Flux dependence of redshift distribution and clustering of LOFAR radio sources

¹ Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
² School of Physics and Astronomy, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, EH9 3HJ Edinburgh, UK
³ Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
⁴ Dipartimento di Fisica, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
⁵ INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁶ INAF – Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino, Strada Osservatorio 20, 10025 Pino Torinese, Italy
⁷ Department of Physics & Astronomy, University of the Western Cape, Cape Town 7535, South Africa
⁸ Institute for Theoretical Physics, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany
⁹ Division of Physics, Mathematics and Astronomy, California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA
¹⁰ Department of Astrophysics, National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw, Poland
¹¹ Leiden Observatory, Leiden University, PO Box 9513 2300 RA Leiden, The Netherlands
¹² Department of Physics, Guangdong Technion - Israel Institute of Technology, Shantou, Guangdong 515063, PR China
¹³ GEPI & ORN, Observatoire de Paris, Université PSL, CNRS, 5 Place Jules Janssen, 92190 Meudon, France
¹⁴ Department of Physics & Electronics, Rhodes University, PO Box 94 Grahamstown 6140, South Africa

^⋆ Corresponding author; nitesh.b0804@gmail.com

Received: 22 March 2024
Accepted: 1 May 2024

Abstract

Context. We study the flux density dependence of the redshift distribution of low-frequency radio sources observed in the LOFAR Two-metre Sky Survey (LoTSS) deep fields and apply it to estimate the clustering length of the large-scale structure of the Universe, examining flux density limited samples (1 mJy, 2 mJy, 4 mJy and 8 mJy) of LoTSS wide field radio sources.

Methods. We utilise and combine the posterior probability distributions of photometric redshift determinations for LoTSS deep field observations from three different fields (Boötes, Lockman hole and ELAIS-N1, together about 26 square degrees of sky), which are available for between 91% to 96% of all sources above the studied flux density thresholds and observed in the area covered by multi-frequency data. We estimate uncertainties by a bootstrap method. We apply the inferred redshift distribution on the LoTSS wide area radio sources from the HETDEX field (LoTSS-DR1; about 424 square degrees) and make use of the Limber approximation and a power-law model of three dimensional clustering to measure the clustering length, r₀, for various models of the evolution of clustering.

Results. We find that the redshift distributions from all three LoTSS deep fields agree within expected uncertainties. We show that the radio source population probed by LoTSS at flux densities above 1 mJy has a median redshift of at least 0.9. At 2 mJy, we measure the clustering length of LoTSS radio sources to be r₀ = (10.1 ± 2.6) h⁻¹ Mpc in the context of the comoving clustering model.

Conclusions. Our findings are in agreement with measurements at higher flux density thresholds at the same frequency and with measurements at higher frequencies in the context of the comoving clustering model. Based on the inferred flux density limited redshift distribution of LoTSS deep field radio sources, the full wide area LoTSS will eventually cover an effective (source weighted) comoving volume of about 10 h⁻³ Gpc³.