We have obtained deep ultraviolet imaging of the lensing cluster Abell 1689 with the WFC3/UVIS camera onboard the Hubble Space Telescope ( HST ) in the F275W ( 30 orbits ) and F336W ( 4 orbits ) filters .
These images are used to identify z \sim 2 star-forming galaxies via their Lyman break , in the same manner that galaxies are typically selected at z \geq 3 .
Because of the unprecedented depth of the images and the large magnification provided by the lensing cluster , we detect galaxies 100 \times fainter than previous surveys at this redshift .
After removing all multiple images , we have 58 galaxies in our sample between -19.5 < M _ { 1500 } < -13 AB mag .
Because the mass distribution of Abell 1689 is well constrained , we are able to calculate the intrinsic sensitivity of the observations as a function of source plane position , allowing for accurate determinations of effective volume as a function of luminosity .
We fit the faint-end slope of the luminosity function to be \alpha = -1.74 \pm 0.08 , which is consistent with the values obtained for 2.5 < z < 6 .
Notably , there is no turnover in the luminosity function down to M _ { 1500 } = -13 AB mag .
We fit the UV spectral slopes with photometry from existing Hubble optical imaging .
The observed trend of increasingly redder slopes with luminosity at higher redshifts is observed in our sample , but with redder slopes at all luminosities and average reddening of < E ( B - V ) > = 0.15 mag .
We assume the stars in these galaxies are metal poor ( 0.2 Z _ { \sun } ) compared to their brighter counterparts ( Z _ { \sun } ) , resulting in bluer assumed intrinsic UV slopes and larger derived values for dust extinction .
The total UV luminosity density at z \sim 2 is 4.31 \substack { +0.68 \ -0.60 } \times 10 ^ { 26 } erg s ^ { -1 } Hz ^ { -1 } Mpc ^ { -3 } , more than 70 % of which is emitted by galaxies in the luminosity range of our sample .
Finally , we determine the global star formation rate density from UV-selected galaxies at z \sim 2 ( assuming a constant dust extinction correction of 4.2 over all luminosities and a Kroupa IMF ) of 0.148 \substack { +0.023 \ -0.020 } M _ { \sun } yr ^ { -1 } Mpc ^ { -3 } , significantly higher than previous determinations because of the additional population of fainter galaxies and the larger dust correction factors .