# Multiplicity functions of quasars: Predictions from the MassiveBlackII simulation

## TL;DR

This paper predicts the abundance and properties of multiple AGN systems, including triples and quadruples, across cosmic time using the MassiveBlackII simulation, highlighting their detectability and implications for black hole growth.

## Contribution

It provides the first detailed predictions of AGN multiplicity functions and their observable characteristics from a large cosmological simulation.

## Key findings

- Multiple AGN systems are most common at scales less than 0.7 cMpc/h.
- Simulated triples and quadruples are detectable in upcoming surveys like DESI and LSST.
- Most high-luminosity quasar multiples exist at redshifts 1.5 to 3.

## Abstract

We examine multiple AGN systems (triples and quadruples, in particular) in the \texttt{MassiveBlackII} simulation over a redshift range of $0.06\lesssim z \lesssim 4$. We identify AGN systems (with bolometric luminosity $L_{\mathrm{bol}}>10^{42}~\mathrm{ergs/sec}$) at different scales~(defined by the maximum distance between member AGNs) to determine the AGN multiplicity functions. This is defined as the volume/ surface density of AGN systems per unit \textit{richness} $R$, the number of AGNs in a system. We find that gravitationally bound multiple AGN systems tend to populate scales of $\lesssim0.7~\mathrm{cMpc}/h$; this corresponds to angular separations of $\lesssim100~\mathrm{arcsec}$ and a line of sight velocity difference $\lesssim200~\mathrm{km/sec}$. The simulation contains $\sim 10$ and $\sim100$ triples/quadruples per $\mathrm{deg}^2$ up to depths of DESI ($g\lesssim24$) and LSST ($g\lesssim26$) imaging respectively; at least $20\%$ of these should be detectable in spectroscopic surveys. The simulated quasar ($L_{\mathrm{bol}}>10^{44}~\mathrm{ergs/sec}$) triples and quadruples predominantly exist at $1.5\lesssim z \lesssim 3$. Their members have black hole masses $10^{6.5}\lesssim M_{bh}\lesssim 10^{9}~M_{\odot}/h$ and live in separate (one central and multiple satellite) galaxies with stellar masses $10^{10}\lesssim M_{*}\lesssim 10^{12}~M_{\odot}/h$. They live in the most massive haloes (for e.g. $\sim 10^{13}~M_{\odot}/h$ at $z=2.5$; $\sim 10^{14}~M_{\odot}/h$ at $z=1$) in the simulation. Their detections provide an exciting prospect for understanding massive black hole growth and their merger rates in galaxies in the era of multi-messenger astronomy.