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The forward modelling of galaxy surveys has recently gathered interest as one of the primary methods to achieve the required precision on the estimate of the redshift distributions for stage IV surveys. One of the key aspects of forward modelling a galaxy survey is the connection between the physical properties drawn from a galaxy population model and the intrinsic SEDs, achieved through SPS codes (e.g. FSPS). However, SPS requires a large number of detailed assumptions on the constituents of galaxies, for which the model choice or parameter values are currently uncertain. In this work, we perform a sensitivity study of the impact that the variations of the SED modelling choices have on the mean and scatter of the tomographic galaxy redshift distributions. We assumed the Prospector beta model as the fiducial input galaxy population model and used its SPS parameters to build 9 bands magnitudes of a fiducial sample of galaxies. We then built samples of galaxy magnitudes by varying one SED modelling choice at a time. We modelled the colour redshift relation of these galaxy samples using the SOM approach. We placed galaxies in the SOM cells according to their observed frame colours and used their cell assignment to build colour selected tomographic bins. Finally, we compared each variant's binned redshift distributions against the estimates obtained for the fiducial model. We find that the SED components related to the IMF, AGNs, gas physics, and the attenuation law substantially bias the mean and the scatter of the tomographic redshift distributions with respect to those estimated with the fiducial model. Regardless of the applied stellar mass function based re-weighting strategy, the bias in the mean and the scatter of the tomographic redshift distributions are greater than the precision requirements set by next-generation Stage IV galaxy surveys, such as LSST and Euclid.

In today's modern wide-field galaxy surveys, there is the necessity for parametric surface brightness decomposition codes characterised by accuracy, small degree of user intervention, and high degree of parallelisation. We try to address this necessity by introducing \\(\\mathrm{morphofit}\\), a highly parallelisable \\(\\mathrm{Python}\\) package for the estimate of galaxy structural parameters. The package makes use of wide-spread and reliable codes, namely \\(\\mathrm{SExtractor}\\) and \\(\\mathrm{GALFIT}\\). It has been optimised and tested in both low-density and crowded environments, where blending and diffuse light makes the structural parameters estimate particularly challenging. \\(\\mathrm{morphofit}\\) allows the user to fit multiple surface brightness components to each individual galaxy, among those currently implemented in the code. Using simulated images of single Sérsic and bulge plus disk galaxy light profiles with different bulge-to-total luminosity (\\(\\mathrm{B/T}\\)) ratios, we show that \\(\\mathrm{morphofit}\\) is able to recover the input structural parameters of the simulated galaxies with good accuracy. We also compare its estimates against existing literature studies, finding consistency within the errors. We use the package in Tortorelli et al. 2023 to measure the structural parameters of cluster galaxies in order to study the wavelength dependence of the Kormendy relation of early-type galaxies. The package is available on github (https://github.com/torluca/morphofit) and on the Pypi server (https://pypi.org/project/morphofit/).

Accurate redshift calibration is required to obtain unbiased cosmological information from large-scale galaxy surveys. In a forward modelling approach, the redshift distribution n(z) of a galaxy sample is measured using a parametric galaxy population model constrained by observations. We use a model that captures the redshift evolution of the galaxy luminosity functions, colours, and morphology, for red and blue samples. We constrain this model via simulation-based inference, using factorized Approximate Bayesian Computation (ABC) at the image level. We apply this framework to HSC deep field images, complemented with photometric redshifts from COSMOS2020. The simulated telescope images include realistic observational and instrumental effects. By applying the same processing and selection to real data and simulations, we obtain a sample of n(z) distributions from the ABC posterior. The photometric properties of the simulated galaxies are in good agreement with those from the real data, including magnitude, colour and redshift joint distributions. We compare the posterior n(z) from our simulations to the COSMOS2020 redshift distributions obtained via template fitting photometric data spanning the wavelength range from UV to IR. We mitigate sample variance in COSMOS by applying a reweighting technique. We thus obtain a good agreement between the simulated and observed redshift distributions, with a difference in the mean at the 1\\(\\sigma\\) level up to a magnitude of 24 in the i band. We discuss how our forward model can be applied to current and future surveys and be further extended. The ABC posterior and further material will be made publicly available at https://cosmology.ethz.ch/research/software-lab/ufig.html.

A forward modelling approach provides simple, fast and realistic simulations of galaxy surveys, without a complex underlying model. For this purpose, galaxy clustering needs to be simulated accurately, both for the usage of clustering as its own probe and to control systematics. We present a forward model to simulate galaxy surveys, where we extend the Ultra-Fast Image Generator to include galaxy clustering. We use the distribution functions of the galaxy properties, derived from a forward model adjusted to observations. This population model jointly describes the luminosity functions, sizes, ellipticities, SEDs and apparent magnitudes. To simulate the positions of galaxies, we then use a two-parameter relation between galaxies and halos with Subhalo Abundance Matching (SHAM). We simulate the halos and subhalos using the fast PINOCCHIO code, and a method to extract the surviving subhalos from the merger history. Our simulations contain a red and a blue galaxy population, for which we build a SHAM model based on star formation quenching. For central galaxies, mass quenching is controlled with the parameter M\\(_{\\mathrm{limit}}\\), with blue galaxies residing in smaller halos. For satellite galaxies, environmental quenching is implemented with the parameter t\\(_{\\mathrm{quench}}\\), where blue galaxies occupy only recently merged subhalos. We build and test our model by comparing to imaging data from the Dark Energy Survey Year 1. To ensure completeness in our simulations, we consider the brightest galaxies with \\(i<20\\). We find statistical agreement between our simulations and the data for two-point correlation functions on medium to large scales. Our model provides constraints on the two SHAM parameters M\\(_{\\mathrm{limit}}\\) and t\\(_{\\mathrm{quench}}\\) and offers great prospects for the quick generation of galaxy mock catalogues, optimized to agree with observations.

The analysis of cosmological galaxy surveys requires realistic simulations for their interpretation. Forward modelling is a powerful method to simulate galaxy clustering without the need for an underlying complex model. This approach requires fast cosmological simulations with a high resolution and large volume, to resolve small dark matter halos associated to single galaxies. In this work, we present fast halo and subhalo clustering simulations based on the Lagrangian perturbation theory code PINOCCHIO, which generates halos and merger trees. The subhalo progenitors are extracted from the merger history and the survival of subhalos is modelled. We introduce a new fitting function for the subhalo merger time, which includes a redshift dependence of the fitting parameters. The spatial distribution of subhalos within their hosts is modelled using a number density profile. We compare our simulations with the halo finder ROCKSTAR applied to the full N-body code GADGET-2. The subhalo velocity function and the correlation function of halos and subhalos are in good agreement. We investigate the effect of the chosen number density profile on the resulting subhalo clustering. Our simulation is approximate yet realistic and significantly faster compared to a full N-body simulation combined with a halo finder. The fast halo and subhalo clustering simulations offer good prospects for galaxy forward models using subhalo abundance matching.

We present GalSBI, a phenomenological model of the galaxy population for cosmological applications using simulation-based inference. The model is based on analytical parametrizations of galaxy luminosity functions, morphologies and spectral energy distributions. Model constraints are derived through iterative Approximate Bayesian Computation, by comparing Hyper Suprime-Cam deep field images with simulations which include a forward model of instrumental, observational and source extraction effects. We developed an emulator trained on image simulations using a normalizing flow. We use it to accelerate the inference by predicting detection probabilities, including blending effects and photometric properties of each object, while accounting for background and PSF variations. This enables robustness tests for all elements of the forward model and the inference. The model demonstrates excellent performance when comparing photometric properties from simulations with observed imaging data for key parameters such as magnitudes, colors and sizes. The redshift distribution of simulated galaxies agrees well with high-precision photometric redshifts in the COSMOS field within \\(1.5\\sigma\\) for all magnitude cuts. Additionally, we demonstrate how GalSBI's redshifts can be utilized for splitting galaxy catalogs into tomographic bins, highlighting its potential for current and upcoming surveys. GalSBI is fully open-source, with the accompanying Python package, \\(\\texttt{galsbi}\\), offering an easy interface to quickly generate realistic, survey-independent galaxy catalogs.

Large-scale structure surveys measure the shape and position of millions of galaxies in order to constrain the cosmological model with high precision. The resulting large data volume poses a challenge for the analysis of the data, from the estimation of photometric redshifts to the calibration of shape measurements. We present GalSBI, a model for the galaxy population, to address these challenges. This phenomenological model is constrained by observational data using simulation-based inference (SBI). The \\(\\texttt{galsbi}\\) Python package provides an easy interface to generate catalogs of galaxies based on the GalSBI model, including their photometric properties, and to simulate realistic images of these galaxies using the \\(\\texttt{UFig}\\) package.

The galaxy Luminosity Function (LF) is a key observable for galaxy formation, evolution studies and for cosmology. In this work, we propose a novel technique to forward model wide-field broad-band galaxy surveys using the fast image simulator UFig and measure the LF of galaxies in the B-band. We use Approximate Bayesian Computation (ABC) to constrain the galaxy population model parameters of the simulations and match data from CFHTLS. We define a number of distance metrics between the simulated and the survey data. By exploring the parameter space of the galaxy population model through ABC to find the set of parameters that minimize these distance metrics, we obtain constraints on the LFs of blue and red galaxies as a function of redshift. We find that \\(\\mathrm{M^*}\\) fades by \\(\\Delta \\mathrm{M}^*_{\\mathrm{0.1-1.0,b}} = 0.68 \\pm 0.52\\) and \\(\\Delta \\mathrm{M}^*_{\\mathrm{0.1-1.0,r}} = 0.54 \\pm 0.48\\) magnitudes between redshift \\(\\mathrm{z = 1}\\) and \\(\\mathrm{z = 0.1}\\) for blue and red galaxies, respectively. We also find that \\(\\phi^*\\) for blue galaxies stays roughly constant between redshift \\(\\mathrm{z = 0.1}\\) and \\(\\mathrm{z=1}\\), while for red galaxies it decreases by \\(\\sim 35\\%\\). We compare our results to other measurements, finding good agreement at all redshifts, for both blue and red galaxies. To further test our results, we compare the redshift distributions for survey and simulated data. We use the spectroscopic redshift distribution from the VIMOS Public Extragalactic Redshift Survey (VIPERS) and we apply the same selection in colours and magnitudes on our simulations. We find a good agreement between the survey and the simulated redshift distributions. We provide best-fit values and uncertainties for the parameters of the LF. This work offers excellent prospects for measuring other galaxy population properties as a function of redshift using ABC.

For the next generation of spectroscopic galaxy surveys, it is important to forecast their performances and to accurately interpret their large data sets. For this purpose, it is necessary to consistently simulate different populations of galaxies, in particular Emission Line Galaxies (ELGs), less used in the past for cosmological purposes. In this work, we further the forward modeling approach presented in Fagioli et al. 2018, by extending the spectra simulator Uspec to model galaxies of different kinds with improved parameters from Tortorelli et al. 2020. Furthermore, we improve the modeling of the selection function by using the image simulator Ufig. We apply this to the Sloan Digital Sky Survey (SDSS), and simulate \\(\\sim157,000\\) multi-band images. We pre-process and analyse them to apply cuts for target selection, and finally simulate SDSS/BOSS DR14 galaxy spectra. We compute photometric, astrometric and spectroscopic properties for red and blue, real and simulated galaxies, finding very good agreement. We compare the statistical properties of the samples by decomposing them with Principal Component Analysis (PCA). We find very good agreement for red galaxies and a good, but less pronounced one, for blue galaxies, as expected given the known difficulty of simulating those. Finally, we derive stellar population properties, mass-to-light ratios, ages and metallicities, for all samples, finding again very good agreement. This shows how this method can be used not only to forecast cosmology surveys, but it is also able to provide insights into studies of galaxy formation and evolution.

From Hubble Frontier Fields photometry, and data from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, we build the Fundamental Plane (FP) relation for the early-type galaxies of the cluster Abell S1063. We use this relation to develop an improved strong lensing model of the total mass distribution of the cluster, determining the velocity dispersions of all 222 cluster members included in the model from their measured structural parameters. Fixing the hot gas component from X-ray data, the mass density distributions of the diffuse dark matter haloes are optimised by comparing the observed and model-predicted positions of 55 multiple images of 20 background sources, distributed over the redshift range \\(0.73-6.11\\). We determine the uncertainties on the model parameters with Monte Carlo Markov chains. Compared to previous works, our model allows for the inclusion of a scatter on the relation between the total mass and the velocity dispersion of cluster members, which also shows a shallower slope. We notice a lower statistical uncertainty on the value of some parameters, such as the core radius, of the diffuse mass component of the cluster. Thanks to a new estimate of the stellar mass of all members, we measure the cumulative projected mass profiles out to a radius of 350 kpc, for all baryonic and dark matter components of the cluster. At the outermost radius, we find a baryon fraction of \\(0.147 \\pm 0.002\\). We compare the sub-haloes as described by our model with recent hydrodynamical cosmological simulations. We find good agreement in terms of the stellar over total mass fraction. On the other hand, we report some discrepancies in terms of the maximum circular velocity, which is an indication of their compactness, and the sub-halo mass function in the central cluster regions.