Data-driven Galaxy Population Prior for Photometric Redshifts

Abstract: Stage-IV cosmological surveys rely on well-characterised photometric redshift distributions for constraining cosmological models, yet the projected weak lensing requirements are about an order of magnitude more accurate than current state-of-the-art methods. Any photometric redshift inference depends - explicitly or implicitly - on a prior over galaxy SEDs, luminosities, and redshifts. In this paper, we develop a purely data-driven approach for modelling the galaxy population prior based on learning the distribution of galaxy SEDs and evaluate its induced systematic uncertainties for photometric redshift calibration. Under controlled conditions, we build a template-free model for galaxy SEDs with minimal physical assumptions and assess how well it can reproduce the colour-redshift relation. We train a generative model on a realistic population of noisy mock galaxy spectra, simulated using the GalSBI-SPS galaxy population model, to learn the joint distribution of intrinsic spectra, luminosities, and redshifts. We employ a probabilistic autoencoder that compresses spectra into a low-dimensional latent space and performs neural density estimation with a normalising flow. The autoencoder can reconstruct the shape of galaxy spectra with Gaussian noise of standard deviation $σ$ to $\sim0.1\,σ$ of the ground truth, thereby building a model for noiseless SEDs from noisy spectra only. We construct colour-selected tomographic bins with a self-organising map and compare the predicted mean redshift. We find that deviations in each bin are smaller than the per-mille Stage-IV requirements, with $| Δ\langle z \rangle |\lesssim 0.0007 (1+z)$. This work serves as a proof-of-concept that generative models can learn the prior of galaxy observations accurately enough for upcoming surveys under controlled conditions.