We find that the fraction of classical Broad Absorption Line quasars ( BALQSOs ) among the FIRST radio sources in the Sloan Data Release 3 , is 20.5 ^ { +7.3 } _ { -5.9 } % at the faintest radio powers detected ( L _ { 1.4 GHz } \sim 10 ^ { 32 } { erg s ^ { -1 } } ) , and rapidly drops to \lesssim 8 % at L _ { 1.4 GHz } \sim 3 \times 10 ^ { 33 } { erg s ^ { -1 } } .
Similarly , adopting the broader Absorption Index ( AI ) definition of Trump et al .
( 2006 ) we find the fraction of radio BALQSOs to be 44 ^ { +8.1 } _ { -7.8 } % reducing to 23.1 ^ { +7.3 } _ { -6.1 } % at high luminosities .
While the high fraction at low radio power is consistent with the recent near-IR estimates by Dai et al .
( 2008 ) , the lower fraction at high radio powers is intriguing and confirms previous claims based on smaller samples .
The trend is independent of the redshift range , the optical and radio flux selection limits , or the exact definition of a radio match .
We also find that at fixed optical magnitude , the highest bins of radio luminosity are preferentially populated by non-BALQSOs , consistent with the overall trend .
We do find , however , that those quasars identified as AI-BALQSOs but not under the classical definition , do not show a significant drop in their fraction as a function of radio power , further supporting independent claims for which these sources , characterized by lower equivalent width , may represent an independent class with respect to the classical BALQSOs .
We find the balnicity index , a measure of the absorption trough in BALQSOs , and the mean maximum wind velocity to be roughly constant at all radio powers .
We discuss several plausible physical models which may explain the observed fast drop in the fraction of the classical BALQSOs with increasing radio power , although no one is entirely satisfactory .
A strictly evolutionary model for the BALQSO and radio emission phases requires a strong fine-tuning to work , while a simple geometric model , although still not capable of explaining polar BALQSOs and the paucity of FRII BALQSOs , is statistically successful in matching the data if part of the apparent radio luminosity function is due to beamed , non-BALQSOs .