CLUSTER CANDIDATES AROUND LOW-POWER RADIO GALAXIES AT z ∼ 1–2 IN COSMOS

As discussed above, the C09 sample was selected using the radio fluxes from the FIRST survey (Becker et al. 1995) which was performed by using the VLA B-configuration at 1.4 GHz and it covers 10,000 square degrees of the North and South Galactic Caps. The COSMOS field entirely resides within the area mapped by FIRST. Post-pipeline radio maps have a resolution of ∼5 arcsec. The detection limit of the FIRST catalog is ∼1 mJy with a typical rms of 0.15 mJy. When we make use of the FIRST survey, we adopt the flux densities from the catalog as of 2011 October 10. However, the FIRST radio maps may be missing a substantial fraction of any extended low surface brightness radio emission from the lobes of our radio sources, which are close to the detection limit. This is particularly important because of the relatively high angular resolution provided by the VLA configuration used, which is more suitable for detecting compact or unresolved radio sources.

While being slightly shallower than FIRST, the NRAO VLA Sky Survey (NVSS) survey (Condon et al. 1998) may be more suitable for our purposes, since it was obtained by using the VLA-D configuration at 1.4 GHz. The angular resolution of the NVSS radio maps is 45 arcsec (FWHM). Thus, it is more suitable for detecting extended emission of the sources in our sample. Therefore, in order to derive the total radio luminosity of our sources, we use the NVSS fluxes and upper limits (as of 2011 October 10), when possible. In the NVSS catalog¹⁰ at the coordinates of the C09 objects, we find 26 of the 36 sources.

While the FIRST survey is complete down to a flux of 1 mJy, the completeness of the NVSS catalog is only 50% at its formal limit of 2.5 mJy, while it rises rapidly to 99% at 3.4 mJy (Condon et al. 1998). Thus, the drawbacks of using NVSS sources are as follows: (1) sources with total radio flux <3.4 mJy might not be included. (2) The identification of the NVSS counterpart of each source is not trivial. Due to the lower angular resolution rms uncertainties are about 7 arcsec at the NVSS limit, as affected by confusion. Furthermore, the extended radio morphology of many of the radio sources might be complex. Therefore, since NVSS is more sensitive to the extended emission than FIRST, the centroid of the FIRST source could not coincide with that in the NVSS map. Also note that, even if the limit of the NVSS catalog is set at 2.5 mJy, some of our fainter sources are detected in the radio maps.

To overcome these inconveniences, we use FIRST (Becker et al. 1995) and VLA COSMOS (Schinnerer et al. 2007). FIRST has a flux density threshold of 1 mJy and a positional accuracy of ≲1 arcsec for radio pointlike sources. VLA COSMOS has an angular resolution of 15 × 14 and a sensitivity limit of 45 μJy beam⁻¹. It is therefore deeper and with higher angular resolution than FIRST. For the majority of the objects it is straightforward to identify the radio sources in the above surveys. The few cases in which the identification is problematic are discussed in the following.

For these cases we consider the VLA COSMOS maps to clearly identify the radio sources, as described in the following for source 05. In Figure 1 we show the NVSS radio map of the field around object 05. Visual inspection reveals the presence of a complex radio morphology, which might be (erroneously) identified with either the narrow-angle tail (e.g., NGC 1265, O'Dea & Owen 1986) or the wide-angle tail (e.g., 3C 465; Venturi et al. 1995) radio morphology. The NVSS catalog reports sources at distances of ∼60 and ∼67 arcsec to the SW and SE from the VLA-COSMOS coordinates of source 05, and fluxes of 3.4 and 3.7 mJy, respectively. A third radio source located at the position of 05 is visible in the map, but it is below the threshold of the NVSS catalog.

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In Figure 2 (left) we show the same field as seen with VLA-COSMOS, at a much higher angular resolution. Such image shows the presence of a number of point-like sources and some extended emission. In the right panel we report the HST image of the same field, taken with the Advanced Camera for Surveys (ACS) and the F814W filter, as part of the COSMOS survey. The radio contours from VLA-COSMOS are overplotted in yellow. It is clear that the radio sources seen in VLA-COSMOS overlap with foreground galaxies. This generates the complex extended emission seen in the NVSS map. By using higher resolution radio data and the optical image, we are able to overcome the confusion problem in the NVSS map. The NVSS catalog misses our source and detects only the two unrelated brighter radio emitting regions.

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Similarly, other sources have extended radio morphology, as is clear from visual inspection of the NVSS maps. The angular separation between the coordinates reported in the NVSS catalog and those obtained by using VLA-COSMOS is about ∼15 arcsec. This is the case with sources 26, 52, 202, 224, and 228, where such angular separations are 15.37, 16.4, 12.82, 12.43, and 18.52 arcsec, respectively. In Figure 3 we report the NVSS fields of 26 and 224 as examples. These sources show a radio morphology similar to that of 05. However, a bright source is clearly present in each of these two fields, very close to the radio galaxy. They are merged in the NVSS map in a single structure due to the low NVSS angular resolution.

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We consider the radio NVSS maps of all eight sources that are not present in the NVSS catalog. We visually inspect each map and search for the presence of radio contours centered around the position of the radio source. For five out of the eight, we find evidence of a radio source located at the coordinates of the radio galaxy. This is the case with sources 11, 20, 22, 27, and 39, where the radio contours are consistent with a radio flux close to the NVSS formal limit of 2.5 mJy. In Figure 4 we report the fields of 22 and 39 as examples. Being very close to or below the formal completeness limit, we expect that possible systematics might occur in the flux measurements. Therefore, we adopt a fiducial 2.5 mJy upper limit for all eight sources which are not included in the NVSS catalog.

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The fiducial FIRST and NVSS flux uncertainties for the sources in our sample are within ∼0.1–0.2 mJy and ∼0.4–0.6 mJy, respectively. However, we prefer not to report the flux uncertainty associated with each source. This is because we are considering fluxes down to the completeness limit of both the FIRST and the NVSS surveys and, therefore, the flux uncertainties might be underestimated.

We adopt accurate photometric redshifts derived by Baldi et al. (2013, hereinafter B13) through a careful analysis of the spectral energy distribution (SED) of the host galaxies. As mentioned in Section 2, throughout this paper we adopt the photometric redshifts derived in B13, which we specifically focus on in the sample considered here. These photometric redshifts have a great advantage with respect to those in Mobasher et al. (2007) and Ilbert et al. (2009, hereinafter I09), which were automatically derived by using the COSMOS photometric catalogs.

I09 estimated photometric redshifts by using the photometric data points from 30 bands for those sources with I < 25 in in the deep Subaru area of the COSMOS field (Taniguchi et al. 2007). B13 carefully identified the optical counterparts of the radio sources in all of the photometric bands. The authors discovered that, in a few cases, sources in different bands were misidentified in the COSMOS source list, therefore leading to erroneous photometric redshift estimates. B13 also performed a more refined SED modeling, with the inclusion of two stellar populations. At variance with the I09 catalog, B13 considered only broad band photometric data and excluded narrow and medium band data, which can be strongly contaminated by emission lines that are not included in the stellar templates.

We also search for the spectroscopic redshift of our sources in the zCOSMOS-bright (Lilly et al. 2007) and MAGELLAN (Trump et al. 2007) catalogs. Only 7 out of the 36 sources in our sample are found.

In agreement with B13, we do not use the spectroscopic redshift for object 25. This is because of its clear misidentification in the MAGELLAN catalog (see Section 6.1 in B13). Therefore, for the great majority of the sources we have to rely on photometric redshifts.

The redshifts of three (namely, 27, 52, and 66) out of the seven sources for which spectroscopic redshifts are available are significantly outside the z ∼ 1–2 range of C09 selection. Therefore, we exclude them from the sample. Redshifts z = 0.2847 and z = 0.7417 are reported in the MAGELLAN catalog for sources 27 and 52, respectively. The redshifts reported for source 66 in the MAGELLAN and the zCOSMOS-bright catalog are consistent with each other and equal to z = 0.6838 and z = 0.6803, respectively. Searching for cluster candidates at intermediate or low redshifts (i.e., z ≲ 0.8) is not the aim of this project. Therefore, we naturally reject sources 27, 52, and 66, which are all located at z ⩽ 0.75. We also exclude source 07 from the sample because it is a peculiar radio source (as suggested in Baldi et al. 2013). It might be an FR II radio galaxy at significantly high redshift. It will be studied in a forthcoming paper. Conversely, we do not exclude those sources (e.g., 28 and 32) that have a photometric redshift formally above z ∼ 2. This is because, even if they are at redshifts well outside the fiducial range of our interest, they were not rejected during the C09 selection. Therefore, they could have similar properties to those of the other galaxies in our sample. Furthermore, since such sources populate the high-redshift tail of our sample, their megaparsec-scale environments are still worth investigating (see also Section 7 for further discussion about source 28).

Summarizing, with respect to the original list given in C09, we reject sources 07, 27, 52, and 66 (in addition to 236, the QSO we already discussed above). The sample is thus reduced to 32 objects.

In agreement with C09, we assume that the radio spectrum in the region around 1.4 GHz is a power law of the form S_ν∝ν^−α, where S_ν is the radio flux density at the observed frequency ν, and α is the spectral index assumed to be α = 0.8, according to C09. Such an assumption requires that the flat (α ∼ 0) radio emission of the core is negligible with respect to the extended emission (jets and lobes) in the considered spectral range. This is formally correct at the lowest radio frequencies, but it is less certain at higher frequencies. However, since the radio data do not allow us to separate the emission of our sources into different components, we assume that the measured flux at 1.4 GHz is dominated by extended emission. If α = 0.3 instead of 0.8, the luminosity would increase by only a factor of <1.8, for the worst case of a source at z = 2.

Thus the isotropic rest frame 1.4 GHz luminosity density is given by:

$$\begin{equation} L_{1.4} = 4\pi S_{1.4}D_L(z)^2\left(1+z\right)^{\alpha -1}, \end{equation} \tag{ 1 }$$

where S_1.4 is the observed flux density at 1.4 GHz and D_L is the luminosity distance.

In Figure 5 (left panel) we report the luminosity versus redshift scatterplot. The lower/upper thick black lines in the plot are the FIRST sample selection lower/upper boundaries adopted in C09 (1.0 mJy and 13.0 mJy, respectively). Since NVSS fluxes are in general higher than FIRST fluxes, we expect all sources to lie above the lower line.

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Since we are interested in searching for clusters around FR Is, we consider the 1.4 GHz luminosity intervals spanned for each source, within the redshift uncertainties, for an assigned 1.4 GHz radio flux.

Therefore, we conservatively select only those sources whose 1.4 GHz luminosity intervals lie entirely below the FR I/FR II radio luminosity divide of 4 × 10³² erg s⁻¹ Hz⁻¹. According to this criterion, we select 21 bona fide LLRGs, whose redshifts span the range z = 0.88–1.33 and have radio luminosities between L_1.4 = (0.84–3.24) × 10³² erg s⁻¹ Hz⁻¹. In Figure 5 (right panel) we plot the scatterplot focused on the LLRGs only. The median redshift and 1.4 GHz luminosity of the LLRGs are z_median = 1.1 and L_{1.4, median} = 1.84 × 10³² erg s⁻¹ Hz⁻¹, respectively. For comparison, radio galaxies of similar power, selected within the 3C catalog, span a much smaller redshift range. Chiaberge et al. (1999) report a range z = 0.0037–0.29 and a median value z = 0.03 for their sample of 33 FR Is.

The LLRGs span a limited range of luminosity and slightly broader range of redshift. However, because of the steepness of the radio luminosity function, most sources are at z ∼ 1.

Being at relatively low redshifts, these objects and their megaparsec-scale environment can be studied in greater detail than the whole sample of FR I candidates considered in this work. This is mainly because COSMOS field number densities are much higher and statistical photometric redshift uncertainties are smaller than at higher redshifts (Ilbert et al. 2009). Furthermore, spectroscopic redshift information is available for some of the LLRGs only and photometric redshifts from B13 are more accurate for the LLRGs than for the HLRGs, with the latter, on average, being at higher redshifts.

Therefore we separate the LLRGs from the remaining sources, that are generally at higher luminosities and redshifts than the HLRGs. In particular, the photometric redshifts of the LLRGs are better constrained, since the typical statistical uncertainty dramatically increases above z ∼ 1.3 (see, e.g., Figure 9 in I09) and because all of the sources in our sample with spectroscopic redshifts belong to the LLRG class.

We consider in this section the remaining sources in the sample, i.e., the HLRGs, that do not belong to the LLRG subclass. Note that the radio morphology of both LLRGs and the HLRGs is not of FR II type. In fact, sources with a clear FR II morphology have been rejected as part of the original sample selection in C09. Furthermore, the cosmological evolution of the FR I/FR II radio divide is still unknown, i.e., high-z FR I sources might have higher radio power than those of local FR Is, as suggested by Heywood et al. (2007).

This makes the nature of these HLRGs very unclear and deserving investigation. In the following, we consider the HLRGs separately from the rest of the sample (i.e., the LLRGs) in order to avoid any bias due to possible differences in the megaparsec-scale environments of low and high luminosity sources.

We find 11 HLRGs. Their redshifts and radio luminosities span the intervals z = 1.30–2.90 and L_1.4 = (2.18–15.44) × 10³² erg s⁻¹ Hz⁻¹, respectively. The median redshift and luminosity are z_median = 2.01, L_{1.4, median} = 8.64 × 10³² erg s⁻¹ Hz⁻¹, respectively.

In Table 1 we summarize the properties of the sources in our sample, separating them between the LLRGs (top) and the HLRGs (bottom). We refer to C09 and their Table 1 for more details about the sample. In Figure 6 we report the radio power distribution for our sample obtained by considering NVSS fluxes (left panel) and FIRST fluxes (right panel). Limited to this section only, we also consider the FIRST instead of the NVSS radio powers only. This is because FIRST fluxes are available for all sources in our sample, while this is not the case for NVSS.

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Table 1. Sample Properties

ID	R.A.	Decl.	Redshift	FIRST Flux	NVSS Flux	L1.4 GHz	Radio Morphology
	(deg)	(deg)		(mJy)	(mJy)	(1032 erg s−1 Hz−1)
The Low Luminosity Radio Galaxy Subsample
COSMOS FR I 01	150.20744	2.2818749	0.8823a–0.8827b	1.06	—	0.85	Compact
COSMOS FR I 02	150.46751	2.7598829	1.33±$^{0.10}_{0.09}$	2.25	2.6	2.36	Extended
COSMOS FR I 13	149.97784	2.5042069	1.19±$^{0.08}_{0.11}$	1.50	2.4	1.67	Compact
COSMOS FR I 16	150.53772	2.2673550	0.9687a	5.70	4.4	1.87	Unresolved
COSMOS FR I 18	149.69325	2.2674670	0.92±$^{0.14}_{0.11}$	4.39	5.1	1.91	Extended
COSMOS FR I 20	149.83209	2.5695460	0.88±$^{0.02}_{0.02}$	1.33	—	0.84	Extended
COSMOS FR I 22	149.89508	2.6292144	1.30±$^{0.05}_{0.04}$	2.74	—	2.14	Compact
COSMOS FR I 25	150.45673	2.5597000	1.33±$^{0.11}_{0.13}$	2.18	2.7	2.45	Compact
COSMOS FR I 26	149.62114	2.0919881	1.09±$^{0.12}_{0.07}$	1.88	3.2	1.80	Extended
COSMOS FR I 29	149.64587	1.9529760	1.32±$^{0.23}_{0.24}$	2.13	2.3	2.05	Compact
COSMOS FR I 30	149.61542	1.9910541	1.06±$^{0.11}_{0.07}$	1.26	2.4	1.27	Compact
COSMOS FR I 31	149.61916	1.9163600	0.9123a–0.9132b	3.71	4.1	1.51	Compact
COSMOS FR I 36	150.55662	1.7913361	1.07±$^{0.10}_{0.04}$	3.19	3.3	1.78	Unresolved
COSMOS FR I 39	149.95804	2.8288901	1.10±$^{0.05}_{0.05}$	1.37	—	1.44	Compact
COSMOS FR I 202	149.99506	1.6324950	1.31±$^{0.09}_{0.12}$	1.08	3.3	2.89	Extended
COSMOS FR I 219	150.06444	2.8754051	1.03±$^{0.02}_{0.04}$	1.85	—	1.23	Compact
COSMOS FR I 224	150.28999	1.5408180	1.10±$^{0.10}_{0.04}$	3.31	3.2	1.84	Extended
COSMOS FR I 228	149.49455	2.5052481	1.31±$^{0.05}_{0.07}$	2.04	3.7	3.24	Compact
COSMOS FR I 234	150.78925	2.4539680	1.10±$^{0.14}_{0.08}$	4.43	5.2	3.00	Extended
COSMOS FR I 258	149.55934	1.6310670	0.9009b	2.24	3.7	1.32	Compact
COSMOS FR I 285	150.72131	1.5823840	1.10±$^{0.13}_{0.08}$	2.95	3.5	2.02	Extended
The High Luminosity Radio Galaxy Subsample
COSMOS FR I 03	150.00253	2.2586310	2.20±$^{0.32}_{0.44}$	4.21	5.2	15.44	Unresolved
COSMOS FR I 04	149.99153	2.3027799	1.37±$^{0.10}_{0.06}$	5.99	7.5	7.30	Extended
COSMOS FR I 05	150.10612	2.0144780	2.01±$^{0.22}_{0.35}$	1.30	—	6.01	Compact
COSMOS FR I 11	150.07816	1.8985500	1.57±$^{0.14}_{0.09}$	1.13	—	3.36	Compact
COSMOS FR I 28	149.60064	2.0918673	2.90±$^{0.20}_{0.26}$	1.77	2.4	13.46	Compact
COSMOS FR I 32	149.66830	1.8379777	2.71±$^{0.38}_{0.34}$	1.39	3.1	14.88	Compact
COSMOS FR I 34	150.56023	2.5861051	1.55±$^{0.41}_{0.19}$	5.25	4.5	5.87	Unresolved
COSMOS FR I 37	150.74336	2.1705379	1.38±$^{0.43}_{0.42}$	1.87	2.2	2.18	Compact
COSMOS FR I 38	150.53645	2.6842549	1.30±$^{0.17}_{0.28}$	10.01	11.6	9.95	Compact
COSMOS FR I 70	150.61987	2.2894360	2.32±$^{0.53}_{0.20}$	3.90	4.5	15.10	Compact
COSMOS FR I 226	150.43864	1.5934480	2.35±$^{0.63}_{0.31}$	1.25	—	8.64	Compact

Notes. Column description: (1) source ID number; (2) R.A.J2000 [degree]; (3) Decl.J2000 [degree]; (4) Redshifts. Photometric from B13 and spectroscopic from either MAGELLAN (Trump et al. 2007) or zCOSMOS-bright (Lilly et al. 2007) catalogs are denoted with the superscript a or b, respectively; (5) 1.4 GHz FIRST fluxes [mJy]; (6) 1.4 GHz NVSS fluxes [mJy]. We assume 2.5 mJy flux (reported as—in the table) for those sources that are not in the NVSS catalog; (7) 1.4 GHz radio power [10³² erg s⁻¹ Hz⁻¹]. NVSS flux or 2.5 mJy upper limit adopted. Radio spectrum assumed: L_ν∝ν^−α, α = 0.8; (8) radio morphology as in C09.

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The averages of the logarithmic FIRST and NVSS luminosities of the sources in our sample are log [L_{1.4, FIRST}/(erg s⁻¹ Hz⁻¹)] = 32.32 ± 0.41 and log [L_{1.4, NVSS}/(erg s⁻¹ Hz⁻¹)] = 32.47 ± 0.37, respectively, where the reported uncertainties are the rms dispersions around the averages. This shows that the sources in our sample have, on average, 1.4 GHz radio luminosities slightly below the FR I/FR II radio luminosity divide and that this result is independent of the two different sets of radio fluxes adopted (i.e., FIRST or NVSS). However, the logarithmic difference between the FIRST and NVSS luminosities for the sources in our sample is, on average, 〈log (L_{1.4, NVSS}/L_{1.4, FIRST})〉 = 0.15 and the rms dispersion around the average is 0.14 dex. This can be translated into the fact that, on average, the 1.4 GHz luminosities estimated from the NVSS fluxes are 1.5 times than those estimated by adopting FIRST fluxes.

Therefore, NVSS are slightly higher than FIRST luminosities for the FR Is in our sample. This suggests that the NVSS survey is more sensitive to extended emission and it might be more effective than FIRST to estimate the true radio luminosity of our sources.

We test the presence of bimodality in both the FIRST and NVSS radio power distributions by applying the KMM algorithm described in Ashman et al. (1994). The KMM test assumes that the considered distributions are Gaussian functions or a sum of them. We find that the luminosity distribution is strongly inconsistent with being unimodal at 99.75% confidence level (i.e., more than 3σ) if the NVSS fluxes (or upper limits) are adopted. If we adopt the FIRST fluxes for those sources for which we have the NVSS upper limits we find that the unimodality is rejected at 70.10% confidence level (i.e., just above 1σ). The unimodality is rejected at a level less than 1σ (i.e., 63.88%) if the FIRST fluxes are instead considered for all sources.

The presence of bimodality in the NVSS radio power distribution of the FR Is in our sample suggests that the HLRGs might be drawn from a different parent population. However, the bimodality disappears when the FIRST fluxes are included. Furthermore, the Gaussian approximation is a strong assumption and it might not correspond to our case. Therefore, even if we find evidence of bimodality in the radio power distribution, we cannot draw firm conclusions.

In Table 2 we report the overdensities found in the fields of our sample that are associated with the corresponding sources, according to the PPM procedure. We distinguish between the LLRGs (top table) and the HLRGs (bottom table). We discuss the estimated sizes in Section 6.6. All of the overdensities are robustly detected with respect to slightly different choices of the involved parameters (e.g., a different choice of the redshift bin Δz, a different selection threshold, a different choice in the parameters of the tessellation of the projected space).

Table 2. Cluster Candidates and Their Properties as Inferred with the PPM

ID	zsource	zoverdensity	Significance	rmin	rmax	rmax, phys.	rmax, comov.
				(arcsec)	(arcsec)	(kpc)	(kpc)
The Low Luminosity Radio Galaxy Subsample
01	0.8823a–0.8827b	0.84 ± 0.07	3.5	0.0 ——	70.7 ——	536 —–	987 —–
02	1.33±$^{0.10}_{0.09}$	1.33 ± 0.09	4.3	19.2±$^{+24.3}_{-19.2}$ (0.0)	119.3 ± 16.2 (122.5)	1008 ± 136	2349 ± 319
16	0.9687a	1.12 ± 0.06	3.5	0.0   ——	100.5 ± 3.3 (100.0)	830 ± 27	1760 ± 57
18	0.92±$^{0.14}_{0.11}$	0.80 ± 0.08	5.6	0.0   ——	110.4 ± 25.4 (132.3)	834 ± 191	1501 ± 345
20	0.88±$^{0.02}_{0.02}$	0.96 ± 0.06	3.9	0.0   ——	80.4 ± 8.3 (86.6)	637 ± 65	1249 ± 129
22	1.30±$^{0.05}_{0.04}$	1.41 ± 0.09	3.3	20.8±$^{+24.6}_{-20.8}$ (0.0)	94.2 ± 11.6 (86.6)	800 ± 98	1929 ± 237
25c	1.33±$^{0.11}_{0.13}$	1.23 ± 0.07	2.8	57.2 ± 9.9 (50.0)	120.9 ± 19.5 (132.3)	1009 ± 162	2250 ± 363
		1.37 ± 0.08	2.7	51.1 ± 4.6 (50.0)	86.6   ——	736  —–	1745  —–
26	1.09±$^{0.12}_{0.07}$	1.15 ± 0.07	3.9	42.6 ± 27.4 (50.0)	149.0 ± 12.3 (158.1)	1237 ± 102	2659 ± 219
29	1.32±$^{0.23}_{0.24}$	1.34 ± 0.09	2.1	77.5 ± 7.9 (70.7)	120.5 ± 11.2 (122.5)	1020 ± 94	2387 ± 221
36	1.07±$^{0.10}_{0.04}$	1.18 ± 0.07	3.0	0.0   ——	82.6 ± 6.9 (86.6)	685 ± 57	1494 ± 124
39	1.10±$^{0.05}_{0.05}$	1.27 ± 0.06	3.5	0.0   ——	70.7   ——	597  —–	1356  —–
228	1.31±$^{0.05}_{0.07}$	1.17 ± 0.06	3.2	0.0   ——	70.7   ——	588  —–	1276  —–
234d	1.10±$^{0.14}_{0.08}$	0.93 ± 0.08	2.5	0.0   ——	108.7 ± 8.3 (111.8)	854 ± 65	1649 ± 125
285	1.10±$^{0.13}_{0.08}$	1.01 ± 0.07	2.1	50.0   ——	70.7   ——	568  —–	1143  —–
The High Luminosity Radio Galaxy Subsample
03c	2.20±$^{0.32}_{0.44}$	1.82 ± 0.08	2.6	0.0   —–	58.7 ± 11.4 (50.0)	502 ± 97	1416 ± 275
		2.39 ± 0.09	2.5	15.8±$^{+23.2}_{-15.8}$ (0.0)	74.9 ± 7.0 (70.7)	617 ± 57	2093 ± 195
04	1.37±$^{0.10}_{0.06}$	1.57 ± 0.09	2.0	0.0   —–	62.4 ± 10.1 (70.7)	532 ± 86	1368 ± 221
05	2.01±$^{0.22}_{0.35}$	1.97 ± 0.07	2.2	0.0   —–	50.0  —–	424  —–	1261  —
28c	2.90±$^{0.20}_{0.26}$	2.71 ± 0.07	2.0	86.3 ± 11.0 (86.6)	129.9 ± 4.2 (132.3)	1044 ± 33	3876 ± 125
		2.98 ± 0.09	2.5	0.0   —–	101.0 ± 11.7 (100.0)	793 ± 91	3159 ± 366
34	1.55±$^{0.41}_{0.19}$	1.31 ± 0.07	2.7	45.7 ± 27.9 (50.0)	103.6 ± 8.3 (100.0)	871 ± 69	2012 ± 161
37	1.38±$^{0.43}_{0.42}$	1.95 ± 0.07	3.0	86.6   —–	121.6 ± 2.9 (122.5)	1035 ± 24	3054 ± 72
38	1.30±$^{0.17}_{0.28}$	0.88 ± 0.07	3.7	0.0   —–	90.0 ± 9.4 (86.6)	698 ± 72	1312 ± 137
226	2.35±$^{0.63}_{0.31}$	1.99 ± 0.06	2.5	70.5 ± 4.9 (70.7)	107.2 ± 5.8 (111.8)	910 ± 49	2723 ± 147

Notes. Cluster candidates in the fields of the LLRGs (top) and HLRGs (bottom) associated with the corresponding source. Column description: (1) source ID number; (2) photometric redshift of the source along with uncertainties from B13. Spectroscopic redshifts from either MAGELLAN (Trump et al. 2007) or zCOSMOS-bright (Lilly et al. 2007) catalogs are denoted with the superscript ^aor ^b, respectively; (3) redshift of the overdensity and corresponding rms dispersion, both estimated with the PPM; (4) significance of the overdensity estimated by the PPM in terms of σ; (5) average minimum radius (arcsec) of the overdensity along with the rms dispersion around the average (both estimated with the PPM). The median value (arcsec) is written between the parentheses; (6) average maximum radius (arcsec) of the overdensity along with its rms dispersion around the average (both estimated with the PPM). The median value (arcsec) is written between the parentheses; (7) average physical size (kpc) of the overdensity along with the rms dispersion; (8) average comoving size (kpc) of the overdensity along with the rms dispersion. The rms dispersions and the median values in Columns 5, 6, 7, and 8 are not reported in those cases where the rms dispersion is null. ^cSources 03, 25, 28 are counted twice because multiple peaks are found to be associated with the corresponding radiogalaxies within the photometric redshift uncertainties. ^dPhotometric redshifts from Ilbert et al. (2009) denoted as zpbest are adopted. They do not include masked sources, stars, and X-ray AGN.

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According to the overdensity selection procedure outlined in Section 5 we find that 22 out of the 32 sources in our sample are hosted in a dense megaparsec-scale environment. The cluster candidates associated with the sources in the sample have an average redshift of z_avg = 1.41 with an rms dispersion around the average of 0.55. The median redshift is z_median = 1.31. When calculating these quantities for the fields in which multiple associations between distinct overdensities and the beacon radio galaxy are identified we only consider the overdensity whose estimated redshift is the closest to that of the radio galaxy.

In particular, we find that 14 radio galaxies out of the 21 LLRGs and 8 out of the 11 HLRGs are associated with overdensities. These correspond to percentages of 67% ± 10% and 73% ± 13% for the two subsamples, respectively, where the 1σ uncertainties are estimated according to binomial statistics. These percentages fully agree within the reported errors. Therefore the environments of the two subsamples are statistically indistinguishable. Thus, if we do not distinguish between the two different classes (i.e., the LLRGs and the HLRGs) we find that 22 out of the 32 radio galaxies in our sample (i.e., 69% ± 8%) are found in dense megaparsec-scale environments.

The overdensity in the field of 16 is not formally associated with the radio galaxy, according to the outlined procedure. However, we do not reject it from Table 2 because it would be included if the photometric redshift of the radio source ($z=0.97^{+0.12}_{-0.07}$, see Table 6 in B13) would be considered instead of the spectroscopic redshift.

Note that, a posteriori, the redshift estimated for each overdensity in the sample is remarkably consistent with that of the source estimated in B13. The overdensity redshift uncertainties are generally small and comparable to typical statistical photometric redshift uncertainties in I09.

As expected, the overdensities associated with the LLRGs are generally at lower redshifts than those of the HLRGs. These lower redshift overdensities are also detected, on average, with higher significances (σ_avg = 3.36) than those associated with the HLRGs (σ_avg = 2.64). This effect is in agreement with that pointed out in Paper I and it is mainly due to both increasing photometric redshift errors and to the smaller number counts that occur for increasing redshifts. If we focus on the overdensities found among the two different subsamples, separately (i.e., the LLRGs and the HLRGs) we find that the average, the rms dispersion around the average, and the median values of the redshifts of the overdensities associated with the LLRGs are z_avg = 1.13, rms = 0.20, and z_median = 1.17, respectively. The average, the rms dispersion around the average and the median values of the redshifts of the overdensities associated with the HLRGs are z_avg = 1.88, rms = 0.65, and z_median = 1.97, respectively.

C10 suggested the presence of overdensities around three of our highest redshift sources, namely, sources 03, 05, and 226. Based on galaxy number counts, the authors found that the megaparsec-scale environments of these source are 1.7 times denser with respect to the mean COSMOS density. They translated this into a 4σ overdensity significance. Interestingly, we find this is in full agreement with our results, since we find that all three sources reside in high significance (∼2.5σ) and high-redshift (z ≃ 2) megaparsec-scale overdensities. The cluster candidate associated with our source 03 is also present in the proto-cluster and group catalog of Diener et al. (2013). They estimated a redshift of 2.44, which is in good agreement with our estimate (z = 2.39) for one of the two megaparsec-scale overdensities associated with source 03. Spitler et al. (2012) found a cluster candidate that is about ∼3.8–5.4 arcmin from source 03. The authors estimated a redshift of z = 2.2, on the basis of photometric redshift information. Even if both the redshift and the projected coordinates are only marginally consistent with those of our cluster candidate, it might be possible that the source 03 belongs to the same large-scale cluster structure presented in Spitler et al. (2012). We also report the PPM plot for the field of this source in Figure 9, panel (b). Interestingly, whereas the independent Papovich (2008, see Section 7) method suggests that source 03 is in a ∼3.3σ overdensity, it does not detect any overdensity in the fields of sources 05 and 226. We will discuss this in details in Sections 7.1 and 7.2.

We searched for cluster candidates in catalogs of z ≲ 1 groups in the COSMOS field that were obtained by using spectroscopic redshift information (Knobel et al. 2009, 2012) or photometric redshifts combined with previous X-ray-selected cluster samples (George et al. 2011). Interestingly, five groups in the fields and redshifts of our FR Is are present in these catalogs. These five source are 01, 16, 18, 20, and 31. However, we note that the coordinates reported in Knobel et al. (2012) for the groups and in the fields of 16, 18 and 20 and those of the FR Is are separated by ∼63, 40, and 42 arcsec, respectively. Therefore, these three associations are only marginally consistent. Conversely, the offsets for the other two FR Is (i.e., 01 and 31) are ≲ 14''; hence the associations are more robust. Source 258 is the only FR I in our sample with a photometric or spectroscopic redshift less than z = 1 for which no group was found in these catalogs. Similarly, the PPM does not find any megaparsec-scale overdensity associated with that source. We also note that the cluster candidate in the field of 01 was previously suggested in Finoguenov et al. (2007).

Redshifts z = 0.88, 0.92, 0.79, and 0.96 are reported for the groups associated with sources 01, 16, 18, and 20, respectively (Finoguenov et al. 2007; Knobel et al. 2009, 2012; George et al. 2011). The redshifts fully agree with our estimates obtained with the PPM method (see Table 2) for all these overdensities. A group is also present in the field of our source 31 at an estimated redshift z = 0.91 in Knobel et al. (2009). This is exactly the spectroscopic redshift of the FR I. Based on spectroscopic redshifts, Knobel et al. (2009) associated only two members with this group. They also estimated a relatively low mass of M = 8.9 × 10¹² M_☉. The PPM does not find this group. It might be explained by the fact that the PPM is more effective at finding more massive structures, as discussed in Section 8 and tested in Paper I.

We now consider those fields in which no overdensity associated with the radio source is found. In Table 3 we report for such fields the overdensities that would be associated with the radio galaxies if their photometric redshifts, as estimated in B13, had significantly higher photometric redshift errors. We adopt the same column description as in Table 2. We do not consider source number 31, for which a spectroscopic redshift is available. We also report only those overdensities that are still detected if a smaller redshift bin Δz is chosen throughout the PPM procedure. Interestingly, among these other overdensities, there is a high significance 3.5σ overdensity which is detected in the field of 13 at a redshift z = 1.42 ± 0.06. Zatloukal et al. (2007) also found the presence of a cluster candidate (i.e., their cluster candidate number 13) in the same field at the redshift z = 1.45. We suggest that the two overdensities correspond in fact to the same cluster.

Table 3. Cluster Candidates not Associated with the Radio Galaxies as Inferred with the PPM

ID	zsource	zoverdensity	Significance	rmin	rmax	rmax, phys.	rmax, comov.
				(arcsec)	(arcsec)	(kpc)	(kpc)
The Low Luminosity Radio Galaxy Subsample
13	1.19±$^{0.08}_{0.11}$	1.42 ± 0.06	3.50	0.0   ——	84.4 ± 8.0 (86.6)	719 ± 68	1741 ± 165
202	1.31±$^{0.09}_{0.12}$	0.91 ± 0.08	2.30	7.6±$^{17.9}_{7.6}$ (0.0)	114.3 ± 16.6 (122.5)	899 ± 130	1718 ± 249
219	1.03±$^{0.02}_{0.04}$	1.20 ± 0.06	2.60	0.0   ——	70.7  ——	589  ——	1297  ——
The High Luminosity Radio Galaxy Subsample
32	2.71±$^{0.38}_{0.34}$	2.22 ± 0.07	2.20	0.0   ——	67.1 ± 7.8 (70.7)	561 ± 65	1808 ± 210

Notes. Cluster candidates in the fields of the LLRGs (top table) and HLRGs (bottom table) not associated with the radio galaxies. Column description: (1) source ID number; (2) photometric redshift of the source along with uncertainties from B13. (3) redshift of the overdensity and corresponding rms dispersion, both estimated with the PPM; (4) significance of the overdensity estimated by the PPM in terms of σ; (5) average minimum radius (arcsec) of the overdensity along with the rms dispersion around the average (both estimated with the PPM). The median value (arcsec) is written between the parentheses; (6) average maximum radius (arcsec) of the overdensity along with its rms dispersion around the average (both estimated with the PPM). The median value (arcsec) is written between the parentheses; (7) average physical size (kpc) of the overdensity along with the rms dispersion; (8) average comoving size (kpc) of the overdensity along with the rms dispersion; The rms dispersions and the median values in Columns 5, 6, 7, 8 are not reported in those cases where the rms dispersion is null.

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We discuss in this section the remaining cases for which the difference between the redshift of the source and the redshift of any overdensity detected in the field is too large to make the association plausible. This is the case for sources 11, 30, 31, 70, 224, and 258.

Source 11 is an HLRG with a photometric redshift $z=1.57^{+0.14}_{-0.09}$. No overdensity is found in its field within the redshift range z_centroid = 0.4–4.0 considered by the PPM.

Source 30 is an LLRG with a photometric redshift $z=1.06^{+0.11}_{-0.07}$. Three overdensities are found in its fields. Their estimated redshifts are z = 1.36, 1.82, and 2.30, respectively. Their detection significances are 2.0σ, 2.0σ, 2.7σ.

Source 31 is an LLRG at z_spec = 0.91. Four overdensities are detected in its field at redshifts z = 0.70, 1.91, 2.27, and 3.62, respectively. They are detected at a significance level of 3.6σ, 2.1σ, 3.1σ, and 2.7σ. Note that none of these overdensities would be associated with the radio galaxy if the photometric redshift $z=0.88^{+0.03}_{-0.05}$ were adopted from B13, instead of the spectroscopic redshift. As outlined in Section 6.1, a group was found by previous work in the field of 31. The estimated redshift and mass are z = 0.91 and M = 8.9 × 10¹² M_☉, respectively (Knobel et al. 2009). As discussed in Section 8 and tested in Paper I the PPM is more effective at finding richer groups and clusters. Therefore, it is not surprisingly that our method does not detect this relatively low mass group.

Source 70 is an HLRG with a photometric redshift $z=2.32^{+0.53}_{-0.20}$. One single overdensity at z = 0.49 is detected in its field, with a significance of 2.0σ.

Source 224 is an LLRG with a photometric redshift $z=1.10^{+0.10}_{-0.04}$. In Figure 9 (panel (d)), we report the corresponding PPM plot. Three overdensities are detected in its field at redshifts z = 0.46, 2.58, and 3.88, respectively. Their high significance patterns are in fact clearly visible in the PPM plot. Their significance levels are 2.3σ, 2.5σ, and 2.6σ.

Source 258 is an LLRG with at z_spec = 0.9009. Four overdensities are detected in this field at redshifts z = 2.07, 2.40, 3.03, and 3.24, respectively. They are detected with significances of 3.4σ, 2.4σ, 2.5σ, and 2.3σ.

As is clear from Table 2, multiple associations are found in the case of sources 03, 25, and 28, only. As outlined in Paper I, multiple overdensities might be detected (1) in the presence of projection effects; (2) because of incorrect photometric redshift estimates that might be affected by systematics, especially in the case of the dimmer cluster members (e.g., those with AB magnitude i⁺ ∼ 24 in the I09 catalog); and (3) as a result of multiple local maxima that characterize the patterns of the PPM plot around a given redshift z_centroid.

We here reconsider in detail all cases where we find multiple overdensities associated with a single galaxy. As mentioned above, two overdensities are associated with source 25 (see also Figure 9, panel (c)). They have similar significances (∼2.5σ) and they are also both detected starting from 50 arcsec from the location of the FR I. Such an angular separation corresponds to ∼400 kpc at the redshift of the LLRG. Similar sizes of ∼0.7–1.0 Mpc are estimated for the two overdensities (see Table 2).

We visually inspected the field of this source and we did not find any evidence that the non-null offset and the multiple association are present because of an artificiality or a technical bias of the I09 catalog occur at the redshift of the radio galaxy (e.g., that some sources at the redshift of the cluster candidate and in the field of the FR I are not included in the I09 catalog or that their redshifts are erroneously estimated). Since we do not find any clear discrepancy between the two overdensities and, furthermore, we estimate similar properties for these two megaparsec-scale structures, we suggest that both the detections are real and they could also correspond to a single cluster candidate associated with source 25.

As mentioned above, two ∼2.5σ overdensities are associated with HLRG 03 (see also Figure 9, panel (b)). They are both detected starting from the coordinates of the radio galaxy (i.e., r_min ∼ 0 arcsec) and their estimated sizes are similar (i.e., ∼500–600 kpc; see Table 2). However, they are detected at significantly different redshifts z = 1.82 and 2.39, respectively. Analogously to the case of source 25, we visually inspected the field of 03 and we did not find any evidence that the multiple association is present because of a technical bias. Therefore, both overdensities are equally considered good, but distinct, cluster candidates, since they are found at different redshifts.

Two overdensities are associated with source 28. They are detected at similar (but different) redshifts z = 2.71 and 2.98, and with similar significances (∼2.0σ–2.5σ). We also estimate similar sizes for both of them (i.e., ∼0.8–1.0 Mpc; see Table 2). However, we find that the overdensity at the lower redshift starts to be detected from 87 arcsec from the radio galaxy. This corresponds to ∼700 kpc at the redshift of the overdensity. Analogously to the case of sources 03 and 25, we visually inspected the field of 28 and we did not find any evidence that the non-null offset and the multiple association are present because of a technical bias. Since we do not find any clear discrepancy between the two overdensities, but nevertheless we estimate different redshifts, we are not able to conclude if the associations correspond either to two separate megaparsec-scale overdensities at different redshifts or to a single megaparsec-scale structure that is identified as a double pattern in the PPM plot.

We repeat all analyses not considering sources that are classified as stars, X-ray AGNs, or that are in masked areas in the I09 list. Hereinafter we refer to this as the clean catalog. Stars and X-ray AGNs are about ∼4% of the sources in the catalog, while masked sources are about ∼13%–18% (in the redshift range of our interest). The fields of 36 and 285 were almost completely masked-out most likely because the seeing in the Subaru optical images (Taniguchi et al. 2007) was poor. We visually inspect the HST image of these fields and we find that all masked-out objects are in fact galaxies. Therefore, in these cases we include these masked out objects in our analysis. If the full I09 catalog is adopted we find evidence of overdensities in both of these fields.

Interestingly, we find evidence for a 2.5σ overdense region associated with the radio galaxy 234 only if the clean catalog is adopted, while no overdensity is found if the complete I09 catalog is adopted. We visually inspect the HST image of that field and verify that some sources have been masked south of the location of source 234 because they are most likely foreground bright sources. We also find evidence for a segregation of z ∼ 0.93 sources in the proximity of the radio galaxy 234. We believe that the discrepancy in adopting the two I09 catalogs is due to the fact that the estimated mean number density of the COSMOS field is lower if the clean catalog is adopted rather than if the full catalog is considered, while the number of masked sources in the field of 234 is low enough to detect the overdensity only if the clean catalog is used. For the sake of completeness, we report the overdensity associated with source 234 in Table 2. The fields of 36, 234, and 285 are the only cases for which we find a significant difference adopting the two I09 catalogs.

In this section we limit our discussion to the cluster core sizes estimated by the PPM. The PPM detects all of the overdensities within given areas in the projected sky around the location of each radio galaxy. The procedure is fully described in Paper I and summarized in Section 5. The PPM infers the minimum and maximum distances from the coordinates of the radio galaxy at which the overdensity is detected.

The distances are estimated by averaging over all the points of the PPM plot having the significance of the overdensity and located around the redshift of the overdensity at the fixed bin (Δz = 0.28). Such estimates are shown in Table 2 for our cluster candidates. Both the average and median values are reported. The median values are less affected by the outliers and are always nevertheless consistent with the corresponding averages within the rms uncertainties. These aspects suggest that the overdensities are detected in the projected space with good accuracy and that these detections are stable with respect to a different choice of parameters (i.e., a different centroid of the redshift bin adopted).

In Figure 10 we plot the comoving (right panel) and physical (left panel) average maximum radii for each overdensity, along with the corresponding rms dispersions as a function of the estimated redshift of the overdensity along with its formal uncertainty. We conservatively reject all sources with multiple overdensity detections.

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The cluster candidates around the LLRGs have, on average, comoving (physical) estimated sizes of r_avg = 1672(784) kpc, with an rms dispersion around the average of 522 (211) kpc and a median value r_median = 1501(800) kpc. The overdensities around the HLRGs have an estimated average comoving (physical) size of r_avg = 1955(745) kpc, an rms dispersion around the average of 780 (236) kpc, and a median value r_median = 2012(871) kpc. If we do not distinguish between the two different classes we have an average comoving (physical) value of r_avg = 1762(772) kpc, an rms dispersion around the average of 607 (213) kpc, and a median value r_median = 1501(800) kpc.

Note that these are only rough estimates of the core size of our cluster candidates. However, concerning our project, we can use them to infer interesting considerations (see also Sections 8.7 and 8.8). In general, these results suggest that the overdensities in our sample have similar core sizes, independently of the class considered (i.e., the LLRGs or the LHRGs).

More in general, there seems to be a trend where high-redshift sources are also found in overdensities with higher comoving sizes. We do not find any statistical significance by performing the Spearman test. Nevertheless, we cannot exclude that less dense overdensities occur at high redshifts. Diffuse protoclusters with star-forming galaxies have been in fact found at redshifts higher than z ∼ 2.0 (Steidel et al. 2000; Venemans et al. 2007; Capak et al. 2011; Noble et al. 2013). However, we suspect that this trend is artificial and due to the dependence of the estimated size with redshift or by the low number count statistics. Another possibility is that the cluster size could be overestimated at most by a factor of ∼2 if (1) the radio galaxy were not located in the central regions of the cluster core (as tested in Paper I), and (2) in the cases when r_min is not null (the crosses in Figure 10), where ${\rm r_{\rm max}}$ might not be a good cluster size estimator (see also discussion in Section 8.8).

The cases where the minimum distances are estimated to be small or null likely correspond to those where the coordinates of the radio galaxy fairly coincide with the center of the associated overdensity.

However, some of the overdensities are detected starting from a positive angular separation of ≳50 arcsec from the coordinates of the radio galaxy. Such an offset corresponds to a physical scale of 422 kpc at the median redshift estimated for our cluster candidates (i.e., z = 1.3).

These cases are controversial and are further discussed in Section 8.8. They might be megaparsec-scale overdensities where the radio galaxy is in the outskirts of the overdensity. This has been investigated in Paper I through the help of simulations. We have found that the method is able to detect cluster candidates even if the coordinates of the cluster are known with an accuracy of ∼100 arcsec and that the inferred minimum radii are only in some cases greater than zero. Alternatively, in these cases the radio galaxies might be hosted in underdense regions within their cluster environment.

As outlined above, we also visually inspected the fields of some sources (namely, 25 and 28) for which the overdensity starts to be detected from a non-null separation from the location of radio galaxy. Even if we find a depletion in the number of photometric redshifts around the radio galaxy around its assumed redshift, we are confident that no technical bias occurred, concerning the estimation of photometric redshifts in the I09 catalog.

We compare our results with those obtained independently by using the P08 method, as described in Section 7. All six cluster candidates found with the P08 method are also detected by the PPM. Five of them are associated with radio galaxies in the sample, according to the PPM procedure. The sixth overdensity is the cluster candidate found in the field of 13 by both the PPM and the P08 method. However, according to the method, such an overdensity is not associated with the radio galaxy by the PPM (see Section 6.2). Note that all of the six overdensities detected by both the P08 method and the PPM are at redshift z ≳ 1.3 (within the corresponding uncertainties), as estimated by the PPM procedure. This is also true for the overdensities in the fields of 13 and 39. Even if the radio sources are at redshifts $z= 1.19\pm ^{0.08}_{0.11}$ and $z=1.10\pm ^{0.05}_{0.05}$, the PPM detects overdensities in their fields at z = 1.42 ± 0.06 and z = 1.27 ± 0.06, respectively. These results are not surprising since the P08 method is effective at finding clusters at z > 1.3.

Excluding the overdensity in the field of 13 that is not associated with source 13, only 5 out of the 12 cluster candidates at z ≳ 1.3 in our catalog are also found with the P08 method. Among the 12 clusters we conservatively do not consider the overdensities in the fields of sources 38 and 228. Even if these sources have photometric redshifts $z=1.30\pm ^{0.17}_{0.28}$ and $z= 1.31\pm ^{0.05}_{0.07}$, respectively, the PPM detects clusters in their fields at redshifts below z = 1.3.

Two out of the five clusters, namely, 29 and 39, that are associated with the radio galaxies and detected by both the P08 method and the PPM, are around LLRGs, the other three (namely, source 03, 04, and 28) are around HLRGs. As discussed above, source 39 is the only source out of those five that has a photometric redshift below z = 1.3.

If we consider our seven cluster candidates at z ≳ 1.3 in our catalog that are not detected by the P08 method we find that three of them are associated with LLRGs (i.e., sources 2, 22, and 25). The remaining four out of the seven are associated with z ≳ 1.3 HLRGs (i.e., 05, 34, 37, and 226). Since the P08 method was primarily designed to search megaparsec-scale overdensities at these redshifts, it is interesting that many of our z ≳ 1.3 cluster candidates are not detected by such a method. It is therefore worth reconsidering in more detail our cluster candidates found around our z ≳ 1.3 sources.

Three of our cluster candidates are at z ≃ 2. These are the overdensities associated with sources 03, 05, and 226. As mentioned before, the presence of megaparsec-scale overdensities around those sources were previously suggested in C10. Interestingly, the P08 method finds the overdensity in the field of 03 only.

If we focus on the nine 1.3 ≲ z ≲ 2 sources that the PPM finds to be in dense megaparsec-scale environments, (i.e., sources 02, 04, 22, 25, 29, 34, 37, 38 and 228) we find that only two out of the nine are found in dense environments by the P08 method (i.e., sources 04 and 29). However, among them, the estimated redshifts of the cluster candidates associated with sources 37 and 38 are only marginally consistent within the redshift uncertainties of the two sources. These two cases could correspond to false positive overdensity PPM detections. Furthermore, the P08 method should not be able to detect the z = 0.88 overdensity associated with source 38, since such a redshift is well below the redshift range where the method is effective. The case of 37 is different; this is because the overdensity associated with this source has an estimated redshift z = 1.95. Therefore it falls within the redshift range allowed by the method.

Excluding source 38, the results reported above imply that 75% ± 15} of our 1.3 ≲ z ≲ 2 cluster candidates are not detected by the P08 method (we have conservatively excluded the above mentioned source 39 that is at a redshift formally below z = 1.3). Such a percentage decreases down to to 71% ± 17% if source 37 is also not considered.

We consider separately the high-redshift z ∼ 3 source 28 that is detected to be in a dense environment at ∼2.6σ and ∼2.5σ significance levels by the P08 method and by the PPM method, respectively. Even if such a redshift is formally beyond the redshift interval (z ∼ 1–2) of our interest, we do not reject the source.

These results suggest that the great majority (≳ 70}) of our z ≳ 1.3 cluster candidates are not detected by the P08 method, while all the seven cluster candidates found with such a method are also detected by the PPM. This suggests that our method might be more effective at finding cluster candidates, at least limited to our sample and data set used. We will further discuss these results in the following section.

In the previous section we found that the great majority (i.e., ∼70%) of our z ≳ 1.3 cluster candidates are not detected with the P08 method, while all of the cluster candidates detected by such a method are also found with the PPM. This is interesting, since such redshifts correspond to the range within which the P08 method is effective (Galametz et al. 2012). Although we cannot fully understand the details for such a discrepancy we believe that the method might miss those overdensities that do not fulfill the specific P08 color selection.

This result could also have physical implications. The P08 method searches for segregations of red ([3.6] − [4.5])_AB galaxies. In principle, it is sensitive to both passively evolving and star-forming galaxies. However, the method might miss overdensities that are populated by a great amount of bluer galaxies than those required in order to detect the overdensity.

As argued by Muzzin et al. (2013), foreground galaxies at redshift 0.2 < z < 0.4 have colors similar to those at redshift z > 1.0 and might add noise, thus affecting the detections.

Furthermore, we also found that the majority of the objects that are used for the PPM and are selected within the I09 catalog are not included in the S-COSMOS survey and, therefore, they are not used by the P08 method. Hence, a mismatch between the P08 method and the PPM is not surprising.

Note that we applied the P08 method by performing a counts-in-cell analysis, i.e., we counted objects within a fixed circle centered at a given position in the sky, as done in previous work (e.g., Galametz et al. 2012; Mayo et al. 2012; Wylezalek et al. 2013).

On the contrary, the search for cluster candidates performed in this work by adopting the PPM is based on number counts and does not rely on peculiar and specific properties (e.g., colors of the sources) and a specific segregation of the galaxies within the cluster core (see also Section 8.8).

Since the P08 method is applied performing a counts-in-cell analysis, some of the clusters that are not detected by such a method might be populated by galaxies that are not completely segregated in the cluster core.

Interestingly, C10 suggested the presence of a high fraction of star forming galaxies in the z ∼ 2 cluster candidates associated with sources 03, 05, and 226, on the basis of the visual inspection of the RGB images of their fields.

In a forthcoming paper we will analyze the color magnitude diagrams to study the star formation activity of the galaxies in our clusters and address the problems of detecting and studying the red sequence, as well as understanding where star forming and quiescent galaxies are located within the cluster.

The evidence for star formation activity in some of our clusters is not surprising, especially at z ≳ 1.5, where cluster galaxies are expected to have ongoing or increasing star formation (Zeimann et al. 2012). In fact, in some of these high-redshift clusters, a significant fraction of the cluster galaxy population is constituted by highly dust reddened sources (Strazzullo et al. 2013) or by blue and irregular galaxies (Tozzi et al. 2013).

From a theoretical point of view, previous studies made predictions for the mass function of galaxy clusters (e.g., Bode et al. 2001; Tinker et al. 2008). However, since the cluster/group population at redshift z ≳ 1.5 is limited to a few known spectroscopically confirmed clusters, observational studies are limited to single high-redshift clusters. This implies that the mass function is only poorly determined by observations.

The spectroscopic confirmation of our z ≳ 1.5 cluster candidates would increase the number count statistics. This will help in constraining the cluster mass function and will support previous cluster studies from both a theoretical and observational point of view.

As reported in Section 6 both LLRGs and HLRGs are found in dense environments. The fraction of galaxies in groups or clusters is about ∼70% for both subsamples, consistent within the 1σ uncertainties. We also found that the detected overdensities have comparable (within a factor of ∼2–3) estimated sizes, independent of both the subsample and the redshift considered (we will discuss this in detail in Section 8.7). Therefore, a posteriori, this result strongly suggests that, on a statistical basis, the two subsamples constitute a single population of radio galaxies with similar megaparsec-scale environments and similar properties.

We found that the majority (69% ± 8%) of the radio galaxies in our sample reside in dense environments. Here we quantitatively compare our results with the results obtained for samples of low redshift FR Is.

Note that it is difficult to compare the estimated cluster richness of our candidates with that of other samples of low redshift clusters associated with radio galaxies. This is mainly because of the different data sets used and of the different techniques employed in measuring the cluster richness.

Zirbel (1997) found that 70% (with an estimated uncertainty of 11%)¹³ of low redshift (i.e., z < 0.25) FR Is in their sample reside in intermediate or rich groups (i.e., structures with 10 or more members). In terms of richness, these groups could roughly correspond to the overdensities detected by the PPM around the radio galaxies in our sample.

Instead, only (24 ± 8)% of the low redshift (i.e., z < 0.25) FR IIs in the Zirbel (1997) sample reside in intermediate or rich groups. Such a percentage increases up to (41 ± 8)% if high-redshift (i.e., 0.25 ≲ z ≲ 0.5) FR IIs are considered. The results obtained by Zirbel (1997) are also in agreement with that independently found for FR IIs at z < 0.3 by Smith & Heckman (1990) and that found by Ramos Almeida et al. (2013) for a z ⩽ 0.7 sample of luminous radio galaxies, mainly comprised of FR IIs.

Interestingly, the fraction we found for the z ≳ 1 sources in our sample is fully consistent with the percentage (i.e., 70%) found by Zirbel (1997) for their sample of low redshift (i.e., z < 0.25) FR Is. Note that this holds not only for the LLRGs but also for the HLRGs. This implies that the environments of FR Is and FR IIs are different and that they also evolve differently with redshift. While the majority of FR Is seem to be found in rich groups or clusters at all redshifts, the FR IIs seem to inhabit rich environments only at z > 0.25. However, as discussed in the following section, the fraction of FR IIs that reside in rich groups or clusters is significantly lower than that of FR Is even at higher redshifts.

In this section we compare our results with the environment properties found for high-redshift FR IIs. Note that, thanks to the analysis of the C09 sample, this is the first time that the environments of FR Is and FR IIs can be directly compared at such high redshifts.

High-redshift (z ∼ 1–2), low-power radio galaxies (i.e., FR Is) are found in rich environments more frequently than high-power FR IIs at similar redshifts. In fact, if we consider the sample of high-redshift (z ≳ 1.3) powerful FR IIs studied by Galametz et al. (2012), 11 out of 48 objects (i.e., 23% ± 7%) reside in megaparsec-scale environments that are at least 2σ denser than the field.

However, Wylezalek et al. (2013) extended this analysis to a larger sample of 387 radio galaxies at 1.3 < z < 3.2. They found evidence for dense environments for 55% of these sources. Interestingly, this percentage is consistent with that found for FR II radio galaxies at redshifts z ∼ 0.5 (∼50%; Hill & Lilly 1991).

Note that the radio powers that characterize the objects in all of the samples cited above (L_1.4 ≳ 10³⁴ erg s⁻¹ Hz⁻¹) are about two order of magnitudes higher than those of all of the radio galaxies in our sample, including the HLRGs. Hence, they undoubtedly represent a different class of radio galaxies.

The comparison between our results and those cited above for powerful high-z FR IIs confirms that the environment of high-redshift FR Is and FR IIs is different.

This implies that the megaparsec-scale environments of FR Is and FR IIs undergo a different evolution. If we adopt a ∼50% level of FR IIs in clusters at high redshifts as a fiducial value, we could conclude that at z > 0.5 the environments of FR Is and FRII s are similar (but not identical!). However, as we already discussed above, this is clearly not true at lower redshifts. Furthermore, the values reported in Galametz et al. (2012) and Wylezalek et al. (2013) are not consistent with each other within the number count uncertainties. Wylezalek et al. (2013) suggested that this may be due to the small size of the Galametz et al. (2012) sample. It might be interesting to study in more detail the selection criteria of these two samples in order to test whether the differences are due to significant discrepancies in the two sample selections.

Therefore, in light of the results presented here, we confirm that the connection between the active nucleus and its large-scale environment could play a fundamental role in determining the specific properties of each radio galaxy. Clearly, it would be interesting to study X-ray or optically selected samples of clusters of galaxies at redshifts z ≳ 1 to investigate how the cluster properties (e.g., richness, halo mass, gas content, and X-ray luminosities) are related to those of the hosted radio galaxies (e.g., their radio power, their number within the cluster sample, and the mass and size of the host galaxy) and more in general, to those of the entire cluster galaxy population. However, these studies require complete and well studied samples of clusters. Therefore, previous work has been so far limited to low or intermediate redshifts (e.g., Ledlow & Owen 1996).

We here focus on previous studies on intermediate (0.3 ≲ z ≲ 1) redshift cluster samples. Radio sources with radio power L_1.4 ≃ 10^{32 − 33} erg s⁻¹ Hz⁻¹ which is typical of those of the objects in our sample, are found in 10%–20% of the X-ray and optically selected clusters (Branchesi et al. 2006; Gralla et al. 2011).

However, such a percentage rapidly increases up to ≳ 90% if lower power radio sources are included (L_1.4 ≃ 10³⁰ erg s⁻¹ Hz⁻¹; Branchesi et al. 2006). This is in agreement with previous studies on local Abell clusters (Ledlow & Owen 1995, 1996).

The fact that such a fraction increases for low-power sources might be explained as a straightforward consequence of the steepness of the radio luminosity function of the radio galaxies in clusters (Branchesi et al. 2006). This strongly confirms that low-power radio galaxies can be more successfully used to search for clusters of galaxies than radio galaxies with higher power.

The number density per unit redshift (dn/dz/dΩ) in the COSMOS survey is low and it is equal to ≃ 25, 10, and 3 arcmin⁻² at redshifts z ≃ 1, 1.5, and 2.0, respectively (Ilbert et al. 2009). The steep decrease of the number counts for increasing redshifts is a strong constraint for all of the methods (including the PPM) that search for megaparsec-scale overdensities on the basis of number counts (Scoville et al. 2013).

In addition, photometric and spectroscopic redshifts cannot be easily obtained within z ∼ 1–2, where most of the relevant spectral features fall outside of the instrumental wavelength bands (Steidel et al. 2004; Banerji et al. 2011).

Therefore, methods that are based on number counts and redshift information and that are used to search for clusters and groups in the COSMOS survey are usually applied up to redshifts z ≲ 1 (e.g., Knobel et al. 2009; George et al. 2011; Knobel et al. 2012), or at redshifts higher than z ≃ 2 (e.g., Diener et al. 2013). Note also that such methods commonly use spectroscopic redshifts so that a small number (i.e., ≲ 5) of cluster galaxies is sufficient to establish the presence of a cluster or group candidate.

The clusters in our sample are detected within the entire redshift range z ∼ 1–2 of our interest. For each overdensity we estimate detection significance, redshift, and size. The overdensities are detected up to 5.6σ significance. All these results are ultimately due to the flexibility of the PPM to obtain robust results in presence of low number counts. The overdensities are detected with median significances of 3.3σ and 2.5σ for the LLRGs and the HLRGs, respectively. Since the cluster candidates around the LLRGs and the HLRGs have a median redshift z = 1.17 and z = 1.97, respectively, we suggest that the discrepancy between the detection significances of the clusters associated with the two different subsamples is due to the decreasing number counts in the COSMOS survey for increasing redshifts. However, such discrepancy is relatively small considering that the number density in the COSMOS field dramatically drops down by a factor of ∼8 from z = 1 to z = 2 (Ilbert et al. 2009).

In Paper I we tested the ability of the PPM to detect overdensities at different redshifts, with richness and size spanned within the ranges found for the cluster candidates in our sample. Interestingly, we found that our method is able to efficiently detect clusters within our redshift interval, despite the wide range allowed for the cluster richness and size.

Therefore, we are confident that the detection efficiency (i.e., the number of clusters with homogeneous properties that are potentially detectable per unit redshift by the PPM) is fairly constant with redshift. The fact that the detection rate is about 70% for both our subsamples confirms it a posteriori. Conversely, if the detection efficiency dramatically decreased for increasing redshifts, we would significantly underestimate the fraction of HLRGs in clusters.

Six overdensities in our sample are found at redshift z > 1.5. These correspond to sources 03, 04, 05, 28, 37, and 226. All of them are HLRGs. The fact that we find six overdensities at such a high redshift, despite the small area of the COSMOS survey, further suggests that these might be clusters with a low or intermediate mass (i.e., M ≃ 10^{13 − 14} M_☉).

Furthermore, the number density of clusters of higher mass (i.e., M ≳ 10¹⁴ M_☉) is expected to drop down by more than an order of magnitude between z = 1 and z = 2, according to the current ΛCDM scenario (e.g., Bode et al. 2001; Tinker et al. 2008). In fact, clusters with masses M ≳ 10¹⁴ M_☉, at redshift z ∼ 2, are most likely the progenitors of massive M ≳ 10¹⁵ M_☉ clusters at z = 0 (Chiang et al. 2013). Conversely, assuming hierarchical clustering (Cooray & Sheth 2002), at z ∼ 2, groups of lower mass could represent a larger fraction of the group/cluster population than at lower redshifts.

Furthermore, by definition, groups have a lower richness than clusters, they exhibit fainter X-ray emission, and they have lower mass content in terms both of dark matter and gas than clusters of galaxies. They are therefore more difficult to find with the conventional techniques adopted for clusters. High-redshift groups are in fact usually identified up to z ≲ 1 with methods such as those based on number counts (Knobel et al. 2012; More et al. 2012), or searching for strong lensing signatures originating from megaparsec-scale dark matter halos (Cabanac et al. 2007; Limousin et al. 2009; More et al. 2012, see also Section 8.9). Interestingly, if our cluster candidates were confirmed to be rich groups (see Section 8.7.1), they would constitute a high-redshift sample.

Diener et al. (2013) obtained a number of 42 candidate groups at z ≳ 2 in the COSMOS field. They used spectroscopic redshifts, so that a small number (i.e., ≲ 5) of members is effective at establishing the detection of a cluster candidate. Impressively, for the only object in common with our list (i.e., their cluster candidate 22 corresponds to our cluster candidate 03) the redshift and the size of the cluster estimated by the PPM fully agree with the spectroscopic measurement and the cluster size estimated in Diener et al. (2013).¹⁴ Note that this cluster candidate was suggested by previous work (Chiaberge et al. 2010). With its five spectroscopically selected cluster members, this is the richest among the groups in the Diener et al. (2013) catalog.

On the basis of the redshift information, the authors also estimated the velocity dispersion of the cluster members (526 km s⁻¹) which is significantly higher than the average ∼300 km s⁻¹ among the group candidates in their sample. This might suggest that the cluster members are still encompassing a spatial segregation and that the cluster is still forming, as also discussed for other cluster candidates in our sample (see also Section 7.2).

The general relationship among richness, size of the cluster, and the cluster mass is quite complex (i.e., it depends on the depth of the photometric catalog, the redshifts, the evolution of the luminosity function), especially at the redshifts of our interest (z ∼ 1–2), where the properties of the cluster galaxy population in terms of luminosity and segregation within the cluster are expected to evolve and are not fully understood. In the following sections we discuss size, mass, and richness estimates for the clusters we find in COSMOS.

8.7.1. Size and Mass Estimates for the z ∼ 1 Clusters

8.7.2. Cluster Richness and Mass

Previous work investigated the position of BCGs and radio galaxies in clusters. Ledlow & Owen (1995) found that about 90% of the radio galaxies hosted in local (z < 0.09) Abell clusters are located within 200 kpc from the cluster center. Furthermore, the great majority of such local radio galaxies are FR Is. Similarly, Smolčić et al. (2011) studied a sample of X-ray-selected groups up to z ≃ 1.3. They found that low-power radio galaxies (L_1.4 ≃ 10^{30.6 − 32.0} erg s⁻¹ Hz⁻¹) are preferentially found within 0.2 × r₂₀₀ from the group center (i.e., about ≲ 60 kpc).

This could also be true at our redshifts. In fact, for the six cluster candidates that are found by other authors in the fields and at the redshifts of our sources (namely, 01, 03, 16, 18, 20, and 31) using different techniques (i.e., X-ray emission and overdensities based on redshift information, Finoguenov et al. 2007; Knobel et al. 2009; George et al. 2011; Knobel et al. 2012; Diener et al. 2013) we can compare the locations of our FR I beacons with the coordinates of the cluster centers, as estimated by these authors. We find that in the cases of 01, 03 and 31 the offset is less than ∼14 arcsec. They correspond to ≲ 120 kpc at the redshifts of the overdensities. In the cases of sources 16, 18, and 20 the association between our FR I beacons and the cluster candidates found in other catalogs (Knobel et al. 2009, 2012) is less certain. This is because the offset is higher than the cases outlined above. It is about 40 arcsec for sources 18 and 20 (i.e., ∼300 kpc at their redshifts) and it is ∼1 arcmin (i.e., ∼500 kpc) for source 16. All these values statistically agree, on average, with the result reported by Ledlow & Owen (1995).

This is also consistent with the offset of ∼100 kpc, typically found between the optical and the X-ray cluster centroids (Dai et al. 2007). Furthermore (as pointed out in Section 1), at variance with FR II radio galaxies or other types of AGNs, low-redshift FR Is are typically hosted by undisturbed ellipticals or cD galaxies (Zirbel 1996), which are often associated with the BCGs (von der Linden et al. 2007). To the best of our knowledge, the bright BCG discovered by Liu et al. (2013) at z = 1.1 is the most distant cD galaxy confirmed to date. Therefore, in light of the results presented here, the hosts of our FR Is could also constitute a sample of high-z cD galaxy candidates.

Concerning the BCGs, previous work found that they preferentially reside within ≲ 41 kpc from the X-ray cluster center up to z ≃ 1 (Semler et al. 2012). However, Zitrin et al. (2012) found that the offset, if estimated from the optical cluster centroid, increases for increasing redshifts (i.e., up to ∼14 kpc at 0.52 < z < 0.55). A similar trend is not excluded for our cluster candidates. In fact, we find that six of our cluster candidates are detected within an annulus centered at the coordinates of the radio galaxy and an internal radius of ≳ 50 arcsec (see also Table 2 and related discussion in Section 6.4). Note that 50 arcsec correspond to 427 kpc at redshift z = 1.5. These six overdensities correspond to 32% ± 11% of our 19 cluster candidates.¹⁷

The six sources are the LLRGs 26, 29, and 285 and the HLRGs 34, 37, and 226. Although the statistics is extremely poor, this result implies that half of the sample of the HLRGs show significant offsets (i.e., ⩾50 arcsec), while a non-null offset occurs for only ∼20% of the LLRGs. However, based on such a small sample we do not draw firm conclusions.

In order to investigate the marginal discrepancy found between the two subsamples, it would be interesting (1) to look for FR I radio galaxies in COSMOS at redshifts similar to those of the HLRGs, but with radio powers comparable with those of the LLRGs, and (2) to search for radio galaxies with redshifts similar to those of LLRGs and radio powers comparable with those of the HLRGs. This will improve the sample statistics and will allow us to understand if the trend is due either to evolutionary properties (being the LLRGs, on average, at lower redshifts than the HLRGs) or to the difference in radio power between the LLRGs and the HLRGs.

A possibility is that such radio galaxies are hosted in underdense regions within their cluster environment. To further investigate the above scenario we visually inspected the fields of the six sources. We did not find any evidence that the non-null offsets are present because of an artificiality or a technical bias of the I09 catalog (e.g., that some sources at the redshift of the cluster candidate and in the field of the corresponding FR I are not included in the I09 catalog or that their redshifts are erroneously estimated). We also found that the galaxies in each of these fields at redshifts around that of the corresponding FR I are homogeneously distributed around the position of the radio galaxy. This means that, although these overdensities are detected with significant offsets from the location of the corresponding FR I, each radio source is still likely located around the barycentric center of the galaxies in the field, in the projected sky, and not in the outskirts of the cluster candidate.

Furthermore, our results could also imply that our cluster candidates are still encompassing a strong evolution in terms of the spatial segregation of the galaxies within the core (see, e.g., Bassett et al. 2013, for a very detailed study about a z ∼ 1.6 forming cluster).

In this section we discuss the serendipitous discovery of a bright arc detected with the ACS camera on board HST in the field of source 01, at z_spec = 0.88. In Figure 12 we report the ACS image (Koekemoer et al. 2007) of the field of 01. Source 01 and the arc are marked in the figure with the left and the right ellipses, respectively.

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The arc is clearly visible about ∼5 arcsec westward of the pair formed by the radio galaxy host and a larger elliptical companion. Such a projected angular separation corresponds to ∼39 kpc at the redshift of the source. The arc is very close to the radio galaxy, and it resides within the core of the megaparsec-scale overdensity associated with source 01.

Strong lensing phenomena are expected to be originated close to the densest regions of dark matter halos. Since such a projected separation is consistent with the typical size (i.e., ∼60 kpc; Halkola et al. 2007) of the dark matter halos of BCGs, it is likely that the arc originated from the dark matter halo of the galaxy pair.

An alternative scenario is motivated by the fact that the overdensity associated with source 01 is a relatively compact rich group with an estimated core size of about 70 arcsec (as suggested by Finoguenov et al. 2007; George et al. 2011; Knobel et al. 2012, and in this work). Therefore, it is also possible that the group halo itself is responsible for the observed effect. In fact, groups with intermediate masses in the range 10¹²–10¹⁴ M_☉ are usually more massive than galactic halos and concentrated enough to act as lenses (More et al. 2012).

The I09 catalog reports a photometric redshift z = 0.715 for the arc. However such a redshift is significantly lower than that of 01. This is unexpected, since the dark matter halo should be located between the observer and the lensed object. In order to understand the discrepancy we visually inspected the COSMOS archival images of the field at different wavelengths, roughly between the i and the u bands. In Figure 13 we report four images (10'' × 10'' each) of the field of the arc, which is clearly marked with a green circle in each of them.

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We find that the arc is very bright from the F814W filter to the B-band, but it completely disappears in the u*-band. Therefore, we suspect that this is a u-band drop out and that the source associated with the arc is located at redshift z ≃ 2.3 or even higher.

While the arc clearly disappears in the u-band image, a close companion SW of the arc is clearly visible in all four images. We suspect that, during their automatic procedure, I09 erroneously associated with the bright arc the u*-band flux measurement that corresponds to this companion. This likely leads to an incorrect photometric redshift estimate.

Hence, our serendipitous discovery suggests that this project might also be promising for systematic studies of (strong) lensing features observed in rich groups or clusters. Our method might be complementary and would extend to higher redshifts projects that find rich groups on the basis of strong lensing signatures (e.g., Cabanac et al. 2007; Limousin et al. 2009; More et al. 2012).

One limitation of such searches is that lensing features are less likely at increasing redshifts. This is mainly because the projected number density of background objects decreases as the redshift of the lens increases. This has so far limited the number of high-redshift groups detected by means of strong lensing phenomena to z ≲ 1.2. Similarly, we expect to have a better chance of observing possible occurrence of lensing phenomena for our z ≃ 1 cluster candidates than at higher redshifts. Therefore, our sample might not include a large number of strongly lensed objects while it includes an extremely useful number of high-redshift groups.

HLRGs represent the class of relatively higher power radio galaxies in our sample. As discussed in Section 3 and clearly shown in Figure 5, such sources have radio power slightly above the formal FR I/FR II radio power divide. Furthermore, the possible presence of bimodality in the radio power distribution of FR Is in our sample suggests that HLRGs might be drawn from a different parent population (see Section 3.6). In this section we will discuss the properties of HLRGs with respect to their radio properties.

Radio galaxies with clear FR II morphology (i.e., which showed evidence of clearly separated hot spots) were rejected during the C09 sample selection procedure. This immediately excludes the possibility that the HLRGs might be classical FR II radio sources based on their radio morphology.

8.10.1. Radio Galaxies of Transitional Type

8.10.2. Compact Radio Sources