Extended Radio AGN at z ∼ 1 in the ORELSE Survey: The Confining Effect of Dense Environments

The relation between Radio Active Galactic Nuclei (RAGN) and their large-scale environments has been explored in numerical simulations and observational programs. RAGN are preferentially found in dense cluster environments at low redshift (e.g., Miller & Owen 2002; Best 2004; Argudo-Fernández et al. 2016) and such a preference appears to persist up to z ∼2 (e.g., Hatch et al. 2014; Malavasi et al. 2015; Magliocchetti et al. 2016; Shen et al. 2017; Mo et al. 2018). A relationship between radio luminosity and environmental richness has been revealed by a number of works (e.g., Best 2004; Ineson et al. 2013, 2015; Ching et al. 2017; Croston et al. 2019). In general, richer environments appear to host more luminous radio galaxies, with such a relationship possibly linked both to AGN accretion mode (Ineson et al. 2015) and to radio morphology (Croston et al. 2019).

In addition to the linkage between radio luminosity and the environment, the interaction between the jet powered by the RAGN and the intracluster medium (ICM) can potentially provide insights into the RAGN—environment complexity. There are several channels that may enable RAGN to efficiently interact with the ICM, including the displacement of gas, shocks, or the transportation of low-entropy gas and heavy elements outward from the cluster cores (see Fabian 2012 for review). Meanwhile, it has been argued that group or cluster-like external pressures are required in order to provide a medium to confine the expanding radio-lobe plasma, at least for RAGN observed in the local universe (e.g., McNamara et al. 2000; Fabian et al. 2000; Johnstone et al. 2002; Fabian et al. 2005; Forman et al. 2007). In addition, hydrodynamic simulations of radio jets have shown that, for a given jet power, the cluster or group environment in which the radio jet is propagating affects the resulting radio morphology, lobe dynamics, and other observable properties (Yates et al. 2018). Recently, Moravec et al. (2019, 2020) found evidence that the size of the jets increases with the clustocentric radius, after investigating ∼50 extended RAGN located in massive galaxy clusters detected by infrared-selected galaxy overdensities at z ∼ 1. They argued that more compact jets occur near the center where the ICM pressure is the highest and confines the jets. However, while they identified low redshift interlopers through a color–color analysis, due to the lack of redshifts of individual galaxies, they assumed that each radio source was at the redshift of the cluster. This assumption introduces an uncertainty on the real membership of their extended RAGN, and thus potentially complicates the interpretation of their results.

While attempts to understand the environmental effects on the size of extended RAGN (ERAGN) have been made, very few observational investigations across a wide range of environments (i.e., from cluster center to the field) have been conducted outside of the local universe where the relaxed fraction of clusters starts to decrease and ICM profiles become more complex. Thanks to its well-defined wide dynamic range of environments and its spectroscopic and photometric redshift measurements with high-degree of accuracy, the Observation of Redshift Evolution in Large-Scale Environments (ORELSE; Lubin et al. 2009) survey facilitates such an investigation. Hence, we study a sample of 50 ERAGN over a wide range of local and global environments at intermediate redshifts (0.55  ≤ z  ≤ 1.3) across 12 ORELSE fields. In this paper, we describe the available ORELSE catalogs, the radio observations, sample selection, and the measurement of radio size in Section 2. In Section 3, we show our results on the environmental effect of the size of ERAGN and analyses of its potential causes. In Section 4, we conduct a simulation based on our observations. We conclude with a summary in Section 5. Throughout this paper, we adopt the AB system for all magnitudes (Oke & Gunn 1983; Fukugita et al. 1996), a concordance ΛCDM cosmology with ${{\rm{H}}}_{0}=70\ \mathrm{km}\ {{\rm{s}}}^{-1}{\mathrm{Mpc}}^{-1}$, Ω_Λ = 0.73, and Ω_M = 0.27, and a Chabrier stellar initial mass function (IMF; Chabrier 2003).

2.1. The ORELSE Survey and Available Data

2.2. Radio Observations and Sample Selection

All of the 12 fields under consideration here were mapped using the Karl G. Jansky Very Large Array (VLA) at 1.4 GHz in its B configuration, where the synthesized beam is about 5'' (FWHM) and the field of view (i.e., the FWHM width of the primary beam) is approximately 31' in diameter. Data reduction and source catalogs for the fields (SC1604, SG0023, SC1324, RXJ1757, and RXJ1821) mapped with the traditional VLA are described in Shen et al. (2017, 2019). Those of the remaining seven fields (XLSS005, RXJ1053, RXJ0910, RXJ1716, Cl1137, Cl1429, and Cl1350) mapped with the new JVLA are obtained following the same methodology as in Shen et al. (2020). For those catalogs, we automatically detect radio sources down to a 4σ detection flux density limit, where σ is the local rms noise. The relevant information is summarized in Table 1.

Table 1.  Depth of Imaging Data

Field	R.A.	Decl.	$\langle {z}_{\mathrm{spec}}\rangle$	Depth	Num of
				(μJy)	ERAGN
(1)	(2)	(3)	(4)	(5)	(6)
SG0023	00:24:29	+04:08:22	0.845	13.9	4
XLSS005	02:27:10	-04:18:05	1.056	14.1	2+3
SC0910	09:10:45	+54:22:09	1.110	14.7	1
RXJ1053	10:53:40	+57:35:18	1.140	10.2	3+1
Cl1137	11:37:33	+30:00:04	0.955	7.3	3
SC1324	13:24:46	+30:34:11	0.717	11.0	10
Cl1350	13:50:48	+60:07:07	0.804	9.8	2
Cl1429	14:29:06	+42:41:02	0.987	17.1	3+1
SC1604	16:04:15	+43:21:37	0.898	9.3	9
RXJ1716	17:16:50	+67:08:30	0.813	15.2	2+2
RXJ1757	17:57:20	+66:31:32	0.693	10.5	1
RXJ1821	18:21:38	+68:27:52	0.818	9.3	4

Note. (1) (2) (3) Field and the coordinates of the center of radio imaging. (4) Mean spectroscopic redshift of the main structure in each field. (5) The depth of observations is the source-free rms in the full image area derived from the task SAD in the AIPS. Due to the variation of rms across each pointing, this corresponds to ∼15 arcmin from the center of that pointing. ERAGN are located on average 66 from the center of fields and in the range of 01 ∼ 216. (6) Numbers of ERAGN automatically detected in the radio catalogs plus those detected by eye that are matched to optical counterparts.

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When we extract extended radio sources from the constructed catalogs, these sources are required to subtend a major axis of at least 6.5'' (50 kpc at z = 1), a threshold 30% larger than the FWHM = 5'' resolution of our VLA data. We then search for additional radio sources that contain multiple components by eye. The task IMFIT in the NRAO's Astronomical Image Processing System (AIPS) is employed to fit multiple Gaussian components simultaneously to these sources. The total integrated flux density is the combined integrated flux density of the individual components, and the associated error is the square-sum of their errors. The center is either the halfway point between the flux peak of each component for a two-component system or the flux peak of the middle component for a three-component system.

To identify the optical counterparts to these extended radio sources, we perform a maximum likelihood ratio (LR) technique following Rumbaugh et al. (2012; Section 3.4). We adopt a search radius of 2'' between the overall photometric catalogs and the extended sources to account for astrophysical and astrometric offsets. We note that moving to a 5'' search radius did not yield any additional sources.

Considering our local overdensity footprints (see Section 2.4), the completeness/representativeness of our spectroscopic catalogs, and consistencies with previous radio galaxy studies in ORELSE, we require host galaxies to have 0.55 ≤z ≤1.35, $18.5\leqslant i^{\prime} /z\leqslant 24.5$, and ${M}_{* }\ \geqslant \ {10}^{10}{M}_{\odot }$ (Shen et al. 2017; Lemaux et al. 2019). As a result, we have a total sample of 50 ERAGN (Table 1) of which 24 have spectroscopically confirmed redshifts (hereafter ERAGN-spec) and the rest have accurate photometric redshifts (hereafter ERAGN-phot). We note that the stellar mass cut excludes four ERAGN-phot. However, the main conclusions do not change if we instead included all ERAGN. From the original design of the ORELSE survey, we have preferentially targeted galaxies that might reside in the clusters/groups for spectroscopic observations. In this study, we use both spectroscopic and photometric galaxies and account for their associated z_phot to mitigate this selection effect. In addition, the high-priority targets (red sequence cluster members) are always sub-dominant in our observations (Lemaux et al. 2019), and the resultant spectral galaxy sample is mostly representative of the underlying galaxy population at these redshifts (Shen et al. 2017; Lemaux et al. 2019).

We expect high completeness and purity of the ERAGN sample. The fluxes of the ERAGN are all above the 80% completeness level of the overall radio sources in the photometric footprint of the 12 fields, and the fluxes of those ERAGN detected by eye are above the 95% completeness level. Thus, we are not biased by the different depth of radio images and local rms variance. As for the purity, all ERAGN are detected ≥33σ significant, and ≥90σ for those ERAGN detected by eye, which are much higher than the 4σ detection limit of the automatically detected radio sources. They are also associated with an optical counterpart. Thus, it is unlikely that these radio detections are spurious. Another possible case that might affect the purity is that two blended sources are detected as a single extended source. Here, we relied mostly on the visual check from the contour plots and do not think that could be the case for any of them. We do not find any correlation between size and redshift in the ERAGN sample (see discussion in Section 3.1), so adopting a physical (i.e., kpc) or angular size cut does not affect our selection and results. We show their radio map cutouts of our sample in Figure 1 and overlay radio contours on their optical identification images in Figure 2. The properties of 50 ERAGN are presented in Appendix B (Table 2).

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Radio power is calculated in the same way as used in previous radio galaxy studies in ORELSE:

$$\begin{eqnarray*}&&{L}_{1.4{GHz}}=4\pi {D}_{L}^{2}{S}_{1.4{GHz}}{(1+z)}^{(\alpha -1)}\end{eqnarray*}$$

where D_L is the luminosity distance at the redshift, ${S}_{1.4{GHz}}$ is the total integrated radio flux, and ${(1+z)}^{(\alpha -1)}$ includes both the distance dimming and K correction. To be consistent to previous radio galaxy studies in ORELSE, we adopt the same α = 0.7. Typical values of spectral index α for extended radio sources range from 0.5 to 1 (Condon 1992; Peterson 1997; Lin & Mohr 2007; Miley & De Breuck 2008; Chhetri et al. 2012). The associated error on the radio power is calculated from the error of total integrated radio flux. To account for the uncertainty of z_phot of ERAGN-phot, we add an extra error on the ${L}_{1.4\mathrm{GHz}}$ by adopting a Monte-Carlo sampling method based on the z_phot error (see Appendix A for the description of this method).

2.3. Extent of Radio Sources

We adopt the largest angular size (LAS) as the primary measurement of the extent of radio sources, following Moravec et al. (2019). It is defined as the largest angular distance between a pair of points that belongs to this radio source. For the majority of our sample, we measure the LAS from the 4σ radio contours, the same as our radio detection threshold (Shen et al. 2017, 2019). In case of blending of radio sources, we adopt a higher threshold so that deblending barely happens, which is 8σ for SG0023+82 and XLSS005+F4, and 32σ for Cl1137+784 and Cl1137+783. In Figures 3 and 4, these four ERAGN are marked by black open diamonds. Note that they are not outliers in any other property analyzed in this paper, and excluding these four sources would not affect any of our results. The uncertainty in an LAS is defined as one-half of the beam size base on the Nyquist limit of our radio observations. For ERAGN-phot, we add an extra error on the LAS based on the 16/84 percentile values of the mock LAS distributions calculated from the Monte-Carlo z_phot samplings (see Appendix A).

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Considering that the LAS is sensitive to the dynamic variety of radio morphology, we also calculate the area of the radio sources to enhance the robustness of our analysis. This is done by counting the number of pixels enclosed by the same contours as used in the LAS measurements, including the fractional pixels. The uncertainty in an area is defined as the square root of the number of pixels based on the Poisson uncertainty. For ERAGN-phot, we add an extra error on the area (in physical units) based on the 16/84 percentile values of the mock area distributions calculated from the Monte-Carlo z_phot samplings (see Appendix A).

2.4. Environmental Measurements

In the left top panel of Figure 3, we plot the radio size against the local overdensity for the full ERAGN sample. A lack of large radio sources in dense regions is evident. To quantify this lack, we divide the full sample into low- and high-density subsamples at log(1 + δ_gal) = 1. The median of these two subsamples are depicted by black dots with errorbars.¹⁵ The log(LAS) median of the high-density bin is 2.07 ± 0.02, in contrast to 2.20 ± 0.02 for the low-density bin, leading to a discrepancy at a 4.5σ significance level. There are 2 out of 14 (14%) high-density ERAGN with an LAS larger than 160 kpc, while 17 out of 36 low-density ERAGN (47%) are larger than this threshold. We quantify this lack of large ERAGN in the dense regions using the following Monte-Carlo approach. In each realization, we randomly sample the same number of high-density ERAGN from the LAS distribution of the low-density sample. Only 1% of the 1000 realizations have less than or equal to two ERAGN with an LAS larger than this threshold. Therefore, it is unlikely that the high-density ERAGN are just a random subsampling of those ERAGN in the low-density sample.

The cumulative distribution functions (CDFs) of log(LAS) for the low- and high-density ERAGN are shown in the left bottom panel A of Figure 3. We perform a Kolmogorov–Smirnov (K–S) test to assess the similarity of two distributions and adopt p < 0.1 as the suggestive threshold for judging whether the samples are drawn from different distributions. The small value of p = 0.06 found in the LAS comparison again suggests that the size distribution of low- and high-density ERAGN are likely drawn from different distributions. Because this p value does not definitively reject the null hypothesis, we attempt further tests below to explore the potential differences.

We investigate the possible correlation between the local overdensity and LAS based on a nonparametric Spearman rank correlation test. We regard a returned p  <  0.1 as the suggestive criterion for the existence of a correlation and p  <  0.003 as 3σ significant threshold. We run the Spearman rank correlation test using the entire ERAGN sample. The large p value, as shown in the top corner of the plot, suggests no correlation between these two properties. However, the difference between the size of ERAGN in high- and low-density is significant. We further perform several diagnostic tests to eliminate uncertainties associated with the LAS measurement, binning, and projection effects.

To account for the uncertainty associated with individual LAS values, we adopt a Monte-Carlo approach, where 10,000 realizations of the median are computed after randomly perturbing each LAS value as per their errors. The median LAS of high- and low-density ERAGN are 121.0 ± 7.5 and 164.2 ± 8.0 kpc, respectively, where the errors are the 16th/84th percentiles. Hence, in terms of medians, the LAS of high-density ERAGN is smaller than that of low-density ERAGN by a factor of 1.4 at a significance level of 4σ.

To test the robustness of the above results due to different binning, we vary the log(1 + δ_gal) threshold successively from 0.1 to 1.5 with a step of 0.1, and perform a K–S test in each step. The p value is found to be consistently below 0.1 when log(1 + δ_gal) reaches ∼0.4, indicating that the difference of LAS distributions is robust against binning variation. We also noticed that one of the high-density ERAGN might change to the low-density subsample due to its large error on log(1 + δ_gal) (see Figure 3). However, none of our results would be meaningfully affected if this ERAGN was classified in the low-density subsample.

Last, we test the potential projection effects using a bootstrap approach. To do this, we assume that the low-density ERAGN subsample represents the overall distribution of radio sources with random viewing angles. We randomly resample the 14 LAS values from the low-density ERAGN subsample and calculate the median and spread¹⁶ for 10,000 realizations. As a result, our bootstrapping leads to a distribution of log(LAS) with a median of 2.18, larger than the measured value of the actual high-density ERAGN in 9570 out of the 10,000 realizations. The spread of log(LAS) is 0.42, larger than the measured value of high-density ERAGN in 9930 realizations.

As mentioned in Section 2.3, we characterize the size of the radio sources using their area as a complementary tracer. The CDFs of log(area) for the low- and high-density ERAGN are shown in the left bottom panel B of Figure 3. The K–S test result from the area comparison is inconclusive. We perform the same Monte-Carlo sampling as run in the LAS analyses. We find only 4% of the realizations where there were less than or equal to two ERAGN with an emitting region larger than 10⁴ kpc², to compare to the two observed high-density ERAGN that are larger than this threshold. Together with the differences shown in the LAS comparison, these results hint at the emitting regions of high-density ERAGN being more isotropic than those of the low-density ERAGN.

These tests confirm the existence of the size difference between high- and low-density ERAGN, a phenomenon that is likely a consequence of the host galaxies' internal properties and intracluster environment. Previous works have shown that the length of radio jets depend on the jet power, the local density profile, and the time that has elapsed since the jets started (e.g., Falle 1991; Hardcastle 2018; Yates et al. 2018), and that massive galaxies reside in the inner portion of clusters and tend to host compact jets (Moravec et al. 2020). Our discussion on the potential effects due to hosts, radio power, and the large-scale environment are presented below.

3.1. Effect of Hosts

3.2. Effect of Radio Power

In the top right panel of Figure 3, we plot the LAS with the radio power (L${}_{1.4\mathrm{GHz}}$). Overall, the size increases with increasing radio power for the entire sample. The small p value obtained in Spearman rank test (p = 0.0003) implies the existence of a correlation between the two variables at >3σ level; while ρ = 0.5 suggests a positive correlation between the two variables. Consequently, the radio power likely acts as a driver of the size of ERAGN. This is intuitive as the further a jet is driven, the more energetic the outburst is likely to be. This conclusion is in line with simulations reporting that the length of jets depends on the jet power and is positively correlated with radio luminosity (e.g., Falle 1991; Hardcastle 2018; Yates et al. 2018).

To alleviate this effect on the size difference between high- and low-density ERAGN, we normalize the LAS and area to correct for their radio power following the method in Moravec et al. (2019) that

$$\begin{eqnarray*}&&{\mathrm{LAS}}_{\mathrm{norm}}=\mathrm{LAS}{\left(\displaystyle \frac{{{\rm{L}}}_{0}}{{{\rm{L}}}_{1.4\mathrm{GHz}}}\right)}^{1/5},\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\mathrm{Area}}_{\mathrm{norm}}=\mathrm{Area}{\left(\displaystyle \frac{{{\rm{L}}}_{0}}{{{\rm{L}}}_{1.4\mathrm{GHz}}}\right)}^{2/5},\end{eqnarray*}$$

where L₀ = 2 × 10²⁶ W Hz⁻¹ and ${L}_{1.4\mathrm{GHz}}$ is the radio power at 1.4 GHz. The errors associated with each quantity are calculated by standard propagation of the individual LAS/Area and ${L}_{1.4\mathrm{GHz}}$ errors. The CDFs of LAS_norm and area_norm for low-/high-density ERAGN are shown in right bottom panel C and D of Figure 3. These corrections result in a more obvious difference between the high- and low-density ERAGN subsamples, compared to the non-normalized LAS and the area measurement. Consistently, we find a smaller p = 0.04 returned from the K–S test performed on the two log(LAS_norm) distributions. The K–S test result is still inconclusive in the area comparison.

3.3. Effect of Cluster Environments

The environmental dependence of radio jets' properties has been investigated in environments from that of poor galaxy groups to rich clusters (e.g., Krause et al. 2012; Hardcastle & Krause 2013; Yates et al. 2018). To summarize the results of these simulations, of which the majority concentrate on FR II sources, are (a) the gas pressure in a rich cluster is relatively high, which collimates the jet relatively early and thus produces a narrow beam; (b) the high cluster density ensures that the lobes are bright radio emitters; (c) in general, jets in groups are collimated at a later stage, subtend a wider angle, and thus are more difficult to observe.

To delineate the size difference of jets solely due to variation in the ICM density, we conduct numerical simulations by propagating the same radio jet in environments with relatively low, intermediate, and high densities, using the hydrodynamics (HD) code, PLUTO¹⁹ (Mignone et al. 2007, 2012). The setup of our simulation is similar to that in Yates et al. (2018), with exception of jet's kinetic power, initial opening angle, and gas density. We adopt a larger opening angle of 30° to facilitate inclusion of FR I morphology (Krause et al. 2012), and a jet kinetic power of Q = 10^44.7 erg/s, which is converted from the median radio power in our sample (L _1.4GHz = 10^24.9 W Hz⁻¹) following the kinetic versus radio power scaling relations given in Cavagnolo et al. (2010). We choose three gas densities: 5.8 × 10⁻²³, 2.9 × 10−23, and 5.8 × 10⁻²⁴ kg m⁻³, following the isothermal NFW gas density profile (Navarro et al. 1996) at 0, 100, and 500 kpc from the center of a 3 × 10¹⁴ M_⊙ cluster (Yates et al. 2018, Figure 1). Figure 5 shows the density plot of the radio jets in three density profiles when the jet switches off 60 Myr after launched. With the same evolving time elapsed, the effective area of the jet increases with decreasing density. As a consequence, the maximum length of the jet in the highest/intermediate density is ∼60%/40% less than that in the lowest density, supporting our observational conclusion that high ICM density may restrict the development of the length of jet.

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Admittedly, we only propagated a single burst of the jet; in the case of multiple bursts, the ICM gas may have been partially cleared by previous jets, and the jet we observe has actually propagated along a low-density path. This scenario would weaken our interpretation. Note that the gas density changes along the y-axis only, so that we are not able to make any conclusion about the area of the jet nor make direct comparisons to real observations. Further complications exist due to the actual ICM density profile deviating from our isotropic simplification and to neglected factors (e.g., magnetic fields, density/temperature turbulence) that introduce uncertainties. Our simulations, presented here for heuristic purposes, focus solely on a qualitative reproduction of the dependence of radio sources jet spatial scale on the ICM density. Future work on more realistic simulations promises to provide more clues to how the observable properties of jets varies as a result of the jet–environment interaction.

In this paper, by constructing a sample of 50 ERAGN at intermediate redshift (0.55  ≤ z  ≤ 1.3) from 12 fields in the ORELSE survey, we conduct a search for evidence of environmental effects on the ERAGN across a broad dynamical range of environments. All ERAGN have either spectropically confirmed redshifts or accurate photometric redshifts, allowing us to quantify accurate local and global environmental measurements. Below is a summary of our findings.

• 1.  
  We find the radio size in high-density regions to be consistently more compact than that in low-density regions at a significance level of 4.5σ.
• 2.  
  We find no significant correlations between the radio size and their host internal properties (i.e., stellar mass and color) and redshift, which eliminates the possibility of effects resulting from internal and evolutionary factors.
• 3.  
  A positive correlation is found to exist between the size and the radio power of ERAGN, suggesting that radio power is a driver of the extent of the radio jet. The difference of radio size between high-density and low-density ERAGN persists when a radio power correction is applied.
• 4.  
  We find no correlations between the radio size and any environmental properties, i.e., local overdensity, distance from the cluster center, or global environment measurement. However, our analysis of the large-scale environment shows that ERAGN in the cluster/group central regions are preferentially compact with the smallest scatter in size, compared to those in the cluster/group intermediate regions and the field.
• 5.  
  We perform a numerical simulation of radio jets in three different density environments, which shows the length of the jet decreases as the surrounding gas density increases, supporting our observational conclusion that the conditions at the centers of groups and clusters play an important role in confining the size of the radio sources in question.

For future studies, we plan to follow up our ERAGN with higher resolution radio observations to better measure the size of radio jets. Future simulations that have more constraining power in two dimensions and are more realistic will allow us to fully compare to our observational results. In addition, we plan to continue the investigation of ERAGN in clusters that have X-ray detections, to search for signs of the ICM variation which might allow us to prove or disprove this hypothesis.

We thank Paolo Padovani for helpful comments and suggestions. L.S. and G.L. acknowledge the grant from the National Key R&D Program of China (2016YFA0400702), the National Natural Science Foundation of China (No. 11673020 and No. 11421303). W.F. acknowledges the NSFC grants No. 11773024. This material is based upon work supported by the National Science Foundation under grant No. 1411943. P.F.W. acknowledges the support of an EACOA Fellowship from the East Asian Core Observatories Association. This study is based on data taken with the Karl G. Jansky Very Large Array which is operated by the National Radio Astronomy Observatory. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. SPIRE has been developed by a consortium of institutes led by Cardiff University (UK) and including Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA). This work is based in part on data collected at the Subaru Telescope and obtained from the SMOKA, which is operated by the Astronomy Data center, National Astronomical Observatory of Japan; observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA; and data collected at UKIRT which is supported by NASA and operated under an agreement among the University of Hawaii, the University of Arizona, and Lockheed Martin Advanced Technology center; operations are enabled through the cooperation of the East Asian Observatory. When the data reported here were acquired, UKIRT was operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the UK. This study is also based, in part, on observations obtained with WIRCam, a joint project of CFHT, Taiwan, Korea, Canada, France, and the Canada-France-Hawaii Telescope which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawai'i. The scientific results reported in this article are based in part on observations made by the Chandra X-ray Observatory and data obtained from the Chandra Data Archive. The spectrographic data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. We wish to thank the indigenous Hawaiian community for allowing us to be guests on their sacred mountain, a privilege, without with, this work would not have been possible. We are most fortunate to be able to conduct observations from this site.

In this paper, we adopt the global environment from Shen et al. (2017) as

$$\begin{eqnarray*}&&\eta ={R}_{\mathrm{proj}}/{R}_{200}\times | {\rm{\Delta }}v| /{\sigma }_{v},\end{eqnarray*}$$

where R_proj is the distance of a given galaxy to the center of its parent structure, R₂₀₀ is the radius of its parent structure at which the matter density is 200 times the critical density, Δv is the velocity offset of the galaxy from the systemic redshift of its parent structure, and σ_v is the measured line-of-sight galaxy velocity dispersion of its parent structure. The parent structure is determined as the one with the smallest R_proj/R₂₀₀ in projected space and within ±6000 km s⁻¹ in velocity space. If for a given galaxy, no cluster/group within ±6000 km s⁻¹ are found, the parent structure is the one with the smallest η. See Shen et al. (2019) and Pelliccia et al. (2019) for more details on this calculation. Here, we discuss all possible uncertainties on the global environment measurement.

The final cluster/group catalog includes the preexisting spectroscopically confirmed clusters/groups (Gal et al. 2008; Lemaux et al. 2019) and overdensity candidate regions (Hung et al. 2020). In the former case, the cluster/group centers are the ith luminosity-weighted centers of spectral member galaxies calculated using the method described in Ascaso et al. (2014), while their systemic redshifts, velocity dispersions, and associated errors are computed using the method described in Lemaux et al. (2012). In the latter case, their centers and systemic redshift are the barycenters detected in the Voronoi Monte-Carlo maps from Hung et al. (2020), and the σ_vs are calculated from the estimated log(M_tot) according to Equations (1) and (2) in Lemaux et al. (2012), along with their associated errors. The cluster-hosted ERAGN (see discussion in Section 3.3) reside in the massive end of the ORELSE structures with their median mass of ${10}^{14.5}{{\rm{M}}}_{\odot }$ versus the median mass of 10^13.9 M_⊙ for all ORELSE structures. The purity and completeness of clusters/groups increase with increasing structure mass. For our new cluster/group overdensity candidates, the purity/completeness of our catalog are very high for M_tot ≥ 10^13.5 M_⊙ (0.92/0.83 and 0.60/0.49 at z = 0.8 and z = 1.2, respectively) using mock catalogs with spectroscopic fractions of ∼20%, a typical value for the ORELSE fields (Hung et al. 2020). It is therefore unlikely that we are assigning these ERAGN to the wrong structures because either they are not real structures or we have missed a true overdensity that is closer.

The two methods described above to measure centers and systemic redshifts are well correlated (Hung et al. 2020). In addition, both measurements of cluster centers are well correlated to the X-ray centers for relaxed structures (Rumbaugh et al. 2018). As for the velocity dispersion, both methods have measured the error on σ_v (see Lemaux et al. 2012 and Hung et al. 2020 for more details). We adopt a Monte-Carlo test to see if this uncertainty can affect on the determination of the parent structure and the calculation of the η value. In each Monte-Carlo iteration, we assign a mock σ_v to each cluster/group sampled from a Gaussian distribution centered on the measured σ_v and its associated error. Then, we redetermine the parent structures and recalculate the η values for all ERAGN. In all 100 iterations, none of ERAGN change their parent structure. We define the uncertainty of log(η) to be the average of the 16/84 percentile values of the log(η) distributions. The uncertainty of log(η) is very small with a median of 0.06 and a range of 0.04  ∼  0.27. Thus, η and R_proj are both highly accurate.

Furthermore, an accurate redshift is the key to confirming group/cluster membership and measuring precise environmental metrics (i.e., R_proj and η). For galaxies that only have z_phot, we adopt a Monte-Carlo sampling method to eliminate the concern of their real membership due to the uncertainty of z_phot. For each galaxy, we sample 100 z_phot from a Gaussian distribution centered on the peak with σ derived from the the reconstructed probability density function of the photometric redshift estimated by the code Easy and Accurate Redshifts from Yale (EAZY: Brammer et al. 2008, also see Tomczak et al. 2017 for more details on the z_phot measurement). The median of σ of z_phot is 0.03 for ERAGN that only have z_phot, the same as the value of the full sample of galaxies with high-quality spectroscopic redshifts in ORELSE. This Monte-Carlo z_phot sampling has also been used for the calculation of additional errors on radio power (Section 2.2), size (Section 2.3), and local overdensity (Section 2.4) for ERAGN-phot. Mock R_proj, Δv and η values are then recalculated with respect to their mock parent structures. As plotted in Figure 4, the final R_proj, Δv and η are the median of the 100 mock values. The lower and upper limits of them are calculated as the 16/84 percentile values. The median of the uncertainty on log(η) due to the uncertainty of ${{\rm{z}}}_{\mathrm{phot}}$ is 0.21, with a range of 0.01  ∼ 0.65. We note that varying the z_phot does also change the parent structure for some ERAGN, which causes asymmetric distributions of mock R_proj and η, manifested as asymmetric uncertainties in Figure 4. We note that we run a parallel Monte-Carlo sampling allowing both ${\sigma }_{v}$ and z_phot varying at the same time. The uncertainties of z_phot contribute the most to the uncertainties of the R_proj and η. Therefore, the uncertainties of global environment properties are calculated based solely on the uncertainty of z_phot in this paper.

We present the properties of ERAGN in Table 2.

Table 2.  Properties of ERAGN

Field	IDa	Coordsb	zc	log(L${}_{1.4\mathrm{GHz}}$)	LAS	log(Area)	log($1+{\delta }_{\mathrm{gal}}$)	log(η)	local rmse
				log(W Hz−1)	kpc	log(kpc2)			μJy
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
SG0023	82	00hr23m053 +04d21m251	0.97*	25.16 ± 0.02	131 ± 20	4.01 ± 0.01	0.49${}_{-0.07}^{+0.12}$	1.97${}_{-0.30}^{+0.55}$	12.8
SG0023	127	00hr23m138 +04d26m030	0.72*	25.37 ± 0.02	410 ± 19	4.52 ± 0.02	0.24${}_{-0.10}^{+0.05}$	1.86${}_{-0.13}^{+0.26}$	12.5
SG0023	230	00hr23m382 +04d17m004	1.33	26.89 ± 0.01	192 ± 21	4.32 ± 0.01	1.03	2.62	10.5
SG0023	256	00hr23m449 +04d25m352	0.75	24.72 ± 0.01	104 ± 18	3.77 ± 0.01	0.23	1.95	10.7
XLSS005	F4	02hr25m549 -04d28m540	1.07*	25.29 ± 0.02	315 ± 20	4.43 ± 0.01	0.13${}_{-0.07}^{+0.14}$	1.65${}_{-0.11}^{+0.29}$	22.0
XLSS005	F2	02hr26m198 -04d25m314	1.21*	25.97 ± 0.04	199 ± 21	4.20 ± 0.01	0.29${}_{-0.24}^{+0.15}$	1.17${}_{-0.54}^{+0.79}$	13.1
XLSS005	E47	02hr27m022 -04d17m461	1.19	24.72 ± 0.02	316 ± 21	3.53 ± 0.01	0.72	−0.81	7.0
XLSS005	E49	02hr27m335 -04d33m179	0.62*	24.27 ± 0.06	197 ± 18	3.99 ± 0.02	0.36${}_{-0.08}^{+0.08}$	0.73${}_{-0.29}^{+0.67}$	15.0
XLSS005	E46	02hr27m432 -04d21m283	0.73*	24.41 ± 0.06	328 ± 18	3.99 ± 0.01	0.53${}_{-0.45}^{+0.14}$	0.68${}_{-0.35}^{+0.55}$	8.5
RXJ0910	886	09hr10m227 +54d22m494	0.56*	24.92 ± 0.03	194 ± 51	4.17 ± 0.02	0.25${}_{-0.02}^{+0.16}$	1.44${}_{-0.09}^{+0.28}$	10.5
RXJ1053	F10	10hr52m256 +57d33m226	0.62*	24.78 ± 0.03	98 ± 17	3.76 ± 0.01	0.57${}_{-0.08}^{+0.03}$	2.08${}_{-0.01}^{+0.01}$	6.7
RXJ1053	1027	10hr53m276 +57d45m439	0.85*	25.15 ± 0.02	203 ± 19	4.17 ± 0.01	0.22${}_{-0.12}^{+0.13}$	2.27${}_{-0.05}^{+0.05}$	6.4
RXJ1053	E39	10hr53m373 +57d42m406	0.72*	24.43 ± 0.04	272 ± 18	3.56 ± 0.01	0.40${}_{-0.19}^{+0.10}$	2.26${}_{-0.02}^{+0.02}$	5.5
RXJ1053	1028	10hr53m422 +57d44m367	0.70*	24.89 ± 0.02	210 ± 18	4.23 ± 0.01	0.31${}_{-0.13}^{+0.05}$	2.38${}_{0.03}^{+0.03}$	6.5
Cl1137	785	11hr37m187 +30d00m400	0.62*	23.87 ± 0.03	164 ± 17	3.85 ± 0.02	0.37${}_{-0.25}^{+0.05}$	2.29${}_{-0.03}^{+0.02}$	5.8
Cl1137	783	11hr37m330 +30d00m023	0.96	25.06 ± 0.01	117 ± 20	3.85 ± 0.01	2.03	−1.32	5.9
Cl1137	784	11hr37m338 +30d00m104	0.99*	25.00 ± 0.02	139 ± 20	3.86 ± 0.01	0.41${}_{-0.20}^{+0.15}$	0.52${}_{-0.28}^{+0.36}$	5.9
SC1324	55	13hr24m037 +30d43m404	0.70	24.94 ± 0.01	366 ± 18	4.07 ± 0.01	0.87	0.12	20.0
SC1324	102	13hr24m155 +30d46m449	0.66*	24.32 ± 0.02	146 ± 18	3.47 ± 0.01	0.35${}_{-0.01}^{+0.05}$	1.37${}_{-0.83}^{+0.29}$	16.0
SC1324	115	13hr24m201 +30d48m386	1.20*	24.87 ± 0.03	132 ± 21	3.37 ± 0.01	0.03${}_{-0.06}^{+0.02}$	2.07${}_{-0.18}^{+0.46}$	14.7
SC1324	614	13hr24m246 +30d21m214	1.24*	26.10 ± 0.02	196 ± 21	3.79 ± 0.01	0.04${}_{-0.03}^{+0.04}$	2.49${}_{-0.05}^{+0.04}$	12.2
SC1324	148	13hr24m311 +30d49m283	0.58*	24.05 ± 0.02	90 ± 16	3.18 ± 0.02	0.05${}_{-0.02}^{+0.01}$	1.79${}_{-0.09}^{+0.09}$	12.8
SC1324	212	13hr24m434 +30d49m380	1.10	25.63 ± 0.00	313 ± 20	4.23 ± 0.01	0.50	−0.81	13.3
SC1324	699	13hr24m449 +30d12m298	1.08	25.19 ± 0.01	221 ± 20	3.81 ± 0.01	0.24	2.19	11.1
SC1324	271	13hr24m545 +30d49m159	0.70	23.88 ± 0.03	117 ± 18	3.34 ± 0.01	1.04	−0.45	13.1
SC1324	323	13hr25m062 +30d44m198	0.68*	24.22 ± 0.04	116 ± 18	3.31 ± 0.03	0.34${}_{-0.13}^{+0.06}$	1.41${}_{-0.54}^{+0.44}$	12.6
SC1324	410	13hr25m277 +30d42m524	0.72*	24.22 ± 0.03	115 ± 18	3.44 ± 0.02	-0.19${}_{-0.11}^{+0.12}$	1.69${}_{-0.40}^{+0.61}$	17.5
Cl1350	617	13hr50m501 +60d08m035	0.81	24.41 ± 0.03	98 ± 19	3.53 ± 0.01	0.88	−0.20	9.6
Cl1350	327	13hr50m596 +60d06m095	0.80	25.43 ± 0.01	156 ± 19	3.98 ± 0.01	1.51	−1.01	9.6
Cl1429	F3	14hr28m187 +42d50m352	0.60*	24.15 ± 0.09	61 ± 17	3.29 ± 0.03	-0.70${}_{-0.08}^{+0.09}$	1.98${}_{-0.13}^{+0.19}$	22.0
Cl1429	F10	14hr28m215+42d35m064	1.12*	25.70 ± 0.04	118 ± 21	3.77 ± 0.01	-0.60${}_{-0.08}^{+0.14}$	1.87${}_{-0.18}^{+0.38}$	20.0
Cl1429	E25	14hr28m380 +42d44m399	0.62*	25.25 ± 0.05	196 ± 18	4.08 ± 0.01	0.13${}_{-0.04}^{0.04}$	1.78${}_{-0.15}^{+0.23}$	18.0
Cl1429	F9	14hr28m462 +42d38m137	0.83	25.05 ± 0.02	85 ± 19	3.56 ± 0.01	0.51	0.46	16.0
SC1604	409	16hr04m042 +43d23m577	0.68*	24.64 ± 0.02	87 ± 18	3.67 ± 0.01	0.46${}_{-0.32}^{+0.07}$	1.56${}_{-0.19}^{+0.38}$	8.2
SC1604	427	16hr04m064 +43d18m080	0.92	24.29 ± 0.01	99 ± 20	3.65 ± 0.01	1.07	0.87	6.9
SC1604	F11	16hr04m236 +43d14m071	0.86	24.98 ± 0.03	131 ± 19	3.89 ± 0.01	1.42	−1.50	7.0
SC1604	557	16hr04m248 +43d04m254	0.90	23.95 ± 0.04	96 ± 19	3.63 ± 0.01	1.45	−0.78	8.1
SC1604	561	16hr04m251 +43d04m505	0.90	24.34 ± 0.01	122 ± 19	3.82 ± 0.01	2.05	−1.61	8.1
SC1604	574	16hr04m268 +43d15m041	0.86	24.18 ± 0.01	81 ± 19	3.55 ± 0.01	1.20	−0.54	7.0
SC1604	620	16hr04m308 +43d16m362	0.90	24.32 ± 0.02	153 ± 19	3.76 ± 0.01	0.34	0.69	7.1
SC1604	697	16hr04m399 +43d21m142	0.92	25.10 ± 0.00	110 ± 20	3.79 ± 0.01	1.19	−1.19	7.7
SC1604	701	16hr04m404 +43d22m204	1.27	25.13 ± 0.00	99 ± 21	3.79 ± 0.01	0.63	−0.27	7.8
RXJ1716	E18	17hr15m039 +67d12m032	0.70*	24.87 ± 0.07	271 ± 24	4.12 ± 0.04	-0.19${}_{-0.10}^{+0.03}$	1.71${}_{-0.20}^{+0.55}$	16.0
RXJ1716	E17	17hr16m370 +67d08m294	0.790	26.82 ± 0.04	336 ± 19	4.50 ± 0.01	1.14	−0.10	16.1
RXJ1716	567	17hr16m569 +67d09m040	0.81*	24.21 ± 0.05	105 ± 19	3.46 ± 0.02	1.24${}_{-0.31}^{+0.37}$	0.03${}_{-0.20}^{+0.48}$	14.8
RXJ1757	152	17hr56m423 +66d33m340	1.34*	26.63 ± 0.13	221 ± 22	3.98 ± 0.03	0.10${}_{-0.08}^{+0.08}$	2.16${}_{-0.16}^{+0.44}$	11.7
RXJ1821	196	18hr21m072 +68d26m097	1.30*	24.88 ± 0.03	132 ± 21	3.47 ± 0.01	0.08${}_{-0.06}^{+0.04}$	1.53${}_{-0.07}^{+0.14}$	9.4
RXJ1821	255	18hr21m307 +68d29m280	0.82	24.60 ± 0.02	151 ± 19	3.82 ± 0.01	1.40	−0.65	9.9
RXJ1821	269	18hr21m371 +68d27m507	0.82	24.41 ± 0.01	111 ± 19	3.38 ± 0.01	1.91	−1.49	9.4
RXJ1821	294	18hr21m474 +68d21m032	1.28	24.71 ± 0.01	126 ± 21	3.32 ± 0.01	−0.02	2.08	9.3

Note. (1) (2) The field and ID of ERAGN. ERAGN detected by eye start with an "E"; (3) the R.A. and Decl. of the radio centers of ERAGN; (4) the redshift of ERAGN with z_phot marked by *. (5) The radio power of radio sources, see Section 2.2; (6) (7) the extent of radio sources and their associated error, see Section 2.3; (8) (9) the local and global environment measurements, described in Section 2.4 with more details in Appendix A for their error calculation; (10) the local rms is measured in a 2'  ×  2' empty region close to the radio source in the radio image. The size of the region is chosen to eliminate the local variations and not to include other radio sources.

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