Research Articles (Physics)

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Expanding covariant cosmography of the local universe: incorporating the snap and axial symmetry
(Institute of Physics, 2025) Maartens, Roy; Clarkson, Chris; Kalbouneh, Basheer
Studies show that the model-independent, fully non-perturbative covariant cosmographic approach is suitable for analyzing the local Universe (z ≲ 0.1). However, accurately characterizing large and inhomogeneous mass distributions requires the fourth-order term in the redshift expansion of the covariant luminosity distance dL (zn ). We calculate the covariant snap parameter S and its spherical harmonic multipole moments using the matter expansion tensor and the evolution equations for lightray bundles. The fourth-order term adds 36 degrees of freedom, since the highest independent multipole of the snap is the 32-pole (dotriacontapole) (ℓ=5). Including this term helps to de-bias estimations of the covariant deceleration parameter. Given that observations suggest axially symmetric anisotropies in the Hubble diagram for z ≲ 0.1 and theory shows that only a subset of multipoles contributes to the signal, we demonstrate that only 12 degrees of freedom are needed for a model-independent description of the local universe. We use an analytical axisymmetric model of the local Universe, with data that matches the Zwicky Transient Facility survey, in order to provide a numerical example of the amplitude of the snap multipoles and to forecast precision.
Disparate effects of circumgalactic medium angular momentum in IllustrisTNG and SIMBA
(EDP Sciences, 2025) Davé, Romeel; Liu, Kexin; Guo, Hong
In this study, we examine the role of the circumgalactic medium (CGM) angular momentum (jCGM) on star formation in galaxies, whose influence is currently not well understood. The analysis utilises central galaxies from two hydrodynamical simulations, SIMBA and IllustrisTNG. We observe a substantial divergence in how star formation rates correlate with CGM angular momentum between the two simulations. Specifically, quenched galaxies in IllustrisTNG show higher jCGM than their star-forming counterparts with similar stellar masses, while the reverse is true in SIMBA. This difference is attributed to the distinct active galactic nucleus (AGN) feedback mechanisms active in each simulation. Moreover, both simulations demonstrate similar correlations between jCGM and environmental angular momentum (jEnv) in star-forming galaxies, but these correlations change notably when kinetic AGN feedback is present. In IllustrisTNG, quenched galaxies consistently show higher jCGM compared to their star-forming counterparts with the same jEnv, a trend not seen in SIMBA. Examining different AGN feedback models in SIMBA, we further confirm that AGN feedback significantly influences the CGM gas distribution, although the relationship between the cold gas fraction and the star formation rate (SFR) remains largely stable across different feedback scenarios.
In search of truth: In memory of Balraj Singh
(Elsevier B.V, 2025) Orce, José Nicolás; Pritychenko, Boris; Kibédi, Tibor
Born in Punjab (India) in December 1941, Balraj Singh is not only the single most prolific nuclear data evaluator and disseminator of nuclear structure and decay data with 148 evaluations in Nuclear Data Sheets — 85 as the first and often only author — plus other journals, but his upmost curiosity and dedication brought him to be one of the finest nuclear physicists, with an everlasting influence on many of us. Balraj passed away about a year ago on 9 October 2023 in Ottawa, Ontario (Canada) at the age of 81, and at Atomic Data and Nuclear Data Tables we would like to commemorate some of his scientific achievements.
The multiple classes of ultra-diffuse galaxies: can we tell them apart?
(Oxford University Press, 2025) Jarrett, Thomas H; Buzzo, Maria Luisa; Forbes, Duncan A
This study compiles stellar populations and internal properties of ultra-diffuse galaxies (UDGs) to highlight correlations with their local environment, globular cluster (GC) richness, and star formation histories. Complementing our sample of 88 UDGs, we include 36 low surface brightness dwarf galaxies with UDG-like properties, referred to as NUDGes (nearly UDGs). All galaxies were studied using the same spectral energy distribution fitting methodology to explore what sets UDGs apart from other galaxies. We show that NUDGes are similar to UDGs in all properties except for being, by definition, smaller and having higher surface brightness. We find that UDGs and NUDGes show similar behaviours in their GC populations, with the most metal-poor galaxies hosting consistently more GCs on average. This suggests that GC content may provide an effective way to distinguish extreme galaxies within the low surface brightness regime alongside traditional parameters like size and surface brightness. We confirm previous results using clustering algorithms that UDGs split into two main classes, which might be associated with the formation pathways of a puffy dwarf and a failed galaxy. The clustering applied to the UDGs + NUDGes data set yields an equivalent result. The difference in mass contained in the GC system suggests that galaxies in different environments have not simply evolved from one another but may have formed through distinct processes.
The hobby-eberly telescope dark energy experiment survey (HETDEX) active galactic nuclei catalog: the fourth data release
(American Astronomical Society, 2025) Jarvis, Matt; Liu, Chenxu; Gebhardt, Karl
We present the active galactic nuclei (AGN) catalog from the fourth data release (HDR4) of the Hobby-Eberly Telescope Dark Energy Experiment Survey (HETDEX). HETDEX is an untargeted spectroscopic survey. HDR4 contains 345,874 Integral Field Unit observations from 2017 January to 2023 August covering an effective area of 62.9 deg2. With no imaging preselection, our spectroscopic confirmed AGN sample includes low-luminosity AGN, narrow-line AGN, and/or red AGN down to g ∼ 25. This catalog has 15,940 AGN across the redshifts of z = 0.1 ∼ 4.6, giving a raw AGN number density of 253.4 deg−2. Among them, 10,499 (66%) have redshifts either confirmed by line pairs or matched to the Sloan Digital Sky Survey Quasar Catalog. For the remaining 5441 AGN, 2083 are single broad-line AGN candidates, while the remaining 3358 are single intermediate broad-line (full width at half-maximum, FWHM ∼1200 km s−1) AGN candidates. A total of 4060 (39%) of the 10,499 redshift-confirmed AGN have emission-line regions 3σ more extended than the image quality, which could be strong outflows blowing into the outskirts of the host galaxies or ionized intergalactic medium.
Radio galaxies in simba: a mightee comparison
(University of the Western Cape, 2024) Whittam, Imogen H; Thomas, Nicole L; Hale, Catherine L
We present a qualitative comparison between the host and black hole properties of radio galaxies in the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) survey with the radio galaxy population in the SIMBA suite of cosmological hydrodynamical simulations. The MIGHTEE data include a ∼1 deg2 pointing of the COSMOS field observed at 1.28 GHz with the MeerKAT radio telescope and cross-matched with multiwavelength counterparts to provide classifications of high- and low-excitation radio galaxies (HERGs and LERGs) along with their corresponding host properties. We compare the properties of the MIGHTEE HERGs and LERGs with that predicted by the SIMBA simulations where HERGs and LERGs are defined as radio galaxies dominated by cold or hot mode accretion, respectively. We consider stellar masses M∗, star formation rates SFR, AGN bolometric luminosity Lbol , and Eddington fraction fEdd , as a function of 1.4 GHz radio luminosity and redshift. In both MIGHTEE and SIMBA, the properties of HERGs and LERGs are similar across all properties apart from SFRs due to differences in host cold gas content in SIMBA. We predict a population of HERGs with low fEdd in SIMBA that are confirmed in the MIGHTEE observations and tied to the faint population at low z. The predictions from SIMBA with the MIGHTEE observations describe a regime where our understanding of the radio galaxy dichotomy breaks down, challenging our understanding of the role of AGN accretion and feedback in the faint population of radio galaxies
Model-agnostic assessment of dark energy after DESI DR1 BAO
(Institute of Physics, 2025) Dinda, Bikash; Maartens, Roy
Baryon acoustic oscillation measurements by the Dark Energy Spectroscopic Instrument (Data Release 1) have revealed exciting results that show evidence for dynamical dark energy at ∼ 3σ when combined with cosmic microwave background and type Ia supernova observations. These measurements are based on the w 0 w a CDM model of dark energy. The evidence is less in other dark energy models such as the wCDM model. In order to avoid imposing a dark energy model, we reconstruct the distance measures and the equation of the state of dark energy independent of any dark energy model and driven only by observational data. Our results show that the model-agnostic (in terms of late-time models) evidence for dynamical dark energy from DESI is not significant. Our analysis also provides model-independent constraints on cosmological parameters such as the Hubble constant and the matter-energy density parameter at present. Although we used CMB distance priors (not full CMB data) from a ΛCDM early-time model, our results remain largely similar for other cosmological models, provided that these models do not differ significantly from the standard model.
The multiple classes of ultra-diffuse galaxies: can we tell them apart?
(Oxford University Press, 2024) Jarrett, Thomas H.; Buzzo, Maria Luisa; Forbes, Duncan A
This study compiles stellar populations and internal properties of ultra-diffuse galaxies (UDGs) to highlight correlations with their local environment, globular cluster (GC) richness, and star formation histories. Complementing our sample of 88 UDGs, we include 36 low surface brightness dwarf galaxies with UDG-like properties, referred to as NUDGes (nearly UDGs). All galaxies were studied using the same spectral energy distribution fitting methodology to explore what sets UDGs apart from other galaxies. We show that NUDGes are similar to UDGs in all properties except for being, by definition, smaller and having higher surface brightness. We find that UDGs and NUDGes show similar behaviours in their GC populations, with the most metal-poor galaxies hosting consistently more GCs on average. This suggests that GC content may provide an effective way to distinguish extreme galaxies within the low surface brightness regime alongside traditional parameters like size and surface brightness. We confirm previous results using clustering algorithms that UDGs split into two main classes, which might be associated with the formation pathways of a puffy dwarf and a failed galaxy. The clustering applied to the UDGs + NUDGes data set yields an equivalent result. The difference in mass contained in the GC system suggests that galaxies in different environments have not simply evolved from one another but may have formed through distinct processes.
A classifier-based approach to multiclass anomaly detection for astronomical transients
(Oxford University Press, 2025) Lochner, Michelle.; Gupta, Rithwik.; Muthukrishna, Daniel.
Automating real-time anomaly detection is essential for identifying rare transients, with modern survey telescopes generating tens of thousands of alerts per night, and future telescopes, such as the Vera C. Rubin Observatory, projected to increase this number dramatically. Currently, most anomaly detection algorithms for astronomical transients rely either on hand-crafted features extracted from light curves or on features generated through unsupervised representation learning, coupled with standard anomaly detection algorithms. In this work, we introduce an alternative approach: using the penultimate layer of a neural network classifier as the latent space for anomaly detection. We then propose a novel method, Multi-Class Isolation Forests, which trains separate isolation forests for each class to derive an anomaly score for a light curve from its latent space representation. This approach significantly outperforms a standard isolation forest. We also use a simpler input method for real-time transient classifiers which circumvents the need for interpolation and helps the neural network handle irregular sampling and model inter-passband relationships. Our anomaly detection pipeline identifies rare classes including kilonovae, pair-instability supernovae, and intermediate luminosity transients shortly after trigger on simulated Zwicky Transient Facility light curves. Using a sample of our simulations matching the population of anomalies expected in nature (54 anomalies and 12 040 common transients), our method discovered anomalies (recall) after following up the top 2000 () ranked transients. Our novel method shows that classifiers can be effectively repurposed for real-time anomaly detection.
Matvis: a matrix-based visibility simulator for fast forward modelling of many-element 21 cm arrays
(Oxford University Press, 2025) Kittiwisit, Piyanat; Bull, Philip; Murray, Steven
Detection of the faint 21 cm line emission from the Cosmic Dawn and Epoch of Reionization will require not only exquisite control over instrumental calibration and systematics to achieve the necessary dynamic range of observations but also validation of analysis techniques to demonstrate their statistical properties and signal loss characteristics. A key ingredient in achieving this is the ability to perform high-fidelity simulations of the kinds of data that are produced by the large, many-element, radio interferometric arrays that have been purpose-built for these studies. The large scale of these arrays presents a computational challenge, as one must simulate a detailed sky and instrumental model across many hundreds of frequency channels, thousands of time samples, and tens of thousands of baselines for arrays with hundreds of antennas. In this paper, we present a fast matrix-based method for simulating radio interferometric measurements (visibilities) at the necessary scale. We achieve this through judicious use of primary beam interpolation, fast approximations for coordinate transforms, and a vectorized outer product to expand per-antenna quantities to per-baseline visibilities, coupled with standard parallelization techniques. We validate the results of this method, implemented in the publicly available matvis code, against a high-precision reference simulator, and explore its computational scaling on a variety of problems.
Timing and noise analysis of five millisecond pulsars observed with MeerKAT
(Oxford University Press, 2025) Andrianomena, Sambatra; Geyer, Marisa; Enwelum, U
Millisecond pulsars (MSPs) in binary systems are precise laboratories for tests of gravity and the physics of dense matter. Their orbits can show relativistic effects that provide a measurement of the neutron star mass and the pulsars are included in timing array experiments that search for gravitational waves. Neutron star mass measurements are key to eventually solving the neutron star equation of state and these can be obtained by a measure of the Shapiro delay if the orbit is viewed near edge-on. Here, we report on the timing and noise analysis of five MSPs observed with the MeerKAT radio telescope: PSRs J0900–3144, J0921–5202, J1216–6410, J1327–0755, and J1543–5149. We searched for the Shapiro delay in all of the pulsars and obtain weak detections for PSRs J0900–3144, J1216–6410, and J1327–0755. We report a higher significance detection of the Shapiro delay for PSR J1543–5149, giving a precise pulsar mass of Mp = 1.349+0.043-0.061M☉ and companion white-dwarf mass Mc = 0.223+0.005-0.007M☉. This is an atypically low-mass measurement for a recycled MSP. In addition to these Shapiro delays, we also obtain timing model parameters including proper motions and parallax constraints for most of the pulsars.
Probing the cosmological principle with weak lensing shear
(Institute of Physics, 2025) Adam, James; Maartens, Roy; Larena, Julien
The Cosmological Principle is a cornerstone of the standard model of cosmology and shapes how we view the Universe and our place within it. It is imperative, then, to devise multiple observational tests which can identify and quantify possible violations of this foundational principle. One possible method of probing large-scale anisotropies involves the use of weak gravitational lensing. We revisit this approach in order to analyse the imprint of late-time anisotropic expansion on cosmic shear. We show that the cross-correlation of shear Eand B-modes on large scales can be used to constrain the magnitude (and possibly direction) of anisotropic expansion. We estimate the signal to noise for multipoles 10 ≲ ℓ ≲ 100 that is achievable by a Euclid-like survey. Our findings suggest that such a survey could detect the E-B signal for reasonable values of the late-time anisotropy parameter.
Finding radio transients with anomaly detection and active learning based on volunteer classifications
(Oxford University Press, 2025) Lochner, Michelle; Andersson, Alex; Woudt, Patrick
In this work, we explore the applicability of unsupervised machine learning algorithms to finding radio transients. Facilities such as the Square Kilometre Array (SKA) will provide huge volumes of data in which to detect rare transients; the challenge for astronomers is how to find them. We demonstrate the effectiveness of anomaly detection algorithms using 1.3 GHz light curves from the SKA precursor MeerKAT. We make use of three sets of descriptive parameters ('feature sets') as applied to two anomaly detection techniques in the astronomaly package and analyse our performance by comparison with citizen science labels on the same data set. Using transients found by volunteers as our ground truth, we demonstrate that anomaly detection techniques can recall over half of the radio transients in the 10 per cent of the data with the highest anomaly scores. We find that the choice of anomaly detection algorithm makes a minor difference, but that feature set choice is crucial, especially when considering available resources for human inspection and/or follow-up. Active learning, where human labels are given for just 2 per cent of the data, improves recall by up to 20 percentage points, depending on the combination of features and model used. The best-performing results produce a factor of 5 times fewer sources requiring vetting by experts. This is the first effort to apply anomaly detection techniques to finding radio transients and shows great promise for application to other data sets, and as a real-Time transient detection system for upcoming large surveys.
Euclid preparation: lix. angular power spectra from discrete observations
(EDP Sciences, 2025) Cañas-Herrera,Guadalupe; Tessore, Nicolas; Joachimi, Benjamin
In this paper we present the framework for measuring angular power spectra in the Euclid mission. The observables in galaxy surveys, such as galaxy clustering and cosmic shear, are not continuous fields, but discrete sets of data, obtained only at the positions of galaxies. We show how to compute the angular power spectra of such discrete data sets, without treating observations as maps of an underlying continuous field that is overlaid with a noise component. This formalism allows us to compute the exact theoretical expectations for our measured spectra, under a number of assumptions that we track explicitly. In particular, we obtain exact expressions for the additive biases ('shot noise') in angular galaxy clustering and cosmic shear. For efficient practical computations, we introduce a spin-weighted spherical convolution with a well-defined convolution theorem, which allows us to apply exact theoretical predictions to finite-resolution maps, including HEALPix. When validating our methodology, we find that our measurements are biased by less than 1% of their statistical uncertainty in simulations of Euclid's first data release.
A study of dipolar signal in distant quasars with various observables
(Springer, 2024) Kothari, Rahul; Panwar, Mohit; Singh, Gurmeet
We study the signal of anisotropy in AGNs/quasars of CatWISE2020 catalogue using different observables. It has been reported earlier that this data shows a strong signal of dipole anisotropy in the source number counts. We test this claim using two independent data analysis procedures and find our number count dipole consistent with the earlier results. In addition to number counts, we test for the anisotropy signal in two other observables – mean spectral index α¯ and mean flux density S¯. We find a strong dipole signal both in the mean spectral index and the mean flux density. The dipole in mean flux density points towards the galactic center and becomes very weak after imposing a flux cut to remove sources with flux greater than 1 mJy. This can be attributed to the presence of some (∼ 26,600) bright sources. The signal in the mean spectral index, however, is relatively stable as a function of both flux and galactic cuts. The dipole in this observable points roughly opposite to the galactic center and hence most likely arises due to galactic bias. We consider a simple model of galactic extinction which nicely explains the dipole both in mean spectral index and mean flux density for a wide range of flux and galactic cuts. Hence, the signal in both these parameters does not appear to be of cosmological origin.
Gravitational waves and galaxies cross-correlations: a forecast on GW biases for future detectors
(Oxford University Press, 2025) Fonseca, José; Clarkson, Chris; Baker, Tessa
Gravitational waves (GWs) have rapidly become important cosmological probes since their first detection in 2015. As the number of detected events continues to rise, upcoming instruments like Einstein Telescope (ET) and Cosmic Explorer (CE) will observe millions of compact binary mergers. These detections, coupled with galaxy surveys by instruments such as the Dark Spectroscopic Energy Instrument (DESI), Euclid, and the Vera Rubin Observatory, will provide unique information on the large-scale structure of the universe by cross-correlating GWs with the distribution of galaxies hosting them. In this paper, we focus on how cross-correlations constrain the clustering bias of GWs emitted by the coalescence of binary black holes (BBHs). This parameter links BBHs to the underlying dark matter distribution, hence informing us how they populate galaxies. Using a multitracer approach, we forecast the precision of these measurements under different survey combinations. Our results indicate that current GW detectors will have limited precision, with measurement errors as high as ∼ 50 per cent. However, third-generation detectors like ET, when cross-correlated with Legacy Survey of Space and Time (LSST) data, can improve clustering bias measurements to within 2.5 per cent. Furthermore, we demonstrate that these cross-correlations can enable a per cent-level measurement of the magnification lensing effect on GWs. Despite this, there is a degeneracy between magnification and evolution biases, which hinders the precision of both. This degeneracy is most effectively addressed by assuming knowledge of one bias or targeting an optimal redshift range of 1 < z < 2.5. Our analysis opens new avenues for studying the distribution of BBHs and testing the nature of gravity through large-scale structure.
MIGHTEE polarization early science fields: The deep polarized sky
(Oxford University Press, 2024) Taylor, Andrew Russell; Sekhar, Srikrishna; Collier, Jordan D.
The MeerKAT International GigaHertz Tiered Extragalactic Exploration (MIGHTEE) is one of the MeerKAT large survey projects, designed to pathfind SKA key science. MIGHTEE is undertaking deep radio imaging of four well-observed fields (COSMOS, XMM-LSS, ELAIS S1, and CDFS) totaling 20 square degrees to μJy sensitivities. Broad-band imaging observations between 880 and1690 MHz yield total intensity continuum, spectro-polarimetry, and atomic hydrogen spectral imaging. Early science data from MIGHTEE are being released from initial observations of COSMOS and XMM–LSS. This paper describes the spectro-polarimetric observations, the polarization data processing of the MIGHTEE early science fields, and presents polarization data images and catalogues. The catalogues include radio spectral index, redshift information, and faraday rotation measure synthesis results for 13 267 total intensity radio sources down to a polarized intensity detection limit of ∼20 μJy bm−1. Polarized signals were detected from 324 sources. For the polarized detections, we include a catalogue of faraday depth from both faraday synthesis and Q, U fitting, as well as total intensity and polarization spectral indices. The distribution of redshift of the total radio sources and detected polarized sources are the same, with median redshifts of 0.86 and 0.82, respectively. Depolarization of the emission at longer-wavelengths is seen to increase with decreasing total-intensity spectral index, implying that depolarization is intrinsic to the radio sources. No evidence is seen for a redshift dependence of the variance of faraday depth.
Theoretical strong-line metallicity diagnostics for the JWST era
(Institute of Physics, 2024) Garg, Prerak; Dave, Romeel; Sanders, Ryan L
The ratios of strong rest-frame optical emission lines are the dominant indicators of metallicities in high-redshift galaxies. Since typical strong-line-based metallicity indicators are calibrated on auroral lines at z = 0, their applicability for galaxies in the distant Universe is unclear. In this paper, we make use of mock emission-line data from cosmological simulations to investigate the calibration of rest-frame optical emission lines as metallicity indicators at high redshift. Our model, which couples the SIMBA cosmological galaxy formation simulation with CLOUDY photoionization calculations, includes contributions from H II regions, post-asymptotic-giant-branch stars, and diffuse ionized gas (DIG). We find mild redshift evolution in the 12 indicators that we study, which implies that the dominant physical properties that evolve in our simulations do have a discernible impact on the metallicity calibrations at high redshifts. When comparing our calibrations with high-redshift auroral line observations from the James Webb Space Telescope, we find a slight offset between our model results and the observations and find that a higher ionization parameter at high redshifts can be one of the possible explanations. We explore the physics that drives the shapes of strong-line metallicity relationships and propose calibrations for hitherto unexplored low-metallicity regimes. Finally, we study the contribution of DIG to total line fluxes.
Characterization of herschel-selected strong lens candidates through HST and sub-mm/mm observations
(Oxford University Press, 2024) Borsato E.; Baker A.J.; Negrello M
We have carried out hubble space telescope (HST) snapshot observations at 1.1 μm of 281 candidate strongly lensed galaxies identified in the wide-area extragalactic surveys conducted with the Herschel space observatory. Our candidates comprise systems with flux densities at 500 μm, S500 ≥ 80 mJy. We model and subtract the surface brightness distribution for 130 systems, where we identify a candidate for the foreground lens candidate. After combining visual inspection, archival high-resolution observations, and lens subtraction, we divide the systems into different classes according to their lensing likelihood. We confirm 65 systems to be lensed. Of these, 30 are new discoveries. We successfully perform lens modelling and source reconstruction on 23 systems, where the foreground lenses are isolated galaxies and the background sources are detected in the HST images. All the systems are successfully modelled as a singular isothermal ellipsoid. The Einstein radii of the lenses and the magnifications of the background sources are consistent with previous studies. However, the background source circularized radii (between 0.34 and 1.30 kpc) are ∼3 times smaller than the ones measured in the sub-millimetre/millimetre for a similarly selected and partially overlapping sample. We compare our lenses with those in the sloan lens advanced camera for surveys (ACS) survey confirming that our lens-independent selection is more effective at picking up fainter and diffuse galaxies and group lenses. This sample represents the first step towards characterizing the near-infrared properties and stellar masses of the gravitationally lensed dusty star-forming galaxies.
Radio spectral properties of star-forming galaxies between 150 and 5000 MHz in the ELAIS-N1 field
(Oxford University Press, 2024) Fangxia ,An; Vaccari , Mattia; Taylor, Andrew Russell
By combining high-sensitivity LOFAR 150 MHz, uGMRT 400 MHz and 1250 MHz, GMRT 610 MHz, and VLA 5 GHz data in the ELAIS-N1 field, we study the radio spectral properties of radio-detected star-forming galaxies (SFGs) at observer-frame frequencies of 150-5000 MHz. We select ∼3500 SFGs that have both LOFAR 150 MHz and GMRT 610 MHz detections, and obtain a median two-point spectral index of α150610 = −0.51 ± 0.01. The photometric redshift of these SFGs spans z = 0.01−6.21. We also measure the two-point radio spectral indices at 150-400-610-1250 MHz and 150-610-5000 MHz, respectively, for the GMRT 610-MHz-detected SFGs, and find that, on average, the radio spectrum of SFGs is flatter at low frequency than at high frequency. At observer-frame 150-5000 MHz, we find that the radio spectrum slightly steepens with increasing stellar mass. However, we only find that the radio spectrum flattens with increasing optical depth at V band at ν ≲ 1 GHz. We suggest that spectral ageing due to the energy loss of CR electrons and thermal free-free absorption could be among the possible main physical mechanisms that drive the above two correlations, respectively. In addition, both of these mechanisms could physically explain why the radio spectrum is flatter at low frequency than at high frequency.

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