In light of recent indications for a large population of obscured active galactic nuclei ( AGNs ) , we revisit the mean radiation efficiency from accretion onto supermassive black holes ( SMBHs ) , \langle \epsilon \rangle , applying a bayesian approach .
We use the integrated comoving energy density emitted by AGNs and compare it to the mass density of local SMBHs .
When considering only optically-selected unobscured AGNs , we derive log _ { 10 } [ \langle \epsilon \rangle ] = -1.77 ^ { +0.16 } _ { -0.11 } or \langle \epsilon \rangle = 1.7 ^ { +0.8 } _ { -0.4 } % .
Using the AGNs selected using hard X-rays , which include unabsorbed and Compton-thin absorbed AGNs , we find log _ { 10 } [ \langle \epsilon \rangle ] = -1.20 ^ { +0.15 } _ { -0.10 } or \langle \epsilon \rangle = 6.4 ^ { +2.6 } _ { -1.3 } % .
Using optically-selected AGNs , and correcting for the obscured population , we inferr log _ { 10 } [ \langle \epsilon \rangle ] = -1.17 ^ { +0.11 } _ { -0.08 } or \langle \epsilon \rangle = 6.7 ^ { +1.9 } _ { -1.1 } % , which we consider our best estimate .
We also repeat this calculation for intrinsically luminous AGNs ( M _ { B } < -23 , quasars ) , comparing to the SMBH mass density in local elliptical galaxies , and find log _ { 10 } [ \langle \epsilon \rangle ] = -1.27 ^ { +0.15 } _ { -0.11 } or \langle \epsilon \rangle = 5.4 ^ { +2.2 } _ { -1.2 } % .
We discuss how our results can be used to estimate the mean spin of accreting SMBHs , both assuming the standard thin-disk model of accretion onto black holes and also comparing to more recent simulations .
Our results can rule out maximally rotating SMBHs ( \langle a \rangle = 0.998 { Gm _ { \bullet } \over c ^ { 2 } } ) at the \geq 98 % confidence level , as well as high rotation values ( \langle a \rangle \geq 0.9 { Gm _ { \bullet } \over c ^ { 2 } } ) with \geq 92 % confidence .
Our preferred values of \langle a \rangle are \sim 0.25-0.60 { Gm _ { \bullet } \over c ^ { 2 } } , although even these might be overestimated .
Hence , we find that on average , SMBHs are not rapidly spinning during accretion .
Finally , using an independent measurement of Eddington ratios , we estimate the SMBH e -folding time for the brightest AGNs ( quasars ) to be \langle \tau \rangle = 100 ^ { +151 } _ { -60 } Myr .