High-redshift quasars at $z \geq 3$ -- I. Radio spectra

We present the radio properties of optically selected quasars with $z\geq3$. The complete sample consists of 102 quasars with a flux density level $S_{1.4}\geq100$ mJy in a declination range -35$^{\circ}$ $\leq$ Dec $\leq$ +49$^{\circ}$. The observations were obtained in 2017-2020 using the radio telescope RATAN-600. We measured flux densities at six frequencies 1.2, 2.3, 4.7, 8.2, 11.2, and 22 GHz quasi-simultaneously with uncertainties of 9-31 %. The detection rate is 100, 89, and 46 % at 4.7, 11.2, and 22 GHz, respectively. We have analysed the averaged radio spectra of the quasars based on the RATAN and literature data. We classify 46 % of radio spectra as peaked-spectrum, 24 % as flat, and none as ultra-steep spectra ($\alpha\leq-1.1$). The multifrequency data reveal that a peaked spectral shape (PS) is a common feature for bright high-redshift quasars. This indicates the dominance of bright compact core emission and the insignificant contribution of extended optically thin kpc-scale components in observed radio spectra. Using these new radio data, the radio loudness $\log~R$ was estimated for 71 objects with a median value of 3.5, showing that the majority of the quasars are highly radio-loud with $\log~R>2.5$. We have not found any significant correlation between $z$ and $\alpha$. Several new megahertz-peaked spectrum (MPS) and gigahertz-peaked spectrum (GPS) candidates are suggested. Further studies of their variability and additional low-frequency observations are needed to classify them precisely.