JWST NIRCam Defocused Imaging: Photometric Stability Performance and How it Can Sense Mirror Tilts

We observed the hot Jupiter HAT-P-14 b to test the instrument performance and verify that the NIRCam Grism Time Series mode was suitable for science. The planet was selected to have a short duration transit (2.3 hr), high brightness that enables high precision, low stellar activity and high planet surface gravity to have a small atmospheric signal. The short duration requirement was selected to minimize the needed observing time but has the flip side of preferring targets with near-grazing transits (high impact parameters). HAT-P-14 b’s impact parameter is 0.91 (Fukui et al., 2016), so fitting the limb darkening without the planet crossing through the stellar mid-point can complicate the transit depth measurement and stellar models may be preferred for the limb darkening law, as described in Section 4.1. The observation exposure started at 2022-05-02T06:43 UTC, which was the earliest start time allowed by the Astronomy Proposal Tool (APT) special requirements to ensure a long baseline before transit ingress. The lightcurve was observation 1 of Commissioning Program ID 1442, which is available on the Barbara A. Mikulski Archive for Space Telescopes (MAST). Table 1 lists key times during the observations.

The exposure duration was 6 hours, which enabled 2.6 hours of stabilization time before planet ingress. The SW channel was configured with the Weak Lens+8 pupil, F210M filter which covers approximately 1.9 to 2.2 $\mu$m. This was paired with the GRISMR pupil and F322W2 filter on the long wavelength channel, discussed in Beatty et al. (2022). The exposure setup was a single exposure with the BRIGHT2 readout pattern, 20 groups integrated up the ramp and 780 integrations for a 2048$\times$128 subarray (SUBGRISM128) with 4 output amplifier channels. NIRCam readout electronics sample non-destructive reads (ie. frames) to create a ramp and then reset the detector at the end of an integration. Detector groups are a set of 1 or more detector image frames where the frames have been either averaged or skipped by onboard electronics and the average frame (ie. a group) is downloaded from the spacecraft. The averaging or else skipping of frames between groups is done to reduce the data volume on some observations. Observations when more than one frame is averaged or skipped per group reduce the data volume as compared to saving every frame per integration. In BRIGHT2, there are 2 frames (ie. detector samples) averaged per group and zero frames skipped. This resulted in a frame time of 0.67597 seconds, a group time of 1.35194 seconds and a cadence of 27.72001 seconds per integration for 780 integrations.

The 6 hour observation was continuous with no interruptions. Pointing performance was extremely stable as discussed in Section 4.3 below. There was one high gain antenna (HGA) move during the exposure but no interruptions or pauses to the integrations in the 6 hour exposure. This allows detector charge trapping effects to approach a steady state, unlike with HST where each satellite orbit around Earth results in a new charge trapping ramp effect approximately every 90 minutes (e.g. Berta et al., 2012).

The point spread function (PSF) with the Weak Lens+8 pupil is shown in Figure 1. The Weak Lens +8 (along with the -8 wave and +4 wave lenses) is designed to measure the optical path differences of the primary mirror surface. It was enabled as an option in the grism time series and imaging time series modes to spread out the light over more pixels and also reduce the saturation on bright targets. Having the light spread out over more pixels reduces the intrapixel sensitivity, which strongly affected Spitzer Space Telescope lightcurves because the PSF was highly undersampled (Ingalls et al., 2016). It also allows realtime monitoring of the mirror surface along with the long wavelength grism spectroscopy, discussed in Section 3.1. We note that the full extent of the PSF is asymmetrically truncated by the subarray. This will be mitigated in Cycle 1 science observations because an update was made to better center the subarray position. Even with better centering, the SUBGRISM128 subarray truncates some of the wings of the PSF. In other words, the commissioning observations (Figure 1) had the PSF is asymmetrically truncated and in science observations it will be still truncated in the wings but more symmetrically. Fortunately, JWST pointing is so stable (to be discussed in Section 4.3) that there were no impacts from the PSF truncation on the lightcurve and zero-padding the image for wavefront analysis resulted in high quality wavefront phase retrievals (to be discussed in Section 3.1).

We begin with the uncal data (also known as “MAST level 1 uncalibrated”, “User Data Product Stage 0 Fully-Populated FITS file” or Data Processing Level 1b). We then run Stage 1 of the Calwebb STScI pipeline (Bushouse et al., 2022) with some modifications described below, to produce a rateints file which contains the counts in DN/s for each integration.

We started with the STScI JWST Detector 1 Stage 1 pipeline version 1.6.0 and the Calibration Reference Data System (CRDS) context jwst_0822.pmap to convert the raw data values to signal slopes (DN/s) per integration. The Detector Stage 1 pipeline begins by scaling the groups (which doesn’t affect NIRCam readout modes), initializing the data quality flags, flagging saturated pixels and then subtracting a superbias. When examining the superbias subtraction, we note that every 4 integrations has a bias offset structure due to the fast frame resets that reset pixels across the whole detector to ensure that charge doesn’t migrate into the subarray. For this SUBGRISM128 subarray, the fast frame reset occurs every 4 integrations. However, accounting for the different superbias every 4 integrations resulted in very little change to the lightcurve so we used a single superbias subtraction for all integrations.

Normally, detector stage 1 processing then does a reference pixel correction step. The reference pixels are light-insensitive pixels that share the same electronic noise sources as the regular light-sensitive pixels and thus allow efficient subtraction of common-mode noise sources. Normally, the bottom and side reference pixels are used to mitigate odd/even column effects, pre-amplifier resets and 1/f noise. However, the SUBGRISM128 subarray for the short-wavelength time series mode has no reference pixels along the top or bottom detector rows.²²2The SW subarray is designed to be centered on the defocused PSF when the same source is centered near the Y=34 long wavelength pixel on the LW subarray. See section A for a diagram. The relative positions of the short and long wavelength detectors when projected on the sky result in the weak lens +8 image being centered at Y= 167.5 in 1-based counting absolute coordinates on the short wavelength detector. The subarray position was adjusted to better center the PSF after HAT-P-14 was observed. Thus, the reference pixel step does not correct for large pre-amplifier offsets and smaller odd/even offsets. We instead replace the reference pixel step with a similar step that uses background instead of reference pixels to remove many of the same effects.

We use a shorthand for this modified reference pixel step ROEBA, which stands for row-by-row, odd/even by amplifier correction, which lists the steps in reverse order. First, we select one of the four amplifiers for correction at a time. In this case a block pixels from 1 to 512, 513 to 1024, 1025 to 1536 or 1537 to 2048 pixels in the X direction and the entire 128 pixel tall subarray in the Y direction. For this correction, it is necessary to define a background region to use as a proxy for reference pixels that has minimal contamination from bright sources. We select all pixels that are more than 201 pixels away from the central PSF as shown in Figure 2. We then apply a slow-read correction, which subtracts the median odd count level in the background region from all odd numbered columns and the median even count level from in the background region from all even numbered columns. This removes the pre-amplifier offsets. We then calculate the row-by-row median count level from the background region and subtract this from all pixels in that row. This largely removes the longer time scale (low frequency) components of the 1/f noise (e.g. Schlawin et al., 2020). The resulting correction from ROEBA shown in Figure 2 (bottom) has substantially smaller pre-amplifier reset offsets in each amplifier as well as less 1/f noise banding along the horizontal direction. We note that the ROEBA method uses many more pixels across the horizontal fast-read direction than the side reference pixels on the detector so it can improve results even when reference pixels are available in a subarray. Another advantage of the ROEBA correction is that many fewer pixels are erroneously marked as jumps at the jump detection step (described below). One assumption in the ROEBA step is that it relies on a clean background region and could potentially over-subtract when there is faint scattered light or background sources so inspection for neighboring sources and faint emission is necessary before applying it to all NIRCam data.

We next apply the non-linearity correction with default parameters. The result of the bias subtraction and ROEBA step is that the signal level is close to 0 DN at the background before applying the linearity correction step. The stage 1 pipeline normally has a dark current subtraction step after non-linearity correction, but dark current on the NIRCam short wavelength detectors is less than 0.05 e^-/sec and there is currently too much signal from cosmic rays and persistence to measure well and subtract on these detectors. We next run the jump step correction with a threshold of 6 sigma. Without the ROEBA correction, many pixels are erroneously flagged as “jumps” (e.g. cosmic rays) because the pre-amplifier offsets and 1/f noise can appear as jumps in signal from one detector group to another. With the ROEBA correction, we note that these erroneous jumps are much less frequent and instead the jump step flags true outliers such as cosmic rays. One exception where the jump step does not flag a cosmic ray perfectly is the outer radii of ‘snowball“ events (Rigby et al., 2022), as shown in Figure 2 near X=737,Y=101. Here, only the brighter portions of the snowball are flagged with the jump detection algorithm used in the analysis for this paper. As the final step of stage 1, we run the ramp fit step with default parameters to calculate a count rate per pixel in Data Numbers (DN) per second. There is another gain scaling step for NIRSpec data but it does not affect the NIRCam data presented in this paper.

We next use aperture photometry with photutils (Bradley et al., 2016) to measure the flux for each integration to derive a flux as a function of time. We fit the central peak of the PSF with a Gaussian and used this to determine the aperture center for each integration. We use a circular source aperture with a radius of 81 pixels, and the mean background rate from a background annulus with an inner radius of 81 and an outer radius of 101 pixels. These pixels were found to produce the minimum lightcurve scatter from an aperture size grid search. Although the ROEBA step described above largely removes the background, we found that the additional background annulus subtraction improved the precision, likely because of residual 1/f not removed by ROEBA. We found the same level of noise whether we did aperture centering or kept the apertures fixed, with the exception of better photometry during the HGA move affecting one integration to compensate for the small amount of image motion within that one integration. We normalize the flux time series to a value near 1.0 (1000 parts per thousand, ppt) for lightcurve fitting and noise analysis, which we describe in Section 4.1.

We originally noticed a large jump in the long wavelength time series (Beatty et al., 2022) but also found one at the same time at some aperture sizes in the short wavelength and a smaller jump later in the time series. The jumps in flux correspond to changes in the mirror surface, known as “tilt events” (Rigby et al., 2022). These were first noticed by choosing an arbitrary reference image (in this case the rate from the 6th integration) and dividing the rate from all other integrations by it. Figure 3 shows three example ratio images from 1) before the tilt events, 2) after the first tilt event and 3) after the second tilt event. The tilt events show up as clear wave patterns in these differential images due to changes in the mirror surface. The short wavelength Weak Lens +8 defocused PSF is part of the wavefront sensing tools aboard JWST and is thus highly sensitive to changes in the mirror surface.

We used a non-linear optimization based phase retrieval algorithm (Fienup, 1982, 1993) based on the algorithmic differentiation (Jurling & Fienup, 2014). The coherent propagation model used a flexibly sampled discrete Fourier transform (Jurling et al., 2018). We used a bias and gain invariant error metric (Thurman & Fienup, 2009) as the cost function. The phase retrieval model was initialized using the wavefront and pupil data calculated from the JWST optical model for the nearest available field point, the NRCA3-FP2MIMF multi-instrument multi-field point. Because PSF data were only available with the +8 wave weak lens, this was a single image phase retrieval problem. We configured the model with 128 pixels across the array storing the pupil and 256 pixels across the cropped and padded image. Because of the band-pass of the F210M filter used for imaging, we used a broadband point-spread function model (Fienup, 1999; Jurling et al., 2018). We ran the phase retrieval optimization in two steps.

In the first step we used the first image in the time series to establish a starting point. We sequentially estimated image position (using a sub-pixel cross correlation method (Guizar-Sicairos et al., 2008)), global low order Zernike aberrations, segment level piston, and tip/tilt errors (1st order segment Zernike aberrations). Finally, we performed joint estimation over a smoothly interpolated low resolution grid in wavefront and amplitude. With a single image the ability to distinguish between phase and amplitude errors in this last step is limited.

In the second step, we begin from the reference point established by the first phase retrieval. In this case the optimization was done jointly over global and segment Zernike aberrations without sequential bootstrapping. This facilitates change detection by requiring the pupil amplitude and higher order wavefront variation to be the same throughout the time series, but still allowing low order and segment wavefront changes through time.

The phase retrieval results are shown in Figure 3 and it is clear that the C6 mirror segment changed orientation (tilted) at event 1 and that the C1 mirror segment tilted at event 2. In event 1, the wavefront over C6 changed by 18 nm RMS (evaluated over the segment) compared to the initial wavefront, and in event 2, C1 changed by 26 nm (again evaluated over the segment). These changes are much smaller than the wavelength of the light, so both the individual segments and the overall telescope remain diffraction limited.

As shown in Figure 4, the C6 event produced a larger change with a magnitude that varies from 200 ppm to 1000 ppm across the 2.4 µm to 4.0 µm wavelength range for the long wavelength and 254 $\pm$ 22 ppm in the short wavelength photometry using an aperture radius of 79 pixels or 2.45 arcsec. Using the wavefront phase retrieval described in this section above (Jurling & Fienup, 2014) for the optical path differences, we make a prediction for the magnitude of the flux jump by comparing the enboxed or encircled energy before and after the jumps. We use enboxed energy for the long wavelength spectroscopic extraction box and encircled energy for the short wavelength photometry. The short wavelength (SW) model prediction of 260 ppm is very close to the measured 254 $\pm$ 22 ppm for the large aperture used in the short wavelength time series. The long wavelength (LW) jump model prediction under-predicts the jump size from 2.5 to 3.5 $\mu$m but agrees from 2.7 to 4.1 $\mu$m. Some of the difference between the model and measurement could be the difference between an imaging and dispersed PSF and how they are extracted. Preliminary models with a dispersed LW grism image can reproduce the 1000 ppm change at 2.5 $\mu$m.

It is possible to quantitatively measure tilt events in addition to visually inspecting the differential images or doing the phase retrieval shown in Figure 3. The mirror changes can be evaluated with photometric apertures on key parts of mirror surfaces, such as in Figure 5 (right plot). The time series of these apertures can cleanly sense the two tilt events like step functions as shown in Figure 5 (left second from the top). We also calculate this photometry on the difference between pairs of adjacent detector groups to assess the mirror changes at a higher time cadence (colored points in Figure 5).

The NIRCam grism time series and time series imaging modes are the only modes currently supported that allows simultaneous high cadence wavefront sensing along with the time series. In some time series modes such as the NIRSpec Bright Object Time Series (Birkmann et al., 2022) or MIRI low resolution time series (Kendrew et al., 2015), defocused imaging is not currently available for real-time wavefront sensing of the primary mirrors, so other measures are desirable to sense tilt events. NIRISS Single Object Slitless mode (SOSS) (Doyon et al., 2012) has a de-focusing lens so this mode has some analogous capabilities as the short wavelength weak lens.

We explored some ways to sense tilt events with the NIRCam grism time series spectroscopy and the fine guidance sensor (FGS) fine guide data streams (Doyon et al., 2012). We experimented with a few different statistics for the FGS images. We found that the flux from the telemetry stream³³3See the SA_ZFGINSTCT keyword https://jwst-docs.stsci.edu/methods-and-roadmaps/jwst-time-series-observations/jwst-time-series-observations-noise-sources, (STScI, 2016) can sense the first tilt event (C6) but could not easily reveal the second tilt event (C1). In addition, the first tilt event (C6) could be detected with a dot product with the average PSF or the $3\times 3$ pixel flux of the time series but the second tilt event from the C1 mirror was harder to pull out of the noise. The FWHM of the FGS 8$\times$8 images also shows step-like changes with the two tilt events but at low signal to noise. We found that principal component analysis (PCA) could reveal evidence of both tilt events but is also not easily distinguishable above the noise.

The noise-weighted “differential dot product” was most effective in detecting tilt events with FGS.

where $D_{i}$ is the differential dot product of 8$\times$8 images reshaped to 64-pixel linear vectors. In the expression, $\vec{A_{i}}$ is a single FGS cal data image, $\vec{R}$ is a reference image after the tilt event, $\vec{V}$ is the variance image, and $\vec{M}$ is a reference image before the tilt. This method did use prior information about the timing of tilt events from NIRCam data to find the average image from before the tilt $\vec{M}$ and the average image after the tilt $\vec{R}$, but it may be possible to iteravely scan the time series to determine $\vec{M}$ and $\vec{R}$ from FGS alone. This statistic essentially magnifies the differences between the shape of the PSF before and after the tilt event and weights by the noise. Figure 5 shows that both tilt events can be sensed with FGS using a dot product, where the $\vec{M}$ and $\vec{R}$ are chosen for the first tilt event (C6) and second tilt event (C1).

Additionally, the full width at half maximum (FWHM, bottom left plot in Figure 5) of the long wavelength grism PSF is sensitive to tilt events because the PSF changes with the mirror tilt. Thus, even when weak lens imaging is not available, the FGS images and science instrument FWHM can be used in all time series modes to give clues about tilt events. However, Equation 1 requires some knowledge of the timing to find $\vec{M}$ and $\vec{R}$ unless they can be found iteratively. Therefore, a more general-purpose indicator of tilt events may be the FWHM of science data, which can be tracked in all time series observations.

Tilt events are hypothesized to be structural microdynamics in the telescope that may occur when stresses in the backplane structure behind the mirrors are suddenly relaxed. As these stresses are released, the frequency of tilt events is expected to decrease in time. Regular wavefront measurements indicate that they are less frequent in the transition from commissioning to science observations in July 2022 than earlier in commissioning. However, tilt events were common even 4.5 months between launch and these observations, and similar tilt events may occur during Cycle 1 science observations.

The mirror changes appear to be step functions in Figure 5, so the change happens on a timescale faster than the 27 second cadence of integrations. We inspect the mirror changes at a higher cadence (but noisier) time series by calculating the mirror tilt specific photometry on the group-by-group difference images, which have a cadence of 1.351 seconds. In this analysis, adjacent points are thus anti-correlated because they share a detector group so if one sample is anomalously high, the next one will be anomalously low. As shown in Figure 6, there is a rapid change that takes 2 sampling durations of 1.351 seconds each to go from low to high or high to low, or in other words one sample between the low and high values. There are two causes for the intermediate sample: 1) the tilt timescale is between 1.351 and 2.702 seconds and 2) the timescale is shorter than 1.351 seconds and occurs midway through the group. We consider the first scenario less likely as it would require some fine-tuning to cause a tophat-like disturbance between these two time intervals that shows little sign of change in the PSF beyond 2.702 seconds. We therefore expect that the timescale is faster than the shortest measurable time with the NIRCam photometry which is the 1.351 second group time. We also note that these observations used the BRIGHT2 mode, which includes two frames within a group so the tilt could happen between these two frames within a group or within one of the frames. We do not see any discontinuities within the image that would indicate a change within the frame, but the PSF only covers a fraction of the field of view so it is not a strong constraint.

The HST WFC3 IR detector, which is an earlier generation HgCdTe detector, exhibits ramps with an exponential settling behavior (e.g. Berta et al., 2012; Zhou et al., 2017). Ground-based laboratory tests showed likely negligible effects for typical JWST detectors (e.g. Schlawin et al., 2021). However, the NRCA3 short wavelength detector exhibits the most persistent charge and likely charge trap density of the 10 NIRCam detectors that are used in flight (Leisenring et al., 2016). NRCA3 is the same detector used for the short wavelength component of the grism time-series observations when the long wavelength filter is selected to be F277W, F322W2, F356W.⁴⁴4https://jwst-docs.stsci.edu/jwst-near-infrared-camera/nircam-operations/nircam-target-acquisition/nircam-grism-time-series-target-acquisition The NRCA1 detector that is paired with the F444W filter, had about half the accumulated counts from charge trap release as the NRCA3 detector in ground based tests (Leisenring et al., 2016), so it is expected to have a smaller amplitude exponential ramp.

We fit an exponential model to the charge trapping behavior, as is common with HST charge trapping ramps (e.g. Berta et al., 2012) and show the results in Figure 7. We first correct the small 260 ppm jump in the lightcurve using a wavefront model described in Section 3.1. We fit the lightcurve with the following planet and systematics model:

where A, B and C are coefficients in the quadratic baseline trend and normalization, $x$ is barycentric time, $R$ is the exponential amplitude, $x_{0}$ is the exposure start time, $f_{a}(x)$ is the astrophysical limb darkened lightcurve (starry, Luger et al., 2019), with a 4 parameter polynomial limb darkening law from ExoCTK and $x^{\prime}$ is the normalized time,

where $x_{med}$ is the median time, $x_{max}$ is the maximum time and $x_{min}$ is the minimum time. We fit the lightcurves by fixing $C=0$ (ie. a linear fit) and also letting it be a free parameter (ie a quadratic fit). As will be shown in Section 4.2, significant correlated errors are seen in the residuals if a linear baseline trend is adopted instead of a quadratic trend.

We find an exponential amplitude $R$ of 731 ppm and an exponential time $\tau$ of 5.1 minutes for a linear trend and $R$ of 656 ppm and $\tau=$15 of minutes for a quadratic trend. The normalization and polynomial trend constants for the quadratic trend are A=${1000.24\pm 0.01}$ parts per thousand (ppt), B=${-0.911\pm 0.03}$ ppt and C=${0.80\pm 0.14}$ ppt. In absolute units, this corresponds to a slope of -0.15 ppt/hr and derivate of the slope of 0.022 (ppt/hr²). We note that initially, we fit the baseline and exponential start to just the initial part of the lightcurve and found an order-of-magnitude exponential settling timescale of 11 minutes (Rigby et al., 2022). The 5.1 and 15 minutes minutes came from a MCMC Bayesian fit to the full lightcurve with a linear and quadratic baseline respectively, whereas the 11 minutes comes from least squared minimization of the first 300 points (before planet ingress) and has a steeper linear slope. We have not determined the cause of the long timescale trend, but note a that different linear trends were seen on the NRS1 and NRS2 detectors (Espinoza et al., 2022) so it may be detector-related. The quadratic slope and exponential ramp terms in Equation 3 are correlated and thus the change in slope is fit with a different exponential settling time. We also looked through the previous JWST activities and found that NIRCam’s previous use was 37 hours before for wavefront sensing. NIRCam detectors remained in idle reset mode for those 37 hours so it is unlikely any long timescale traps were filled and are being released to create the downward slope seen in the data.

The H2RG detectors used in the near infrared instruments on JWST are never strictly linear at any well filling fraction, ranging from sub-percent non-linearity to tens of percent at 98% the hard saturation value (e.g. Canipe et al., 2017). However, they become increasingly non-linear as the detector approaches full well capacity and saturation (e.g. Plazas et al., 2017). Correction polynomials are applied by the CalWebb JWST pipeline (Bushouse et al., 2022) to linearize the counts as function of counts (DN). A different but analogous method has been shown that linearity corrections are possible even up to high well filling fractions ($\sim$97% Canipe et al., 2017).

We assessed the difference between pairs of groups up the ramp to look for evidence of non-linearity. The stellar flux is highly stable within a 27 second long integration so it is expected that a linearity-corrected ramp should have a constant difference between each successive group. We find however that the first 4 group differences and the last 9 have a higher rate of flux than the middle 6 group differences, as shown in Figure 8. The early higher fluxes may be related to the release of trapped charge (e.g. Smith et al., 2008; Leisenring et al., 2016) or a type of reset anomaly (Rauscher et al., 2007). We do not perform a dark current subtraction, as discussed in Section 2.2. However, the dark current is less than 0.05 e^-/sec on the short wavelength NIRCam detectors, and the 1% change in the differential samplings (shown in Figure 8) on top of a representative rate of 400 e^-/s would require 4 $e^{-}$/s of dark current. So the reset anomaly seen here may be different from the anomaly seen on other H2RG devices (Rauscher et al., 2007).

Exoplanet time series observations with a small number of groups ($\lesssim 5$) could have an absolute photometric flux offsets but also systematic differences in the transit depth as compared to observations with many groups ($\gtrsim 5$). This is because the non-linearity effects can change the response of the detector to a differential signal (ie. a non-constant derivative of count rate as a function of signal in e-/s/Mjy). With the observed 1% change in signal from group 2-1 to group 4-3 in Figure 8, a 2% deep transit of a hot Jupiter could have a measured transit depth of up to $\sim$ 1% $\times$ 2% $\times$ 1/4 = 50 ppm deeper if just using group 2 and 1. This difference is below the measurement noise for a single transit of HAT-P-14 b using only group 2 - 1 but could be assessed on a brighter target. There is also a possibility of reciprocity failure with HgCdTe detectors that can cause systematic changes in transit depth (Biesiadzinski et al., 2011; Schlawin et al., 2021).

We fit the lightcurve with a transit model to determine the lightcurve performance, discussed in Section 4.2 and the timing accuracy, discussed in Section 4.5. We remove a 260 ppm jump in the F210M (2.1 µm) time series due to a tilt event using a wavefront model of the optics discussed in Section 3.1, allow a quadratic trend with time and fit an exponential settling ramp discussed in Section 3.4. We use the integration mid-times in the barycentric reference frame and barycentric dynamical time standard int_mid_BJD_TDB included in the INT_TIMES extension of the JWST data products.

We fit the corrected lightcurve with a starry transit lightcurve model (Luger et al., 2019), an exponential ramp, a quadratic trend in time and the 260 ppm jump correction. The planet’s near-grazing impact parameter (0.91 Fukui et al., 2016)) means that the planet does not traverse near the stellar midpoint and fitting the limb darkening parameters as free parameters can lead to large uncertainties in the planet’s radius. We fix the limb darkening law to a 6600 K, [Fe/H]=0.11, $\log{g}$ = 4.25 (Stassun et al., 2017) ATLAS9 model (Kurucz, 2017) calculated with ExoCTK for the F210M filter for $\mu>0.05$ where $\mu$ is the cosine of the angle between the line of signt and the emergent intensity (e.g. Kipping, 2013) for a 4 parameter non-linear law. We use the starry lightcurve model, which uses a polynomial limb darkening law (Agol et al., 2020), so we fit the intensity function from a 4 parameter nonlinear law with a 6 parameter polynomial limb darkening law, which has been shown to be accurate to $\lesssim 0.5$ ppm differences in flux (Agol et al., 2020). We start with priors centered on the values from Bonomo et al. (2017) for the period, inclination, eccentricity and argument of pericenter, but widened these in case of systematic errors to 83.5 $\pm 0.3^{\circ}$, $e$=0.1071 $\pm$ 0.01 and $\omega$=106.1 $\pm 5^{\circ}$. We use the ephemeris from publicly vailable TESS data and a wide a/R_∗ of 8.9 $\pm$ 1.0 centered on the value from Stassun et al. (2017). The resulting lightcurve fits and resiuals are shown in Figure 9. We show a model fit that does not account for two of the systematics to better illustrate them as well as another that accounts for them (the charge trap ramp and tilt event jump).

After fitting the lightcurve with a transit model that includes a jump correction from a phase retrieval, an exponential charge trapping ramp and quadratic baseline described in Section 4.1, we analyze the statistical properties of the residuals. We include all points that are not marked as outliers (all points within 5 $\sigma$ of the best fit model) which includes 775 out of 780 total integrations. The standard deviation (scatter) in all of the non-outlier residuals is 152 ppm, compared to a theoretical limit of 107 ppm from photon and read noise. Thus, the measured noise is 42% larger than the theoretical limit, some of which could be due to 1/f noise (Schlawin et al., 2020). Even after ROEBA subtraction, there remains higher frequency (shorter timescale than the 5.24 ms row read time) noise. We note that the background annulus subtraction reduced the standard deviation of out-of-transit flux in the lightcurve by 37% over skipping the background annulus subtraction so there is likely residual 1/f noise. We next assess time-correlations in the data by binning the residuals.

A key metric in the performance of the NIRCam photometry is how well the noise scales as a function of bin size. This commonly is presented in the form of an Allan Variance plot (e.g. Pont et al., 2006; Croll et al., 2011). In this plot, the photometric scatter is computed as a standard deviation as a function of bin size. In the case where each time sample is independent, the noise drops as $1/\sqrt{N}$ and this is plotted as “white noise scaling”. When the measured photometric scatter begins to diverge from the $1/\sqrt{N}$ power law, this is a sign that the time samples are correlated and time-dependent systematics are present.

Figure 10 (left) shows that the noise falls with $1/\sqrt{N}$. Thus, no noise floor is measurable down to the 20 ppm level, but 1/f noise limits the precision in our current analysis to 42% above the theoretical limit. It may be possible to optimize the aperture to a hexagonal aperture, but previous tests with a circular annulus had little difference in noise performance on simulated data. For this Allan variance analysis, we have removed the first tilt event from the lightcurve using a model discussed in Section 3.1, a quadratic trend with time and an exponential settling ramp discussed in Section 3.4. For comparison, we also calculated an Allan variance curve when the baseline trend was fit with a linear polynomial instead of a quadratic polynomial in time. In this curve, the noise begins to grow near 5 minutes where the noise is about 60 ppm. Thus, there is some curvature to the lightcurve either related to instrument or astrophysical trends.

The measured 20 ppm lightcurve scatter at a time bin size of 30 minutes can be compared to the state-of-the-art best precision lightcurves from space-based photometers. For the brightest targets observed by Kepler, the precision was measured to be $\sim$15 ppm (Jenkins et al., 2010). For the bright exoplanet system 55 Cnc, the precision with TESS was 10 ppm for 30 minutes (Meier Valdés et al., 2022) and for CHEOPS the precision achievable on a 1.6 hour eclipse observed 41 times using only out-of-eclipse data was 3 ppm (Demory et al., 2022), which would scale to 3 ppm * sqrt(1.6 hours/0.5 hours * 41 eclipses /2)=20 ppm for 30 minutes. The scaling uses the relative time of the eclipse and the half hour benchmark, 41 separate eclipse events that were averaged and finally a factor of 2 accounting for the fact that the out-of-transit to in-transit ratio adds another factor of sqrt(2) in noise. Elsewhere, the instrumental noise on hour-long timescales for CHEOPS is reported to be 15 to 80 ppm (Maxted et al., 2022). In the JWST photometry presented in this work, precision is limited by photon counting statistics, so brighter sources with more photons per minute will be needed to assess what is the highest possible precision as compared to the state-of-the-art performance.

Target acquisition was successful and placed the target at X=1060.7 px, Y=167.5 px on the NRCA3 detector in full frame 1-based Data Management System coordinates. Pointing was stable to 0.01 pixels (0.3 mas) in the X direction and 0.009 px (0.3 mas) in the Y direction. Some of the higher frequency jitter is thus averaged over the 27 second long integrations. Thus, JWST attitude control provides incredible pointing stability at the 10^-2 pixel level and this produces no noticeable changes in flux with position and jitter, likely constituting a negligible part of the error budget. The guide star has an FGS magnitude of 15.3 and we expect similarly high precision pointing performance for guide stars from magnitude 12.5 to 15.5. Under the HgCdTe crosshatching structures on the NIRCam ALONG/A5 detector, 2 mas pointing was expected to produce 6 ppm changes of flux, so 0.3 mas jitter is likely to matter at the single digit ppm level and flux changes at this level cannot be measured for the HAT-P-14 target.

JWST high gain antenna moves maintain pointing at the designated ground stations on Earth’s Deep Space Network. While high gain antenna moves should happen during slews or between exposures, the moves are permitted to occur after 10,000 s during long time series observations with JWST. We had a high gain antenna adjustment at 2022-05-02T10:10:01 UTC, which was measurable with the Fine Guidance Sensor and NIRCam short wavelength time series centroids. As shown in Figure 11, the pointing change from the HGA move settles very quickly in less than 0.5 minutes. Furthermore, the position was returned back to the original pointing to within 1 mas. The data around an HGA move can be discarded and in the case of weak lens photometry that is spread over many pixels, only produced a transient 500 ppm change in flux. Thus, HGA moves are not expected to cause significant issues to most time series observations as long as the Fine Guide mode does not lose a guide star from its subarray.

We find a transit center time of 2022-05-02T10:34:55 +/- 7 seconds BJD_TDB, which is consistent (within 1.7 $\sigma$) with a prediction from the TESS ephemeris of 2022-05-02T10:36:35.1 +/- 60 seconds BJD_TDB. Other planets with higher precision ephemerides will test JWST timing to higher accuracy. There is also a dedicated GO program program identification number 1666 (PI Poshak Gandhi) that will use a double white dwarf binary and is expected to calibrate the absolute timing of an exposure to the 100 ms level.

The HAT-P-14 system was observed from the ground with Palomar adaptive optics (AO) on 2021-08-08 UTC to assess the contamination and dilution of the transit depth and find any unknown companions. No companions were detected with a contrast less than $\Delta$mag = 7.0 within 0.5″. The nearby stellar companion HAT-P-14 B (Ngo et al., 2015) was also imaged with Palomar AO to better constrain the infrared colors and contamination on the transit depth. The separation is 0.85″ at a position angle of 264 degrees, which is well within the 2.5″ source aperture used in the lightcurves of the central (hexagonal) portion of the PSF shown in Figure 1. With the Palomar AO imaging, we find a delta K magnitude between the HAT-P-14 A and B of $\Delta$K=4.99, which is a similar wavelength to this JWST F210M photometry. The JWST target acquisition image shown in Figure 12 shows both HAT-P-14 A and HAT-P-14 B. Using the target acquisition image, we find that the contrast is $\Delta$ Mag_F335M=5.03 $\pm$ 0.05 for the F335M filter (3.35 µm) and the separation is 0.83″. This contrast is a similar to $K$ band, as expected for the Raleigh Jeans limit for long wavelengths.

Using webbpsf, we simulate the overlap of two Weak Lens +8 PSFs for a 81 pixel aperture and estimate the transit depth dilution. We use the flight wavefront optical path difference evaluated at a time of 2022-05-02T10:30 UTC using webbpsf and perform aperture photometry on the simulated PSFs of HAT-P-14 A and HAT-P-14 B separately. For the F210M filter at 2.1 µm, we find that HAT-P-14 B should dilute the fitted 6540 $\pm$ 22 ppm transit depth by 59 ppm for an undiluted transit depth 6599 $\pm$ 22 ppm. This is within 3.2 $\sigma$ of the long wavelength F322W2 broadband result of 6670 ppm, but with independent fitting methods and priors on orbital parameters and limb darkening. This is also consistent with the NIRSpec time series broadband fit with 6627 $\pm$ 8 ppm with an independent analysis (Espinoza et al., 2022), with different priors on orbital parameters and limb darkening. We do not expect the atmosphere to contribute much more than 15 ppm as described in Section 1 for 0.9 atmospheric scale heights, but atmospheric gases could contribute at 1.5$\sigma$ level for 2 atmospheric scale heights of absorption.