Symbolic regression and differentiable fits in beyond the standard model physics

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences The Royal Society 384:2317 (2026) 20240593

Authors:

Shehu AbdusSalam, Steven Abel, Deaglan Bartlett, Miguel Crispim Romao

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’.

A black hole in a near pristine galaxy 700 Myr after the big bang

Monthly Notices of the Royal Astronomical Society Oxford University Press 548:1 (2026) staf2109

Authors:

Roberto Maiolino, Hannah Übler, Francesco D’Eugenio, Jan Scholtz, Ignas Juodžbalis, Xihan Ji, Michele Perna, Volker Bromm, Pratika Dayal, Sophie Koudmani, Boyuan Liu, Raffaella Schneider, Debora Sijacki, Rosa Valiante, Alessandro Trinca, Saiyang Zhang, Marta Volonteri, Kohei Inayoshi, Stefano Carniani, Kimihiko Nakajima, Yuki Isobe, Joris Witstok, Gareth C Jones, Sandro Tacchella, Santiago Arribas, Andrew Bunker

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.

Constraining the Subgalactic Relationship between Star Formation and the Hot Interstellar Medium in NGC 4254

The Astrophysical Journal American Astronomical Society 1001:1 (2026) 42

Authors:

Erik B Monson, Bret D Lehmer, Amirnezam Amiri, Karina Barboza, Ashley T Barnes, Antara R Basu-Zych, Daniel A Dale, Sanskriti Das, Simthembile Dlamini, Simon Glover, Kathryn Kreckel, Laura A Lopez, Sebastian Lopez, Smita Mathur, Hsi-An Pan, Jennifer A Rodriguez, Karin Sandstrom, Sumit K Sarbadhicary, Jiayi Sun, Thomas G Williams

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.

Identifying Transient Hosts in LSST’s Deep Drilling Fields with Galaxy Catalogs

The Astrophysical Journal American Astronomical Society 1000:2 (2026) 289

Authors:

JG Weston, DR Young, SJ Smartt, M Nicholl, MJ Jarvis, IH Whittam

Abstract:

The upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will enable astronomers to discover rare and distant astrophysical transients. Host-galaxy association is crucial for selecting the most scientifically interesting transients for follow-up. LSST deep drilling field (DDF) observations will detect distant transients occurring in galaxies below the detection limits of most all-sky catalogs. Here, we investigate the use of preexisting, field-specific catalogs for host identification in the DDFs and a ranking of their usefulness. We have compiled a database of 70 deep catalogs that overlap with the Rubin DDFs and constructed thin catalogs to be homogenized and combined for transient-host matching. A systematic ranking of their utility is discussed and applied based on the inclusion of information such as spectroscopic redshifts and morphological information. Utilizing this data against a Dark Energy Survey sample of supernovae with pre-identified hosts in the XMM-Large Scale Structure and the Extended Chandra Deep Field-South fields, we evaluate different methods for transient-host association in terms of both accuracy and processing speed. We also apply light data-cleaning techniques to identify and remove contaminants within our associations, such as diffraction spikes and blended galaxies where the correct host cannot be determined with confidence. We use a lightweight machine learning approach in the form of extreme gradient boosting to generate confidence scores in our contaminant selections and associated metrics. Finally, we discuss the computational expense of implementation within the LSST transient alert brokers, which will require efficient, fast-paced processing to handle the large stream of survey data.

Clumps in High-redshift Galaxies: Mass Scaling and Radial Trends from JADES

The Astrophysical Journal American Astronomical Society 1000:2 (2026) 303

Authors:

Yongda Zhu, Marcia J Rieke, Zhiyuan Ji, Andrew J Bunker, Courtney Carreira, A Lola Danhaive, Qiao Duan, Eiichi Egami, Daniel J Eisenstein, Kevin Hainline, Benjamin D Johnson, Zheng Ma, Dávid Puskás, George H Rieke, Pierluigi Rinaldi, Brant Robertson, Sandro Tacchella, Hannah Übler, Natalia C Villanueva, Christina C Williams, Christopher NA Willmer, Zihao Wu, Junyu Zhang

Abstract:

Massive star-forming clumps are a prominent feature of high-redshift galaxies and are thought to trace gravitational fragmentation, feedback, and bulge growth in gas-rich disks. We present a statistical analysis of clumps in ∼3600 galaxies spanning 2 ≲ z ≲ 8 from deep JWST/NIRCam imaging in the JADES GOODS–South field. Clumps are identified as residual features after subtracting smooth Sérsic profiles, enabling a uniform, rest-frame optical census of subgalactic structure. We characterize their physical properties, size–mass relations, and spatial distributions to constrain models of subgalactic structure formation and evolution. We find that clumps in our sample are typically low-mass (10∼7−8M⊙), actively star-forming, and show diverse gas-phase metallicity, dust attenuation, and stellar population properties. Their sizes and average pairwise separations increase with cosmic time (toward lower redshift), consistent with inside-out disk growth. The clump mass function follows a power law with slope α=−1.50−0.17+0.19 , consistent with fragmentation in turbulent disks. We find a deficit of relatively young clumps near galaxy centers and a radial transition in the size–mass relation: outer clumps exhibit steeper, near-virial slopes ( Re∝M*∼0.3 ), while inner clumps follow flatter trends ( Re∝M*∼0.2 ), consistent with structural evolution via migration or disruption. These results provide new constraints on the formation, survival, and dynamical evolution of clumps, highlighting their role in shaping galaxy morphology during the peak of cosmic star formation.