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At least 19 records

Young but fading radio sources: searching for remnants among compact steep-spectrum radio sources

The incidence of young but fading radio sources provides important information on the life cycle of radio emission in radio-loud active galactic nuclei. Despite its importance for constraining the models of radio source evolution, there are no systematic studies of remnants in complete samples of young radio sources. We report results of the study of 18 compact steep-spectrum (CSS) radio sources, selected from the statistically complete B3-VLA (Very Large Array) CSS sample, characterized by a steep optically thin spectrum (α ≥ 1.0) and no core detection in earlier studies. Our deep multifrequency VLA, pc-scale Very Long Baseline Array, and enhanced Multi Element Remotely Linked Interferometer Network (e-MERLIN) observations allowed us to locate the core component in 10 objects. In three CSS sources, there is no clear evidence of present-time active regions, suggesting that they are likely in a remnant phase. Among sources with core detection, we find three objects that have no clear active regions (hotspots) at the edges of the radio structure, suggesting that the radio emission may have just restarted. Our results support a power-law distribution of the source ages, although the poor statistics prevents us from setting solid constraints on the percentage of remnants and restarted sources in subpopulations of radio sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Redshifts of radio sources in the Million Quasars Catalogue from machine learning

ABSTRACT With the aim of using machine learning techniques to obtain photometric redshifts based upon a source’s radio spectrum alone, we have extracted the radio sources from the Million Quasars Catalogue. Of these, 44 119 have a spectroscopic redshift, required for model validation, and for which photometry could be obtained. Using the radio spectral properties as features, we fail to find a model which can reliably predict the redshifts, although there is the suggestion that the models improve with the size of the training sample. Using the near-infrared–optical–ultraviolet bands magnitudes, we obtain reliable predictions based on the 12 503 radio sources which have all of the required photometry. From the 80:20 training–validation split, this gives only 2501 validation sources, although training the sample upon our previous SDSS model gives comparable results for all 12 503 sources. This makes us confident that SkyMapper, which will survey southern sky in the u, v, g, r, i, z bands, can be used to predict the redshifts of radio sources detected with the Square Kilometre Array. By using machine learning to impute the magnitudes missing from much of the sample, we can predict the redshifts for 32 698 sources, an increase from 28 to 74 per cent of the sample, at the cost of increasing the outlier fraction by a factor of 1.4. While the ‘optical’ band data prove successful, at this stage we cannot rule out the possibility of a radio photometric redshift, given sufficient data which may be necessary to overcome the relatively featureless radio spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

Optical properties of Peaked Spectrum radio sources

ABSTRACT In this work, we study the optical properties of compact radio sources selected from the literature in order to determine the impact of the radio-jet in their circumnuclear environment. Our sample includes 58 Compact Steep Spectrum (CSS) and GigaHertz Peaked Spectrum (GPS) and 14 Megahertz-Peaked spectrum (MPS) radio sources located at z ≤ 1. The radio luminosity (LR) of the sample varies between Log LR ∼ 23.2 and 27.7 W Hz−1. We obtained optical spectra for all sources from SDSS-DR12 and performed a stellar population synthesis using the starlight code. We derived stellar masses (M⋆), ages 〈t⋆〉, star formation rates (SFR), metallicities 〈Z⋆〉 and internal reddening AV for all young AGNs of our sample. A visual inspection of the SDSS images was made to assign a morphological class for each source. Our results indicate that the sample is dominated by intermediate to old stellar populations and there is no strong correlation between optical and radio properties of these sources. Also, we found that young AGNs can be hosted by elliptical, spiral and interacting galaxies, confirming recent findings. When comparing the optical properties of CSS/GPS and MPS sources, we do not find any significant difference. Finally, the Mid-Infrared WISE colours analysis suggests that the compact radio sources defined as powerful AGNs are, in general, gas-rich systems.

79 ASTRONOMY AND ASTROPHYSICS↗

Powerful Radio Sources in the Southern Sky. II. A Swift X-Ray Perspective

We recently constructed the G4Jy-3CRE, a catalog of extragalactic radio sources based on the GLEAM 4-Jy (G4Jy) sample, with the aim of increasing the number of powerful radio galaxies and quasars with similar selection criteria to those of the revised release of the Third Cambridge Catalog (3CR). The G4Jy-3CRE consists of a total of 264 radio sources mainly visible from the Southern Hemisphere. Here, we present an initial X-ray analysis of 89 G4Jy-3CRE radio sources with archival X-ray observations from the Neil Gehrels Swift Observatory. We reduced a total of 624 Swift observations, for about 0.9 Ms of integrated exposure time. We found X-ray counterparts for 59 radio sources belonging to the G4Jy-3CRE, nine of them showing extended X-ray emission. The remaining 30 sources do not show any X-ray emission associated with their radio cores. Our analysis demonstrates that X-ray snapshot observations, even if lacking uniform exposure times, as those carried out with Swift, allow us to (i) verify and/or refine the host galaxy identification; (ii) discover the extended X-ray emission around radio galaxies of the intracluster medium when harbored in galaxy clusters, as the case of G4Jy 1518 and G4Jy 1664; and (iii) detect X-ray radiation arising from their radio lobes, as for G4Jy 1863.

79 ASTRONOMY AND ASTROPHYSICS↗

Powerful Radio Sources in the Southern Sky. I. Optical Identifications

Since the early sixties, our view of radio galaxies and quasars has been drastically shaped by discoveries made thanks to observations of radio sources listed in the Third Cambridge Catalog and its revised version (3CR). However, the largest fraction of data collected to date on 3CR sources was performed with relatively old instruments, rarely repeated and/or updated. Importantly, the 3CR contains only objects located in the Northern Hemisphere, thus having limited access to new and innovative astronomical facilities. To mitigate these limitations, we present a new catalog of powerful radio sources visible from the Southern Hemisphere, extracted from the GLEAM 4 Jy (G4Jy) catalog and based on equivalent selection criteria as the 3CR. This new catalog, named G4Jy-3CRE, where the E stands for “equivalent,” lists a total of 264 sources at decl. below -5° and with 9 Jy limiting sensitivity at ~178 MHz. We explored archival radio maps obtained with different surveys and compared them with optical images available in the Pan-STARRS, DES, and DSS databases to search for optical counterparts of their radio cores. We compared mid-infrared counterparts, originally associated in the G4Jy, with the optical ones identified here, and we present results of a vast literature search carried out to collect redshift estimates for all G4Jy-3CRE sources resulting in a total of 145 reliable z measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Compact Steep Spectrum Radio Sources with Enhanced Star Formation Are Smaller Than 10 kpc

Compact steep spectrum (CSS) radio sources are active galactic nuclei (AGN) that have radio jets propagating only on galactic scales, defined as having projected linear size (LS) of up to 20 kpc. CSS sources are generally hosted by massive early-type galaxies with little ongoing star formation; however, a small fraction are known to have enhanced star formation. Using archival data from the Faint Images of the Radio Sky at Twenty cm survey, the Very Large Array Sky Survey, and the Sloan Digital Sky Survey, we identify a volume-limited sample of 166 CSS sources at z < 0.2 with L 1.4 GHz > 10 24 W Hz -1 . Comparing the star formation rates and linear sizes of these CSS sources, we find that the ≈14% of CSS sources with specific star formation rates above 0.01 Gyr -1 all have LS < 10 kpc. We discuss the possible mechanisms driving this result, concluding that it is likely the excess star formation in these sources occurred in multiple bursts and ceased prior to the AGN jet being triggered.

79 ASTRONOMY AND ASTROPHYSICS↗

Parsec-scale Properties of Steep- and Flat-spectrum Extragalactic Radio Sources from a VLBA Survey of a Complete North Polar Cap Sample

We observed with the Very Long Baseline Array (VLBA) at 2.3 and 8.6 GHz a complete flux-density-limited sample of 482 radio sources with decl. > +75° brighter than 200 mJy at 1.4 GHz drawn from the NVSS catalog. A total of 34% of the sources show parsec-scale emission above the flux density detection limit of 30 mJy; their accurate positions and parsec-scale structure parameters are determined. Among all the sources detected at least at the shortest VLBA baselines, the majority, or 72%, have a steep single-dish spectrum. The fraction of the sources with a detectable parsec-scale structure is above 95% among the flat-spectrum objects and close to 25% among the steep-spectrum objects. We identified 82 compact steep-spectrum source candidates, which make up 17% of the sample; most of them are reported for the first time. The compactness and the brightness temperature of the sources in our sample show a positive correlation with single-dish and VLBA spectral indices. All the sources with a significant 8 GHz variability were detected by the VLBA snapshot observations, which independently confirmed their compactness. We demonstrated that 54% of the sources detected by the VLBA at 2.3 GHz in our sample have a steep VLBA spectrum. The compact radio emission of these sources is likely dominated by optically thin jets or mini-lobes, not by an opaque jet core. These results show that future VLBI surveys aimed at searching for new sources with parsec-scale structure should include not only flat-spectrum sources but also steep-spectrum ones in order to reach an acceptable level of completeness.

47 OTHER INSTRUMENTATION↗

Search and identification of transient and variable radio sources using MeerKAT observations: a case study on the MAXI J1820+070 field

ABSTRACT Many transient and variable sources detected at multiple wavelengths are also observed to vary at radio frequencies. However, these samples are typically biased towards sources that are initially detected in wide-field optical, X-ray, or gamma-ray surveys. Many sources that are insufficiently bright at higher frequencies are therefore missed, leading to potential gaps in our knowledge of these sources and missing populations that are not detectable in optical, X-rays, or gamma-rays. Taking advantage of new state-of-the-art radio facilities that provide high-quality wide-field images with fast survey speeds, we can now conduct unbiased surveys for transient and variable sources at radio frequencies. In this paper, we present an unbiased survey using observations obtained by MeerKAT, a mid-frequency (∼GHz) radio array in South Africa’s Karoo Desert. The observations used were obtained as part of a weekly monitoring campaign for X-ray binaries (XRBs) and we focus on the field of MAXI J1820+070. We develop methods to efficiently filter transient and variable candidates that can be directly applied to other data sets. In addition to MAXI J1820+070, we identify four likely active galactic nuclei, one source that could be a Galactic source (pulsar or quiescent XRB) or an AGN, and one variable pulsar. No transient sources, defined as being undetected in deep images, were identified leading to a transient surface density of <3.7 × 10−2 deg−2 at a sensitivity of 1 mJy on time-scales of 1 week at 1.4 GHz.

Rowlinson, A. (ORCID:0000000211957022)↗

Measuring photometric redshifts for high-redshift radio source surveys

With the advent of deep, all-sky radio surveys, the need for ancillary data to make the most of the new, high-quality radio data from surveys like the Evolutionary Map of the Universe (EMU), GaLactic and Extragalactic All-sky Murchison Widefield Array survey eXtended, Very Large Array Sky Survey, and LOFAR Two-metre Sky Survey is growing rapidly. Radio surveys produce significant numbers of Active Galactic Nuclei (AGNs) and have a significantly higher average redshift when compared with optical and infrared all-sky surveys. Thus, traditional methods of estimating redshift are challenged, with spectroscopic surveys not reaching the redshift depth of radio surveys, and AGNs making it difficult for template fitting methods to accurately model the source. Machine Learning (ML) methods have been used, but efforts have typically been directed towards optically selected samples, or samples at significantly lower redshift than expected from upcoming radio surveys. This work compiles and homogenises a radio-selected dataset from both the northern hemisphere (making use of Sloan Digital Sky Survey optical photometry) and southern hemisphere (making use of Dark Energy Survey optical photometry). We then test commonly used ML algorithms such as k-Nearest Neighbours (kNN), Random Forest, ANNz, and GPz on this monolithic radio-selected sample. We show that kNN has the lowest percentage of catastrophic outliers, providing the best match for the majority of science cases in the EMU survey. We note that the wider redshift range of the combined dataset used allows for estimation of sources up to z = 3 before random scatter begins to dominate. When binning the data into redshift bins and treating the problem as a classification problem, we are able to correctly identify ≈ 76% of the highest redshift sources—sources at redshift z > 2.51 —as being in either the highest bin (z > 2.51) or second highest (z = 2.25).

79 ASTRONOMY AND ASTROPHYSICS↗

A unique, ring-like radio source with quadrilateral structure detected with machine learning

ABSTRACT We report the discovery of a unique object in the MeerKAT Galaxy Cluster Legacy Survey (MGCLS) using the machine learning anomaly detection framework astronomaly. This strange, ring-like source is 30′ from the MGCLS field centred on Abell 209, and is not readily explained by simple physical models. With an assumed host galaxy at redshift 0.55, the luminosity (1025 W Hz−1) is comparable to powerful radio galaxies. The source consists of a ring of emission 175 kpc across, quadrilateral enhanced brightness regions bearing resemblance to radio jets, two ‘ears’ separated by 368 kpc, and a diffuse envelope. All of the structures appear spectrally steep, ranging from −1.0 to −1.5. The ring has high polarization (25 per cent) except on the bright patches (<10 per cent). We compare this source to the Odd Radio Circles recently discovered in ASKAP data and discuss several possible physical models, including a termination shock from starburst activity, an end-on radio galaxy, and a supermassive black hole merger event. No simple model can easily explain the observed structure of the source. This work, as well as other recent discoveries, demonstrates the power of unsupervised machine learning in mining large data sets for scientifically interesting sources.

Astronomy & Astrophysics↗

Discovery of a new extragalactic circular radio source with ASKAP: ORC J0102–2450

ABSTRACT We present the discovery of another odd radio circle (ORC) with the Australian Square Kilometre Array Pathfinder (ASKAP) at 944 MHz. The observed radio ring, ORC J0102–2450, has a diameter of ∼70 arcsec or 300 kpc, if associated with the central elliptical galaxy DES J010224.33–245039.5 (z ∼ 0.27). Considering the overall radio morphology (circular ring and core) and lack of ring emission at non-radio wavelengths, we investigate if ORC J0102–2450 could be the relic lobe of a giant radio galaxy seen end on or the result of a giant blast wave. We also explore possible interaction scenarios, for example, with the companion galaxy, DES J010226.15–245104.9, located in or projected on to the south-eastern part of the ring. We encourage the search for further ORCs in radio surveys to study their properties and origin.

Koribalski, Bärbel S. (ORCID:000000034351993X)↗

Radio Morphology of Red Geysers

We present 150 MHz, 1.4 GHz, and 3 GHz radio imaging (LoTSS, FIRST, and VLASS) and spatially resolved ionized gas characteristics (SDSS IV-MaNGA) for 140 local ($z$ < 0.1) early-type red geyser galaxies. These galaxies have a low star formation activity (with a star formation rate, SFR, ~ 0.01 $M$ ⊙ yr -1 ) but show unique extended patterns in spatially resolved emission-line maps that have been interpreted as large-scale ionized winds driven by active galactic nuclei (AGN). In this work, we confirm that red geysers host low-luminosity radio sources ($L$ 1.4GHz ~ 10 22 $WHz$ -1 ). Out of 42 radio-detected red geysers, 32 are spatially resolved in LoTSS and FIRST, with radio sizes varying between ~5–25 kpc. Three sources have radio sizes exceeding 40 kpc. A majority display a compact radio morphology and are consistent with either low-power compact radio sources (FR0 galaxies) or radio-quiet quasars. They may be powered by small-scale AGN-driven jets that remain unresolved at the current 5'' resolution of radio data. The extended radio sources, not belonging to the "compact" morphological class, exhibit steeper spectra with a median spectral index of -0.67, indicating the dominance of lobed components. Furthermore, the red geysers hosting extended radio sources also have the lowest specific SFRs, suggesting they either have a greater impact on the surrounding interstellar medium or are found in more massive halos on average. The degree of alignment of the ionized wind cone and the extended radio features are either 0° or 90°, indicating possible interaction between the interstellar medium and the central radio AGN.

79 ASTRONOMY AND ASTROPHYSICS↗

A study on the clustering properties of radio-selected sources in the Lockman Hole region at 325 MHz

Studying the spatial distribution of extragalactic source populations is vital in understanding the matter distribution in the Universe. It also enables understanding the cosmological evolution of dark matter density fields and the relationship between dark matter and luminous matter. Clustering studies are also required for EoR foreground studies since it affects the relevant angular scales. This paper investigates the angular and spatial clustering properties and the bias parameter of radio-selected sources in the Lockman Hole field at 325 MHz. The data probes sources with fluxes ≳0.3 mJy within a radius of 1.8° around the phase centre of a 6° × 6° mosaic. Based on their radio luminosity, the sources are classified into Active Galactic Nuclei (AGNs) and Star-Forming Galaxies (SFGs). Clustering and bias parameters are determined for the combined populations and the classified sources. The spatial correlation length and the bias of AGNs are greater than SFGs- indicating that more massive haloes host the former. This study is the first reported estimate of the clustering property of sources at 325 MHz, intermediate between the pre-existing studies at high and low-frequency bands. It also probes a well-studied deep field at an unexplored frequency with moderate depth and area. Clustering studies require such observations along different lines of sight, with various fields and data sets across frequencies to avoid cosmic variance and systematics. Thus, an extragalactic deep field has been studied in this work to contribute to this knowledge.

79 ASTRONOMY AND ASTROPHYSICS↗

High-resolution Giant Metrewave Radio Telescope H I 21 cm Imaging of the Host Galaxy of FRB 20250316A

We report Giant Metrewave Radio Telescope (GMRT) H I 21 cm imaging of NGC 4141, the host galaxy of FRB 20250316A at z = 0.0063. Our GMRT H I 21 cm images have spatial resolutions, at z ≈ 0.0063, of ≈0.48–8.0 kpc, and provide evidence for (i) a companion galaxy, LEDA 2582852, to the southwest, (ii) a nearby (27 kpc distant) H i cloud to the southwest, (iii) disturbances in the H I distributions of both NGC 4141 and LEDA 2582852, and (iv) high H I column densities in the southwestern outskirts of NGC 4141. A Sloan Digital Sky Survey spectrum yields a low metallicity and a high star formation rate (SFR) surface density in the southwestern disk of NGC 4141, and an Hα-based SFR estimate that is significantly higher than that at the same location from the Galaxy Evolution Explorer near-ultraviolet image, indicating a recent burst of star formation. The total SFR of NGC 4141 is also found to be higher via the Hα line than from the 1.4 GHz radio continuum. The above evidence indicates that NGC 4141 has recently (within the last ≈3 Myr) acquired metal-poor gas, via either a merger or accretion, that resulted in the southwestern starburst and that may also have triggered large-scale star-formation activity in NGC 4141, resulting in the formation of the stellar progenitor of FRB 20250316A and the other transients. Our highest-resolution (480 pc) GMRT H I 21 cm image finds no H I 21 cm emission from the location of FRB 20250316A or the nearby star-forming region, suggesting that most of the H I here has been either ionized or converted into the molecular phase. Our nondetection of continuum emission at the location of FRB 20250316A yields the 3σ upper limit νL 1.38 GHz < 4.4 × 10 34 erg s −1 on the 1.38 GHz radio luminosity of a putative persistent radio source associated with FRB 20250316A, one of the strongest constraints on the radio luminosity of such an associated persistent radio source.

Kaur, Balpreet [Pune University (India)] (ORCID:00↗

Radioimaging for real-time tracking of high-voltage breakdown

Development of a radioimaging diagnostic for high-voltage component reliability testing and electrical breakdown computational model validation is described. Radioimaging has its roots in radio astronomy, where aperture synthesis (also known as synthesis imaging) has been utilized for decades to image radio sources far from Earth. Radioimaging as described herein, in contrast, seeks to image radio sources in close proximity to its receivers (i.e., in a laboratory environment). Here it is shown that corona discharge, a non-destructive precursor to catastrophic (thermal) arc discharge, electromagnetically radiates strongly within a 250 kHz – 2.5 GHz bandwidth, and is readily detected and located by postprocessing the received radio signals. The ability of radioimaging to detect both corona and arc discharge (grouped together herein as high voltage breakdown or HVB) makes it a valuable tool for 100% HVB detection in materials, components, and devices, and has the ability to indicate electrical weakness (via corona detection) prior to a destructive arc discharge event. Radioimaging enables HVB to be located both internal and external to dielectric components under test in near-real-time, with multiple and/or extended HVB events located simultaneously. In contrast, existing non-destructive diagnostics (at the time of this writing) either indicate electrical breakdown without resolving failure locations (e.g., current, voltage, and chemical measurements), locate external HVB (e.g., high-speed optical and ultraviolet (UV) measurements or photography), or locate both external and internal HVB but with low fidelity (e.g., a single HVB source can be located by existing time-of-arrival (TOA) UHF or acoustic emissions). Radioimaging instead creates a sequence of high-fidelity images similar to an optical high-speed camera but at radiofrequencies (RF), and is not limited to two-dimensions. Moreover, radioimaging has already served one internal and two external industry customers, the results of which are detailed in this report. The radioimaging results described herein were part of a three-year effort funded by the Sandia Lab Directed Research and Development (LDRD) program within the Radiation, Electromagnetic, High Energy Density Science (REHEDS) investment area.

47 OTHER INSTRUMENTATION↗

Polarization and variability of compact sources measured in Planck time-ordered data

This paper introduces a new Planck Catalog of Polarized and Variable Compact Sources (PCCS-PV) comprising 153 sources, the majority of which are extragalactic. The data include both the total flux density and linear polarization measured by Planck with frequency coverage from 30 to 353 GHz, and temporal spacing ranging from days to years. We classify most sources as beamed, extragalactic radio sources; the catalog also includes several radio galaxies, Seyfert galaxies, and Galactic and Magellanic Cloud sources, including H II regions and planetary nebulae. An advanced extraction method applied directly to the multifrequency Planck time-ordered data, rather than the mission sky maps, was developed to allow an assessment of the variability of polarized sources. Our analysis of the time-ordered data from the Planck mission, tod2flux, allowed us to catalog the time-varying emission and polarization properties for these sources at the full range of polarized frequencies employed by Planck, 30-353 GHz. PCCS-PV provides the time-and frequency-dependent, polarized flux densities for all 153 sources. To illustrate some potential applications of the PCCS-PV, we conducted preliminary comparisons of our measurements of selected sources with published data from other astronomical instruments. In summary, we find general agreement between the Planck and the Institut de Radioastronomie Millimétrique (IRAM) polarization measurements as well as with the Metsähovi 37 GHz values at closely similar epochs. Here, these combined measurements also show the value of PCCS-PV results and the PCCS2 catalog for filling in missing spectral (or temporal) coverage and helping to define the spectral energy distributions of extragalactic sources. In turn, these results provide useful clues as to the physical properties of the sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Lightning Interferometry with the Long Wavelength Array

The Long Wavelength Array is a radio telescope array located at the Sevilleta National Wildlife Refuge in La Joya, New Mexico, well suited and situated for the observation of lightning. The array consists of 256 high-sensitivity dual polarization antennas arranged in a 100 m diameter. This paper demonstrates some of the capabilities that the array brings to the study of lightning. Once 32 or more antennas are used to image lightning radio sources, virtually every integration period longer than the impulse response of the array includes at least one identifiable lightning emitter, independent of the integration period used. The use of many antennas also allows multiple simultaneous lightning radio sources to be imaged at sub-microsecond timescales; for the flash examined, 51% of the images contained more than one lightning source. Finally, by using many antennas to image lightning sources, the array is capable of locating sources fainter than the galactic background radio noise level, yielding possibly the most sensitive radio maps of lightning to date. This incredible sensitivity enables, for the first time, the emissions originating from the positive leader tips of natural in-cloud lightning to be detected and located. The tip emission is distinctly different from needle emission and is most likely due to positive breakdown.

Stock, Michael (ORCID:0000000193336790)↗

Three New Spiral Galaxies with Active Nuclei Producing Double Radio Lobes

Abstract Double radio lobes are generally believed to be produced by active nuclei of elliptical galaxies. However, several double-lobed radio sources have been solidly found to be associated with spiral galaxies. By cross-matching ∼9 × 10 5 spiral galaxies selected from the Sloan Digital Sky Survey DR8 data with the full 1.4 GHz radio source catalogs of NRAO VLA Sky Survey and Faint Images of the Radio Sky at Twenty-centimeters, we identify three new spiral galaxies: J0326−0623, J1110+0321 and J1134+3046 that produce double radio lobes, and five double-lobed spirals previously known. By combining the newly discovered and all the other known cases in literature, we confirm the relation that more massive spiral galaxies could produce more powerful radio lobes. We find that most of these spiral galaxies are located in a galaxy group or a poor cluster, in which the environment is denser than in the field, and about half of them are the central brightest galaxies in their parent system. We therefore suggest that the environment is one of the key factors for a spiral to produce double radio lobes.

Astronomy & Astrophysics↗