We have used deep GALEX observations at the infall region of the Coma cluster to measure the faintest UV luminosity functions ( LFs ) presented for a rich galaxy cluster thus far .
The Coma UV LFs are measured to M _ { \mathrm { UV } } = -10.5 in the GALEX FUV and NUV bands , or 3.5 mag fainter than previous studies , and reach the dwarf early-type galaxy population in Coma for the first time .
The Schechter faint-end slopes ( \alpha \approx - 1.39 in both GALEX bands ) are shallower than reported in previous Coma UV LF studies owing to a flatter LF at faint magnitudes .
A Gaussian-plus-Schechter model provides a slightly better parametrization of the UV LFs resulting in a faint-end slope of \alpha \approx -1.15 in both GALEX bands .
The two-component model gives faint-end slopes shallower than \alpha = -1 ( a turnover ) for the LFs constructed separately for passive and star forming galaxies .
The UV LFs for star forming galaxies show a turnover at M _ { \mathrm { UV } } \approx -14 owing to a deficit of dwarf star forming galaxies in Coma with stellar masses below M _ { * } = 10 ^ { 8 } ~ { } \msun .
A similar turnover is identified in recent UV LFs measured for the Virgo cluster suggesting this may be a common feature of local galaxy clusters , whereas the field UV LFs continue to rise at faint magnitudes .
We did not identify an excess of passive galaxies as would be expected if the missing dwarf star forming galaxies were quenched inside the cluster .
In fact , the LFs for both dwarf passive and star forming galaxies show the same turnover at faint magnitudes .
We discuss the possible origin of the missing dwarf star forming galaxies in Coma and their expected properties based on comparisons to local field galaxies .