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Mass accretion rate is a key parameter in accretion disk theory. Itdetermines black hole accretion mode. In large scale cosmological simulationsstudying galaxy formation and evolution, Bondi radius can at most be marginallyresolved. In those simulations, Bondi accretion formula is always used toestimate black hole accretion rate. Bondi solution is too simple, which cannotrepresent the real accretion process. We perform simulations of hot accretionflow at parsec scale irradiated by a low luminosity active galactic nucleus(AGN). We perform 77 simulations with varying density and temperature at outerboundary (10 parsec). Our purpose is to find a formula to calculate real blackhole accretion rate based on the gas density and temperature at parsec scale.We define Eddington accretion rate to be $\dot M_{\rm Edd}=10L_{\rm Edd}/c^2$,with $L_{\rm Edd}$ and $c$ been Eddington luminosity and speed of lightrespectively. We set black hole mass to be $10^8M_{\odot}$, $M_{\odot}$ issolar mass. We find that black hole accretion rate can be expressed as$\frac{\dot M_{\rm BH} }{\dot M_{\rm Edd}}=10^{-3.11} (\rho_0/10^{-22}{\rm gcm}^{-3})^{1.36} (T_0/10^7 {\rm K})^{-1.9}$, with $\rho_0$ and $T_0$ beingdensity and temperature at parsec scale, respectively. We find the formula canaccurately predict the luminosity of observed low-luminosity AGNs (with blackhole mass $\sim 10^8M_{\odot}$). This formula can be used in the sub-gridmodels in large scale cosmological simulations with a black hole mass of $\sim10^8M_{\odot}$.

What is the real accretion rate onto a black hole for low angular momentum accretion?