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Sung Kei Li

Publications and source records attributed to Sung Kei Li.

At least 19 recordsLinked to original sources

Observing population III stars in the pristine region

The detection of the long-sought Population III (Pop III) stars is, perhaps, one of the most intriguing missing links in modern astronomy. Caustic crossing events (CCE) -- extreme magnification at the critical curves of galaxy clusters of individual stars at cosmological distances -- are postulated to allow for the direct detection of individual Pop III stars. However, in the usual CCE regime, the abundant existence of intracluster stars as microlenses limits the maximum magnification attainable, thus limiting the theoretical detection of luminous stars to relatively low redshifts, significantly smaller than the redshifts where Pop III stars are expected to exist. Here in this letter, we propose to observe Pop III stellar populations as CCEs in the pristine regions of merging clusters. Pristine regions are defined as areas in the lens where the intracluster light, and hence the corresponding stelalr microlenses, is exceptionally low. In thes regions, the low density of microlenses allows background stellar populations to achieve magnification closer to the theoretical limit (whitout microlenses). We show that the maximum magnification in the pristine region scales inversely with the surface mass density of stellar microlenses. Adopting Pop III isochrones, regular James-Webb $\sim29\,$mag observations are sufficient to detect individual Pop III stars in pristine regions, offering a unique observational strategy to detect Pop III stars with the incoming cluster observations. The intermediate regions between high-redshift merging clusters (such as El Gordo) are naturally devoid of microlenses and constitute exceptional targets for the search of Pop III stars.

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Extragalactic microlensing through Ultra Diffuse Galaxies

Stellar microlensing is a powerful method to constrain compact dark matter models, uncover binary stars, and exoplanets during caustic crossing events. At cosmological distances, {\it James-Webb Space Telescope} ({\it JWST}) is routinely detecting microlensed giant stars in highly magnified galaxies behind massive lensing clusters. Here, we explore for the first time microlensing in modest redshift galaxies commonly seen through local Ultra Diffuse Galaxies (UDGs). Using the UDG NGC1052-DF2 as a proof-of-concept, we find that detecting microlensing events through UDGs is possible. Euclid is ideal for identifying samples of low-redshift star-forming galaxies seen through local galaxies for deeper cadenced follow-up, where our zeroth-order calculation estimates that $\mathcal{O}(1-10)$ events per year are expected over the whole sky under the monitoring of LSST, assuming all UDGs share similar distance and stellar content as NGC1052-DF2. Such measurements can help settle the DM issue for UDG galaxies by providing a stellar mass estimate weighted more by the low end of the stellar initial mass function (IMF) than standard stellar synthesis estimates. Note, lower efficiency is estimated for {\it JWST} of $\sim 5.6\times10^{-2}\,\textrm{yr}^{-1}$ over its five background galaxies is expected for typical {\it JWST}$\sim29$\,mag visits, and a low Vera Rubin Legacy Survey of Space and Time (LSST) detection rate of$\sim 0.03\,\textrm{yr}^{-1}$ such that NGC1052-DF2 might not be a prime target given its lack of low-redshift background galaxies.

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Model independent lensing sub-structure detection with multiply-imaged star clusters constellations

A broad class of dark matter (DM) models predicts the existence of sub-structures residing in DM haloes on sub-resolvable angular scales. Techniques to extract such a generic feature from diffraction-limited observations are lacking. In this work, we propose a model-independent 'super-resolving' method applicable to strong gravitational lens systems that is fully data-driven, without reference to any lens models. This method relies on a specific way of applying the optical Liouville theorem across multiple scales in the imaging data, a technique we refer to as geometrical-duality. We test this method using realistic simulations and apply it to a 'constellation' consists of 11 compact star clusters seen in two giant arcs in the lensing cluster SMACS0723 imaged by JWST as a proof-of-concept. We find reasonable self-consistency with the expectation of non-detection given the statistical sensitivity, except for one pair of star clusters. Such an outlier can be explained in the context of CDM as sub-haloes lensing in the mass range $M_{\rm sub} = 10^8 - 10^9\,M_\odot$, for which the corresponding Einstein radius is smaller than the diffraction limit of JWST.

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Multi-copy Axion Transfer Function and Observational Implications of Effective de Broglie Scales

Ultra-light axions are viable fuzzy/wave-like dark matter ($ψ$DM) candidates generically predicted by the String Axiverse paradigm with multiple particle copies, whereas most of the discussions/constraints on $ψ$DM from astronomical observations to date are based on the assumption of a single particle copy. Here, we aim to complete this gap by exploring the generic multi-axion scenario motivated in the String Axiverse context, and investigate its astronomical implications in both the linear and nonlinear regimes. In the linear regime, with linear density perturbation analysis, we provide a simplified prescription for obtaining multi-copy axion transfer functions and also identify an "equivalence" among all axion copies owing to the mutual coupling to the gravitational potential. As a result of this 'equivalence', we argue the suppression to LSS is governed by an effective mass $m_{eff}^{-2}=\sum_i w_i m_i^{-2}$, with $\{ w_i\}$ being fractional contributions of different copies to the full cosmic dark matter density. In non-linear regime within galaxy halos, we show that similar notions of effective mass, with expressions provided, to govern the collective wave interference and hence determine the net stellar heating rates and the substructure-induced spread of JWST transients near critical curves. Distinctive to the multi-copy scenario, the effective mass within galaxy halos is generically anticipated to be radially decreasing following the stronger concentration of heavier copies to the galactic center. Such a spatial variation leads to radially increasing spreading scales for micro-lensed transients at different radial positions, a signature that may be tested with future JWST lensing observations.

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First Statistical Study of Over 100 Magnified Stellar Events at Redshift $z \approx 0.725$ with JWST

Highly magnified stars at cosmological distances ($z \gtrsim 0.7$) become detectable thanks to microlensing by intracluster stars near the critical curves of galaxy clusters. Multi-epoch photometric campaigns targeting caustic crossing galaxies magnified by massive galaxy clusters enable the detection of these objects as transient events. Such stars provide unique opportunities to study stellar populations at early cosmic times, probe the nature of dark matter, reveal small-scale structure in the cluster, and improve lens models. To date, only a few dozen high-redshift stars have been reported, with a single lensed galaxy, the Dragon, holding the current record of 44 detections. These numbers, however, remain insufficient to exploit their full potential. In this paper, owing to the inclusion of new observations, we report the identification of more than 100 magnified stellar events in the Dragon, behind the massive galaxy cluster Abell 370. The relatively low redshift of the Dragon ($z\approx0.725$) facilitates the detection of its most massive stars. Using imaging data from three different cycles (2022--2024) with the James Webb Space Telescope, we apply a time-domain technique to identify flux variations associated with caustic-crossing events. From the spatial distribution of stellar events we constrain the high-end slope of the stellar luminosity function, finding $β=2.18^{+0.20}_{-0.30}$. Alternatively, assuming a fixed slope, we constrain the microlens surface mass density. In addition, we examine the parity asymmetry of the detected caustic-crossing events, a proposed probe of wave dark matter, and find that it remains present. We also use the events to trace the regions of highest magnification, offering an alternative way to map the system critical curves.

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Lensed stars in galaxy-galaxy strong lensing -- a JWST prediction for the Cosmic Horseshoe

We explore for the first time the possibility of detecting lensed star transients in galaxy-galaxy strong lensing systems upon repeated, deep imaging using the {\it James-Webb Space Telescope} ({\it JWST}). Our calculation predicts that the extremely high recent star formation rate of $\sim 140\,M_{\odot}\textrm{yr}^{-1}$ over the last 50 Myr (not accounting for image multiplicity) in the ``Cosmic Horseshoe'' lensed system ($z = 2.381$) generates many young, bright stars, of which their large abundance is expected to lead to a detection rate of $\sim 60$ transients per pointing in {\it JWST} observations with a $5σ$ limiting magnitude of $\sim 29\,m_{AB}$. With the high expected detection rate and little room for uncertainty for the lens model compared with cluster lenses, our result suggests that the Cosmic Horseshoe could be an excellent tool to test the nature of dark matter based on the spatial distribution of transients, and can be used to constrain axion mass if dark matter is constituted of ultra-light axions. We also argue that the large distance modulus of $\sim46.5\,$mag at $z \approx 2.4$ can act as a filter to screen out less massive stars as transients and allow one to better constrain the high-mass end of the stellar initial mass function based on the transient detection rate. Follow-up {\it JWST} observations of the Cosmic Horseshoe would allow one to better probe the nature of dark matter and the star formation properties, such as the initial mass function at the cosmic noon, via lensed star transients.

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Massive stars as gravitationally lensed transients -- Insights on the high-mass initial mass function

A robust stellar initial mass function (IMF) is crucial in any studies related to star formation. However, the direct measurement of the stellar IMF is confined to the local universe, limited by the resolving power of telescopes. Recently, a new method for accessing the stellar IMF beyond the local universe has been developed. The observed detection rate of transient lensed stars -- individual, massive, thus luminous stars in strongly lensed galaxies that are temporarily detectable upon stellar microlensing -- can serve as a probe to break the IMF-star formation history degeneracy in studies utilizing spectral energy distribution fitting, hence providing a window to look at the IMF at a subsample of gravitationally lensed galaxies. In this proceeding, I summarize the contributed talk given at IAUS402 entitled the same as this contribution and highlight some key results, which currently show no evidence for a top-heavy IMF in $z \approx 1$ galaxies.

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JWST's PEARLS: Temperatures of Nine Highly Magnified Stars in a Galaxy at Redshift 0.94 and Simulated Stellar Population Dependence on Stellar Metallicity and the Initial Mass Function

We present stellar atmosphere modeling of JWST NIRCam photometry of nine highly magnified individual stars in a single galaxy at redshift z=0.94 known as the Warhol arc, which is strongly lensed by the galaxy cluster MACSJ0416. Seven of these transients were identified by Yan et al. (2023). The nine sources are all likely red supergiants with temperatures of T~4000K. We present new longslit spectroscopy of the Warhol arc acquired with Keck-I and the Large Binocular Telescope, and use these data to constrain the arc's oxygen abundance to be 12+log(O/H)=8.45+-0.08. We perform a microlensing simulation on synthetic stellar populations using a range of stellar metallicities and initial mass function slopes. The temperature distribution of the simulated detectable stars is sensitive to the choice of stellar metallicity, and setting the stellar metallicity equal to the arc's nebular metallicity (log(Z*/Zsun)=-0.24) produces a simulated temperature distribution that is consistent with the observations, while lower stellar metallicities (log(Z*/Zsun)<-0.75) produce simulated temperatures that are inconsistent with the observations. The expected detection rate is strongly anticorrelated with the IMF slope for alpha>1.2. For the canonical IMF slope alpha=2.35, the simulation yields expected transient detection rates that agree with the observed detection rates in the HST Flashlights filters, but over predicts the detection rate by a factor of ~3-12 (<2sigma tension) in the JWST filters. The simulated detection rate is sensitive to the choice of stellar metallicity, with lower metallicities (log(Z*/Zsun)<-0.75) yielding a significantly lower simulated detection rate that further reduces the modest tension with the observations.

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Transient star B/R ratio and star formation in $z\gtrsim 1$ lensed galaxies

The extreme magnification from galaxy clusters and microlenses therein allows the detection of individual, luminous stars in lensed galaxies as transient events, and hence provides a valuable window into the high mass stellar population in $z>1$ galaxies. As these bright stars can only be formed at specific ages, the relative abundance of transient events at blue (B) and red (R) optical wavelengths ($B/R$ ratio) can provide insights into the recent star formation history of galaxies that are not well constrained by their spectral energy distributions (SEDs). Here, we forward model the transient detection rates in an idealized mock scenario to find that the $B/R$ ratio of strongly lensed $z>1$ galaxies decreases quickly with increasing age. This ratio has moderate sensitivity to metallicity and comparatively low sensitivity to dust attenuation, with no significant dependency on the stellar initial mass function. Fitting model stellar populations to either the SED or $B/R$ ratio alone of ``Warhol'' arc ($z = 0.94$), we find that neither a simple single starburst nor a more complex star formation can simultaneously reproduce both constraints. We then demonstrate that a best-fit model constrained by both the B/R ratio and SED requires a star-formation rate that has varied quite dramatically over the past $\sim$50 Myr, for which the total stellar mass formed over this time is a factor of 10 (with $2-3σ$ significance) different from the best-fit models to the SED alone. Our work shows that the transient $B/R$ ratio can be used as an additional powerful constraint on the recent star formation history of higher-redshift galaxies in future works that are strongly lensed by galaxy clusters.

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Flashlights: Prospects for constraining the Initial Mass Function around cosmic noon with caustic-crossing events

The Flashlights program with the Hubble Space Telescope imaged the six Hubble Frontier Fields galaxy clusters in two epochs and detected twenty transients. These are primarily expected to be caustic-crossing events (CCEs) where bright stars in distant lensed galaxies, typically at redshift $z\approx1$--3, get temporarily magnified close to cluster caustics. Since CCEs are generally biased toward more massive and luminous stars, they offer a unique route for probing the high end of the stellar mass function. We take advantage of the Flashlights event statistics to place preliminary constraints on the stellar initial mass function (IMF) around cosmic noon. The photometry (along with spectral information) of lensed arcs is used to infer their various stellar properties, and stellar synthesis models are used to evolve a recent stellar population in them. We estimate the microlens surface density near each arc and, together with existing lens models and simple formalism for CCEs, calculate the expected rate for a given IMF. We find that, on average, a Salpeter-like IMF ($α=2.35$) underpredicts the number of observed CCEs by a factor of ${\sim}0.7$, and a top-heavy IMF ($α=1.00$) overpredicts by a factor of ${\sim}1.7$, suggesting that the average IMF slope may lie somewhere in between. However, given the large uncertainties associated with estimating the stellar populations, these results are strongly model-dependent. Nevertheless, we introduce a useful framework for constraining the IMF using CCEs. Observations with JWST are already yielding many more CCEs and will soon enable more stringent constraints on the IMF at a range of redshifts.

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Magnification bias reveals severe contamination in Hubble Frontier Field photo-z catalogs

Gravitational lensing by massive galaxy clusters enables faint distant galaxies to be more abundantly detected than in blank fields, thereby allowing one to construct galaxy luminosity functions (LFs) to an unprecedented depth at high redshifts. Intriguingly, photometric redshift catalogs (e.g. Shipley et al. (2018)) constructed from the Hubble Frontier Fields survey display an excess of z$\gtrsim$4 galaxies in the cluster lensing fields and are not seen in accompanying blank parallel fields. The observed excess, while maybe a gift of gravitational lensing, could also be from misidentified low-z contaminants having similar spectral energy distributions as high-z galaxies. In the latter case, the contaminants may result in nonphysical turn-ups in UV LFs and/or wash out faint end turnovers predicted by contender cosmological models to $Λ$CDM. Here, we employ the concept of magnification bias to perform the first statistical estimation of contamination levels in HFF lensing field photometric redshift catalogs. To our great worry, while we were able to reproduce a lower-z lensed sample, it was found $\sim56\%$ of $3.5 < z_{phot} < 5.5$ samples are likely low-z contaminants! Widely adopted Lyman Break Galaxy-like selection rules in literature may give a 'cleaner' sample magnification bias-wise but we warn readers the resulting sample would also be less complete. Individual mitigation of the contaminants is arguably the best way for the investigation of faint high-z Universe, and this may be made possible with JWST observations.

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Constraining the z $\sim$ 1 Initial Mass Function with {\it HST} and {\it JWST} Lensed Stars in MACS J0416.1-2403

Our understanding of galaxy properties and evolution is contingent on knowing the initial mass function (IMF), and yet to date, the IMF is constrained only to local galaxies. Individual stars are now becoming routinely detected at cosmological distances, where luminous stars such as supergiants in background galaxies strongly lensed by galaxy clusters are temporarily further magnified by huge factors (up to $10^{4}$) by intracluster stars, thus being detected as transients. The detection rate of these events depends on the abundance of luminous stars in the background galaxy and is thus sensitive to the IMF and the star-formation history (SFH), especially for the blue supergiants detected as transients in the rest-frame ultraviolet/optical filters. As a proof of concept, we use simple SFH and IMF models constrained by spectral energy distributions (SEDs) to see how well we can predict the {\it HST} and {\it JWST} transient detection rate in a lensed arc dubbed ``Spock'' ($z = 1.0054$). We find that demanding a simultaneous fit of the SED and the transient detection rate places constraints on the IMF, independent of the assumed simple SFH model. We conclude our likelihood analysis indicates that the data definitively prefers the ``Spock'' galaxy to have a Salpeter IMF ($α= 2.35$) rather than a Top-heavy IMF ($α= 1$) -- which is thought to be the case in the early universe -- with no clear excess of supergiants above the standard IMF.

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Signatures of Fuzzy Dark Matter Inside Radial Critical Curves

We investigate the strong gravitational lensing properties of fuzzy dark matter (FDM) halos, focusing on the magnification properties near radial critical curves (CCs). Using simulated lenses we compute magnification maps for a range of axion masses and halo configurations. We show that FDM produces enhanced central magnification and secondary CCs that are not easily reproduced by standard cold dark matter (CDM), even when including subhalos. The strength and scale of these effects depend primarily on the de~Broglie wavelength, governed by the axion and halo masses. We find that axion masses in the range $m_ψ\sim 10^{-22}$--$10^{-21}\,\mathrm{eV}$ in galaxy-mass halos lead to distinctive magnification distributions. Our results suggest that observations of highly magnified, compact sources near radial arcs, such as quasars or supernovae, could serve as a powerful test for the presence of FDM.

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Microlensing at Cosmological Distances: Event Rate Predictions in the Warhol Arc of MACS 0416

Highly magnified stars ($μ$ $>$ 100) are now outinely identified as transient events at cosmological distances thanks to microlensing by intra-cluster stars near the critical curves of galaxy clusters. Using the {\it James Webb} Space Telescope (JWST) in combination with the {\it Hubble} Space Telescope (HST), we outline here an analytical framework that is applied to the Warhol arc (at $z=0.94$) in the MACS 0416 galaxy cluster (at $z=0.396)$ where over a dozen microlensed stars have been detected to date. This method is general and can be applied to other lensed arcs. Within this lensed galaxy we fit the spatially resolved SED spanned by eight JWST-NIRCam filters combined with three ACS filters, for accurate lensed star predictions in 2D. With this tool we can generate 2D maps of microlensed stars for well resolved arcs in general, including dependence on wavelength and limiting apparent magnitude, for comparison with with planned cadenced campaigns for JWST and Hubble, for constraining directly the IMF and the level of dark matter substructure.

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Are Models of Strong Gravitational Lensing by Clusters Converging or Diverging?

The increasingly large numbers of multiple images in cluster-scale gravitational lenses have allowed for tighter constraints on the mass distributions of these systems. Most lens models have progressed alongside this increase in image number. The general assumption is that these improvements would result in lens models converging to a common solution, suggesting that models are approaching the true mass distribution. To test whether or not this is occurring, we examine a sample of lens models of MACS J0416.1$-$2403 containing varying number of images as input. Splitting the sample into two bins (those including $<150$ and $>150$ images), we quantify the similarity of models in each bin using three comparison metrics, two of which are novel: Median Percent Difference, Frechet Distance, and Wasserstein Distance. In addition to quantifying similarity, the Frechet distance metric seems to also be an indicator of the mass sheet degeneracy. Each metric indicates that models with a greater number of input images are no more similar between one another than models with fewer input images. This suggests that lens models are neither converging nor diverging to a common solution for this system, regardless of method. With this result, we suggest that future models more carefully investigate lensing degeneracies and anomalous mass clumps (mass features significantly displaced from baryonic counterparts) to rigorously evaluate their model's validity. We also recommend further study into alternative, underutilized lens model priors (e.g. flux ratios) as an additional input constraint to image positions in hopes of breaking existing degeneracies.

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BUFFALO Wild Wings: A High Precision Free-Form Lens Model of MACSJ0416 with Constraints on Dark Matter from Substructure and Highly Magnified Arcs

We present new free-form and hybrid mass reconstructions of the galaxy cluster lens MACS J0416.1$-$2403 at $z=0.396$ using the lens inversion method GRALE. The reconstructions use 237 spectroscopically confirmed multiple images from Bergamini et. al. 2023 as the main input. Our primary model reconstructs images to a positional accuracy of 0.191", thus representing one of the most precise reconstructions of this lens to date. Our models find broad agreement with previous reconstructions, and identify two $\sim 10^{12} M_{\odot}$ light-unaffiliated substructures. We focus on two highly magnified arcs: Spock and Mothra. Our model features a unique critical curve structure around the Spock arc with 2 crossings. This structure enables sufficient magnification across this arc to potentially explain the large number of transients as microlensing events of supergiant stars. Additionally, we develop a model of the millilens substructure expected to be magnifying Mothra, which may be a binary pair of supergiants with $μ\sim 6000$. This model accounts for flexibility in the millilens position while preserving the observed flux and minimizing image position displacements along the Mothra arc. We constrain the millilens mass and core radius to $\lesssim 10^6 M_{\odot}$ and $\lesssim 17$ pc, respectively, which would render it one of the smallest and most compact substructures constrained by lensing. If the millilens is dominated by wave dark matter, the axion mass is constrained to be $\lesssim 3.0 \times 10^{-21}$ eV. Further monitoring of this lens with JWST will uncover more transients, permitting tighter constraints on the structure surrounding these two arcs.

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Flashlights: Transients among Gravitationally-Lensed Star Clusters in the Dragon Arc. I. Stellar Microlensing vs Stellar Outbursts

We report the discovery of transients among star clusters in a distant galaxy that is gravitationally lensed by a foreground galaxy cluster, and explore whether these transients correspond to: (i) intrinsic variations associated with stellar outbursts; or (ii) extrinsic variations imposed through microlensing by intraclusters stars along, perhaps, with primordial black holes. From images at two epochs separated by nearly a year, we discovered ten such transients -- displaying brightness variations of $\sim$10\%--20\% -- among 55 persistent knots identified as young star clusters in the Dragon arc. Two of these transients are associated with a triply-lensed star cluster, permitting a test of intrinsic variability by checking whether their light variations are repeated among the different lensed counterparts with a suitable time delay given their different light arrival times at the observer. Despite considerable care in constructing a lens model for Abell 370 that is optimized at the Dragon arc, we found that the predicted lensing magnifications are not sufficiently accurate to provide a definitive test of intrinsic variability based only on two images -- although such a test will become feasible as more observations are made. On the other hand, we perform simulations demonstrating that the observed level of brightness variations, as well as the observed transient event rate, can be explained entirely by stellar microlensing: as stars in the background star cluster move across the sky relative to intracluster stars, changes in their individual brightnesses can result in an overall change in the brightness of their parent star cluster.

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A high-resolution view of the source-plane magnification near cluster caustics in wave dark matter models

We present the highest resolution images to date of caustics formed by wave dark matter ($ψ$DM) fluctuations near the critical curves of cluster gravitational lenses. We describe the basic magnification features of $ψ$DM in the source plane at high macromodel magnification and discuss specific differences between the $ψ$DM and standard cold dark matter (CDM) models. The unique generation of demagnified counterimages formed outside the Einstein radius for $ψ$DM is highlighted. Substructure in CDM cannot generate such demagnified images of positive parity, thus providing a definitive way to distinguish $ψ$DM from CDM. Highly magnified background sources with sizes $r\approx 1pc$, or approximately a factor of ten smaller than the expected de Broglie wavelength of $ψ$DM, offer the best possibility of discriminating between $ψ$DM and CDM. These include objects such as very compact stellar clusters at high redshift that JWST is finding in abundance.

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