Compact steep-spectrum sources as the parent population of flat-spectrum radio-loud NLS1s

Narrow-line Seyfert 1 galaxies (NLS1s) 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 oriented along the line of sight. 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 the recent literature it has been proposed that a specific class of radio-galaxies, compact-steep sources (CSS) classified as high excitation radio galaxies (HERG), can represent the parent population of F-NLS1s. To test this hypothesis in a quantitative way,in this paper 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.