# Dusty Gas Accretion onto Massive Black Holes and Infrared Diagnosis of the Eddington Ratio

## TL;DR

This study uses radiative-hydrodynamics simulations to explore dust's role in SMBH growth, revealing that dust influences accretion rates and spectral signatures, which can be used to estimate Eddington ratios via infrared observations.

## Contribution

It provides new insights into dust's secondary role in black hole growth and proposes infrared diagnostics for Eddington ratios using JWST, ALMA, and Spitzer.

## Key findings

- Dust causes gentle accretion with small fluctuations.
- Eddington ratio ranges from 10^{-4} to 10^{-2} in dusty clouds.
- Infrared flux ratios correlate with accretion activity.

## Abstract

Evidence for dust around supermassive black holes (SMBHs) in the early Universe is strongly suggested by recent observations. However, the accretion mechanism of SMBHs in dusty gas is not well understood yet. We investigate the growth of intermediate-mass black-holes (IMBHs) of $\sim 10^{5}~M_{\odot}$ in dusty clouds by using one-dimensional radiative-hydrodynamics simulations. We find that the accretion of dusty gas onto IMBHs proceeds gently with small fluctuations of the accretion rate, whereas that of pristine gas causes more violent periodic bursts. At dust-to-gas mass ratios similar to the solar neighborhood, the time averaged luminosity becomes smaller than that for primordial gas by one order of magnitude and the time-averaged Eddington ratio ranges from $\sim 10^{-4}$ to $\sim 10^{-2}$ in clouds with initial gas densities of $n_{\rm H} = 10 - 1000~\rm cm^{-3}$. Our calculations show that the effect of dust opacity alone is secondary compared to the radiation pressure on dust in regulating the BH growth. We also derive spectral energy distributions at IR bands by calculating dust thermal emission and show that the flux ratio between $\lambda \lesssim 20~\rm \mu m$ and $\gtrsim 100~\rm \mu m$ is closely related to the Eddington ratio. Thermal emission from hot dust near the BH dominates only during the high accretion phase, producing higher flux density at $\lesssim 20~\rm \mu m$. Therefore, we suggest that the combinations of MIR observations by JWST and FIR observation by ALMA or Spitzer can be used to estimate the Eddington ratio of massive BHs.