Spectroscopic AGN survey at $z$ $\sim$ 2 with NTT/SOFI for GRAVITY+ observations

With the advent of GRAVITY+, the upgrade to the beam combiner GRAVITY at the Very Large Telescope Interferometer (VLTI), fainter and higher redshift active galactic nuclei (AGNs) are becoming observable, opening an unprecedented opportunity to further our understanding of the cosmic coevolution of supermassive black holes and their host galaxies. To identify an initial sample of high-redshift type~1 AGNs that can be observed with GRAVITY+, we have obtained spectroscopic data with NTT/SOFI of the most promising candidates. Our goal is to measure their broad line region (BLR) fluxes and assess their physical geometries by analysing the spectral profiles of their Balmer lines. We present 29 $z$ $\sim$ 2 targets with strong H$\alpha$ emission in the $K$-band. Their line profiles are strongly non-Gaussian, with a narrow core and broad wings. This can be explained as a combination of rotation and turbulence contributing to the total profile or two physically distinct inner and outer regions. We find small H$\alpha$ virial factors, which we attribute to the low full-width-half-maximum (FWHM)/$\sigma$ ratios of their non-Gaussian profiles, noting that this can lead to discrepancies in black hole masses derived from scaling relations. We also find two targets that show tentative evidence of BLRs dominated by radial motions. Lastly, we estimate the expected differential phase signals that will be seen with GRAVITY+, which will provide guidance for the observing strategy that will be adopted.