Constraints on the state of the intergalactic medium at z∼8 − 10 using redshifted 21 cm observations with LOFAR

¹ Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, WB 741 246, India
² Kapteyn Astronomical Institute, University of Groningen, PO Box 800 9700AV Groningen, The Netherlands
³ ARCO (Astrophysics Research Center), Department of Natural Sciences, The Open University of Israel, 1 University Road, PO Box 808 Ra’anana 4353701, Israel
⁴ Max-Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany
⁵ The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden
⁶ Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
⁷ Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
⁸ LUX, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, F-75014 Paris, France
⁹ Astron, PO Box 2 7990 AA Dwingeloo, The Netherlands
¹⁰ Astronomy Centre, Department of Physics and Astronomy, Pevensey II Building, University of Sussex, Brighton BN1 9QH, UK
¹¹ INAF – Istituto di Radioastronomia, Via P. Gobetti 101, 40129 Bologna, Italy
¹² Laboratoire de Physique de l’ENS, ENS, Université PSL, CNRS, Sorbonne Université, Universitée Paris Cité, 75005 Paris, France
¹³ School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550001, PR China
¹⁴ Department of Computer Science, University of Nevada, Las Vegas, Nevada 89154, USA
¹⁵ Center for Fundamental Physics of the Universe, Department of Physics, Brown University, Providence, 02914 RI, USA

^⋆ Corresponding author: ghara.raghunath@gmail.com

Received: 17 February 2025
Accepted: 1 May 2025

Abstract

The power spectra of the redshifted 21 cm signal from the Epoch of Reionization (EoR) contain information about the ionization and thermal states of the intergalactic medium (IGM) and depend on the properties of the sources that existed during that period. Recently, the LOFAR-EoR Key Science Project team has analysed ten nights of LOFAR high-band data and estimated upper limits on the 21 cm power spectrum at redshifts 8.3, 9.1, and 10.1. Here, we used these upper limit results to constrain the properties of the IGM at those redshifts. We focus on the properties of the ionized and heated regions where the temperature is larger than that of the cosmic microwave background (CMB). We modelled the power spectrum of the 21 cm signal with the code GRIZZLY and used a Bayesian inference framework to explore the source parameters for uniform priors on their ranges. The framework also provides information about the IGM properties in the form of derived parameters. We do not include constraints from other observables except for some very conservative limits on the maximum ionization fraction at those redshifts, which we estimated from the CMB Thomson scattering optical depth. In a model that includes a radio background in excess of the CMB, the 95% (68%) credible intervals of disfavoured models at redshift 9.1 for the chosen priors correspond to IGM states with an averaged ionization and heated fraction below 0.46 (≲ 0.05), an average gas temperature below 44 K (4 K), and a characteristic size of the heated region of ≲14 h⁻¹ Mpc (≲3 h⁻¹ Mpc). The 68% credible interval suggests an excess radio background that is more than 100% of the CMB at 1.42 GHz, while the 95% credible interval of the radio background efficiency parameter spans the entire prior range. The behaviour of the credible intervals is similar at all redshifts. The models disfavoured by the LOFAR upper limits are extreme, as they are mainly driven by rare and large ionized or heated regions. We find that the inclusion of upper limits from other radio interferometric observations in the Bayesian analysis significantly increases the number of disfavoured EoR models, thus enhancing the disfavoured credible intervals of the IGM parameters, especially those related to the average gas temperature and size distribution of the heated regions. While our constraints are not yet very strong, more stringent upcoming results from 21 cm observations together with the detection of many high-z galaxies, for example with the James Webb Space Telescope, will strengthen understanding of this crucial phase of the Universe.