The majority of low-mass (
Almost 30 yr ago, Hubble Space Telescope (HST) observations revealed that faint early galaxies preferentially appear elongated in projection (L. L. Cowie et al. 1995;S. van den Bergh et al. 1996). This has since been confirmed with newer instruments and statistical samples from larger surveys with HST (D. M. Elmegreen et al. 2005; S. Ravindranath et al. 2006;A. van der Wel et al. 2014;H. Zhang et al. 2019). Most recently, V. Pandya et al. (2024) revived interest in this puzzle by showing that low-mass galaxies with / * M M log 9 10 10 at z > 1 continue to appear preferentially elongated with axis ratios b/a ∼ 0.3-0.6 even in deeper observations with the James Webb Space Telescope (JWST) at rest-frame optical wavelengths (see also J. S. Kartaltepe et al. 2023;B. E. Robertson et al. 2023;J. Vega-Ferrero et al. 2024).
These early elongated galaxies have continued to defy a clear explanation. The safest bet is that there is a surface brightness selection effect against detecting rounder face-on disks (J. J. Dalcanton & S. A. Shectman 1996;D. M. Elmegreen et al. 2005;A. Loeb 2024) or that we are preferentially seeing an elongated star-forming "proto-bar" but not the extended stellar disk. H. Zhang et al. (2019) showed that at most ∼20% of elongated galaxies would be missed by HST if their light profiles were reprojected into the face-on view, which is not enough to explain the high inferred elongated fractions of ∼50%-70%. V. Pandya et al. (2024) demonstrated that JWST should be even more complete to disks with all orientations at z ∼ 1-8 down to
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their formation via mergers along cosmic web filaments (D. Ceverino et al. 2015;M. Tomassetti et al. 2016).
Here, we explore a possibility not previously considered in the literature: Are early galaxies preferentially elongated because they have a higher probability of being gravitationally lensed? It is already well known that the optical depth to lensing increases for higher-redshift systems (e.g., R. Barkana & A. Loeb 2000) and that this results in a "magnification bias," which modifies the number counts of high-redshift galaxies (E. L. Turner et al. 1984; J. S. B. Wyithe et al. 2011;C. A. Mason et al. 2015). The larger covering fraction of possible foreground lenses combined with bigger angular diameter distances to high-redshift sources can also help maximize the Einstein radius for strong lensing (T. Treu 2010). JWST has already identified multiple strongly lensed background galaxies in massive clusters missed by Hubble (e.g., L. Mowla et al. 2022Mowla et al. , 2024;;M. Pascale et al. 2022;B. L. Frye et al. 2023;L. D. Bradley et al. 2024), with roughly ∼25-65 cases expected in "blank" JWST deep fields (C. M. Casey et al. 2023;P. Holloway et al. 2023). One new Einstein ring has already been detected in COSMOS-Web based on serendipitous visual inspection (W. Mercier et al. 2024;P. van Dokkum et al. 2024).
Perhaps the most relevant connection is to weak lensing, which is sensitive to the assumed intrinsic shapes of galaxies. JWST is uniquely enabling the use of lower-mass, higherredshift sources for weak-lensing studies around massive clusters (K. Finner et al. 2023a; D. R. Harvey & R. Massey 2024), but the intrinsic shapes and intrinsic alignments of these preferentially elongated background galaxies remain poorly understood. V. Pandya et al. (2019) proposed that if most early galaxies are indeed nearly prolate and forming along cosmic web filaments, then they are expected to show very strong intrinsic alignments, which may be an underappreciated source of bias for weak lensing. On the other hand, lensing by foreground large-scale structure may itself contribute a nonnegligible amount of "cosmic shear" that leads to some net elongation and alignments of distant sources. Of course, the fact that it is the lower-mass systems at high redshift that preferentially appear elongated suggests that this phenomenon is due to their intrinsic shapes rather than lensing, but it is still important to quantify the magnitude of the effect and possible implications.
With these fundamental questions in mind, here, we pursue a systematic search for both galaxy-galaxy lensing candidates and large-scale alignments in "blank" JWST deep fields. This is complementary to traditional lensing studies around bright foreground clusters and involves looking for the statistical correlations between ellipticity, orientation, and shear that are the hallmarks of gravitational lensing (e.g., J. A. Tyson et al. 1990;T. G. Brainerd et al. 1996). For this pilot study, we will use the JWST Cosmic Evolution Early Release Science (CEERS) survey (program ID 1345; S. L. Finkelstein et al. 2023), which was selected to not have an obvious bright cluster in the foreground but may still have overdensities at higher redshift. By averaging over the orientations of background galaxies on multiple scales, we will demonstrate the potential of JWST for constraining the presence of any such foreground mass concentration even if it is "dark" (e.g., D. J. Bacon et al. 2000;N. Kaiser et al. 2000; D. M. Wittman et al. 2000;R. Maoli et al. 2001;J. Rhodes et al. 2001;A. Refregier 2003; M. Kilbinger 2015). With that said, it is not our goal to measure the precise amplitude of any lensing signal but rather to place an upper limit on its contribution to the elongation of early galaxies.
This paper is organized as follows. In Section 2, we describe the data, and in Section 3, we detail our methods. We present our results on galaxy-galaxy lensing in Section 4 and on largescale alignments in Section 5. We discuss possible explanations and implications in Section 6. Finally, we summarize in Section 7. We assume a standard Planck Collaboration et al. (2016) cosmology throughout with h = 0.6774, Ω m,0 = 0.3075, Ω Λ,0 = 0.691, and Ω b,0 = 0.0486.
We use data from the JWST-CEERS survey (program ID 1345; S. L. Finkelstein et al. 2023).foot_0 CEERS covers a ∼100 arcmin 2 portion of the Extended Groth Strip (EGS; E. J. Groth et al. 1994; M. Davis et al. 2007) with NIRCam imaging in 10 pointings. Data reduction details are given in M. B. Bagley et al. (2023). Here, we use a source catalog derived by S. L. Finkelstein et al. (2023) with the original SExtractor code (E. Bertin & S. Arnouts 1996). We use photometric redshifts and stellar masses derived from 13-filter spectral energy distribution (SED) fitting by G. Barro et al. (2024) using the EAZY code (G. B. Brammer et al. 2008). The 13 filters include six broadband ones from NIRCam (F115W, F150W, F200W, F277W, F356W, F444W), one medium-band NIRCam filter (F410M), and six broadband filters from the HST Advanced Camera for Surveys (ACS)/WFC3 (F606W, F814W, F105W, F125W, F140W, F160W). The multiwavelength SEDs give reasonably well constrained photometric redshifts and stellar masses for our selected sample as described below in Section 3.6.
Our galaxy shape measurements are based on single-component Sérsic fits with galfit (C. Y. Peng et al. 2002) by E. J. McGrath et al. (2025, in preparation). This provides the key quantities that we need for our lensing analysis: effective (halflight) radius, projected axis ratio, and position angle of the major axis measured for each galaxy independently in all six broadband NIRCam filters. The shape catalog also includes empirical errors for these quantities that are derived by matching each observed galaxy to 100 simulated sources, which were inserted into blank regions of the mosaic, and which have a similar magnitude, size, and Sérsic index. These empirical errors help quantify the systematic uncertainties that generally dominate galaxy shape measurements and are not accounted for by the formal statistical uncertainties from galfit. During the Sérsic model fitting process, an empirical, filter-dependent global point-spread function (PSF) was used to recover "intrinsic" galaxy sizes, axis ratios, and position angles before convolution with a global empirical PSF. These global PSFs were created by stacking stars throughout the CEERS footprint (see Section 3.2 S. L. Finkelstein et al. 2023). In the Appendix, we investigate the spatial dependence of the PSF in CEERS by measuring the quadrupole moments of individual stars and quantify the level of bias expected.
Here, we describe our methods to study galaxy-galaxy lensing and large-scale alignments (in that order).
We select possible foreground massive lens galaxies by requiring z < 1, ( ) / > * M M log 10.5 10 and good Sérsic fits (galfit flag of zero or one) in the F115W filter, which traces the rest-frame optical/near-infrared. Of the 53,885 galaxies available in the catalog, this leads to 77 massive lens galaxies. Based on visual inspection, we discard one that is clearly a deblending artifact resulting in 76 lenses.
For background source galaxies, we impose z > 1 and
, which is above the CEERS galaxy completeness limit to at least z = 8 for a reasonable range of sizes and apparent magnitudes (Appendix B of V. Pandya et al. 2024). We do not make any cut on the color or star formation rate. Of the 53,385 sources in the catalog, this yields 6648 galaxies. We further require that the galaxies have good Sérsic fits (galfit flag of zero or one) in the filter that most closely tracks the restframe optical (∼5000 Å) at their redshift. This means F115W for z = 1.0-1.5, F150W for z = 1.5-2.0, F200W for z = 2-3, F356W for z = 3-6, and F444W for z > 6. We only include galaxies whose intrinsic (i.e., PSF-deconvolved) Sérsic effective radius is greater than the PSF FWHM of their assigned rest-optical filter. These cuts yield 4135 source galaxies, but we discard 267 that are clearly artifacts based on visual inspection, and another 20 that have catastrophically high uncertainty estimates of Δ(b/a) > 1, Δ(PA) > 30 � , or Δ(r e ) > 1″. This leaves 3848 sources of which 3073 (∼80%) are low mass with
For every background galaxy, we start by computing its onsky separation to all 76 possible foreground lenses. We define a subset of these as "nearest" source-lens pairs by assigning the closest on-sky lens to each background galaxy. We verified that our results would be identical if we had instead assigned to each source the lens with the highest predicted shear.
Figure 1 shows the demographics of our source-lens pairs in terms of the joint distribution of the lens redshift, source redshift, and on-sky pair separation. The lenses are roughly uniformly distributed over z ∼ 0.3-1.0, but there appears to be an overdensity at z ∼ 0.75 (top gray histogram). The background sources span a range of redshifts but drop off steeply from z ∼ 1 to 10 (top cyan histogram). Interestingly, the highest-redshift background galaxies (orange/red points) are preferentially found near lenses with z ∼ 0.75. It is unclear if this is due to magnification bias, a selection effect, cosmic variance, or some combination thereof. At a given lens redshift, background sources span a range of on-sky pair separations θ ≲ 250″. For the average background galaxy, the nearest massive foreground lens is ∼1′ away.
We assume a singular isothermal sphere (SIS) lens model for all 76 massive foreground galaxies. For this initial exploratory study, we believe this strikes a balance between the simplicity of point lens models and the complex shear analysis that is standard in weak lensing (P. Schneider et al. 1992).
Since we are interested in calculating the galaxy-galaxy lensing shear, we begin by computing the angular diameter distances to the lens (D L ), to the source (D S ), and between the lens and source (D LS ). Then, we can compute the Einstein radius as (e.g., see R.
Narayan & M. Bartelmann 1996; T. Treu 2010; P. Schneider 2015) ( ) = D D c 4 , 1 E LS S SIS 2
where c is the speed of light, and σ SIS is the (radially constant) 1D velocity dispersion of the SIS halo. For massive early-type lenses, the central stellar velocity dispersion σ * has been shown to correlate well with σ SIS (i.e., being roughly equal; A. S. Bolton et al. 2008;H. J. Zahid et al. 2016H. J. Zahid et al. , 2018)). We thus approximate the central stellar velocity dispersion of all lenses assuming their centers are baryon dominated via
This yields a roughly log-normal distribution of σ * with the shape parameter s ∼ 0.3 and scale parameter 275 km s -1 , which peaks at ∼250 km s -1 and has a tail out to ∼580 km s -1 . The distribution is reasonable and compares well with, e.g., the range of σ * measured for luminous red galaxies (LRGs) at z < 0.7 in the SDSS-III/BOSS survey (D. Thomas et al. 2013). In detail, since our lens sample extends down to / > * M M log 10.5 10 , it likely includes many "fast rotator" early-type galaxies (e.g., M. Cappellari 2016). Equation (2) may need a correction to account for the greater fraction of rotation in these stellar systems. We forgo any such correction here, leaving it as a systematic that is only relevant for our galaxy-galaxy lensing analysis but not cosmic shear calculations (the latter is described next in Section 3.5).
Taking σ SIS = σ * , we can thus compute θ E . The shear experienced by a background galaxy a projected distance θ away from the center of a foreground lens is then simply
.
This shear can be thought of as a differential change in projected ellipticity. It is larger for smaller on-sky source-lens separations and for more massive lenses, which have larger Einstein radii. For a given on-sky separation θ and SIS lens, the shear is maximized as D LS → D S .
In addition to shear, we also compute the tangential alignment angle for every source-lens pair as illustrated in Figure 2. Every background galaxy already has a position angle f for its major axis from the best-fitting Sérsic model. We compute another position angle δ from the vector that connects the centers of the background and lens galaxies. Both position angles are defined with the same astronomical convention where 0 � is north (up), and we limit the range between -90 � and 90 � east of north. The absolute difference between the two is ψ ≡ |f -δ| and lies between 0 � and 90 � . When ψ ≈ 0 � , it means the major axis of the background galaxy is pointing toward its nearest lens. When ψ ≈ 90 � , it instead means the major axis of the background galaxy is perpendicular to the vector connecting the source-lens pair, i.e., we say the background galaxy is tangentially aligned with the lens.
Since we are dealing with small sample sizes, we opt for a Bayesian analysis of galaxy-galaxy lensing. Specifically, we will perform Bayesian "quantile regression," which predicts the conditional distribution of different quantiles of some property and their dependence on other variables. This provides more information than linear regression, which instead fits for a single mean relation and is susceptible to outliers and nonlinearities. Unlike simple linear regression, quantile regression can also capture heteroscedasticity in the data such as the scatter in y changing with x. While quantile regression can be done in a parametric way (e.g., fitting different lines for different quantiles of y), here, we opt for a nonparametric approach using Bayesian Additive Regression Trees (BART; H. A. Chipman et al. 2010;J. Hill et al. 2020;O. A. Martin et al. 2021). BART approximates a function by summing over many small regression trees whose individual sizes and depths are subject to priors that avoid overfitting. 13In addition to the sum-of-trees, there is an error term that is fit as part of the overall model.
We use the implementation of BART in the probabilistic programming language PyMC (A.-P. Oriol et al. 2023;M. Quiroga et al. 2023), which utilizes Hamiltonian Monte Carlo for accelerated gradient-based sampling of the error term, and particle Gibbs sampling for BART. BART has a number of hyperparameters that characterize its internal priors for the depths, splitting rules, and values of its trees to minimize overfitting. The default values have been shown to work well for a variety of problems, so we do not vary those. We use 100 trees to fit our thousands of points in the e log and log planes, but using 50 or 200 trees did not change our results. Note that γ has to be inferred while e and ψ are direct observables, so we treat the latter as "independent" variables.
We assume an asymmetric Laplace likelihood, which is naturally well suited for quantile regression (R. It has three parameters: one controlling the mean, another controlling the scale, and yet another controlling the asymmetry. The location parameter of this likelihood is the BART random variable with its default internal priors as described above. For the scale parameter (which quantifies uncertainty around the BART-based mean), we use a halfnormal prior with the standard deviation arbitrarily set to 5. We verified that our results are not sensitive to wider and narrower choices of half-normal or exponential priors. We sum this scale parameter in quadrature with the shear uncertainty estimated for each source as described in Section 3.6 below. Finally, the asymmetry parameter is set to the quantile we are trying to fit. In this work, we will fit five quantiles: 0.1, 0.5, 0.9, 0.95, and 0.997.
We ran four chains with 3000 tuning (burn-in) and 3000 sampling draws. We verified the convergence of the chains as follows. Trace plots revealed that the posteriors of the scale parameter for the asymmetric Laplace likelihood were similar from all four independent chains. Since the BART random variable is really a collection of predictions from multiple trees for each of our thousands of observed points, the recommended convergence check involves the cumulative distribution function of the effective sample size and Gelman-Rubin statistic for each chain. We verified that the effective sample size was ≫1000, and the Gelman-Rubin statistic was ≲1.02 for all BART components of each chain, thus implying convergence.
We will average over the orientations of background galaxies both in bins of galaxy-galaxy shear and more generally on the scale of individual NIRCam chips (64″ × 64″), modules ( × 2. 2 2. 2), and pointings ( × 2. 2 5. 1). For this, we will follow the standard practice in gravitational lensing studies (e.g., P. Schneider et al. 1992) and assign each galaxy a complex number:
ie exp 2 cos 2 sin 2 , 4
where |e| ≡ (1b/a) is the usual projected ellipticity, and f is the position angle measured east of north (up). 14 The use of 2f accounts for the symmetry of rotating an ellipse by π, i.e., galaxy shape vectors do not point in one or the other direction for a given orientation. This formalism makes it easy to compute the average ellipticity as the magnitude of the average complex number 〈e〉 and the average orientation as its phase. 15We will also compute the "shear variance" 2 , which quantifies the degree of correlation between the complex ellipticities of all possible pairs of galaxies in some region. This summary statistic is frequently used in cosmic shear studies (A. Refregier 2003;M. Kilbinger 2015) and can be thought of as a simpler alternative to more sophisticated shearshear correlation functions, which otherwise depend continuously on pair separation. Specifically, we adapt Equation (8) of H. Hämmerle et al. (2002):
( ) ( ) = = = + * N N e e 1 1 , 5 i N j i N i j reg 2 gal gal 1 1 gal gal
where the normalization accounts for the number of unique pairs. Note that the inner summation is staggered by one to prevent double counting pairs and that the product involves the complex conjugate * e j . This reg 2 is the shear variance for a single chip, module, or pointing, but we want the average over all regions of a given type:
where the sum involves the norm of reg,n 2 , which in general is a complex number. We will compute this shear variance for both galaxies and our PSF stars (Appendix) with the latter serving as null tests for systematics.
We use an efficient vectorized Monte Carlo method to estimate uncertainties on the galaxy-galaxy lensing shear. First, we assume negligible astrometric uncertainties, which allows us to fix the combination of source-lens pairs for simplicity. This is sensible since we have so few possible lens galaxies, and the nearest one in projection to each source would maximize its shear. Then, for each source-lens pair, we draw 1000 random realizations of the source redshift, lens redshift, lens stellar mass, and lens effective radius using the uncertainty estimates for those quantities.
The median fractional uncertainties are σ z /(1 + z phot ) ≈ 0.014 for source redshifts, σ z /(1 + z phot ) ≈ 0.012 for lens redshifts, / * * M log 0.002 M log for lens stellar masses, and /R 0.074 R F115W eff F115W eff
for the lens effective radius. 16 Finally, we compute the distribution of galaxy-galaxy lensing shear over all realizations for a given source-lens pair. The standard deviation around the mean of that shear distribution gives the uncertainty on the shear for that source-lens pair.
We use a similarly efficient Monte Carlo approach to propagate errors on 〈e〉, 2 and the star-galaxy cross correlation. When computing these summary statistics for any sample of N galaxies or stars, we first create 1000 random realizations of a size N each. For every observed galaxy, we randomly draw an ellipticity, position angle, and any other quantity of interest from a Gaussian with the mean equal to the fiducial catalog value and standard deviation equal to the empirical error from McGrath et al. (2025, in preparation). For stars, we do the same thing, but in lieu of errors on quadrupole moments, we use the standard deviation of e 1 and e 2 from the star sample itself as a measure of uncertainty on those quantities. For simplicity, we do not propagate errors on galaxy redshift or mass since our analysis is not done in fine z or M * intervals. Then, we can compute our summary statistics in all realizations and take the mean and standard deviation with the latter quantifying the uncertainty due to galaxy/star shape error propagation. It is almost always the case that the summary statistics are well constrained, e.g., µ 〈e〉 /σ 〈e〉 ≫ 1. However, this cannot, by itself, be used to assess the significance of an alignment signal. For that, we need a null hypothesis test to rule out randomly oriented galaxies, which we describe in Section 3.7.
Our Monte Carlo error propagation method gives a formal uncertainty for summary statistics computed on the scale of the entire survey. However, we only have one survey limited to a small (∼0.028 deg 2 ) part of the sky, so our shear variance 2 is almost certainly dominated by the cosmic variance. It is not our goal in this paper to constrain cosmological parameters or perform detailed comparisons to theory, so we do not attempt to estimate the cosmic variance uncertainty on 2 . Instead, we will simply place an upper limit on the weak-lensing shear experienced by high-redshift galaxies. We defer an estimation of the cosmic variance uncertainty to future weak-lensing analyses, which can empirically constrain the field-to-field variance using multiple "blank" JWST deep fields.
We can adapt the shear variance calculation of Equation (5) to compute the star-galaxy cross correlation as a check of systematics:
e e 1 . 7 i N j N i j gal star gal star 1 1 gal, star, gal star
For this, we measured the complex ellipticity of individual stars throughout CEERS using quadrupole moments as described in the Appendix. This provides an important null test for baselining possible PSF systematics, but we caution that we have only ∼130 stars throughout the survey footprint and typically only ∼1-2 stars per NIRCam chip, with ∼30% of chips having no star. To ensure that galaxies are only paired up with stars in their corresponding rest-frame optical filter, we will compute this separately for each NIRCam filter. Since we want to know the fractional contribution of the star-galaxy cross correlation to the total shear variance, we record the ratio of the norms / * e e gal star reg 2 for all individual regions before taking the average as in Equation ( 6). This approach of averaging ratios should be more robust especially on smaller scales where "shot noise" from the galaxy ellipticity distribution can dominate the variance between regions of the same size. Note that our galaxy shapes were measured by fitting a Sérsic model convolved with a global empirical PSF and that we do not attempt to perform local PSF corrections here (but see the Appendix). The star-galaxy cross correlation thus reflects any additional local PSF contamination unaccounted for by the global PSF.
For any sample of galaxies that show elevated 〈e〉 suggestive of alignments, we need to compare their observed 〈e〉 to the distribution of 〈e〉 expected under the null hypothesis that they are randomly oriented. For N observed galaxies, we create 1 million realizations, each of which is assigned N random complex ellipticity vectors. We randomly draw orientations f from a uniform distribution ( ) U 90 , 90 , which should "break" any alignments (if present). Since there is no good, universal distribution from which to randomly draw ellipticities, we fix the distribution of complex magnitudes e to the actual observed ellipticities of the galaxies. 17 This lets us compute the distribution of the average 〈e〉 under the null hypothesis that the N galaxies are randomly oriented. We then calculate the p-value for a given chip as the fraction of its random realizations where the null 〈e〉 exceeds the observed 〈e〉. This procedure is used both for our galaxygalaxy lensing candidates and when averaging over the orientations of all background galaxies in a given NIRCam chip, module, pointing, and the scale of the entire survey.
In this section, we present our results on galaxy-galaxy lensing in JWST-CEERS.
Figure 3 shows the joint distribution of galaxy-galaxy lensing shear and source ellipticity. 18 The ellipticity distribution of background galaxies is clearly nonuniform and biased toward elongated objects with e ∼ 0.6 on average. The ellipticity distribution of massive sources alone is flatter, 16 The redshift and mass uncertainties reflect the difference between the 84th and 16th percentile estimates from G. Barro et al. (2024). The size uncertainty from McGrath et al. (2025, in preparation) accounts for the formal Galfit error as well as systematics using the approach of A. van der Wel et al. (2012). 17 A uniform distribution is clearly not a good choice for high-redshift, lowmass bins, which are biased toward high e (V. Pandya et al. 2024), or for highmass spheroid-dominated bins, which are biased toward low e (e.g., Y.-Y. Chang et al. 2013). 18 Recall that γ = 0.5θ E /θ. The distribution of θ E itself for all source-lens pairs is roughly a log-normal with mean µ ∼ 0.4 and scale σ ∼ 1.1. It peaks at θ E ≈ 0.7 and extends to 7″. consistent with them being randomly oriented disks, but this implies that the low-mass sources are the preferentially elongated ones. Most pairs have very small shear with the mean being 〈γ〉 ≈ 0.02 consistent with what is expected for weak lensing (e.g., M. Oguri et al. 2012). Because the mean ellipticity of background galaxies is much larger than the typical expected shear, galaxy-galaxy lensing cannot be the primary driver for the preferential elongation of low-mass high-redshift galaxies.
However, there is a nonnegligible tail toward larger shears in excess of 0.1, which is beyond the conventional weaklensing regime. One object that is highly elongated with e ≈ 0.7 has an unusually large shear of γ ≈ 0.6. Our Bayesian nonparametric quantile regression with BART reveals that shear does not correlate with ellipticity for the majority of pairs below the 95% quantile of shear. Even for shears in the 99.7% quantile, the data do not show a strong correlation with ellipticity, and the Bayesian credible interval is large. At very high e > 0.7, we see a downturn in the median γ of the 99.7% shear quantile, but the uncertainty is large due to the small number of such extreme objects. We confirmed that the 19 objects with e > 0.85 and γ < 0.1 are in fact highly elongated galaxies and not artifacts (coincidentally, two of them are shown as prolate candidates in Figure 17 of V. Pandya et al. 2024). The tail of large shear pairs motivates looking for correlations with the source-lens tangential alignment angle, which we turn to next. There is a hint that high-shear pairs with γ > 0.2 tend to be tangentially aligned with larger ψ, but this is only significant at the ∼96.6% level (p = 0.0337) based on a two-sample Kolmogorov-Smirnov test using the unbinned, unweighted distributions of ψ. While this hypothesis test based on the 1D marginalized distribution of ψ is useful, it is not entirely appropriate since we are dealing with multidimensional data and really looking for correlations (E. D. Feigelson & G. J. Babu 2012).
Our Bayesian nonparametric quantile regression confirms that most pairs have low shear (the 95% quantile is γ ≲ 0.1), and that those low-shear pairs have no correlation with the alignment angle. The conditional distribution of the extreme ). The colored solid lines show the conditional distribution of shear on ellipticity in five quantiles from our nonparametric quantile regression with Bayesian additive regression trees: 10% (blue), 50% (orange), 90% (green), 95% (magenta), and 99.7% (red). The light and dark shaded regions reflect the 50% and 95% credible intervals, respectively. Most background galaxies are predicted to have very small shear, but there is a strong tail toward γ > 0.1. The data does not show a strong correlation between shear and ellipticity regardless of shear quantile. The projected ellipticity distribution of background galaxies is nonuniform and biased toward high values (top gray histogram). If we restrict to high-mass background galaxies, they show a flatter distribution (top cyan histogram) as expected for randomly oriented disks, meaning that it is the low-mass galaxies that are preferentially elongated.
99.7% quantile of shear shows hints of a positive correlation with the alignment angle as expected, but our Bayesian credible intervals (i.e., uncertainties) are large. At the low-ψ end, there is one source-lens pair with high γ ∼ 0.38. Visual inspection reveals that this is clearly a high-redshift dropout galaxy that only appears in redder NIRCam filters and is almost perfectly radially aligned with a massive foreground galaxy ∼2.8 away. For pairs in the 99.7% quantile of shear, when ψ is large, the shear tends to be larger by ∼5%. There is also a hint of heteroscedasticity in the data such that the scatter in shear increases with ψ. In other words, at small ψ, the 99.7% quantile of shear may simply be a tail of the log-normal distribution of shear of all pairs, but at large ψ, the extremes of the conditional shear distribution may comprise a broader tail. This would imply that, among the many tangentially aligned pairs, there may be some that are lensed, precisely those with high shear. With that said, our sample size is small, and this heteroscedasticity appears to be driven by one tangentially aligned source with high shear γ ∼ 0.63. We next inspect this and other sources with γ > 0.1 and ψ > 75 � , but note that our simple quantile regression method should be tested in the future on larger surveys with known strong lenses.
Figure 5 shows images of the 17 source-lens pairs that have γ > 0.1 and ψ > 75 � . We will refer to these as our tangentially aligned galaxy-galaxy lensing candidates. Table 1 lists their properties to facilitate follow-up observations. The cut on γ > 0.1 places these candidates in a shear regime that is an order of magnitude above the conventional weak-lensing limit. Many of them are elongated, and some even show arc-like distortions that may be suggestive of intermediate lensing. None of these are truly in the stronglensing regime (i.e., all have θ > θ E ) except possibly one, which we now discuss.
The highest-shear candidate is a ∼10 9.5 M ⊙ galaxy that is clearly elongated with e ∼ 0.72 and has a photometric redshift z ∼ 2.1. It is nearly perfectly tangentially aligned (ψ ≈ 88 � ) and lies within the Einstein radius of its associated lens (θ ∼ 3.75, θ E ∼ 4.75), making it our only strong-lensing candidate within the JWST-CEERS footprint. If its associated lens, which happens to be our most massive one with the highest σ * , satisfies our SIS assumption, then we expect another brighter image on the opposite side outside the Einstein radius with an image separation Δθ = 2θ E = 9.5. We do not find any obvious source there with a similar redshift as the main image. The massive foreground lens galaxy itself is spectroscopically confirmed to be at z ∼ 0.78, and our formal Monte Carlo uncertainty on the shear is only γ = 0.638 ± 0.044. If we overestimated its stellar velocity dispersion by a factor of 2, then, with all else fixed, θ E would be halved, and the source would no longer lie within the ). The colored lines show the conditional distribution of shear on tangential alignment angle in five quantiles from our nonparametric quantile regression with Bayesian additive regression trees: 10% (blue), 50% (orange), 90% (green), 95% (magenta), and 99.7% (red). The light and dark shaded regions reflect the 50% and 95% Bayesian credible intervals, respectively. Most pairs have small shear (right gray histogram), and there is no correlation with ψ even in the 95% quantile of shear (magenta curve). In contrast, there is a hint of an excess of tangentially aligned pairs at high shear with γ > 0.2 (top cyan histogram). There is also a hint of a positive correlation in the 99.7% shear quantile (red curve) wherein γ tends to be ∼5% higher for tangentially aligned pairs, but the uncertainties are large. We will refer to pairs with γ > 0.1 and ψ > 75 � as tangentially aligned lensing candidates.
Einstein radius, so a second image would not be expected (it would still have γ ∼ 0.3 in this case). Of course, another possibility is that the photometric redshift of our lensing candidate is very wrong, and it is instead physically associated with the lens as a satellite. Note that the rest of our results in this paper do not hinge on whether or not this candidate is confirmed (namely, the large-scale alignments in Section 5 are independent of this galaxy-galaxy lensing issue).
Figure 6 shows that all of our lensing candidates fall within twice the projected virial radius of their associated lens. Here, we have estimated the projected halo virial radius assuming R eff /R vir = 0.02 (A. V. Kravtsov 2013; R. S. Somerville et al. 2018). Importantly, the shear of our lensing candidates falls off with "impact parameter" /R vir proj as γ ∝ θ -1 , as it should. The scatter around this relation must come from additional θ E dependence in Equation (3) or due to our simple scatter-free approximation that R eff /R vir = 0.02. We can estimate the magnification due to an SIS lens as
, 8
where β = θ ± -θ E is the "true" source position, θ ± is the two image positions, and µ ± is their corresponding magnifications (R. Narayan & M. Bartelmann 1996). All of our sources, except possibly the one strong-lensing candidate, lie outside their Einstein radii, so there is only one image θ + , and these all have µ ∼ 1-2. Our strong-lensing candidate has µ + ∼ -3.7 for the inner image (where the negative sign means the image parity is flipped with respect to the true source), and the second image is predicted to be ∼1.5× brighter with µ -∼ 5.7.
Figure 7 shows the joint distribution of lens σ * , the angular diameter distance ratio D LS /D S , and the pair separation θ, all of which go into predicting the shear (Equation ( 3)). The lensing candidates are associated with preferentially more massive lenses, smaller on-sky separations, and higher D LS /D S since that maximizes the Einstein radius θ E for an SIS lens with a given σ * . In other words, the distribution of θ E is biased toward larger values (∼1.5-6″) for lensing candidates compared to the overall log-normal distribution given in footnote 18.
Figure 7 also plots the joint distribution of the source redshift, source apparent magnitude, and source Sérsic effective radius with the latter two in the NIRCam filter that most closely tracks the rest-frame optical. The lensing candidates appear well mixed with the general population of sources except that they are biased toward z ≳ 2, which just reflects the need for some minimal source-lens angular diameter distance so that θ E is maximized. The highestredshift candidate is at z ∼ 5, and all candidates have apparent magnitudes in the range ∼22-26 AB mag in their rest-optical filters. The candidates have rest-optical R eff ∼ 0.1-0.5, which requires adaptive optics or space-based telescopes for observational follow-up.
The possible excess of tangentially aligned source-lens pairs in the 99.7% quantile of shear in Figure 4 motivates averaging over the orientations of background galaxies in bins of galaxy-galaxy lensing shear. For galaxies with negligible (γ < 0.01) and weak (0.01 < γ < 0.1) shear, we expect the magnitude of their average complex ellipticity vector to be negligible, assuming they are randomly oriented, and there are no systematics. Figure 8 confirms this even when splitting by mass. However, at moderate (0.1 < γ < 0.2) and high (γ > 0.2) shear, we start to see evidence for a nonzero average complex ellipticity and hence preferred orientation. The standard errors come from our Monte Carlo error propagation method (Section 3.6) and show that the trend is well constrained modulo any systematics. We compare these observed averages to the null distribution of 〈e〉 assuming the galaxies are randomly oriented (Section 3.7). Given the small sample sizes, only the combined and low-mass subsamples in the moderate shear bin remain statistically significant at the >95% level (the p-values are reported above each point in Figure 8).
This follows the expectation that, as shear increases, there must be some residual orientation dictated by lensing. The complex average 〈e〉 ∼ 10%-30% is at least an order of magnitude above the conventional weak-lensing regime and unlikely to be due to PSF systematics (Appendix). These coherent alignments are surprising because our sources trace a number of different foreground lens galaxies. Of course, if this were repeated using galaxy-galaxy lensing candidates from multiple widely spaced surveys, we would expect 〈e〉 → 0 even in the moderate and strong shear regimes. But the fact that our galaxy-galaxy lensing candidates have correlated orientations within the relatively small (∼0.028 deg 2 ) CEERS footprint motivates a more detailed spatial analysis of alignments on larger scales, which we turn to next.
In this section, we present results on large-scale alignments by averaging over the complex ellipticities of background galaxies on multiple scales defined by the NIRCam instrument. We start with individual NIRCam chips (64″ × 64″), then individual modules ( × 2. 2 2. 2), followed by entire pointings ( × 2. 2 5. 1 with a 0. 7 gap), and finally the scale of the entire survey ( × 30 6 ). For this pilot study, restricting ourselves to the on-sky survey geometry imposed by NIRCam mitigates systematics from detector gaps and otherwise arbitrary binning. The Appendix quantifies the expected bias from PSF systematics.
Figure 9 shows that, on average, there are ∼50-100 background galaxies per arcmin 2 that satisfy our / > * M M log 9 10 cut in CEERS, which covers a total area of about ∼100 arcmin 2 (∼0.028 deg 2 ). This is sufficient for weak lensing and cosmic shear studies. First, we show the on-sky positions of our galaxy-galaxy lensing candidates with γ > 0.1 and ψ > 75 � compared to the foreground lenses and our overall background source sample. The galaxy-galaxy lensing candidates appear clustered near the southwest, which may help explain why we see correlated orientations in Figure 8. The lenses themselves appear roughly uniformly distributed throughout the field, although we showed in Figure 1 that there is an overabundance of lenses at z ∼ 0.75. There is generally at least one, if not multiple, z ∼ 0.75 foreground lenses near each lensing candidate. The projected R vir of our lenses are 0. 1 3. 5, i.e., extending over a single NIRCam chip or entire module.
Figure 9 also shows the magnitude of the average complex ellipticity when averaging over background galaxies in individual NIRCam chips. The average complex ellipticity is nonnegligible and clearly in excess of 〈e〉 ∼ 10% in many bins. This is an order of magnitude above the conventional weak-lensing regime and implies strong alignments in the ellipticities and orientations of background galaxies. The standard error on the mean 〈e〉 from our Monte Carlo error propagation is quite low, so in the next subsection, we will use statistical null tests to quantify the significance of these alignments.
Figure 10 splits the chip-scale "shear map" into three separate ones for high-mass, low-mass, and high-redshift (z > 2) low-mass background galaxies. There are a large number of NIRCam chips where high-mass galaxies show strong alignments with 〈e〉 > 10%. Despite the relative scarcity of high-mass galaxies, the standard error on 〈e〉 from our Monte Carlo error propagation is quite low, although we are likely dominated by systematics. The low-mass sample down to z > 1 shows nonnegligible 〈e〉 ≫ 0.01 similar to the combined map from Figure 9. Interestingly, restricting to just low-mass galaxies at z > 2 (in the predominantly elongated regime; A. van
Figure 11 quantifies the statistical significance of our results with the null hypothesis test described in Section 3.7. We find that the majority of chips do not have statistically significant alignments since p ≫ 0.05. However, there are multiple cells where the null hypothesis can be ruled out at >95% significance, including a handful at >99% significance. All of these have 〈e〉 ≳ 0.1, which, again, is at least an order of magnitude larger than the conventional weak-lensing regime. Interestingly, some of these significant regions are in the southwest where we saw the clustering of tangentially aligned galaxy-galaxy lensing candidates in Figure 9.
In addition to "internal" chip-scale significance, it is useful to think about the "map-scale" significance. Given that we have 80 NIRCam chips, we expect ∼80 × 0.05 ≈ 4 detections by random chance at the 95% confidence level assuming every bin is independent. We have more detections than this simple threshold in the combined (6), high-mass (6), and z > 2 lowmass (8) maps. However, the low-mass map has only three detected chips, and even though all of these are at ≳99% significance, on the scale of the map, this may be a statistical fluke. Formally, when we use the Benjamini-Hochberg false discovery rate and Bonferroni methods to "correct" the individual chip-scale p-values to account for the large number (80) of tests being done, none of the chips in any of the subsamples remain significant at the >95% level. However, these conservative statistical methods may not be using all of the available information (e.g., the clustering of chips with detections), so it is also useful to look at images of individual chips with alignments, which we turn to next. Figure 12 shows three example chips that have the highest statistical significance (p ≲ 0.01). The distribution of 〈e〉 under the null hypothesis of random orientations can be ruled out with ≳99% confidence given the large observed 〈e〉. Coherent alignments in the orientations of background galaxies can be Figure 6. Radial dependence of shear on "impact parameter" for all sourcelens pairs (small circles) and for our tangentially aligned lensing candidates with γ > 0.1 and ψ > 75 � (stars). All of our lensing candidates fall within twice the projected virial radius of their associated foreground lens, and their shear drops off as γ ∝ θ -1 . The color bar denotes the lensing magnification µ, which is ∼1-2 for most candidates. If our highest-shear object is truly strongly lensed, the inner image has |µ| ∼ 3.7, and the outer image is predicted to have µ ∼ 5.7 (small inset square).
seen with hints of circular polarization patterns. Whether these alignments are due to lensing from foreground substructure, intrinsic alignments, systematics, or pure random chance remains to be seen and will require detailed follow-up spectroscopy and lens modeling. The Appendix shows that PSF uncertainties are unlikely to explain these alignments. Another way to get a handle on such systematics is to search for alignments on even larger scales, which we turn to next.
On large scales, assuming background galaxies are randomly oriented, we should find fewer regions with statistically significant alignments unless lensing or systematics are playing a role. Here, we increase the map "pixel" size from the scale of an individual NIRCam chip (64″ × 64″) to an individual NIRCam module ( × 2. 2 2. 2 comprising four chips). 19 Figure 13 identifies a handful of NIRCam modules with statistically significant alignments at the >95% level using our null test described in Section 4.5. A few of these have module-scale significance at the >99% level. Given that we have 20 such modules, we expect 20 × 0.05 ≈ 1 such detection by random chance at the 95% level. We have two to three modules with detections for each subsample, so we pass this simple threshold. Formally, the Benjamini-Hochberg and Bonferroni corrections lead to p > 0.05 for all modules except one in the z > 2 low-mass map, which remains significant at the ∼98% level (p = 0.01882).
Figure 14 shows the module with the most significant alignments in the orientations of low-mass galaxies at z > 2. Even on these larger × 2. 2 2. 2 scales, coherent alignments can be seen. Some of these alignments appear like linear "chains" whereas others arise from nearly circular arrangements of background galaxies. The latter motivates future decomposition of the shear map into E-and B-mode polarizations to assess whether this signal is due to lensing, intrinsic alignments, or systematics (e.g., R. G. Crittenden et al. 2001Crittenden et al. , 2002)).
Here, we increase the map "pixel" size to even larger scales of an entire NIRCam pointing, which encompasses two × 2. 2 2. 2 modules separated by a 0. 7 gap. Figure 15 shows that we continue to find one to two pointings for each subsample with significant alignments at the >95% level. Two of these are significant at the >99% level: one in the southwest corner of the high-mass map and another in the northwest corner of the z > 2 low-mass map. Since we have 10 pointings, we expect 10 × 0.05 ≈ 0.5 pointings with a detection by random chance alone. We are above this simple threshold for all subsamples, but the more formal Benjamini-Hochberg and Bonferroni methods lead to corrected p-values in excess of 0.05 for all pointings. However, in addition to these . Demographics of our lensing candidates relative to all source-lens pairs. Left: joint distribution of SIS lens velocity dispersion, angular diameter distance ratio D LS /D S , and on-sky pair separation θ for all source-lens pairs (small gray squares). These three quantities set the level of shear. Darker colors correspond to smaller pair separations. The large crosses are for our lensing candidates with γ > 0.1 and ψ > 60 � . Lensing candidates are preferentially found around more massive lenses (higher σ * ), at smaller pair separations (darker colors), and at greater angular diameter distance from their nearest lens, which maximizes the Einstein radius θ E . Right: joint distribution of source redshift, source apparent magnitude, and source Sérsic effective radius with the latter two measured in the NIRCam filter that most closely tracks the rest-frame optical. Lensing candidates roughly track the underlying population of source-lens pairs except they are biased toward z ≳ 2 to maximize the angular diameter distance to our lenses at z < 1. Their rest-optical sizes are ∼0.1-0.5 and apparent magnitudes ∼22-26 AB mag.
conservative statistical tests, it is still instructive to look at images of pointings with detections.
Figure 16 shows an image of the southwest pointing with significant alignments of high-mass galaxies at z > 1. Largescale alignments are clearly obvious by eye in both modules of this pointing. Many of these galaxies also show circular alignment patterns, which reinforces the need to decompose the shear map into E-and B-mode polarizations, which can help constrain whether this is due to lensing, intrinsic alignments, or systematics. More generally, our results motivate computing galaxy-shear and shear-shear correlation functions in "blank" JWST deep fields like CEERS that are far away from obvious, bright foreground clusters. Such an analysis would naturally capture the dependence of the alignment signal as a continuous function of spatial scale and offer constraints on cosmology and the foreground lens mass. However, this is nontrivial and requires careful consideration of survey geometry, so we leave it for the future.
Figure 17 shows that, on the scale of the entire field ( × 30 6 ), we do not find any statistically significant alignments (p > 0.05). This makes sense since, over such a large area, background galaxies should be randomly oriented, and lensing must be weak. It also confirms the lack of systematics in the data and our shape measurements, at least on such large scales. Note that we also found a similar lack of net alignments in Figure 8 for galaxy-galaxy lensing pairs with negligible shear, which comprise most of our background galaxies distributed throughout the entire field.
Figure 18 shows the redshift distributions of background galaxies in the NIRCam chips, modules, and pointings where we found significant alignments (p < 0.05 based on Figures 11,13,and 15). Every region has its own distinct overall redshift distribution as shown with the different shaped violins. In many regions, there are several galaxies that overlap in redshift, which suggests clustering in redshift space. However, the uncertainties on ( ) + z log 1 10 are typically of the order ( ) / / + z 1 ln10 0.01 z (see Section 3.6). At z ∼ 2, this translates to σ z ∼ 0.07, which implies an angular diameter distance uncertainty of ≳30 proper Mpc. The maximum transverse (on-sky) separation probed by the overall CEERS footprint is only ∼15 physical Mpc at z ∼ 2 (individual chips, modules, and pointings span only ∼0.5, ∼1, and ∼2.5 proper Mpc at z ∼ 2, respectively). Thus, the redshift uncertainties are likely too large to associate galaxies along the line of sight, and we have to wait for future spectroscopic follow-up (as also originally argued by V. Pandya et al. 2019). Without precise redshift clustering constraints, the background galaxies in any region can be assumed to lie along widely separated largescale structures and thus may not be expected to show strong intrinsic alignments. We thus next consider whether the alignments vary as a function of scale in the same way expected for cosmic shear. . Average ellipticity and orientation as a function of galaxy-galaxy lensing shear. Left: magnitude of the average complex ellipticity vector in increasing bins of shear from left to right, negligible (γ < 0.01), weak (0.01 < γ < 0.1), moderate (0.1 < γ < 0.2), and strong (γ > 0.2). All points reflect the mean and standard error from our Monte Carlo error propagation method (Section 3.6). Our combined background sample is shown in black, high mass only in red, low mass only in blue, and z > 2 low mass in green. At small shear, the average ellipticity is very small as it should be for randomly oriented galaxies. At larger shear, we find a significantly larger average residual ellipticity. The p-value from our null hypothesis test is written above each point. Given the small sample sizes, only the two moderate shear points enclosed in circles are significant at the >95% level. Right: complex ellipticity vectors in bins of shear for individual galaxies and the complex average of the combined sample (black lines). For visualization, the symmetric complex ellipticity vectors have been "folded" back onto the range -90 � to 90 � measured east of north (up). The magnitude of the average complex ellipticity vector is very small for the negligible and weak shear bins, but is clearly nonzero with a preferred orientation for the two higher-shear bins. details about the latter). Recall that 〈e〉 gives the average orientation and ellipticity of all galaxies in some region whereas 2 quantifies the degree of correlation between pairwise shapes (as detailed in Section 3.5). In this context, since foreground stars should not be sheared (unlike highredshift galaxies), they serve as a null test for PSF systematics by providing a "floor" on 〈e〉 and 2 . This is complementary to our null test for statistical significance in previous subsections.
Using our combined background galaxy sample without splitting by mass, redshift, or alignment significance, we find that 〈e〉 drops from an average of ∼8% at the NIRCam chip scale to ∼5% for NIRCam modules and ∼3% for NIRCam pointings. If we restrict ourselves only to chips, modules, and pointings where the null hypothesis of randomly oriented galaxies could be ruled out at >95% significance, then 〈e〉 is somewhat larger due to the alignments, as expected. The exact same calculation the stars gives 〈e〉 that is almost constant with scale but drops monotonically from ∼2% to 2.5% for short-wavelength NIRCam filters (F115W, F150W, F200W) to ∼0.5%-1.5% for long-wavelength NIRCam filters (F277W, F356W, F444W). This is several times lower than our 〈e〉 measured for galaxies at the chip and module scales, and to a lesser extent for pointings. This implies that the alignments we have detected on these smaller scales cannot be attributed to percent-level PSF systematics (see the Appendix for more justification). In contrast, on the scale of the entire survey, the residual 〈e〉 ∼ 0.9% of galaxies is comparable to or even exceeded by the 〈e〉 of PSF stars, which is consistent with the alignments vanishing on large scales as they should.
The middle panel of Figure 19 similarly shows that the shear variance drops from × 4 10 2 3 at chip scales to 10 -3 for modules and 6 × 10 -4 for pointings. The exact same calculation for the PSF stars leads to 2 that is almost constant with scale and drops nearly monotonically from 4 × 10 -4 for the bluest filter (F115W) to ∼1-3 × 10 -5 for the reddest filter (F444W). Thus, pairs of galaxies have significant shear correlations above that expected from PSF systematics on the scale of chips, modules, and pointings. In contrast, on the scale of the entire survey, 3 10 2 5 for galaxies, which is comparable to or even smaller than that of the stars. Thus, the shear variance on the survey scale is consistent with being zero since it is so low as to be in the PSF systematicsdominated regime.
If our alignments were due to cosmic shear, we would expect a typical 3 10 2 4 on chip scales that decreases to ∼3 × 10 -5 on the scale of the survey (based on Figure 7 of the review by A. Refregier 2003). Our measured shear variance is an order of magnitude larger at the chip scale and several times larger at the module and pointing scales, although consistent on the survey scale. The right panel of Figure 19 shows that the contribution of the star-galaxy cross correlation is of an order ∼10% the shear variance on the chip scale, which means that star-galaxy alignments must be weaker than galaxy-galaxy alignments on these small scales. However, the fractional contribution of the star-galaxy cross correlation becomes more significant on larger scales where the shear signal itself is lower and thus in the systematicsdominated regime. Thus, our measured shear variance is an upper limit, and it implies an rms shear 2 , which is still too small to explain the preferentially high ellipticity e ∼ 0.4-0.7 of early low-mass galaxies. The actual shear is likely even smaller, and future studies that correct galaxy shapes for the local rather than global PSF may be able to overcome systematics and measure a much weaker cosmic shear signal expected in the data that we cannot.
Table 2 gives alignment summary statistics for each of the four subsamples in all 111 regions (entire survey, 10 pointings, 20 modules, 80 chips).
We presented evidence for large-scale alignments of highredshift galaxies in a "blank" JWST deep field far away from any obvious foreground cluster. Galaxies at z > 1 with / > * M M log 9 10
appear to be aligned on the scale of multiple NIRCam chips (64″ × 64″), modules ( × 2. 2 2. 2), and pointings ( × 2. 2 5. 1) throughout the JWST-CEERS survey footprint. When averaging over background galaxies in these regions, the norm of the complex ellipticity vector is often 〈e〉 ≳ 10%, which is at least an order of magnitude above the conventional weak-lensing regime. Many of these chips, modules, and pointings reveal circular alignment patterns that are suggestive of nonrandom effects and motivate follow-up E/B-mode polarization decomposition. In addition, our tangentially aligned galaxy-galaxy lensing candidates, including one possible strong lens, tend to cluster in the southwest (Figure 9). This clustering of galaxy-galaxy lensing candidates on scales of ∼0°.1 as well as the detection of alignments in multiple regions on scales up to × 2. 2 5. 1 equates to several Mpc at z ∼ 0.75 where we found an overdensity of massive foreground lens galaxies (Figure 1). It is plausible that a cluster, protocluster, or filament at z ∼ 0.75 may be responsible for the lensing in which case detailed follow-up modeling may help us learn something about the intrinsic 3D geometry and lensing mass profile of this overdensity (e.g., I. Kovner 1987; C. R. Keeton et al. 1997).
On the other hand, we cannot rule out intrinsic alignments in the background galaxies (D. Kirk et al. 2015;R. Mandelbaum 2018;C. Lamman et al. 2024). V. Pandya et al. (2019) showed that if early low-mass galaxies are intrinsically prolate, then they are expected to show strong intrinsic alignments with each other as they form along cosmic web filaments. Since our analysis is not done in bins of the source redshift, we are presumably averaging over this, and therefore, our signal should not be driven by intrinsic alignments. V. Pandya et al. (2019) did not detect the expected intrinsic alignments and claimed that it was due to a lack of spectroscopically confirmed background pairs in HST-CANDELS (N. A. Grogin et al. 2011;A. M. Koekemoer et al. 2011). However, they also did not use the complex ellipticity formalism employed here, so the issue is worth revisiting in light of our results. The fact that we are detecting coherent alignments on the scale of entire NIRCam pointings ( × 2. 2 5. 1) and finding 〈e〉 ≳ 10% in multiple areas spread across the entire ∼0.3 deg extent of the survey (several Mpc at z ∼ 0.75) does point toward lensing. But because we lack spectroscopic redshifts for most of our background galaxies, we cannot precisely identify highredshift pairs to robustly constrain intrinsic alignments (see Figure 18).
Of course, there could be other systematics at play. It is unlikely that we are contaminated by satellite-central pair alignments (C. M. Hirata et al. 2004) because moderate/strong galaxy-galaxy shear requires maximizing the angular diameter distance between the source and lens, which implies very different photometric redshift distributions. The Appendix shows that our PSF systematics are at the few percent-level, which, while inadequate for traditional weak lensing, are an order of magnitude lower than our 〈e〉 ≳ 10% from averaging over the orientations of background galaxies on the chip scale. Thus, PSF uncertainties are unlikely to explain our alignments in terms of 〈e〉 but are prohibitively large for measuring the precise amplitude of the cosmic shear variance signal 2 (Figure 19). Astrometric misalignments could cause distortions that produce spurious shear signals (K. Finner et al. 2023b), but the CEERS imaging we use is already tied to Gaia (M. B. Bagley et al. 2023
), and we have visually inspected all of our galaxies, so this is unlikely. Future decomposition of the shear field into E-and B-mode polarizations can help constrain some of these systematics including signatures of intrinsic alignments.
We note that JWST-CEERS is only the latest in a long line of multiwavelength observations of EGS (E. J. Groth et al. 1994) whose early HST-WFPC2 observations enabled the first detection of cosmic shear from space in this very same field (J. Rhodes et al. 2000Rhodes et al. , 2001)). Those authors found mean shear values similar to ours of ∼10% using ∼50 background galaxies in many 1.27 × 1.27 arcmin 2 regions along the strip (see Figure 1 of J. Rhodes et al. 2001). After carefully subtracting off systematics, they estimated the shear variance to be 0.018 3 10 2 2 4 on the scale of a single HST-WFPC2 chip ( × 1. 27 1. 27). This is an order of magnitude lower than our 4 10 2 3 on the slightly smaller scale of a NIRCam chip (64″ × 64″). The discrepancy is likely due to PSF systematics on our end (Figure 19), which is why we consider our measurement of shear variance to be an upper limit rather than a detection. However, differences in source selection and rest-frame optical versus rest-frame ultraviolet morphology (HST-WFPC2 probed the latter) may also play a role. Future efforts to correct for the complicated spatially varying PSF of JWST should enable precise measurements of the amplitude of the cosmic shear signal in multiple "blank" JWST deep fields. These can then be averaged to mitigate the cosmic variance and help constrain the cosmological parameters σ 8 and Ω M (as has been done from the ground and with HST; D. J. Bacon et al. 2000;N. Kaiser et al. 2000; D. M. Wittman et al. 2000;N. Pirzkal et al. 2001;J. Rhodes et al. 2001J. Rhodes et al. , 2004;;H. Hämmerle et al. 2002; J. M. Miralles et al. 2002;T. Schrabback et al. 2007). Indeed, the shallower but ∼10× larger COSMOS-Web survey is designed in part to enable this kind of measurement with JWST (C. M. Casey et al. 2023), building off of the long history of cosmic shear studies in the HST-COSMOS field (A. Leauthaud et al. 2007; R. Massey et al. 2007b; J. D. Rhodes et al. 2007).
EGS has benefited greatly from dedicated panchromatic imaging and spectroscopic redshift surveys such as AEGIS, DEEP2, and DEEP3 (M. Davis et al. 2003Davis et al. , 2007;;S. M. Faber et al. 2003;M. C. Cooper et al. 2007M. C. Cooper et al. , 2012;;J. A. Newman et al. 2013). This wealth of data led previous groups to identify a number of groups and clusters in EGS between z ∼ 0.4-1.4, some of which are located at z ∼ 0.75 consistent with our claimed overdensity of lenses there (e.g., see Figure 6 of B. F. Gerke et al. 2012). The galaxy color-magnitude bimodality and color-density relations are also observed for EGS galaxies at z ∼ 0.75, which suggests the presence of rich groups (M. C. Cooper et al. 2007;S. M. Faber et al. 2007; and see also later work by V. Pandya et al. 2017a using HST-CANDELS). The abundance and clustering of X-ray-selected active galactic nuclei also point toward a number of massive groups in EGS at z ∼ 0.7-1.4 (A. L. Coil et al. 2009). We note that our most massive lens has a spectroscopic redshift of z ∼ 0.78, and although its σ * ∼ 580 km s -1 is very high compared to that of the most massive local galaxies (C.-P. Ma et al. 2014;V. Pandya et al. 2017b; J. E. Greene et al. 2019), it seems consistent with the tail of high σ * LRGs out to z ∼ 0.7 (D. Thomas et al. 2013). This massive lens is also associated with our only strong-lensing candidate (Figure 5). Spectroscopic constraints on the stellar kinematics and environment of this massive galaxy combined with secure redshifts for background sources would enable more sophisticated source-lens reconstruction. Finally, L. A. Moustakas et al. (2007) conducted a visual search for strong lenses in EGS using ∼650 arcmin 2 of HST-ACS imaging. They found three (an Einstein Cross, one with two pairs of arcs, and one with a single pair of arcs), but unfortunately those are all outside of the JWST-CEERS footprint, which covers only ∼100 arcmin 2 of EGS. However, they also found that each of these lenses Figure 11. Statistical significance of chip-scale "shear maps" for all background galaxies combined (left column), high-mass sources (second from left column), lowmass sources (second from right column), and z > 2 low-mass sources (right column). The top row shows the p-value in individual 64″ × 64″ chips calculated as described in the text. There are multiple regions with "internal" chip-scale alignments at the >95% confidence level. The middle row shows the average complex ellipticity magnitude 〈e〉 (colors) and phase (lines in the "north-up" frame) for these statistically significant bins alone. Note how 〈e〉 ≳ 0.1 in all significant cases suggestive of strong alignments. Our galaxy-galaxy lensing candidates (cyan crosses and gold star) tend to be clustered near the southwest where there are multiple chips with coherent alignments. required ∼10% external shear, which supports our claim that there may be significant cosmic shear throughout CEERS leading to 〈e〉 ∼ 0.1.
Our study suggests that "blank" JWST deep fields may provide complementary constraints on lensing and intrinsic alignments beyond what is traditionally available from massive cluster surveys, provided that the systematics are better understood. For example, the high resolution of JWST imaging may allow one to study higher order distortions due to lensing such as flexion (which, to quote P. Schneider & X. Er 2008, happens when "weak lensing goes bananas"). The prospect of searching for overdensities in "blank" fields is tantalizing because one of the strengths of lensing is that it is sensitive to mass concentrations even if it is "dark." JWST will also enable the selection of lower-mass, higher-redshift sources for weak lensing, which, while improving number statistics, may introduce new biases due to the unknown intrinsic shapes and intrinsic alignments of the early galaxy population. On the galaxy-galaxy lensing side, P. Holloway et al. (2023) used mock data to show that JWST deep fields should expect to have ∼25-65 strongly lensed systems. One new Einstein ring has already been detected in COSMOS-Web (W. Mercier et al. 2024;P. van Dokkum et al. 2024). We verified that if we had a source-lens pair in CEERS with parameters similar to the COSMOS-Web Einstein ring, we would have identified it. Assuming rings/arcs/clumps were optimally deblended, this implies there are no Einstein rings in CEERS. 20 Given the small sizes and faint magnitudes of many of our tangentially aligned source-lens pairs (Figure 7), follow-up observations may be challenging but required to enable confirmation and more detailed lensing modeling.
Looking to the near future, the Roman Space Telescope, with its ∼0.28 deg 2 field of view and ∼0.1 resolution, has the potential to dramatically transform our understanding of lensing, intrinsic alignments, and origin of low-mass elongated Figure 12. Three example NIRCam chips in which the null hypothesis of random orientations can be ruled out at ≳99% significance when averaging over the combined background sample (leftmost column of Figure 11). A 2″ rectangle is plotted at the location of each background galaxy denoting the orientation of its major axis. The bottom three panels of each column show the distribution of 〈e〉 under the null hypothesis of random orientations (top), distribution of ellipticities (middle), and distribution of position angles (bottom). Coherent alignments in the orientations of background galaxies can be seen. 20 We repeated our search allowing for massive lenses at any redshift and background sources down to / = * M M log 8 10 but did not find any convincing strong-lensing candidates in JWST-CEERS.
There are a few modules with alignments at the >95% significance level for each subsample, with many showing 〈e〉 ∼ 10% even on these larger scales. Those modules do not, however, typically overlap with the galaxy-galaxy lensing candidates. 13). Again, coherent alignments can be seen even on these larger × 2. 2 2 2 scales, with hints of circular patterns that motivate future E/B-mode polarization decomposition and weak-lensing mass reconstruction. ). As expected, we do not find any statistically significant alignments implying that the background galaxies are randomly oriented over such large scales. and 15). The overall redshift distributions are visualized as violins, and each individual galaxy redshift is denoted by a thin horizontal stripe. The thick overlapping stripes suggest that galaxies in many regions are clustered in redshift space. However, the typical fractional photometric redshift uncertainty is indicated below each violin and is generally too large to precisely identify overdensities. calculation of galaxy-shear and shear-shear correlation functions over much larger areas than possible with HST or JWST. Multiple such Roman deep fields spread across the sky would help mitigate the cosmic variance that has plagued the field for decades (P. Madau & M. Dickinson 2014) and allow us to test whether the alignments are indeed due to lensing since the foreground mass distribution should vary across the sky. We caution that the current plan for the Roman High Latitude Wide Area Survey over ∼2000 degfoot_7 is only designed to reach 26.5 AB mag for point sources (M. A. Troxel et al. 2021;Y. Wang et al. 2022;M. Montes et al. 2023). A rule of thumb is that the completeness limit for extended high-redshift galaxies is ∼2 mag fainter than the point-source limit (V. Pandya et al. 2024), so a deeper imaging component is necessary for our science case. Note that Euclid, with its sensitivity and ∼0.2 resolution, is not expected to be complete to such low-mass galaxies beyond z ∼ 0.5 even in its Deep Surveys spanning ∼50 deg 2 (Euclid Collaboration et al. 2022).
Despite the evidence for galaxy-galaxy lensing and largescale alignments with 〈e〉 ∼ 10%, the fact that most of our background sources have much higher ellipticities of e ∼ 0.4-0.7 (top panel of Figure 3) implies that gravitational lensing cannot be primarily responsible for their elongation. Thus, we are led back to the original question that motivated this study: why are early low-mass galaxies preferentially elongated as observed by HST (L. L. Cowie et al. 1995;D. M. Elmegreen et al. 2005;S. Ravindranath et al. 2006;A. van der Wel et al. 2014;H. Zhang et al. 2019) and JWST (V. Pandya et al. 2024)?
The remaining explanations for this puzzle range from the mundane to the exotic. There may still be a surface brightness detection bias against rounder, face-on disks (A. Loeb 2024). V. Pandya et al. (2024) claimed that JWST-CEERS is sufficiently complete, but deeper surveys have not yet been checked. Relatedly, we may be seeing elongated star-forming protobars at the centers of extremely low surface brightness disks. Alternatively, the elongated shapes reflect tidal debris from ongoing mergers. Finally, early low-mass galaxies may not start out as disks as commonly assumed but rather as triaxial/prolate structures that reflect the cosmic web filaments in which they form (D. Ceverino et al. 2015;M. Tomassetti et al. 2016;V. Pandya et al. 2019). V. Pandya et al. (2024) emphasized that the stellar masses of early elongated galaxies at z ∼ 2-3 are consistent with them being Milky Way progenitors, broadly defined, implying that our own Galaxy may have been elongated in its past. There are hints of this early elongation from Galactic archeology (R. P. Naidu et al. 2021), and the recent discovery of a strongly lensed, elongated, clumpy Milky Way-like progenitor at z ∼ 8.3 evokes connections to chain galaxies (L. Mowla et al. 2024; see also A. H. Zonoozi et al. 2019).
It is imperative that we try to rule out the prolate/triaxial interpretation because so much of our current understanding of galaxy formation depends on them starting out as disks due to tidal torques and angular momentum conservation (H. J. Mo et al. 1998). Although prolate galaxies can form in ΛCDM, this has only been seen in some cosmological zoom-in simulations (D. Ceverino et al. 2015;M. Tomassetti et al. 2016), and there is no consensus on subgrid models for uncertain baryonic physics (e.g., R. S. Somerville & R. Davé 2015). What we really want to know is the largescale clustering, orientation, dynamical stability, and cosmological evolution of prolate galaxies, but large-volume simulations typically do not have the resolution required to robustly predict the internal dynamics and therefore 3D shapes of early low-mass galaxies (e.g., A. Pillepich et al. 2019). All of this invites an exploration of more exotic scenarios such as alternatives to cold dark matter. For example, it has already been shown that warm and axionic (fuzzy) dark matter naturally leads to more elongated halos and therefore possibly more elongated galaxies at early times as observed (P. All points denote averages and standard errors. Solid black lines show results for galaxies in all regions whereas dashed black lines are only based on regions where the null hypothesis of randomly oriented galaxies could be ruled out at >95% significance. Colored lines show the exact same calculations for PSF stars in each filter. Both 〈e〉 and 2 are above the floor set by stars on smaller scales, but drop into the systematics-dominated regime on larger scales. The shear variance in particular is several times larger than the typical value from cosmic shear (gray shaded region). The fractional contribution of the star-galaxy cross correlation to the shear variance is subdominant on the chip scale but becomes significant on larger scales where the expected shear signal is lower. Note that we do not cross correlate stars and galaxies in F277W because that filter is not used. This implies that our measured shear variance is an upper limit, but even the large value on the chip scale only implies an rms shear of V. Pandya et al. (2024) claimed that stellar kinematics will be required to definitively distinguish between these interpretations. However, our analysis suggests a new test: if galaxy-shear and shear-shear correlation functions can be measured over large deep fields for ( ) / * M M log 9 10 galaxies out to z ∼ 2, then we will be able to constrain whether these early elongated galaxies show strong intrinsic alignments and trace cosmic web filaments at high redshift as predicted by V. Pandya et al. (2019). The Euclid Deep Surveys are not expected to detect and resolve such low-mass galaxies beyond z ∼ 0.5 (Euclid Collaboration et al. 2022), but the Roman Space Telescope may be able to do so. We therefore strongly recommend that a Roman Deep Field (A. Koekemoer et al. 2019) be planned to enable this potentially transformative science: Are early elongated galaxies reliable probes of lensing, do they represent an unrecognized source of significant additive bias, and can they tell us anything fundamentally new about cosmology?
We used data from JWST-CEERS (S. L. Finkelstein et al. 2023;E. J. McGrath et al. 2025, in preparation) to explore an idea not previously considered in the literature: Are early lowmass galaxies preferentially elongated because of gravitational lensing? First, we investigated galaxy-galaxy lensing for which we selected 76 massive foreground lens galaxies at z < 1 and 3848 background sources at z > 1 with / > * M M log 9 10
. Above this mass limit, CEERS has, on average, ∼50-100 background galaxies per arcmin 2 over its ∼100 arcmin 2 footprint, making it a good test bed for lensing studies in "blank" JWST deep fields. For each source, we assigned the nearest on-sky massive lens and estimated the shear γ assuming an SIS lens model as well as the tangential alignment angle. Second, we looked for alignments on larger scales by averaging over the orientations of background galaxies on the scale of individual NIRcam chips (64″ × 64″), modules ( × 2. 2 2. 2), and pointings ( × 2. 2 5. 1) across the survey. Our results are summarized as follows.
1. Galaxy-galaxy lensing cannot be the primary driver for the elongated appearance of most early low-mass galaxies because our typical predicted shear is of an order of only γ ≈ 1%. This is much lower than the typical ellipticity e ∼ 0.4-0.7 of high-redshift galaxies (Figure 3). However, there is a broad tail toward larger shears in excess of 10%. We use nonparametric quantile regression with BART to show that there is a hint of an excess of tangentially aligned source-lens pairs with such high shear (Figure 4). We identify 17 tangentially aligned lensing candidates, only one of which may truly be in the strong-lensing regime (Figure 5 and Table 1). These galaxy-galaxy lensing candidates are clustered in the southwest region of the survey (Figure 9) and show evidence that their orientations are correlated (Figure 8). 2. We find evidence for coherent large-scale alignments when averaging over the orientations of background galaxies in multiple NIRCam chips (64″ × 64″), modules ( × 2. 2 2. 2), and pointings ( × 2. 2 5. 1). We can rule out the null hypothesis of random orientations at the ≳99% confidence level for multiple individual regions (Figures 11,13,and 15,and Table 2). The number of such regions is small on the scale of the survey, so formally, the detections may be due to random chance, but the imaging clearly reveals nonrandom alignment patterns (Figures 12,14,and 16). On the chip scale, the average complex ellipticity 〈e〉 ≳ 10% and shear variance 4 10 2 3 are an order of magnitude above the conventional weak-lensing regime (Figure 19). We consider these to be upper limits due to PSF uncertainties (Appendix), intrinsic alignments, cosmic variance, and other lensing systematics. The maximum implied "cosmic shear" is still only 2 , much lower than the ellipticity of early low-mass galaxies. 3. We speculate that the large-scale alignments may be due to lensing from a foreground protocluster or filament spanning several Mpc at z ∼ 0.75 where we found an overabundance of massive lens galaxies (Figure 1). Future spectroscopic surveys of the regions with net alignments are needed to confirm whether galaxies are clustered in redshift space and intrinsically aligned along the same high-redshift large-scale structures (Figure 18). We also strongly recommend the planning of a deep field with the forthcoming Roman Space Telescope whose sensitivity, resolution, and 0.28 deg 2 field of view will uniquely enable the calculation of galaxy-shear and shear-shear correlation functions for elongated galaxies with ( ) / M M log 9 10 out to z ∼ 2. This will provide a novel way to constrain the intrinsic shapes of early elongated galaxies, which, if they are Note. The central R.A. and decl. of each region are in decimal degrees. N is the number of galaxies. We give the p-value from our null test, magnitude of the average complex ellipticity 〈e〉, and the associated phase angle -90 � < 〈f〉 < 90 � defined east of north. All uncertainties are standard errors from our Monte Carlo method.
We give these values for all four subsamples denoted by the superscript in the column name: all, high mass, low mass, or "early" for z > 2 low-mass galaxies. The shear variance and star-galaxy cross correlation are given only for the combined sample. The full table is available for download from the journal.
(This table is available in its entirety in machine-readable form in the online article.)
forming along filaments, are expected to show strong intrinsic alignments (V. Pandya et al. 2019). This would also help calibrate any bias from this population for weak-lensing analyses.
( ¯) ( ) ( ) ( ) ( ) ( ) = W W Q y y x y I x y x y I x y , , , , , A 4 yy 2 ( ¯)( ¯) ( ) ( ) ( ) ( ) ( ) = W W Q x x y y x y I x y x y I x y , , , , . A 5 xy
Finally, this lets us assign to every star (i.e., PSF) a complex ellipticity
6 xx yy xy xx yy xx yy xy 1 2 2
This is analogous to the complex ellipticity that we assigned to every galaxy in Equation (4) except here we are using quadrupole moments. The complex magnitude = + e e e
1 2 2 2
gives us the PSF ellipticity, and the complex phase f = 0.5arctan2(e 2 , e 1 ) gives us the orientation. The size is defined as = + R Q Q xx yy . As an example, Figure 20 shows the global empirical PSF in each filter from S. L. Finkelstein et al. (2023) along with our quadrupole moments. As expected, the ellipticities are very small with e ≲ 0.02. The size R translated to a Gaussian FWHM, as is common practice, yields similar values as S. L. Finkelstein et al. (2023) with the resolution decreasing from ∼0.08 in F115W to ∼0.13 in F444W. Results for individual stars are similar. Before proceeding, we caution that, although this kind of quadrupole analysis is standard in weak lensing, the NIRCam PSF is clearly very complicated (i.e., not a simple Gaussian or Airy disk). The features outside the "core" of the PSF are due to JWST's hexagonally segmented primary mirror and the "tripod" structure that supports the secondary mirror (J. Rigby et al. 2023). Other recent JWST studies (K. Finner et al. 2023a;S. Cha et al. 2024; M.-Y. Zhuang & Y. Shen 2024) also use quadrupole moments or fit an elliptical 2D Gaussian to the "core" of the PSF and arrive at similar conclusions as us, but we recommend a more detailed follow-up analysis.
Figure 21 shows the distribution of our individual stars and the global PSF in the complex (e 1 , e 2 ) plane. Nearly all stars in every filter have e < 0.05, i.e., the PSF is very round as expected. The short-wavelength NIRCam filters (F115W, F150W, F200W) have average components 〈e 1 〉 ∼ 0.02 and 〈e 2 〉 ∼ -0.01, and there is clearly a bias toward the lower right quadrant. The long-wavelength NIRCam filters (F277W, F356W, F444W) have substantially rounder PSFs as evidenced by their smaller 〈e 1 〉 ≲ 0.01 and 〈e 2 〉 ∼ ±0.001. These percent-level PSF systematics are unlikely to explain our much larger observed 〈e〉 ≳ 0.1 when averaging over galaxies in individual NIRCam chips, modules, and pointings (Figure 19). At most, they would lead to an additive bias in 〈e〉 of a few percent, not tens of percent.
Figure 22 shows a map of the PSF ellipticity and orientation across the entire CEERS footprint using our individual stars. Most stars have very small ellipticity, but there are a handful with e ∼ 0.05-0.08. The cores of these stars do look slightly elliptical, and it is not clear whether they are outliers since other stars near them show smaller ellipticities. The orientations of PSF stars in the long-wavelength filters appear random due to their very small ellipticities. In contrast, for the shortwavelength filters, there is an overall pattern of many stars pointing toward the upper left of each panel (45 � east of north). However, again, since the individual PSF ellipticities are very small, their additive bias due to these alignments cannot contribute more than a few percent to our much larger observed 〈e〉 > 10% from averaging over background galaxies.
Finally, Figure 23 shows that our actual background galaxy sample spans a much larger range in this same complex (e 1 , e 2 ) plane. Only ∼2% of our galaxies have e < 0.05 similar to our PSF stars, and they are roughly uniformly split between the different quadrants (phase angles). Note that the majority of our galaxies (2972/3848 ∼ 77%) are assigned to a shortwavelength NIRCam filter (F115W, F150W, F200W) to obtain the rest-frame morphology corresponding to their redshift. Moreover, our smallest size galaxies (which would be preferentially subject to PSF systematics) are also roughly uniformly spread out in this plane, i.e., not biased toward any one quadrant. This is true regardless of whether we look at the combined sample or only galaxies in individual pointings. Given that the PSF tends to round out objects, the fact that our galaxies have intrinsic ellipticities that are much larger than that of the stars implies that correcting for the small bias toward the lower right quadrant in Figure 21 would not cause most of our galaxies to change quadrants. Thus, we do not believe that the percent-level PSF systematics remaining in the data can explain our observed alignments in regions with 〈e〉 ≳ 10%. However, measuring the precise amplitude of the shear variance 2 will require correcting galaxy shapes for this spatially varying PSF because the expected signal is weak, especially on larger scales (Figure 19). It is unclear whether CEERS itself has enough stars to interpolate the PSF shape to the position of every galaxy, so a more sophisticated strategy may be required. We defer that to a future more detailed weaklensing analysis of "blank" JWST deep fields. ) plane. This is in the standard "north up" frame. Nearly all stars in every filter have e < 0.05, i.e., the PSF is very round. It is slightly more elliptical in the short-wavelength filters (F115W, F150W, F200W) with 〈e 1 〉 ∼ 0.02 and 〈e 2 〉 ∼ -0.01, and there is clearly a bias toward the lower right quadrant. The long-wavelength filters (F277W, F356W, F444W) have even rounder PSFs as expected. These percent-level PSF systematics cannot explain our much larger 〈e〉 ≳ 10% when averaging over background galaxies (Figure 19) but must be corrected in any future analysis of the conventional weak-lensing regime. This is in the standard "north up" frame. The ellipticities are very small and appear random in the long-wavelength filters. In contrast, for the short-wavelength filters, there are systematic PSF alignments toward 45 � east of north but the small ellipticities mean that these will cause an additive bias of at most a few percent, which is an order of magnitude lower than our 〈e〉 ≳ 10% from averaging background galaxies (Figure 19). However, future studies in the conventional weak-lensing regime must correct for this bias.
Figure 23. Distribution of our background galaxy sample in the complex (e 1 , e 2 ) plane (standard "north-up" frame). The large center panel shows our combined background sample whereas the smaller panels show the distributions in individual pointings. In all cases, ∼2% of our galaxies have e < 0.05, which is the PSFdominated regime (within the central black circle). Our galaxies also tend to be roughly uniformly distributed between the four quadrants. This is particularly true for our smaller-size galaxies (bluer colored points), which would be most susceptible to PSF effects. The fact that most of our galaxies have intrinsic ellipticities that are much larger than that of our stars implies that the small bias toward the lower right quadrant in Figure 21 is unlikely to dictate the orientations and hence alignments of our galaxies.
aa aa aa aa aa aa aa aa aa aa aa aa
These data can be found on MAST: 10.17909/z7p0-8481.
The Astrophysical Journal, 986:72 (29pp), 2025 June 10 Pandya et al.
In the limit of infinite regression trees, BART approaches a Gaussian process but without the need to choose and tune a covariance function (i.e., kernel). BART can also be thought of as a Bayesian cousin of machine learning techniques like random forests and gradient-boosted decision trees.
In weak lensing, it is common practice to instead define |e| = (ab)/ (a + b) or |e| = (a 2b 2 )/(a 2 + b 2 ). Our results are not sensitive to the choice of a particular definition for the norm |e|.
It is common practice to divide individual ellipticities by a "shear polarizability tensor" P γ or "shear responsivity factor" R (R.Massey et al. 2007a). These are of order unity and may depend on galaxy morphology, so we neglect them here for simplicity.
Note that a single NIRCam module can sometimes fit a single bright foreground cluster used for conventional strong and weak-lensing studies (e.g., K. M.Pontoppidan et al.
2022) whereas here we are searching for alignments over multiple modules or pointings.
, which is much smaller than the preferentially high ellipticity e ∼ 0.4-0.7 of early low-mass galaxies. Future work that corrects galaxy shapes for the local rather than global PSF may be able to measure the weak expected cosmic shear signal in "blank" JWST deep fields.