The Massive and Distant Clusters of WISE Survey. VIII. Radio Activity in Massive Galaxy Clusters

The main cluster catalog we refer to is the MaDCoWS cluster survey (Gonzalez et al. 2019). The MaDCoWS algorithm searches for overdensities in data from WISE (Wright et al. 2010). MaDCoWS uses a combination of updated AllWISE data (Cutri et al. 2013) in 3.4 μm and 4.6 μm, with enhanced photometry and astrometry from the All-Sky data release, and optical data from Pan-STARRS Data Release 1 (Chambers et al. 2016) in the Northern Sky or SuperCOSMOS (Hambly et al. 2001) for δ < −30° to reject foreground galaxies. The MaDCoWS candidates of highest significance were targeted with Spitzer IRAC 3.6 and 4.5 μm snapshot follow-up. We obtained observations of 200 MaDCoWS clusters in Cycle 9 and an additional 1759 in Cycles 11 and 12 (PIs: Gonzalez, Brodwin; PIDs 90177, 11080, 12101).

The additional Spitzer data enable us to estimate both photometric redshifts and richnesses for the clusters. We summarize the method for these estimations below, and refer the reader to Gonzalez et al. (2019) for details. Photometric redshifts are determined by comparing the effective Spitzer [3.6]–[4.5] and Pan-STARRS i − [3.6] colors of cluster galaxies within 1'of cluster center to that expected for a passively evolving galaxy formed at z = 3. Comparing the photometric redshifts to a sample of 29 MaDCoWS clusters with spectroscopic redshifts yields a scatter of ${\sigma }_{z}/(1+z)\,=0.03$. The scatter does not show strong dependence on redshift (Figure 13, Gonzalez et al. 2019). The richness is the number of galaxies matching the same color criteria above the 4.5 μm threshold F_4.5 > 15 μJy (5 × 10¹⁰ M_⊙) within 1 Mpc of cluster center. A richness of λ₁₅ = 22 corresponds to a cluster mass of ${M}_{500,c}={10}^{14}$ M_⊙.

Cluster centroids are determined using density-smoothed maps of the WISE overdensity. The cluster center is the pixel containing the peak value after smoothing. The major limitation of this method is the resolution of the smoothed density maps, resulting in a positional uncertainty ${\sigma }_{\alpha }={\sigma }_{\delta }=15^{\prime\prime}$. Because the centroid is computed before the photometric redshift is determined, the uncertainty in the photometric redshift does not factor into the uncertainty in the centroid.

Out of 1695 clusters with Spitzer-based photometric redshift and cluster richness estimations, 873 clusters fall within the region covered by FIRST.

The Very Large Array (VLA) carried out the Faint Images of the Radio Sky at 20 cm (FIRST) survey (Becker et al. 1995). FIRST offers the largest sky coverage at 1.4 GHz, complete to 1 mJy with a resolution of 5''. We use the 14 Dec 2017 version of the catalog covering roughly 10,575 square degrees. The catalog includes radio source position (accurate to 1'' at 90% confidence for point sources), integrated flux calculations, and size estimations after Gaussian deconvolution.

In order to avoid edge effects and low-quality data in the survey outskirts, we limit the survey region to 110° < α < 262° and −8° < δ < 63° in the north and 325° < α < 40° and −10° < δ < 10° in the south. Also, we only consider FIRST sources above the limiting flux (1 mJy) and with a low probability of being a side lobe ($\mathrm{SIDEPROB}\leqslant 0.015$). After these selection limits, the FIRST catalog is culled to 595,526 radio sources. We find 213 FIRST sources within 500 kpc of MaDCoWS cluster centers.

Our cluster galaxy selection technique is similar to those developed by Papovich (2008) and Muzzin et al. (2013), further explained in Gonzalez et al. (2019). We select for cluster galaxies by using Spitzer [3.6] and [4.5] data crossmatched with optical photometry from Pan-STARRS. A passively evolving galaxy will become redder in optical–mid-infrared (MIR) color space between z = 0–2. We only consider cluster galaxies with i − [3.6], consistent with a passive galaxy within the redshift range 0.7 < z < 1.5 for MaDCoWS clusters. We include all galaxies within 500 kpc of the cluster center with 4.5 μm flux F_4.5 > 10 μJy, ⁷ i − [3.6] ≥ 4.85, and 5σ detections in [3.6], [4.5], and Pan-STARRS i.

The caveat to this approach is that ∼40% of galaxies within 500 kpc and F_4.5 > 10 μJy are not detected in Pan-STARRS. We assume these sources to be fainter than the Pan-STARRS limit (i = 23.1, 5σ) (Chambers et al. 2016), which allows us to obtain a lower limit on the i − [3.6] color. Thus, the majority of these sources would also match our selection criteria. We include all galaxies without Pan-STARRS detections but with F_4.5 > 10 μJy and S/N > 5 in [4.5]. Within 500 kpc of the centers of 873 clusters within the FIRST footprint, 37,078 galaxies matched our flux and color criteria.

We calculate the stellar masses for cluster galaxies from the Spitzer 4.5 μm magnitude, adopting the cluster redshift as the redshift of the IR counterpart. We assume a Conroy et al. (2009) stellar synthesis population (SSP) model and Chabrier (2003) initial mass function (IMF), simulating a passively evolving galaxy with a formation redshift of z_f  = 3 (Mancone et al. 2010; Wylezalek et al. 2014). ⁸

Estimating the stellar mass from [4.5] assumes the flux is stellar-dominated with a minimal AGN contribution. To verify that this assumption is reasonable, we examine the distribution of $[3.6]-[4.5]$ colors of the IR counterparts. Stern et al. (2012) presented an AGN selection based on an MIR color of [3.6]–[4.5] ≥ 0.8. We find only five counterparts (2.9%) have MIR color consistent with the emission being AGN-dominated. We also crossmatch the counterparts to optically selected quasar catalogs from Richards et al. (2015), considering both the master and optical-MIR selected samples from their work. Only four counterparts (2.3%) are identified in the Richards et al. (2015) quasar catalogs.

We conclude that AGN emission is not a significant contaminant of the [4.5] stellar mass estimation. To be prudent, we exclude cluster galaxies with [3.6]–[4.5] > 0.6 from any analysis involving cluster galaxy fractions or stellar mass calculations, i.e., 12% of counterparts.

In MaDCoWS clusters within the FIRST footprint, we find 213 FIRST radio sources within 500 kpc of cluster centers. To avoid a radio-luminosity bias when comparing radio sources across redshift, we impose a luminosity limit on the radio sources. Radio luminosity is calculated as ${L}_{1.4\mathrm{GHz}}\,=4\pi {S}_{1.4}{D}_{A}^{2}{(1+z)}^{3+\alpha }$, where S_1.4 is the radio flux at 1.4 GHz, D_A is the angular diameter distance, and α is the spectral index, for a power law defined as ${S}_{1.4}\propto {\nu }^{-\alpha }$. We assume that the radio source is at the cluster redshift. We only consider radio sources with FIRST luminosity ${L}_{1.4\mathrm{GHz}}\geqslant 1\times {10}^{25}$ W Hz⁻¹, which ensures that a radio source at the FIRST flux limit (1 mJy) can still be detected at the highest cluster redshift under consideration (z = 1.5). At this luminosity limit, we are most likely only observing radio emission related to the supermassive black hole (e.g., Kellermann et al. 2016). Coincidentally, this is also the canonical threshold for FR type I and II sources (Fanaroff & Riley 1974). Out of the 213 central 500 kpc FIRST sources, 194 were above our luminosity threshold.

We identified Spitzer−[4.5] counterparts to FIRST radio sources via visual inspection. The visual inspection technique allows us to identify one counterpart for radio sources that were resolved into multiple components in FIRST, decreasing the misassociation of radio sources with complex morphology. We successfully identified 140 IR counterparts for 194 radio sources, where the reduction in the number of identified counterparts to radio sources is due to multiple-component radio sources. We were unable to determine counterparts for 19 radio sources.

To ensure that the counterpart galaxy is a likely member of the cluster, we apply the same color and magnitude selections as discussed in Section 3.1. We obtain i-band magnitudes for counterparts by crossmatching Spitzer positions to Pan-STARRS using a 1'' radius. A total of 118 counterparts matched the cluster galaxy criteria.

To estimate the interloper contamination, we use the i − [3.6] color of the radio source counterpart as a proxy for the galaxy's redshift. A passive galaxy at z ≥ 0.7 has i − [3.6] > 4.85, ⁹ using the same assumptions for stellar synthesis and metallicity as in Section 3.2. Thus, counterparts with color below this threshold are most likely at redshifts lower than that of MaDCoWS clusters. We find 12% of counterparts with color consistent with that of passive galaxies at z < 0.7 and where emission is not AGN-dominated, and therefore are likely foreground interlopers.

The cluster radio active fraction (RAF) is defined as the fraction of galaxy clusters with central radio activity. Any cluster with at least one FIRST radio source above ${L}_{1.4\mathrm{GHz}}\,\geqslant 1\times {10}^{25}$ W Hz⁻¹ and coincident within the central 500 kpc cluster center is deemed a "radio-active galaxy cluster." This luminosity threshold, driven by the depth of the FIRST survey, corresponds to roughly 10× the luminosity of the traditional radio-loudness threshold, and implies that our sources are not just radio-loud, but are "radioluminous." We are only investigating cluster radio activity, and not specifically radio sources, and thus do not require visual identification of the radio-source counterpart. We find that 136 out of 873 MaDCoWS clusters within the FIRST footprint are radio-active, resulting in a MaDCoWS cluster RAF = 0.156 ± 0.014, where the uncertainty is calculated from propagation of Poisson error. ¹⁰

We define a cluster galaxy as radioluminous if it matches the criteria for the cluster radio source selection, detailed in Section 3.3. To summarize, a radio-loud cluster galaxy must match these criteria:

• 1.  
  The cluster galaxy matches the color selection described in Section 3.1.
• 2.  
  The cluster galaxy is visually identified to be associated with a radio source.
• 3.  
  The associated radio source has a luminosity L_{1.4 GHz} ≥ 1 × 10²⁵ W Hz⁻¹, assuming the photometric redshift of the host galaxy cluster.

The cluster galaxy radioluminous fraction (f_rl) is then defined as the fraction of radioluminous cluster galaxies.

In 873 clusters with a total membership of $37,078$ galaxies, we find 118 counterparts that matched the cluster galaxy color selection, which we consider to be radioluminous cluster galaxies. This equates to a total f_rl  = (3.18 ± 0.29) × 10⁻³.

We investigate the dependence of cluster RAF on the cluster richness and by proxy cluster mass. We split the clusters into richness bins spanning λ₁₅ = 0–123. ¹¹ We then calculate the cluster RAF in each richness range. The number of clusters within each richness bin is shown as the top panel of Figure 1.

Zoom In Zoom Out Reset image size

The bottom panel of Figure 1 shows the relationship between the cluster RAF and richness. The uncertainties were calculated as the propagation of the Poisson uncertainty of the number of radio-active clusters and the number of total clusters per bin. We fit a linear model of the form y = ax + b to our data via a least-squares method. The best-fit results were a = (2.7 ± 1.2) × 10⁻³ and b = (6.5 ± 3.7) × 10⁻², with a reduced χ² = 0.92 indicating a reasonable fit. Our results suggest that the likelihood that a radioluminous galaxy is within the central 500 kpc of a galaxy cluster increases with cluster richness. The significance of the trend is marginal (positive slope with 2.25σ significance). This would imply that more massive galaxy clusters have a higher probability of hosting a radioluminous galaxy within the central 500 kpc than clusters of lower mass. If confirmed, such a trend could physically be due to the fact that more massive galaxy clusters are, by definition, richer and contain more galaxies. The probability is therefore higher that at least one of the galaxies in the central 500 kpc is radioluminous.

In Figure 2, we show the distribution of cluster galaxies within the clusters of each richness bin and the radioluminous cluster galaxy fraction as a function of cluster richness. The uncertainties on f_rl were calculated by propagating the Poisson uncertainty on the number of radioluminous cluster galaxies and the number of total cluster galaxies per richness bin. The calculation of f_rl accounts for the increase in the number of galaxies for richer clusters. Similar to the cluster RAF, the cluster galaxy f_rl also shows an increase toward richer clusters. A linear relationship between f_rl and cluster richness has best-fit parameters of a = (4.7 ± 2.5) × 10⁻⁵ and b = (1.6 ± 0.8) × 10⁻³ with reduced χ² = 1.0. While the increase in f_rl is suggestive that the central cluster environment contributes to the increasing RAF with richness, neither trend is statistically significant.

Zoom In Zoom Out Reset image size

We investigate how the cluster RAF has evolved with cosmic time by comparing MaDCoWS to lower-redshift clusters. The redMaPPer cluster algorithm finds galaxy clusters via their red sequence (Rykoff et al. 2014). We use the redMaPPer catalog for SDSS Data Release 8, which contains 25,000 galaxy clusters ranging in redshift of 0 < z < 0.6. The catalog includes a cluster photometric redshift and richness estimate. The redMaPPer richness estimate is based on the methods developed in Rozo et al. (2009) for maxBCG galaxy clusters. Each galaxy within some cutoff radius of the cluster R_c is given a probability of cluster membership based on optically observed properties like color and magnitude. The cluster richness is defined as the sum of the probability of membership for all galaxies within R_c above a luminosity threshold (also see Rykoff et al. 2012, 2014, for details). To compare redMaPPer and MaDCoWS clusters, we use the mass-richness relations for both samples (Figure 11 and Equation B6 in Rykoff et al. (2012) and Figure 16 and Equation (2) in Gonzalez et al. (2019)) to define a threshold corresponding to ${M}_{500,c}\gtrsim 1\times {10}^{14}\,{M}_{\odot }$. For redMaPPer, this corresponds to richness λ_redMaPPer > 20 and for MaDCoWS it corresponds to a richness of λ₁₅ > 22. We split the redMaPPer catalog into 4 redshift bins at z = 0.2, z = 0.3, and z = 0.4 and MaDCoWS into 2 bins at z = 1.0. The number of total and radio-active clusters per redshift interval is listed in Table 1.

Table 1. Cluster RAF Redshift Evolution

Cluster	z	$\langle z\rangle$	$\langle \lambda \rangle$	$\langle {M}_{500}\rangle$	Total	Radio Active	Radio
Catalog				(1014 M⊙)	Clusters	Clusters	Sources
redMaPPer	0.08–0.20	0.16	33.33 ± 0.36	1.72 ± 0.02	1830	25	32
	0.20–0.30	0.25	32.83 ± 0.26	1.69 ± 0.01	3874	143	191
	0.30–0.40	0.36	33.06 ± 0.18	1.7 ± 0.01	7520	333	440
	0.40–0.60	0.46	46.71 ± 0.21	2.44 ± 0.01	8334	575	744
MaDCoWS	0.77–1.00	0.93	33.5 ± 0.67	2.35 ± 0.1	262	37	52
	1.00–1.50	1.17	33.96 ± 0.43	2.4 ± 0.06	594	95	121

Note. Column 2: redshift bin. Column 3: mean cluster redshift within bin. Column 4: mean cluster richness within bin. Column 5: mean cluster mass within bin. Column 6: number of galaxy clusters within redshift bin. Column 7: number of clusters with central 500 kpc radio activity. Column 8: number of FIRST radio sources within 500 kpc of radio active clusters.

Download table as:  ASCIITypeset image

To calculate the RAF in redMaPPer clusters, we again identify all FIRST radio sources with ${L}_{1.4\mathrm{GHz}}\gt {10}^{25}$ W Hz⁻¹ that lie within 500 kpc of the cluster center. As with the MaDCoWS clusters, we define a cluster as being radio-active if there is a FIRST source satisfying these criteria.

The results of the redshift evolution of the cluster RAF are shown in Figure 3. We find that the RAF rises as a function of redshift, increasing more than tenfold between 0.2 < z < 1.2. Our results indicate that radioluminous galaxies in the centers of clusters are much more abundant in the earlier universe than in the present.

Zoom In Zoom Out Reset image size

The increase in RAF toward higher redshift may in part be due to the inherent differences in cluster populations at different redshifts in, for example, their recent star formation or cluster merger history. Though we control for cluster mass when comparing redMaPPer and MaDCoWS clusters, this does not constitute an evolutionary sequence due to cluster mass growth. However, our aim is to compare equivalent mass clusters at different epochs.

We investigate the effects of Malmquist bias at the highest redshift bins (where the radio flux limit is faintest) to quantify how much we may be overestimating radio-source counts. We simulate the flux for a sample of sources well below the 1 mJy flux limit, using a power-law distribution constructed from the FIRST catalog and assigning a flux uncertainty. We then calculate the ratio of the number of simulated sources to the number of observed sources above each flux limit equivalent to luminosity L_{1.4 GHz} = 1 × 10²⁵ W Hz⁻¹ at each redshift bin. If we assign an uncertainty from a Gaussian distribution centered around 0.5 mJy with standard deviation 0.1 mJy, we find that the ratio at z = 1.0 and z = 1.5 is 1.1 and 1.5, respectively. The increase in the cluster RAF from z = 0.5–1.0 and z = 0.5–1.2 is on the factor of ∼2–2.5. Thus, even though the effects of Malmquist bias could be driving up the RAF at higher redshifts, the increase toward higher redshifts would still exist even taking into account Malmquist bias.

We investigate the dependence of the cluster RAF upon radio luminosity. We calculate the cluster RAF as a function of radio luminosity, RAF(L), where we consider radio sources located in the central 500 kpc with luminosity within a set luminosity bin. Instead of using FIRST luminosity, we opt for data from the NRAO VLA Sky Survey (NVSS, Condon et al. 1998), which surveyed the radio sky north of δ > −40° at 1.4 GHz. Though at lower resolution than FIRST, NVSS has a FWHM of 45^'', allowing for more accurate flux estimation of extended sources that may be resolved into multiple components in FIRST, and larger sky coverage.

One disadvantage of NVSS compared to FIRST is the higher flux limit. NVSS is only complete to 2.5 mJy, and we adjust our luminosity limit accordingly. Another is the increased chance of confusion, especially in clusters with multiple radio sources. When calculating RAF, we only consider if the cluster has at least one radio source in the central 0.5 Mpc. We expect confusion to be minimal in lower-redshift clusters due to the higher flux limit. Of the 136 radio-active MaDCoWS clusters identified with FIRST, 92% of those clusters were identified as radio-active using NVSS, and all NVSS-identified radio-active clusters were also identified as radio-active in FIRST. Therefore, we do not expect radio source confusion to affect the calculation of the RAF.

Our results from Section 4.2 motivate us to also consider the redshift while investigating the cluster RAF as a function of radio luminosity. We again draw upon the redMaPPer clusters as a low-redshift comparison. We split the redMaPPer clusters into redshift bins of 0 < z ≤ 0.3 and 0.3 < z ≤ 0.6 and MaDCoWS into bins of 0.7 < z ≤ 1.0 and 1.0 < z ≤ 1.5. There are 6802, 19257, 559, and 1050 clusters within the footprint of NVSS in the lowest to highest redshift bins, again only considering clusters with a richness equivalent to M₅₀₀ > 1 × 10¹⁴ M_⊙.

The left side of Figure 4 shows the cluster RAF for NVSS 1.4 GHz luminosity in bins of 0.5 dex, considering clusters of different redshift. The luminosity sensitivity changes as a function of redshift, so we only calculate the cluster RAF to the luminosity given the flux limit 2.5 mJy and highest redshift cluster within the bin. The minimum luminosity considered is L_{1.4 GHz} = 10²⁴, 10^24.5, 10²⁵, and 10^25.5 W Hz⁻¹ from lowest to highest redshift bins. We only plot the cluster RAF if at least one cluster contains an NVSS radio source within the luminosity bin. Figure 4 shows that the cluster RAF is dependent on the redshift, where higher-redshift clusters have a higher fraction of clusters hosting a central radio source of L_{1.4 GHz} > 3 × 10²⁵ W Hz⁻¹.

Zoom In Zoom Out Reset image size

To add a low-frequency comparison, we also calculate the cluster RAF as a function of radio luminosity at 150 MHz with data from the TIRF Giant Metrewave Radio Telescope (GMRT) Sky Survey (TGSS) Alternative Data Release 1 (ADR1, Intema et al. 2017). TGSS is currently the highest-resolution low-frequency survey, covering the entire sky above δ = −50° with FWHM 25^'' × 25^'' and 25^'' × 25^''/cos19° north and south of δ > −19°, respectively. The survey threshold is 25 mJy. ¹² We are thus sensitive to sources above $\mathrm{log}{L}_{150\mathrm{MHz}}\,=24.8$, 25.5, 26, and 26.5 from lowest to highest cluster richness bin. The number of clusters per redshift bin remains the same as for NVSS. The right panel of Figure 4 shows the cluster RAF as a function of 150 MHz luminosity for clusters of 0 < z < 1.5. The cluster RAF as a function of 150 MHz radio luminosity shows a similar trend to that at 1.4 GHz.

We next construct a radio luminosity function (RLF) at 1.4 GHz for radio sources in MaDCoWS clusters by calculating the fraction of cluster galaxies as a function of radio luminosity. We include a field RLF comparison. To calculate the f_rl in the field, we use the Spitzer Deep, Wide-Field Survey (SDWFS, Ashby et al. 2009) with galaxy photometric redshifts from Chung et al. (2014). We select SDWFS galaxies of the same flux ([4.5] > 10 μJy, M_* > 3 × 10¹⁰ M_⊙) and color criteria as cluster galaxy candidates, as described in Section 3.1. We also limit the sample to galaxies with photometric redshifts of 0.7 < z < 1.5 to match the photometric redshift range of MaDCoWS clusters. There were 3 MaDCoWS galaxy clusters that fall within the SDWFS field of view. We exclude the 49 SDWFS galaxies within 1' of these galaxy clusters. A total of 45,520 SDWFS galaxies matched these criteria. Crossmatching the SDWFS galaxies with FIRST using a 2'' crossmatching radius, we find 61 radioluminous galaxies in SDWFS, where the crossmatched FIRST luminosity is L_{1.4 GHz} ≥ 1 × 10²⁵ W Hz⁻¹, calculated assuming the photometric redshift of the galaxy. The redshift distribution in cluster galaxies and field galaxies is well matched, as expected from using the cluster galaxy color selection criteria. The mean redshift of radioluminous MaDCoWS cluster galaxies is z = 1.09 while that of the radioluminous field galaxies is z = 1.15.

The cluster and field RLFs are plotted in Figure 5. The top panel of Figure 5 shows the number of cluster and field radio sources per luminosity bin. The fraction of radio galaxies as a function of FIRST 1.4 GHz luminosity is shown in the bottom panel for both clusters and the field. In the field, the most luminous galaxy had luminosity L_{1.4 GHz} = 4 × 10²⁶ W Hz⁻¹. Thus, we can only calculate the field f_rl up to L_{1.4 GHz} < 10^26.5 W Hz⁻¹.

Zoom In Zoom Out Reset image size

The radioluminous fractions for both field and cluster galaxies decrease as a function of increasing radio luminosity. However, the radioluminous fractions in cluster galaxies are higher than those in field galaxies at all radio luminosities. We also show the field radioluminous fraction scaled by the ratio of the average radioluminous fraction between cluster and field (dotted line). The average radioluminous fraction is simply the radioluminous fraction calculated for all sources in the luminosity range of the field radio sources ($3\times {10}^{25}\leqslant {L}_{1.4\mathrm{GHz}}\lt 5.0\times {10}^{26}$ W Hz⁻¹). The ratio between average cluster and field radioluminous fractions is 1.70 ± 0.31. We calculate an R-squared score of 0.84, indicating that scaling the field by a constant is a reasonable representation of the radio activity in the cluster environment.

We next try to quantify the effects of the environment on triggering radio activity. To identify radioluminous galaxies in SDWFS, we apply the cluster galaxy color and flux criteria (described in Section 3.1) and crossmatch the selected galaxies to FIRST radio source positions with a 2'' crossmatching radius and apply the same L_{1.4 GHz} > 10²⁵ W Hz⁻¹ selection, calculated assuming the galaxy's photometric redshift and spectral index of α = 0.70. For 0.7 < z < 1.5, we find 42 radioluminous galaxies in SDWFS, or an overall radioluminous fraction in the field of (9.22 ± 0.14) × 10⁻⁴.

The bottom panel of Figure 6 shows f_rl for galaxies in MaDCoWS clusters and in SDWFS as a function of stellar mass. The numbers of field and cluster galaxies per bin are shown in the top panel. The f_rl increases with increasing stellar mass by a factor of ∼150 in clusters and in the field between 10^10.5 < M_* ≲ 10^11.7 M_⊙. The average ratio between cluster and field f_rl is 3.6 ± 0.6 for 10^10.5 < M_* ≲ 10¹³ M_⊙.

Zoom In Zoom Out Reset image size

Our results are in agreement with those of M18, who find that the radioluminous ¹³ fraction in the innermost 0.5 Mpc of MaDCoWS clusters is ∼3 times higher than that in the field. They also find the field-relative radioluminous fraction in 10.5 < log(M_*) ≤ 11.6 and log(M_*) > 11.6 galaxies are comparable, albeit slightly higher in the former M_* range.

In Section 4.1, we found tentative evidence that cluster RAF appears to increase as a function of cluster richness, though we cannot statistically constrain that the f_rl also increases with richness. M18 find an increase in the central radioluminous fraction (presented as the radio-selected AGN fraction) as a function of increasing cluster richness, though the radioluminous fractions of each richness bin are comparable to each other within the central 1'. In this work, we benefit from visually identified radio source counterparts instead of a matching radius, physical as opposed to angular distances, and a uniform luminosity cut rather than a flux limit. Despite these differences, our results remain consistent with those of M18.

Many studies have previously found a link between cluster richness and radio activity. Both observational (e.g., Hatch et al. 2014) and theoretical (e.g., Orsi et al. 2016) studies have shown that radio sources trace denser environments than mass-matched counterparts without evidence for radio activity. This relationship extends to the fraction of BCGs with radio activity. Though we do not identify BCGs in our clusters, there is a high likelihood that much of the observed radio activity is attributed to the BCG given that we only consider the central 500 kpc (though see Sections 4.2 and 5.2).

Multiple studies find a similar mass dependence in lower-redshift clusters. In z ≤ 0.2 clusters, Lin & Mohr (2007) find that the radio active fraction of BCGs in $\mathrm{log}{M}_{200}({M}_{\odot })\,\gt 14.2$ clusters are higher than that in lower-mass clusters, for $\mathrm{log}{L}_{1.4\mathrm{GHz}}\gt 24$ and BCGs brighter than M_K  = −24. Similarly, in z < 0.3 clusters, Stott et al. (2012) find that the fraction of clusters with radioluminous BCGs is 0.10 ± 0.04 in clusters with X-ray temperature T_X  < 2.4 keV, equivalent to M₅₀₀ < 1.4 × 10¹⁴ M_⊙. This fraction rises to 0.38 ± 0.09 in clusters of higher X-ray temperatures, considering radio luminosities to L_{1.4 GHz} = 2 × 10²³ W Hz⁻¹. Bird et al. (2008) also cite a correlation between increasing richness in local galaxy groups and a probability of extended radio emission in BCGs.

While the above studies do see such a trend, one exception is Best et al. (2007). Studying the radio-loud BCG fraction in 625 nearby optically selected groups and clusters, they do not observe a strong dependence of the fraction of radio-loud BCGs and the cluster's velocity dispersion. Also, the redshift dependence was not previously well-constrained. Gralla et al. (2011) find that the radio-loud BCG fraction increases more significantly for clusters between 0.35 < z < 0.65 than in their sample at 0.65 < z < 0.95, implying that the radio active fraction as a function of richness could be dependent on redshift.

We showed in Section 4.2 and Figure 3 that the cluster RAF increases by more than tenfold between 0.2 < z < 1.2. Many authors have noted an increase in the frequency of luminous radio sources toward higher redshifts in both cluster and non-cluster environments (e.g., Lin & Mohr 2007; Sommer et al. 2011; Yuan et al. 2016). Donoso et al. (2009) construct the radio luminosity function (RLF) of the MegaZ luminous red galaxy catalog between 0.4 < z < 0.8 and compare with an RLF of local galaxies at redshift range 0.03 < z < 0.3 (Best et al. 2005a, 2005b, 2006). They find that the number of radio sources with L_{1.4 GHz} > 10²⁴ W Hz⁻¹ increases by a factor of 1.5 between the lowest and highest redshifts, while the number of higher luminosity radio sources with L_{1.4 GHz} > 10²⁶ W Hz⁻¹ increases tenfold. For radio sources in clusters in the redshift range 0.3 < z < 1.2, Bîrzan et al. (2017) find that the fraction of clusters that host a cluster radio source with L_{843 MHz} ≥ 10²⁶ W Hz⁻¹ is ∼7 times higher in z > 0.6 than in z < 0.6. Our results agree with previous studies, and add that the frequency of cluster radio sources with luminosity ${L}_{1.4\mathrm{GHz}}\gt {10}^{25}$ W Hz⁻¹ continues to increase out to z = 1.2.

It is interesting to compare these results for evolution in the cluster RAF with the evolution in the fraction of radioluminous BCGs. Gralla et al. (2011) found that, for a luminosity threshold of ${L}_{1.4\mathrm{GHz}}=4.1\times {10}^{24}$ W Hz⁻¹, there is negligible evolution in the fraction of radioluminous BCGs out to z = 0.95. Similarly, Lin et al. (2017) find little evolution in the radioluminous BCG fraction at 0.3 < z < 1.2 for L_{1.4 GHz} = 5. 0 × 10²⁴ W Hz⁻¹. At the same luminosity threshold as Lin et al. (2017), we find that the cluster RAF increases by a factor of 3 from z = 0.2 to z = 1.

The above results are not contradictory, but rather indicative that the observed evolution is driven by an increase in radio activity among the non-BCG galaxy population with increasing redshift. Indeed, Gralla et al. (2011) found a 2.9σ increase in the radio-loud fraction of non-BCG cluster galaxies at 0.65 < z < 0.95 compared to 0.35 < z < 0.65, which translates into a higher cluster RAF at high redshift. However, studies have different radius and luminosity limits, which may also contribute to the different results between studies.

The increase in the number of luminous radio sources toward higher-redshift clusters, as stated in Section 4.3 and shown in Figure 4, is most likely due to the shift in the RLF as a function of redshift. Many studies have cited an evolution in the RLF toward higher radio luminosities in radio-selected sources in the field. Studying a sample of VLA-COSMOS radio-selected AGN, Smolčić et al. (2009) find that the RLF for low-luminosity (${L}_{1.4\mathrm{GHz}}\sim {10}^{25}$ W Hz⁻¹) radio AGN is 3 times higher at 0.9 < z ≤ 1.3 than at 0.1 < z ≤ 0.35. Donoso et al. (2009) find a factor of 2 increase for radio AGN samples at $\langle z\rangle =0.55$ compared with $\langle z\rangle =0.14$ for L_{1.4 GHz} = 10²⁵ W Hz⁻¹, and this increases to a factor of 8 for L_{1.4 GHz} = 10²⁶ W Hz⁻¹.

Extending to higher redshifts and luminosities, Rigby et al. (2011), using steep-spectrum (α > 1.06) radio sources only, find that the RLF increases by a factor of 2.5 for log(L_{1.4 GHz}) = 25.5 and a factor of 15 for $\mathrm{log}({L}_{1.4\mathrm{GHz}})\,=26.3$ between z = 0.2 − 1.0 (see their Figure 9). In our results, the cluster RAF at z = 1.2 is a factor of 2 higher than that at z = 0.2 at $\mathrm{log}({L}_{1.4\mathrm{GHz}})=25.5$ and 20 for $\mathrm{log}({L}_{1.4\mathrm{GHz}})=26.3$, which is on par with previous results found for the field RLF. However, our results highlight that more luminous radio sources are more likely to reside in higher-redshift galaxy clusters, and that higher-redshift clusters must experience associated radio-mode feedback.

In Section 4.4 and Figure 6, we found that both higher galaxy mass and the cluster environment drive increased cluster radio activity. Comparing the environments around radio galaxies and radio-loud quasars at 1.3 < z < 3.2 to the environments around radio-quiet galaxies matched in mass and redshift, Hatch et al. (2014) found that the radio-loud population traces denser environments than the radio-quiet population, and that the cluster environment enhances the likelihood of radio jet formation in galaxies. Our results quantify these findings that the cluster environment is more conducive to radio activity in galaxies than the field environment by an overall factor of 3.6.

It is also worth noting that the enhancement of the field-relative radioluminous fraction in clusters is not limited to the highest stellar mass cluster galaxies. The f_rl is higher in clusters versus field over the entire stellar mass range in consideration. For ${M}_{* }\lt {10}^{11.2}\,{M}_{\odot }$, the ratio of the cluster to field level is 2.6 ± 0.8. This indicates that all galaxies in the cluster have a higher probability of being radioluminous, not just the BCG. Similar BCG-only studies are most likely missing the environmental component of radio activity enhancement.

The cluster RAF can be directly applied to the duty cycle of radio emission in galaxy clusters, defined as the fraction of time that a galaxy cluster has at least one radio source with ${L}_{1.4\mathrm{GHz}}\gt {10}^{25}$ W Hz⁻¹ in the central 500 kpc region. We find that the cluster radio emission duty cycle is 15% for radio luminosity ${L}_{1.4\mathrm{GHz}}\gt {10}^{25}$ W Hz⁻¹, assuming that all clusters alternate between on and off states (though see Hardcastle et al. 2019, on radio AGN lifetimes). However, we showed that the cluster RAF is dependent on cluster richness and redshift. Richer clusters would experience a longer time frame or greater fraction of time where the radio emission is deposited onto the central cluster environment. Nearby clusters are less likely to host powerful radio sources in the central regions compared to z ∼ 1 clusters, though the cluster RAF is also shown to depend on radio luminosity.

Radio sources have been used as beacons for galaxy cluster surveys (e.g., Wylezalek et al. 2013; Castignani et al. 2014; Paterno-Mahler et al. 2017). Because the MaDCoWS sample is unbiased toward clusters with radio sources, we can constrain the rarity of galaxy clusters selected by their central radio source. Specifically, we apply the selection functions of the CARLA and COBRA surveys, which target radio sources with high luminosity and bent radio morphology, respectively.

CARLA obtained Spitzer snapshot imaging of the environments around 421 luminous radio-loud AGN at 1.2 < z < 3.2 (Wylezalek et al. 2013, 2014). They found that 55% of radio-loud AGN were in overdense regions, and likely to trace high-redshift cluster/protocluster environments. The radio-loud targets considered by CARLA had 500 MHz luminosity ${L}_{500\mathrm{MHz}}\geqslant {10}^{27.5}$ W Hz⁻¹. We convert NVSS 1.4 GHz luminosity to 500 MHz luminosity assuming ${\alpha }_{150-1400}\,=0.70$, the average spectral index for radio sources in clusters. We consider NVSS instead of FIRST in this case because of the larger coverage area of NVSS. Also, since we are interested in the most luminous radio sources, the higher resolution and lower flux limit of FIRST do not benefit our analysis. We only find 3 galaxy clusters (0.2%) with a radio source above ${L}_{500\mathrm{MHz}}\geqslant {10}^{27.5}$ W Hz⁻¹. We do not correct for the fact that CARLA environments are most likely less massive and more distant than MaDCoWS clusters, factors that both impact the cluster RAF, although in opposite senses. To first order though, we can infer that the clusters discovered by CARLA represent a small faction of the total cluster population in a uniformly selected cluster sample.

The COBRA survey (Paterno-Mahler et al. 2017) searched for dense environments around FIRST radio sources with tails bent by the cluster ICM. Bent-tailed radio sources were visually identified in FIRST contours, avoiding the most obvious low-redshift sources and verifying the status of the bent-tail. Wing & Blanton (2011) successfully identify 653 bent-tailed sources. We adopt the same visual inspection approach to identifying bent-tailed radio sources. However, because we consider higher-redshift radio sources, FIRST data will be less resolved than that considered in Wing & Blanton (2011). We find six MaDCoWS clusters containing a possible bent-tail radio source. This implies that only 0.4% of MaDCoWS clusters would have been discovered by targeting bent-tailed sources. Thus both CARLA and COBRA detect a very specific subpopulation of clusters and protoclusters.

The flux of a radio source can fill in the SZ decrement from a galaxy cluster. We have established that radio sources are more likely to be in the centers of galaxy clusters. Thus, there is the potential for radio sources to affect and possibly even overwhelm the signal of their host galaxy cluster.

We use the method described in Gupta et al. (2017) to estimate a galaxy cluster's SZ decrement as radio fluxes at the 90 and 150 GHz bands commonly used by SZ surveys. We also employ the SZ-mass relation of Arnaud et al. (2010). Together, these predict the (negative) flux from the galaxy cluster. We then convert the 1.4 GHz flux from the central radio source to the flux expected at SZ frequencies. For clusters that contain more than one central radio source, we use the combined flux from those sources.

The spectral index α chosen to convert from 1.4 GHz to SZ frequencies is the largest uncertainty in this calculation. Lin & Mohr (2007) find that the spectral index for 1.4–4.85 GHz for non-BCG radio sources is 0.47 ± 0.15. Improving upon the methods developed in Lin & Mohr (2007), Lin et al. (2009) calculate a steeper mean 1.4–4.85 GHz spectral index of 0.754 ± 0.024 for 139 galaxies within r₂₀₀ of the centers of z < 0.25 galaxy clusters. At higher frequencies, they find that 60% of sources flatten above 8 GHz and a third of sources remain steep from 4.9–43 GHz. Further, Baek et al. (2016) report a difference in spectral index as a function of the cluster's dynamical state. In a sample of 10 cluster AGN in clusters at z ∼ 0.02–0.10 observed at 4.85 GHz and 22 GHz , they observed that cluster AGN in non-cool-core clusters had steeper spectral indices (α ≳ 1.0) than those in relaxed clusters (α ≲ 1.0). For the radio population not limited to those within galaxy clusters, Gralla et al. (2014) find that the spectral index for 1.4 − 4.8 GHz and 1.4 − 218 GHz steepens with increasing average flux of the radio source, from α ∼ 0.5 at S_1.4 = 10 mJy to α ∼ 0.9 at S_1.4 = 90 mJy. Given the uncertainty in the spectral index toward higher frequencies, we compute the calculation using a range of assumed spectral indices. We choose spectral indices of α = [0.5,0.7,1.0] to represent the range of spectral indices reported from 1.4 GHz to higher frequencies.

The total number and percentage of MaDCoWS clusters that contain central 1 Mpc radio sources with radio flux above 20%, 50%, and 100% of the cluster's expected SZ decrement is listed in Table 2. We list these values as a function of the assumed 1.4–90 GHz and 1.4–150 GHz spectral index. At 90 GHz (150 GHz), no more than 1.7% (1.0%) of MaDCoWS clusters contain central 1 Mpc radio sources that overwhelm the expected signal from SZ.

We compare our results to those of Lin et al. (2009), who find the distribution of spectral indices between multiple frequencies for 139 radio sources to determine the RLF, then generate central r₂₀₀ radio sources in dark matter halos using a Monte Carlo method to extrapolate a contamination percentage at 145 GHz. They estimate ∼0.1% of M₂₀₀ = 10¹⁴ M_⊙ clusters at z = 1.1 would be 100% contaminated by the flux of the central radio source and 0.5% of clusters at the 20% contamination level. For M₂₀₀ = 10¹⁵ M_⊙ clusters, the percentages are at negligible amounts for both contamination levels. Comparing to our results at 150 GHz, we find a much higher fraction of contaminated clusters, at both the 20% and 100% contamination level. This is likely due to the discrepancy in the evolution of radio galaxies in clusters relative to the evolution assumed in Lin et al. (2009). They assume that the cluster radio source density increases by a factor of 2 between z = 0.25–1, while in this work, we find that the increase is a factor of 4-5. We also assume a straight spectral index between 1.4 GHz and 90 GHz and 150 GHz, when there could be steepening and flattening of the flux between those frequencies. Nevertheless, we observationally demonstrate that the number of MaDCoWS clusters that would have been missed by SZ surveys is larger than previously estimated, but still small.

Our analysis indicates that SZ-based cluster masses are expected to be biased low by at least 20% for ∼1%–7% of MaDCoWS-like clusters, and about half of these will be biased low by 50% or more. Beyond suffering from biased mass estimates, samples selected in the SZ may have higher incompleteness near the survey S/N limit due to partial fill-in of the decrement. Cosmological measurements using cluster abundances should account for both incompleteness and mass bias due to emission from radioluminous AGN in high-redshift clusters.