated K2 stars. The improved precision of these light curves will aid in exoplanet detection and characterization, investigations of stellar variability, asteroseismology, and other photometric studies. The EVEREST pipeline can also easily be applied to future surveys, such as the TESS mission, to correct for instrumental systematics and enable the detection of low signal-to-noise transiting exoplanets. The EVEREST light curves and the source code used to generate them are freely available online.

REPEATABILITY AND ACCURACY OF EXOPLANET ECLIPSE DEPTHS MEASURED WITH POST-CRYOGENIC SPITZER

ABSTRACT We examine the repeatability, reliability, and accuracy of differential exoplanet eclipse depth measurements made using the InfraRed Array Camera (IRAC) on the Spitzer Space Telescope during the post-cryogenic mission. We have re-analyzed an existing 4.5 μm data set, consisting of 10 observations of the XO-3b system during secondary eclipse, using seven different techniques for removing correlated noise. We find that, on average, for a given technique, the eclipse depth estimate is repeatable from epoch to epoch to within 156 parts per million (ppm). Most techniques derive eclipse depths that do not vary by more than a factor 3 of the photon noise limit. All methods but one accurately assess their own errors: for these methods, the individual measurement uncertainties are comparable to the scatter in eclipse depths over the 10 epoch sample. To assess the accuracy of the techniques as well as to clarify the difference between instrumental and other sources of measurement error, we have also analyzed a simulated data set of 10 visits to XO-3b, for which the eclipse depth is known. We find that three of the methods (BLISS mapping, Pixel Level Decorrelation, and Independent Component Analysis) obtain results that are within three times the photon limit of the true eclipse depth. When averaged over the 10 epoch ensemble, 5 out of 7 techniques come within 60 ppm of the true value. Spitzer exoplanet data, if obtained following current best practices and reduced using methods such as those described here, can measure repeatable and accurate single eclipse depths, with close to photon-limited results.

A BLIND METHOD TO DETREND INSTRUMENTAL SYSTEMATICS IN EXOPLANETARY LIGHT CURVES

The study of the atmospheres of transiting exoplanets requires a photometric precision, and repeatability, of one part in $\sim 10^4$. This is beyond the original calibration plans of current observatories, hence the necessity to disentangle the instrumental systematics from the astrophysical signals in raw datasets. Most methods used in the literature are based on an approximate instrument model. The choice of parameters of the model and their functional forms can sometimes be subjective, causing controversies in the literature. Recently, Morello et al. (2014, 2015) have developed a non-parametric detrending method that gave coherent and repeatable results when applied to Spitzer/IRAC datasets that were debated in the literature. Said method is based on Independent Component Analysis (ICA) of individual pixel time-series, hereafter "pixel-ICA". The main purpose of this paper is to investigate the limits and advantages of pixel-ICA on a series of simulated datasets with different instrument properties, and a range of jitter timescales and shapes, non-stationarity, sudden change points, etc. The performances of pixel-ICA are compared against the ones of other methods, in particular polynomial centroid division (PCD), and pixel-level decorrelation (PLD) method (Deming et al. 2014). We find that in simulated cases pixel-ICA performs as well or better than other methods, and it also guarantees a higher degree of objectivity, because of its purely statistical foundation with no prior information on the instrument systematics. The results of this paper, together with previous analyses of Spitzer/IRAC datasets, suggest that photometric precision and repeatability of one part in $10^4$ can be achieved with current infrared space instruments.

SPITZERSECONDARY ECLIPSES OF THE DENSE, MODESTLY-IRRADIATED, GIANT EXOPLANET HAT-P-$20{\rm b}$ USING PIXEL-LEVEL DECORRELATION

HAT-P-20b is a giant exoplanet that orbits a metal-rich star. The planet itself has a high total density, suggesting that it may also have a high metallicity in its atmosphere. We analyze two eclipses of the planet in each of the 3.6- and 4.5 micron bands of Warm Spitzer. These data exhibit intra-pixel detector sensitivity fluctuations that were resistant to traditional decorrelation methods. We have developed a simple, powerful, and radically different method to correct the intra-pixel effect for Warm Spitzer data, which we call pixel-level decorrelation (PLD). PLD corrects the intra-pixel effect very effectively, but without explicitly using - or even measuring - the fluctuations in the apparent position of the stellar image. We illustrate and validate PLD using synthetic and real data, and comparing the results to previous analyses. PLD can significantly reduce or eliminate red noise in Spitzer secondary eclipse photometry, even for eclipses that have proven to be intractable using other methods. Our successful PLD analysis of four HAT-P-20b eclipses shows a best-fit blackbody temperature of 1134 +/-29K, indicating inefficient longitudinal transfer of heat, but lacking evidence for strong molecular absorption. We find sufficient evidence for variability in the 4.5 micron band that the eclipses should be monitored at that wavelength by Spitzer, and this planet should be a high priority for JWST spectroscopy. All four eclipses occur about 35 minutes after orbital phase 0.5, indicating a slightly eccentric orbit. A joint fit of the eclipse and transit times with extant RV data yields e(cos{omega}) = 0.01352 (+0.00054, -0.00057), and establishes the small eccentricity of the orbit to high statistical confidence. Given the existence of a bound stellar companion, HAT-P-20b is another excellent candidate for orbital evolution via Kozai migration or other three-body mechanism.