The Massive and Distant Clusters of WISE Survey. VII. The Environments and Properties of Radio Galaxies in Clusters at z ∼ 1

The FIRST survey covers 10,575 deg² of the North and South Galactic Caps. These data were taken using the VLA in the B configuration in L-band. FIRST has a typical rms of 0.15 mJy and a resolution of 5''. Table 2 lists relevant properties obtained from the FIRST catalog.

We calculate the power (radio luminosity) of the FIRST sources,

$$\begin{eqnarray}&&{P}_{1.4}=4\pi {{D}_{L}}^{2}{S}_{1.4}{\left(1+z\right)}^{\alpha -1},\end{eqnarray} \tag{ 1 }$$

where D_L is the luminosity distance at the redshift of the cluster, S_1.4 is the integrated radio flux at 1.4 GHz from FIRST, (1 + z)^α−1 includes both the distance dimming and K-correction, and α is the radio spectral index (${S}_{\nu }\propto {\nu }^{-\alpha }$). Typical values of α for extended radio sources range from 0.7 to 0.8 (Kellermann & Owen 1988; Condon 1992; Peterson 1997; Lin & Mohr 2007; Miley & De Breuck 2008; Tiwari 2019) and we adopt α = 0.8 as in Chiaberge et al. (2009), Gralla et al. (2011), and Yuan et al. (2016). We assume the radio source is at the photometric redshift of the cluster (see Table 1 and Section 2.3).

Table 1.  Cluster Properties and VLA Observations

Cluster	zphot	λ15	Band-Config.-	Beam	rms
		N	Obs. Sem.	''	(μJy/beam)
MOO J0015+0801	${0.9}_{-0.04}^{+0.04}$	58 ± 8	L-A-16B	17 × 12	45.0
MOO J0100−0151	${1.1}_{-0.05}^{+0.06}$	36 ± 6	L-A-18A	21 × 12	50.0
MOO J0121−0145	${0.98}_{-0.07}^{+0.07}$	37 ± 6	L-A-16B	11 × 10	24.0
MOO J0228−0644	${0.86}_{-0.06}^{+0.09}$	22 ± 5	L-A-16B	25 × 11	30.0
MOO J0231−0212	${1.43}_{-0.07}^{+0.08}$	22 ± 4	C-B-17B	19 × 10	8.35
MOO J0250−0443	⋯a	⋯	L-A-16B	17 × 11	20.0
MOO J0300+0124	${1.33}_{-0.06}^{+0.04}$	37 ± 6	L-A-16B	14 × 11	33.0
MOO J0900+0407	${0.84}_{-0.05}^{+0.07}$	13 ± 5	C-B-17B	28 × 10	8.7
MOO J0901+3341	${1.02}_{-0.07}^{+0.08}$	26 ± 5	C-B-17B	20 × 11	6.7
MOO J0903+1319	⋯a	⋯	C-B-17B	15 × 11	7.0
MOO J0917+1456	${1.05}_{-0.07}^{+0.07}$	30 ± 6	C-B-17B	20 × 11	7.3
MOO J0920−0755	${1.1}_{-0.06}^{+0.06}$	31 ± 6	C-B-17B	24 × 10	7.8
MOO J0928−0126	⋯a	⋯	C-B-17B	30 × 10	7.2
MOO J0959+3903	⋯a	⋯	C-B-17B	18 × 10	7.0
MOO J1004−0257	${0.98}_{-0.07}^{+0.07}$	31 ± 6	L-A-18A	24 × 11	30.0
MOO J1007+0139	${0.94}_{-0.06}^{+0.06}$	28 ± 6	C-B-17B	12 × 10	7.2
MOO J1011+3919	⋯a	⋯	C-BnA-17B	24 × 05	7.6
MOO J1012+0843	${1.14}_{-0.08}^{+0.1}$	25 ± 5	L-A-18A	18 × 12	32.0
MOO J1020+1231	${0.89}_{-0.07}^{+0.09}$	13 ± 5	L-A-18A	21 × 13	30.0
MOO J1020+2412	${1.01}_{-0.06}^{+0.06}$	25 ± 5	L-A-18A	19 × 13	32.0
MOO J1021+1800	⋯a	⋯	C-B-17B	14 × 12	6.7
MOO J1034+3104	⋯a	⋯	L-A-18A	15 × 12	40.0
MOO J1037+0433	⋯a	⋯	L-A-18A	22 × 12	34.0
MOO J1053+1052	${0.99}_{-0.06}^{+0.07}$	43 ± 7	L-A-18A	19 × 11	14.0
MOO J1117+1514	${1.13}_{-0.09}^{+0.1}$	24 ± 5	C-BnA-17B	24 × 04	7.6
MOO J1138+5031	${1.29}_{-0.1}^{+0.07}$	23 ± 5	C-B-17B	29 × 10	6.8
MOO J1140+4454	${1.09}_{-0.04}^{+0.04}$	35 ± 6	C-B-17B	27 × 10	7.9
MOO J1215−0630	${1.02}_{-0.06}^{+0.07}$	26 ± 6	L-A-18A	⋯	⋯
MOO J1238−0232	${0.94}_{-0.09}^{+0.1}$	12 ± 4	L-A-18A	15 × 11	13.0
MOO J1252+0700	${0.94}_{-0.08}^{+0.09}$	28 ± 6	L-A-18A	13 × 12	12.0
MOO J1308+1622	${1.02}_{-0.09}^{+0.09}$	18 ± 5	C-B-17B	11 × 11	7.0
MOO J1312+2002	${0.94}_{-0.07}^{+0.07}$	25 ± 6	C-B-17B	24 × 11	7.4
MOO J1319+5519	${0.94}_{-0.04}^{+0.05}$	44 ± 7	C-B-17B	18 × 10	7.1
MOO J1334+1443	${0.98}_{-0.1}^{+0.11}$	20 ± 5	C-B-17B	12 × 10	6.2
MOO J1353−0541	${0.94}_{-0.07}^{+0.07}$	22 ± 5	L-A-18A	16 × 11	33.0
MOO J1355+6116	${0.38}_{-0.05}^{+0.03}$	51 ± 8	C-B-17B	13 × 10	6.5
MOO J1358+2158	${0.99}_{-0.06}^{+0.07}$	39 ± 6	L-A-16B	11 × 10	310
MOO J1401+0750	${1.08}_{-0.08}^{+0.08}$	38 ± 6	C-B-17B	12 × 10	6.75
MOO J1412+4846	⋯a	⋯	L-A-16B	35 × 10	30.0
MOO J1435+4759	${1.02}_{-0.05}^{+0.06}$	43 ± 7	L-A-16B	35 × 10	27.0
MOO J1440+2628	⋯a	⋯	C-B-17B	13 × 11	6.45
MOO J1506+5137	${1.09}_{-0.03}^{+0.03}$	74 ± 8	C-B-17B	10 × 08	8.0
MOO J1507+3126	${0.88}_{-0.04}^{+0.03}$	40 ± 6	C-B-17B	16 × 10	6.7
MOO J1516−0435	⋯a	⋯	L-A-18A	15 × 11	33.0
MOO J1555+3259	${0.98}_{-0.07}^{+0.07}$	24 ± 5	C-BnA-17B	11 × 04	5.9
MOO J1619+5323	${1.21}_{-0.09}^{+0.08}$	25 ± 5	L-A-18A	15 × 10	33.0
MOO J1622+1324	⋯a	⋯	C-B-17B	11 × 10	6.9
MOO J1634+4021	${1.16}_{-0.02}^{+0.02}$	37 ± 6	C-B-17B	17 × 11	6.0
MOO J1731+5857	${1.02}_{-0.08}^{+0.08}$	29 ± 6	L-A-16B	14 × 10	19.0
MOO J2247+0507	${1.02}_{-0.05}^{+0.05}$	21 ± 5	L-A-16B	14 × 11	49.0
MOO J2306+0951	${1.09}_{-0.11}^{+0.12}$	20 ± 5	L-A-18A	⋯	⋯
MOO J2321+0119	⋯a	⋯	C-B-17B	16 × 13	6.0

Notes. The prefix of the cluster name stands for Massive Overdense Object. Column 2: the photometric redshift.

^aWe note that some clusters lack IRAC data for the calculation of a photometric redshift, thus we assume the median redshift of the MaDCoWS survey for these clusters (z = 1.06, Gonzalez et al. 2019). Column 3: richness of the cluster defined in Section 2.3. Those that do not have Spitzer data do not have a richness. Column 4: the VLA band, configuration, and observing semester of the observation. Column 5: the beam size of each observation. Column 6: the rms of the VLA image. MOO J1215−0630 and MOO J2306+0951 had unusable data sets.

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We note that at z = 1, a 1 mJy (the FIRST flux limit) source corresponds to P_1.4 = 4.7 × 10²⁴ W Hz⁻¹. This limit is barely below the frequently quoted power boundary between the two Fanaroff–Riley (FR) classes (P_1.4 ∼ 10²⁵ W Hz⁻¹; Fanaroff & Riley 1974; Ledlow & Owen 1996). Thus, any FR I sources we detect will be at the luminous end of the FR I distribution.

VLA high-resolution follow-up observations were taken over three observing semesters: 16B (PI: Gonzalez, 16B-289), 17B (PI: Gonzalez, 17B-197), and 18A (PI: Moravec, 18A-039). See Table 1 for details. The results of the 10 clusters observed in 16B are published in Moravec et al. (2019), but are also included in this work.

The data taken in 16B and 18A were taken in L-band in the A configuration. The observations were centered at 1.4 GHz (21 cm) with a bandwidth of 600 MHz. Given this configuration and band, the resolution was ∼13 using robust weighting (see Table 1 for exact beam sizes). The primary beam was 30' and the largest angular scale that we can detect is 36 During 16B, each target was observed twice for nine and a half minutes within a scheduling block (a total of ∼19 minutes on source) to reach the desired sensitivity. Between 16B and 18A, updated L-band system equivalent flux density (SEFD) measurements were integrated into the exposure time calculator and thus we required less integration time in 18A to reach the equivalent sensitivity that was achieved in 16B. During 18A, each target was observed twice for six minutes within a scheduling block for a total of ∼12 minutes on source.

The data taken in 17B were taken in C-band in the B configuration. The observations were centered at 5.5 GHz with a bandwidth of 1.9 GHz. Given this configuration and band, the resolution was ∼10 using robust weighting (see Table 1 for exact beam sizes). The primary beam was 8' and the largest angular scale that we can detect is 29 During 17B, each target was observed three times for nine minutes each within a scheduling block for a total of ∼28 minutes on source. A few cluster C-band data sets were taken in the BnA hybrid configuration during the transition from B configuration to A configuration in 2018 early February where the northern arm is in the extended A configuration and eastern and western arms are in B configuration. The resolution achieved with this configuration is similar to those achieved in B configuration. For all observations the correlator was configured with 16 spectral windows, each with 64 channels.

Most of the data were flagged, calibrated, and imaged with Common Astronomy Software Applications (CASA) version 5.0 or later (McMullin et al. 2007). All measurement sets were first processed through the VLA CASA Calibration Pipeline for basic flagging and calibration. We created images of each cluster by applying the TCLEAN algorithm. We cleaned the L-band images to an average depth of ∼28 μJy per beam and ∼7 μJy per beam for the C-band images.

The rms (μJy/beam) value for each image was determined by the following process. If possible, four rectangular regions that were near the targeted source, but that did not encompass the source, were drawn in the viewer. These regions were drawn in such a way as to be free of detected radio sources. Then, these individual rms measurements were averaged together to produce the final rms which is reported in Table 1 for each image.

A pixel scale of 028 for L-band images and 024 for C-band images, specmode = "mfs," and WEIGHTING = BRIGGS (robust = 0.5) were used for all images. Analysis is restricted to the inner 3' of the primary beam and in most cases to the inner 1'. Thus, primary beam correction was not necessary. In many cases, we performed several rounds of phase-only self-calibration to increase the signal-to-noise ratio (S/N; typically by a factor of 3), reduce the prominence of improper cleaning artifacts, and recover more of the source structure.

Two clusters (MOO J1215−0630 and MOO J2306+0951) had unusable data. MOO J1215−0630 had a bright source in the upper right portion of the field that could not be cleaned well enough to allow the source of interest to be distinguished. For MOO J2306+0951, an extended source was unintentionally used for calibration which made imaging difficult. Due to these data quality issues, the final sample is reduced from 52 to 50.

A total of 36 of the 50 clusters presented in this work were also observed with Spitzer (90177 and 11080, PI: Gonzalez). Each cluster was observed in both [3.6] and [4.5] for a total of ∼180 seconds using a set of 6 × 30 s exposures, with a medium scale cycling dither pattern.

The catalogs were generated using a procedure similar to that of Wylezalek et al. (2013) in which the Corrected Basic Calibrated Data (cBCD) was reduced and mosaicked using IRACproc (Schuster et al. 2006), the MOPEX package (Makovoz & Khan 2005), and a resampled pixel scale of 06. The MOPEX outlier (e.g., cosmic ray, bad pixel) rejection was optimized for the regions of deepest coverage in the center of the maps corresponding to the position of the MaDCoWS detection. Photometry was performed using SExtractor (Bertin & Arnouts 1996) with an aperture diameter of 4'', corrected to total. The catalogs reach a uniform limit of 10 μJy in [3.6] and [4.5].

The photometric redshifts are listed in Table 1 and are derived from the [3.6]−[4.5] and Pan-STARRS i−[3.6] colors of galaxies within 1' of the cluster location, which are compared with a Flexible Stellar Population Synthesis (FSPS) model (Conroy et al. 2009; Conroy & Gunn 2010). Details can be found in Gonzalez et al. (2019). For those clusters that lack IRAC data, we assume the median photometric redshift of the MaDCoWS survey (z = 1.06, Gonzalez et al. 2019).

For the clusters that have Spitzer data the richness is defined as λ₁₅ = N − N_field, where N is the total number of color-selected galaxies within the metric aperture that have fluxes that satisfy f_4.5 > 15 μJy. Details can be found in Gonzalez et al. (2019). The richnesses are recorded in Table 1.

While the primary cluster coordinates are from the original survey (Gonzalez et al. 2019), the Spitzer photometry provides an independent measurement of the cluster center in a similar manner. We use the average distance from the WISE and Spitzer centers when possible (see Section 5.1). Some clusters do not have a robust Spitzer center and in these cases the WISE center is adopted as the center.

Double-lobed radio sources are a prevalent radio morphology and are divided into two classes: FR classes I and II (Fanaroff & Riley 1974). FR I sources are "edge-darkened" in appearance in that the emission is brighter near the radio core and becomes fainter radially outward. FR II sources are "edge-brightened" in appearance in that the well-separated lobes end in distinctive areas of brightest emission (i.e., "hot spots"). Beyond morphological distinction, FR Is and FR IIs have other differences. Though there is still debate concerning the connection between accretion mode and jet morphology, the FR dichotomy is typically explained by a difference in jet dynamics where FR IIs have jets that remain relativistic throughout terminating in hot spots whereas FR Is are disrupted on kiloparsec scales (see Tchekhovskoy & Bromberg 2016; Mingo et al. 2019). The environment is often invoked as the cause of this disruption (Kaiser & Best 2007; Gendre et al. 2013; Croston et al. 2019). Additionally, FR II sources are generally more luminous than FR I sources (Fanaroff & Riley 1974; Ledlow & Owen 1996), though this distinction is not absolute (Mingo et al. 2019). And lastly, it has been shown that the internal composition of radio-lobe plasma is systematically different in these two types of radio galaxies (Croston et al. 2018); the particle content of FR I lobes is dominated by protons and ions, whereas FR IIs are primarily composed of an electron-positron plasma.

With the resolution of the VLA, we were able to visually determine the radio morphologies of the sources in our sample, which are shown in Figure 1. We visually classified the primary sources per the following definitions:

• 1.  
  FR I: "Edge-darkened" meaning that the emission is brighter near the radio core and becomes fainter radially outward. Jets do not have a large amount of rounded extended emission at the ends of the jets (like that of an FR II).
• 2.  
  FR II: "Edge-brightened" meaning that the well-separated lobes "end" in distinctive areas of brightest emission (i.e., hot spots). Jets end in rounded extended emission and have hot spots closer to the edge of the rounded emission than to the origin of the jet.
• 3.  
  Bent Tail (BT): An FR source (either FR I or FR II) that is bent.
• 4.  
  Undetermined (UD): Has an extended morphology that is too ambiguous to categorize and/or authors could not agree on a classification.

Four of the authors independently visually classified these sources. A majority was needed to assign a classification. In two cases the authors were split as to whether the source was an FR I or an FR II, thus we have given these sources the classification of FR I/II as the authors agree that the source morphology is one of the FR types. In three cases (MOO J0228−0644, MOO J0928−0126, and MOO J1053+1052), there was an even split between two different classifications and in these cases the first author assigned a final classification. We report these morphology classifications in Table 2.

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In the sample of 50 total primary sources (from the full sample of 52 observations minus two data sets that were unusable due to data quality issues—see Section 2.2), we find 26 FR IIs, 4 FR Is, 2 FR I/II s, 4 BTs, and 14 UDs.

The LOFAR Two-meter Sky Survey (LoTSS) is an ongoing sensitive, high-resolution 120–168 MHz survey of the entire northern sky.⁹ In 2019 February, the first full-quality public data release of the LOFAR Two-meter Sky Survey became available, presenting 2% of the eventual coverage (Shimwell et al. 2019). The median sensitivity is S_144MHz = 71 μJy beam⁻¹ and the resolution of the images is 6''.

Several of our targets were contained within the LoTSS DR1 (see Figure 2). We used this low-frequency data to aid us in classifying the sources. With constant energy injection, the synchrotron radiation from an AGN produces a power-law radio spectrum. However, as the AGN activity fades, energy losses cause the initial power-law spectrum to steepen beyond a break frequency (whose position is related to the time since acceleration). Thus, high-frequency radio observations trace the current energy injection through the jets and hot spots, while low-frequency radio observations allow exploration of the full extent of the jet emission and the history of emission.

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In the case of MOO J1412+4846, the LoTSS data reveal extended, connected emission around the hot spots shown in the VLA data. The LoTSS data makes the FR II classification obvious, whereas it was not entirely clear from the VLA data alone. The low-frequency data also confirm the FR II classification for MOO J1435+4759. In general, the VLA data highlight the hot spots and the emission from the host galaxy and the LoTSS data allow exploration of the lobes in a different regime as the recoverable angular extent is larger at lower frequencies. Thus, we see that having lower frequency data increases the number of correctly classified FR IIs. In these cases, the VLA data, revealing only well-separated (sometimes oddly shaped) hot spots, might lead one to classify something as undetermined, particularly if their separation is beyond the detectable largest angular size (LAS). In contrast, in the low-frequency data one can clearly see the connection between the hot spots, as we see in the cases of MOO J1412+4846 and MOO J1435+4759. Overall, the LoTSS data reveal the extended emission, reducing the classification ambiguity and thus decreases the number of undetermined sources and increases the number of FR IIs, FR Is, and BTs. In order to make a one-to-one comparison, all sizes are based on the VLA data since it has higher resolution and only a few clusters have LoTSS data.

Lastly, in the case of MOO J0121−0145, it is possible that it might be similar to MOO J1412+4846 in that the primary and secondary sources are the hot spots of two lobes. However, there is no LoTSS data to confirm this as there is for MOO J1412+4846 (see Section 3.2). Additionally, there was no obvious optical counterpart where the host galaxy is expected to be. Thus, MOO J0121−0145 is classified as UD and excluded from the analysis that follows.

As described in Moravec et al. (2019), we measure the extent of the radio sources as a diagnostic of the local environment. The LAS is defined as the length of a straight line between the most distant points belonging to the same radio source. To determine the LAS, we measure the largest projected angular extent of the source contained within the lowest reliable contour. For most cases in this study the lowest reliable contour was 4σ, but for a few cases (MOO J0228−0644 and MOO J2247+2247), due to residual artifacts from the cleaning process, the lowest reliable contour was 8σ. These LAS measurements are given in Table 2 and shown as a function of luminosity in Figure 3. We note that the measured LAS from the VLA data is a lower limit on the true LAS given that these data are high resolution and extended emission beyond ∼30'' will be resolved out. Additionally, we convert the LAS into a largest linear projected size (LLS) using a scale factor that assumes the radio source is at the cluster redshift.

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We can identify low redshift interloper sources by comparing the observed infrared colors to those of a model passively evolving galaxy. For those sources that have infrared counterparts, we use a 1'' matching radius to obtain the i-band photometry from Pan-STARRS and calculate the observed-frame [3.6]—[4.5] and i − [3.6] colors (see Table 3). In the cases of nondetections in Pan-STARRS, we assume that the counterpart has an i-band magnitude fainter than the limiting magnitude i = 23.1 (AB; Chambers et al. 2016) and place a lower limit on the i − [3.6] color. We use the PS1 DR2 stacked PSF magnitudes and positions.¹⁰ In the case that there are two magnitudes at one position due to overlaps in the stack tessellations, we adopt the one with labeled as the primary detection.

We compare the observed colors to the expected colors of a passively evolving galaxy as a function of redshift using "EzGal" (Mancone & Gonzalez 2012). Following the parameters used in Gonzalez et al. (2019) for MaDCoWS, we use an FSPS model (Conroy et al. 2009) with a simple stellar population, a Chabrier (2003) initial mass function (IMF), and a formation redshift of z_f = 3. Because the brightest galaxies in clusters have supersolar metallicities (Connor et al. 2019), we also assume Z = 0.03.

In Figure 5, we plot the counterparts compared to the evolutionary track to identify the counterparts that are low redshift interlopers (the dashed gray line is the color expected for a passive galaxy at z = 0.7) or those whose emission is dominated by an AGN (shown by the shaded region; Stern et al. 2012). When comparing the colors of the host galaxies to the evolutionary track, we find that seven counterparts (two are associated with MOO J1401+0750) have evidence of being low redshift interlopers and we exclude these from the following analysis (marked as likely interlopers in Table 3). We find one counterpart (MOO J0901+3341) whose color is indicative of being AGN dominated rather than stellar dominated (Stern et al. 2012). Thus, we do not calculate the stellar mass for this object. We do, however, include it in analysis that does not pertain to stellar mass. In total, we identify 23 as being consistent with being in the cluster, 6 low redshift interlopers, and one that has no redshift estimate due to being dominated by AGN emission. We note that spectroscopy will be required to better estimate the true contamination level.

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Under the assumptions that (1) these counterparts are cluster members and (2) the emission of the AGN is subdominant to that of the galaxy at these mid-infrared wavelengths, we can use IRAC photometry to estimate stellar masses (supported by the color analysis above). We convert [4.5] to a stellar mass using "EzGal" assuming a FSPS model (Conroy et al. 2009) with a simple stellar population, a formation redshift z_f = 3, a supersolar metallicity Z = 0.03, a Chabrier (2003) IMF, and the cluster photometric redshift. The stellar mass changes by ±25% for 2 ≤ z_f ≤ 5. We report the stellar masses in Table 3 for a formation redshift z_f = 3.

The average stellar mass is 2.9 × 10¹¹ M_⊙ with 21 out of the 23 galaxies having M_* ≥ 10¹¹ M_⊙. The highest mass is 7.6 × 10¹¹ M_⊙ and the lowest is 0.4 × 10¹¹ M_⊙.

Using the Spitzer data, we can determine candidate brightest cluster galaxies (BCGs) within each cluster. We identify the candidate BCG using the following procedure. First, we identify the galaxies that are not dominated by AGN emission (Stern et al. 2012) by applying a color cut of [3.6] − [4.5] < 0.6. Then, for the 30 brightest in [4.5] we find Pan-STARRS cross matches within 1'' using "astroquery" (Ginsburg et al. 2019). We label the galaxy with the brightest [4.5] magnitude and i − [3.6] greater than the color expected for a passive galaxy at z = 0.7 (4.85; calculated using "EzGal") the brightest cluster galaxy. Out of the 23 counterparts consistent with the galaxy population expected in clusters at z > 0.7, 9 of them are the candidate BCG. In total, 12 of the candidate BCGs have radio emission associated with them. One of the BCGs (MOO J0901+3341) has a [3.6] − [4.5] that is consistent with being AGN dominated, which qualifies it as an optically bright quasar. As such, though its [4.5] is consistent with being the BCG, we exclude it from this BCG analysis.

A total of 19 out of the 23 counterparts (83%) are consistent with being one of the six most massive galaxies in the cluster. Predictably, all of the five most massive host galaxies in this sample are the candidate brightest galaxy in the cluster. These observations are consistent with the expectation that extended radio lobes are predominantly hosted by massive galaxies (e.g., Seymour et al. 2007). They are also consistent with previous studies that find that the prevalence and strength of radio activity is a strong function of stellar mass, hence BCGs are likely to be radio active (Best et al. 2005; Janssen et al. 2012; Sabater et al. 2019). BCGs would therefore be expected to be radio active based upon stellar mass alone.

We investigate correlations between stellar mass and both the distance of the source from the cluster center and LAS (see Figure 6). We observe M_* < 4 × 10¹¹ M_⊙ radio hosts at all radii, but M_* > 4 × 10¹¹ M_⊙ hosts only at distances less than 40'' (∼325 kpc) from the cluster center, indicating that the highest stellar mass hosts are confined to the cluster center. This could be explained by mass segregation in which more massive galaxies are preferentially found near the cluster center (e.g., Abell & Richard 1967; Quintana 1979; Roberts et al. 2015) or, if the host of the radio galaxy is a BCG, it will be preferentially near the center of the cluster.

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We find a similar trend with respect to LAS. We observe M_* < 4 × 10¹¹ M_⊙ radio hosts at all sizes, but M_* > 4 × 10¹¹ M_⊙ only at sizes less than 15'' (∼120 kpc). Taken together, these correlations with stellar mass indicate that the highest stellar mass galaxies host compact jets and tend to be in the inner portion of the cluster.

It is well known that the ICM found in galaxy clusters has a decreasing density profile radially outward (Cavaliere & Fusco-Femiano 1978; Vikhlinin et al. 2006; Croston et al. 2008). It is also known that the jet length of an AGN depends on the density of the medium that it is in, the power of the AGN, and its age (Falle 1991; Alexander 2000; Kaiser & Best 2007). The result that the highest stellar mass galaxies host compact jets and tend to be in the inner portion of the cluster can be understood in the context of this decreasing ICM density profile found in galaxy clusters (Moravec et al. 2019). It is known that a higher density ICM like that found in the center of a cluster will more efficiently pressure confine jets than a lower density ICM like that found at the outskirts of a cluster (Kaiser & Alexander 1997; Alexander 2000; Kaiser & Best 2007). Thus, one explanation for the smaller jets of the higher stellar mass galaxies at the center of the cluster is that these jets are being more confined by the denser ICM compared to jets farther from the cluster center (Moravec et al. 2019).

This interpretation is strengthened by the fact that radio power does not increase with stellar mass (Spearman's rank-order correlation r_s = 0.23, p = 0.29), which has been noted previously by Best et al. (2007), Lin & Mohr (2007), and Gupta et al. (2019); (see Figure 6). As noted earlier in Section 5.1, the size of the jets depends on power, the density of the surrounding medium, and the age of the source. This lack of correlation between stellar mass and power indicates that the power does not affect the relationship between stellar mass and angular size, leading to the conclusion that there are perhaps environmental factors affecting the size of these sources, as described above.

In Moravec et al. (2019), we observe a strong correlation between the largest angular extent and the distance from the cluster center. In this work, we are able to explore this relation in depth given the larger sample size. After applying the color cut described in Section 4.1, there are 44 sources available to investigate this relation (see Figure 7). As in Moravec et al. (2019), we normalize the size to a fiducial power according to

$$\begin{eqnarray}&&L=c{\left(\displaystyle \frac{P}{{\rho }_{0}(R)}\right)}^{1/5}{t}^{3/5}\end{eqnarray} \tag{ 2 }$$

such that

$$\begin{eqnarray}&&{L}_{\mathrm{norm}}=L{\left(\displaystyle \frac{{P}_{0}}{{P}_{1.4}}\right)}^{1/5}\end{eqnarray} \tag{ 3 }$$

where P₀ = 2 × 10²⁶ W Hz⁻¹ using the P_1.4 from Table 2.

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The distance of the source from the cluster center is defined as the angular distance between the inferred origin of the radio emission based on the morphological classification and the cluster center. The distance of the radio source from the center of the cluster for all morphology types, plotted in Figure 7, is the average of the distance of the source from the WISE and Spitzer cluster centers (see Section 2.3). We take the uncertainty in the distance from the cluster center to be the difference between the two distances and dividing by two. For those clusters that do not have a robust Spitzer center, we adopt the WISE center as the center and the error in the distance to be an average of the errors of the points that had robust Spitzer centers.

The scatter of this relationship visually increases from that in Moravec et al. (2019) when the full sample of radio sources consistent with being high redshift is considered. While there exists an overdensity of sources along the previous relation, a substantial subset now lies to the upper left, off the relation. Projection of the radio galaxy locations could explain these points (which we explore below). Likewise, the points to the lower right of the relation could be explained by projection of the jets to lower apparent angular sizes. This subset could also be explained by unidentified low redshift interlopers (not all clusters had Spitzer data). Interlopers would contaminate the plot by adding sources that have a larger LAS than predicted by the relation because sources are inherently larger at a lower redshift. For completeness, we note that projection could also shift a source onto the relation.

We ran simulations to investigate whether projection effects can explain the distribution of the data. Below are the steps of the projection simulations:

• 1.  
  Assume that the pilot relation still holds and randomly choose a distance (d) on the relation.
• 2.  
  Randomly choose a projected point on a unit sphere and scale it by d to obtain a projected distance, d_obs.
• 3.  
  Scatter d_obs using a Gaussian distribution with a standard deviation of 51, the mean error of the observed cluster center.
• 4.  
  Find the corresponding LAS for the original unprojected distance.
• 5.  
  Project the LAS to account for the orientation using a similar approach to above, but scatter it by 12, the mean error of LASs.
• 6.  
  For any simulated point that has an LAS less than 65, regenerate the point as the size threshold imposed in this study is greater than 65 (see Section 2).

To compare these simulations to the data, we define a normalized distance

$$\begin{eqnarray}&&{d}^{{\prime} }=\displaystyle \frac{{d}_{\mathrm{obs}}}{{d}_{\mathrm{relation}}}-1\end{eqnarray} \tag{ 4 }$$

where d_obs is the distance from the cluster center of the particular data point and d_relation is the corollary distance of d_obs on the pilot relation. In Figure 8, we compare the normalized distribution of d' values for the data (green histogram) to the normalized distribution of the 100,000 simulated projected points (black histogram outline).

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Compared to the simulation, the observed distribution of radio sources is similar in shape (see Figure 8) around d' = 0. To quantify the similarity of the two distributions, we perform a two sample Kolmogorov–Smirnov test on the simulated data and the real data. We obtain p = 0.086, which is above the typical cutoff value of 0.05, above which the data are consistent with the null hypothesis. We choose a bin size of 0.3 in order to minimize Poisson noise in the most populated bins and showcase the similarity between the distributions. The distribution of the data is undoubtedly influenced by unidentified low redshift interlopers. For instance, the removal of the most extreme outlier at low distance from the cluster center increases the p-value to 0.014. Thus, we consider the two distributions to be consistent with originating from the same underlying distribution.

Compared to the simulation, there is an excess of sources on the order of a few percent at d' ≲ −0.2. This excess of sources is a population of radio-AGN that have a large angular extent, but are near the cluster center. One possible explanation is that there are interlopers at lower redshift. If not, a physical explanation might be that these are cases in which AGN activity at the center of the cluster creates bubbles of low pressure (Blanton et al. 2010). Over time the jets continue to inject energy episodically into the ICM, the bubbles of low pressure expand, and thus the jets are able to expand further into the ICM and have a larger extent.

Overall, we conclude that the effects of projection account for a majority of the spread in angular size that is seen in this work. A future improvement to increase the certainty in the origin of the scatter would be to obtain spectroscopic redshifts for these sources to identify and discard any interlopers.

We investigate the correlation between luminosity and distance of the source from the cluster center (see Figure 9) and see no evidence of a correlation (r_s = −0.15, p = 0.35). In contrast, in a study of radio galaxies associated with clusters at z < 0.4 using LoTSS, Croston et al. (2019) find that luminosity increases toward the cluster center. One explanation for this discrepancy in trends at different redshift ranges is that radio galaxies at high redshift could be triggered stochastically based on the availability of fuel in a more dynamically evolving environment (this work), while at lower redshift the galaxies have settled into a more evolved state where the AGN activity is more linked to the environment (Croston et al. 2019).

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We investigate whether there are any relationships between radio source properties and the richness of the cluster (λ₁₅) in Figure 9. There is a tentative suggestion of a trend of increasing luminosity with richness, but this correlation is visually weak. We quantify the weakness of this correlation by calculating Spearman's rank coefficient (r_s = 0.27) and the p-value (p = 0.15) which show that the data are consistent with the null hypothesis that there is no association between the two variables.

In the literature, varying degrees of strength of a correlation between luminosity and cluster properties have been seen at a range of redshifts. At z < 0.5, there is strong evidence for a correlation between luminosity and measures of the density of the environment which is measured by galaxy counts and X-ray luminosity (Best 2004; Ineson et al. 2013, 2015; Ching et al. 2017; Croston et al. 2019). However, at higher redshift (0.5 ≲ z ≲ 1.0), the existence of a relationship between these two quantities is still unclear and studies have found evidence for and against correlation (Wold et al. 2000; Belsole et al. 2007; Falder et al. 2010; Wylezalek et al. 2013). Overall, there is clear evidence of correlations between power and the cluster environment at z ≲ 0.5, but at z > 0.5 a clear, uncontested relationship has not emerged. These studies and our results could be congruent with the idea posed in Section 5.2 that radio galaxies at high redshift could be triggered stochastically based on the availability of fuel in a more dynamically evolving environment. At lower redshift the galaxies would then have settled into a more evolved state where the AGN activity is more linked to the environment.

We find no correlation between richness and LAS (r_s = 0.26, p = 0.15), which is similar to the results of low redshift studies (Croston et al. 2019). This could be expected given the number of factors that contribute scatter to the LAS, which will dilute and weaken any relationship between richness and LAS. We note that this analysis does not consider the entire radio source population, only those that are extended which limits the range of LAS probed in this work.