The Luminosity Function of Void Galaxies in the Sloan Digital Sky Survey

(Abridged) The Sloan Digital Sky Survey now extends over a large enough region that galaxies in low density environments can be detected. Rojas et al. have developed a technique to extract more than 1000 void galaxies with delta rho/rho < -0.6 on scales r>7 h^{-1} Mpc from the SDSS. In this paper, we present the luminosity function of these galaxies and compare it to that of galaxies at higher densities. We obtain a measurement of the void galaxy luminosity function over the range -21.5<M_r*<-14.5 in the SDSS r-band. The void galaxy luminosity function (LF) is well fit by a Schechter function with values of Phi*=(0.19 +- 0.04)*0.01 h^3 Mpc^{-3}, M_r* - 5logh=-19.74 +- 0.11 and alpha=-1.18 +- 0.13, where as the LF of the wall galaxy has Schechter function parameters Phi*=(1.42 +- 0.03)*0.01 h^3 Mpc^{-3}, M_r* - 5logh=-20.62 +- 0.08 and alpha=-1.19 +- 0.07. The fainter value of M_r* is consistent with the work of Rojas et al.who found that void galaxies were fainter than galaxies at higher densities but the value of alpha is very similar to that of galaxies at higher densities. To investigate this further, the LF of wall and void galaxies as a function of density is considered. Only the wall galaxies in the highest density regions have a shallower faint end slope. The LF of the void galaxies is also compared to the LF of the wall galaxies with similar properties to the void galaxies. The LF of the bluest, Sersic index n<2 and EW(Halpha)>5A wall galaxies is very similar in shape to that of the void galaxies, with only slightly brighter M_r* values and similar values of alpha. The value of alpha ~ -1.2 found from the void galaxy LF is shallower that that found from CDM models, suggesting that voids are not filled with a large population of dwarf galaxies.