Spectral indices in active galactic nuclei as seen by Apertif and LOFAR

¹ ASTRON, The Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD, Dwingeloo, The Netherlands
² Kapteyn Astronomical Institute, P.O. Box 800 9700 AV, Groningen, The Netherlands
³ School of Physical Sciences and Nanotechnology, Yachay Tech University, Hacienda San José S/N, 100119 Urcuquí, Ecuador

^⋆ Corresponding author: kutkin@astron.nl

Received: 4 March 2025
Accepted: 27 May 2025

Abstract

We present two new radio continuum images obtained with Apertif at 1.4 GHz. The images, produced with a direction-dependent calibration pipeline, cover 136 square degrees of the Lockman Hole and 24 square degrees of the ELAIS-N fields, with an average resolution of 17 × 12″ and a residual noise of 33 μJy beam⁻¹. With the improved depth of the images, we find a total of 63 692 radio sources, many of which are detected for the first time at this frequency. With the addition of the previously published Apertif catalog for the Boötes field, we cross-matched it with the LOFAR deep-fields value-added catalogs at 150 MHz, resulting in a homogeneous sample of 10 196 common sources with spectral index estimates – one of the largest to date. We analyze and discuss the correlations between the spectral index, redshift, linear source size, and radio luminosity, taking into account biases of flux-density-limited surveys. Our results suggest that the observed correlation between spectral index and redshift of active galactic nuclei can be attributed to the Malmquist bias, reflecting an intrinsic relation between radio luminosity and the spectral index. We also find a correlation between the spectral index and linear source size, with more compact sources having steeper spectra.