We present the discovery of five quasars at z \sim 6 selected from 260 deg ^ { 2 } of the Sloan Digital Sky Survey ( SDSS ) southern survey , a deep imaging survey obtained by repeatedly scanning a stripe along the Celestial Equator .
The five quasars with 20 < z _ { AB } < 21 are 1–2 magnitudes fainter than the luminous z \sim 6 quasars discovered in the SDSS main survey .
One of them was independently discovered by the UKIRT Infrared Deep Sky Survey .
These quasars , combined with another z \sim 6 quasar known in this region , make a complete flux-limited quasar sample at z _ { AB } < 21 .
The sample spans the redshift range 5.85 \leq z \leq 6.12 and the luminosity range -26.5 \leq M _ { 1450 } \leq - 25.4 ( H _ { 0 } = 70 km s ^ { -1 } Mpc ^ { -1 } , \Omega _ { m } = 0.3 , and \Omega _ { \Lambda } = 0.7 ) .
We use the 1 / V _ { a } method to determine that the comoving quasar spatial density at \langle z \rangle = 6.0 and \langle M _ { 1450 } \rangle = -25.8 is ( 5.0 \pm 2.1 ) \times 10 ^ { -9 } Mpc ^ { -3 } mag ^ { -1 } .
We model the bright-end quasar luminosity function ( QLF ) at z \sim 6 as a power law \Phi ( L _ { 1450 } ) \propto L _ { 1450 } ^ { \beta } .
The slope \beta calculated from a combination of our sample and the luminous SDSS quasar sample is -3.1 \pm 0.4 , significantly steeper than the slope of the QLF at z \sim 4 .
Based on the derived QLF , we find that the quasar/AGN population can not provide enough photons to ionize the intergalactic medium ( IGM ) at z \sim 6 unless the IGM is very homogeneous and the luminosity ( L _ { 1450 } ^ { \ast } ) at which the QLF power law breaks is very low .