Cosmological constraints from HSC survey first-year data using deep learning

We present cosmological constraints from the Subaru Hyper Suprime-Cam (HSC) first-year weak lensing shear catalogue using convolutional neural networks (CNNs) and conventional summary statistics. We crop 19 $3\times3\,\mathrm{{deg}^2}$ sub-fields from the first-year area, divide the galaxies with redshift $0.3\le z\le1.5$ into four equally-spaced redshift bins, and perform tomographic analyses. We develop a pipeline to generate simulated convergence maps from cosmological $N$-body simulations, where we account for effects such as intrinsic alignments (IAs), baryons, photometric redshift errors, and point spread function errors, to match characteristics of the real catalogue. We train CNNs that can predict the underlying parameters from the simulated maps, and we use them to construct likelihood functions for Bayesian analyses. In the $\Lambda$ cold dark matter model with two free cosmological parameters $\Omega_\mathrm{m}$ and $\sigma_8$, we find $\Omega_\mathrm{m}=0.278_{-0.035}^{+0.037}$, $S_8\equiv(\Omega_\mathrm{m}/0.3)^{0.5}\sigma_8=0.793_{-0.018}^{+0.017}$, and the IA amplitude $A_\mathrm{IA}=0.20_{-0.58}^{+0.55}$. In a model with four additional free baryonic parameters, we find $\Omega_\mathrm{m}=0.268_{-0.036}^{+0.040}$, $S_8=0.819_{-0.024}^{+0.034}$, and $A_\mathrm{IA}=-0.16_{-0.58}^{+0.59}$, with the baryonic parameters not being well-constrained. We also find that statistical uncertainties of the parameters by the CNNs are smaller than those from the power spectrum (5--24 percent smaller for $S_8$ and a factor of 2.5--3.0 smaller for $\Omega_\mathrm{m}$), showing the effectiveness of CNNs for uncovering additional cosmological information from the HSC data. With baryons, the $S_8$ discrepancy between HSC first-year data and Planck 2018 is reduced from $\sim2.2\,\sigma$ to $0.3\text{--}0.5\,\sigma$.Comment: 22 pages, 14 figure

Three-Dimensional Reconstruction of Weak-Lensing Mass Maps with a Sparsity Prior. II. Weighing Triaxial Cluster Halos

Continuing work presented in Li et al. (2021), we performed a series of tests to our high-resolution three-dimensional mass map reconstruction algorithm \splinv{}. We test the mass reconstruction accuracy against realistic mock catalogs generated using shear field produced by triaxial halos with the inner density profile of $\rho \propto r^{-1}$ and of $\rho \propto r^{-1.5}$. The galaxy shape noise is modeled based on the Year-1 Subaru Hyper Suprime-Cam (HSC) Survey. After reviewing mathematical details of our algorithm and dark matter halo models, we determine an optimal value of the coefficient of the adaptive LASSO regression penalty term for single halo reconstruction. We successfully measure halo masses for massive triaxial halos; the mass determination accuracy is 5 percent for halos with $M = 10^{14.6}~M_\odot$ at $0.0625\leq z \leq 0.2425$, and 5 percent for those with $10^{14.8}~M_\odot$ at $0.0625\leq z \leq 0.4675$, and 20 percent for $M= 10^{15.0} ~M_\odot$ and $M=10^{15.2}~M_\odot$ in the redshift range $0.0625\leq z \leq 0.4675$. The redshift estimate accuracy is consistently below $\Delta z /z \leq 0.05$ for the above halo masses in the range $0.1525\leq z \leq 0.4675$. We also demonstrate that the orientation of triaxial halos and systematic error in our halo model do not affect reconstruction result significantly. Finally, we present results from reconstruction of mass distribution using shear catalogs produced by multiple halos, to show \splinv{}'s capability using realistic shear maps from ongoing and future galaxy surveys.Comment: 20 pages, 20 figure

A Differentiable Perturbation-based Weak Lensing Shear Estimator

Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding sub-percent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based shear estimator (FPFS), using JAX, which is publicly available as part of a new suite of analytic shear algorithms called AnaCal. This code can analytically calibrate the shear response of any nonlinear observable constructed with the FPFS shapelets and detection modes utilizing auto-differentiation (AD), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the AD capability of JAX, it calculates the full Hessian matrix of the non-linear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new AnaCal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the ten-year LSST. For the generic shear estimator, the magnitude of the multiplicative bias $|m|$ is below $3\times 10^{-3}$ (99.7% confidence interval), and the effective galaxy number density is improved by 5%. We also discuss some planned future additions to the AnaCal software suite to extend its applicability beyond the FPFS measurements.Comment: 9 pages, 7 figures, submitted to MNRA

Photometric Redshift Uncertainties in Weak Gravitational Lensing Shear Analysis: Models and Marginalization

Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution $n(z)$. Due to the challenge of running Markov Chain Monte-Carlo (MCMC) in the high dimensional parameter spaces in which the $n(z)$ uncertainties may be parameterized, it is common practice to simplify the $n(z)$ parameterization or combine MCMC chains that each have a fixed $n(z)$ resampled from the $n(z)$ uncertainties. In this work, we propose a statistically-principled Bayesian resampling approach for marginalizing over the $n(z)$ uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalog, and find that these methods recover similar cosmological parameter constraints, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for datasets with the constraining power of the full HSC survey dataset (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over $n(z)$ uncertainty among the several methods from the literature may significantly impact the statistical uncertainties on cosmological parameters, and a careful model selection is needed to ensure credible parameter intervals.Comment: 15 pages, 8 figures, submitted to mnra

The stellar halo of isolated central galaxies in the Hyper Suprime-Cam imaging survey

We study the faint stellar halo of isolated central galaxies, by stacking galaxy images in the HSC survey and accounting for the residual sky background sampled with random points. The surface brightness profiles in HSC $r$-band are measured for a wide range of galaxy stellar masses ($9.2<\log_{10}M_\ast/M_\odot<11.4$) and out to 120 kpc. Failing to account for the stellar halo below the noise level of individual images will lead to underestimates of the total luminosity by $\leq 15\%$. Splitting galaxies according to the concentration parameter of their light distributions, we find that the surface brightness profiles of low concentration galaxies drop faster between 20 and 100 kpc than those of high concentration galaxies. Albeit the large galaxy-to-galaxy scatter, we find a strong self-similarity of the stellar halo profiles. They show unified forms once the projected distance is scaled by the halo virial radius. The colour of galaxies is redder in the centre and bluer outside, with high concentration galaxies having redder and more flattened colour profiles. There are indications of a colour minimum, beyond which the colour of the outer stellar halo turns red again. This colour minimum, however, is very sensitive to the completeness in masking satellite galaxies. We also examine the effect of the extended PSF in the measurement of the stellar halo, which is particularly important for low mass or low concentration galaxies. The PSF-corrected surface brightness profile can be measured down to $\sim$31 $\mathrm{mag}/\mathrm{arcsec}^2$ at 3-$\sigma$ significance. PSF also slightly flattens the measured colour profiles.Comment: accepted by MNRAS - Significant changes have been made compared with the first version, including discussions on the extended PSF wings, robustness of our results to source detection and masking thresholds and more detailed investigations on the indications of positive colour gradient

Weak Lensing Tomographic Redshift Distribution Inference for the Hyper Suprime-Cam Subaru Strategic Program three-year shape catalogue

We present posterior sample redshift distributions for the Hyper Suprime-Cam Subaru Strategic Program Weak Lensing three-year (HSC Y3) analysis. Using the galaxies' photometry and spatial cross-correlations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial cross-correlations are derived using a subsample of Luminous Red Galaxies (LRGs) with accurate redshift information available up to a photometric redshift of $z < 1.2$. We derive the photometry-based constraints using a combination of two empirical techniques calibrated on spectroscopic- and multiband photometric data that covers a spatial subset of the shear catalog. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our cross-correlation analysis models the photometric redshift error of the LRGs to correct for systematic biases and statistical uncertainties. We demonstrate consistency between the sample redshift distributions derived using the spatial cross-correlations, the photometry, and the posterior of the combined analysis. Based on this assessment, we recommend conservative priors for sample redshift distributions of tomographic bins used in the three-year cosmological Weak Lensing analyses.Comment: 23 pages, 11 figures, 1 table, submitted to the MNRAS; comments welcom