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Abstract:

Abstract Dust attenuation is a major source of systematic uncertainty in both spectral energy distribution (SED) fitting and forward modeling of galaxy populations, yet the functional form used to parameterize attenuation curves has received surprisingly little systematic scrutiny. Particular unanswered questions include: how many free parameters are genuinely needed, and which analytic expression best captures the full diversity of attenuation curve shapes in galaxies across cosmic time? Using a large library of synthetic attenuation curves from TNG50 and TNG100 galaxies post-processed with the skirt radiative transfer code using three dust mixtures (Milky Way, SMC, and stellar dust), we show via Information-Ordered Bottleneck analysis that exactly four parameters are needed to capture the diversity of attenuation curves. Guided by this result, we use symbolic regression to derive a new, interpretable four-parameter attenuation model that outperforms existing parameterizations in recovering both attenuation curves and emergent fluxes across all dust mixtures explored. The four parameters of this model have clear physical interpretations: UV bump strength, far-ultraviolet slope, UV-bump transition curvature, and large-scale optical slope. Their correlations with galaxy properties are primarily regulated by star formation rate surface density, metallicity, and stellar–dust geometry, and are largely preserved across dust mixtures—except for the bump-sensitive parameters, which retain a stronger dependence on grain composition. We further provide symbolic-regression scaling relations linking all four parameters to quasi-observable galaxy properties, offering a physically motivated route to assign realistic attenuation curves in SED fitting and forward modeling without radiative-transfer calculations.

Abstract:

Abstract The structure of dark matter haloes is often described by radial density profiles motivated by cosmological simulations. These are typically assumed to have a fixed functional form (e.g. NFW), with some free parameters. However, relying on simulations has the disadvantage that the resulting profiles depend on the dark matter model and the baryonic physics implementation, which are highly uncertain. Instead, we present a method to constrain halo density profiles directly from observations. This is done using a symbolic regression algorithm called Exhaustive Symbolic Regression (ESR). ESR searches for the optimal analytic expression to fit data, combining both accuracy and simplicity. We apply ESR to a sample of 149 galaxy clusters from the HSC-XXL survey to identify which functional forms perform best across the entire sample of clusters. We identify density profiles that statistically outperform NFW under a minimum-description-length criterion. Within the radial range probed by the weak-lensing data (R ~ 0.3 − 3 h−1 Mpc), the highest-ranked ESR profiles exhibit shallow inner behaviour and a maximum in the density profile. As a practical application, we show how the best-fitting ESR models can be used to obtain enclosed mass estimates. We find masses that are, on average, higher than those derived using NFW, highlighting a source of potential bias when assuming the wrong density profile. These results have important knock-on effects for analyses that utilise clusters, for example cosmological constraints on σ8 and Ωm from cluster abundance and clustering. Beyond the HSC dataset, the method is applicable to any data constraining the dark matter distribution in galaxies and galaxy clusters, such as other weak lensing surveys, galactic rotation curves, or complementary probes.

Abstract:

There is tentative evidence for a mismatch between the rest frames of matter and the cosmic microwave background, the “quasar dipole anomaly.” We consider such a dipole in tilted anisotropic models, for a range of scenarios and sources: spatial curvature, cosmic heat flux, large scale electromagnetic fields, and a Khronon field. Crucially, we determine the ancillary effects on other cosmological observables in each of these models, and we show that, apart from the case of the Khronon field, it is unlikely that one can obtain a dipole with the amplitude that is being observed unless one considers additional exotica.

Abstract:

Abstract The galaxy luminosity and stellar mass function (LF, SMF), and halo mass function (HMF), are fundamental quantities in astrophysics and crucial inputs to a range of astrophysical and cosmological analyses. They are typically parametrised by fitting functions that have been chosen ‘by eye’ to match observed or simulated data. We apply symbolic regression—specifically the Exhaustive Symbolic Regression (ESR) algorithm—to automate the search for optimal LF, SMF and HMF functional forms. ESR scores all functions up to a maximum complexity composed of a user-defined basis set of operators using the description length, an approximation to the Bayesian evidence that balances accuracy with complexity. We find many functions that outperform the Schechter and double Schechter functions for the LF and SMF, and that outperform all investigated literature functions (that outperform the Press–Schechter, Warren, Tinker, Sheth–Tormen and Jenkins) for the HMF. By additionally imposing ‘physicality checks’ on functions’ extrapolation and integration properties, we identify the optimal, low-complexity functional forms in terms of accuracy, simplicity and behaviour beyond the data range. As well as providing drop-in replacements for literature LF, SMF and HMF fitting functions, and identifying robust behaviour across well-fitting functions, we present a framework with which symbolic regression may be used to automate the discovery of optimal functions for any astrophysical dataset.