## Abstract

Context. Many massive galaxies launch jets from the accretion disk of their central black hole, but only ∼103 instances are known in which the associated outflows form giant radio galaxies (GRGs, or giants): luminous structures of megaparsec extent that consist of atomic nuclei, relativistic electrons, and magnetic fields. Large samples are imperative to understanding the enigmatic growth of giants, and recent systematic searches in homogeneous surveys constitute a promising development. For the first time, it is possible to perform meaningful precision statistics with GRG lengths, but a framework to do so is missing.

Aims. We measured the intrinsic GRG length distribution by combining a novel statistical framework with a LOFAR Two-metre Sky Survey (LoTSS) sample of freshly discovered giants. In turn, this allowed us to answer an array of questions on giants. For example, we can now assess how rare a 5 Mpc giant is compared with one of 1 Mpc, and how much larger – given a projected length – the corresponding intrinsic length is expected to be. Notably, we can now also infer the GRG number density in the Local Universe.

Methods. We assumed the intrinsic GRG length distribution to be Paretian (i.e. of power-law form) with tail index ξ, and predicted the observed distribution by modelling projection and selection effects. To infer ξ, we also systematically searched the LoTSS for hitherto unknown giants and compiled the largest catalogue of giants to date.

Results. We show that if intrinsic GRG lengths are Pareto distributed with index ξ, then projected GRG lengths are also Pareto distributed with index ξ. Selection effects induce curvature in the observed projected GRG length distribution: angular length selection flattens it towards the lower end, while surface brightness selection steepens it towards the higher end. We explicitly derived a GRG’s posterior over intrinsic lengths given its projected length, laying bare the ξ dependence. We also discovered 2060 giants within LoTSS DR2 pipeline products; our sample more than doubles the known population. Spectacular discoveries include the largest, second-largest, and fourth-largest GRG known (lp = 5.1 Mpc, lp = 5.0 Mpc, and lp = 4.8 Mpc), the largest GRG known hosted by a spiral galaxy (lp = 2.5 Mpc), and the largest secure GRG known beyond redshift 1 (lp = 3.9 Mpc). We increase the number of known giants whose angular length exceeds that of the Moon from 10 to 23; among the discoveries is the angularly largest known radio galaxy in the Northern Sky, which is also the angularly largest known GRG (ϕ = 2°). Combining theory and data, we determined that intrinsic GRG lengths are well described by a Pareto distribution, and measured the index ξ = −3.5 ± 0.5. This implies that, given its projected length, a GRG’s intrinsic length is expected to be just 15% larger. Finally, we determined the comoving number density of giants in the Local Universe to be nGRG = 5 ± 2(100 Mpc)−3.

Conclusions. We developed a practical mathematical framework that elucidates the statistics of giant radio galaxy lengths. Through a LoTSS search, we also discovered 2060 new giants. By combining both advances, we determined that intrinsic GRG lengths are well described by a Pareto distribution with index ξ = −3.5 ± 0.5, and that giants are truly rare in a cosmological sense: most clusters and filaments of the Cosmic Web are not currently home to a giant. Thus, our work yields new observational constraints for analytical models and simulations featuring radio galaxy growth.

Aims. We measured the intrinsic GRG length distribution by combining a novel statistical framework with a LOFAR Two-metre Sky Survey (LoTSS) sample of freshly discovered giants. In turn, this allowed us to answer an array of questions on giants. For example, we can now assess how rare a 5 Mpc giant is compared with one of 1 Mpc, and how much larger – given a projected length – the corresponding intrinsic length is expected to be. Notably, we can now also infer the GRG number density in the Local Universe.

Methods. We assumed the intrinsic GRG length distribution to be Paretian (i.e. of power-law form) with tail index ξ, and predicted the observed distribution by modelling projection and selection effects. To infer ξ, we also systematically searched the LoTSS for hitherto unknown giants and compiled the largest catalogue of giants to date.

Results. We show that if intrinsic GRG lengths are Pareto distributed with index ξ, then projected GRG lengths are also Pareto distributed with index ξ. Selection effects induce curvature in the observed projected GRG length distribution: angular length selection flattens it towards the lower end, while surface brightness selection steepens it towards the higher end. We explicitly derived a GRG’s posterior over intrinsic lengths given its projected length, laying bare the ξ dependence. We also discovered 2060 giants within LoTSS DR2 pipeline products; our sample more than doubles the known population. Spectacular discoveries include the largest, second-largest, and fourth-largest GRG known (lp = 5.1 Mpc, lp = 5.0 Mpc, and lp = 4.8 Mpc), the largest GRG known hosted by a spiral galaxy (lp = 2.5 Mpc), and the largest secure GRG known beyond redshift 1 (lp = 3.9 Mpc). We increase the number of known giants whose angular length exceeds that of the Moon from 10 to 23; among the discoveries is the angularly largest known radio galaxy in the Northern Sky, which is also the angularly largest known GRG (ϕ = 2°). Combining theory and data, we determined that intrinsic GRG lengths are well described by a Pareto distribution, and measured the index ξ = −3.5 ± 0.5. This implies that, given its projected length, a GRG’s intrinsic length is expected to be just 15% larger. Finally, we determined the comoving number density of giants in the Local Universe to be nGRG = 5 ± 2(100 Mpc)−3.

Conclusions. We developed a practical mathematical framework that elucidates the statistics of giant radio galaxy lengths. Through a LoTSS search, we also discovered 2060 new giants. By combining both advances, we determined that intrinsic GRG lengths are well described by a Pareto distribution with index ξ = −3.5 ± 0.5, and that giants are truly rare in a cosmological sense: most clusters and filaments of the Cosmic Web are not currently home to a giant. Thus, our work yields new observational constraints for analytical models and simulations featuring radio galaxy growth.

Original language | English |
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Article number | A163 |

Pages (from-to) | 1-41 |

Number of pages | 41 |

Journal | Astronomy & Astrophysics |

Volume | 672 |

Issue number | April 2023 |

Early online date | 19 Apr 2023 |

DOIs | |

Publication status | Published - 19 Apr 2023 |

## Keywords

- astro-ph.GA
- astro-ph.CO
- Galaxies: kinematics and dynamics
- Intergalactic medium
- Radio continuum: galaxies
- Galaxies: active
- Galaxies: jets