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Rachel Mandelbaum

Publications and source records attributed to Rachel Mandelbaum.

At least 37 records · Page 2Linked to original sources
arXiv2025

DESC DC2 Data Release Note

In preparation for cosmological analyses of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), the LSST Dark Energy Science Collaboration (LSST DESC) has created a 300 deg$^2$ simulated survey as part of an effort called Data Challenge 2 (DC2). The DC2 simulated sky survey, in six optical bands with observations following a reference LSST observing cadence, was processed with the LSST Science Pipelines (19.0.0). In this Note, we describe the public data release of the resulting object catalogs for the coadded images of five years of simulated observations along with associated truth catalogs. We include a brief description of the major features of the available data sets. To enable convenient access to the data products, we have developed a web portal connected to Globus data services. We describe how to access the data and provide example Jupyter Notebooks in Python to aid first interactions with the data. We welcome feedback and questions about the data release via a GitHub repository.

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arXiv2025

Matching Cosmic Shear Analysis in Harmonic and Real Space

Recent cosmic shear analyses have exhibited discrepancies of up to $1σ$ between the inferred cosmological parameters when analyzing summary statistics in real space versus harmonic space. In this paper, we demonstrate the consistent measurement and analysis of cosmic shear two-point functions in harmonic and real space using the $i${\sc Master} algorithm. This algorithm provides a unified prescription to model the survey window effects and scale cuts in both real space (due to observational systematics) and harmonic space (due to model limitations), resulting in a matching estimation of the cosmic shear power spectrum from both harmonic and real space estimators. We show that the $i$\textsc{Master} algorithm gives matching results using measurements from the HSC Y1 mock shape catalogs in both real and harmonic space, resulting in matching inferences of $S_8=σ_8(Ω_m/0.3)^{0.5}$. This method provides an unbiased estimate of the cosmic shear power spectrum, and $S_8$ inference that has a correlation coefficient of 0.997 between analyses using measurements in real space and harmonic space when $S_8$ is the only free parameter. We observe the mean difference between the two inferred $S_8$ values to be 0.0004 across noise-free mock realizations, far below the observed difference of 0.042 for the published HSC Y1 analyses and well below the statistical uncertainties. While the notation employed in this paper is specific to photometric galaxy surveys, the methods are equally applicable and can be extended to spectroscopic galaxy surveys, intensity mapping, and CMB surveys.

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arXiv2025

Chromatic Effects on the PSF and Shear Measurement for the Roman Space Telescope High-Latitude Wide Area Survey

Weak gravitational lensing (WL) is a key cosmological probe that requires precise measurement of galaxy images to infer shape distortions, or shear, and constrain cosmology. Accurate estimation of the Point Spread Function (PSF) is crucial for shear measurement, but the wavelength dependence of the PSF introduces chromatic biases that can systematically impact shear inference. We focus on biases arising from spectral energy distribution (SED) differences between stars, used for PSF modeling, and galaxies, used for shear measurement. We investigate these effects in $\textit{Roman's}$ four design reference mission WL bands (Y106, J129, H158, F184) and wide filter (W146). Using $\textit{Roman}$-like image simulations, we quantify the induced shear biases and compare them to requirements on those biases. Multiplicative biases over all galaxies hover around $\sim$0.2% in the WL bands and 2% in the wide filter, exceeding the mission requirement of $|m| < 0.032\%$ and relaxed requirement of $|m| < 0.1\%$. In individual redshift bins, biases can reach 0.4$\unicode{x2013}$0.9% for the WL bands and 3$\unicode{x2013}$6% for the wide filter. Additive biases remain acceptable in the WL bands but exceed systematic limits in the wide filter. We develop and test PSF-level corrections, showing that a first-order correction reduces biases within survey requirements for the WL bands; however, higher-order terms are necessary for the wide filter. Our results highlight the necessity of chromatic corrections for precision WL with $\textit{Roman}$ and provide a framework for mitigating these biases. Finally, we compare analytical color-based corrections to self-organizing maps (SOMs) and find that both methods effectively reduce biases.

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arXiv2025

Analytical Noise Bias Correction for Precise Weak Lensing Shear Inference

Noise bias is a significant source of systematic error in weak gravitational lensing measurements that must be corrected to satisfy the stringent standards of modern imaging surveys in the era of precision cosmology. This paper reviews the analytical noise bias correction method and provides analytical derivations demonstrating that we can recover shear to its second order using the 'renoising' noise bias correction approach introduced by Metacalibration. We implement this analytical noise bias correction within the AnaCal shear estimation framework and propose several enhancements to the noise bias correction algorithm. We evaluate the improved AnaCal using simulations designed to replicate Rubin LSST imaging data. These simulations feature semi-realistic galaxies and stars, complete with representative distributions of magnitudes and Galactic spatial density. We conduct tests under various observational challenges, including cosmic rays, defective CCD columns, bright star saturation, bleed trails, and spatially variable point spread functions. Our results indicate a multiplicative bias in weak lensing shear recovery of less than a few tenths of a percent, meeting LSST DESC requirements without requiring calibration from external image simulations. Additionally, our algorithm achieves rapid processing, handling one galaxy in less than a millisecond.

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arXiv2024

Accurate Shear Estimation with Fourth-Order Moments

As imaging surveys progress in exploring the large-scale structure of the Universe through the use of weak gravitational lensing, achieving subpercent accuracy in estimating shape distortions caused by lensing, or shear, is imperative for precision cosmology. In this paper, we extend the \texttt{FPFS} shear estimator using fourth-order shapelet moments and combine it with the original second-order shear estimator to reduce galaxy shape noise. We calibrate this novel shear estimator analytically to a subpercent level accuracy using the \texttt{AnaCal} framework. This higher-order shear estimator is tested with realistic image simulations, and after analytical correction for the detection/selection bias and noise bias, the multiplicative shear bias $|m|$ is below $3\times10^{-3}$ ($99.7\%$ confidence interval) for both isolated and blended galaxies. Once combined with the second-order \texttt{FPFS} shear estimator, the shape noise is reduced by $\sim35\%$ for isolated galaxies in simulations with HSC and LSST observational conditions. However, for blended galaxies, the effective number density does not significantly improve with the combination of the two estimators. Based on these results, we recommend exploration of how this framework can further reduce the systematic uncertainties in shear due to PSF leakage and modelling error, and potentially provide improved precision in shear inference in high-resolution space-based images.

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arXiv2024

Third-order intrinsic alignment of SDSS BOSS LOWZ galaxies

Cosmic shear is a powerful probe of cosmology, but it is affected by the intrinsic alignment (IA) of galaxy shapes with the large-scale structure. Upcoming surveys like Euclid and Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) require an accurate understanding of IA, particularly for higher-order cosmic shear statistics that are vital for extracting the most cosmological information. In this paper, we report the first detection of third-order IA correlations using the LOWZ galaxy sample from the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey (BOSS). We compare our measurements with predictions from the MICE cosmological simulation and an analytical NLA-inspired model informed by second-order correlations. We also explore the dependence of the third-order correlation on the galaxies' luminosity. We find that the amplitude $A_\mathrm{IA}$ of the IA signal is non-zero at the $4.7σ$ ($7.6σ$) level for scales between $6 h^{-1} \mathrm{Mpc}$ ($1 h^{-1} \mathrm{Mpc}$) and $20 h^{-1} \mathrm{Mpc}$. For scales above $6 h^{-1}\mathrm{Mpc}$ the inferred AIA agrees both with the prediction from the simulation and estimates from second-order statistics within $1σ$ but deviations arise at smaller scales. Our results demonstrate the feasibility of measuring third-order IA correlations and using them for constraining IA models. The agreement between second- and third-order IA constraints also opens the opportunity for a consistent joint analysis and IA self-calibration, promising tighter parameter constraints for upcoming cosmological surveys.

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arXiv2024

A Hamiltonian, post-Born, three-dimensional, on-the-fly ray tracing algorithm for gravitational lensing

The analyses of the next generation cosmological surveys demand an accurate, efficient, and differentiable method for simulating the universe and its observables across cosmological volumes. We present Hamiltonian ray tracing (HRT) -- the first post-Born (accounting for lens-lens coupling and without relying on the Born approximation), three-dimensional (without assuming the thin-lens approximation), and on-the-fly (applicable to any structure formation simulations) ray tracing algorithm based on the Hamiltonian formalism. HRT performs symplectic integration of the photon geodesics in a weak gravitational field, and can integrate tightly with any gravity solver, enabling co-evolution of matter particles and light rays with minimal additional computations. We implement HRT in the particle-mesh library $\texttt{pmwd}$, leveraging hardware accelerators such as GPUs and automatic differentiation capabilities based on $\texttt{JAX}$. When tested on a point-mass lens, HRT achieves sub-percent accuracy in deflection angles above the resolution limit across both weak and moderately strong lensing regimes. We also test HRT in cosmological simulations on the convergence maps and their power spectra.

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arXiv2024

Geometric deep learning for galaxy-halo connection: a case study for galaxy intrinsic alignments

Forthcoming cosmological imaging surveys, such as the Rubin Observatory LSST, require large-scale simulations encompassing realistic galaxy populations for a variety of scientific applications. Of particular concern is the phenomenon of intrinsic alignments (IA), whereby galaxies orient themselves towards overdensities, potentially introducing significant systematic biases in weak gravitational lensing analyses if they are not properly modeled. Due to computational constraints, simulating the intricate details of galaxy formation and evolution relevant to IA across vast volumes is impractical. As an alternative, we propose a Deep Generative Model trained on the IllustrisTNG-100 simulation to sample 3D galaxy shapes and orientations to accurately reproduce intrinsic alignments along with correlated scalar features. We model the cosmic web as a set of graphs, each graph representing a halo with nodes representing the subhalos/galaxies. The architecture consists of a SO(3) $\times$ $\mathbb{R}^n$ diffusion generative model, for galaxy orientations and $n$ scalars, implemented with E(3) equivariant Graph Neural Networks that explicitly respect the Euclidean symmetries of our Universe. The model is able to learn and predict features such as galaxy orientations that are statistically consistent with the reference simulation. Notably, our model demonstrates the ability to jointly model Euclidean-valued scalars (galaxy sizes, shapes, and colors) along with non-Euclidean valued SO(3) quantities (galaxy orientations) that are governed by highly complex galactic physics at non-linear scales.

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arXiv2024

An Empirical Model For Intrinsic Alignments: Insights From Cosmological Simulations

We extend current models of the halo occupation distribution (HOD) to include a flexible, empirical framework for the forward modeling of the intrinsic alignment (IA) of galaxies. A primary goal of this work is to produce mock galaxy catalogs for the purpose of validating existing models and methods for the mitigation of IA in weak lensing measurements. This technique can also be used to produce new, simulation-based predictions for IA and galaxy clustering. Our model is probabilistically formulated, and rests upon the assumption that the orientations of galaxies exhibit a correlation with their host dark matter (sub)halo orientation or with their position within the halo. We examine the necessary components and phenomenology of such a model by considering the alignments between (sub)halos in a cosmological dark matter only simulation. We then validate this model for a realistic galaxy population in a set of simulations in the IllustrisTNG suite. We create an HOD mock with TNG-like correlations using our method, constraining the associated IA model parameters, with the $χ^2_{\rm dof}$ between our model's correlations and those of Illustris matching as closely as 1.4 and 1.1 for orientation--position and orientation--orientation correlation functions, respectively. By modeling the misalignment between galaxies and their host halo, we show that the 3-dimensional two-point position and orientation correlation functions of simulated (sub)halos and galaxies can be accurately reproduced from quasi-linear scales down to $0.1~h^{-1}{\rm Mpc}$. We also find evidence for environmental influence on IA within a halo. Our publicly-available software provides a key component enabling efficient determination of Bayesian posteriors on IA model parameters using observational measurements of galaxy-orientation correlation functions in the highly nonlinear regime.

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arXiv2024

Photometric redshifts and intrinsic alignments: degeneracies and biases in 3$\times$2pt analysis

We present a systematic study of cosmological parameter bias in weak lensing and large-scale structure analyses for upcoming imaging surveys induced by the interplay of intrinsic alignments (IA) and photometric redshift (photo-z) model mis-specification error. We first examine the degeneracies between the parameters of the Tidal Alignment - Tidal Torquing (TATT) model for IA and of a photo-z model including a mean shift ($Δ\bar{z}$) and variance ($σ_{z}$) for each tomographic bin of lenses and sources, under a variety of underlying true IA behaviors. We identify strong degeneracies between: (1) the redshift scaling of the tidal alignment amplitude and the mean shift and variances of source bins, (2) the redshift scaling of the tidal torquing amplitude and the variance of the lowest-$z$ source bin, and (3) the IA source density weighting and the mean shift and variance of several source bins. We then use this information to guide our exploration of the level of cosmological parameter bias which can be induced given incorrect modelling of IA, photo-z, or both. We find that marginalizing over all the parameters of TATT is generally sufficient to preclude cosmological parameter bias in the scenarios we consider. However, this does not necessarily mean that IA and photo-z parameters are themselves unbiased, nor does it mean that the best-fit model is a good fit to the data. We also find scenarios where the inferred parameters produce $χ^2_{\rm DOF}$ values indicative of a good fit but cosmological parameter bias is significant, particularly when the IA source density weighting parameter is not marginalized over.

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arXiv2024

Joint inference of multiplicative and additive systematics in galaxy density fluctuations and clustering measurements

Galaxy clustering measurements are a key probe of the matter density field in the Universe. With the era of precision cosmology upon us, surveys rely on precise measurements of the clustering signal for meaningful cosmological analysis. However, the presence of systematic contaminants can bias the observed galaxy number density, and thereby bias the galaxy two-point statistics. As the statistical uncertainties get smaller, correcting for these systematic contaminants becomes increasingly important for unbiased cosmological analysis. We present and validate a new method for understanding and mitigating both additive and multiplicative systematics in galaxy clustering measurements (two-point function) by joint inference of contaminants in the galaxy overdensity field (one-point function) using a maximum-likelihood estimator (MLE). We test this methodology with KiDS-like mock galaxy catalogs and synthetic systematic template maps. We estimate the cosmological impact of such mitigation by quantifying uncertainties and possible biases in the inferred relationship between the observed and the true galaxy clustering signal. Our method robustly corrects the clustering signal to the sub-percent level and reduces numerous additive and multiplicative systematics from $1.5 σ$ to less than $0.1σ$ for the scenarios we tested. In addition, we provide an empirical approach to identifying the functional form (additive, multiplicative, or other) by which specific systematics contaminate the galaxy number density. Even though this approach is tested and geared towards systematics contaminating the galaxy number density, the methods can be extended to systematics mitigation for other two-point correlation measurements.

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arXiv2024

Accurate field-level weak lensing inference for precision cosmology

We present $\texttt{Miko}$, a catalog-to-cosmology pipeline for general flat-sky field-level inference, which provides access to cosmological information beyond the two-point statistics. In the context of weak lensing, we identify several new field-level analysis systematics (such as aliasing, Fourier mode-coupling, and density-induced shape noise), quantify their impact on cosmological constraints, and correct the biases to a percent level. Next, we find that model misspecification can lead to both absolute bias and incorrect uncertainty quantification for the inferred cosmological parameters in realistic simulations. The Gaussian map prior infers unbiased cosmological parameters, regardless of the true data distribution, but it yields overconfident uncertainties. The log-normal map prior quantifies the uncertainties accurately, although it requires careful calibration of the shift parameters for unbiased cosmological parameters. We demonstrate systematics control down to the $2\%$ level for both models, making them suitable for ongoing weak lensing surveys.

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arXiv2024

The little coadd that could: Estimating shear from coadded images

Upcoming wide field surveys will have many overlapping epochs of the same region of sky. The conventional wisdom is that in order to reduce the errors sufficiently for systematics-limited measurements, like weak lensing, we must do simultaneous fitting of all the epochs. Using current algorithms this will require a significant amount of computing time and effort. In this paper, we revisit the potential of using coadds for shear measurements. We show on a set of image simulations that the multiplicative shear bias can be constrained below the 0.1% level on coadds, which is sufficient for future lensing surveys. We see no significant differences between simultaneous fitting and coadded approaches for two independent shear codes: Metacalibration and BFD. One caveat of our approach is the assumption of a principled coadd, i.e. the PSF is mathematically well-defined for all the input images. This requires us to reject CCD images that do not fully cover the coadd region. We estimate that the number of epochs that must be rejected for a survey like LSST is on the order of 20%, resulting in a small loss in depth of less than 0.1 magnitudes. We also put forward a cell-based coaddition scheme that meets the above requirements for unbiased weak lensing shear estimation in the context of LSST.

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arXiv2024

Increasing the power of weak lensing survey data with multipole-based intrinsic alignment estimators

It has long been known that galaxy shapes align coherently with the large-scale density field. Characterizing this effect is essential to interpreting measurements of weak gravitational lensing, the deflection of light from distant galaxies by matter overdensities along the line of sight, as it also produces coherent galaxy alignments that we wish to interpret in terms of a cosmological model. Existing direct measurements of intrinsic alignments using galaxy samples with high-quality shape and redshift measurements typically use well-understood but sub-optimal projected estimators, which do not make good use of the information in the data when comparing those estimators to theoretical models. We demonstrate a more optimal estimator, based on a multipole expansion of the correlation functions or power spectra, for direct measurements of galaxy intrinsic alignments. We show that even using the lowest order multipole alone increases the significance of inferred model parameters using simulated and real data, without any additional modeling complexity. We apply this estimator to measurements of parameters of the non-linear alignment model using data from the Sloan Digital Sky survey, demonstrating consistent results with a factor of $\sim$2 greater precision in parameter fits to intrinsic alignments models. This result is functionally equivalent to quadrupling the survey area, but without the attendant costs -- thereby demonstrating the value in using this new estimator in current and future intrinsic alignments measurements using spectroscopic galaxy samples.

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arXiv2024

Simulating image coaddition with the Nancy Grace Roman Space Telescope: II. Analysis of the simulated images and implications for weak lensing

One challenge for applying current weak lensing analysis tools to the Nancy Grace Roman Space Telescope is that individual images will be undersampled. Our companion paper presented an initial application of Imcom - an algorithm that builds an optimal mapping from input to output pixels to reconstruct a fully sampled combined image - on the Roman image simulations. In this paper, we measure the output noise power spectra, identify the sources of the major features in the power spectra, and show that simple analytic models that ignore sampling effects underestimate the power spectra of the coadded noise images. We compute the moments of both idealized injected stars and fully simulated stars in the coadded images, and their 1- and 2-point statistics. We show that the idealized injected stars have root-mean-square ellipticity errors (1 - 6) x 10-4 per component depending on the band; the correlation functions are >= 2 orders of magnitude below requirements, indicating that the image combination step itself is using a small fraction of the overall Roman 2nd moment error budget, although the 4th moments are larger and warrant further investigation. The stars in the simulated sky images, which include blending and chromaticity effects, have correlation functions near the requirement level (and below the requirement level in a wide-band image constructed by stacking all 4 filters). We evaluate the noise-induced biases in the ellipticities of injected stars, and explain the resulting trends with an analytical model. We conclude by enumerating the next steps in developing an image coaddition pipeline for Roman.

astro-ph.IM↗
arXiv2024

Simulating image coaddition with the Nancy Grace Roman Space Telescope: I. Simulation methodology and general results

The upcoming Nancy Grace Roman Space Telescope will carry out a wide-area survey in the near infrared. A key science objective is the measurement of cosmic structure via weak gravitational lensing. Roman data will be undersampled, which introduces new challenges in the measurement of source galaxy shapes; a potential solution is to use linear algebra-based coaddition techniques such as Imcom that combine multiple undersampled images to produce a single oversampled output mosaic with a desired "target" point spread function (PSF). We present here an initial application of Imcom to 0.64 square degrees of simulated Roman data, based on the Roman branch of the Legacy Survey of Space and Time (LSST) Dark Energy Science Collaboration (DESC) Data Challenge 2 (DC2) simulation. We show that Imcom runs successfully on simulated data that includes features such as plate scale distortions, chip gaps, detector defects, and cosmic ray masks. We simultaneously propagate grids of injected sources and simulated noise fields as well as the full simulation. We quantify the residual deviations of the PSF from the target (the "leakage"), as well as noise properties of the output images; we discuss how the overall tiling pattern as well as Moiré patterns appear in the final leakage and noise maps. We include appendices on interpolation algorithms and the interaction of undersampling with image processing operations that may be of broader applicability. The companion paper ("Paper II") explores the implications for weak lensing analyses.

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arXiv2024

The Intrinsic Alignment of Galaxy Clusters and Impact of Projection Effects

Galaxy clusters, being the most massive objects in the Universe, exhibit the strongest alignment with the large-scale structure. However, mis-identification of members due to projection effects from the large scale structure can occur. We studied the impact of projection effects on the measurement of the intrinsic alignment of galaxy clusters, using galaxy cluster mock catalogs. Our findings showed that projection effects result in a decrease of the large scale intrinsic alignment signal of the cluster and produce a bump at $r_p\sim 1h^{-1}/Mpc$, most likely due to interlopers and missed member galaxies. This decrease in signal explains the observed similar alignment strength between bright central galaxies and clusters in the SDSS redMaPPer cluster catalog. The projection effect and cluster intrinsic alignment signal are coupled, with clusters having lower fractions of missing members or having higher fraction of interlopers exhibiting higher alignment signals in their projected shapes. We aim to use these findings to determine the impact of projection effects on galaxy cluster cosmology in future studies.

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