Cosmic Ray Electrons Research Articles

On the 3D Transport of Low-energy Galactic Cosmic-ray and Jovian Electrons in the Inner Heliosphere in the Presence of a Fisk-type Heliospheric Magnetic Field

Modeling the transport of low-energy (1−10 MeV) cosmic-ray electrons can lead to valuable insights as to the behavior of the heliospheric magnetic field (HMF), due to the fact that the mean free path (MFP) of these particles parallel to the HMF is significantly larger than their perpendicular MFP, and that these particles experience little in the way of drift due to gradients/curvatures in the HMF and along the heliospheric current sheet. Jovian electrons are particularly suitable for such an endeavour, as they originate from a decentral source in the inner heliosphere. To this end, the transport of these electrons is studied using a 3D, ab initio particle transport code that incorporates theoretical expressions for electron diffusion coefficients, and utilizes as inputs for these transport coefficients turbulence quantities calculated using a two-component turbulence transport model. The effects of a novel Fisk-type field on the transport of these Jovian electrons are investigated and compared with the effects of a standard Parker field.

Radio–FIR correlation: A probe into cosmic ray propagation in the nearby galaxy IC 342

Resolved studies of the correlation between the radio and far-infrared (FIR) emission from galaxies at different frequencies can unveil the interplay between star formation and the relativistic interstellar medium (ISM). Thanks to the LOFAR LoTSS observations combined with VLA, Herschel, and WISE data, we study the role of cosmic rays and magnetic fields in the radio–FIR correlation on scales of ≳200 pc in the nearby galaxy IC 342. The thermal emission traced by the 22 μm emission, constitutes about 6%, 13%, and 30% of the observed radio emission at 0.14, 1.4, and 4.8 GHz, respectively, in star-forming regions and less in other parts. The nonthermal spectral index becomes flatter at frequencies lower than 1.4 GHz (αn = −0.51 ± 0.09, Sν ∝ ναn) than between 1.4 and 4.8 GHz (αn = −1.06 ± 0.19) on average, and this flattening occurs not only in star-forming regions but also in the diffuse ISM. The radio–FIR correlation holds at all radio frequencies; however, it is tighter at higher radio frequencies. A multi-scale analysis shows that this correlation cannot be maintained on small scales due to diffusion of cosmic ray electrons (CREs). The correlation breaks at a larger scale (≃320 pc) at 0.14 GHz than at 1.4 GHz (≃200 pc), indicating that the CREs traced at lower frequencies have diffused a longer path in the ISM. We find that the energy index of CREs becomes flatter in star-forming regions, in agreement with previous studies. Cooling of CREs due to the magnetic field is evident globally only after compensating for the effect of star formation activity that both accelerates CREs and amplifies magnetic fields. Compared with other nearby galaxies, we show that the smallest scale of the radio–FIR correlation is proportional to the propagation length of the CREs on which the ordered magnetic field has an important effect.

CHANG-ES. XXXIII. A 20 kpc radio bubble in the halo of the star-forming galaxy NGC 4217

Cosmic rays may be dynamically very important in driving large-scale galactic winds. Edge-on galaxies give us an outsider's view of radio haloes, and of their extra-planar cosmic-ray electrons and magnetic fields. We present a new radio continuum imaging study of the nearby edge-on galaxy NGC\,4217. We examine the distribution of extra-planar cosmic rays and magnetic fields. We observed it with both the Jansky Very Large Array (JVLA) in the $S$ band (2--4\,GHz) and the LOw Frequency ARray (LOFAR) at 144\,MHz. We measured vertical intensity profiles and exponential scale heights. We re-imaged both the JVLA and LOFAR data at matched angular resolution in order to measure radio spectral indices between 144\,MHz and 3\,GHz. Confusing point-like sources were subtracted prior to imaging. We then fitted intensity profiles with cosmic-ray electron advection models, using an isothermal wind model that is driven by a combination of pressure from the hot gas and cosmic rays. We discover a large-scale radio halo on the north-western side of the galactic disc. The morphology is reminiscent of a bubble extending up to 20\,kpc from the disc. We find spectral ageing in the bubble, which allowed us to measure the advection speeds of the cosmic-ray electrons, which accelerate from 300 to $600\ $. Assuming energy equipartition between the cosmic rays and the magnetic field, we estimate the bubble may have been inflated by a modest 10\,<!PCT!> of the kinetic energy injected by supernovae over its dynamical timescale of 35\,Myr. While no active galactic nucleus (AGN) has been detected, such activity in the recent past cannot be ruled out. Non-thermal bubbles with sizes of tens of kiloparsecs may be a ubiquitous feature of star-forming galaxies, and if so this would demonstrate the influence of feedback. Determining possible contributions by AGN feedback will require deeper observations.

A Simple Model of the Radio–Infrared Correlation Depending on Gas Surface Density and Redshift

We introduce a simple parametric model of the radio–infrared correlation (i.e., the ratio between the IR luminosity and the 1.4 GHz radio luminosity, q IR) by considering the energy loss rate of high-energy cosmic-ray (CR) electrons governed by radiative cooling (synchrotron, bremsstrahlung, inverse Compton scattering), ionization, and adiabatic expansion. Each process of CR electron energy loss is explicitly computed and compared to each other. We rewrite the energy loss rate of each process to be dependent on the gas surface density and redshift using the relevant scaling relations. By combining each energy loss rate, the fraction of the synchrotron energy loss rate is computed as a function of gas surface density and redshift and used to extrapolate the well-established “local” radio–infrared correlation to the high-redshift Universe. The locally established q IR is reformulated to be dependent upon the redshift and the gas surface density and applied for understanding the observed distribution of the radio–infrared correlation of high-redshift galaxies in I. Delvecchio et al. Our model predicts that the q IR value is anticorrelated with gas surface density and the redshift dependency of the q IR value changes by the gas surface density of galaxies, which captures the observed trend of q IR values for stellar-mass-selected star-forming galaxies with a minimal impact of radio–infrared selection bias.

Origin of the break in the cosmic-ray electron plus positron spectrum at ∼1 TeV

Recent measurements of the cosmic-ray electron plus positron spectrum in several experiments have confirmed the presence of a break at ∼1 TeV. The origin of the break is still not clearly understood. In this work, we explored different possibilities for the origin, which include an electron source spectrum with a broken power law, a power law with an exponential or super-exponential cutoff, and the absence of potential nearby cosmic-ray sources. Based on the observed electron plus positron data from the DAMPE and the H.E.S.S experiments, and considering supernova remnants as the main sources of cosmic rays in the Galaxy, we find statistical evidence in favor of the scenario with a broken power-law source spectrum, with the best-fit source parameters obtained as Γ = 2.39 for the source spectral index, E0 ≈ 1.6 TeV for the break energy, and f = 1.59 × 1048 ergs for the amount of supernova kinetic energy injected into cosmic-ray electrons. This power-law break in the spectrum has been predicted for electrons confined inside supernova remnants after acceleration via diffusive shock acceleration process, and also indicated by the multi-wavelength study of supernova remnants. All of this evidence shows that the observed spectral break provides a strong indication of a direct link between cosmic-ray electrons and their sources. Our findings further show that electrons must undergo spectral changes while escaping the source region in order to reconcile the difference between the spectral index of electrons observed inside supernova remnants and that obtained from Galactic cosmic-ray propagation studies.

Identification of positrons and electrons at TeV energy scale using the AMS tracker, time-of-flight counters, and electromagnetic calorimeter

The Alpha Magnetic Spectrometer, AMS, is successfully collecting data since its installation on the International Space Station on May 19, 2011. One of the main AMS objectives is the measurement of cosmic ray positrons and electrons at the highest energies. We present a new technique for the identification of electrons and positrons, which is used in the AMS data analysis in the energy range up to a few TeV. The focus of this article is on the rejection of the proton background using the AMS silicon tracker, the time-of-flight counters, and the electromagnetic calorimeter.

Search for Cosmic-Ray Boosted Sub-MeV Dark-Matter–Electron Scattering in PandaX-4T

We report the first search for the elastic scatterings between cosmic-ray boosted sub-MeV dark matter (DM) and electrons in the PandaX-4T liquid xenon experiment. Sub-MeV DM particles can be accelerated by scattering with electrons in the cosmic rays and produce detectable electron recoil signals in the detector. Using the commissioning data from PandaX-4T of 0.63 tonne·year exposure, we set new constraints on DM-electron scattering cross sections for DM masses ranging from 10 eV/c2 to 3 keV/c2. Published by the American Physical Society 2024

The Coherent Magnetic Field of the Milky Way

We present a suite of models of the coherent magnetic field of the Galaxy based on new divergence-free parametric functions describing the global structure of the field. The model parameters are fit to the latest full-sky Faraday rotation measures (RMs) of extragalactic sources and polarized synchrotron intensity (PI) maps from the Wilkinson Microwave Anisotropy Probe and Planck. We employ multiple models for the density of thermal and cosmic-ray electrons in the Galaxy, needed to predict the sky maps of RMs and PI for a given Galactic magnetic field (GMF) model. The robustness of the inferred properties of the GMF is gauged by studying many combinations of parametric field models and electron density models. We determine the pitch angle of the local magnetic field (11° ± 1°), explore the evidence for a grand-design spiral coherent magnetic field (inconclusive), determine the strength of the toroidal and poloidal magnetic halo fields below and above the disk (magnitudes the same for both hemispheres within ≈10%), set constraints on the half-height of the cosmic-ray diffusion volume (≥2.9 kpc), investigate the compatibility of RM- and PI-derived magnetic field strengths (compatible under certain assumptions), and check if the toroidal halo field could be created by the shear of the poloidal halo field due to the differential rotation of the Galaxy (possibly). A set of eight models is identified to help quantify the present uncertainties in the coherent GMF spanning different functional forms, data products, and auxiliary input. We present the corresponding sky maps of rates for axion–photon conversion in the Galaxy and deflections of ultrahigh-energy cosmic rays.

The enhanced effect of key microorganisms in chromium contaminated soil in Cr(VI) reduction

The escalating threat of Cr(VI) pollution to the environment and human health can be effectively controlled through microbial methods, which are promising, safe, and ecofriendly. To enhance Cr(VI) removal efficiency, scholars have been optimizing strains. However, synergies between in-situ soil particles and crucial microorganisms in soil have rarely been investigated. In this study, Cr(VI) was removed by collaborating with in-situ soil particles and key microorganisms in the soil. The results indicated that within 48 hours, the removal rate of Cr(VI) reached over 99% in the soils+microflora system, which was 45% higher than that of the microflora system alone. Factors such as Cr(VI) concentration, soil dosage, pH level, oxygen availability, and electron donors influenced the removal efficiency of Cr(VI) in the soils+microflora system. The cyclic experiments showed that soil particles effectively prevented chromium invasion on microflora, promoting the growth of crucial microorganisms. The addition of microflora can effectively regulate the composition of soil flora and enhance the efficiency of chromium reduction. Moreover, two strains each of Ochrobactrum sp. and Paenarthrobacter sp., exhibiting remarkable tolerance to Cr(VI), were successfully isolated from these soils, significantly enhancing the reduction capacity of the indigenous microflora towards Cr(VI). Additionally, 16S rRNA-PCR sequence analysis revealed that in-situ soil particles not only synergistically collaborated with the resident microflora for efficient removal of Cr(VI), but also facilitated the proliferation of key microbiota such as Ochrobactrum sp. and Paenarthrobacter sp. Remarkably, when exposed to an initial concentration of 50 mg/L Cr(VI), complete removal was achieved by Paenarthrobacter-2 within a time frame as short as 60 hours. This research found four novel highly efficient strains for reducing Cr(VI) and provides an innovative method for the synergistic interaction between indigenous soil microflora and soil particles to remove heavy metal ions from wastewater.

Radio continuum emission from a tidal dwarf galaxy

ABSTRACT Tidal dwarf galaxies (TDGs) form in the debris of galaxy mergers, making them ideal testbeds for investigating star formation in an extreme environment. We present radio continuum EVLA observations spanning 1–2 GHz of the interacting system Arp 94, which contains the TDG J1023+1952. We detect extended radio continuum emission from the disc of the TDG’s putative parent galaxy, the spiral NGC 3227. The TDG lies in front of the spiral disc, partially overlapping in projection. This challenging alignment complicates the separation of the respective contributions of radio emission from the TDG and disc. However, we show that the radio continuum appears more prominent around the TDG’s location, suggesting the detection of emission from the TDG. Quantifying this argument, we derive an upper limit of 2.2 mJy for the whole TDG’s emission. Our derived inband spectral index map of the system generally shows the expected behaviour of combined thermal and synchrotron radio emission in a galaxy disc, except for a region at the periphery of the disc and the TDG with a flat spectrum (spectral index $\sim$−0.4) unrelated to regions with high H $\alpha$ emission. We speculate that at this location – which coincides with the intersection of faint tidal tails – the collision of gas clouds produces shocks which re-accelerate cosmic ray electrons, and thereby enhance the radio emission. Overall, this study provides new insights about the Arp 94 system and expands the sample of TDGs studied at radio frequencies, with only two confirmed detections so far.

A new analytical model of the cosmic-ray energy flux for Galactic diffuse radio emission

Low-frequency radio observations of diffuse synchrotron radiation offer a unique vantage point from which to investigate the intricate relationship between gas and magnetic fields in the formation of structures within the Galaxy, spanning from the diffuse interstellar medium (ISM) to star-forming regions. Achieving this pivotal objective hinges on a comprehensive understanding of cosmic-ray properties; these dictate the effective energy distribution of relativistic electrons, which are primarily responsible for the observable synchrotron radiation. Notably, cosmic-ray electrons (CRe) with energies of between 100 MeV and 10 GeV play a crucial role in determining the majority of the sky brightness below the GHz range. However, their energy flux (je) remains elusive because of solar modulation. We propose a way to derive observational constraints on this energy gap of interstellar CRe through the brightness temperature spectral index of low-frequency radio emission, here denoted βobs. We introduce a new parametric analytical model that fits available data for je in accordance with the βobs values measured in the literature between 50 MHz and 1 GHz for diffuse emission in the Milky Way. Our model accounts for multiple observations considering magnetic-field strengths consistent with existing measurements below 10 μG. We present a first all-sky map of the average component of the magnetic field perpendicular to the line of sight and validate our methodology against state-of-the art numerical simulations of the diffuse ISM. This research makes headway in modeling Galactic diffuse emission with a practical, parametric form. It provides essential insights that will help preparations for the imminent arrival of the Square Kilometre Array.

Far-red emitting Li2TiO3: Cr3+ phosphor: Synthesis, luminescence properties and potential applications

The Cr[Formula: see text]-activated phosphor can emit far-red light under the excitation of an external light source, mainly due to the transition of the outermost electrons of Cr[Formula: see text] from the 2E level to the 4A2 level in a strong crystal field environment. A novel far-red Li2TiO3: Cr[Formula: see text] phosphor was prepared by the solid-state method. Under the excitation of 356[Formula: see text]nm, the Li2TiO3: Cr[Formula: see text] phosphors emit intense far-red light in 600–850[Formula: see text]nm with a central wavelength of 732[Formula: see text]nm. The emission band of all samples was matched with the absorption bands of phytochrome P[Formula: see text]. The experimental data and theoretical calculation confirmed that Cr[Formula: see text] is surrounded by a strong crystal field environment. The effect of Cr[Formula: see text] doping concentration on the luminescence intensity was analyzed. These research works demonstrate that far-red Li2TiO3: Cr[Formula: see text] phosphors have potential applications in plant growth lights.

DEVILS/MIGHTEE/GAMA/DINGO: the impact of SFR time-scales on the SFR-radio luminosity correlation

ABSTRACT The tight relationship between infrared luminosity (LTIR) and 1.4 GHz radio continuum luminosity ($L_\mathrm{1.4\, GHz}$) has proven useful for understanding star formation free from dust obscuration. Infrared emission in star-forming galaxies typically arises from recently formed, dust-enshrouded stars, whereas radio synchrotron emission is expected from subsequent supernovae. By leveraging the wealth of ancillary far-ultraviolet – far-infrared photometry from the Deep Extragalactic VIsible Legacy Survey and Galaxy and Mass Assembly surveys, combined with 1.4 GHz observations from the Meer Karoo Array Telescope International GHz Tiered Extragalactic Exploration survey and Deep Investigation of Neutral Gas Origin projects, we investigate the impact of time-scale differences between far-ultraviolet – far-infrared and radio-derived star formation rate (SFR) tracers. We examine how the spectral energy distribution (SED)-derived star formation histories (SFHs) of galaxies can be used to explain discrepancies in these SFR tracers, which are sensitive to different time-scales. Galaxies exhibiting an increasing SFH have systematically higher LTIR and SED-derived SFRs than predicted from their 1.4 GHz radio luminosity. This indicates that insufficient time has passed for subsequent supernovae-driven radio emission to accumulate. We show that backtracking the SFR(t) of galaxies along their SED-derived SFHs to a time several hundred megayears prior to their observed epoch will both linearize the SFR–$L_\mathrm{1.4\, GHz}$ relation and reduce the overall scatter. The minimum scatter in the SFR(t)–$L_\mathrm{1.4\, GHz}$ is reached at 200 – 300 Myr prior, consistent with theoretical predictions for the time-scales required to disperse the cosmic ray electrons responsible for the synchrotron emission.

Radio surface fluctuations in radio relics

Recent observations have revealed detailed structures of radio relics across a wide range of frequencies. In this work, we performed three-dimensional magnetohydrodynamical (3D MHD) simulations of merger shocks propagating through a turbulent magnetized intracluster medium. We then employed on-the-fly Lagrangian particles to explore the physical processes behind the origination of radio substructures and their appearance in high and low-frequency observations. We employed two cosmic-ray (CR) electron acceleration models, with a fresh injection of electrons from the thermal pool and the re-acceleration of mildly relativistic electrons. We used the relative surface brightness fluctuations, δSν, to define a “degree of patchiness.” First, we found that patchiness is produced if the shock’s surface has a distribution of Mach numbers, rather than a single Mach number. Second, radio relics appear patchier if the Mach number distribution consists of a large percentage of low Mach numbers (ℳ ≲ 2.5). Furthermore, as the frequency increases, the patchiness also becomes larger. Nevertheless, if radio relics are patchy at high frequencies (e.g., 18.6 GHz), they necessarily will also be patchy at low frequencies (e.g., 150 MHz). Then, to produce noticeable differences in the patchiness at low and high frequencies, the shock front should have a Mach number spread of σℳ ≳ 0.3 − 0.4. Finally, the extent of the patchiness depends on the Mach number distribution as well as the CR acceleration model. We propose δSν as a potential tool for extracting merger shock properties and information on particle acceleration processes at shocks in radio observations.

The Seeding of Cosmic Ray Electrons by Cluster Radio Galaxies: A Review

Radio galaxies in clusters of galaxies are a prominent reservoir of magnetic fields and of non-thermal particles, which become mixed with the intracluster medium. We review the observational and theoretical knowledge of the role of these crucial ingredients for the formation of diffuse radio emission in clusters (radio halos, relics, mini halos) and outline the open questions in this field.

CONGRuENTS (COsmic-ray, Neutrino, Gamma-ray and Radio Non-Thermal Spectra) – II. Population-level correlations between galactic infrared, radio, and γ-ray emission

ABSTRACT Galaxies obey a number of empirical correlations between their radio, γ-ray, and infrared emission, but the physical origins of these correlations remain uncertain. Here, we use the CONGRuENTS model for broad-band non-thermal emission from star-forming galaxies, which self-consistently calculates energy-dependent transport and non-thermal emission from cosmic ray hadrons and leptons, to predict radio and γ-ray emission for a synthetic galaxy population with properties drawn from a large deep-field survey. We show that our synthetic galaxies reproduce observed relations such as the far infrared (FIR)–radio correlation, the FIR–γ correlation, and the distribution of radio spectral indices, and we use the model to explain the physical origins of these relations. Our results show that the FIR–radio correlation arises because the amount of cosmic ray electron power ultimately radiated as synchrotron emission varies only weakly with galaxy star formation rate as a result of the constraints imposed on gas properties by hydrostatic balance and turbulent dynamo action; the same physics dictates the extent of proton calorimetry in different galaxies, and thus sets the FIR–γ–ray correlation. We further show that galactic radio spectral indices result primarily from competition between thermal free–free emission and energy-dependent loss of cosmic ray electrons to bremsstrahlung and escape into galactic haloes, with shaping of the spectrum by inverse Compton, synchrotron, and ionization processes typically playing a subdominant role. In addition to explaining existing observations, we use our analysis to predict a heretofore unseen correlation between the curvature of galaxies’ radio spectra and their pion-driven γ-ray emission, a prediction that will be testable with upcoming facilities.

Compton Scattering of Electrons in the Intergalactic Medium

This paper investigates the distribution and implications of cosmic-ray electrons within the intergalactic medium (IGM). Utilizing a synthesis model of the extragalactic background, we evolve the spectrum of Compton-included cosmic rays. The energy density distribution of cosmic-ray electrons peaks at redshift z ≈ 2, and peaks in the ∼MeV range. The fractional contribution of cosmic-ray pressure to the general IGM pressure progressively increases toward lower redshift. At mean density, the ratio of cosmic-ray electron to thermal pressure in the IGM PCRe/Pth is 0.3% at z = 2, rising to 1.0% at z = 1, and 1.8% at z = 0.1 (considering only the cosmic rays produced locally by Compton scattering). We compute the linear Landau damping rate of plasma oscillations in the IGM caused by the ∼MeV cosmic-ray electrons, and find it to be of order ∼10−6 s−1 for wavenumbers 1.2 ≲ ck/ω p ≲ 5 at z = 2 and mean density (where ω p is the plasma frequency). This strongly affects the fate of TeV e + e − pair beams produced by blazars, which are potentially unstable to oblique instabilities involving plasma oscillations with wavenumber ck/ωp≈secθ (θ being the angle between the beam and wavevector). Linear Landau damping is at least thousands of times faster than either pair beam instability growth or collisional effects; it thus turns off the pair beam instability except for modes with very small θ (ck/ω p → 1, where linear Landau damping is kinematically suppressed). This leaves open the question of whether the pair beam instability is turned off entirely, or can still proceed via the small-θ modes.

The Calorimetric Electron Telescope (CALET) on the International Space Station: Results from the first eight years on orbit

The Calorimetric Electron Telescope, CALET, is an astroparticle physics mission installed on the International Space Station, ISS. The primary objective of the mission is studying the details of galactic cosmic-ray acceleration and propagation, and searching for the possible nearby sources of high-energy electrons and dark matter signatures. The CALET experiment measure the flux of cosmic-ray electrons (including positrons) to 20 TeV, gamma-rays to 10 TeV and nuclei to 1000 TeV. The detector is an all-calorimetric instrument with a total vertical thickness of 30 radiation lengths and fine imaging capability, optimized for the measurement of the electron and positron (all-electron) spectrum well into the TeV energy region. It consists of a charge detector (CHD) with two layers of segmented plastic scintillators for the identification of cosmic-rays via a measurement of their charge over the range Z=1∼40, a 3 radiation length thick tungsten-scintillating fiber imaging calorimeter (IMC) and a 27 radiation length thick lead-tungstate calorimeter (TASC). The instrument was launched on August 19, 2015 to the ISS and installed on the Japanese Experiment Module-Exposed Facility. Since the start of operation in October, 2015, CALET has been collecting scientific data without any major interruption for more than eight years. The number of triggered events over 10 GeV is nearly 1.97 billion events as of November 30, 2023. In this paper, we present the results of the CALET mission so far, including the all-electron energy spectrum, the spectra of protons and other nuclei, gamma-ray observations, as well as the characterization of on-orbit performance. Some results on the electromagnetic counterpart search for LIGO/Virgo gravitational wave events and the observations of solar modulation and gamma-ray bursts are also included.

Circumventing the Theoretical Scaling Relation Limit for the Oxygen Evolution Reaction.

Transition metal hydr(oxy)oxides (TMHs) are considered efficient electrocatalysts for the oxygen evolution reaction (OER) under alkaline conditions. Toward identification of potential descriptors to circumvent the scaling relation limit for the OER, first-principles calculations were used to quantify the effects on the overpotential of different s (Mg), p (Al), and d (Ti, V, Cr, Fe, Co, Sc, and Zn) electron dopants in Ni-based TMHs. Both the adsorbate evolution mechanism (AEM) and the lattice oxygen-mediated mechanism (LOM) were examined. The results demonstrate that the formation energy of oxygen vacancies (EVO) is strongly affected by the chemical nature of the dopants. A linear relationship is identified between EVO and the free energy difference for the oxygen-oxygen coupling. A descriptor could be employed to discriminate whether the LOM is energetically favored over the AEM. These findings fill existing gaps in appropriate yet computationally light descriptors for direct identification between the AEM and LOM.

Radio spectral properties of star-forming galaxies between 150 and 5000 MHz in the ELAIS-N1 field

ABSTRACT 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 $\alpha _{150}^{610}=-0.51\pm 0.01$. 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 $\nu \lesssim 1$ 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.