We present a joint analysis of the rest-frame ultraviolet ( UV ) luminosity functions of continuum-selected star-forming galaxies and galaxies dominated by active galactic nuclei ( AGNs ) at z \sim 4 .
These 3,740 z \sim 4 galaxies are selected from broad-band imaging in nine photometric bands over 18 deg ^ { 2 } in the Spitzer /HETDEX Exploratory Large Area Survey ( SHELA ) field .
The large area and moderate depth of our survey provide a unique view of the intersection between the bright end of the galaxy UV luminosity function ( M _ { AB } < - 22 ) and the faint end of the AGN UV luminosity function .
We do not separate AGN-dominated galaxies from star-formation-dominated galaxies , but rather fit both luminosity functions simultaneously .
These functions are best fit with a double power-law ( DPL ) for both the galaxy and AGN components , where the galaxy bright-end slope has a power-law index of -3.80 \pm 0.10 , and the corresponding AGN faint-end slope is \alpha _ { AGN } = -1.49 ^ { +0.30 } _ { -0.21 } .
We can not rule out a Schechter-like exponential decline for the galaxy UV luminosity function , and in this scenario the AGN luminosity function has a steeper faint-end slope of -2.08 ^ { +0.18 } _ { -0.11 } .
Comparison of our galaxy luminosity function results with a representative cosmological model of galaxy formation suggests that the molecular gas depletion time must be shorter , implying that star formation is more efficient in bright galaxies at z = 4 than at the present day .
If the galaxy luminosity function does indeed have a power-law shape at the bright end , the implied ionizing emissivity from AGNs is not inconsistent with previous observations .
However , if the underlying galaxy distribution is Schechter , it implies a significantly higher ionizing emissivity from AGNs at this epoch .