The High-Redshift Clusters Occupied by Bent Radio AGN (COBRA) Survey: Radio Source Properties
Emmet Golden-Marx, Elizabeth Blanton, Rachel-Paterno-Mahler, Mark Brodwin, Matt Ashby, Emily Moravec, Lu Shen, Brian Lemaux, Lori Lubin, Roy Gal, Adam Tomczak
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THE HIGH-REDSHIFT CLUSTERS OCCUPIED BY BENT RADIO AGN (COBRA) SURVEY: RADIO SOURCEPROPERTIES
Emmet Golden-Marx , E. L. Blanton , R. Paterno-Mahler , M. Brodwin , M. L. N. Ashby , E. Moravec , L.Shen , B.C. Lemaux , L.M. Lubin , R.R. Gal , A.R. Tomczak Department of Astronomy, Tsinghua University, Beijing 100084, China Department of Astronomy and The Institute for Astrophysical Research, Boston University, 725 Commonwealth Avenue, Boston, MA02215, USA WM Keck Science Center, 925 N. Mills Avenue, Claremont, CA 91711, USA Department of Physics & Astronomy, University of Missouri-Kansas City, 5110 Rockhill Road, Kansas City, MO 64110, USA Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA Astronomical Institute of the Czech Academy of Sciences, Boˇcn´ı II 1401/IA, 14000 Praha 4, Czech Republic CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China,Hefei 230026, China School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei 230026, China Department of Physics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA University of Hawai’i, Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
ABSTRACTThe shape of bent, double-lobed radio sources requires a dense gaseous medium. Bent sources cantherefore be used to identify galaxy clusters and characterize their evolutionary history. By combiningradio observations from the Very Large Array Faint Images of the Radio Sky at Twenty centimeters(VLA FIRST) survey with optical and infrared imaging of 36 red sequence selected cluster candidatesfrom the high- z Clusters Occupied by Bent Radio AGN (COBRA) survey (0.35 < z < z samples of bent sources and may indicate that the intracluster medium is lessdense in these high- z clusters. Keywords: galaxies: clusters: general - galaxies:evolution - galaxies:high-redshift - infrared:galaxies -radio continuum:galaxies INTRODUCTIONGalaxy clusters are the largest gravitationally-boundstructures in the universe. Clusters are partially char-acterized observationally by their galaxy populationsand hot, X-ray emitting gas in the form of the intra-cluster medium (ICM). At low redshift, cluster galaxypopulations are very well established (e.g., Eisenhardtet al. 2007), with most clusters hosting large, denselypopulated cluster cores of massive, quiescent, early-type galaxies. Although most galaxies in low- z clusters [email protected] are quiescent, these galaxies were not always “red anddead”. The epoch of cluster formation is predicted tobe at high redshift ( z > z >
2, the galaxy populations in clusters have beenobserved to be wildly diverse. Some clusters have largequiescent galaxy populations (e.g., Strazzullo et al. 2016;Willis et al. 2020), while other clusters host galaxies withlarge star-forming populations (e.g., Wang et al. 2016;Miller et al. 2018), and still others host populations of a r X i v : . [ a s t r o - ph . GA ] N ov Golden-Marx et al. galaxies that strongly resemble the distribution of fieldgalaxies (e.g., Alcorn et al. 2019). It is at 0.5 < z < z universe. During this epoch, cluster-cluster merg-ers with hot ICMs are also expected to become moreprevalent and the processes associated with the typicalevolution of cluster galaxies (e.g., ram pressure strip-ping, harassment) begin to mature. These processes, alloccurring in tandem, make this redshift range a dynamictime to examine the components of clusters.Observationally, at 0.5 < z < z clusters (e.g., Gladders & Yee 2000; An-dreon et al. 2014; Cooke et al. 2016; Cerulo et al. 2016),although an increasing number of counter examples exist(e.g., Brodwin et al. 2013; Hennig et al. 2017). Addition-ally, the color-density and star formation rate-densityrelations, which characterize the rate of star formationin clusters, are observed to persist in similar values as inlow- z clusters out to z ≈ z > < z < z galaxy clusters that might be the pro-genitors of less massive galaxy clusters and groups tofully trace the role of cluster mass in cluster evolution.To that end, identifying strong tracers of galaxy clus-ter candidates of all masses is vitally important. Oneaccurate tracer of high- z galaxy clusters is radio activegalactic nuclei (AGNs). These energetic radio sourceshave long been known to be associated with galaxyclusters and were used in some of the earliest detec-tions of what were then considered high- z galaxy clusters(Minkowski 1960). More recently, radio loud AGNs havebeen used to trace both low- and high- z clusters andprotoclusters (e.g. Blanton et al. 2003; Wing & Blan-ton 2011; Galametz et al. 2012; Wylezalek et al. 2013,2014; Castignani et al. 2014; Rigby et al. 2014; Blantonet al. 2015; Cooke et al. 2015, 2016; Noirot et al. 2016;Paterno-Mahler et al. 2017; Shen et al. 2017; Noirot et al.2018; Shimakawa et al. 2018; Croston et al. 2019; Garonet al. 2019; Moravec et al. 2019; Golden-Marx et al.2019; Moravec et al. 2020b). For example, the Clus-ters Around Radio Loud AGN (CARLA) survey foundthat ≈
55% of their 387 radio loud AGNs at 1.3 < z < σ , with 10% of sources in overdense environments at the 5 σ level when compared to a background field (Wylezaleket al. 2013).More importantly, radio AGNs trace clusters withstrong red sequences as well as clusters hosting youngerstellar populations and dusty, star-forming galaxies,making radio AGNs an excellent tracer of clusters ofall types (Cooke et al. 2016; Noirot et al. 2016, 2018;Golden-Marx et al. 2019). Although there are a numberof studies of the environments of radio AGN at low red-shift ( z < z > . < W Hz − (e.g., Fa-naroff & Riley 1974; Ledlow & Owen 1996) and are alsofound in similarly rich environments at high redshift,which makes them important cluster tracers (e.g., Hill& Lilly 1991; Zirbel 1997; Stocke et al. 1999; Fujita et al.2016; Shen et al. 2017). By contrast, radio AGNs char-acterized by brighter radio lobes and a fainter radio corewith P . > W Hz − (e.g., Fanaroff & Riley 1974;Ledlow & Owen 1996) are classified as Fanaroff-Riley II(FRII) radio sources. Unlike FRI radio sources, FRIIradio sources are generally found in poor cluster envi-ronments and groups at low redshift and in richer proto-cluster environments at high redshift (e.g., Best 2000),although examples of FRII radio sources in richer low- z galaxy clusters do exist (e.g., Wing & Blanton 2011).Due to this dichotomy and our desire to build a sampleof high- z clusters, incorporating FRI and FRII sourcesyields added diversity among cluster populations.One unique type of radio source that allows for a clus-ter sample across all ranges of cluster mass and mor-phology are bent, double-lobed radio sources (e.g., Blan-ton et al. 2000, 2001, 2003, 2015; Paterno-Mahler et al.2017; Silverstein et al. 2018; Garon et al. 2019; Golden-Marx et al. 2019). Unlike their straight counterparts,the “C” shape of these radio sources hints at the pres-ence of a dense, gaseous medium acting on the radiosource. Physically, the bent nature of these radio sourceshas been linked directly to ram pressure exerted by theICM (e.g., Owen & Rudnick 1976; O’Donoghue et al.1993; Hardcastle et al. 2005; Morsony et al. 2013), wherethe relative motion of the ICM with respect to the host adio Parameters for the COBRA Survey ◦ thatare commonly hosted by bright central elliptical galax-ies (e.g., Owen & Rudnick 1976; Valentijn 1979; O’Dea& Owen 1985). Morphologically, WATs are typicallyFRI sources, but have radio powers near the FRI/FRIIborder (10 . W Hz − < P . < . W Hz − ) (e.g.,Blanton et al. 2000, 2001; Wing & Blanton 2011). Thismakes WATs an ideal tracer for clusters of all masses,assuming those clusters host a dense ICM.At low redshift, Blanton et al. (2001) examined a sam-ple of 40 bent sources, finding 54% are in clusters, whilethe remaining 46% are in groups, some of which arepoor. Wing & Blanton (2011) built on this work usingthe Very Large Array Faint Images of the Radio Sky atTwenty centimeters (VLA FIRST) survey (Becker et al.1995) to identify thousands of bent radio AGNs. AsVLA FIRST was designed to cover the same area ofthe sky as the Palomar Sky Survey, which is the sameregion of the sky covered by the Sloan Digital Sky Sur-vey (SDSS), Wing & Blanton (2011) cross-matched eachbent radio AGN with SDSS galaxies with m r < < z < z SDSS sample and found that bent radio sourcesare no more likely to be in mergers than their straightcounterparts. Thus, this range of masses and morpholo-gies make bent AGNs an ideal tracer for clusters.As the ICM is a dense gaseous medium, bent radiosources without low- z host galaxies are excellent trac-ers of high- z clusters when other detection methods fail(e.g., Blanton et al. 2003, 2015; Paterno-Mahler et al.2017; O’Brien et al. 2018; Silverstein et al. 2018; O’Brienet al. 2018; Golden-Marx et al. 2019). To this end, the high- z Clusters Occupied by Bent Radio AGN (CO-BRA) survey of 646 bent, double-lobed radio sourcesidentified from the VLA FIRST survey was built (seeBlanton et al. 2015, Paterno-Mahler et al. 2017, andGolden-Marx et al. 2019 for a complete overview of thehigh- z COBRA survey). Using a subset of the high- z COBRA survey, we investigate the properties of theradio galaxies (bending angle, radio luminosity, and pro-jected physical size) with respect to the optical and in-frared properties of their host clusters (richness, hostmagnitude, offset from the cluster center). In Section 2,we discuss our sample selection, observations, and mea-surements. In Section 3, we discuss the properties of theradio sources with respect to their host clusters. In Sec-tion 4, we investigate how our results compare to similarstudies of high- z ( z > H = 70 km s − Mpc − ,Ω m = 0.3, and Ω Λ = 0.7. Unless otherwise noted, allmagnitudes are given in AB magnitudes. Additionally,all distances related to either the offset of radio sourcesfrom the cluster center or the size of the radio sourcesare given as projected distances. DATATo accurately characterize the relationship betweenbent radio AGNs and the clusters they reside in, we re-quire a large sample of bent sources as well as the nec-essary optical, infrared, and radio observations neededto characterize cluster galaxies. To that end, we utilizethe high- z COBRA Survey (Section 2.1) and the follow-up optical observations that allowed Golden-Marx et al.(2019) to create the red sequence selected cluster sam-ple (Sections 2.2 and 2.3). From the identification of redsequence galaxies, we introduce our measurement of thered sequence cluster center in Section 2.4. To describeeach radio source, we include our methodology for mea-suring the size, power, and opening angles of our bent,double-lobed radio sources in Section 2.5. To determinethe dynamics of bent radio AGNs in these clusters, wepresent the offset between the bent radio AGNs and thecluster centers in Section 2.6.2.1.
The High- z COBRA Survey Sample
The high- z COBRA survey consists of 646 bent,double-lobed radio sources that were initially identifiedin Wing & Blanton (2011) using either visual selectionor an automated selection process. All of these sourceslacked an SDSS identified host galaxy in Wing & Blan-ton (2011), making them high- z candidates. However,not all 646 sources are found in galaxy clusters. As pre-sented in Paterno-Mahler et al. (2017), each of the 646sources in the high- z COBRA survey were observed aspart of a
Spitzer
Snapshot program (PI: Blanton) inIRAC 3.6 µ m and 135 were observed in 4.5 µ m. Using Spitzer
IRAC 3.6 µ m imaging, Paterno-Mahler et al.(2017) identified 190 cluster candidates based on a 2 σ single-band overdensity when compared to a backgroundfield. Golden-Marx et al.
To further verify which COBRA radio sources residein clusters, Golden-Marx et al. (2019) analyzed 90 fieldswith optical and IR observations (see Table 1 in Golden-Marx et al. 2019 for the complete list of all COBRAfields with optical follow-up). These fields were chosenbecause they were the strongest cluster candidates fromPaterno-Mahler et al. (2017), the radio source was aquasar, or their radio morphology was particularly sug-gestive of a cluster (see Figure 1 in Golden-Marx et al.2019 for a breakdown of the fraction of overdense fieldsobserved with optical follow-up). By combining thesedatasets to measure photometric redshifts for the hostgalaxies of the bent radio AGNs, Golden-Marx et al.(2019) found that 39 fields have a red sequence over-density at or above 2 σ when compared to backgroundfields, bringing the total number of cluster candidatesidentified to 195 (see Section 2.3 or Golden-Marx et al.(2019) for a complete description of red sequence over-densities). As in Blanton et al. (2001), the remainingsources are primarily in overdense regions but below the2 σ threshold used to identify cluster candidates.2.2. The Optical Follow-up Campaign
Summarized here, the optical follow-up consists of ob-servations taken on the 4.3 m Lowell Discovery Tele-scope (LDT) at Lowell Observatory using the LargeMonolithic Imager (LMI). LMI has a 12 . (cid:48) × . (cid:48) ≈ (cid:48) × (cid:48) F.O.V.on
Spitzer
IRAC, allowing us to observe both the clus-ter and the surrounding field. Observations consist of90 fields in i -band and 38 in r -band for either 3 ×
600 sor 3 ×
900 s. Golden-Marx et al. (2019) measured aunique zero-point for each field using the SDSS catalogand found that the limiting magnitudes of our i -bandimaging was 24.0 mag for 3 ×
600 s exposures (24.5 magfor 3 ×
900 s exposures) and for our r -band imagingwas 24.5 mag for 3 ×
600 s exposures (25.0 mag for 3 ×
900 s exposures). To measure the color of each detectedgalaxy, Golden-Marx et al. (2019) matched sources inthe shorter waveband of the desired color to sources inthe longer waveband within a 1 (cid:48)(cid:48) search radius (e.g.,Golden-Marx et al. 2019 match i -band with 3.6 µ m,3.6 µ m with 4.5 µ m, and r -band with i -band) across theentire shared F.O.V. A complete description of the datareduction and SExtractor parameters used is found inGolden-Marx et al. (2019).2.3. The Red Sequence Cluster Candidate Sample
Of the 90 fields with optical observations, Golden-Marx et al. (2019) determined redshift estimates for77 of them. The redshift estimates come primarilyfrom comparisons between the color of the host galaxy The Lowell Discovery Telescope was previously named theDiscovery Channel Telescope (DCT) from 2003 - 2019. The obser-vations attributed to the LDT are the same observations Golden-Marx et al. (2019) referred to as being taken on the DCT. Here,we refer to the telescope as the LDT to reflect the name change. and EzGal (Mancone & Gonzalez 2012) Spectral En-ergy Distribution (SED) models of early-type galaxieswithout an AGN component (see Section 3 in Golden-Marx et al. 2019 for a full description of the redshiftestimates and EzGal modeling), spectroscopic redshiftsof detected quasars (of the six quasars discussed in thispaper, five are SDSS-detected broadline quasars, whileCOBRA130729.2+274659 lacks further classification onits quasar identification on the SDSS archive), or SDSSphotometric redshifts.To determine which fields host cluster candidates witha strong red sequence, Golden-Marx et al. (2019) mea-sured the overdensity of red sequence galaxies in eachfield relative to a background field. Golden-Marx et al.(2019) defined the red sequence for fields with i − [3 . r − i colors as within ± Spitzer
IRAC F.O.V. and locate the clus-ter center (see Section 2.4 or Golden-Marx et al. (2019)for a complete description of how the cluster center isselected). Red sequence cluster candidates have an over-density of red sequence galaxies above 2 σ within 1 (cid:48) ofeither the AGN or the red sequence determined clustercenter as compared to various background fields withunique magnitude limits set for each field (due to thesmall expected background contamination in the i − [3 . i − [3 .
6] redsequence clusters have at least five red sequence galax-ies).In this analysis, we use all 39 red sequence clustercandidates identified in Golden-Marx et al. (2019). Be-cause we are analyzing the bent radio AGNs relative tothe cluster as a whole, we focus on the overdensity mea-surements using the red sequence cluster center. We dothis despite some fields showing a slight decrease in theoverdensity of red sequence galaxies relative to the back-ground (e.g., when centered on the radio source, four redsequence galaxies are detected within 1 (cid:48) , but when cen-tered on the distribution of red sequence galaxies, onlythree of these galaxies are within 1 (cid:48) ). This is why two ofour fields have a red sequence overdensity measurementbelow 2 σ , even though we include them as cluster can-didates. By measuring the overdensity relative to thered sequence center, we can relate the geometry of eachbent radio source to the location of the strongest densitypeak of red sequence galaxies.2.3.1. Cluster Candidate Subsamples
To determine which radio sources lie in cluster can-didates, we use three colors ( i − [3 . . − [4 . adio Parameters for the COBRA Survey COBRA121712 . COBRA170614.5+243707 C O BR A COBRA164611.2+512915
Figure 1 . The strongest cluster candidates from the two m*+1 subsamples. Each panel shows a 5 (cid:48) × (cid:48) cutout of an LDTLMI i -band image centered on the radio host. The top row shows two examples drawn from the m*+1 i − [3 .
6] subsample(COBRA0121712.2+241525 at z ≈ z ≈ r − i subsample (COBRA135136.2+543955 at z = 0.55 and COBRA164611.2+512915 at z = 0.351). Theblue contours reflect the 20 cm VLA FIRST imaging. The red circles indicate red sequence galaxies. The cyan contours indicatethe surface density of red sequence galaxies as described in Golden-Marx et al. (2019). Galaxy overdensity measurements andradio source information for these and all COBRA cluster candidates analyzed here are given in Tables A1 and A2. r − i ) and two magnitude limits (either a uniform depthof m*+1 depending on the redshift of the cluster or afixed detected magnitude limit). The magnitude limitof our 3.6 µ m observations is 21.4 mag. Based on themagnitude of a modeled m* galaxy from EzGal, thislimits the m*+1 subsample to cluster candidates at z< i − [3 .
6] analysis and z < r − i analysis. Using these colors and magnitude limits, we di-vide our sample into four non-overlapping subsamples: the m*+1 i − [3 .
6] subsample, the magnitude limited i − [3 .
6] subsample, the magnitude-limited [3 . − [4 . r − i subsample (see Figures 1and 2 for examples of these cluster candidates and thered sequence galaxies selected and Table A1 for the listof cluster candidates in each subsample).Of these subsamples, the m*+1 i − [3 .
6] subsample isthe most statistically robust. This subsample includes18 fields that span 0.4 < z <
Golden-Marx et al. list of cluster candidates). The strength of the i − [3 . z ≈ < z < i -band (as opposed to r -band) and,due to our observing scheme, these fields generally haveseeing < . (cid:48)(cid:48) i − [3 .
6] subsample the most robust and the primarysubsample used in this analysis.The second subsample we analyze is the magnitude-limited i − [3 .
6] subsample. This subsample includes 9cluster candidates that span 1.1 < z < i − [3 .
6] subsample. However, due to the fixed magnitudelimit, we probe different depths for each field dependingon the redshift of the cluster.The third subsample we analyze is the magnitude-limited [3 . − [4 .
5] subsample. We use it to identifysome of the highest redshift cluster candidates in oursample (1.2 < z < i − [3 .
6] clusterdetections, we chose to use this color to analyze thesefields because the [3 . − [4 .
5] color cut is extremely ef-fective and our i -band images are relatively shallow athigh redshift. The strength of the magnitude-limited[3 . − [4 .
5] subsample comes from the shape of the color-redshift relation for this color (see Figure 4 in Golden-Marx et al. 2019). At z > z> . − [4 . > − z star-forming and qui-escent galaxies (e.g., Papovich 2008; Cooke et al. 2015).Golden-Marx et al. (2019) further reinforced the efficacyof the [3 . − [4 .
5] color-cut in detecting high- z galaxiesusing the extensive multi-band photometric and spec-troscopic data from the ORELSE survey (Lubin et al.2009), finding the fewest low- z interlopers in this color-cut as compared to their red sequence completeness frac-tions. However, despite the accuracy in removing fore-ground galaxies, the [3 . − [4 .
5] color cut is limited inisolating galaxies of a specific redshift given the flat na-ture of the color-redshift distribution, allowing for possi-ble contamination within the sample. Furthermore, the[3 . − [4 .
5] color cut is most effective in the redshiftregime beyond our m*+1 magnitude limit, which againmeans we probe different depths for each field.The fourth subsample is the m*+1 r − i subsample.This subsample contains 5 cluster candidates and weuse it to probe some of the lowest redshift sources in our sample (0.35 < z < i − [3 .
6] subsample arenot included in this subsample because they either lack r -band imaging or have r -band observations with poorseeing ( > . (cid:48)(cid:48) r − i subsampleprobes a uniform depth, the r − i color - redshift relationis only linear out to z ≈ < z < Determining the Cluster Center
Because bent, double-lobed radio sources are not al-ways located at the centers of clusters (e.g., Sakelliou &Merrifield 2000; Garon et al. 2019), Golden-Marx et al.(2019) developed a Python pipeline to measure the lo-cal surface density of red sequence galaxies in COBRAfields. Golden-Marx et al. (2019) did this by placing auniformly spaced 10 (cid:48)(cid:48) grid over the combined F.O.V. ofthe i -band and 3.6 µ m images and measuring the num-ber of red sequence galaxies within 10 (cid:48)(cid:48) of each grid point(they also did this in a uniform manner for the other col-ors). Golden-Marx et al. (2019) used Gaussian Kernelsmoothing to identify the peak of the red sequence over-density and determine a unit-weighted cluster center. Indoing this, Golden-Marx et al. (2019) determined wherethe dense core of red sequence galaxies in an evolved,relaxed cluster is regardless of the location of the bentradio source (see Table A1 for the coordinates of the redsequence cluster centers for each cluster candidate andFigures 1 and 2 for examples of the red sequence sur-face density contours). While most clusters, especiallythe strongest candidates, show a singular strong over-density, some fields show multiple smaller overdensitypeaks. Because Sakelliou & Merrifield (2000) found thatmost bent AGNs in their low- z sample of clusters are atclustocentric radii <
300 kpc (which is ≈ . (cid:48) z = 1.0),Golden-Marx et al. (2019) selected the nearest overden-sity to the AGNs in these cases.2.5. Radio Source Parameters
Radio Source Opening Angle & Physical Size
The success of the COBRA survey in identifyinggalaxy clusters is predicated on bent, double-lobed ra-dio sources being found nearly exclusively in dense clus-ter and group environments (e.g., Blanton et al. 2000,2001; Wing & Blanton 2011; Paterno-Mahler et al. 2017;Garon et al. 2019; Golden-Marx et al. 2019). Becauseour radio observations are from the VLA FIRST survey,we measure the size and opening angle of our bent ra-dio sources using the publicly available FIRST CatalogDatabase updated as of December 17, 2014. The up-dated FIRST values result in slightly different parame-ters than those reported in Paterno-Mahler et al. (2017),specifically with regards to the total integrated flux ofeach radio source. As a result, we remeasure all radiosource properties previously reported in Paterno-Mahleret al. (2017). Although VLA FIRST was designed toreach a uniform depth over all observed regions (Becker adio Parameters for the COBRA Survey COBRA + C O BR A . COBRA100841 . COBRA + Figure 2 . The strongest cluster candidates from the two magnitude-limited subsamples. The top row shows 5 (cid:48) × (cid:48) cutouts of LDTLMI i -band images centered on the radio host, while the bottom row shows 5 (cid:48) × (cid:48) cutouts Spitzer
IRAC 3.6 µ m images centeredon the radio host. The top row shows two examples of the magnitude-limited i − [3 .
6] subsample (COBRA103434.2+310352 at z ≈ z ≈ . − [4 . z ≈ . − [4 .
5] color cut for thatsample). The cyan contours indicate the surface density of red sequence galaxies as described in Golden-Marx et al. (2019). InCOBRA104254.8+290719, the host galaxy does not follow the [3 . − [4 .
5] color cut indicative of z > i − [3 . Golden-Marx et al.
Figure 3 . Illustration of the opening angle mea-surement technique, in this particular case for CO-BRA074410.9+274011. The greyscale image is an ≈ . (cid:48) × . (cid:48) µ m IRAC mosaic. The VLA FIRST ra-dio contours are overlaid in blue. The cyan lines that traceboth rays of the opening angle are drawn from the centerof each lobe component to the radio core. The magenta arcindicates where the opening angle was measured. et al. 1995), we probe a wide range of redshifts. Thus, weare not sensitive to lower power radio sources at higherredshifts.To verify which VLA FIRST detected radio com-ponents are associated with each COBRA bent radiosource, we individually search each field for the radiodetections within 120 (cid:48)(cid:48) of the central radio source coor-dinates reported in Paterno-Mahler et al. (2017). Wevisually inspect each component to confirm which de-tections are associated with each bent source. For 36of the 39 red sequence cluster candidates reported inGolden-Marx et al. (2019), we identified an obvious bentradio source consisting of at least two radio components(see Table A1 for these fields). For the remaining threeclusters, our further analysis of the radio source left usuncertain whether a bent radio source was truly presentin these cases or whether the initial detection was con-sistent with a chance alignment of unassociated radiosources. Due to this ambiguity, we remove these threefields from our analysis (these fields are marked in Ta-ble A1).To measure the opening angle of each bent, double-lobed radio source, we use the VLA FIRST radio com-ponents identified for all 36 sources. As mentioned pre-viously, these bent sources consist of two or three VLAFIRST identified radio detections (some bent sourceslack a radio detected core; see Table A2). We notethat although these are individual sources, the contoursshown in Figures 1, 2, and 3 are displayed to create asingle connected radio source when possible. They are not reported in the VLA FIRST catalog in this manner.Thus, to measure the opening angle, we use the posi-tion of each radio component’s central RA and DEC asreported in the VLA FIRST catalog. By visual inspec-tion, we identify which component is the central radiocore associated with the host galaxy and which compo-nents are radio lobes. For sources without a detectedradio core, we use the location of the optical/IR hostgalaxy as the core.To measure the opening angle of each bent source,we use the law of cosines, where the Opening Angle isdefined as:Opening Angle = arccos (cid:18) (H) − (L ) − (L ) − )(L ) (cid:19) . (1)In Equation 1, L and L represent the angular distancebetween the center of the radio core and the center ofeach radio lobe based on the reported RA and DECfrom the VLA FIRST catalog. Geometrically, L andL represent the sides of the triangle used to measurethe opening angle. H represents the line connecting thecenters of both radio lobes. Figure 3 shows a schematicof how the opening angle is measured.From these measurements of the opening angle, weconfirm that the majority of our sources are WAT-likesources with only a few sources being narrow-angle tail(NAT)-like sources; 27 of our bent radio sources haveopening angles greater than 90 ◦ , the minimum openingangle of typical WAT sources (e.g., Owen & Rudnick1976; Valentijn 1979; O’Dea & Owen 1985) and only 2 ofour sources are NAT-like, with opening angles less than45 ◦ (e.g., Owen & Rudnick 1976; Valentijn 1979; O’Dea& Owen 1985). This difference is vital to our analysisas WATs are typically found near cluster centers andhosted by more massive elliptical and cD galaxies, al-though counter examples exist (e.g., Sakelliou & Merri-field 2000), while NATs are typically associated with ra-dio AGNs at larger peculiar velocities farther from clus-ter centers (Owen & Rudnick 1976). That our sample isprimarily WATs indicates that these sources should bestrong tracers of cluster cores and generally near clustercenters (as seen in Figure 6; see Sections 3.1 and 4.1 fora description of how richness and opening angle relate).Beyond the opening angle, we are also interested inthe projected physical extent of each radio source. Tomeasure the physical size of the radio source, we firstmeasure the length of each arm of the “C” shape, bymeasuring the distance between the RA and DEC ofeach component reported in VLA FIRST. However, us-ing only the distance between the central position ofeach VLA FIRST source will result in an underestima-tion of the projected length of the radio source. Tocorrect for this, we follow Wing & Blanton (2011) andinclude the measured size of each radio component re-ported in the VLA FIRST database. Specifically, theVLA FIRST database reports the deconvolved majorand minor axis of an approximate elliptical fit for eachdetected radio component. Thus, to better measure the adio Parameters for the COBRA Survey
20 40 60 80 100 120 140 160 180
Opening Angle ( ◦ ) P r o j e c t e d P h y s i c a l S i z e o f t h e R a d i o S o u r c e ( k p c ) (r s = 0.27, p = 0.11) Figure 4 . The projected physical size of each cluster candi-date’s bent, double-lobed radio source as a function of theopening angle, measured as described in Section 2.5.1. Al-though no strong correlation exists between opening angleand physical size, we do find that the radio sources with thelargest physical sizes have the largest opening angles. full extent of each radio source, we add the length ofthe semi-major axis of each lobe component of the ra-dio source to the distance between the centers of theradio components measured earlier. We then convertour angular length measurement into a physical mea-surement by assuming the radio source at is at the hostcluster redshift using the Astropy Cosmology tool (As-tropy Collaboration et al. 2013, 2018).Although we aimed to measure the projected phys-ical size uniformly for each radio source, for CO-BRA074410.9+274011 (see Figure 3), the second lobehas no deconvolved semi-major or semi-minor axis be-cause the angular size is smaller than the deconvolu-tion. For this source, we use the reported convolvedsemi-major axis from the VLA FIRST survey catalogas our estimate of the additional length of the radiosource, although this yields an upper limit. For the fewsources where there are more than three components(i.e., multiple components in a single lobe), we deter-mine the size by measuring the distance between thecore and the radio component at the greatest distancefrom the core (again adding an additional factor of thebeam-deconvolved semi-major axis for that component).We estimate the error in the opening angle and an-gular size of the radio source (see Table A2) by prop-agating the reported positional uncertainty from VLAFIRST through the law of cosines and inverse cosineequations used to determine the length of the radio lobesand the size of the opening angle. For the size of the ra-dio sources, we convert the angular size of each radiosource to physical size and account for an additionalfactor of uncertainty associated with the redshift.For the 36 bent AGNs, we compare the physical sizeof the radio source and the opening angle, to one an-other in Figure 4. We adopt a Spearman Test (see Ap- pendix A) to determine if a correlation exists betweenthe opening angle and the projected physical size. Itreturns r s = 0.27 and p = 0.11, which corresponds to aweak correlation with insufficient evidence to reject thenull hypothesis, thus implying no strong correlation be-tween these measures. When we evaluate the mean andnormalized mean absolute deviation for bent AGNs withopening angles below and above 80 ◦ , we find that thesetwo samples are statistically similar. Interestingly, asshown in Figure 4 the only difference appears to be thatthe largest bent AGNs all have opening angles above80 ◦ , with the largest being the least bent. It is possiblethat the difference in the spread of the physical size ofthe radio sources is the result of small number statis-tics. We discuss if these radio properties are linked toany cluster properties in Sections 3 and 4.2.5.2. Radio Source Power
To measure the radio power of each AGN, we firstsum the integrated 20 cm flux density for each compo-nent reported in the VLA FIRST Catalog Database todetermine a total radio flux for each bent source. Weconvert this flux into power using Equation 2, P . = 4 π D L S . (1 + z ) α − , (2)where the (1+z) α − includes both the k-correction to1.4 GHz and distance dimming. In Equation 2, D L is theluminosity distance at the redshift of the AGN, whichis calculated in the same manner as for the size of theradio source, S . is the summed integrated flux densityof each component of our bent radio sources at the ref-erence frequency of the VLA FIRST survey (1.44 GHz),and α is the spectral index. Although there is some ob-served scatter in the measured values of α , with typicalvalues ranging from 0.7 to 0.8 (e.g., Kellermann & Owen1988; Condon 1992; Peterson 1997; Lin & Mohr 2007;Miley & De Breuck 2008), we chose to use a spectral in-dex of 0.8 for all of our bent radio sources, as this valueis typical of such extragalactic radio sources (Sarazin1988) and used in similar studies of AGN in high- z clus-ters (e.g., Paterno-Mahler et al. 2017; Moravec et al.2019, 2020b). We find a range of radio powers at1.44 GHz, from 6.4 × - 3.5 × W Hz − . As ex-pected, the least powerful sources are our lowest red-shift radio sources (COBRA15313.0 − z ≈ z ≈ W Hz − ,are at z ≥ ≈ W Hz − , making our sample similar to that ofMoravec et al. (2019). Also, as discussed in Golden-Marx et al. (2019), the majority of our sample are fainterthan the minimum radio power of the CARLA sample(P MHz ≈ . W Hz − (e.g., Wylezalek et al. 2013;Cooke et al. 2015).The typical P . divide between FRI and FRII radiosources is ≈ W Hz − (e.g., Fanaroff & Riley 1974;0 Golden-Marx et al.
Projected Physical Size of the Radio Sources (kpc) P . ( W H z − ) (r s = 0.55, p = 0.0005) Figure 5 . The radio power (P . ) of each radio source as afunction of the projected physical size of each radio source.We measure the radio power in Section 2.5.2. We determinethe physical size of each source using the redshift estimatesreported in Golden-Marx et al. (2019) and the radio sourcepositions and component sizes from VLA FIRST. We usethe radio fluxes reported in the FIRST Catalog Databaseto measure our radio power. We find strong evidence for apositive correlation between radio power and physical size. Ledlow & Owen 1996), and all but our two faintest andlowest redshift radio sources are above this threshold.Additionally, 16 of the 36 bent radio sources in our sam-ple fall within the range of the values reported for WATs(10 . W Hz − < P . < . W Hz − ) (e.g., Blan-ton et al. 2000, 2001; Wing & Blanton 2011). Given thelarge range of measured radio power, this implies thatbent morphology is not strongly tied to radio luminosity,though we do not report any sources that are more thantwo orders of magnitude above the FRI/FRII divide.As the radio sources in our sample are not singularpoint sources, we compare the physical extent of each ra-dio source with the power of the source. As expected, inFigure 5, we find that generally the most energetic radiosources are also those with the largest physical extent,in agreement with Moravec et al. (2020b). We furtherverify the strength of this correlation using the Spear-man test. We obtain r s = 0.55 and p = 0.0005, whichstrongly suggests a positive correlation and a rejectionof the null hypothesis. However, despite the uniformityof the VLA FIRST survey (Becker et al. 1995), these de-tections and any analysis are subject to Malmquist biasdue to the wide redshift range. In order to address thevalidity of this correlation, we note that the 1 mJy fluxlimit for VLA FIRST (Becker et al. 1995) correspondsto ≈ × W Hz − at z = 2.2, the redshift of ourhighest redshift cluster candidate. Thus, we are likelyunderestimating the true number of faint, high- z bentradio sources. In terms of the physical size of these radiosources, however, we are not limited by the angular reso-lution of VLA FIRST. The 5 (cid:48)(cid:48) beam size corresponds to ≈
41 kpc at z = 2.2, much smaller than our smallest ra-dio source. Thus, the lack of small ( <
200 kpc), bright
Projected Physical Offset between Cluster Center and AGN (kpc) N u m b e r o f C l u s t e r s Cluster Candidates
Figure 6 . Histogram showing the distribution of projectedphysical offsets between the bent, double-lobed radio sourcesand the red sequence cluster center. These offsets use themeasurements of the cluster center presented in Golden-Marx et al. (2019). We find that most radio sources are lessthan 200 kpc from the red sequence cluster center, althoughwe see sources offset by as much as ≈ ( > W Hz − ) radio sources is likely real, while thelack of large ( >
200 kpc), faint ( < W Hz − ) radiosources may not be.2.6. Radio Source Offsets from the Cluster Center
A cluster center based on the surface density of red se-quence galaxies was determined by Golden-Marx et al.(2019). Although Golden-Marx et al. (2019) showedthat the majority of their bent radio sources are off-set from the cluster center, we refine that measurementby focusing only on the cluster candidates. As men-tioned in Section 2.3.1, we determine the cluster cen-ter using a unit-weighted red sequence surface densitymeasurement, where we treat all red sequence galaxiesequally, using either the i − [3 . r − i , or [3 . − [4 . <
200 kpc. This isconsistent with the vast majority of our sources beingnear the cluster center because they are either brightestcluster galaxies (BCGs), other massive central galaxies,infalling galaxies near the cluster center, or outgoinggalaxies that have fallen through the cluster center. Toaddress whether the host galaxy is a BCG, we explorethe 3.6 µ m absolute magnitude of our host galaxies inrelation to the other surrounding red sequence galaxiesand the orientation of the bent radio lobes relative to ourcluster center (see Sections 3.1.1 and 3.3). We treat the3.6 µ m absolute magnitude as a proxy for stellar massas IR magnitudes at such wavelengths show no bias tostellar mass estimates (Lemaux et al. 2012) and typical,non-quasar, radio detected AGN should have IR bandsthat are generally uncontaminated by the AGN).However, the red sequence surface density measure- adio Parameters for the COBRA Survey µ m observations).To determine the difference between the two measure-ments of the cluster center, we compare the offset of theAGN to the BCG and to the new cluster center. Asseen in the top panel of Figure 7, most sources remainwithin 300 kpc, with the maximum offset between theAGN and BCG being ≈
530 kpc. As compared to thevalues from Sakelliou & Merrifield (2000), this is wellwithin the expected range of bent radio source offsets.We also compare the location of the BCG to our redsequence cluster centers. We find strong agreement be-tween the two locations, with 16 of the 27 sources beingoffset by less than 150 kpc. For these sources, our red se-quence center should not impact our analysis, althoughthe sources with larger offsets are obviously more im-pacted, especially in regards to the infall angle (see Sec-tion 3.3). Additionally, while misidentification of clustermembers is more likely for fainter galaxies, it is possiblethat some of our red sequence BCGs, especially thosenot hosting a bent AGN, are not true cluster members.That we see similar values between the location of theBCG and the red sequence cluster center reinforces theuse of the red sequence surface density, which should beless impacted by the misidentification of a single galaxy. COMPARING AGN PROPERTIES TO CLUSTERPOPULATION PROPERTIESIn this section, we compare the properties of COBRAbent, double-lobed radio sources to properties of theirhost clusters. Our goal is to elucidate the details of theevolutionary history of COBRA clusters. We begin bydetermining the relationship between the opening an-gle of the bent radio source and cluster richness (Sec-tion 3.1). We then determine the BCG fraction (Sec-tion 3.1.1) and examine the relationship between theAGN’s offset from the cluster center and the openingangle of the bent radio source (Section 3.2). Further-more, we measure the orientation of each bent radioAGN relative to the cluster center (Section 3.3). Lastly,we examine any correlation between the power of eachradio source and the richness of the surrounding cluster(Section 3.4). 3.1.
Cluster Richness
As bent radio AGNs are found in a wide variety ofclusters and groups, we aim to determine how the clus-ter environment impacts the bent radio AGN morphol-ogy, specifically in regards to the opening angle. Asboth Hardcastle et al. (2005) and Morsony et al. (2013)
Projected Physical Offset between AGN and BCG (kpc) N u m b e r o f C l u s t e r s Cluster Candidates with Red Sequence BCGs0 100 200 300 400 500 600 700 800
Projected Physical Offset between BCG and Cluster Center (kpc) N u m b e r o f C l u s t e r s Cluster Candidates with Red Sequence BCGs
Figure 7 . Histograms showing the distribution of the offsetbetween the red sequence BCG and the AGN or the newcluster center. The top panel shows the distribution of off-sets between the AGN and the BCG, while the bottom panelshows the distribution of offsets between the BCG and thered sequence cluster center. In each case, we remove thosesources without a red sequence selected host galaxy (primar-ily the quasars). In the top histogram, we find that 55%of our radio AGN are BCGs. In the bottom histogram, wefind general agreement between the location of the BCG andthe red sequence cluster center, implying that these differentestimates of the cluster center yield similar results. showed, the morphology of bent, double-lobed radiosources depends on the density of the ICM, as well as anumber of other factors relating to both the cluster andthe AGN. For our analysis, we quantify the cluster envi-ronment using the red sequence overdensities and com-bined overdensities as proxies for richness as reportedin Golden-Marx et al. (2019). We use the significanceand not the overall number of galaxies because we haveclusters at redshifts between 0.35 < z < i − [3 . Golden-Marx et al. m*+1 r − i , magnitude-limited i − [3 . . − [4 . s = − p = 0.034). If we fo-cus on the two m*+1 subsamples, both of which areat z < s = − p = 0.08). Ultimately, both the entire sample and them*+1 subsample show similar degrees of certainty as tothe likelihood of this trend.Since the overdensity significance is measured differ-ently in each subsample with respect to completenessand galaxy type, we examine the individual subsets. Be-cause the m*+1 i − [3 .
6] sample is the primary focus ofour analysis and the most statistically robust sample,that we detect evidence of a moderate anti-correlation(r s = − p = 0.008) strengthens the likelihood that thiscorrelation is real. The clusters in this sample are sta-tistically similar as they are limited to galaxies brighterthan m*+1, and thus the same relative absolute mag-nitude, as opposed to the magnitude-limited sample. Ifwe assume the significance of the overdensity of red se-quence members is indicative of the overall cluster mass(e.g., Rykoff et al. 2014; Gonzalez et al. 2019), then ourresult implies more massive clusters have narrower bentAGNs. As more massive clusters will, all else beingequal, have a denser ICM and ICM density directly im-pacts the opening angle, it follows that massive clustersshould host narrower bent sources.We further verify the anti-correlation between ourmeasure of cluster richness and the opening angle of thebent AGN by comparing the significance of the com-bined overdensity to the opening angle (bottom panelof Figure 8). As the combined overdensity weights thelikelihood each red sequence galaxy is at the redshiftwe estimate via EzGal, as well as the likelihood that thegalaxies that are redder and bluer than our red sequencecolor range are at our target redshift using detailed pho-tometric redshift estimates from the ORELSE survey(see Golden-Marx et al. 2019 for a complete descriptionof the combined overdensity and Lubin et al. 2009 forthe ORELSE survey), seeing a stronger relation confirmsthat the opening angle is tied to cluster richness (r s = − p = 0.003 for the entire sample, while r s = − p = 0.002 for the m*+1 subsample).These correlations between cluster richness and open-
20 40 60 80 100 120 140 160 180
Opening Angle ( ◦ ) S i g n i f i c a n c e o f R e d S e q u e n c e O v e r d e n s i t y Entire Sample (r s = -0.35, p = 0.034)m*+1 Sample (r s = -0.39, p = 0.08)m*+1 i − [3 . Cluster Candidates (r s = -0.64, p = 0.008magnitude-limited i − [3 . Cluster Candidates (r s = 0.48, p = 0.23)magnitude-limited [3 . − [4 . Cluster Candidates (r s = -0.68, p = 0.09)m*+1 r − i Cluster Candidates (r s = 0.10, p = 0.87)
20 40 60 80 100 120 140 160 180
Opening Angle ( ◦ ) S i g n i f i c a n c e o f C o m b i n e d O v e r d e n s i t y Entire Sample (r s = -0.48, p = 0.003)m*+1 Sample (r_ s = -0.64, p = 0.002)m*+1 i − [3 . Cluster Candidates (r s = -0.64, p = 0.008)magnitude-limited i − [3 . Cluster Candidates (r s = -0.02, p = 0.95)magnitude-limited [3 . − [4 . Cluster Candidates (r s = -0.68, p = 0.09)m*+1 r − i Cluster Candidates (r s = -0.90, p = 0.04) Figure 8 . The significance of the red sequence overdensity(top) and combined overdensity (bottom) as a function of theopening angle of the bent radio source. The m*+1 i − [3 . i − [3 .
6] sample is indicated by pink diamonds, the magnitude-limited [3 . − [4 .
5] sample is indicated by blue triangles, andthe m*+1 r − i sample is indicated by red squares. We boldthe two m*+1 samples because they are statistically simi-lar samples based on the magnitude of a modeled m* galaxywith EzGal. All significances reported are from Golden-Marxet al. (2019). We find a weak to moderate correlation be-tween the narrowness of the opening angle and both over-density measurements, which is reinforced when examiningthe m*+1 i − [3 .
6] subsample. ing angle point towards the cluster environment beinga strong indicator of the opening angle. We also findno evidence of a relation between the absolute magni-tude of the host galaxy and the opening angle, whichfurther points to the cluster environment being the pri-mary driver of the bent appearance of each radio source.However, the opening angle of a bent radio sourcedepends on the ICM density and velocity of the hostgalaxy relative to the ICM (e.g., Hardcastle et al. 2005;Morsony et al. 2013). Because massive clusters havegalaxies with a greater velocity dispersion at large off- adio Parameters for the COBRA Survey s = − p value increases from 0.034 for thefull sample to 0.12 for the subsample). However, withinthe m*+1 i − [3 .
6] sample, we see stronger evidence ofthis anti-correlation for the clusters with closer AGN(r s = -0.80 and p = 0.003), making this anti-correlationvery likely. Similarly, when we compare the combinedoverdensity to the opening angle for the subsample ofclusters where the AGN is near the cluster center, wefind agreement with our previous result (r s = -0.55 and p = 0.004 for the entire subsample and r s = -0.70 and p = 0.016 for the m*+1 i − [3 .
6] subsample). That theserelationships mirror one another for the complete sampleand the subsample of clusters where the AGN is closerto the cluster center indicates that AGN offset is nota latent parameter in the correlation between openingangle and cluster richness and that the bent nature maybe more linked to the overall cluster richness, or ICMdensity if these two parameters scale.Additionally, there is a greater possibility that thesesources at larger offsets are not associated with the clus-ters with which we identify them. Golden-Marx et al.(2019) note that using the color cuts, especially the i − [3 .
6] color cut, and red sequence range ( ± ≈ (cid:48) background regionswould be detected as cluster candidates, depending onthe color (see Section 6.3 in Golden-Marx et al. 2019 forthe complete description of background contamination).These random regions had a separation of ≈ (cid:48) on av-erage, making random associations with bent sourcesunlikely. However, as noted by the analysis using theORELSE data for the combined overdensity, some frac-tion of redder and bluer galaxies at a given redshift arecluster members, meaning it is possible that we could bemisidentifying the cluster center or the cluster entirely.To further strengthen the result that narrower bentsources are in richer clusters, we plot the significanceof cluster candidates as a function of redshift (Figure 9)to show that this correlation does not come from red-shift differences in our sample since the significance ofthe combined overdensity is not a function of redshift. Redshift (z) S i g n i f i c a n c e o f C o m b i n e d O v e r d e n s i t y m*+1 i − [3 . Cluster Candidatesmagnitude-limited i − [3 . Cluster Candidatesmagnitude-limited [3 . − [4 . Cluster Candidatesm*+1 r − i Cluster Candidates
Figure 9 . The significance of the combined overdensity as afunction of redshift. The same legend is used as in Figure 8.As before, all significances reported are from Golden-Marxet al. (2019). Excluding the magnitude-limited [3 . − [4 . Specifically, the two m*+1 samples show no correlationswith redshift, meaning that we are not biasing thesemeasurements towards the lowest redshift sources in oursample. This highlights that the detected correlationbetween richness and opening angle is not an artifact ofour cluster detection, but representative of a real effectand further strengthens that the opening angle of thebent source is directly correlated with the surroundingcluster environment.3.1.1.
Measurements of the BCG Fraction and aComparison between the Host Galaxies and Cluster
To further understand the relationship between bent,double-lobed radio sources and the cluster environment,we aim to determine if the host galaxies of these radiosources are BCGs. Because we are examining clusters ata range of redshifts (0.35 < z < z BCGthrough galaxy-galaxy mergers (e.g., Lidman et al. 2012;Ascaso et al. 2014).To determine what fraction of our host galaxies areBCGs, we compare the host galaxy for each COBRAbent radio source, identified in Paterno-Mahler et al.(2017) using the
Spitzer µ m observations, to thesurrounding red sequence galaxies. Because the red se-quence is our best tool for identifying potential clustermembers, we focus only on the red sequence galaxieswithin either the 1 (cid:48) ( ≈
480 kpc at z = 1) region centeredon the red sequence cluster center or the 1 (cid:48) region cen-4 Golden-Marx et al. µ m Absolute Magnitude (AB) P r o j e c t e d P h y s i c a l O ff s e t b e t w ee n C l u s t e r C e n t e r a n d A G N ( k p c ) BCG Host ClustersAll Host Galaxies
Figure 10 . The projected physical offset between the hostgalaxy of the bent radio AGNs and the cluster centers (kpc)as a function of the host galaxy’s 3.6 µ m absolute magnitude.Host galaxies that are BCGs are identified by a red box. Wesee a dichotomy, where most of the galaxies brighter than − tered on the bent radio AGN. We examine both regionsbecause in a few cases the center of the red sequencesurface density is offset from a BCG that appears whencentered on the AGN, and this BCG may be more rep-resentative of the cluster than a fainter bright galaxy.Based on the host galaxies, our red sequence color cut,and our redshift estimates, we find that 27 of the hostgalaxies lie along the red sequence. The remaining 9host galaxies are either SDSS-identified quasars, havecolors that differ from their redshift estimate becauseeither the redshift estimate is from SDSS or from thecolor of the surrounding galaxies, or lack an identifiedhost galaxy. Although the SDSS-identified quasar mayhave host galaxies that are the BCG, the photometryis dominated by the emission of the AGN (Stern et al.2012), making these galaxies bluer than our expectedred sequence members and thus the host magnitude apoor proxy for stellar mass.Of this subsample of 27 red sequence galaxy clustercandidates, 15 host galaxies are BCGs ( ≈ µ m absolute magnitude as a functionof the offset between the cluster center and the AGN.To have a uniform proxy for stellar mass for the entiresample, we k-correct each host galaxy’s 3.6 µ m appar-ent magnitude via EzGal using identical parameters tothose reported in Golden-Marx et al. (2019). We note that the host galaxy in COBRA164951.6+310818 is anoutlier (see Figure 10). This galaxy is the faintest hostgalaxy by far (M . = − z ≈ µ m absolute magnitude in Figure 10, we re-iterate that most of our host galaxies are near the clustercenter. However, we also show that although almost allof our host galaxies are luminous, all but one of thegalaxies fainter than − >
400 kpc). In Figure 10,we see that two of the host galaxies at the largest off-sets have M . ≈ − > σ )where the host galaxy is a BCG, we see a strong corre-lation (see Figure 11; r s = − p = − The Relationship Between the Opening Angle andthe Cluster Offset
As shown in Section 2.6, bent, double-lobed radiosources are found both near to and offset from the clus-ter center. Additionally, Figure 10 highlights that someof our faint host galaxies are at the largest offsets fromthe cluster center. Here, we aim to determine if the dis-tributions of offsets from the red sequence cluster centeror the opening angle of the bent AGNs differ among ourBCG and non-BCG galaxy populations. As we see in adio Parameters for the COBRA Survey µ m Absolute Magnitude (AB) S i g n i f i c a n c e o f C o m b i n e d O v e r d e n s i t y Entire Sample (r s = -0.01, p = 0.95)BCG Host Clusters (r s = 0.1, p = 0.73 [if > 3.5 σ , r s = -0.62, p = 0.08]) Figure 11 . The significance of the combined overdensity ofeach cluster candidate as a function of the host galaxy’s3.6 µ m absolute magnitude (AB). All of the overdensities aremeasurements presented in Golden-Marx et al. (2019). Wesee no correlations between the 3.6 µ m absolute magnitudeof the host galaxy and either measurement of richness for theentire sample. When we divide out the bent AGNs hostedby BCGs, we measure a strong anti-correlation between thecombined overdensity significance and host absolute magni-tude for the richest clusters ( > σ overdensity). Figure 6, the majority of the 36 bent radio sources inour sample have offsets from the cluster center less than200 kpc, similar to that of Sakelliou & Merrifield (2000).Figure 12 shows that there is a smaller range of phys-ical offsets for narrower opening angles. This may bean artifact of the relatively few narrow radio sources inour sample. However, we see a similar trend betweenthe BCG host galaxies and the non-BCG/quasar hostgalaxies. We confirm this using a Kolmogorov-Smirnov(KS) test for each of the two parameters and find thatfor both the projected physical offset between the AGNand cluster center and the opening angle of the bent ra-dio source, there is no evidence that these samples aredrawn from different distributions (if we assume p =0.1 as the minimum value indicating two quantities aredrawn from the same population, we find p = 0.14 forthe offsets and p = 0.30 for the opening angles). Thisreinforces that our host galaxies are likely from the samepopulation of cluster galaxies, with all of our host galax-ies being high- z BCGs or BCG candidates/proto-BCGs.Interestingly, all of the quasars have relatively largeopening angles and four of the six quasars are offsetat distances greater than 600 kpc. Similarly, Mo et al.(2018) found that the density of optical, mid-IR, andType II AGNs peaks near the cluster center, but that thepopulation of Type I AGNs peaks away from the clustercenter and approaches field values near the center. Asstated previously, the host galaxies of most bent AGNscan be modeled as typical early-type galaxies, where theAGN’s nucleus is obscured (Type II AGNs). Thus, ourresults, which show most of the bent AGNs are near thecluster center, agree with Mo et al. (2018). Since most
200 0 200 400 600 800 1000 1200 1400Projected Physical Offset between Cluster Center and AGN (kpc)20406080100120140160180 O p e n i n g A n g l e ( ◦ ) Host Galaxies (Non-BCG/Quasars)BCG Host GalaxiesQuasar Host Galaxies
Figure 12 . The opening angle of each bent AGN as afunction of the projected physical offset between the clus-ter center and the AGN host galaxy. We separate the hostgalaxies into three different types, quasars (blue triangles),BCGs (red diamonds; see Section 3.1.1 for a description onhow we determine if a host galaxy is a BCG), and non-BCG/quasar host galaxies (black circles). Both the BCGand non-BCG/quasar host galaxy populations follow similardistributions, indicating that all COBRA radio host galaxiesmay be proto-BCG candidates. Golden-Marx et al. (2019). quasars are Type I AGNs, the COBRA quasars couldbe representative of such a population of radio sourcestypically offset from the cluster center.Although we determine the BCG differently fromGaron et al. (2019), who also study a sample of bentsources made up primarily of WATs, they also find thatnon-BCG galaxies in their 0.02 < z < θ < ◦ and offset more than200 kpc. Given the higher redshift nature of our sam-ple, it is possible that these narrower sources are simi-lar to some of the sources with smaller opening anglesmeasured in the Garon et al. (2019) sample (our lowestredshift source, COBRA164611.2+512915, follows thistrend by being a non-BCG host galaxy that is very nar-row). Within our sample, the lack of lower-mass in-falling host galaxies with narrow opening angles mightbe due to either an evolutionary effect or the detectionlimits of the VLA FIRST survey.3.3. The Direction of Radio Sources Relative to theCluster Center
In order to determine what physical mechanism mightbe responsible for bending the radio lobes in these CO-BRA clusters (e.g., an infalling/outgoing host galaxy ora central host galaxy involved in either a major or mi-nor merger; e.g., Sakelliou & Merrifield 2000; Douglasset al. 2011; Paterno-Mahler et al. 2013), we examine thedirectional component of the radio source relative to the6
Golden-Marx et al.
InfallingOutgoing
Figure 13 . Illustration of the difference in orientation be-tween a directly infalling and outgoing radio source. Here,the cluster is depicted via the large purple circle and thecluster center is shown by the blue triangle. The infallingand outgoing radio sources, both shown in red/orange, arelabeled and have yellow velocity vectors to describe the di-rection of motion relative to the cluster center. cluster center. Although we previously constrain whichradio sources are BCGs (see Section 3.1.1), because wedo not treat these BCGs as the cluster center, we treatall bent radio sources as potentially infalling/outgoinggalaxies in this analysis.If the host galaxy of the bent AGN is infalling radiallytoward the cluster center, the orientation of the open-ing angle of the bent radio source should point towardthe cluster center (see Figure 13). If the radio source isoutgoing, it will open toward the cluster center. Addi-tionally, dynamical friction acting on the bent sourcesas they pass through the cluster center should result inoutgoing galaxies being closer to the cluster center thanthe most offset infalling galaxies.After identifying the infalling and outgoing bentsources, we adjust the offsets shown in Figure 6 to ac-count for this dichotomy. We report outgoing galaxiesas being at negative distances and infalling galaxies asbeing at positive distances. As seen in Figures 6 and 14,the majority of our radio sources are within ±
200 kpcof the cluster center. For sources within ±
100 kpc, it ispossible that some of the discrepancy between infallingand outgoing sources might result from error in our clus-ter center measurement since we do not weight the clus-ter center by galaxy mass or luminosity.The major takeaway from Figure 14 comes from thespread in the offsets. Although we see a similar num-ber of infalling and outgoing radio sources (21 to 15),infalling radio sources extend up to ≈ ≈
600 kpc from the center, which is expected due to dy-namical friction. However, all three infalling sources atdistances greater than 1000 kpc are quasars, where thepossibility of miscentering is higher given the quasarsnon-red color and our use of the red sequence to iden-tify the cluster center. Thus, the difference in the offsetpopulations may be an artifact of our analysis, not a
Directional Projected Physical Offset between Cluster Center and AGN (kpc) N u m b e r o f C l u s t e r s Cluster Candidates
Figure 14 . Histogram showing the distribution of the direc-tional offset of each bent radio source from the cluster center.To differentiate radio sources that are infalling and outgoing,we display outgoing radio sources as negative distances andinfalling radio sources as positive distances. The magnitudeof these distances are identical to those shown in Figure 6,only adjusted for direction. We find that most radio sourcesare ±
200 kpc from the cluster center, but see that the spreadof possible separations is greater for infalling radio sources,as expected due to dynamical friction. physical property. However, it is alternatively possiblethat these quasars represent AGNs that are triggered byinfall into the cluster as shown by their large offsets.For all measurements of the infall angle, projectioneffects are highly problematic. We measure the open-ing angle assuming the radio source is moving on a flat2D projection of space, when the AGNs could be mov-ing into or out of the plane of the sky at any possi-ble angle. When the third dimension is unfolded, it ispossible to have infalling radio sources that appear tobe outgoing from our viewing angle (and vice versa).Thus, although we determine which side the bent radiosource is pointing relative to the cluster center, thesemeasurements have a large associated uncertainty. Fur-thermore, it is possible that some of the host galaxiesclassified as infalling and outgoing galaxies are actuallycentral BCGs where the bent lobes form via the sloshingor large-scale merger motions of the ICM rather than in-falling/outgoing cluster galaxies. As not all bent sourcesare opening directly away from or towards the clustercenter, this is particularly important.Although bent sources can be infalling or outgoing,they do not always follow directly radially paths. As ourprevious measurement assumed this, we explore whetherour bent sources are infalling or outgoing by measuringthe infall angle relative to the cluster center. We dothis by measuring the angle between the line bisectingour bent radio sources and the line connecting our hostgalaxies to our red sequence cluster center (this is donein a similar manner to Sakelliou & Merrifield 2000; seeFigure 15 for an example). Unlike the previous mea-surement, we do not use a strict dichotomy, but instead, adio Parameters for the COBRA Survey Figure 15 . Illustration of the infall angle measurement tech-nique, for the case of COBRA074410.9+274011. The grey-scale image is an ≈ (cid:48) × (cid:48) cutout of the 3.6 µ m IRAC mosaic.The VLA FIRST radio contours are overlaid in blue, whilethe surface density of red sequence galaxies is indicated bythe red contours. The cyan lines trace the opening angle ofthe VLA FIRST radio components. The yellow lines tracethe line connecting the cluster center to the center of theradio source and the center of the radio source about thebisector. The magenta arc indicates where the infall angle ismeasured. Using our initial methodology, this radio source isfound to be infalling at a distance of ≈ ◦ . are less restrictive in our designation. By construction,an angle of 0 ◦ corresponds to an outgoing galaxy thathas fallen through the cluster center along a radial pathwhile an angle of 180 ◦ corresponds to a perfectly radiallyinfalling bent radio source. We define bent sources thatare outgoing as having angles less than 45 ◦ and bentsources that are infalling as having angles greater than135 ◦ . We find peaks in our sample around 35 ◦ and 130 ◦ .Although few of our radio sources follow direct radialpaths relative to our red sequence cluster centers, theypeak near the infalling and outgoing regime (see Fig-ure 16). While we have a number of radio sources thatare infalling/outgoing, we see a large population of ra-dio sources on less radial paths. It is possible that thesesources represent bent sources following circular paths orthat these bent AGNs are actually central BCGs, wherethe bent nature is due to interactions in the ICM (e.g.,sloshing spiral clusters as in Paterno-Mahler et al. 2013or large-scale cluster mergers as in Douglass et al. 2011).As with the previous measurements, projection effectsimpact our measurement of the direction of a galaxy’smotion and will impact our measurement of infall an-gle. In this case, projection effects may account for thelarge number of sources at intermediate angles in ourmeasurement and mean that our errors are likely under- Angular Offset between the Bisector of the Bent Radio Lobes and the Cluster Center ( ◦ ) N u m b e r o f C l u s t e r s Cluster Candidates
Figure 16 . Histogram showing the distribution of infall an-gles of bent radio source relative to the cluster center. Wedefine the infall angle as the projected angle between the bi-sector of the bent radio source’s opening angle and the lineconnecting the bent radio source to the cluster center. An-gles of 0 ◦ - 45 ◦ corresponds to a galaxy that is outgoing,while an angle of 135 ◦ - 180 ◦ corresponds to a galaxy thatis infalling. We find few radio sources are directly infallingor outgoing. Rather, most of our sources are at intermediateangles, though we see a large population of sources that areoutgoing. estimated.3.4. Radio Power and Cluster Richness
Our earlier analysis of the anti-correlation betweencluster richness and the opening angle of the radio sourceleads us to ask whether a similar relationship exists be-tween the power of the radio source and the surroundingcluster environment, quantified via richness. Figure 17presents our measurement of radio power versus clus-ter richness, which shows a slight anti-correlation; richerclusters host less powerful radio sources. However, theSpearman test shows that while there is a weak anti-correlation (r s = − p = 0.11). Using the Spear-man test on the m*+1 i − [3 .
6] subsample, we again finda very weak anti-correlation, and no evidence to rejectthe null hypothesis.The lack of any strong correlations is similar to otherhigh- z cluster surveys. Using the complete CARLA sur-vey (1.3 < z < . − [4 . > − z ≈ < z < Golden-Marx et al.
Significance of Red Sequence Overdensity P . ( W H z − ) Entire Sample (r s = -0.27, p = 0.11)m*+1 i − [3 . Cluster Candidates (r s = 0.15, p = 0.57)magnitude-limited i − [3 . Cluster Candidates (r s = -0.05, p = 0.91)magnitude-limited [3 . − [4 . Cluster Candidates (r s = -0.60 p = 0.16)m*+1 r − i Cluster Candidates (r s = -0.59, p = 0.03) Significance of Combined Overdensity P . ( W H z − ) Entire Sample (r s = -0.27, p = 0.11)m*+1 i − [3 . Cluster Candidates (r s = -0.06, p = 0.81)magnitude-limited i − [3 . Cluster Candidates (r s = -0.23, p = 0.57)magnitude-limited [3 . − [4 . Cluster Candidates (r s = -0.60, p = 0.16)m*+1 r − i Cluster Candidates (r s = -0.10, p = 0.87) Figure 17 . The radio power of bent AGNs as a function ofthe significance of the red sequence overdensity (top) andcombined overdensity (bottom). The same legend as in Fig-ure 8 is used. All significances reported are from Golden-Marx et al. (2019). For the entire sample, we see a weakanti-correlation between significance of the overdensity mea-surement and the radio power. However, the p value for thistrend makes the likelihood that this is a real trend unlikely.Furthermore, the lack of an apparent trend within the m*+1 i − [3 .
6] subsample might instead point to weak to no evidenceof a correlation between these quantities. sources and cluster richness (much stronger than theone presented in Moravec et al. 2020b), while Wing &Blanton (2011) saw no correlation in their sample ofclusters with bent AGNs at similar redshifts. Becauseour clusters are selected via a similar methodology toWing & Blanton (2011) and Croston et al. (2019) sawthis trend only among their richest clusters, this mightindicate that such a relationship only develops withinthe richest and most massive clusters at low-redshift,which we do not expect our sample to include. DISCUSSIONAs shown in Section 3, by correlating the propertiesof bent, double-lobed radio sources with their host clus- ters, we gain insight into what bends double-lobed radiosources. As highlighted in our introduction, althoughCOBRA is unique in its use of bent radio AGNs ascluster finders at high redshift, there are a number oflarge radio AGN targeted cluster surveys, some of whichalso include bent radio sources. To contextualize ourhigh- z bent, double-lobed radio sources with respect toother samples of high- z clusters with radio galaxies andother samples of bent sources, we compare our resultsto other surveys and explore additional potential corre-lating properties of radio galaxies and their host clus-ters. We first compare our anti-correlation of clusterrichness and opening angle to other cluster surveys inSection 4.1. We then compare the infall angle of CO-BRA clusters to similar low- z samples of bent sourcesin Section 4.2. Lastly, we see how these offsets scale withthe radio parameters in Section 4.3.4.1. Cluster Richness and Bending Angle
As shown in Figure 8, we see an anti-correlation be-tween the strength of the overdensity and the size of theopening angle, with narrower bent sources being foundin richer environments. As mentioned previously, thiscould indicate that these richer clusters have a moredense ICM, if all else is equal. Currently, six COBRAclusters, five of which are in this sample, have X-rayobservations, either with XMM-Newton,
Chandra , orSwift (Blanton et al. in prep, Paterno-Mahler et al. inprep) and we are applying for additional Chandra andXMM-Newton observations to characterize the ICM.With these future observations, we aim to determinehow well the optical/IR red sequence overdensities tracecorrespondingly strong ICMs as well as the dynamicalstate of that ICM.To further validate that the opening angle of a bentAGN is narrower in richer clusters, we measured theopening angles of bent sources at similar redshifts thatare not in cluster candidates. Because there is no largesample of field galaxies hosting bent AGNs at high red-shift, we compare the distribution of opening angles forthe 36 bent AGNs in our cluster sample to the sampleof 38 bent AGNs with optical observations that are notred sequence cluster candidates in Golden-Marx et al.(2019). Although this is not a true representation offield bent AGNs because our optical follow-up obser-vations were chosen based on richer 3.6 µ m overdensitymeasurements from Paterno-Mahler et al. (2017), thecluster environment of these sources is measured uni-formly to the sample presented here.Although we again find a range of opening angles, thedistributions between these two samples do not mirrorone another. Within cluster candidates, we find 25.0%of bent radio sources have opening angles < ◦ , while7.9% of bent radio sources in poorer environments haveopening angles < ◦ . We find 41.7% of bent radiosources in cluster environments have opening angles at90 ◦ < θ < ◦ , while 34.2% of bent sources in poor envi-ronments have opening angles in that range. Among the adio Parameters for the COBRA Survey > ◦ , while 57.9% of bentradio sources in poor environments are in this range.The bent AGNs not in red sequence clusters tend to, onaverage, be less bent, which agrees with Wing & Blan-ton (2011), who found that bent sources of any openingangle are more commonly in low- z cluster than theirstraight counterparts. However, despite this apparentagreement, Wing & Blanton (2011) did not find anycorrelation between the opening angle of the bent radiosource and cluster richness. This difference may resultfrom our different richness measurements, as Wing &Blanton (2011) did a single band overdensity based onthe number of galaxies brighter than M r = − Cluster Offsets and Infall Angle
Not all COBRA bent, double-lobed radio sources areat the center of our clusters (see Figure 6). Sakelliou& Merrifield (2000), with their small sample of low- z bent sources, found similar results in terms of the dis-tributions of the offsets of the bent radio sources fromthe cluster center using X-ray observations to locate thecluster centroid. Sakelliou & Merrifield (2000) similarlymeasured the angle of the bent radio source relativeto the cluster center, although they define the anglesslightly differently than our measurement in Section 3.3.Sakelliou & Merrifield (2000) found that 11 of their 17sources are infalling, 4 are outgoing, and 2 are at inter-mediate angles. By contrast, we find that 3 of our 36sources are infalling, 11 are outgoing, and 22 are at inter-mediate angles. Although the distributions of infallingand outgoing galaxies differ between our two samples,both show that the farthest outgoing radio sources arecloser to the cluster center than the farthest infallingsources. As discussed in Section 3.3, this may result fromdynamical friction slowing down infalling galaxies.To determine if the differences in distribution are theresult of inaccuracies in our cluster center, we also mea-sure the infall angle using the BCG as the cluster center.Using the purely directional measure of determining ifsources are infalling or outgoing relative to the BCG,we find that 6 of the 12 non-BCG host galaxies are in-falling and 6 are outgoing relative to that BCG (all areat distances less than 530 kpc). If we instead measurethe infall angle relative to the BCG, we find that 4 are outgoing (at angles < ◦ ), none are infalling, and 8at intermediate angles. While it is intriguing that noneof our sources are directly infalling, that a third of thesources appear outgoing supports the notion that we aredetecting a real population of outgoing cluster galaxies.One cluster with an outgoing radio source is CO-BRA135136.2+543955, which was previously identifiedin Wen et al. (2012). The AGN is offset less than 200 kpcfrom the cluster center, which does not correspond to theBCG. If the BCG is the actual cluster center, then CO-BRA135136.2+543955 still appears to have an outgoingradio source, though at a smaller angle. Interestingly,COBRA135136.2+543955 is one of the few clusters inour sample with two distinct radio sources at the sameredshift, the second of which is associated with the BCG(COBRA151458.0 − σ and greateroverdensities appear in ≈ σ . Using the red sequence overdensity,we include 22 cluster candidates in our sample and find1 is infalling, 7 are outgoing, and 14 are at intermediateangles. These values correspond to very similar frac-tions of sources as the total sample of all cluster candi-dates, with all values falling within Poisson error values(4.5% vs 8.3% for infalling sources, 31.8% vs 33.3% foroutgoing sources, and 63.6% vs 58.3% for intermediatesources). Similarly, using the combined overdensity, weinclude 24 cluster candidates and find 1 is infalling, 8are outgoing, and 15 are at intermediate angles. Again,our fractions mirror those of the total sample (4.2% vs8.3% for infalling sources, 33.3% vs 33.3% for outgoingsources, and 62.5% vs 58.3% for intermediate sources).That we see a similar distribution for this richer cutimplies that our measurements are not biased by ourweakest, less well constrained, cluster candidates.Sakelliou & Merrifield (2000) hypothesized that the0 Golden-Marx et al. lack of a large populations of outgoing radio sources mayresult from the dense ICM at the center of a cluster thatwould be shock heated by cluster-cluster mergers, whichmay also bend the radio lobes. However, the clusters inthe Sakelliou & Merrifield (2000) sample are all at z < σ ) we find 4 outgoing fields (3 have weakercombined overdensities). Additionally, we find that 6 ofour 11 outgoing radio sources are at z > Spitzer
IRAC F.O.V.). Similarly, Novikov et al. (1999)showed that bent radio sources are preferentially ori-ented along supercluster axes. Thus, this discrepancycould be explained if we are not identifying the entirecluster structure.4.3.
Cluster Offset, Radio Source Size, and BendingAngle
Moravec et al. (2019) presented a relationship be- tween the projected physical offset of an AGN from thecluster center and the size of the radio source and fur-ther strengthened this trend using the expanded MaD-CoWS sample in Moravec et al. (2020b). As discussed inMoravec et al. (2019), the size of the radio source shoulddepend on the power of the jet, the density of the sur-rounding medium (both our sample and the Moravecet al. 2019 sample highlight that radio loud AGN arenot always at the center of the cluster, allowing theICM density to be a function of the offset from the clus-ter center), and the age of the radio source. Like theMoravec et al. (2019) sample, our sample has no directmeasurement of the ICM density and the age of the radiosources. As such, we follow Moravec et al. (2019) andnormalize the radio powers to a fiducial power, creatinga normalized radio source size using Equation 3, Le norm = Le (cid:18) P P . (cid:19) , (3)and compare this to the offset between the radio sourceand the cluster center from Golden-Marx et al. (2019).We re-write the relationship in Equation 4, Le norm = 10 − . ± . D . ± . , (4)where D is the distance between the cluster centerand the radio source, Le norm is the normalized size ofthe radio source, P is the normalizing radio power at1.44 GHz (2 × W Hz − ), and P . is the power ofthe radio source in 1.44 GHz.The MaDCoWS subsample from Moravec et al. (2019)followed the trend with only minimal scatter at smallercluster offsets, while the larger sample in Moravec et al.(2020b) showed more scatter (the 1 σ scatter on the trendin Figure 18 is calculated using the full sample fromMoravec et al. 2020b). However, as Figure 18 shows,we see no agreement with Moravec et al. (2019), withmost of our sources falling outside the 1 σ scatter.Because the sample in Moravec et al. (2020b) only in-cludes three bent AGNs, we include the opening anglewithin Figure 18 to determine if the opening angle maybe a latent parameter responsible for this discrepancy.At small offsets ( <
100 kpc), Moravec et al. (2020b) alsosee a separate population of sources well above the trendfrom Moravec et al. (2019). The disagreement betweenthe trend and our measurements in this regime could bethe result of the most central radio sources being funda-mentally different, as shown in the relationship betweencluster offset and opening angle in Garon et al. (2019).When combined with Figure 12, this may suggest thatcentrally located radio sources, which include the fullrange of radio source luminosities and opening anglesfor our sample, are more impacted by the dense cen-tral ICM, rather than the uniform ICM assumed in thisrelation.Interestingly, the bulk of our sources follow a slopesimilar to the one reported in Moravec et al. (2019).These sources are also primarily the narrowest bent ra-dio AGNs, making it possible that the offset from the adio Parameters for the COBRA Survey σ ), wherethe offset is better constrained, it is even more likelythat the bending yields in a fundamental difference.Similar to the least offset sources, most of our moreoffset sources (beyond 300 kpc) follow a similar slope tothe trend in Moravec et al. (2019), although fewer arein rich clusters. These points are primarily wider bentsources and mostly fall within the 1 σ error estimate fromMoravec et al. (2020b). The slightly better agreementwith Moravec et al. (2019) may further indicate that theopening angle is a latent parameter. However, the di-vergence from this trend at the farthest offsets could bedue to AGNs having a finite size. Moravec et al. (2019)and Moravec et al. (2020b) raise the possibility that theradio source size is limited by the density of the ICMacting to prevent the AGN’s outflow. The lack of thistrend at greater distances may indicate that the densityof the ICM only inhibits an AGN’s size up to a certainpoint, where the intrinsic properties of the AGN becomedominant and a shock front forms creating a lobe. Suchan environmental impact could also be similarly linkedto the large population of wide opening angles at largeoffsets (Figure 12) and in less rich cluster environments(Figure 8).Alternatively, the MaDCoWs sample and detectionmethods may differ enough to create the offsets be-tween COBRA sources and the trend from Moravecet al. (2019). While we use a uniformly weighted redsequence surface density to determine the cluster cen-ter, MaDCoWs uses a combination of a number andflux weighted measurement (Gonzalez et al. 2019). Ad-ditionally, MaDCoWs selects some of the most massiveclusters at 0.7 < z < z ORELSE survey. After break-ing their sources into high and low density bins, Shenet al. (2020) found that like Moravec et al. (2019), morecompact radio sources are generally closer to the clustercenter, with most of their more massive structures fallingwithin 1 σ of the trend from Moravec et al. (2019). How-ever, they were also unable to recreate the trend fromMoravec et al. (2019) using their own data. That Shenet al. (2020) saw more agreement among their massivesystems could further illuminate the discrepancy in ourdata since we expect bent sources to trace both rich andpoor clusters. Furthermore, as discussed in Shen et al.(2020), it is also possible that the disagreement betweenour values and the trend from Moravec et al. (2019)stems from the VLA FIRST observations having a 5 (cid:48)(cid:48) Log of Projected Physical Offset between Cluster Center and AGN (kpc) L o g o f N o r m a li z e d P r o j e c t e d P h y s i c a l S i z e o f t h e R a d i o S o u r c e ( k p c ) Trend from Moravec et al. (2019)Error from Moravec et al. (2020)Combined Significance > σ m*+1 i − [3 . Cluster Candidatesmagnitude-limited i − [3 . Cluster Candidatesmagnitude-limited [3 . − [4 . Cluster Candidatesm*+1 r − i Cluster Candidates O p e n i n g A n g l e ( ◦ ) Figure 18 . The log of the normalized physical size of eachradio source as a function of the log of the physical offsetbetween the cluster centers and bent AGNs. We color eachpoint depending on the opening angle, noting that all sourceswith opening angles below 90 ◦ are colored cyan. The pointssurrounded by red hexagons show clusters with combinedoverdensity significances above 3 σ . The trend from Moravecet al. (2019) is overlaid in red and the 1 σ error calculatedusing the full sample from Moravec et al. (2020b) is shownin the dashed black line. We find little agreement with thetrend reported in Moravec et al. (2019) and see instead thatthe most narrow bent radio sources tend to be offset fromthis trend, though they follow a similar slope. resolution, while the JVLA observations from Moravecet al. (2019) have 1 (cid:48)(cid:48) - 2 (cid:48)(cid:48) resolution. This differencewould primarily inflate the size of our smallest sources,which is one regime where we find little agreement withthe trend from Moravec et al. (2019). CONCLUSIONThis is the third in our series of high- z COBRA papersand the first to evaluate the radio properties of eachcluster’s radio host galaxy beyond reporting the radioluminosity. We investigate the radio properties of 39 redsequence cluster candidates identified in Golden-Marxet al. (2019) and combine our optical/IR imaging withthe VLA FIRST radio observations to re-evaluate theradio properties of the bent, double-lobed radio sourcesin each cluster. Below is a summary of our findings. • Radio M orphology and P ower : From our sampleof 39 red sequence cluster candidates, we confirmbent AGNs in 36 cluster candidates. By measuringthe radio power and physical size of each source,we find that the brightest radio sources are gener-ally the largest radio sources, although no correla-tions between the opening angle of the bent AGNand the size of the AGN are detected. • Cluster Richness and Opening Angle : Using thesample of 36 bent radio sources, we examine therichness of the surrounding cluster relative to theopening angle. We find that richer clusters (mea-sured using the significance of our red sequence2
Golden-Marx et al. and combined overdensities) host narrower bentradio AGN. If all things are equal, this implies thatricher clusters in our sample have denser ICMs,which are responsible for bending the radio lobes. • BCG F raction : From our sample of 36 clus-ter candidates, we use the red sequence measure-ments from Golden-Marx et al. (2019) to measurethe fraction of host galaxies that are BCGs. Forthis analysis, we remove the six SDSS-identifiedquasars, two radio sources where the model red-shifts of the host galaxy do not match the SDSSphotometry or the color of the surrounding galax-ies, and one radio source where no host is found.Of the remaining 27 radio sources, 15 are BCGs.The remaining 12 host galaxies are among thethree brightest galaxies we identify in each clus-ter, making them all galaxies that may evolve intoBCGs. • Correlating the Host Galaxy with the RadioSource P roperties : Of the 27 red sequence identi-fied host galaxies, the distribution of opening an-gles as a function of offsets from the cluster centerfollow a similar distribution between BCGs andnon-BCGs, implying that all of our host galaxiesare drawn from a single population (as verified bya KS test). • Inf alling and Outgoing Radio Sources : For oursample of 36 bent, double-lobed radio sources, weclassify each as infalling, outgoing, or intermedi-ate radio sources regardless of the host galaxy be-ing a BCG. Our first measurement is solely basedon whether the radio source opens toward or awayfrom the cluster center. We find 21 sources appearinfalling while 15 appear outgoing. To accountfor clusters being three dimensional, we refine thismeasurement by measuring the infall angle relativeto the cluster center. With this measurement, wefind 3 sources are infalling, 11 are outgoing, while22 are at intermediate angles. The large number ofoutgoing radio sources, especially when comparedto the low- z sample from Sakelliou & Merrifield(2000), might imply that either the central ICMin these high- z clusters is at a low enough densityto allow radio sources to pass through without theradio sources being disrupted or that their non-directly outgoing paths imply they pass their peri-center at large offsets from that center. The lack ofa strong dichotomy could result from bent AGNsfollowing more circular paths or belonging to morecomplex merging clusters than at low redshift. Al-ternatively, much of this measurement is subject toprojection effects, creating large amounts of poten-tial uncertainty, which could account for the largenumber of intermediate sources.To further explore the relationships between bentAGNs and their host clusters, we will continue to ex- plore the cluster environments of these radio sources,particularly using X-ray observations to trace the ICM.To resolve some of the ambiguity of our determination ofinfalling/outgoing/intermediate radio sources, we planto do complimentary follow-up NIR or IR observationsof the extended cluster regions to do a background-subtracted companion analysis in color-space of the re-gions surrounding the bent AGNs. We aim to determineif the bent AGNs lie among spherically symmetric largescale galaxy structures or are biased toward a given di-rection. Additionally, spectroscopic follow-up will aid inour identification of infalling and outgoing host galaxiesand all cluster members as well as the orbital dynamicsof the host galaxy.We plan to complement this study by combining itwith the similarly selected sample of clusters hostinglower redshift bent, double-lobed radio sources fromWing & Blanton (2011) to trace how the cluster prop-erties evolve as a whole. Specifically, by doing a redsequence analysis on the clusters identified in Wing &Blanton (2011), we can create a uniform sample of low-and high- z clusters hosting bent radio sources to de-termine how the radio properties, cluster properties,and host galaxy properties evolve and see if the anti-correlation between richness and opening angle extendsto low- z clusters. Building on this, we plan to use newradio surveys to continue to identify bent radio sourcesin even higher redshift clusters and protoclusters. Ad-ditionally, we plan to further refine our red sequenceanalysis by modeling the red sequence slope to accountfor variety in red sequence populations.APPENDIX A. SPEARMAN TESTWithin this paper, we used the Spearman Test as away to determine the strength of a given correlation (es-timated by r s , which spans values between − p , which spans values be-tween 0 and 1; 1 - p can be thought of as the confidencelevel of the detection) and is thus a statistically realcorrelation. We define the strength of a trend using thefollowing metric based on the discussion given in Fowleret al. (2009): if | r s | = 0.00 to 0.19, this a very weakto no correlation; if | r s | = 0.20 to 0.39, this as a weakcorrelation; if | r s | = 0.40 to 0.69, this as a moderatecorrelation; if | r s | = 0.70 to 0.89, this as a strong corre-lation; and if | r s | = 0.90 to 1.00, this as a very strongcorrelation. Similarly, we defined the p value using thefollowing metric: if p > p = 0.05 to 0.1,this is weak evidence to reject the null hypothesis; if p =0.01 to 0.05, this is strong evidence to reject the null hy-pothesis; and if p < p value less than 0.1 (or greaterthan 90% certainty), although we do report all p values, adio Parameters for the COBRA Survey | r s | , but have weak or no evidence to rejectthe null hypothesis, p > p values.EGM would like to thank the referee for their veryhelpful comments on this paper. EGM would also liketo thank Jesse Golden-Marx for reading drafts of thispaper and useful discussions. EGM would also like tothank Zheng Cai for useful discussions and for readingdrafts of this paper. EGM would also like to thank theLDT telescope operators for their help with taking ob-servations. Additionally, EGM would like to thank theorganizers of the Early Stages of Galaxy Cluster Forma-tion 2017 Conference and the Tracing Cosmic Evolutionwith Clusters of Galaxies 2019 Conference for fosteringstimulating discussions that led to ideas addressed inthis paper.This work has been supported by the National ScienceFoundation, grant AST-1309032.EM acknowledges the support of the EU-ARC.CZLarge Research Infrastructure grant project LM2018106of the Ministry of Education, Youth and Sports of theCzech Republic.These results made use of the Lowell Discovery Tele-scope at Lowell Observatory. Lowell is a private, non-profit institution dedicated to astrophysical research andpublic appreciation of astronomy and operates the LDTin partnership with Boston University, the University ofMaryland, the University of Toledo, Northern ArizonaUniversity, and Yale University. LMI construction wassupported by a grant AST-1005313 from the NationalScience Foundation. This work is based in part on observations made withthe Spitzer a community-developed core Python package for Astronomy (AstropyCollaboration et al. 2013, 2018). Facilities:
LDT,
Spitzer , SloanREFERENCES
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Table A1 . COBRA Red Sequence Clusters and Radio Source Properties
Field Redshift Host Coordinates RS Cluster Center AGN Offset Infall Angle Overdensity Significancez RA a DEC RA DEC (kpc) ( ◦ ) RS Combinedm*+1 i − [3 .
6] cluster candidatesCOBRA005837.2+011326 0.71 00 58 37.03 +01 13 27.8 00 58 36.47 +01 13 26.4 78.6 133.9 4.3 4.4COBRA014741.6 − −
00 47 06.0 01 47 41.29 −
00 46 36.1 − − −
00 10 19.9 01 53 19.46 −
00 10 22.1 − b · · · · · · − − −
01 17 50.0 15 14 56.97 −
01 17 57.0 − − − − − b −
08 13 35.0 22 16 02.88 −
08 14 14.6 · · · · · · r − i cluster candidatesCOBRA012058.9+002140 0.75 01 20 58.87 +00 21 41.7 01 20 57.87 +00 21 49.8 122.5 121.0 5.1 4.6COBRA075516.6+171457 0.64 07 55 17.35 +17 14 54.9 07 55 17.54 +17 14 59.9 95.0 57.8 6.1 5.1COBRA100745.5+580713 0.656 10 07 45.60 +58 07 15.2 10 07 45.09 +58 07 29.8 − − − i − [3 .
6] cluster candidatesCOBRA074025.5+485124 1.10 07 40 25.51 +48 51 25.2 07 40 24.24 +48 51 08.3 − − b · · · · · · − . − [4 .
5] cluster candidatesCOBRA072805.2+312857 1.75 07 28 05.35 +31 28 59.5 07 28 06.26 +31 28 52.1 121.9 120.0 2.5 2.9COBRA100841.7+372513 1.35 10 08 41.71 +37 25 14.2 10 08 41.53 +37 25 32.3 − − − Table A1 continued adio Parameters for the COBRA Survey Table A1 (continued)
Field Redshift Host Coordinates RS Cluster Center AGN Offset Infall Angle Overdensity Significancez RA a DEC RA DEC (kpc) ( ◦ ) RS Combined a All coordinates are given in J2000. b Cluster candidates without evidence of a bent radio AGN and for which we do not report any measurements relating to the AGN. Golden-Marx et al.
Table A2 . COBRA Radio Source Properties
Field Opening Angle Radio Source Length Radio Flux Radio Power (P . ) Host Galaxy( ◦ ) (kpc) Density (10 W Hz − ) m . µ m M . µ m (mJy) (AB) (AB)m*+1 i − [3 .
6] cluster candidatesCOBRA005837.2+011326 85.2 ± +6 . − . +0 . − . − − ± +6 . − . +0 . − . − − ± +13 . − . +0 . − . − ± +4 . − . +0 . − . − ± +5 . − . +0 . − . − ± +9 . − . +1 . − . − ± +8 . − . +1 . − . − ± +8 . − . +1 . − . − ± +5 . − . +1 . − . − − ± +4 . − . +0 . − . − a ± +2 . − . +0 . − . · · · COBRA162955.5+451607 125.2 ± +11 . − . +2 . − . · · · · · · COBRA164951.6+310818 100.3 ± +14 . − . +3 . − . − ± +8 . − . +1 . − . − ± +4 . − . +0 . − . − ± +3 . − . +0 . − . − r − i cluster candidatesCOBRA012058.9+002140 135.8 ± +6 . − . +1 . − . − ± +9 . − . +1 . − . − ± +4 . − . +0 . − . − b ± +17 . − . +0 . − . − ± +3 . − . +0 . − . − i − [3 .
6] cluster candidatesCOBRA074025.5+485124 78.5 ± +6 . − . +1 . − . − c ± +6 . − . +0 . − . − ± +7 . − . +40 . − . − a ± +5 . − . +0 . − . · · · COBRA145023.3+340123 36.0 ± +7 . − . +1 . − . − ± +5 . − . +9 . − . − ± +8 . − . +9 . − . − ± +5 . − . +2 . − . − . − [4 .
5] cluster candidatesCOBRA072805.2+312857 154.7 ± +2 . − . +4 . − . − ± +4 . − . +2 . − . − a ± +4 . − . +0 . − . · · · COBRA104254.8+290719 89.1 ± +5 . − . +3 . − . − a ± +2 . − . +0 . − . · · · COBRA141155.2+341510 a ± +4 . − . +0 . − . · · · COBRA222729.1+000522 a ± +3 . − . +0 . − . · · · Table A2 continued adio Parameters for the COBRA Survey Table A2 (continued)
Field Opening Angle Radio Source Length Radio Flux Radio Power (P . ) Host Galaxy( ◦ ) (kpc) Density (10 W Hz − ) m . µ m M . µ m (mJy) (AB) (AB) a Radio sources that are SDSS quasars b Sources that lack a third radio component cc