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The assembly of massive black holes in the early universe remains a poorly constrained open question in astrophysics. The merger and accretion of light seeds (remnants of Population III stars with mass below ∼ 1000 M ) or heavy seeds (in the mass range 104−106 M ) could both explain the formation of massive black holes, but the abundance of seeds and their merging mechanism are highly uncertain. In the next decades, the gravitational-wave observatories coming online are expected to observe very highredshift mergers, shedding light on the seeding of the first black holes. In this Letter we explore the potential and limitations for LISA, Cosmic Explorer and Einstein Telescope to constrain the mixture ratio of light and heavy seeds as well as the probability that central black holes in merging galaxies merge as well. Since the third generation ground-based gravitational-wave detectors will only observe light seed mergers, we demonstrate two scenarios in which the inference of the seed mixture ratio and merging probability can be limited. The synergy of multi-band gravitational-wave observations and electromagnetic observations will likely be necessary in order to fully characterize the process of high-redshift black hole formation.

The Event Horizon Telescope (EHT) collaboration has produced the first resolved images of M87*, the supermassive black hole at the centre of the elliptical galaxy M87. As both technology and analysis pipelines improve, it will soon become possible to produce spectral index maps of black hole accretion flows on event horizon scales. In this work, we predict spectral index maps of both M87* and Sgr A* by applying the general relativistic radiative transfer (GRRT) code ipole to a suite of general relativistic magnetohydrodynamic (GRMHD) simulations. We analytically explore how the spectral index increases with increasing magnetic field strength, electron temperature, and optical depth. Consequently, spectral index maps grow more negative with increasing radius in almost all models, since all of these quantities tend to be maximized near the event horizon. Additionally, photon ring geodesics exhibit more positive spectral indices, since they sample the innermost regions of the accretion flow with the most extreme plasma conditions. Spectral index maps are sensitive to highly uncertain plasma heating prescriptions (the electron temperature and distribution function). However, if our understanding of these aspects of plasma physics can be tightened, even the spatially unresolved spectral index around 230 GHz can be used to discriminate betweenmore »models. In particular, Standard and Normal Evolution (SANE) flows tend to exhibit more negative spectral indices than Magnetically Arrested Disk (MAD) flows due to differences in the characteristic magnetic field strength and temperature of emitting plasma.« less