Intrapixel Sensitivity Variations Research Articles

Analysis of a JWST NIRSpec Lab Time Series: Characterizing Systematics, Recovering Exoplanet Transit Spectroscopy, and Constraining a Noise Floor

Abstract The James Webb Space Telescope’s (JWST) NIRSpec instrument will unveil the nature of exoplanet atmospheres across the wealth of planet types, from temperate terrestrial worlds to ultrahot Jupiters. In particular, the 0.6–5.3 μm PRISM mode is especially well suited for efficient spectroscopic exoplanet observations spanning a number of important spectral features. We analyze a lab-measured NIRSpec PRISM mode Bright Object Time Series observation from the perspective of a JWST user to understand the instrument performance and detector properties. We create two realistic transiting exoplanet time-series observations by performing injection-recovery tests on the lab-measured data to quantify the effects of real instrument jitter, drift, intrapixel sensitivity variations, and 1/f noise on measured transmission spectra. By fitting the time-series systematics simultaneously with the injected transit, we can obtain more realistic transit-depth uncertainties that take into account noise sources that are currently not modeled by traditional exposure time calculators. We find that sources of systematic noise related to intrapixel sensitivity variations and point-spread function motions are apparent in the data at the level of a few hundred ppm but can be effectively detrended using a low-order polynomial with detector position. We recover the injected spectral features of GJ 436 b and TRAPPIST-1 d and place a 3σ upper limit on the detector noise floor of 14 ppm. We find that the noise floor is consistent with <10 ppm at the 1.7σ level, which bodes well for future observations of challenging targets with faint atmospheric signatures.

Thermal Phase Curves of XO-3b: An Eccentric Hot Jupiter at the Deuterium Burning Limit

Abstract We report Spitzer full-orbit phase observations of the eccentric hot Jupiter XO-3b at 3.6 and 4.5 μm. Our new eclipse depth measurements of 1770 ± 180 ppm at 3.6 μm and 1610 ± 70 ppm at 4.5 μm show no evidence of the previously reported dayside temperature inversion. We also empirically derive the mass and radius of XO-3b and its host star using Gaia DR3's parallax measurement and find a planetary mass M p = 11.79 ± 0.98 M Jup and radius R p = 1.295 ± 0.066 R Jup. We compare our Spitzer observations with multiple atmospheric models to constrain the radiative and advective properties of XO-3b. While the decorrelated 4.5 μm observations are pristine, the 3.6 μm phase curve remains polluted with detector systematics due to larger amplitude intrapixel sensitivity variations in this channel. We focus our analysis on the more reliable 4.5 μm phase curve and fit an energy balance model with solid body rotation to estimate the zonal wind speed and the pressure of the bottom of the mixed layer. Our energy balance model fit suggests an eastward equatorial wind speed of 3.13 − 0.83 + 0.26 km s−1, an atmospheric mixed layer down to 2.40 − 0.16 + 0.92 bars, and a Bond albedo of 0.106 − 0.106 + 0.008 . We assume that the wind speed and mixed layer depth are constant throughout the orbit. We compare our observations with 1D planet-averaged model predictions at apoapse and periapse and 3D general circulation model predictions for XO-3b. We also investigate the inflated radius of XO-3b and find that it would require an unusually large amount of internal heating to explain the observed planetary radius.

Multiwavelength Photometry Derived from Monochromatic Kepler Data

Abstract The Kepler mission has provided a wealth of data, revealing new insights in time-domain astronomy. However, Kepler’s single bandpass has limited studies to a single wavelength. In this work we build a data-driven, pixel-level model for the pixel response function (PRF) of Kepler targets, modeling the image data from the spacecraft. Our model is sufficiently flexible to capture known detector effects, such as nonlinearity, intrapixel sensitivity variations, and focus change. In theory, the shape of the Kepler PRF should also be weakly wavelength-dependent, due to optical chromatic aberration and a wavelength-dependent detector response functions. We are able to identify these predicted changes in shape of the PRF using the residuals between Kepler data and our model. In this work, we show that these PRF changes correspond to wavelength variability in Kepler targets using a small sample of eclipsing binaries. Using our model, we demonstrate that pixel-level light curves of eclipsing binaries show variable eclipse depths, ellipsoidal modulation, and limb darkening. These changes at the pixel level are consistent with multiwavelength photometry. Our work suggests that each pixel in the Kepler data of a single target has a different effective wavelength, ranging from ≈550 to 750 nm. In this proof of concept, we demonstrate our model, and discuss possible uses for the wavelength-dependent PRF of Kepler. These uses include characterizing variable systems, and vetting exoplanet discoveries at the pixel level. The chromatic PRF of Kepler is due to weak wavelength dependence in the optical systems and detector of the telescope, and similar chromatic PRFs are expected in other similar telescopes, notably the NASA TESS telescope.

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.

Astro-comb calibrator and spectrograph characterization using a turn-key laser frequency comb

Using a turn-key Ti:sapphire femtosecond laser frequency comb, an off-the-shelf supercontinuum device, and Fabry-Perot mode filters, we report the generation of a 16 GHz frequency comb spanning a 90 nm band about a center wavelength of 566 nm. The light from this astro-comb is used to calibrate the HARPS-N astrophysical spectrograph for precision radial velocity measurements. The comb-calibrated spectrograph achieves a stability of $\sim$ 1 cm/s within half an hour of averaging time. We also use the astro-comb as a reference for measurements of solar spectra obtained with a compact telescope, and as a tool to study intrapixel sensitivity variations on the CCD of the spectrograph.

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.

A uniform analysis of HD 209458b Spitzer/IRAC light curves with Gaussian process models

We present an analysis of Spitzer/IRAC primary transit and secondary eclipse lightcurves measured for HD209458b, using Gaussian process models to marginalise over the intrapixel sensitivity variations in the 3.6 micron and 4.5 micron channels and the ramp effect in the 5.8 micron and 8.0 micron channels. The main advantage of this approach is that we can account for a broad range of degeneracies between the planet signal and systematics without actually having to specify a deterministic functional form for the latter. Our results do not confirm a previous claim of water absorption in transmission. Instead, our results are more consistent with a featureless transmission spectrum, possibly due to a cloud deck obscuring molecular absorption bands. For the emission data, our values are not consistent with the thermal inversion in the dayside atmosphere that was originally inferred from these data. Instead, we agree with another re-analysis of these same data, which concluded a non-inverted atmosphere provides a better fit. We find that a solar-abundance clear-atmosphere model without a thermal inversion underpredicts the measured emission in the 4.5 micron channel, which may suggest the atmosphere is depleted in carbon monoxide. An acceptable fit to the emission data can be achieved by assuming that the planet radiates as an isothermal blackbody with a temperature of $1484\pm 18$ K.

A new technique of characterization of intrapixel response dedicated to astronomical detectors

This paper is devoted to the presentation of a new technique of characterization of the intra-pixel sensitivity variations (IPSVs) of astronomical detectors. The IPSV is the spatial variation of the pixel response function (PRF). In the case of under-sampled instruments for high quality imaging and accurate photometry, IPSV can contribute to the instrument global error and it should be considered carefully. Our measurement technique is based in the Fourier transform (FT) approach. It consists into the sampling of the pixel transfer function (PTF) by projecting high-resolution periodic patterns onto the whole sensor without classic optics but using the self-imaging property (the Talbot effect) of a continuously self imaging grating (CSIG) illuminated by a plane wave. The PRF is determined by computing the inverse FT. Our measurement technique permits to determine the PRF with a resolution of pixel/10 (10 times Nyquist frequency).

AN IMAGE-PLANE ALGORITHM FORJWST'S NON-REDUNDANT APERTURE MASK DATA

The high angular resolution technique of non-redundant masking (NRM) or aperture masking interferometry (AMI) has yielded images of faint protoplanetary companions of nearby stars from the ground. AMI on James Webb Space Telescope (JWST)'s Near Infrared Imager and Slitless Spectrograph (NIRISS) has a lower thermal background than ground-based facilites and does not suffer from atmospheric instability. NIRISS AMI images are likely to have 90 - 95% Strehl ratio between 2.77 and 4.8 micron. In this paper we quantify factors that limit the raw point source contrast of JWST NRM. We develop an analytic model of the NRM point spread function which includes different optical path delays (pistons) between mask holes and fit the model parameters with image plane data. It enables a straightforward way to exclude bad pixels, is suited to limited fields of view, and can incorporate effects such as intra-pixel sensitivity variations. We simulate various sources of noise to estimate their effect on the standard deviation of closure phase, sigma_CP (a proxy for binary point source contrast). If sigma_CP < 10^-4 radians --- a contrast ratio of 10 magnitudes --- young accreting gas giant planets (e.g. in the nearby Taurus star-forming region) could be imaged with JWST NIRISS. We show the feasibility of using NIRISS' NRM with the sub-Nyquist sampled F277W, which would enable some exoplanet chemistry characterization. In the presence of small piston errors, the dominant sources of closure phase error (depending on pixel sampling, and filter bandwidth) are flat field errors and unmodeled variations in intra-pixel sensitivity. The in-flight stability of NIRISS will determine how well these errors can be calibrated by observing a point source. Our results help develop efficient observing strategies for space-based NRM.

ORBITAL PHASE VARIATIONS OF THE ECCENTRIC GIANT PLANET HAT-P-2b

We present the first secondary eclipse and phase curve observations for the highly eccentric hot Jupiter HAT-P-2b in the 3.6, 4.5, 5.8, and 8.0 \mu m bands of the Spitzer Space Telescope. The 3.6 and 4.5 \mu m data sets span an entire orbital period of HAT-P-2b, making them the longest continuous phase curve observations obtained to date and the first full-orbit observations of a planet with an eccentricity exceeding 0.2. We present an improved non-parametric method for removing the intrapixel sensitivity variations in Spitzer data at 3.6 and 4.5 \mu m that robustly maps position-dependent flux variations. We find that the peak in planetary flux occurs at 4.39+/-0.28, 5.84+/-0.39, and 4.68+/-0.37 hours after periapse passage with corresponding maxima in the planet/star flux ratio of 0.1138%+/-0.0089%, 0.1162%+/-0.0080%, and 0.1888%+/-0.0072% in the 3.6, 4.5, and 8.0 \mu m bands respectively. We compare our measured secondary eclipse depths to the predictions from a one-dimensional radiative transfer model, which suggests the possible presence of a transient day side inversion in HAT-P-2b's atmosphere near periapse. We also derive improved estimates for the system parameters, including its mass, radius, and orbital ephemeris. Our simultaneous fit to the transit, secondary eclipse, and radial velocity data allows us to determine the eccentricity and argument of periapse of HAT-P-2b's orbit with a greater precision than has been achieved for any other eccentric extrasolar planet. We also find evidence for a long-term linear trend in the radial velocity data. This trend suggests the presence of another substellar companion in the HAT-P-2 system, which could have caused HAT-P-2b to migrate inward to its present-day orbit via the Kozai mechanism.

3.6 AND 4.5 μm PHASE CURVES AND EVIDENCE FOR NON-EQUILIBRIUM CHEMISTRY IN THE ATMOSPHERE OF EXTRASOLAR PLANET HD 189733b

We present new, full-orbit observations of the infrared phase variations of the canonical hot Jupiter HD 189733b obtained in the 3.6 and 4.5 micron bands using the Spitzer Space Telescope. When combined with previous phase curve observations at 8.0 and 24 micron, these data allow us to characterize the exoplanet's emission spectrum as a function of planetary longitude. We utilize improved methods for removing the effects of intrapixel sensitivity variations and accounting for the presence of time-correlated noise in our data. We measure a phase curve amplitude of 0.1242% +/- 0.0061% in the 3.6 micron band and 0.0982% +/- 0.0089% in the 4.5 micron band. We find that the times of minimum and maximum flux occur several hours earlier than predicted for an atmosphere in radiative equilibrium, consistent with the eastward advection of gas by an equatorial super-rotating jet. The locations of the flux minima in our new data differ from our previous observations at 8 micron, and we present new evidence indicating that the flux minimum observed in the 8 micron is likely caused by an over-shooting effect in the 8 micron array. We obtain improved estimates for HD 189733b's dayside planet-star flux ratio of 0.1466% +/- 0.0040% at 3.6 micron and 0.1787% +/- 0.0038% at 4.5 micron; these are the most accurate secondary eclipse depths obtained to date for an extrasolar planet. We compare our new dayside and nightside spectra for HD 189733b to the predictions of models from Burrows et al. (2008) and Showman et al. (2009). We find that HD 189733b's 4.5 micron nightside flux is 3.3 sigma smaller than predicted by the Showman et al. models, which assume that the chemistry is in local thermal equilibrium. We conclude that this discrepancy is best-explained by vertical mixing, which should lead to an excess of CO and correspondingly enhanced 4.5 micron absorption in this region. [abridged]

Laser frequency comb techniques for precise astronomical spectroscopy

Precise astronomical spectroscopic analyses routinely assume that individual pixels in charge-coupled devices (CCDs) have uniform sensitivity to photons. Intra-pixel sensitivity (IPS) variations may already cause small systematic errors in, for example, studies of extra-solar planets via stellar radial velocities and cosmological variability in fundamental constants via quasar spectroscopy, but future experiments requiring velocity precisions approaching ~1 cm/s will be more strongly affected. Laser frequency combs have been shown to provide highly precise wavelength calibration for astronomical spectrographs, but here we show that they can also be used to measure IPS variations in astronomical CCDs in situ. We successfully tested a laser frequency comb system on the Ultra-High Resolution Facility spectrograph at the Anglo-Australian Telescope. By modelling the 2-dimensional comb signal recorded in a single CCD exposure, we find that the average IPS deviates by <8 per cent if it is assumed to vary symmetrically about the pixel centre. We also demonstrate that series of comb exposures with absolutely known offsets between them can yield tighter constraints on symmetric IPS variations from ~100 pixels. We discuss measurement of asymmetric IPS variations and absolute wavelength calibration of astronomical spectrographs and CCDs using frequency combs.

A Search for a Sub-Earth-Sized Companion to GJ 436 and a Novel Method to Calibrate Warm Spitzer IRAC Observations

ABSTRACTWe discovered evidence for a possible additional 0.75 R⊕ transiting planet in the NASA EPOXI observations of the known M dwarf exoplanetary system GJ 436. Based on an ephemeris determined from the EPOXI data, we predicted a transit event in an extant Spitzer Space Telescope 8 μm data set of this star. Our subsequent analysis of those Spitzer data confirmed the signal of the predicted depth and at the predicted time, but we found that the transit depth was dependent on the aperture used to perform the photometry. Based on these suggestive findings, we gathered new warm Spitzer observations of GJ 436 at 4.5 μm spanning a time of transit predicted from the EPOXI and Spitzer 8 μm candidate events. The 4.5 μm data permit us to rule out a transit at high confidence, and we conclude that the earlier candidate transit signals resulted from correlated noise in the EPOXI and Spitzer 8 μm observations. In the course of this investigation, we developed a novel method for correcting the intrapixel sensitivity variations of the 3.6 and 4.5 μm channels of the Infrared Array Camera (IRAC) instrument. We demonstrate the sensitivity of warm Spitzer observations of M dwarfs to confirm sub-Earth-sized planets. Our analysis will inform similar work that will be undertaken to use warm Spitzer observations to confirm rocky planets discovered by the Kepler mission.

The University of New South Wales Extrasolar Planet Search: methods and first results from a field centred on NGC 6633

We report on the current status of the University of New South Wales Extrasolar Planet Search project, giving details of the methods we use to obtain millimagnitude precision photometry using the 0.5-m Automated Patrol Telescope. We use a novel observing technique to optimally broaden the point spread function and thus largely eliminate photometric noise due to intrapixel sensitivity variations on the CCD. We have observed eight crowded Galactic fields using this technique during 2003 and 2004. Our analysis of the first of these fields (centred on the open cluster NGC 6633) has yielded 49 variable stars and four shallow transit candidates. Follow-up observations of these candidates have identified them as eclipsing binary systems. We use a detailed simulation of our observations to estimate our sensitivity to short-period planets, and to select a new observing strategy to maximize the number of planets detected. Ke yw ords: methods: data analysis ‐ methods: observational ‐ binaries: eclipsing ‐ planetary systems ‐ open clusters and associations: individual: NGC 6633.

Intra-Pixel Sensitivity Variation and Charge Transfer Inefficiency — Results of CCD Scans

AbstractThe efficiency with which a charge-coupled device (CCD) detects photons depends, amongst other factors, on where within a pixel the photon hits. To explore this effect we have made detailed scans across a pixel for a front-illuminated three-phase EEV05-20 CCD using the standard astronomical B, V, R, and I colour filters. Pixel response functions and photometric sensitivity maps are derived from the scan images. Nonlinear charge transfer inefficiency (CTI) effects were observed and corrected for. The resulting images clearly show the intra-pixel sensitivity variations (IPSVs) due to the CCD electrode structure, and its dependence on wavelength. We briefly comment on the implications of IPSVs and CTI for high-precision photometry and astrometry.

Advanced Exposure‐Time Calculations: Undersampling, Dithering, Cosmic Rays, Astrometry, and Ellipticities

ABSTRACTThe familiar tools of Fourier analysis and Fisher matrices are applied to derive the uncertainties on photometric, astrometric, and weak‐lensing measurements of stars and galaxies in real astronomical images. Many effects or functions that are ignored in basic exposure‐time calculators can be included in this framework: pixels of size comparable to the stellar image, undersampled and dithered exposures, cosmic‐ray hits, intrapixel sensitivity variations, and positional and ellipticity errors, as well as photometric errors. I present a formalism and a C++ implementation of these methods. As examples of their use, I answer some commonly arising questions about imaging strategies: What amount of dithering is ideal? What pixel size optimizes the productivity of a camera? Which is more efficient—space‐based or ground‐based observing?

The Photometry of Undersampled Point‐Spread Functions

ABSTRACTAn undersampled point‐spread function (PSF) may interact with the microstructure of a solid‐state detector such that the total flux detected can depend sensitively on where the PSF center falls within a pixel. Such intrapixel sensitivity variations will not be corrected by flat‐field calibration and may limit the accuracy of stellar photometry conducted with undersampled images, as are typical for Hubble Space Telescope observations. The total flux in a stellar image can vary by up to 0.03 mag in F555W WFC images depending on how it is sampled, for example. For NIC3, these variations are especially strong, up to 0.39 mag, strongly limiting its use for stellar photometry. Intrapixel sensitivity variations can be corrected for, however, by constructing a well‐sampled PSF from a dithered data set. The reconstructed PSF is the convolution of the optical PSF with the pixel response. It can be evaluated at any desired fractional pixel location to generate a table of photometric corrections as a function of relative PSF centroid. A caveat is that the centroid of an undersampled PSF can also be affected by the pixel response function; thus sophisticated centroiding methods, such as cross‐correlating the observed PSF with its fully sampled counterpart, are required to derive the proper photometric correction.