FRIs and FRIIs in LoTSS DR2 with galaxy clusters

In the paired sample, 45.6_-3.1_^+3.1^% of FRIs and 32.6_-2.8_^+3.0^% of FRIIs are associated with clusters. This difference in cluster match fractions between FRIs and FRIIs in both samples becomes more pronounced at higher radio luminosities (L_144MHz_>10^26^W/Hz). In the volume-limited sample, 55.6_-9.6_^+9.2^% of luminous FRIs and 19.0_-4.6_^+5.7^% of luminous FRIIs are associated with clusters.

In the paired sample, 50.0_-12.9_^+12.9^% of luminous FRIs and 6.7_-3.9_^+9.5^% of luminous FRIIs are associated with clusters. Nevertheless, those FRIs and FRIIs that are associated with clusters show similar properties. In particular, the distributions of radio luminosity and stellar mass as functions of cluster richness and M500 are similar for FRIs and FRIIs.

The radial density profiles of cluster-associated FRIs and FRIIs both peak at 0.5xR_500_ and decline beyond R_500_, showing very similar spatial distributions within clusters. Furthermore, in the volume-limited sample, 74.8_-2.3_^+2.2^% of cluster-associated FRIs and 61.9_-4.6_^+4.4^% of cluster-associated FRIIs are identified as brightest cluster galaxies (BCGs). In the paired sample, 78.1_-4.0_^+3.5^% of cluster-associated FRIs and 65.9_-5.3_^+4.9^% of cluster-associated FRIIs are identified as BCGs.

The median properties of these FRI-BCGs and FRII-BCGs, as well as those of their host clusters, do not show significant differences. Compared to FRIs, FRIIs are less frequently found in galaxy clusters, particularly at high radio luminosities. This pattern may be explained by the jet disruption scenario, in which the dense gas in galaxy clusters can slow down or disturb radio jets, making it more difficult for powerful FRII structures to form or remain stable.

However, when FRIs and FRIIs do reside in clusters, they appear to inhabit similar environments in terms of richness, mass, and radial position. These findings suggest that, while the cluster-scale environment may influence the cluster match fraction, the morphological distinction between FRIs and FRIIs is unlikely to be primarily driven by cluster-scale properties alone. Improved estimates of cluster richness and mass will help to further clarify the extent to which the cluster environment influences the radio morphology of FRIs and FRIIs.