Luminosity function of flat-spectrum radio-loud narrow-line Seyfert 1 galaxies

Narrow-line Seyfert 1 galaxies are an interesting subclass of active galactic nuclei (AGN), which tipically does not exhibit any strong radio emission. Seven percent of them, though, are radio-loud and often show a flat radio-spectrum (F-NLS1s). This, along to the detection of $\gamma$-ray emission coming from them, is usually interpreted as a sign of a relativistic beamed jet harbored in these objects. An important aspect of these AGN that must be understood is the nature of their parent population, in other words how do they appear when observed under different angles. In this paper we investigated whether compact steep-spectrum sources with an high excitation spectrum (CSS/HERGs) are good parent candidates. To do this, we analyzed the only two statistically complete samples of CSS/HERGs and F-NLS1s available in the literature. We derived the black hole mass and Eddington ratio distributions, and we built for the first time the radio luminosity function of F-NLS1s. Finally, we applied a relativistic beaming model to the luminosity function of CSS/HERGs, and compared the result with the observed function of F-NLS1s. We found that compact steep-spectrum sources are valid parent candidates and that F-NLS1s, when observed with a different inclination, might actually appear as CSS/HERGs.