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V. Motta

Publications and source records attributed to V. Motta.

At least 19 recordsLinked to original sources

TDCOSMO XXVIII. The Hubble constant from the quadruply lensed quasar J1537$-$3010 with precise time delays

We present the first measurement of the Hubble constant ($H_0$) from the quadruply-lensed quasar J1537$-$3010, which has optically-measured time delays at $\sim2 \%$ precision. We combine these delays with multi-band imaging data from the Hubble Space Telescope (HST) and model the system with two independent software and teams. We adopt a mass profile that is maximally degenerate with $H_0$ to fully incorporate the mass-sheet degeneracy in the error budget, with nuisance parameters constrained by spatially resolved stellar kinematics from the Multi Unit Spectroscopic Explorer (MUSE) and a line-of-sight (LoS) analysis using the Euclid Flagship simulation. The entire analysis is performed blindly to $H_0$, distances and mass density slope of the main deflector. After unblinding, we measure $H_0 = 75.5^{+9.3}_{-5.8}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, corresponding to a $10\%$ precision measurement from a single system. This precision is driven by conservative lens modeling assumptions including differences between lens modeling methods and the limited stellar kinematics constraints, from which we infer a total mass-sheet parameter $\lambda\equiv(1-\kappa_{\rm ext})\lambda_{\rm int} = 0.89^{+0.11}_{-0.06}$ ($\lambda_{\rm int}=0.89^{+0.09}_{-0.07}$) that is consistent with current results for elliptical galaxies ($\lambda \approx 1$). Our lensing constraints, stellar kinematic measurements and LoS characterization will be included in subsequent population-level measurements of $H_0$. Moreover, our lens models combined with future near-infrared spectroscopy and imaging from the James Webb Space Telescope will further reduce the uncertainties on $H_0$ from J1537$-$3010 alone, bringing it closer to the few percents precision of the time delays.

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TDCOSMO. XXVII. JWST-based Lens Models and H$_0$ Measurement of WFI2033, HE0435, and PG1115

Time-delay cosmography offers a one-step, distance-ladder-independent route to the Hubble-Lemaitre constant, H_0. We present new cosmography-grade lens models of three quadruply imaged quasars based on JWST-NIRCam/F115W imaging (WFI2033-4723, HE0435-1223, PG1115+080). We use the STARRED modeling technique, introduced in our previous analysis of WFI2033-4723, to reconstruct the complex JWST-NIRCam Point Spread Function at high fidelity. We combine NIRCam-based lens models with improved external convergence estimates, published time delays, and aperture-integrated stellar velocity dispersions from JWST NIRSpec to infer H_0. The analysis was carried out blindly for HE0435-1223 and PG1115+080, while it was not blind for WFI2033-4723, as we build upon the previous published model. For comparison with previous HST-based work, we limit our analysis to the case of no internal mass-sheet degeneracy ($\lambda_{\rm int}=1$). We quantify the impact of improved imaging, single-aperture kinematics, and environment measurements on central values and uncertainties. Within flat $\Lambda$CDM, assuming a uniform prior on $\Omega_{\rm m}$, we find H_0 = 71.8$_{-7.0}^{+9.2}$ $\lambda_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$ for PG1115+080, 74.2$_{-4.2}^{+4.2}$ $\lambda_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$ for HE0435-1223, and 73.4$_{-4.4}^{+3.4}$ $\lambda_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$ for WFI2033-4723. Combining the three lenses yields H_0 = 73.5$_{-2.8}^{+2.7}$ $\lambda_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$, consistent with HST-based results (73.6$_{-2.6}^{+2.6}$ $\lambda_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$), but with reduced scatter between the three systems. These models will be incorporated in the TDCOSMO-2026 milestone paper with free $\lambda_{\rm int}$ in a hierarchical fashion. We close by outlining how 16 forthcoming JWST NIRCam targets will further tighten uncertainties toward percent-level precision on H_0.

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Accretion Disk Sizes and Temperature Profiles in Lensed Quasars: NIR Microlensing Challenges Thin Disk Theory

Microlensing and reverberation mapping measurements of quasar accretion disk sizes and temperature gradients disagree with thin disk theory predictions. Previous microlensing results rely on heterogeneous wavelength coverage -primarily UV broad emission lines (BELs) from small samples -probing the disk only out to a typical radius of $\lesssim$5 light days on average. We use microlensing estimates from an homogeneous sample of near-infrared (NIR) observations of lensed quasars (21 image-pairs from 7 lens systems) to extend disk size measurements out to 14 light days. This analysis leverages narrow emission lines (NELs), which provide a more reliable microlensing-free baseline than BEL cores. We derive Bayesian accretion disk size estimates that reproduce the observed microlensing magnifications, as simulated from magnification maps. NEL-based sizes yield a logarithmic slope of $p=0.68\pm0.23$, consistent with prior estimates corresponding to inner disk regions ($r \lesssim$5 light days). Using a new homogeneous NIR dataset that allows us to reach radial distances of up to 14 light days, we find that accretion disks in these previously unexplored regions are also larger and exhibit steeper temperature gradients than thin disk theory predicts. The increased precision allows us to reject the theoretical logarithmic slope $p=4/3$ at the 98\% confidence level. Any hypothesis invoking BLR contamination to explain this discrepancy must account for how such contamination modulates the underlying accretion disk such that the combination of both results in a power law with logarithmic slope $p=0.68\pm0.23$ across a broad wavelength baseline spanning from $\sim$X-Ray to $\sim 5000$\AA.

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A comparative study of emergent dark energy models

Late (emergent) dark energy models that involve a hyperbolic tangent in their dynamic equations have achieved success due to their simplicity, the possibility of resolving the Hubble tension, and, in some cases their consistency with the Dark Energy Spectroscopic Instrument (DESI) results. Among the most studied are the Phenomenological and General Emergent Dark Energy Models (PEDE and GEDE, respectively), the variable curvature model, and the graduated dark energy model. Our goal is to include the curvature term in the models and perform a robust comparative study using diverse data samples, in particular, Cosmic Chronometers, Type Ia supernovae, Baryon Acoustic Oscillations from DESI-DR1, and Cosmic Microwave Background Radiation. This study presents the Universe age, the deceleration, the $w_{eff}$ parameter reconstruction, the redshift transition, and the best fit for the free parameters of each model. Our collected evidence from Akaike Information Criterion and Bayesian Information Criterion indicates that the best candidate is the PEDE model. Nevertheless, the variable-curvature model is the only model that exhibits a decelerated phase near $z=0$, consistent with the results from DESI.

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The free-streaming length of dark matter from JWST observations of 28 strong gravitational lenses

The formation of gravitationally bound overdensities of dark matter (DM), or \textit{halos}, is a generic prediction of theories with particle DM. We present a measurement of halo properties in 28 quadruple image strong lens systems recently observed by JWST, and use these observations to constrain the free-streaming length, $\lambda_{\rm{FS}}$, of DM, a quantity that depends on the DM particle mass and formation mechanism. We improve on previous lensing analyses by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications, enhancing sensitivity to perturbations by halos. Our analysis rules out deviations from the predictions of cold dark matter (CDM) on scales above $10^{7.2} M_{\odot}$ and $10^{7.4} M_{\odot}$ for subhalo abundance predicted by cosmological $N$-body simulations and semi-analytic models, respectively. These bounds correspond to upper limits $\lambda_{\rm{FS}}<6.0 \ \rm{kpc}$ and $\lambda_{\rm{FS}}<7.0 \ \rm{kpc}$, and lower limits on the mass of a spin--1/2 thermal relic DM particle $m_{\rm{therm}}>7.4 \ \rm{keV}$ and $m_{\rm{therm}}>6.5 \ \rm{keV}$. Conversely, assuming a negligible free-streaming length, as predicted by CDM, we measure a projected mass in subhalos around elliptical galaxies $1.7_{-1.2}^{+2.6} \times 10^7 \ \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$ at $95 \%$ confidence. These inferences confirm key predictions of the CDM paradigm.

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Spectral Handling and Estimation of AGN Parameters (SHEAP), The first AGN fitting GPU-based code

In the coming years, the number of discovered active galactic nuclei (AGN) is expected to increase significantly due to upcoming spectroscopic surveys. This growth will challenge current analysis and modeling techniques, requiring scalable methods for large, heterogeneous datasets with diverse signal-to-noise ratios, spectral resolutions, and host-galaxy contamination. We present SHEAP (Spectral Handling and Estimation of AGN Parameters), a spectral-fitting framework designed to analyze large AGN samples efficiently while preserving physical interpretability, reproducibility, and robust uncertainty estimation. SHEAP uses JAX, a Python GPU-powered framework, to implement a flexible model with modular components, including continuum, host galaxy, FeII pseudo-continuum, and multi-component emission lines, together with parameter tying and physically motivated constraints. By combining gradient-based optimization with automatic differentiation, vectorization, and just-in-time compilation, SHEAP achieves stable convergence in blended regions, such as H$\beta$, while substantially reducing runtime. We compare SHEAP measurements with literature results and public fitting pipelines across four samples covering the CIV, MgII, H$\beta$, and H$\alpha$ regions. We find good agreement for the main AGN spectral parameters, with $\sim85$--$100%$ of objects lying within the $\pm0.3$ dex band and reduced chi-square distributions close to unity. Relative to the runtime reported by \citet{2026Bernal} using \texttt{pPXF}, the fitting stage requires only $\sim1.7%$ of the computational time, corresponding to an improvement of approximately $100$ times. These results show that \texttt{SHEAP} delivers reliable AGN spectral decompositions at substantially lower computational cost, making it suitable for massive spectroscopic datasets.

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Microlensing time-scales and flux magnification probabilities of a sample of 204 lensed quasars

Quasar microlensing is both a very useful tool in cosmology and astrophysics, and a source of uncertainty in some studies like the determination of the Hubble constant from lensed quasars. Microlensing probability and time-scales have been statistically studied using as a reference scale the Einstein ring crossing time of an isolated mass. Our goal is to extend the statistical analysis of microlensing to all currently known lensed quasars with available data, considering realistic optical depths and the gravitational effect of the lens galaxy. We take into account new observational results about quasar sizes and peculiar velocities of lens galaxies. We apply automatic lens modeling to the 204 systems available. For each image, we compute microlensing magnification maps and histograms. Using thin disk source sizes scaled to take into account recent measurements of accretion disk sizes, we find a mean source crossing time of $2.59\pm 0.07$ years. The mean Einstein radius crossing time is $ 11.29 \pm 0.05$ years. When a fraction of mass in microlenses $\alpha=0.2$ is adopted, we find a good matching between the modeled histogram of mean microlensing magnifications for the images in our sample and the experimental histogram of microlensing magnifications. From the modeling of microlensing magnification histograms, we estimate the average half-light radius of the quasar source, $R_{1/2}=5.4\pm 2.7$ light-days, and a lower limit to the mass fraction in microlenses, $\alpha\ge 0.15$. From the microlensing magnification maps, we find that a lensed quasar image has a mean probability of approximately 9% of being involved in a high-magnification event ($\Delta m \le -0.32$). We select a group of images with the largest probabilities and the smallest crossing times.

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Enhancing Gravitational Lens Study with Deep Learning: A Study on Effects of Dropout Regularization

Strong gravitational lensing provides valuable insights into the mass distribution of galaxies and the nature of dark matter. However, its modeling is computationally demanding due to the large volume of strong lensing observations. In this work, we explore the application of Convolutional Neural Networks to infer physical parameters from simulated galaxy-galaxy lens systems, described by the Singular Isothermal Ellipsoid (SIE) profile for the galaxy lens. We construct a dataset of 76,396 synthetic lensing images derived from the China Space Station Telescope catalog and employ it to train a modified CNN model, based on AlexNet architecture, to predict four key SIE parameters, Einstein radius, axis ratio and ellipticity components. We analyze the network performance under three distinct dropout configurations to quantify their influence on generalization and parameter inference accuracy. The results indicate that the incorporation of dropout is critical for enhancing the precision and robustness of the estimated parameters, as demonstrated using a 4-fold cross-validation procedure. When dropout tools are included we obtain yields coefficients of determination up to $R^2 \sim 0.96$ for most SIE parameters and mean Peak Signal-to-Noise Ratios of up to $\sim 37$ dB. Relative to the configuration without dropout, the use of dropout reduces the relative errors in the inferred SIE parameters by approximately $60-76\%$, resulting in errors of at most $\sim 9\%$ at the $90\%$ confidence level for the majority of parameters. These findings highlight the potential of deep learning approaches to enable scalable, computationally efficient, and high-precision modeling of strong gravitational lensing systems.

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JWST Lensed Quasar Dark Matter Survey III: Dark Matter Sensitive Flux Ratios and Warm Dark Matter Constraint from the Full Sample

We present the full sample of measurements of the warm dust emission of 31 strongly-lensed, multiply imaged quasars, observed with JWST MIRI multiband imaging, which we use to constrain the particle properties of dark matter. The strongly lensed warm dust region of quasars is compact and statistically sensitive to a population of dark matter halos down to masses of $10^6$ M$_\odot$. The high spatial resolution and infrared sensitivity of MIRI make it uniquely suited to measure multiply imaged warm dust emission from quasars and thus to infer the properties of low-mass dark halos. We use the measured flux ratios to test for a warm dark matter turnover in the halo mass function. To infer the dark matter parameters, we use a forward modeling pipeline which explores dark matter parameters while also accounting for tidal stripping effects on subhalos, globular clusters, and complex deflector macromodels with $m=1, m=3, \text{ and } m=4$ elliptical multipole moments. Adopting a comparable prior on the projected density of substructure to our previous analyses, the data presented here provide a factor of 2 improvement in sensitivity to a turnover in the halo mass function. Assuming subhalo abundance predicted by the semi-analytic model galacticus we infer with a Bayes factor of 10:1, a half-mode mass $m_{\rm{hm}} < 10^{7.8} M_{\odot}$ (m>5.6 keV for a thermally produced dark matter particle). If instead we use a prior from N-body simulations, we infer $m_{\rm{hm}} < 10^{7.6} M_{\odot}$ (m>6.4 keV). This is one of the strongest constraints to date on a turnover on the halo mass function, and the flux ratios and inference methodology presented here can be used to test a broad range of dark matter physics.

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JWST lensed quasar dark matter survey IV: Stringent warm dark matter constraints from the joint reconstruction of extended lensed arcs and quasar flux ratios

We present a measurement of the free-streaming length of dark matter (DM) and subhalo abundance around 28 quadruple image strong lenses using observations from JWST MIRI presented in Paper III of this series. We improve on previous inferences on DM properties from lensed quasars by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications (flux ratios). Our forward modeling framework generates full populations of subhalos, line-of-sight halos, and globular clusters, uses an accurate model for subhalo tidal evolution, and accounts for free-streaming effects on halo abundance and concentration. Modeling lensed arcs leads to more-precise model-predicted flux ratios, breaking covariance between subhalo abundance and the free-streaming scale parameterized by the half-mode mass $m_{\rm{hm}}$. Assuming subhalo abundance predicted by the semi-analytic model {\tt{galacticus}} ($N$-body simulations), we infer (Bayes factor of 10:1) $m_{\rm{hm}} < 10^{7.4} \mathrm{M}_{\odot}$ ($m_{\rm{hm}} < 10^{7.2} \mathrm{M}_{\odot}$), a 0.4 dex improvement relative to omitting lensed arcs. These bounds correspond to lower limits on thermal relic DM particle masses of $6.5$ and $7.4$ keV, respectively. Conversely, assuming DM is cold, we infer a projected mass in subhalos ($10^6 < m/M_{\odot}<10^{10.7}$) of $1.7_{-1.2}^{+2.6} \times 10^7 \ \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$ at $95 \%$ confidence. This is consistent with {\tt{galacticus}} predictions ($0.9 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$), but in mild tension with recent $N$-body simulations ($0.6 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$). Our results are among the strongest bounds on WDM, and the most precise measurement of subhalo abundance around strong lenses. Further improvements will follow from the large sample of lenses to be discovered by Euclid, Rubin, and Roman.

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DESI and fast radio burst used to constrain modified theories of gravity

This paper is devoted to the study of the viability of DESI and the fast radio burst to constrain the free parameters of modified theories of gravity. Thus, we present a model supported in $f(R)$ gravity involving a function of the Ricci scalar named Starobinsky-type with the peculiarity that the non-commutative essence is intrinsic to the coefficients. Additionally, to understand the dynamics within a flat Friedmann-Lemaitre-Robertson-Walker universe, we explore the possibility of deriving a Friedman equation (in measure) that results from an adequate mathematical treatment. As we mentioned previously, to test the outlined model, a Monte Carlo Markov chain analysis is implemented, using cosmic chronometers, type Ia supernovae, Hydrogen II galaxies, Intermediate-luminosity quasars, Baryon Acoustic oscillations and Fast Radio Bursts data, to constraint the free parameters of the model and presenting $H(z)$, $q(z)$ and $\omega_{eff}(z)$. The final results are compared with the $\Lambda$CDM model and a robust discussion is presented about the viability of DESI and fast radio burst to constraint free parameters in specific to a modified theory of gravity.

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On a model of variable curvature that mimics the observed Universe acceleration

We present a new model based on General Relativity in where a subtle change of curvature at late times is able to produce the observed Universe acceleration and an oscillating behavior in the effective equation of state. This model aims to test the cosmological principle, by introducing a slight modification in the traditional FLRW metric, through a non-constant curvature parameter. This model is defined by a smooth step-like function with a slight transition between two curvature values, fulfilling the premise that the derivative of this curvature parameter is preserved as approximately zero, $\dot{\kappa}\approx0$. To test our model, we implemented a MCMC likelihood analysis using Cosmic Chronometers and Type Ia supernovae data in order to constrain the free parameters of the model and reconstruct $H(z)$, $q(z)$, $w_{eff}(z)$, also comparing the results with the $\Lambda$CDM model. The main result is that this model provides an alternative to the acceleration of the Universe without the need of a dark energy component. In particular, it gives an equivalent phase transition at $z \sim 0.5$, while obtaining the same fraction of matter density, similar to what is expected for the standard $\Lambda$CDM model. Remarkably, it also predicts a slight decelerated state at $z=0$ in agreement with diverse Dark Energy parameterizations. We conclude that the behavior of our proposed model points towards a new and intriguing way to investigate slight violations to the cosmological principle, in particular the case of inhomogenities during low phase transitions.

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Phenomenological emergent dark energy in the light of DESI Data Release 1

This manuscript revisits the phenomenological emergent dark energy model (PEDE) by confronting it with recent cosmological data from early and late times. In particular we analyze PEDE model by using the baryon acoustic oscillation (BAO) measurements coming from both Dark Energy Spectroscopy Instrument (DESI) data release 1 and Sloan Digital Sky Survey (SDSS). Additionally, the measurements from cosmic chronometers, supernovae type Ia (Pantheon+), quasars, hydrogen II galaxies and cosmic background radiation distance priors are considered. By performing a Bayesian analysis based on Monte Carlo Markov Chain, we find consistent results on the constraints when SDSS and DESI are considered. However, we find higher values on the Hubble constant than Supernova $H_0$ for the Equation of State (SH0ES) does although it is still in agreement, within $1\sigma$ confidence level, when BAO measurements are added. Furthermore, we estimate the age of the Universe younger $\sim3\%$ than the one predicted by the standard cosmology. Additionally, we report values of $q_0 = -0.771^{+0.007}_{-0.007}$, $z_T = 0.764^{+0.011}_{-0.011}$ for the deceleration parameter today and the deceleration-acceleration transition redshift, respectively. However, PEDE cosmology is disfavoured by the combined samples.

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JWST Lensed quasar dark matter survey II: Strongest gravitational lensing limit on the dark matter free streaming length to date

This is the second in a series of papers in which we use JWST MIRI multiband imaging to measure the warm dust emission in a sample of 31 multiply imaged quasars, to be used as a probe of the particle nature of dark matter. We present measurements of the relative magnifications of the strongly lensed warm dust emission in a sample of 9 systems. The warm dust region is compact and sensitive to perturbations by populations of halos down to masses $\sim 10^6$ M$_{\odot}$. Using these warm dust flux-ratio measurements in combination with 5 previous narrow-line flux-ratio measurements, we constrain the halo mass function. In our model, we allow for complex deflector macromodels with flexible third and fourth-order multipole deviations from ellipticity, and we introduce an improved model of the tidal evolution of subhalos. We constrain a WDM model and find an upper limit on the half-mode mass of $10^{7.6} M_\odot$ at posterior odds of 10:1. This corresponds to a lower limit on a thermally produced dark matter particle mass of 6.1 keV. This is the strongest gravitational lensing constraint to date, and comparable to those from independent probes such as the Ly$\alpha$ forest and Milky Way satellite galaxies.

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Quasar Microlensing Statistics and Flux-Ratio Anomalies in Lens Models

Precise lens modeling is a critical step in time delay studies of multiply imaged quasars, which are key for measuring some important cosmological parameters (specially $H_0$). However, lens models (in particular those semi-automatically generated) often show discrepancies with the observed flux-ratios between the different quasar images. These flux-ratio anomalies are usually explained through differential effects between images (mainly microlensing) that alter the intrinsic magnification ratios predicted by the models. To check this hypothesis, we collect direct measurements of microlensing to obtain the histogram of microlensing magnifications. We compare this histogram with recently published model flux-ratio anomalies and conclude that they cannot be statistically explained by microlensing. The average value of the model anomalies ($0.74\,$magnitudes) significantly exceeds the mean impact of microlensing ($0.33\,$magnitudes). Moreover, the histogram of model anomalies presents a significant tail with high anomalies ($|\Delta m| \ge 0.7$ magnitudes) which is completely unexpected from the statistics of microlensing observations. Microlensing simulations neither predict the high mean nor the fat tail of the histogram of model anomalies. We perform several statistical tests which exclude that microlensing can explain the observed flux-ratio anomalies (although Kolmogorov-Smirnov, which is less sensitive to the tail of the distributions, is not always conclusive). Thus, microlensing cannot statistically explain the bulk of flux-ratio anomalies, and models may explore different alternatives to try to reduce them. In particular, we propose to complement photometric observations with accurate flux ratios of the broad emission lines obtained from integral field spectroscopy to check and, ideally, constrain lens models.

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Microlensing of strongly lensed quasars

Strong gravitational lensing of quasars has the potential to unlock the poorly understood physics of these fascinating objects, as well as serve as a probe of the lensing mass distribution and of cosmological parameters. In particular, gravitational microlensing by compact bodies in the lensing galaxy can enable mapping of quasar structure to $\lt 10^{-6}$ arcsec scales. Some of this potential has been realized over the past few decades, however the upcoming era of large sky surveys promises to bring this to full fruition. Here we review the theoretical framework of this field, describe the prominent current methods for parameter inference from quasar microlensing data across different observing modalities, and discuss the constraints so far derived on the geometry and physics of quasar inner structure. We also review the application of strong lensing and microlensing to constraining the granularity of the lens potential, i.e. the contribution of the baryonic and dark matter components, and the local mass distribution in the lens, i.e. the stellar mass function. Finally, we discuss the future of the field, including the new possibilities that will be opened by the next generation of large surveys and by new analysis methods now being developed.

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JWST lensed quasar dark matter survey I: Description and First Results

The flux ratios of gravitationally lensed quasars provide a powerful probe of the nature of dark matter. Importantly, these ratios are sensitive to small-scale structure, irrespective of the presence of baryons. This sensitivity may allow us to study the halo mass function even below the scales where galaxies form observable stars. For accurate measurements, it is essential that the quasar's light is emitted from a physical region of the quasar with an angular scale of milli-arcseconds or larger; this minimizes microlensing effects by stars within the deflector. The warm dust region of quasars fits this criterion, as it has parsec-size physical scales and dominates the spectral energy distribution of quasars at wavelengths greater than 10$\mu$m. The JWST Mid-Infrared Instrument (MIRI) is adept at detecting redshifted light in this wavelength range, offering both the spatial resolution and sensitivity required for accurate gravitational lensing flux ratio measurements. Here, we introduce our survey designed to measure the warm dust flux ratios of 31 lensed quasars. We discuss the flux-ratio measurement technique and present results for the first target, DES J0405-3308. We find that we can measure the quasar warm dust flux ratios with 3% precision. Our simulations suggest that this precision makes it feasible to detect the presence of 10$^7$ M$_\odot$ dark matter halos at cosmological distances. Such halos are expected to be completely dark in Cold Dark Matter models.

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Revealing the structure of the lensed quasar Q 0957+561 III. Constraints on the size of the broad-line region

Our aim is to examine the size, kinematics, and geometry of the broad-line region (BLR) in the double-lensed quasar Q 0957+561 by analyzing the impact of microlensing on various rest-frame ultraviolet broad-emission lines (BELs). We explore the influence of intrinsic variability and microlensing on the C IV, C III], and Mg II emission lines through multiple spectroscopic observations taken between April 1999 and January 2017. By utilizing the line cores as a reference for no microlensing and correcting for the long time delay between the images, we estimate the sizes of the regions emitting the broad-line wings using a Bayesian approach. Our study of the microlensing amplitudes between the lensed images of the quasar Q 0957+561 reveals differing sizes of the regions emitting the three prominent BELs C IV, C III], and Mg II. The strength of the differential microlensing indicates that the high-ionization line C IV arises from a compact inner region of the BLR with a half-light radius of $R_{1/2} \gtrsim 16.0$ lt-days, which represents a lower limit on the overall size of the BLR and is comparable to the size of the region emitting the r-band continuum in this system. A somewhat larger size of $R_{1/2}\gtrsim 44$ lt-days is obtained for the semi-forbidden line C III]. Microlensing has a weak impact on the lower-ionization line Mg II, which is emitted from a region with a half-light radius of $R_{1/2} \gtrsim 50$ lt-days. These findings suggest that the BEL regions may have distinct geometries and kinematics, with the more extended ones being spherically symmetric, and the most compact ones being nonspherical, with motions likely confined to a plane.

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