The intrinsic fraction of broad absorption line quasars ( BALQSOs ) is important in constraining geometric and evolutionary models of quasars .
We present the fraction of BALQSOs in 2MASS detected quasars within the SDSS DR3 sample in the redshift range of 1.7 \leq z \leq 4.38 .
The fraction of BALQSOs is 40.4 ^ { +3.4 } _ { -3.3 } % in the 2MASS 99 % database K _ { s } band completeness sample , and 38.5 ^ { +1.7 } _ { -1.7 } % in the larger 2MASS sample extending below the completeness limit .
These fractions are significantly higher than the 26 % reported in the optical bands for the same parent sample .
We also present the fraction of BALQSOs as functions of apparent magnitudes , absolute magnitudes , and redshift in the 2MASS and SDSS bands .
The 2MASS fractions are consistently higher than the SDSS fractions in every comparison , and the BALQSO fractions steadily increase with wavelength from the SDSS u to the 2MASS K _ { s } bands .
Furthermore , the i - K _ { s } color distributions of BALQSOs and non-BALQSOs indicate that BALQSOs are redder than non-BALQSOs , with a K-S test probability of 2 \times 10 ^ { -12 } .
These results are consistent with the spectral difference between BALQSOs and non-BALQSOs including both the absorption troughs and dust extinction in BALQSOs , which leads to significant selection biases against BALQSOs in the optical bands .
Using a simple simulation incorporating the luminosity function of quasars and the amount of obscuration for BALQSOs , we simultaneously fit the BALQSO fractions in the SDSS and 2MASS bands .
We obtain a true BALQSO fraction of 43 \pm 2 % for luminous quasars ( M _ { K _ { s } } \lesssim - 30.1 mag ) .