2023A&A...678A..63S

Context. Narrow-line Seyfert 1 (NLSy1) galaxies have been shown to have high Eddington ratios and relatively small black hole mass. The measurement of these black hole masses is based on the virial relation that is dependent on the distribution of the line-emitting gas and the viewing angle to the source. Spectropolarimetry enables us to probe the geometry of this line-emitting gas and independently estimate the viewing angle of the source by comparing the spectrum viewed under natural light and polarized light.
Aims. We aim to (i) estimate the virial factor using the viewing angles inferred from spectropolarimetric measurements for a sample of NLSy1s which influences the measurement of the black hole masses; (ii) model the natural and polarized spectra around the Hα region using spectral decomposition and spectral fitting techniques; (iii) infer the physical conditions (e.g., density and optical depth) of the broad-line region and the scattering medium responsible for the polarization of the Hα emission line (and continuum); and (iv) model the Stokes parameters using the polarization radiative transfer code STOKES.
Methods. Using the FORS2 instrument at the European Southern Observatory's (ESO) Very Large Telescope, We performed spectropolarimetric observations of three NLSy1: Mrk 1044, SDSS J080101.41+184840.7, and IRAS 04416+1215. We used the ESO REFLEX workflow to perform a standard data reduction and extract the natural and polarized spectra. We then modeled the Hα region in the reduced spectra using IRAF spectral fitting procedures and estimated the Stokes parameters and the viewing angles of the three sources. We modeled the Stokes parameters, inferred the properties of the scattering media located in the equatorial and polar regions, and simulated the spectra observed both in natural light and in polarized light using the polarization radiative transfer code STOKES.
Results. The viewing angles recovered for the three sources indicate that they occupy separate locations in the viewing angle plane, from an almost face-on (IRAS 04416+1215) to an intermediate (SDSS J080101.41+184840.7), to a highly inclined (Mrk 1044) orientation. Nevertheless, we confirm that all three sources are high Eddington ratio objects. We were successful in recovering the observed Hα line profile in both the natural and polarized light using the STOKES modeling. We recovered the polarization fractions of the order of 0.2-0.5% for the three sources although the recovery of the phase angle is sub-optimal, mainly due to the noise in the observed data. Our principal component analysis shows that the sample of 25 sources, collected from the literature and including our sources, are mainly driven by the black hole mass and Eddington ratio. We reaffirm the connection of the strength of the optical FeII emission with the Eddington ratio, but the dependence on the viewing angle is moderate and resembles more of a secondary effect.