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Abstract:

Dark matter haloes are typically characterized by radial density profiles with fixed forms motivated by simulations (e.g. Navarro-Frenk-White [NFW]). However, simulation predictions depend on uncertain dark matter physics and baryonic modelling. Here, we present a method to constrain halo density profiles directly from observations using Exhaustive Symbolic Regression (ESR), a technique that searches the space of analytic expressions for the function that best balances accuracy and simplicity for a given dataset. We test the approach on mock weak lensing excess surface density (ESD) data of synthetic clusters with NFW profiles. Motivated by real data, we assign each ESD data point a constant fractional uncertainty and vary this uncertainty and the number of clusters to probe how data precision and sample size affect model selection. For fractional errors around 5%, ESR recovers the NFW profile even from samples as small as approximately 20 clusters. At higher uncertainties representative of current surveys, simpler functions are favoured over NFW, though it remains competitive. This preference arises because weak lensing errors are smallest in the outskirts, causing the fits to be dominated by the outer profile. ESR therefore provides a robust, simulation-independent framework both for testing mass models and determining which features of a halo's density profile are genuinely constrained by the data. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

In cosmology, emulators play a crucial role by providing fast and accurate predictions of complex physical models, enabling efficient exploration of high-dimensional parameter spaces that would be computationally prohibitive with direct numerical simulations. Symbolic emulators have emerged as promising alternatives to numerical approaches, delivering comparable accuracy with significantly faster evaluation times. While previous symbolic emulators were limited to relatively narrow prior ranges, we expand these to cover the parameter space relevant for current cosmological analyses. We introduce approximations to hypergeometric functions used for the Λ cold dark matter (ΛCDM) comoving distance and linear growth factor which are accurate to better than 0.001% and 0.05%, respectively, for all redshifts and for Ωm∈[0.1,0.5]. We show that integrating symbolic emulators into a Dark Energy Survey Year 1 (DES-Y1)-like 3×2 pt analysis produces cosmological constraints consistent with those obtained using standard numerical methods. Our symbolic emulators offer substantial improvements in speed and memory usage, demonstrating their practical potential for scalable, likelihood-based inference. This article is part of the discussion meeting issue 'Symbolic regression in the physical sciences'.

Abstract:

Abstract We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR, which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focused on the promising regions in order to be equally performant. This article is part of the discussion meeting issue ‘Symbolic regression in the physical sciences’.

Abstract:

The recent discovery of a large number of massive black holes within the first two billion years after the big bang, as well as their peculiar properties, have been largely unexpected based on the extrapolation of the properties of luminous quasars. These findings have prompted the development of several theoretical models for the early formation and growth of black holes, which are, however, difficult to differentiate. We report the metallicity measurement around a gravitationally lensed massive black hole at redshift 7.04 (classified as a Little Red Dot), hosted in a galaxy with very low dynamical mass. The weakness of the [O iii]5007 emission line relative to the narrow H emission indicates extremely low metallicity, about solar, and even more metal poor in the surrounding few 100 pc. We argue that such properties cannot be uncommon among accreting black holes around this early cosmic epoch. Explaining such a low chemical enrichment in a system that has developed a massive black hole is challenging for most theories. Models assuming heavy black hole seeds (such as Direct Collapse Black Holes) or super-Eddington accretion scenarios struggle to explain the observations, although they can potentially reproduce the observed properties in some cases. Models invoking ‘primordial black holes’ (i.e. putative black holes formed shortly after the big bang) may potentially explain the low chemical enrichment associated with this black hole, although this class of models also requires further developments for proper testing.

Abstract:

We investigate the relationship between star formation and X-ray emission from the hot interstellar medium (ISM) on ∼kiloparsec scales in NGC 4254 (M99) by combining spatially resolved star formation histories (SFHs) and Bayesian X-ray spectral fitting. We measure subgalactic star formation rates (SFR) by modeling spectrophotometric UV-IR data with flexible SFHs, and we produce point-source-subtracted maps of the diffuse X-ray emission using Chandra data. We extract and fit the spectra of five regions selected by their SFR density ΣSFR, deriving hot gas luminosities and plasma temperatures. We examine the subgalactic kT–ΣSFR and LXgas−ΣSFR scaling relations in NGC 4254 and compare to predictions from simple models of the feedback into the ISM from core collapse supernovae (CCSNe). The hot gas emission from NGC 4254 is consistent with thermalization of ≈40%–50% of the energy from CCSNe in the ISM, and mass-loading of the CCSNe ejecta, which decreases as ΣSFR−1/3 . Our optimized model implies a temperature and X-ray production efficiency that scale as kT=(0.72−0.18+0.26keV)ΣSFR0.34±0.10 and η=(0.03−0.01+0.02)ΣSFR0.34±0.18 , respectively, for ΣSFR = 0.01–0.13 M⊙ yr−1 kpc−2. We also compare the properties of the hot ISM to other ISM phases using data from the PHANGS program. The diffuse X-ray emission of a given region is on average 200 times fainter than the Hα emission, and we see evidence that the hot ISM is overpressurized compared to the large-scale dynamical equilibrium pressure of the galaxy, consistent with expansion of the hot ISM into the ambient medium.