Increased Prevalence of Bent Lobes for Double-lobed Radio Galaxies in Dense Environments

The first bin of galaxy groups and clusters spans z = 0 to z = 0.20. This entire volume is covered by a flux-complete (down to Galactic-extinction-corrected Petrosian r-magnitude of 17.77) group and cluster catalog (Tempel et al. 2014) containing 82458 groups and clusters.

At higher redshifts, it is more difficult to identify groups and clusters using the relatively shallow SDSS photometry. Instead, we use the catalogs from the SDSS-Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 (Ahn et al. 2014). BOSS is a spectroscopic survey of massive galaxies in the SDSS footprint. There are two sets of catalogs—LOWZ and CMASS—with slightly different photometric selection criteria. The selection criteria are designed such that both catalogs are approximately stellar-mass limited with typical log ${M}_{* }/{M}_{\odot }=11.3$ (Guo et al. 2013; Parejko et al. 2013). At these stellar masses, the BOSS galaxies are predominantly red and highly clustered (Guo et al. 2013), so we take them to be reasonably good tracers of large-scale structure at these redshifts. We therefore select galaxies from the LOWZ catalog with $0.20\lt z\lt 0.47$ for our second redshift bin, and galaxies from the CMASS catalog with $0.47\lt z\lt 0.70$ for our third redshift bin. We placed cuts at z = 0.2, z = 0.47, and z = 0.7 to ensure there was not any double-counting between different catalogs. These bins contain 209,788 and 446,158 central galaxies, respectively.

Together, our total list of galaxies, groups, and clusters contains 738,404 systems. While these systems are primarily galaxy groups and clusters, our coordinates for the BOSS sample will refer to the bright central galaxies, and we will often refer to the galaxies for simplicity, although of course the larger group/cluster is the primary object of interest.

We cross-match the DBW catalog of DLRGs with the galaxies in our various redshift bins. Our initial match criterion is a DLRG falling within 10 projected Mpc and 3000 km s⁻¹ of the galaxy. We compute the projected distance (impact parameter) from the measured angular separation, which we multiply by the comoving distance of the galaxy estimated from its redshift assuming the Planck Collaboration et al. (2016) cosmological parameters. The radial velocity separation cutoff of 3000 km s⁻¹ was chosen as a somewhat arbitrary upper limit on the escape velocity of a large cluster. We find that there is a steep drop-off of DLRG-group pairs at velocity separations greater than 3000 km s⁻¹, so our results are not very sensitive to the exact cutoff employed here.

Using this cross-matching criterion, we found 81 DLRG–galaxy pairs. This method of cross-matching allows for the possibility of a DLRG matching with multiple galaxies, which happens in most cases (61/81). We therefore incorporate the galaxies' impact parameters, velocity separations and halo masses to estimate a relative probability for the DLRG to be associated with each matched galaxy. Under the simplest assumption that the galaxies in a group are isotropically distributed as ${R}^{-3}$ in three-dimensional space (which is the NFW scaling at the Mpc scales we consider here) and that they have an isotropic and Gaussian distribution in velocity space, their projected space density will scale with impact parameter b as ${(b/{b}_{0})}^{-2}$, and their projected velocity density will scale with velocity separation σ as ${e}^{-{\sigma }^{2}/2{\sigma }_{0}^{2}}$. We therefore define the relative probability for a DLRG to be associated with a system i as

$$\begin{eqnarray}&&{P}_{i}=C\times {({M}_{i}/{\sigma }_{0})\times (b/{b}_{0})}^{-2}\times {e}^{-{\sigma }^{2}/2{\sigma }_{0}^{2}}\end{eqnarray} \tag{ 1 }$$

In this expression, M_i is the mass of the cluster or group, and absorbs the mass dependence of b₀ and ${\sigma }_{0}$, allowing our estimator to prefer to associate DLRGs with more massive systems. C is a normalization constant defined for each DLRG such that ${{\rm{\Sigma }}}_{i}{P}_{i}=1$, and the ${\sigma }_{0}$ appears in the denominator in order to normalize the Gaussian term to unity. We set ${b}_{0}=300\,\mathrm{kpc}$ and ${\sigma }_{0}=1100$ km s⁻¹, which are typical values for a massive cluster, although we varied these values by ±25% and the matches were not significantly changed.

For the groups with redshifts $z\lt 0.2$, we define M_i from the mass estimations included in the Tempel et al. (2014) catalog, which are based on the measured velocity dispersion of the galaxies in the group and an assumed halo mass profile (Navarro et al. 1997; Maccio et al. 2008). However, not many galaxies are detected in most of the groups—60% have two galaxies, and 91% have five or fewer galaxies—so these mass estimates are quite uncertain. For the groups with five or fewer detected galaxies, 71% have masses less than $1\times {10}^{13}\,{M}_{\odot }$ in the Tempel et al. catalog, but for such poor groups, the uncertainties in measuring velocity dispersion becomes more important than the measurement itself, and for simplicity, we institute a mass floor of $1\times {10}^{13}\,{M}_{\odot }$ for these poor groups.

For the catalog containing groups with redshifts $0.2\lt z\,\lt 0.7$, we have no straightforward halo mass estimator, so we assign each system the same halo mass (the exact value drops out of Equation (1), but we use $5\times {10}^{13}\,{M}_{\odot };$ van Uitert et al. 2015).

For each DLRG, the galaxy with the largest P_i is selected as the match. Of the 61 DLRGs with multiple potential matches, 33 are matched to the galaxy with the lowest impact parameter out of the potential candidates. In angular space, the median impact parameter is 77, and in physical space it is 3.3 Mpc.

We also visually inspected each of the 81 candidates using the VLA-FIRST images. Because the DLRG catalog was assembled automatically, many "false positives" are obvious by eye, with one or both lobes missing, and/or the outlying sources clearly appearing as point sources instead of radio lobes.

We also performed additional quantitative tests to verify the reality of the DLRGs in our sample. First, we require that the sum of the specific luminosities from the central galaxy and the two lobes be brighter than 1 × 10³¹ erg s⁻¹ Hz⁻¹. This is 10 times fainter than the specific luminosity separating FR II objects from FR I objects Fanaroff & Riley (1974), and serves as a test that the luminosity of the DLRG is physically plausible. No k-correction is applied for this calculation. Only 5 of the 81 DLRGs fail this test, and visual inspection shows that all 5 of these objects appear to be projections of unrelated radio point sources.

Second, we require the lobes to be diffuse objects, not point radio sources, so we discard any DLRG if one or both of its lobes appear less than 25 in radius. This was done by visually assessing the diameter of each lobe in the VLA FIRST images. 56 of the 81 DLRGs pass this cut while 25 fail.

Third, we require the DLRG to be the brightest radio source within a $1^{\prime}$ radius region to ensure that the radio lobes are not mistakenly attributed to the central QSO. In a few cases, we disagreed with the choice of central galaxy in the DWB catalog (i.e., the central galaxy was misidentified as a lobe and vice versa; this is obvious upon visual inspection but difficult to quantify algorithmically). In these cases, we manually changed the lobe placement if it was clear the original placement was incorrect and there was a clear alternative associated with the DLRG core. When there was not a clear alternative, we rejected the DLRG. When a DLRG was accepted yet needed a lobe position update, we repositioned the lobes and recalculated the angle between the DLRG lobes using these new coordinates. In most cases the change is small, but for a handful of objects, we identified one of the lobes with a different radio source than DBW, which caused the bending angle to change significantly. In 13/81 cases, the newly calculated angle changed by at least 10°, but 7 of these 12 cases were rejected by one of the other tests outlined above. The six remaining DLRGs with changed angles have ID numbers of 17, 18, 22, 37, 38, and 41 in Table 1 below.

All objects that fail one or more of these requirements are rejected, along with the objects that failed the visual classification. In the end, we accepted 44 DLRG-group matches from the original 81. Of these 44 DLRGs, 10 are matched to a different cluster or group than the one with the smallest impact parameter, due to the M_i and σ terms in Equation (1). In Table 1, we present basic data for these 44 DLRGs.

The cross-matching, the heterogeneous galaxy catalogs, and the various stages of DLRG verification described in Section 2.3 all introduce complicated biases in the sample selection. Modeling the sample selection in detail would require an unwieldy set of assumptions, including assumptions about galaxy evolution, halo occupation, evolution of the DLRG spectral shape and luminosity function, as well as the parameters in which we are interested, like the connection between DLRGs and large-scale structure. As this work is primarily observational and we want to be as parsimonious with assumptions as possible, we instead construct a "control" sample with the same sample selection biases, in order to compare to the DLRG sample.

To do this, we generate a set of mock coordinates for each DLRG by shifting the true coordinates in R.A. and decl. by various amounts ranging from 4° to 16°, yielding a total of 28 mock DLRGs for each of the 44 true DLRGs, for a total of 1232 mock DLRGs. We perform the same cross-matching as in Section 2.2 for these mock DLRGs. The result is a sample of central galaxies cross-matched with random positions on the sky, but obeying the same redshift distribution as our DLRG sample.

In Figure 1, we plot the surface density of our DLRG matches as a function of projected radius from the central galaxy. Within each annular bin, we compute the uncertainty from the number of counts, assuming Poisson statistics. Due to the low number of DLRGs, we oversample the surface density (i.e., bins are spaced by 0.25 Mpc but span 1.0 Mpc in width). This means that goodness-of-fit tests like the ${\chi }^{2}$ statistic are inappropriate (as they rely on the data points being independent of one another), but the error bars on each individual point are unaffected by the oversampling.

Zoom In Zoom Out Reset image size

The control sample shows a gradual decrease in projected density as a function of impact parameter, declining by a factor of ∼4 over the 5 Mpc range in impact parameters covered in the plot. This decline is probably due to the algorithm (Equation (1)) that favors matches with smaller impact parameters, in combination with our choice to assign the redshifts of the observed DLRGs to the random positions. From 3 Mpc ≲ b ≲ 5 Mpc, the data and the random sample match very well, implying that chance projections on the sky are a plausible explanation for DLRG–galaxy group/cluster pairs with these large impact parameters.

For $b\lesssim 2$ Mpc, there is a clear increase of these pairs in our data relative to the control sample of chance projections. DLRGs are therefore significantly more likely than random positions on the sky to be found near galaxy groups and clusters. In the innermost bin, the projected density of DLRG–central galaxy pairs is 10 times higher than the projected density of random position–central galaxy pairs, and based on Poisson statistics the probability of this occurring by chance is just 3 × 10⁻¹⁰. There is also a small "dip" in the observed DLRG projected density at $b\approx 2.5$ Mpc, but it is not statistically significant.

Our interpretation of Figure 1 is therefore that the majority of the DLRG–galaxy group/cluster matches reflect physical associations when the impact parameter is less than about 2 Mpc. For the pairs with impact parameters greater than about 2 Mpc, the majority (possibly all) of these DLRG–galaxy pairs reflect chance superpositions on the sky. We speculate that there are additional groups that are missing from our catalogs and lie at much smaller projected distances from these DLRGs.

We have also fit a power-law fit to the data in Figure 1 by minimizing ${\chi }^{2}$ (which we mentioned is inappropriate for goodness-of-fit testing due to the oversampling, but still adequate for line fitting). This line has a slope of $m=1.9\pm 0.2$ (with ${\rm{\Sigma }}\propto {b}^{-m}$), corresponding to a real-space decrease in density of $\rho \propto {r}^{2.9\pm 0.2}$. However, this slope is likely too shallow, as the data include a contribution from the "background" of chance superposition as well. We estimate this background by taking the mean from b = 3 Mpc to b = 4 Mpc. Subtracting this "background," the slope steepens to $m={2.5}_{-0.3}^{+0.4}$. Both of these values imply a very steep decrease with density (i.e., at least as steep as an NFW profile), and this will be discussed further below.

In Figure 2, we present the measured angle between the lobes of each DLRG for the sample of 44 verified cross matches. For each of these 44 objects, we have drawn vertical error bars, which encompass our uncertainty in the bending angle, as determined by the visual analysis in Section 2.3. These are obtained by identifying edges for both lobes and computing all of the possible angles that can subtend these edges; these error bars are therefore much more conservative than 1σ error bars.

Zoom In Zoom Out Reset image size

We have also drawn a dashed horizontal line at 170°, which we use to approximately distinguish between "bent" and "unbent" DLRGs; note that due to the measurement uncertainties, most objects with angles greater than 170° are consistent with having an angle of 180°.

In this plot, there are four DLRG–galaxy pairs, circled in red in Figure 2, whose velocity separations are all below 750 km s⁻¹ and whose lobes subtend angles between 170° and 180°. The projected separation between the radio source and the central galaxy is also less than 0.2 Mpc for these four galaxies. We therefore hypothesize that they are the central galaxies of their respective systems. Central galaxies are not the focus of this paper. The evolution of their lobes can also be affected by buoyancy (Gull & Northover 1973; Churazov et al. 2000, 2001) as well as large-scale sloshing motions in the intracluster medium, especially if the cluster is not relaxed (there is some evidence that they are preferentially associated with merging clusters; Sakelliou & Merrifield 2000). Due to the former issue, the focus of this paper is on the behavior of satellite radio galaxies, and we neglect these four central galaxies in this work. We also assume the intracluster medium is quiescent; sloshing motions, if they exist, may introduce noise into our measurement.

The drop-off with radius in projected density of DLRGs (discussed in the previous section) is also visible in Figure 2 (recall that the differential area increases linearly with projected radius). Based on our analysis in the previous section, the DLRG–galaxy matches with an impact parameter ≳2 Mpc are consistent with being chance projections on the sky. Thus, while the three DLRG–galaxy pairs with b = 3.5 Mpc and b = 6.8 Mpc in Figure 2 (which are identified as #25 and #34 in Table 1) have radio lobes that show clear signs of bending, it is unlikely that the bending is caused by the galaxy group/cluster we have identified. As discussed in the previous section, we think that there are likely additional galaxy groups that lie closer to the DLRG but are below the detection threshold for their respective surveys. These two matches in particular lie at z = 0.437 and z = 0.638, which are near the upper ends of their respective redshift bins.

We can model the expected fraction of bent DLRGs using the chance projections on the sky, which we conservatively estimate from Figure 2 using the galaxies with impact parameter of at least 2 Mpc. There are 24 such galaxies, of which 7 are bent, corresponding to an expected bent fraction of 29%. Excluding the four central galaxies in the red circle, the observed bent fraction within 1 (2) Mpc is 7/9 (9/16), corresponding to 78% (56%). The seven bent galaxies within 1 Mpc are shown in Figure 3. Keeping the total number of galaxies within 1 (2) Mpc fixed, the expected number of bent galaxies within this impact parameter is 2.42 (4.31). Assuming binomial statistics, the probability of getting at least the observed number of bent galaxies, given the expected number, is $3.4\times {10}^{-4}$ ($5.6\times {10}^{-3}$).

Zoom In Zoom Out Reset image size

These probabilities indicate that the null hypothesis (DLRG bending being uncorrelated with the central galaxy) should be rejected at $3.6\sigma$ ($2.8\sigma$). We therefore conclude that the bending is correlated with the proximity of these DLRGs to the center of a nearby galaxy group or cluster.