Resolved stellar morpho-kinematics and the M BH-σ relation

[Context] The formation and evolution of galaxies appear linked to the growth of supermassive black holes, as evidenced by empirical scaling relations in nearby galaxies. Understanding this co-evolution over cosmic time requires the revelation of the dynamical state of galaxies and the measurement of the mass of their central black holes (MBH) at a range of cosmic distances. Bright active galactic nuclei (AGNs) are ideal for this purpose. [Aims] The High Angular Resolution Monolithic Optical and Near-infrared Integral field spectrograph (HARMONI), the first light integral-field spectrograph for the Extremely Large Telescope, will transform visible and near-infrared ground-based astrophysics thanks to its advances in sensitivity and angular resolution. We aim to analyse the capabilities of HARMONI to reveal the stellar morpho-kinematic properties of the host galaxies of AGNs at about cosmic noon. [Methods] We made use of the simulation pipeline for HARMONI (HSIM) to create mock observations of representative AGN host galaxies at redshifts around cosmic noon. We used observations taken with the Multi Unit Spectroscopic Explorer of nearby galaxies showing different morphologies and dynamical stages combined with theoretical AGN spectra to create the target inputs for HSIM. [Results] According to our simulations, an on-source integration time of three hours should be enough to measure the MBH and to trace the morphology and stellar kinematics of the brightest host galaxies of AGNs beyond cosmic noon. For host galaxies with stellar masses < 1011 M⊙, longer exposure times are mandatory to spatially resolve the stellar kinematics.B.G.-L. and A.M.-I. acknowledge support from the Spanish Ministry of Science, Innovation and Universities (MCIU), Agencia Estatal de Investigación (AEI), and the Fondo Europeo de Desarrollo Regional (EU-FEDER) under projects with references AYA2015-68217-P and PID2019-107010GB-100. B.G.-L., A.M.-I., C.R.A. and E.M.G. also acknowledge financial support from the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa award to the Instituto de Astrofísica de Canarias (SEV-2015-0548 and CEX2019-000920-S). M.P.S. acknowledges support from the Comunidad de Madrid through the Atracción de Talento Investigador Grant 2018-T1/TIC-11035 and PID2019-105423GA-I00 (MCIU/AEI/EU-FEDER). N.T. acknowledges support from the Science and Technology Facilities Council (grant ST/N002717/1), as part of the UK E-ELT Programme at the University of Oxford. C.R.A. acknowledges financial support from the Spanish MCIU under grant with reference RYC-2014-15779, from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement No. 860744 (BiD4BESt), from the State Research Agency (AEI-MCINN) of the Spanish MCIU under grants PID2019-106027GBC42 and EUR2020-112266. C.R.A. also acknowledges support from the Consejería de Economía, Conocimiento y Empleo del Gobierno de Canarias and the EU-FEDER under grant with reference ProID2020010105. L.G. acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities (MCIU) under the 2019 Ramón y Cajal program RYC2019-027683 and from the Spanish MCIU project HOSTFLOWS PID2020-115253GA-I00