Massive Black Hole Seeds

The pathway(s) to seeding the massive black holes (MBHs) that exist at the heart of galaxies in the present and distant Universe remains an unsolved problem. Here we categorise, describe and quantitatively discuss the formation pathways of both $\textit{light}$ and $\textit{heavy}$ seeds. We emphasise that the most recent computational models suggest that rather than a bimodal-like mass spectrum between $\textit{light}$ and $\textit{heavy}$ seeds with $\textit{light}$ at one end and $\textit{heavy}$ at the other that instead a continuum exists. $\textit{Light}$ seeds being more ubiquitous and the heavier seeds becoming less and less abundant due the rarer environmental conditions required for their formation. We therefore examine the different mechanisms that give rise to different seed mass spectrums. We show how and why the mechanisms that produce the $\textit{heaviest}$ seeds are also among the rarest events in the Universe and are hence extremely unlikely to be the seeds for the vast majority of the MBH population. We quantify, within the limits of the current large uncertainties in the seeding processes, the expected number densities of the seed mass spectrum. We argue that $\textit{light}$ seeds must be at least $10^{3}$ to $10^{5}$ times more numerous than $\textit{heavy}$ seeds to explain the MBH population as a whole. Based on our current understanding of the seed population this makes $\textit{heavy}$ seeds ($\rm{M_{seed}} > 10^3$ M$_{\odot}$) a significantly more likely pathway given that $\textit{heavy}$ seeds have an abundance pattern than is close to and likely in excess of $10^{-4}$ compared to $\textit{light}$ seeds. Finally, we examine the current state-of-the-art in numerical calculations and recent observations and plot a path forward for near-future advances in both domains.