Modeling the Spectral Energy Distribution of Active Galactic Nuclei: Implications for Cosmological Simulations of Galaxy Formation

Abstract Modeling the spectral energy distributions (SEDs) of active galactic nuclei (AGNs) plays a very important role in constraining modern cosmological simulations of galaxy formation. Here, we utilize a physically motivated supermassive black hole (SMBH) accretion disk model to compute the accretion flow structure and AGN SED across a wide range of black hole mass ( M SMBH ) and dimensionless accretion rates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> <mml:mo stretchy="false">(</mml:mo> <mml:mo>≡</mml:mo> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">acc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Edd</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">acc</mml:mi> </mml:mrow> </mml:msub> </mml:math> is the mass flow rate through the disk, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Edd</mml:mi> </mml:mrow> </mml:msub> </mml:math> is the Eddington mass accretion rate. We find that the radiative efficiency is mainly influenced by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> , while contributions of M SMBH and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> to the bolometric luminosity are comparably important. We have developed new bolometric corrections linking the bolometric luminosity of an AGN to its luminosities in the hard X-ray, soft X-ray, and optical bands. Our results align with existing literature at high luminosities but suggest lower luminosities in the hard and soft X-ray bands at lower bolometric luminosities compared to those from commonly adopted empirical relations. Combined with the semianalytic model of galaxy formation L-Galaxies and Millennium dark matter simulation for the distribution of ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">SMBH</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> ) at different redshifts, the model predicted AGN fraction shows good agreement with observational data to z ≲ 2.5, while the luminosity functions align well with observational data at z ≲ 1 but deviate from them for higher redshifts. This deviation may arise from improper treatments of SMBH growth at high redshifts in the galaxy formation model or bias from limited observational data. This AGN SED calculation can be readily applied to other cosmological simulations.