Context. Giant radio galaxies (GRGs, giant RGs, or giants) are megaparsec-scale, jet-driven outflows from accretion disks of supermassive black holes, and represent the most extreme pathway by which galaxies can impact the Cosmic Web around them. A long-standing but unresolved question is why giants are so much larger than other radio galaxies.
Aims: It has been proposed that, in addition to having higher jet powers than most RGs, giants might live in especially low-density Cosmic Web environments. In this work, we aim to test this hypothesis by pinpointing Local Universe giants and other RGs in physically principled, Bayesian large-scale structure reconstructions.
Methods: More specifically, we localised a LOFAR Two-metre Sky Survey (LoTSS) DR2-dominated sample of luminous (lν(ν = 150 MHz)≥1024 W Hz−1) giants and a control sample of LoTSS DR1 RGs, both with spectroscopic redshifts up to zmax = 0.16, in the BORG SDSS Cosmic Web reconstructions. We measured the Cosmic Web density on a smoothing scale of ∼2.9 Mpc h−1 for each RG; for the control sample, we then quantified the relation between RG radio luminosity and Cosmic Web density. With the BORG SDSS tidal tensor, we also measured for each RG whether the gravitational dynamics of its Cosmic Web environment resemble those of clusters, filaments, sheets, or voids.
Results: For both luminous giants and general RGs, the Cosmic Web density distribution is gamma distribution-like. Luminous giants populate large-scale environments that tend to be denser than those of general RGs. This result is corroborated by gravitational dynamics classification and a cluster catalogue crossmatching analysis. We find that the Cosmic Web density around RGs with 150 MHz radio luminosity lν is distributed as 1 + ΔRG | Lν = lν ∼ Γ(k, θ), where k = 4.8 + 0.2 · √, θ = 1.4 + 0.02 · √, and √:= log10(lν (1023 W Hz−1)−1).
Conclusions: This work presents more than a thousand inferred megaparsec-scale densities around radio galaxies, which may be correct up to a factor of order unity - except in clusters of galaxies, where the densities can be more than an order of magnitude too low. We pave the way to a future in which megaparsec-scale densities around RGs are common inferred quantities, which help to better understand their dynamics, morphology, and interaction with the enveloping Cosmic Web. Our data demonstrate that luminous giants inhabit denser environments than general RGs. This shows that - at least at high jet powers - low-density environments are no prerequisite for giant growth. Using general RGs, we quantified the relation between radio luminosity at 150 MHz and Cosmic Web density on a smoothing scale of ∼2.9 Mpc h−1. This positive relation, combined with the discrepancy in radio luminosity between known giants and general RGs, reproduces the discrepancy in Cosmic Web density between known giants and general RGs. Our findings are consistent with the view that giants are regular, rather than mechanistically special, members of the radio galaxy population.

Full Table 1 and an analogous table for all selected general RGs are available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (ftp://130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/686/A137