The evolution of extragalactic peaked-spectrum sources down to 54 megahertz

Peaked-spectrum (PS) sources, known for their distinct peaked radio spectra, represent a type of radio-loud active galactic nuclei (AGN). Among these, megahertz-peaked spectrum (MPS) sources, which exhibit a spectral peak at a frequency of a hundred megahertz, have emerged as a potential tool for identifying high-redshift candidates. However, the potential evolutionary link between the fraction of these sources and redshift remains unclear and requires further investigation. The recent, high sensitivity Low Frequency Array (LOFAR) surveys enable statistical studies of these objects to ultra-low frequencies (< 150 MHz). In this study, we first use the multiradio data to investigate the evolution of spectral index with redshift for 1,187 quasars from the SDSS 16th quasar catalog. For each quasar, we analyze available data from the LOFAR Low Band Antenna (LBA) at 54 MHz, High Band Antenna (HBA) at 144 MHz, and the Very Large Array (VLA) the Faint Images of the Radio Sky at Twenty cm (FIRST) at 1.4 GHz. We measure the spectral index ($\alpha^{144}_{54}$ and $\alpha^{1400}_{144}$) and find no significant change in their median values with the redshift. Extended sources have steeper spectral indices than compact sources, which is consistent with previous findings. Based on the spectral indices information, we identify MPS sources using these criteria: $\rm \alpha^{144}_{54} >= 0.1$ and $\rm \alpha^{1400}_{144} < 0$, and analyze their properties. We find that the fraction of MPS sources is constant with the redshift ($0.1-4.8$), bolometric luminosity ($\rm 10^{44}-10^{48} erg/s$), and supermassive black hole mass ($\rm 10^{7}-10^{10.5} M_{\odot}$), which suggests that MPS sources have relatively stable physical conditions or formation mechanisms across various evolutionary stages and environments.