Recent quasar surveys have revealed that supermassive black holes ( SMBHs ) rarely exceed a mass of M _ { BH } \sim { a~ { } few } \times 10 ^ { 10 } ~ { } M _ { \odot } during the entire cosmic history .
It has been argued that quenching of the BH growth is caused by a transition of a nuclear accretion disk into an advection dominated accretion flow , with which strong outflows and/or jets are likely to be associated .
We investigate a relation between the maximum mass of SMBHs and the radio-loudness of quasars with a well-defined sample of \sim 10 ^ { 5 } quasars at a redshift range of 0 < z < 2 , obtained from the Sloan Digital Sky Surveys DR7 catalog .
We find that the number fraction of the radio-loud ( RL ) quasars increases above a threshold of M _ { BH } \simeq 2 \times 10 ^ { 9 } ~ { } M _ { \odot } , independent of their redshifts .
Moreover , the number fraction of RL quasars with lower Eddington ratios ( out of the whole RL quasars ) , indicating lower accretion rates , increases above the critical BH mass .
These observational trends can be natural consequences of the proposed scenario of suppressing BH growth around the apparent maximum mass of \sim 10 ^ { 10 } ~ { } M _ { \odot } .
The ongoing VLA Sky Survey in radio will allow us to estimate of the exact number fraction of RL quasars more precisely , which gives further insights to understand quenching processes for BH growth .