Preamble

Vol. 43, No. 3

September 2025

PROGRESS IN ASTRONOMY Vol. 43, No. 3 Sept., 2025 doi: 10.3969/j.issn.1000-8349.2025.03.03

Review of Low-Frequency Extragalactic Radio Point Source Catalogues

LIN Jinyang¹, ZHU Zhenghao², MA Renyi¹

(1. College of Physical Science and Technology, Xiamen University, Xiamen 361005, China; 2. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China)

Abstract

Low-frequency radio point sources are of great significance in astronomical research, playing an important role in studying galaxy evolutionary history while also serving as the primary foreground contaminant in Epoch of Reionization signal detection. Low-frequency observations are crucial for investigating and understanding the properties of radio point sources. This paper introduces the radiation mechanisms of radio point sources and current low-frequency radio point source observation catalogues, which are essential for studying the classification, redshift distribution, flux distribution, luminosity function, and spectral indices of radio point sources. Additionally, we provide detailed descriptions of major radio point source simulation software, their simulation methods, and the resulting radio point source catalogues. These software tools and datasets are of great value for deepening our understanding of the statistical properties and cosmological significance of radio point sources.

Keywords: radio galaxies; active galactic nuclei; catalogues

1 Introduction

Radio astronomy, as an important branch of astronomy, primarily studies celestial objects and cosmic phenomena through observations of radio waveband radiation from the universe. Limited by atmospheric windows, our observable frequency range is 10 MHz–1 THz. Although the atmospheric window permits observations down to 10 MHz, technological and instrumental constraints have historically concentrated radio research and observations at frequencies above 1 GHz. Compared with mid- and high-frequency bands, low-frequency bands offer several advantages, such as detecting neutral hydrogen 21 cm radiation from the Epoch of Reionization (EoR), which, after significant redshifting, appears in the low-frequency radio band of 50–200 MHz. Conducting EoR signal detection experiments in this band is of great importance. Additionally, radiation at lower frequencies has longer wavelengths and is less affected by dust, making it easier to observe the central regions of galaxies.

Radiation in the low-frequency band is dominated by synchrotron radiation—radiation produced by high-energy charged particles accelerating in magnetic fields. Synchrotron radiation is brighter and longer-lived at low frequencies, making low-frequency observations more favorable for detecting and studying the diffuse radio emission from galaxy clusters, superclusters, and large-scale filamentary structures. Moreover, because the strength of various plasma effects (such as scattering, dispersion, and Faraday rotation) varies with frequency as ν⁻², the low-frequency band is better suited for studying interstellar magnetic field distributions and electron densities. Low-frequency radio telescopes typically have larger fields of view, which can significantly increase survey speed and are more conducive to finding pulsars and transients.

In low-frequency radio observations and research, the observation and study of extragalactic radio point sources are extremely important components. To understand the processes of galaxy formation and evolution, we need to comprehend the mechanisms by which baryons drive and suppress star formation. In this regard, radio observations provide an important window because they directly reveal three important populations: star-forming galaxies (SFGs), radio-loud active galactic nuclei (RLAGN), and radio-quiet active galactic nuclei (RQ-AGN). These radio point sources are also important foreground contaminants in EoR signal detection, contributing 27% of the total foreground contamination at 150 MHz. On small angular scales of the power spectrum, extragalactic point sources become the strongest and most difficult foreground component to handle. Radio point sources are also important in interferometric array calibration. Flux calibration is typically achieved by observing a bright source with known flux density and transferring the antenna gain solution to the target source data. Calibration sources are selected from sources with known precise flux densities that vary slowly with time. In the northern hemisphere, 3C48, 3C138, 3C147, and 3C286 are commonly used as calibration sources. For phase calibration, such as when affected by the ionosphere, frequent switching to nearby calibrators is required, and the maximum distance between the target source and calibrator is limited by coherence time and isoplanatic patch size.

With advances in observational technology and telescope capabilities, we have observed increasing numbers of radio point sources. Current major low-frequency radio point source catalogues include: the low-frequency radio point source catalogue from the Murchison Widefield Array (MWA) Galactic and Extragalactic All-sky MWA Survey (GLEAM), the low-frequency radio point source catalogue from the LOFAR Two-metre Sky Survey (LoTSS) of the northern sky LOFAR (LOw Frequency ARray), the extragalactic point source catalogue from 21CMA observations, and some low-frequency radio point source catalogues obtained through cross-matching with optical-infrared galaxy catalogues. These point source catalogues provide important support for studying various properties of radio point sources, such as the radio spectra, redshift distribution, and luminosity functions of extragalactic radio point sources.

In extragalactic point source research, radio point source sky simulation is a useful tool, such as for evaluating the completeness of radio surveys or predicting the number of radio sources to be observed in future surveys. Currently, the main simulation tools are SKADS (Square Kilometre Array Design Study) and T-RECS (Tiered Radio Extragalactic Continuum Simulation). To ensure that the generated radio point source sky is consistent with real observations, radio point source simulation programs are designed to model based on information provided by large numbers of radio point source observation catalogues.

This paper systematically introduces radio point sources and their catalogues to support radio point source research. Section 2 mainly introduces the radiation mechanisms of radio point sources; Section 3 introduces low-frequency radio point source observation catalogues; Section 4 introduces radio point source simulation software and the radio point source catalogues they generate; Section 5 summarizes the paper and provides prospects for future radio point source observations and simulations.

2 Radiation Mechanisms of Radio Point Sources

In the low-frequency radio band, the main radiation mechanism for extragalactic point sources is synchrotron radiation, with supernova remnants and processes related to supermassive black holes being the primary sources of synchrotron radiation in galaxies. Synchrotron radiation is produced when charged particles rotate at relativistic speeds in magnetic fields. For relativistic electrons, due to Doppler effects, the radiation has significant directionality. The radiation is concentrated within a narrow cone with a half-opening angle of θ ≈ γ⁻¹ around the direction of the electron's helical motion tangential velocity, where γ is the Lorentz factor, representing the ratio of particle energy to its rest energy. Here we directly present the spectral distribution of synchrotron radiation from a single relativistic electron; detailed derivations can be found in Section 2.7 of reference [22].

$$P(\nu)d\nu = \frac{3e^3B\sin\alpha}{4\pi\epsilon_0 c m_e} F\left(\frac{\nu}{\nu_c}\right) d\nu$$

where ν is the corresponding frequency, B is the magnetic field strength, and α is the pitch angle of the electron's helical motion. The function F(x) contains the spectral shape, which involves an integral of modified Bessel functions of order 5/3: F(x) ≡ x ∫x^∞ K(\xi) dξ. Considering the polarization characteristics of synchrotron radiation, decomposing the radiation into components perpendicular and parallel to the magnetic field involves the function G(x) ≡ x ∫x^∞ K(\xi) dξ. The power spectra for the two polarization components are:

$$P_{\perp,\parallel}(\nu) = \frac{e^3 B \sin\alpha}{8\pi\epsilon_0 c m_e} \left[ F(x) \pm G(x) \right]$$

The linear polarization degree of synchrotron radiation is:

$$\Pi(\nu) = \frac{P_\perp(\nu) - P_\parallel(\nu)}{P_\perp(\nu) + P_\parallel(\nu)} = \frac{G(x)}{F(x)}$$

For most cases, the linear polarization degree of synchrotron radiation is between 0.70 and 0.75, making strong linear polarization a characteristic feature of synchrotron radiation.

We consider a relativistic gas with an energy number density distribution N_E, assuming an isotropic pitch angle distribution: dN_E = CE^{-p}dE, where p is the spectral index and C is a constant. The energy distribution of cosmic rays and the energy distribution of radiating electrons in many other synchrotron radiation sources follow a power-law form. Convolving the electron energy distribution with the synchrotron radiation spectrum of a single electron, the spectral emissivity (radiated power per unit volume, per unit solid angle, and per unit frequency interval) for a power-law distribution with isotropic pitch angles can be written in closed form. The function a(p) (see Table 1 [TABLE:1]) is typically used to simplify the dependence of spectral emissivity on the power-law spectral index. For typical cases encountered in radio astronomy, a(p) is generally on the order of 10⁻¹. The spectral emissivity for electrons with spectral index p, isotropic pitch angle distribution, and power-law distribution is [22]:

$$j_\nu = \frac{3^{(p+1)/2}}{4\pi} \left( \frac{e}{4\pi\epsilon_0 m_e c} \right)^{(p-1)/2} a(p) C B^{(p+1)/2} \nu^{-(p-1)/2}$$

Table 1 Values of the a(p) function for energy spectral index p [46]

For optically thin sources, radiation intensity can be obtained by integrating the spectral emissivity along the line of sight. For a source with uniform density and path length L along the line of sight, integration yields the radiation intensity [22]:

$$I_\nu = 1.35 \times 10^{-25} \left( \frac{\nu}{6.26 \times 10^{18}} \right)^{-(p-1)/2} a(p) C B^{(p+1)/2} L$$

where I_ν has units of W·m⁻²·sr⁻¹·Hz⁻¹.

It is evident that synchrotron radiation from relativistic electrons with a power-law energy distribution also follows a power-law spectrum: dN_E ∝ E⁻ᵖ, I_ν ∝ ν⁻⁽ᵖ⁻¹⁾/². For most extragalactic radio point sources, since their radiation is dominated by synchrotron radiation, their flux density S_ν also follows a power-law spectrum, S_ν ∝ ν⁻ᵅ, where α = (p - 1)/2 is the spectral index. Most radio galaxies or quasars have spectral indices in the range of -2 to 0. This power-law spectrum does not extend infinitely to lower frequency ranges; under certain physical conditions, the radiation source becomes opaque to its own synchrotron radiation, and the spectrum bends, a phenomenon we call synchrotron self-absorption.

When a relativistic electron gas is surrounded by a uniform magnetic field, electrons of all energy ranges produce linearly polarized radiation. The linear polarization degree of a gas with a power-law energy distribution with spectral index p can be obtained by integrating the polarization analysis of a single electron (Equation (3)) over all energies and pitch angles:

$$\Pi = \frac{p + 1}{p + 7/3}$$

For a typical energy spectral index p = 2.5, the resulting linear polarization degree is about 0.72, close to the value for a single electron. In practice, the actually observed radiation is the sum over different regions of non-uniform magnetic fields, and the superposition effects along and perpendicular to the line of sight within the observing beam can significantly reduce the polarization degree.

The radiation mechanisms of extragalactic point sources mainly include synchrotron radiation, free-free radiation, and thermal radiation, with synchrotron radiation dominating at low frequencies; while at frequencies ν ≳ 30 GHz, free-free radiation dominates. Additionally, because different types of extragalactic point sources have different radiation patterns, the classification of extragalactic point sources is also important. In current extragalactic radio surveys, it is generally believed that extragalactic point sources are mainly composed of star-forming galaxies and active galactic nuclei.

Star-forming galaxies are relatively weak radio sources, typically dominating at lower radio flux density ranges. For example, at 150 MHz, their dominance is reflected in the range below 1 mJy. The synchrotron radiation in star-forming galaxies is produced by relativistic plasma accelerated in supernova remnants associated with massive (M ≳ 8M⊙) star formation. Therefore, radio observations can detect recent star formation activity and, to some extent, trace its location, which has led to the confirmation of the far-infrared-radio correlation. In star-forming galaxies, infrared and radio radiation show a strong linear correlation. Currently, there are two main modes of star formation activity: one is the starburst mode, which may be triggered by galaxy mergers or high-density star formation regions; the other is a more normal mode associated with long-term star formation processes. Observations show that most star-forming galaxies are in the second mode. For this second mode of star-forming galaxies, the star formation rate (SFR) is strongly correlated with stellar mass M_, a relationship that can be described by a power law: SFR ∝ M_^β (β = 0.4–1). Such star-forming galaxies are generally considered to be the main sequence of star-forming galaxies.

The basic characteristic of active galactic nuclei is that their energy originates from the relativistic deep potential well of the supermassive black hole at the galaxy's center. AGN have various complex classification schemes, with subclasses often overlapping between different classification methods. Next, we will introduce the main classifications of AGN.

Based on the primary mode of energy output, AGN can be divided into radiative-mode AGN and jet-mode AGN, with the structures of the two modes shown in Figure 1 [FIGURE:1]. Radiative-mode AGN primarily output energy through electromagnetic radiation, while jet-mode AGN produce relatively less electromagnetic radiation, mainly existing in the form of large amounts of kinetic energy transmitted through concentrated jets on both sides. These jets may be driven by gas accretion onto the supermassive black hole or by its spin energy. In the past, jet-mode AGN were generally classified as low-excitation radio galaxies.

Note: (a) Shows the basic structure of radiative-mode AGN. It has a geometrically thin, optically thick accretion disk extending to the radius of the innermost stable orbit around the central supermassive black hole; it has high radiative power that ionizes gas clouds in both the broad-line region and narrow-line region; additionally, it has a dust-containing gas obscuring structure that prevents direct observation of the accretion disk and broad-line region from certain directions. (b) Shows the basic structure of jet-mode AGN. Its thin accretion disk is replaced by a geometrically thick gas accretion flow in the inner region, which may transition to a truncated thin disk at larger radii; its radiative power is lower, only ionizing gas clouds in the narrow-line region.

Figure 1 Radiative-mode and jet-mode active galactic nuclei [55]

The basic structure of the first type, radiative-mode AGN, is that the central supermassive black hole is surrounded by a geometrically thin, optically thick accretion disk that accretes gas. This accretion disk has a radial temperature gradient and therefore produces continuous thermal radiation from the extreme ultraviolet to the visible band; simultaneously, the accretion disk is surrounded by a hot corona that up-scatters soft photons from the accretion disk radiation to the X-ray range through inverse Compton scattering. When X-rays act on the accretion disk, their spectral energy distribution is further altered by reflection from the accretion disk. In addition, ionizing radiation from the accretion disk and heating from the corona ionize dense gas clouds ranging from light-days to several light-years from the supermassive black hole, producing permitted emission lines in the ultraviolet, optical, and near-infrared bands. The velocity dispersion of these clouds is generally several thousand km/s, and based on the emission lines produced, this region is designated the broad-line region. On larger scales, the supermassive black hole and accretion disk are also surrounded by a layer of dusty molecular gas (the dust obscuring structure). In this region, ultraviolet, visible, and soft X-rays from the accretion disk are absorbed by dust and re-emitted as infrared radiation. When ionizing radiation escapes along the polar axis of the obscuring structure, it ionizes gas on scales of hundreds to thousands of parsecs, causing these quieter and less dense gas clouds to produce forbidden and permitted emission lines in the ultraviolet, visible, and infrared. The velocity dispersion of these clouds is several hundred km/s, so this region is designated the narrow-line region [55].

When observing AGN from near the polar axis direction of the dust obscuring structure, the supermassive black hole, accretion disk, corona, and broad-line region can be clearly seen. These AGN are generally called Type I AGN. If observed from near the equatorial plane of the dust obscuring structure, the central region of the AGN cannot be observed, and these are called Type II AGN. This is the standard unified model for radiative-mode AGN, which holds that the difference between Type I and Type II AGN is solely due to different viewing angles. The existence of Type II AGN can still be inferred through thermal infrared radiation from the obscuring structure, hard X-rays propagating through it, or the ratio of characteristic emission lines from the narrow-line region [55].

Jet-mode AGN, on the other hand, have a unique supermassive black hole accretion mode that shows lower radiative efficiency and accretion rate. Their geometrically thin disk may not exist or may be truncated by a geometrically thick structure, where the gas inflow time is shorter than the radiative cooling time [57–61]. This is called advection-dominated or radiatively inefficient accretion flow. A typical feature of these accretion flows is their ability to emit bilateral jets [55]. For jet-mode AGN, the accretion rate is typically below 1% of the Eddington accretion rate; for radiative-mode AGN, the typical accretion rate is generally 1%–10% of the Eddington accretion rate.

Based on the morphology of radio images—that is, according to the ratio between the extent of the lowest surface brightness contour of the central galaxy and the distance between the highest brightness regions on both sides of the central galaxy—AGN can be divided into FRI (ratio less than 0.5) and FRII (ratio greater than 0.5) [62]. FRII have obvious hotspots and bright outer edges, while FRI have more diffuse radio emission. Generally, low-accretion-rate radio sources produce weaker jets and mainly exhibit FRI structure, while galaxies with higher accretion rates produce stronger jets and show FRII structure [55]. In addition, the radio images of radio sources may be influenced by environmental factors, as radio sources in clustered regions are more likely to show FRI morphology, possibly because jets are more easily disrupted in dense radio source regions [63]. Recently, a third class, FR0, has been proposed [64], which has FRI characteristics but lacks obvious extensive radio emission [47].

As previously mentioned, synchrotron radiation dominates radio point sources in the radio band, so most AGN radiation spectra follow a power-law form. Based on the spectral index α, radio point sources can be divided into flat-spectrum sources (α < 0.5) and steep-spectrum sources (α ≥ 0.5) [65–68]. Additionally, a spectral index α = 0.5 can serve as an approximate boundary between extended and point sources [69]. Flat-spectrum radio sources have two subclasses: flat-spectrum radio quasars (FSRQ) and BL Lacertae objects (BL Lacs). In optical spectra, flat-spectrum radio quasars have strong, broad emission lines like standard quasars, while BL Lac objects show at most weak emission lines, sometimes absorption lines, and in many cases no features at all [47].

Furthermore, the most commonly used classification for AGN is dividing them into radio-loud and radio-quiet AGN [70–73]. The main physical difference between the two types of AGN is the presence or absence of strong relativistic jets [47]. Currently, there are two criteria for this division: the first is based on the radio flux density or radio luminosity of the radio source [74]. At 1.4 GHz, the luminosity criterion for dividing the two types of radio sources is L₁.₄GHz = 10²³ W·Hz⁻¹ [22], although some argue for L₁.₄GHz = 7 × 10²⁴ W·Hz⁻¹ [75]. The different division criteria may be related to the redshift range of the selected sample [17]. The other criterion is based on the ratio of radio flux density or luminosity to optical flux density or luminosity [76]. These two types of AGN are essentially different celestial objects: radio-loud AGN release most of their energy non-thermally (through synchrotron radiation) and are associated with powerful relativistic jets, while radio-quiet AGN have multi-band radiation dominated by thermal processes and are directly or indirectly related to the accretion disk [17, 47, 77]. For radio-quiet AGN, they may also have active nuclei that contribute partially to their radio radiation [78, 79]. Radio-quiet AGN show obvious signs of nuclear activity in non-radio bands such as X-ray, mid-infrared, and optical, but show no signs of large-scale radio jets, and their radio radiation is far weaker than that of radio-loud AGN [17, 70]. Therefore, radio-quiet AGN remain controversial, and we still do not clearly understand the formation mechanism of their radio radiation. Current observational indications suggest that the radio radiation of radio-quiet AGN may have two sources: active nuclei and star formation. On the one hand, radio-quiet AGN have infrared-radio flux ratios, evolving luminosity functions, host galaxy colors, optical morphologies, and stellar masses similar to star-forming systems [49, 51], indicating that in radio-quiet AGN, radio radiation is usually dominated by star formation [70, 80, 81]. On the other hand, some studies have found that radio-quiet AGN show higher radio brightness compared to star-forming galaxies of similar mass [73, 82]. However, these different findings may be because the samples detected in related studies are in different luminosity and redshift ranges [72]. Currently proposed models for the radio radiation of radio-quiet AGN include star formation activity like that in star-forming galaxies [83], micro-jets [84], coronae [85], and disk winds [86].

Finally, based on the optical spectral characteristics of AGN, they can be divided into high-excitation radio galaxies and low-excitation radio galaxies. The spectra of high-excitation radio galaxies contain strong emission lines such as [OII]λ3727 Å, [OIII]λ5007 Å, and [NeII]λ3867 Å, while the spectra of low-excitation radio galaxies show absorption lines or weaker [OII]λ3727 Å emission lines [87]. This classification criterion has been extended to use the equivalent width of the strong [OIII]λ5007 Å emission line [88] or high (low) excitation or ionization emission lines as classification criteria [89, 90, 90–92]. Generally, AGN with high-level emission lines in their optical spectra are called high-excitation radio galaxies, and vice versa are called low-excitation radio galaxies. High-excitation radio galaxies are mainly driven by efficient accretion of cold gas onto geometrically thin, optically thick accretion disks [93, 94], with accretion rates typically 1%–10% of the Eddington rate [95]. This accretion mode produces highly excited emission lines in the galaxy spectrum. For low-excitation radio galaxies, they are more likely accreting warm gas from the intergalactic medium onto geometrically thick accretion disks, with accretion rates generally below 1% of the Eddington rate [95]. Low-excitation radio galaxies typically do not show X-ray radiation associated with the accretion process [96] and do not produce infrared radiation from the AGN torus [94, 97].

The different AGN classifications described above have some overlap. For example, radiative-mode AGN include high-excitation radio galaxies, while jet-mode AGN are called low-excitation radio galaxies [55]. Moreover, almost all FRI are low-excitation radio galaxies, while most FRII with strong emission lines are classified as high-excitation radio galaxies. However, FRI and FRII do not correspond completely to low- and high-excitation radio galaxies, as some (20%) FRII have been proven to be low-excitation radio galaxies [63]. Compared to FRII or high-excitation radio galaxies, FRI or low-excitation radio galaxies have less obscuration of the core region, indicating that FRI or low-excitation radio galaxies may lack a dust obscuring structure, or if present, it is not a standard geometrically thick torus [47, 98, 99].

3 Low-Frequency Radio Point Source Observational Catalogues

As the number of observed low-frequency radio point sources increases, observational radio point source catalogues are becoming increasingly complete in terms of redshift, flux, observed sky area, and other aspects, with significant progress in completeness analysis of radio point source brightness. Studying radio point source samples allows us to gain clearer understanding of radio point source properties, spatial distribution (clustering effects), luminosity functions, and size models, while also benefiting research on radio point source foreground contamination in EoR signal detection.

This chapter introduces low-frequency radio point source catalogues. Table 2 [TABLE:2] contains the main information for the low-frequency radio extragalactic point source catalogues to be introduced later: catalogue name, frequency, sky area, redshift information, radio source classification information (such as AGN vs. star-forming galaxies), and completeness information.

Table 2 Summary of extragalactic point source catalogue information

3.1 GLEAM

The GLEAM-I low-frequency extragalactic point source catalogue was calibrated using observation data from the first year (2013–2014) of the MWA telescope survey [23]. This catalogue covers 24,831 square degrees of sky area south of declination +30° and outside the Galactic plane ±10°, containing 307,455 radio sources. The catalogue's observed flux density frequency range covers 72–231 MHz with a frequency bandwidth of 8 MHz. The catalogue placed 25,000 simulated sources with flux densities of 25 mJy–1 Jy into the observed images and identified the simulated sources using the same method to study completeness at different flux levels. At 200 MHz, the sample has 90% completeness at a flux density of 170 mJy, and still maintains 50% completeness at 55 mJy. Additionally, the catalogue assessed its reliability by identifying negative-flux sources (image artifacts near bright sources caused by calibration and deconvolution errors) and determined the catalogue's reliability to be 99.97% based on the ratio of negative-flux sources to total sources.

This catalogue also fitted spectral indices (S ∝ ν^α) for all 245,470 sources with positive flux densities in each frequency sub-band and statistically analyzed the distribution of spectral indices across different flux ranges. At 200 MHz, the median spectral index for 122,959 radio point sources with flux densities less than 0.16 Jy is 0.78 ± 0.20; for 86,548 radio point sources with flux densities of 0.16–0.5 Jy, the median spectral index is 0.79 ± 0.15; for 20,606 radio point sources with flux densities of 0.5–1.0 Jy, the median spectral index is 0.83 ± 0.12; and for 12,723 radio point sources with flux densities greater than 1.0 Jy, the median spectral index is 0.83 ± 0.11. This provides us with rich information on the distribution of low-frequency radio point source spectral indices [23]. In addition to spectral indices, the catalogue also statistically analyzed the flux distribution of radio point sources in low-noise regions (0 h < RA < 3 h and -60° < Dec < -10°; 10 h < RA < 12 h and -40° < Dec < -15°, with average noise of 6.8 ± 1.3 mJy) and compared it with results from other observations, as detailed in Figure 2.

As a supplement to the GLEAM-I observational catalogue, the GLEAM-II low-frequency radio point source catalogue covers 2,860 square degrees of sky in the Galactic plane region with |b| ≤ 10°, Galactic longitude 345°–67° and 180°–240° [24]. Compared with GLEAM-I, GLEAM-II used the multi-scale CLEAN function of WSCLEAN [108] to better deconvolve large-scale Galactic structures. This supplementary catalogue contains 22,037 radio point sources, and using the same method as GLEAM-I for study, it achieved 50% completeness at 120 mJy at 200 MHz, with catalogue reliability of 99.86%. The catalogue also fitted spectral indices for radio point sources in this region and statistically analyzed their distribution, finding that 17,244 sources have power-law spectral energy distributions. At 200 MHz, the median spectral index for radio point sources with flux densities less than 0.16 Jy is -0.89; for those with flux densities of 0.16–0.5 Jy, -0.86; for 0.5–1.0 Jy, -0.88; and for greater than 1.0 Jy, -0.87 [24]. Finally, 5,749 sources in this catalogue were resolved (ratio of integrated flux density to peak flux density greater than 1.1), and 168 sources showed obvious extension (ratio greater than 2).

GLEAM-III used observation data from the first two years (2013–2015) of the MWA telescope survey. This low-frequency radio point source catalogue is centered on the South Galactic Pole (SGP), covering 5,113 square degrees in the range of declination -48° to -2° and right ascension 20h40min to 05h04min, with a total of 108,851 radio point sources. Compared with GLEAM-I observations, GLEAM-III has longer integration time, better uv coverage, and better processing methods, reducing the sky RMS noise in the GLEAM-III observation region by 40% compared to GLEAM-I. The GLEAM-III catalogue does not use calibrator observations for data calibration but instead uses GLEAM-I as the sky model for calibration. This catalogue also fitted spectra for 77% of its sources, measuring mean and median spectral indices of -0.81 and -0.82 for 83,328 radio point sources. The catalogue also separated radio sources into point sources and extended sources by establishing a model of the relationship between the ratio of integrated flux density to peak flux density and signal-to-noise ratio, finding that 8.4% of sources are extended. Additionally, GLEAM-III evaluated the completeness of radio sources and catalogue reliability using the same method as GLEAM-I, with results showing 50% completeness at 25 mJy, 90% completeness at 50 mJy, and catalogue reliability reaching 99.994% [25].

The GLEAM survey project's observed sky area covers most of the southern sky, including many deep-field multi-wavelength observation regions such as Galaxy and Mass Assembly (GAMA), Chandra Deep Field South (CDFS), European Large Area ISO Survey-South 1 (ELAIS-S1), and two regions specifically used by MWA for detecting the global EoR signal, EoR0 (center position 00h, 27°) and EoR1 (04h, 30°). The catalogues released by the GLEAM project not only contain a large amount of information for studying extragalactic radio sources in the southern sky, such as flux density distribution, spectral index distribution, completeness, and extended source distribution, but can also serve as reliable flux calibration catalogues for other low-frequency southern sky observations, such as reionization studies by MWA, PAPER, and the upcoming SKA telescope.

3.2 LoLSS

LoLSS is a northern sky survey project using LOFAR telescope low-band antennas in the frequency range of 42–66 MHz. Its goal is to cover the entire northern sky with 15″ resolution and 1 mJy sensitivity. LoLSS-DR1 is the first catalogue released by the LoLSS project. The LoLSS-DR1 catalogue covers 740 square degrees of sky [109] and contains 25,247 radio point sources. This catalogue uses the Python Blob Detection and Source Finder (PyBDSF) software [110] to extract sources from interferometric images and provides source type results fitted by PyBDSF. "S" represents isolated point sources, "C" represents large complex sources, and "M" represents sources with multiple radio emission components. The catalogue also assessed completeness at different flux densities by adding 6,000 simulated sources with ionospheric effects and using PyBDSF to detect them, repeating this 50 times. The final completeness simulation results show 50% completeness at 17 mJy and 90% completeness at 40 mJy. Additionally, by inverting pixel values of the mosaic image (negative pixels caused by noise and artifacts become positive, while positive pixels from sources become negative) and using the same method with PyBDSF to extract sources from the inverted image, 1,055 radio sources were detected, leading to the conclusion that 4% of sources in the LoLSS-DR1 catalogue are artificially generated false sources.

The LoLSS-DR1 or future complete LoLSS catalogue, with its unique combination of high angular resolution and sensitivity, can be used to study "fossil" steep-spectrum sources, which is crucial for understanding the properties, evolution, and life cycle of synchrotron radiation-dominated radio sources. At the same time, the LoLSS catalogue can be used to study the process by which radio sources change their synchrotron radiation power-law spectrum at very low frequencies (42–66 MHz), providing new information for processes such as absorption by ionized gas and synchrotron self-absorption. Furthermore, the combination of LoLSS and LoTSS will produce a unique dataset that will aid low-frequency radio source research. Finally, conducting long-term ionospheric observations at very low frequencies will help constrain and improve future ionospheric models.

3.3 LoTSS

The LoTSS-DR1 catalogue is the first low-frequency radio point source survey catalogue released by the LOFAR telescope's LoTSS project. This catalogue's observed sky area includes 424 square degrees of sky with right ascension 10h45min00s–15h30min00s and declination 45°00′00″–57°00′00″, detecting a total of 325,694 radio point sources [27] in the frequency range of 120–168 MHz. The LoTSS-DR1 catalogue also performed completeness simulations (adding simulated sources and using PyBDSF to extract them to assess completeness), with results showing 65% completeness at 0.18 mJy, 90% completeness at 0.35 mJy, and 95% completeness at 0.45 mJy [27]. The catalogue also cross-matched with optical data from Pan-STARRS [111, 112] and mid-infrared luminosity observations from the Wide-field Infrared Survey Explorer mission (WISE) [113], with 73% of radio point sources having matching sources in Pan-STARRS and WISE [114]. A novel hybrid photometric redshift method was used to estimate the redshift of each radio point source [115], providing redshift information for most radio sources in this catalogue.

The LoTSS-DR2 catalogue is the second batch of low-frequency radio point source survey catalogues released by the LoTSS project [116]. The catalogue's observed sky area is divided into two regions centered at (12h45min, +44°30′) and (1h00min, +28°00′), covering areas of 4,178 square degrees and 1,457 square degrees respectively, for a total of 5,635 square degrees. A total of 4,396,228 radio point sources were observed, most of which had not been discovered in previous radio observations. The catalogue performed completeness simulations by adding simulated sources, with results showing completeness of 50%, 90%, and 95% at flux densities of 0.34 mJy, 0.8 mJy, and 1.1 mJy respectively. The LoTSS-DR2 catalogue also provides source type results fitted by PyBDSF.

The catalogues released by the LoTTS project contain a large amount of information on flux density distribution, spectral index distribution, and source counts of radio sources at low frequencies. Their high angular resolution and large-area observation catalogues can also serve as reliable flux calibration references for other northern sky low-frequency observation studies.

The LoTSS-DP-DR1 extragalactic point source catalogue was released from LOFAR deep field observations, covering 25.6 square degrees of sky area composed of three small fields: ELAIS-N1, Boötes, and Lockman Hole. The detected radio sources have redshifts up to 7 and a flux limit of 0.003 mJy. The catalogue contains information on 81,951 radio point sources at 150 MHz, including flux density, redshift, point source classification, star formation rate, and stellar mass, making it the largest deep-field observation to date containing radio point source classifications [31].

This catalogue was obtained by cross-matching the initial catalogue of 7.2 × 10⁶ radio point sources from LoTSS deep field observations with optical, mid-infrared, and far-infrared observations [29], and using four spectral energy distribution fitting software packages (MAGPHYS [117], BAGPIPES [118, 119], CIGALE [120–122], AGNFITTER [123]) to fit radio point sources to determine whether their radiation mode is AGN mode, while also using these four software packages to estimate the stellar mass and star formation rate of radio point sources.

Regarding the classification of radio point sources, considering that the radio brightness of star-forming galaxies is closely related to star formation rate, radio point sources whose radio brightness significantly deviates from predictions based on star formation rate are identified as AGN [78, 124, 125]. Therefore, based on observational data, the predicted relationship between star formation rate and radio luminosity is proposed as:

$$\lg(L_{150\text{MHz}}) = 22.24 + 1.08 \lg(\text{SFR})$$

where L₁₅₀MHz (in units of W·Hz⁻¹) is the predicted radio luminosity of the extragalactic point source based on star formation rate, and SFR (in units of M⊙·yr⁻¹) is the star formation rate of the radio point source. If the observed radio luminosity is 0.7 dex greater than that predicted from the star formation rate, the radio point source is considered radio-excess. However, because radio point sources in the Boötes field were found to have increasing scatter between star formation rate and actual radio luminosity with increasing redshift, to ensure consistency in radio source classification, the radio-excess criterion for this field was changed to (0.7 + 0.1z) [31]. Finally, radio point sources with AGN radiation mode and radio-excess are classified as high-excitation radio galaxies; those with non-AGN radiation mode and radio-excess as low-excitation radio galaxies; those with AGN radiation mode but not radio-excess as radio-quiet AGN; and those with non-AGN radiation mode and not radio-excess as star-forming galaxies [31]. The distribution of different types of radio point sources is shown in Table 3 [TABLE:3], where the majority (67.9%) are star-forming galaxies, and the smallest group, high-excitation radio galaxies, account for only 2.1%.

Table 3 Distribution of different types of radio point sources in the LoTSS-DP-DR1 extragalactic point source catalogue

Because this catalogue contains information on radio point source classification, redshift, flux density, star formation rate, and stellar mass, it is important for studying the redshift distribution, flux distribution, star formation rate distribution, and luminosity function of different types of sources [31, 126, 127]. Additionally, the completeness of different types of radio point sources in this catalogue has been obtained through precise simulations, with approximately 0.2 mJy for 50% completeness for all types [126, 127]; for high-excitation and low-excitation radio galaxies, completeness exceeds 90% for flux densities above 1.6 mJy [126]; and for RQ-AGN and star-forming galaxies, completeness exceeds 90% for flux densities above 0.63 mJy [127].

3.4 3CRR

The 3CRR low-frequency radio point source catalogue (Revised Revised Third Cambridge Catalogue of Radio Sources) is a sample of bright radio point sources at 178 MHz, with an observed sky area of 13,886 square degrees, a total of 178 radio sources, a flux limit of 10.9 Jy, and overall sample completeness exceeding 96% [34]. Ninety-six percent of radio point sources have matching optical sources, and based on optical spectral information, the sources are divided into radio galaxies and quasars, with 71% being galaxies and 25% quasars. The 3CRR catalogue also estimates redshifts for all sources based on optical spectral information, providing redshift information for radio sources. Additionally, the catalogue divides these bright sources into FRI and FRII based on morphology. Radio sources with radiation concentrated around the optically identified center are classified as FRI, while those with maximum radiation in radio lobes far from the optically identified center are classified as FRII. If the brightness distribution is found to be dominated by unresolvable components at frequencies ν > 1 GHz, they are classified as "C". The 3CRR catalogue also fits spectral indices for all radio point sources from 178–750 MHz. Furthermore, the catalogue includes magnitude information in blue (B), visual (V), and red (R) bands.

The 3CRR catalogue contains a large number of bright sources, along with optical spectra, radio source classifications, redshifts, and magnitude information in different bands, which is of great use for bright source research. At the same time, because the flux densities of some bright sources in the 3CRR catalogue vary little with time, they are often used as calibration sources for observations, such as 3C48, 3C138, 3C147, and 3C286.

3.5 7CRS

The 7CRS (Seventh Cambridge Redshift Survey) catalogue was observed by the CLFST (Cambridge Low Frequency Synthesis Telescope) and is divided into 7C-I, 7C-II, and 7C-III based on different sky areas. The total observed sky area is 0.022 steradians, the observation frequency is 151 MHz, and the flux limit is 0.5 Jy (1/20 of the 3CRR catalogue) [128, 129]. Through extensive optical and near-infrared observation matching, 130 sources were identified, with redshift information provided for 90% of them, up to a maximum redshift of 3.6. The catalogue also provides K-band magnitude information and has been used to study the relationship between K-band magnitude and redshift z, finding that the M_K-z relationship can be well expressed as M_K = 17.37 + 4.53 lg z - 0.31(lg z)². At all redshifts, there is a significant difference in K-band absolute magnitudes between radio point sources in the 3CRR catalogue and the weaker 7CRS radio sources, possibly because this relationship is affected by black hole mass [130].

3.6 21CMA-NCP

The 21CMA-NCP (21 CentiMeter Array North Celestial Pole) low-frequency radio point source catalogue was obtained by the 21CMA radio interferometric array located in the Tianshan Mountains of Xinjiang, China, observing the north celestial pole. The frequency range is 75–175 MHz with a bandwidth of 12.5 MHz, detecting a total of 624 radio point sources. The catalogue statistically analyzed the distribution of spectral indices, with a peak corresponding to -0.8, consistent with expectations. The catalogue also found steeper radio sources at higher frequency ranges. Source count statistics were performed for all frequency bands, as detailed in Figures 3 [FIGURE:3] and 4 [FIGURE:4]. Additionally, the catalogue performed related completeness simulations for different frequency bands, finding that completeness drops rapidly to 0% below 0.1 Jy, reaches 50% at 0.2 Jy, and achieves 100% completeness above 1 Jy at higher frequencies [32].

Note: The vertical dashed line corresponds to the flux density at 20% completeness for that frequency, and the vertical solid line corresponds to the flux density at 50% completeness for that frequency.

Figure 3 Source counts for different frequency ranges in the 21CMA-NCP catalogue [32]

Figure 4 Source counts for different frequency ranges in the 21CMA-NCP catalogue [32]

3.7 VLSSr

The VLSSr (VLA Low-frequency Sky Survey Redux) low-frequency extragalactic point source catalogue was obtained from the Very Large Array (VLA) low-frequency sky survey [106]. Its observed area is about 30,530 square degrees, at a frequency of 74 MHz, with a flux limit of 0.39 Jy, containing a total of 92,964 sources. To determine the authenticity of radio sources, the catalogue was matched with the 1.4 GHz NVSS point source catalogue [131]. To exclude sources that are components of large radio sources, sources without a second component within 120″ were defined as isolated sources. More than 90,000 isolated sources were matched with the NVSS catalogue, finding that 2.2% of isolated sources had no matching source, which were considered false detections. The catalogue also statistically analyzed the distribution of spectral indices fitted for each radio source from 74–1,400 MHz, with a median value of -0.82. The catalogue also performed corresponding source count statistics but did not conduct related radio source completeness surveys.

This catalogue covers almost the entire sky north of declination -30°, making it one of the larger catalogues in current low-frequency extragalactic point source research. Despite certain limitations, it serves as an important low-frequency reference point for multi-wavelength studies of extragalactic radio sources [132–134], provides low-frequency comparison points for other surveys [135], and offers a global sky model for initial calibration of other low-frequency instruments and arrays [136, 137].

3.8 T-RaMiSu

The T-RaMiSu (Two-meter Radio Mini Survey) low-frequency extragalactic point source catalogue was obtained by the Giant Metrewave Radio Telescope (GMRT) observing the Boötes region [105]. Its frequency is 153 MHz, covering an observed area of 30 square degrees, with a flux limit of 4.1 mJy, containing a total of 1,289 sources. The catalogue uses Monte Carlo simulations to fit a model of the relationship between the ratio of integrated flux density to peak flux density and signal-to-noise ratio, classifies sources as extended or point sources based on this model, and provides semi-major axes and position angles for extended sources. Additionally, the catalogue assessed completeness at different flux densities by adding simulated false sources of different flux densities and using PyBDSF to search for sources. The reliability was obtained by statistically analyzing the number of falsely detected sources. Both completeness and reliability increase with increasing flux density, reaching 95% and 92% respectively at 14 mJy.

The catalogue also provides source count statistics and spectral index statistics. Source count statistics cover a flux density range of 15 mJy–7 Jy, while spectral indices were only statistically analyzed for sources greater than 0.1 Jy, with mean spectral indices of -0.25 and -0.2 for 153–1,400 MHz and 153–327 MHz respectively.

3.9 GLEAM-6dFGS

The GLEAM-6dFGS low-frequency extragalactic point source catalogue was obtained by cross-matching the aforementioned GLEAM-III catalogue with observation data from the 6dFGS project (Six-degree Field Galaxy Survey) [33], covering an observed area of about 16,700 square degrees, with a frequency range of 72–231 MHz, containing a total of 1,590 radio point sources. The median redshift of the sample is 0.064, with a maximum redshift of 0.283. Based on optical spectra, the catalogue divided radio point sources into AGN and star-forming galaxies, with the former accounting for 73% and the latter 27%. The catalogue studied the spectral index distribution of radio point sources in two frequency intervals, 76–227 MHz and 843–1,400 MHz. For AGN, the median spectral indices in the two frequency intervals are 0.704 ± 0.011 and 0.600 ± 0.010 respectively; for star-forming galaxies, they are 0.596 ± 0.015 and 0.650 ± 0.010 respectively. The overall completeness of this catalogue is 95%.

This catalogue has been used to fit local luminosity functions, fitting the luminosity functions of radio point sources in the range of 21.8–27.2 W·Hz⁻¹ [33]. The AGN luminosity function model is:

$$\Phi_{\text{AGN}}(L) = \frac{C}{(L/L_\star)^\alpha + (L/L_\star)^\beta}$$

where the characteristic luminosity L_⋆ = 10²⁵.⁷⁶ W·Hz⁻¹, α = 1.76, β = 0.49, and C = 10⁻⁶.¹³ mag⁻¹·Mpc⁻³ [33].

The star-forming galaxy luminosity function model is:

$$\Phi_{\text{SFG}}(L) = C \left( \frac{L}{L_\star} \right)^{1-\alpha} \exp \left[ -\frac{1}{2\sigma^2} \log^2 \left( 1 + \frac{L}{L_\star} \right) \right]$$

where C = 10⁻².⁸⁴ mag⁻¹·Mpc⁻³, L_⋆ = 10²¹.⁰⁶ W·Hz⁻¹, α = 0.68, and σ = 0.66.

By matching information from the GLEAM-III and 6dFGS catalogues to classify radio sources, and fitting luminosity functions for the two types of radio point sources, this catalogue obtained luminosity function models for AGN and star-forming galaxies at low frequencies (200 MHz). These models are important for studying the luminosity functions, redshift distributions, and spectral index distributions of radio sources.

4 Radio Point Source Simulation Catalogues

Currently, the main simulation software for radio point sources are T-RECS and SKADS. Compared with observations, radio point source catalogues generated by simulations can cover larger sky areas, reach higher redshifts, and break through lower flux limits. They can be used to evaluate the completeness of radio surveys or predict the number of radio sources to be observed in future surveys. At the same time, simulated radio point source catalogues provide a method for studying the extragalactic point source foreground for EoR signals.

Extragalactic point source simulation software can be used in multiple research fields. In recent related work, extragalactic radio point source simulations have been used to evaluate cosmic variance [138]; assess the number of sources that SKA-VLBI interferometric arrays can detect within specific beams and at different flux density levels, showing that finding multiple in-beam calibration sources in the L band is feasible [139]; generate point source catalogues to serve as training datasets for the deep learning galaxy search software YOLO-CIANNA and as training sets for machine learning codes to determine the relationship between source number density and flux density [140, 141]; study extragalactic point source clustering effects [101]; study the impact of peaked-spectrum extragalactic point sources on foreground removal and EoR signal extraction [142]; and evaluate the completeness of extragalactic point source observational catalogues [143]. The following sections introduce SKADS and T-RECS respectively.

4.1 SKADS

SKADS is a semi-empirical radio point source simulation software [40, 41]. The term "semi-empirical" means that simulated sources are obtained by extrapolating observed radio point source luminosity functions [67, 144, 145], mainly modeling the large-scale cosmic distribution of radio sources. The radio point source catalogue provided by SKADS has the following characteristics: sky coverage of 20° × 20°, redshift up to 20, containing 320 million sources; its flux limit is 10 nJy at frequencies of 151 MHz, 610 MHz, 1.4 GHz, 4.86 GHz, and 18 GHz.

For radio point source classification, SKADS divides simulated sources into radio-quiet AGN, radio-loud AGN, and star-forming galaxies. Among them, radio-loud AGN are further divided into FRI and FRII based on morphological components, while star-forming galaxies are divided into normal galaxies and brighter, smaller starburst galaxies. The number, redshift distribution, and flux distribution of different types of radio point sources are all calculated from corresponding luminosity functions. Table 4 [TABLE:4] shows the number of different types of radio sources [40].

Table 4 Number of sources in each subclass in the 20° × 20° continuous radio sky simulated by SKADS

Regarding radio point source morphology, for radio-loud AGN, SKADS models FRI as a point source core and two coaxial elliptical lobes with uniform surface brightness based on the FRI flux distribution, and models FRII as a point source core, two elliptical lobes, and two hotspots based on the FRII flux distribution. The corresponding component flux distributions are determined by parameters such as the core-to-lobe ratio and jet Lorentz factor, with radio jet orientation angles set to random distributions. Other radio point sources and the point source cores of FRI and FRII are all modeled as ellipses [146, 147], with related parameters consisting of major and minor axes in units of arcseconds.

Regarding modeling of the large-scale cosmic distribution of radio point sources, the clustering effect of radio point sources is essential because the clustering of extragalactic point sources changes their power spectrum. SKADS adopts a method that combines radio point sources with an underlying dark matter density field with large-scale clustering effects, while using different matching patterns for different types of radio point sources to obtain the clustering effect of radio point sources [148–151].

SKADS's extragalactic point source catalogue not only contains the clustering effect of radio point sources but also has source count results in various frequency intervals that are relatively consistent with observations. Although observations have shown that SKADS underestimates the number of bright sources greater than 0.15 mJy at redshifts greater than 2 [127], it remains significant for predicting future observations and radio point source research in terms of flux distribution, number of different types of radio sources, and completeness studies.

4.2 T-RECS

T-RECS is a newer radio point source simulation software that mainly simulates AGN and star-forming galaxies [42, 43]. Compared with SKADS, T-RECS's greatest innovation is its modeling of the polarized radiation of radio point sources.

T-RECS simulates frequencies covering 150 MHz–20 GHz, with a redshift limit of 10 and a flux limit of 10 nJy, while providing a 5° × 5° radio point source sky catalogue with clustering effects.

T-RECS sets the spectra of all AGN as power-law spectra (S ∝ ν^α) and divides them into flat-spectrum and steep-spectrum radio sources based on spectral index, with flat-spectrum sources further subdivided into flat-spectrum radio quasars and blazars. The spectral index for steep-spectrum radio sources is set to -0.73 [43], while flat-spectrum sources are set to -0.1 [42]. Then, by combining relevant observational data to fit and extrapolate redshift-dependent luminosity function models [107], simulated radio point sources with a flux limit of 10 nJy are obtained. Based on related research on linear polarization fraction models (ratio of polarized flux to radio flux) [152–154], a polarized flux model is used to calculate the polarized flux of each radio point source.

For star-forming galaxies, since their radio radiation is closely related to star formation rate, T-RECS uses a redshift-evolving star formation rate function to derive the redshift-dependent luminosity function of star-forming galaxies [155–157], and obtains the number of simulated radio point sources with flux limit down to 10 nJy and redshift up to 10 by extrapolating the redshift-dependent luminosity function. The polarization model for star-forming galaxies assigns linear polarization fractions to all star-forming galaxies based on the relationship model between radio source inclination angle and radio linear polarization fraction [40].

Regarding the sizes of radio point sources, the intrinsic size model for AGN uses a purely geometric distribution N(θ) = sin θ for the viewing angle distribution of radio point sources (star-forming galaxies use the same viewing angle distribution) [102]. Then, by simulating the intrinsic sizes of radio point sources using viewing angle size information from three extragalactic point source catalogues and repeating this 1,000 times, the intrinsic size distribution of radio point sources is obtained [158–160]. T-RECS uses this fitted intrinsic size distribution model to assign intrinsic sizes to AGN, and finally calculates the apparent size of AGN based on the source's redshift. For star-forming galaxies, the relationship between star formation rate and stellar mass [156], combined with the relationship between intrinsic size and stellar mass [161], can be used to obtain the relationship between star formation rate and intrinsic size, allowing assignment of intrinsic sizes to star-forming galaxies based on star formation rate. Finally, the corresponding apparent sizes can be calculated based on the redshift of star-forming galaxies.

After obtaining the sizes of radio point sources, T-RECS also models their shapes. For steep-spectrum AGN, T-RECS models the radio point source core and two hotspots, and provides the angular size distance between hotspots and core for each radio point source through a hotspot-to-core distance model [162], but T-RECS does not provide a related flux distribution model for cores and hotspots. For star-forming galaxies, T-RECS assigns ellipticities to each star-forming galaxy based on a galaxy ellipticity distribution model [163], and calculates the corresponding major and minor axis angular scales through ellipticity, redshift, and intrinsic size.

T-RECS also models the clustering effect of radio point sources, using the P-Millennium simulation for dark matter halo simulations, which generates dark matter halo characteristics of 5° × 5° sky coverage and redshift 0–8. Finally, the clustering effect of radio point sources is obtained by matching dark matter haloes with radio point sources by mass [157, 164].

In addition to flux information at different frequencies, T-RECS's simulated radio point source catalogue also contains polarization radiation, size, shape, and viewing angle information for radio point sources, allowing generation of field-of-view images of radio point source skies through software such as galsim [32]. In different frequency intervals, the total flux differential source counts and polarized source counts of T-RECS simulated radio point source catalogues are almost consistent with real observational results. However, observations have also pointed out that T-RECS underestimates the number of bright sources greater than 0.15 mJy at redshifts greater than 4 [127].

5 Summary and Outlook

Research on low-frequency extragalactic radio point sources helps us understand the processes by which baryons drive and suppress star formation and deepens our understanding of galaxy formation and evolution. At the same time, because low-frequency radio point sources are important foreground contaminants for EoR signal detection, studying them helps us remove and suppress radio point source foreground contamination. Current low-frequency radio point source observations are increasingly complete, especially LOFAR deep-field observations providing flux and redshift distribution information for high-redshift low-frequency radio point sources. This paper introduces the main parameters of current low-frequency radio point source observation catalogues, including sky coverage, redshift range, frequency range, source classification methods and results, and spectral indices. We also introduce the current main radio point source simulation software SKADS and T-RECS, including their modeling methods and the information contained in the generated radio point source catalogues.

A complete extragalactic point source catalogue can be applied in many fields of current astronomical research. For example, they can be used to study galaxy clustering effects [101]; they can also be combined with gravitational lensing maps from cosmic microwave background radiation to constrain the bias evolution of radio galaxies and the amplitude of matter perturbations [165]; they can be used to study cosmic variance and the large-sample properties of galaxies and their evolution over time [100]; they can also be used to study the size distribution of extragalactic point sources [102]; deep-field observations of extragalactic point sources can also obtain information on high-redshift bright radio sources to study early universe conditions [166]; in addition, large-area radio point source survey catalogues can be used to search for radio sources with special properties [167]. Extragalactic point source simulation software and their generated simulated point source catalogues are also helpful for clustering effects and interferometric array calibration [138, 139], and have advantages that observational catalogues cannot match, such as completeness, lower flux densities, and higher redshifts. Extragalactic point source simulation software and simulated catalogues can serve as training sets for machine learning and deep learning related to point sources, enabling more comprehensive training [140, 141]; in addition, extragalactic point source simulations can be used to evaluate the degree of contamination of EoR signals by extragalactic point sources [142].

In current low-frequency radio observations, there is still a lack of observations of the polarized intensity of radio point sources. Because the smoothness of radio point source spectra is affected by polarization leakage, obtaining related polarization leakage models is also beneficial for removing radio point source foregrounds. Currently, the world's largest comprehensive aperture radio telescope, SKA, is under active construction. With its extremely high sensitivity and angular resolution, its observation results will further test existing models once completed.

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