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Sébastien Fabbro

Publications and source records attributed to Sébastien Fabbro.

At least 19 recordsLinked to original sources

Measuring satellite galaxy subhalo masses in redMaPPer clusters with UNIONS weak lensing data

In this work, we present the observed galaxy-galaxy lensing signal of satellite galaxies in rich clusters obtained from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS). Such observations are crucial for understanding dark matter halo physics and interaction dynamics in the cluster environment. Our goal is to investigate the tidal stripping of cluster subhalos. Theoretical predictions, supported by recent studies, suggest that as satellite galaxies fall into clusters, their dark matter halos are stripped and dispersed into the cluster's main halo, while their stellar mass remains relatively intact. A robust method to probe this phenomenon is through statistical measurements of the excess surface mass density of satellite galaxies at different cluster-centric distances. Our results reveal a significant lensing signal, with strong statistical power from the large number of lens-source pairs. A simple model used in the fitting process to constrain subhalo masses effectively reproduces the observed lensing signal at relevant satellite-centric distances. However, it lacks the complexity to accurately fit the excess surface density at larger distances, where the host cluster halo dominates. We measure the subhalo-to-stellar mass ratio as a function of cluster-centric radius and find a strong positive trend. These results confirm tidal stripping or other environmental processes that impact the relative masses of a satellite galaxy's stellar component and its dark matter halo.

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Forecasting local Primordial Non-Gaussianities from UNIONS Lyman-Break Galaxies and Planck CMB lensing

Local Primordial non-Gaussianities (PNGs), characterized by $f_{\rm NL}^{\rm loc}$, provide a powerful window into the physics of inflation. Cross-correlating high-redshift tracer samples with the CMB lensing potential offers a particularly robust probe of PNGs, mitigating imaging systematics that typically affect large-scale measurements from tracer auto-spectra. In this context, UNIONS enables the selection of $u$-dropout high-redshift Lyman-Break Galaxies (LBGs). We perform a MCMC-based forecast to estimate the uncertainties on $f_{\rm NL}^{\rm loc}$ and on a galaxy bias parameter, which captures our uncertainty in the tracer bias. From the angular cross-power spectrum between LBGs and Planck CMB lensing, we forecast $σ(f_{\rm NL}^{\rm loc})=34$ for an idealized photometric sample of $r<24.3$ LBGs selected with a Random Forest classification algorithm from UNIONS-like $ugriz$ imaging, with a resulting surface density of $1,100$ deg$^{-2}$. This precision can be improved to $σ(f_{\rm NL}^{\rm loc})=20$ after spectroscopic follow-up with DESI, during its next phase starting in 2029, DESI-II. We test a more realistic $u$-dropout LBG selection using early UNIONS data, which yields a denser sample of $r<24.2$ objects at $1,400$ deg$^{-2}$. From this sample, covering a larger footprint and expected to have a higher large-scale galaxy bias, we forecast $σ(f_{\rm NL}^{\rm loc})=20$, with similar precision achievable after DESI spectroscopic follow-up. In addition, we perform preliminary validation of the redshift distribution using the clustering-redshift method with DESI DR1 data, confirming the calibration from deep, small-area photometric fields. However, accounting for uncertainties in the clustering-redshift distribution significantly degrades the $f_{\rm NL}^{\rm loc}$ constraining power.

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Lensing the darkness: The matter density profile in cosmic voids from UNIONS

We measure the distribution of matter contained within the emptiest regions of the Universe: cosmic voids. We use the large overlap between the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS) and voids identified in the LOWZ and CMASS catalogues of the Baryon Oscillation Spectroscopic Survey (BOSS) to constrain the excess surface mass density of voids using weak lensing. We present and validate a novel method for computing the Gaussian component of the conventional weak lensing covariance, adapted for use with void studies. We detect the stacked weak lensing void density profile at the $6.2σ$ level, the most significant detection of void lensing from spectroscopically-identified voids to date. We find that large and small voids have different matter density profiles, as expected from numerical studies of void profiles. This difference is significant at the $2.3σ$ level. Comparing the void profile to a measurement of the void-galaxy cross-correlation to test the linearity of the relationship between mass and light, we find good visual agreement between the two, and a galaxy bias factor of $2.45\pm0.36$, consistent with other works. This work represents a promising detection of the lensing effect from underdensities, with the goal of promoting its development into a competitive cosmological probe.

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Mitigating Nonlinear Systematics in Weak Lensing Surveys II: Stability and Diagnostics with Intrinsic Alignment

The Bernardeau-Nishimichi-Taruya (BNT) transform provides a powerful framework for analysing tomographic cosmic shear data by improving the localization of shear correlations in physical scale. It operates by performing a linear combination of the shear data vector in $\ell$-space, yielding a transformed vector that is better localized in both redshift and $k$-space. BNT is particularly useful for estimating cosmological parameters while minimizing the impact of poorly understood nonlinear physics, without discarding large amounts of information as is typically done with simple scale cuts. In our previous work, we showed that BNT outperforms traditional weak-lensing analyses; however, that study did not include intrinsic alignments (IA). In the present work, we assess the robustness of our BNT-based $k$-cut framework in the presence of realistic IA models. We consider two cases: (i) when the assumed IA model used in sampling is close to, but not identical to, the true one, and (ii) when the assumed IA model is significantly biased compared to the true one. In the first case, the $k$-cut framework yields precise and unbiased $S_8$ constraints even with limited knowledge of large-scale modes. Using Euclid-like mock data and a stringent $k$-cut of $k \le 0.1\;{\rm Mpc^{-1}}$ for all tomographic bins, we found that BNT can constrain $S_8$ with a precision better than 2\% while non-BNT has lost all constraining power. In the second case, the BNT transform serves as a powerful diagnostic tool, revealing internal inconsistencies in $k$-space and redshift-space both exceeding 5$σ$ when the functional form of the sampling and fiducial IA models differ fundamentally.

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Neural Networks as Surrogate Solvers for Time-Dependent Accretion Disk Dynamics

Accretion disks are ubiquitous in astrophysics, appearing in diverse environments from planet-forming systems to X-ray binaries and active galactic nuclei. Traditionally, modeling their dynamics requires computationally intensive (magneto)hydrodynamic simulations. Recently, Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative. This approach trains neural networks directly on physical laws without requiring data. We for the first time demonstrate PINNs for solving the two-dimensional, time-dependent hydrodynamics of non-self-gravitating accretion disks. Our models provide solutions at arbitrary times and locations within the training domain, and successfully reproduce key physical phenomena, including the excitation and propagation of spiral density waves and gap formation from disk-companion interactions. Notably, the boundary-free approach enabled by PINNs naturally eliminates the spurious wave reflections at disk edges, which are challenging to suppress in numerical simulations. These results highlight how advanced machine learning techniques can enable physics-driven, data-free modeling of complex astrophysical systems, potentially offering an alternative to traditional numerical simulations in the future.

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Unions with UNIONS: Using galaxy-galaxy lensing to probe galaxy mergers

We use galaxy-galaxy lensing to investigate how the dark matter (DM) haloes and stellar content of galaxies with $0.012 \leq z \leq 0.32$ and $10 \leq \log_{10}(M_\star/\mathrm{M}_\odot) \leq 12$ change as a result of the merger process. To this end, we construct two samples of galaxies obtained from the Ultraviolet Near Infrared Optical Northern Survey (UNIONS), comprising 1 623 post-mergers and $\sim$30 000 non-merging controls, that live in low-density environments to use as our lenses. These samples are weighted to share the same distributions of stellar mass, redshift, and geometric mean distance to a galaxy's three nearest neighbours to ensure differences in the lensing signal are due to the merger process itself. We do not detect a statistically significant difference in the excess surface density profile of post-mergers and non-merging controls with current data. Fitting haloes composed of a point-like stellar mass component and an extended DM structure described by a Navarro-Frenk-White profile to the lensing measurements yields, for both samples, halo masses of $M_\text{halo} \sim 4\times10^{12}\,\mathrm{M}_\odot$ and a moderately negative correlation between $M_\text{halo}$ and concentration $c$. This allows us to rule out, at the 95% confidence level, merger-induced starbursts in which more than 60% of the stellar mass is formed in the burst. The application of our methods to upcoming surveys that are able to provide samples $\sim$10$\times$ larger than our current catalogue are expected to detect the weak-lensing signatures of mergers and further constrain their properties.

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Galaxies OBserved as Low-luminosity Identified Nebulae (GOBLIN): a catalog of 43,000 high-probability dwarf galaxy candidates in the UNIONS survey

The detection of low surface brightness galaxies beyond the Local Group poses significant observational challenges, yet these faint systems are fundamental to our understanding of dark matter, hierarchical galaxy formation, and cosmic structure. Their abundance and distribution provide crucial tests for cosmological models, particularly regarding the small-scale predictions of $Λ$CDM. We present a systematic detection framework for dwarf galaxy candidates in Ultraviolet Near Infrared Optical Northern Survey (UNIONS) data covering 4,861 deg$^{2}$. Our pipeline preprocesses UNIONS gri-band data through binning, artifact removal, and stellar masking, then employs MTObjects (MTO) for low surface brightness detection. After parameter cuts and cross-matching, we obtain $\sim$360 candidates per deg$^{2}$, totaling $\sim$1.5 million candidates forming our GOBLIN (Galaxies OBserved as Low-luminosity Identified Nebulae) catalog. We fine-tuned the deep learning model Zoobot, pre-trained on Galaxy Zoo labels, for classification. Training data came from visual inspection of literature candidates with probability labels from expert assessments, capturing consensus and uncertainty. Applied to all MTO objects, our method identifies 42,965 dwarf candidates with probability $>$ 0.8, including 23,072 with probability $>$ 0.9. High-probability candidates correlate spatially with massive galaxies (log$(M_{*}/M_{\odot}) \geq$ 10) within 120 Mpc. While some of these objects may have been previously identified in other surveys, we present this extensive catalog of candidates, including their positions, structural parameter estimates, and classification probabilities, as a resource for the community to enable studies of galaxy formation, evolution, and the distribution of dwarf galaxies in different environments.

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UNIONS: The Ultraviolet Near-Infrared Optical Northern Survey

The Ultraviolet Near-Infrared Optical Northern Survey (UNIONS) is a "collaboration of collaborations" that is using the Canada-France-Hawai'i Telescope, the Pan-STARRS telescopes, and the Subaru Observatory to obtain $ugriz$ images of a core survey region of 6250 deg$^2$ of the northern sky. The $10σ$ point source depth of the data, as measured within a 2-arcsecond diameter aperture, are $[u,g,r,i,z] = [23.7, 24.5, 24.2, 23.8, 23.3]$\ in AB magnitudes. UNIONS is addressing some of the most fundamental questions in astronomy, including the properties of dark matter, the growth of structure in the Universe from the very smallest galaxies to large-scale structure, and the assembly of the Milky Way. It is set to become the major ground-based legacy survey for the northern hemisphere for the next decade and provides an essential northern complement to the static-sky science of the Vera C. Rubin Observatory's Legacy Survey of Space and Time. UNIONS supports the core science mission of the {\it Euclid} space mission by providing the data necessary in the northern hemisphere for the calibration of the wavelength dependence of the {\it Euclid} point-spread function and derivation of photometric redshifts in the North Galactic Cap. This region contains the highest quality sky for {\it Euclid}, with low backgrounds from the zodiacal light, stellar density, extinction, and emission from Galactic cirrus. Here, we describe the UNIONS survey components, science goals, data products, and the current status of the overall program.

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UNIONS: a direct measurement of intrinsic alignment with BOSS/eBOSS spectroscopy

During their formation, galaxies are subject to tidal forces, which create correlations between their shapes and the large-scale structure of the Universe, known as intrinsic alignment. This alignment is a contamination for cosmic-shear measurements as one needs to disentangle correlations induced by external lensing effects from those intrinsically present in galaxies. We constrain the amplitude of intrinsic alignment and test models by making use of the overlap between the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS) covering $3500 \, \mathrm{deg}^2$, and spectroscopic data from the Baryon Oscillation Spectroscopic Survey (BOSS/eBOSS). By comparing our results to measurements from other lensing surveys on the same spectroscopic tracers, we can test the reliability of these estimates and verify they are not survey dependent. We measure projected correlation functions between positions and ellipticities, which we model with perturbation theory to constrain the commonly used non-linear alignment model and its higher-order expansion. Using the non-linear alignment model, we obtain a $13σ$ detection with CMASS galaxies, a $3σ$ detection with LRGs, and a detection compatible with the null hypothesis for ELGs. We test the tidal alignment and tidal torque model, a higher-order alignment model, which we find to be in good agreement with the non-linear alignment prediction and for which we can constrain the second-order parameters. We show a strong scaling of our intrinsic alignment amplitude with luminosity. We demonstrate that the UNIONS sample is robust against systematic contributions, particularly concerning PSF biases. We reached a reasonable agreement when comparing our measurements to other lensing samples for the same spectroscopic samples. We take this agreement as an indication that direct measurements of intrinsic alignment are mature for stage IV priors.

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The Pristine survey -- XXIII. Data Release 1 and an all-sky metallicity catalogue based on Gaia DR3 BP/RP spectro-photometry

We used the spectro-photometric information of ~219 million stars from Gaia's DR3 to calculate synthetic, narrow-band, metallicity-sensitive CaHK magnitudes that mimic the observations of the Pristine survey, a survey of photometric metallicities of Milky Way (MW) stars that has been mapping >6,500 deg^2 of the northern sky with CFHT since 2015. These synthetic magnitudes were used for an absolute recalibration of the deeper Pristine photometry and, combined with broadband Gaia information, synthetic and Pristine CaHK magnitudes were used to estimate photometric metallicities over the whole sky. The resulting metallicity catalogue is accurate down to [Fe/H]~-3.5 and is particularly suited for the exploration of the metal-poor MW ([Fe/H]<-1.0). We make available here the catalogue of synthetic CaHK_syn magnitudes for all stars with BP/RP information in Gaia DR3, as well as an associated catalogue of more than ~30 million photometric metallicities for high S/N FGK stars. This paper further provides the first public data release of the Pristine catalogue in the form of higher quality recalibrated Pristine CaHK magnitudes and photometric metallicities for all stars in common with the BP/RP spectro-photometric information in Gaia DR3. When available, the much deeper Pristine data greatly enhance the quality of the derived metallicities, in particular at the faint end of the catalogue (G_BP > 16). Combined, both photometric metallicity catalogues include more than two million metal-poor star candidates ([Fe/H]_phot<-1.0) as well as more than 200,000 and ~8,000 very and extremely metal-poor candidates ([Fe/H]_phot<-2.0 and <-3.0, respectively). Finally, we show that these metallicity catalogues can be used efficiently, among other applications to hunt for the most metal-poor stars, and to study how the structure of the MW varies with metallicity.

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Galaxy Mergers in UNIONS -- I: A Simulation-driven Hybrid Deep Learning Ensemble for Pure Galaxy Merger Classification

Merging and interactions can radically transform galaxies. However, identifying these events based solely on structure is challenging as the status of observed mergers is not easily accessible. Fortunately, cosmological simulations are now able to produce more realistic galaxy morphologies, allowing us to directly trace galaxy transformation throughout the merger sequence. To advance the potential of observational analysis closer to what is possible in simulations, we introduce a supervised deep learning Convolutional Neural Network (CNN) and Vision Transformer (ViT) hybrid framework, Mummi (MUlti Model Merger Identifier). Mummi is trained on realism-added synthetic data from IllustrisTNG100-1, and is comprised of a multi-step ensemble of models to identify mergers and non-mergers, and to subsequently classify the mergers as interacting pairs or post-mergers. To train this ensemble of models, we generate a large imaging dataset of 6.4 million images targeting UNIONS with RealSimCFIS. We show that Mummi offers a significant improvement over many previous machine learning classifiers, achieving 95% pure classifications even at Gyr long timescales when using a jury-based decision making process, mitigating class imbalance issues that arise when identifying real galaxy mergers from $z=0$ to $0.3$. Additionally, we can divide the identified mergers into pairs and post-mergers at 96% success rate. We drastically decrease the false positive rate in galaxy merger samples by 75%. By applying Mummi to the UNIONS DR5-SDSS DR7 overlap, we report a catalog of 13,448 high confidence galaxy merger candidates. Finally, we demonstrate that Mummi produces powerful representations solely using supervised learning, which can be used to bridge galaxy morphologies in simulations and observations.

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DanceCam: atmospheric turbulence mitigation in wide-field astronomical images with short-exposure video streams

We introduce a novel technique to mitigate the adverse effects of atmospheric turbulence on astronomical imaging. Utilizing a video-to-image neural network trained on simulated data, our method processes a sliding sequence of short-exposure ($\sim$0.2s) stellar field images to reconstruct an image devoid of both turbulence and noise. We demonstrate the method with simulated and observed stellar fields, and show that the brief exposure sequence allows the network to accurately associate speckles to their originating stars and effectively disentangle light from adjacent sources across a range of seeing conditions, all while preserving flux to a lower signal-to-noise ratio than an average stack. This approach results in a marked improvement in angular resolution without compromising the astrometric stability of the final image.

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Probing the Diversity of Type Ia Supernova Light Curves in the Open Supernova Catalog

The ever-growing sample of observed supernovae enhances our capacity for comprehensive supernova population studies, providing a richer dataset for understanding the diverse characteristics of Type Ia supernovae and possibly that of their progenitors. Here, we present a data-driven analysis of observed Type Ia supernova photometric light curves collected in the Open Supernova Catalog. Where available, we add the environmental information from the host galaxy. We focus on identifying sub-classes of Type Ia supernovae without imposing the pre-defined sub-classes found in the literature to date. To do so, we employ an implicit-rank minimizing autoencoder neural network for developing low-dimensional data representations, providing a compact representation of the supernova light curve diversity. When we analyze light curves alone, we find that one of our resulting latent variables is strongly correlated with redshift, allowing us to approximately ``de-redshift'' the other latent variables describing each event. After doing so, we find that three of our latent variables account for $\sim$95\% of the variance in our sample, and provide a natural separation between 91T and 91bg thermonuclear supernovae. Of note, the 02cx subclass is not unambiguously delineated from the 91bg sample in our results, nor do either the over-luminous 91T or the under-luminous 91bg/02cx samples form a clearly distinct population from the broader sample of ``other'' SN Ia events. We identify the physical characteristics of supernova light curves which best distinguish SNe 91T from SNe 91bg \& 02cx, and discuss prospects for future refinements and applications to other classes of supernovae as well as other transients.

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Mitigating the Non-Linearities in a Pyramid Wavefront Sensor

For natural guide start adaptive optics (AO) systems, pyramid wavefront sensors (PWFSs) can provide significant increase in sensitivity over the traditional Shack-Hartmann, but at the cost of a reduced linear range. When using a linear reconstructor, non-linearities result in wavefront estimation errors, which can have a significant impact on the image quality delivered by the AO system. Here we simulate a wavefront passing through a PWFS under varying observing conditions to explore the possibility of using a non-linear machine learning model to estimate wavefront errors better than a linear reconstruction. We find significant improvement even with light-weight models, underscoring the need for further investigation of this approach.

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The shape of dark matter haloes: results from weak lensing in the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS)

Cold dark matter haloes are expected to be triaxial, and so appear elliptical in projection. We use weak gravitational lensing from the Canada-France Imaging Survey (CFIS) component of the Ultraviolet-Near Infrared Optical Northern Survey (UNIONS) to measure the ellipticity of the dark matter haloes around Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Data Release 7 (DR7) and from the CMASS and LOWZ samples of the Baryon Oscillation Spectroscopic Survey (BOSS), assuming their major axes are aligned with the stellar light. We find that DR7 LRGs with masses $M \sim 2.7\times10^{13} \mathrm{M}_{\odot}/h$ have halo ellipticities $e=0.46\pm0.10$. Expressed as a fraction of the galaxy ellipticity, we find $f_h = 2.2\pm0.6$. For BOSS LRGs, the detection is of marginal significance: $e = 0.20\pm0.10$ and $f_h=0.7\pm0.7$. These results are in agreement with other measurements of halo ellipticity from weak lensing and, taken together with previous results, suggest an increase of halo ellipticity of $0.10\pm0.06$ per decade in halo mass. This trend agrees with the predictions from hydrodynamical simulations, which find that at higher halo masses, not only do dark matter haloes become more elliptical, but that the misalignment between major axis of the stellar light in the central galaxy and that of the dark matter decreases.

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The Pristine Inner Galaxy Survey (PIGS) VI: Different vertical distributions between two DIBs at 442.8 nm and 862.1 nm

Although diffuse interstellar bands (DIBs) were discovered over 100 years ago, for most of them, their origins are still unknown. Investigation on the correlations between different DIBs is an important way to study the behavior and distributions of their carriers. Based on stacking thousands of spectra from the Pristine Inner Galaxy Survey, we study the correlations between two DIBs at 442.8 nm ($λ$442.8) and 862.1 nm ($λ$862.1), as well as the dust grains, in a range of latitude spanning ${\sim}22^{\circ}$ ($4^{\circ}\,{<}\,|b|\,{<}\,15^{\circ}$) toward the Galactic center ($|\ell|\,{<}\,11^{\circ}$). Tight linear intensity correlations can be found between $λ$442.8, $λ$862.1, and dust grains for $|b|\,{<}\,12^{\circ}$ or $E(B-V)\,{>}\,0.3$ mag. For $|b|\,{>}\,12^{\circ}$, $λ$442.8 and $λ$862.1 present larger relative strength with respect to the dust grains. A systematic variation of the relative strength between $λ$442.8 and $λ$862.1 with $|b|$ and $E(B-V)$ concludes that the two DIBs do not share a common carrier. Furthermore, the carrier of $λ$862.1 is more abundant at high latitudes than that of $λ$442.8. This work can be treated as an example showing the significance and potentials to the DIB research covering a large latitude range.

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Forecasting Wavefront Corrections in an Adaptive Optics System

We use telemetry data from the Gemini North ALTAIR adaptive optics system to investigate how well the commands for wavefront correction (both Tip/Tilt and high-order turbulence) can be forecasted in order to reduce lag error (due to wavefront sensor averaging and computational delays) and improve delivered image quality. We show that a high level of reduction ($\sim$ 5 for Tip-Tilt and $\sim$ 2 for high-order modes) in RMS wavefront error can be achieved by using a "forecasting filter" based on a linear auto-regressive model with only a few coefficients ($\sim$ 30 for Tip-Tilt and $\sim$ 5 for high-order modes) to complement the existing integral servo-controller. Updating this filter to adapt to evolving observing conditions is computationally inexpensive and requires less than 10 seconds worth of telemetry data. We also use several machine learning models (Long-Short Term Memory and dilated convolutional models) to evaluate whether further improvements could be achieved with a more sophisticated non-linear model. Our attempts showed no perceptible improvements over linear auto-regressive predictions, even for large lags where residuals from the linear models are high, suggesting that non-linear wavefront distortions for ALTAIR at the Gemini North telescope may not be forecasted with the current setup

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ShapePipe: a new shape measurement pipeline and weak-lensing application to UNIONS/CFIS data

UNIONS is an ongoing collaboration that will provide the largest deep photometric survey of the Northern sky in four optical bands to date. As part of this collaboration, CFIS is taking $r$-band data with an average seeing of 0.65 arcsec, which is complete to magnitude 24.5 and thus ideal for weak-lensing studies. We perform the first weak-lensing analysis of CFIS $r$-band data over an area spanning 1700 deg$^2$ of the sky. We create a catalogue with measured shapes for 40 million galaxies, corresponding to an effective density of 6.8 galaxies per square arcminute, and demonstrate a low level of systematic biases. This work serves as the basis for further cosmological studies using the full UNIONS survey of 4800 deg$^2$ when completed. Here we present ShapePipe, a newly developed weak-lensing pipeline. This pipeline makes use of state-of-the-art methods such as Ngmix for accurate galaxy shape measurement. Shear calibration is performed with metacalibration. We carry out extensive validation tests on the Point Spread Function (PSF), and on the galaxy shapes. In addition, we create realistic image simulations to validate the estimated shear. We quantify the PSF model accuracy and show that the level of systematics is low as measured by the PSF residuals. Their effect on the shear two-point correlation function is sub-dominant compared to the cosmological contribution on angular scales <100 arcmin. The additive shear bias is below 5x$10^{-4}$, and the residual multiplicative shear bias is at most $10^{-3}$ as measured on image simulations. Using COSEBIs we show that there are no significant B-modes present in second-order shear statistics. We present convergence maps and see clear correlations of the E-mode with known cluster positions. We measure the stacked tangential shear profile around Planck clusters at a significance higher than $4σ$.

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