This work concerns the physical properties of very faint ( R _ { lim } =28 AB mag ; M _ { stars,lim } \sim 10 ^ { 8 } M _ { \odot } ) , UV-selected sub- L ^ { * } Â BX galaxies at z \sim 2.3 . Stellar masses , dust content , and dust-corrected star formation rates are constrained using broadband spectral energy distribution fitting , resulting in a number of insights into the nature of these low-mass systems . First , a correlation between rest-frame UV luminosity and galaxy stellar mass appears to exist in BX galaxies and its presence suggests that many sub- L ^ { * } Â galaxies at this redshift may have approximately constant , rather than highly variable , star formation histories . A nearly-linear relation between stellar mass and star formation rate is also found , hinting that the rate at which a sub- L ^ { * } Â BX galaxy forms its stars is directly related to the mass of stars that it has already formed . A possible explanation for this phenomenon lies in a scenario in which new gas that falls onto the galaxy ’ s host halo along with accreting dark matter is the main source of fuel for ongoing star formation . The instantaneous efficiency of star formation is low in this scenario , of order one percent . Turning to bulk quantities , it is found that the low-mass end of the stellar mass function at z \sim 2.3 is steeper than expected from extrapolations of shallower surveys , resulting in a stellar mass density at z \sim 2.3 that ’ s \sim 25 % of the present-day value ; this value is \sim 1.5–2 times higher than that given by extrapolations of most of the shallower surveys , suggesting that the build-up of stellar mass in the universe has proceeded somewhat more rapidly than previously thought . With SED-fitting results in hand , an update to the Keck Deep Fields z \sim 2 UV luminosity function finds a steeper faint-end slope than previously reported , \alpha = -1.47 , though this is not as steep as that found by Reddy & Steidel ( 2009 ) . Finally , it is also found that sub- L ^ { * } Â galaxies at z \sim 2 carry very small amounts of dust compared to their more luminous cousins , so that while only \sim 20 % of 1700Ã photons escape from a typical M ^ { * } Â galaxy , more than half make it out of an M ^ { * } +3 one . This paucity of dust highlights the fact that sub- L ^ { * } Â galaxies are not simple scaled copies of their more luminous cousins . Assuming that absorption by neutral hydrogen is not stronger in sub- L ^ { * } Â galaxies than in their more luminous counterparts , it also means that sub- L ^ { * } Â are important contributors to keeping the Universe ionized at z \sim 2 .