We present posterior sample redshift distributions for the Hyper SuprimeCam Subaru Strategic Program Weak Lensing threeyear (HSC Y3) analysis. Using the galaxies’ photometry and spatial crosscorrelations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial crosscorrelations 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 photometrybased constraints using a combination of two empirical techniques calibrated on spectroscopic and multiband photometric data that cover a spatial subset of the shear catalogue. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our crosscorrelation 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 crosscorrelations, 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 threeyear cosmological Weak Lensing analyses.
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ABSTRACT 
ABSTRACT 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 highdimensional parameter spaces in which the n(z) uncertainties may be parametrized, it is common practice to simplify the n(z) parametrization 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 selfconsistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC threeyear shape catalogue, and find that these methods recover statistically consistent error bars for the cosmological parameter constraints for predicted HSC threeyear analysis, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for data sets with the constraining power of the full HSC survey data set (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 modify the 1σ uncertainties on Ωm–S8 constraints by ∼4 per cent, and a careful model selection is needed to ensure credible parameter intervals.

ABSTRACT Studies of cosmology, galaxy evolution, and astronomical transients with current and nextgeneration widefield imaging surveys like the Rubin Observatory Legacy Survey of Space and Time are all critically dependent on estimates of photometric redshifts. Capsule networks are a new type of neural network architecture that is better suited for identifying morphological features of the input images than traditional convolutional neural networks. We use a deep capsule network trained on ugriz images, spectroscopic redshifts, and Galaxy Zoo spiral/elliptical classifications of ∼400 000 Sloan Digital Sky Survey galaxies to do photometric redshift estimation. We achieve a photometric redshift prediction accuracy and a fraction of catastrophic outliers that are comparable to or better than current methods for SDSS main galaxy samplelike data sets (r ≤ 17.8 and zspec ≤ 0.4) while requiring less data and fewer trainable parameters. Furthermore, the decisionmaking of our capsule network is much more easily interpretable as capsules act as a lowdimensional encoding of the image. When the capsules are projected on a twodimensional manifold, they form a single redshift sequence with the fraction of spirals in a region exhibiting a gradient roughly perpendicular to the redshift sequence. We perturb encodings of real galaxy images in this lowdimensional space to create synthetic galaxy images that demonstrate the image properties (e.g. size, orientation, and surface brightness) encoded by each dimension. We also measure correlations between galaxy properties (e.g. magnitudes, colours, and stellar mass) and each capsule dimension. We publicly release our code, estimated redshifts, and additional catalogues at https://biprateep.github.io/encapZulate1.

ABSTRACT In the era of precision cosmology and everimproving cosmological simulations, a better understanding of different galaxy components such as bulges and discs will give us new insight into galactic formation and evolution. Based on the fact that the stellar populations of the constituent components of galaxies differ by their dynamical properties, we develop two simple models for galaxy decomposition using the TNG100 cosmological hydrodynamical simulation from the IllustrisTNG project. The first model uses a single dynamical parameter and can distinguish four components: thin disc, thick disc, counterrotating disc, and bulge. The second model uses one more dynamical parameter, was defined in a probabilistic manner, and distinguishes two components: bulge and disc. We demonstrate the improved robustness of these models compared to a widely used method in literature involving cuts on the circularity parameter. The number fraction of discdominated galaxies at a given stellar mass obtained by our models agrees well with observations for masses exceeding log10(M*/M⊙) = 10. The galaxies classified as bulgedominated by the second model are mostly red; however, the population classified as discdominated contains significant number of red galaxies alongside the blue population. The contributions of the different galaxy components to the total stellar mass budget exhibits similar trends with stellar mass compared to the observational data, although there is a quantitative disagreement at high and low masses. The Sérsic indices and halfmass radii for the bulge and disc components agree well with those of real galaxies.more » « less

Many astrophysical analyses depend on estimates of redshifts (a proxy for distance) determined from photometric (i.e., imaging) data alone. Inaccurate estimates of photometric redshift uncertainties can result in large systematic errors. However, probability distribution outputs from many photometric redshift methods do not follow the frequentist definition of a Probability Density Function (PDF) for redshift  i.e., the fraction of times the true redshift falls between two limits z1 and z2 should be equal to the integral of the PDF between these limits. Previous works have used the global distribution of Probability Integral Transform (PIT) values to recalibrate PDFs, but offsetting inaccuracies in different regions of feature space can conspire to limit the efficacy of the method. We leverage a recently developed regression technique that characterizes the local PIT distribution at any location in feature space to perform a local recalibration of photometric redshift PDFs. Though we focus on an example from astrophysics, our method can produce PDFs which are calibrated at all locations in feature space for any use case.more » « less