Determining the redshift distribution n(z) of galaxy samples is essential for several cosmological probes including weak lensing. For imaging surveys, this is usually done using photometric redshifts estimated on an object-by-object basis. We present a new approach for directly measuring the global n(z) of cosmological galaxy samples, including uncertainties, using forward modeling. Our method relies on image simulations produced using UFig (Ultra Fast Image Generator) and on ABC (Approximate Bayesian Computation) within the MCCL (Monte-Carlo Control Loops) framework. The galaxy population is modeled using parametric forms for the luminosity functions, spectral energy distributions, sizes and radial profiles of both blue and red galaxies. We apply exactly the same analysis to the real data and to the simulated images, which also include instrumental and observational effects. By adjusting the parameters of the simulations, we derive a set of acceptable models that are statistically consistent with the data. We then apply the same cuts to the simulations that were used to construct the target galaxy sample in the real data. The redshifts of the galaxies in the resulting simulated samples yield a set of n(z) distributions for the acceptable models. We demonstrate the method by determining n(z) for a cosmic shear like galaxy sample from the 4band Subaru Suprime-Cam data in the COSMOS field. We also complement this imaging data with a spectroscopic calibration sample from the VVDS survey. We compare our resulting posterior n(z) distributions to the one derived from photometric redshifts estimated using 36 photometric bands in COSMOS and find good agreement. This offers good prospects for applying our approach to current and future large imaging surveys.

Narrow-band imaging surveys allow the study of the spectral characteristics of galaxies without the need of performing their spectroscopic follow-up. In this work, we forward-model the Physics of the Accelerating Universe Survey (PAUS) narrow-band data. The aim is to improve the constraints on the spectral coefficients used to create the galaxy spectral energy distributions (SED) of the galaxy population model in In that work, the model parameters were inferred from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) data using Approximate Bayesian Computation (ABC). This led to stringent constraints on the B-band galaxy luminosity function parameters, but left the spectral coefficients only broadly constrained. To address that, we perform an ABC inference using CFHTLS and PAUS data. This is the first time our approach combining forwardmodelling and ABC is applied simultaneously to multiple datasets. We test the results of the ABC inference by comparing the narrow-band magnitudes of the observed and simulated galaxies using Principal Component Analysis, finding a very good agreement. Furthermore, we prove the scientific potential of the constrained galaxy population model to provide realistic stellar population properties by measuring them with the CIGALE SED fitting code. We use CFHTLS broad-band and PAUS narrow-band photometry for a flux-limited (i < 22.5) sample of galaxies spanning the redshift range 0 < z < 1.0. We find that properties like stellar masses, star-formation rates, mass-weighted stellar ages and metallicities are in agreement within errors between observations and simulations. Overall, this work shows the ability of our galaxy population model to correctly forward-model a complex dataset such as PAUS and the ability to reproduce the diversity of galaxy properties at the redshift range spanned by CFHTLS and PAUS.

Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to be taken into account when inferring properties of galaxies from astronomical images. In the case of cosmic shear, the PSF is one of the dominant sources of systematic errors and must be treated carefully to avoid biases in cosmological parameters. Recently, forward modeling approaches to calibrate shear measurements within the Monte-Carlo Control Loops (MCCL) framework have been developed. These methods typically require simulating a large amount of wide-field images, thus, the simulations need to be very fast yet have realistic properties in key features such as the PSF pattern. Hence, such forward modeling approaches require a very flexible PSF model, which is quick to evaluate and whose parameters can be estimated reliably from survey data. We present a PSF model that meets these requirements based on a fast deep-learning method to estimate its free parameters. We demonstrate our approach on publicly available SDSS data. We extract the most important features of the SDSS sample via principal component analysis. Next, we construct our model based on perturbations of a fixed base profile, ensuring that it captures these features. We then train a Convolutional Neural Network to estimate the free parameters of the model from noisy images of the PSF. This allows us to render a model image of each star, which we compare to the SDSS stars to evaluate the performance of our method. We find that our approach is able to accurately reproduce the SDSS PSF at the pixel level, which, due to the speed of both the model evaluation and the parameter estimation, offers good prospects for incorporating our method into the MCCL framework.

Weak gravitational lensing is a powerful probe of the dark sector, once measurement systematic errors can be controlled. In [1], a calibration method based on forward modeling, called MCCL, was proposed. This relies on fast image simulations (e.g., UFig) [2] that capture the key features of galaxy populations and measurement effects. The MCCL approach has been used in [3] to determine the redshift distribution of cosmological galaxy samples and, in the process, the authors derived a model for the galaxy population mainly based on broad-band photometry. Here, we test this model by forward modeling the 40 narrow-band photometry given by the novel PAU Survey (PAUS). For this purpose, we apply the same forced photometric pipeline on data and simulations using Source Extractor [4]. The image simulation scheme performance is assessed at the image and at the catalogues level. We find good agreement for the distribution of pixel values, the magnitudes, in the magnitude-size relation and the interband correlations. A principal component analysis is then performed, in order to derive a global comparison of the narrow-band photometry between the data and the simulations. We use a 'mixing' matrix to quantify the agreement between the observed and simulated sets of Principal Components (PCs). We find good agreement, especially for the first three most significant PCs. We also compare the coefficients of the PCs decomposition. While there are slight differences for some coefficients, we find that the distributions are in good agreement. Together, our results show that the galaxy population model derived from broad-band photometry is in good overall agreement with the PAUS data. This offers good prospect for incorporating spectral information to the galaxy model by adjusting it to the PAUS narrow-band data using forward modeling.

Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of background galaxies and requires precise control of systematic errors. Monte Carlo control loops (MCCL) is a forward modeling method designed to tackle this problem. It relies on the ultra fast image generator (UFig) to produce simulated images tuned to match the target data statistically, followed by calibrations and tolerance loops. We present the first end-to-end application of this method, on the Dark Energy Survey (DES) Year 1 wide field imaging data. We simultaneously measure the shear power spectrum C l and the redshift distribution nðzÞ of the background galaxy sample. The method includes maps of the systematic sources, point spread function (PSF), an approximate Bayesian computation (ABC) inference of the simulation model parameters, a shear calibration scheme, and a fast method to estimate the covariance matrix. We find a close statistical agreement between the simulations and the DES Y1 data using an array of diagnostics. In a nontomographic setting, we derive a set of C l and nðzÞ curves that encode the cosmic shear measurement, as well as the systematic uncertainty. Following a blinding scheme, we measure the combination of Ω m , σ 8 , and intrinsic alignment amplitude A IA , defined as S 8 D IA ¼ σ 8 ðΩ m =0.3Þ 0.5 D IA , where D IA ¼ 1 − 0.11ðA IA − 1Þ. We find S 8 D IA ¼ 0.895 þ0.054 −0.039 , where systematics are at the level of roughly 60% of the statistical errors. We discuss these results in the context of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that this method and its fast runtime offer good prospects for cosmic shear measurements with future wide-field surveys.