  We present the measurements of the luminosity-dependent redshift-space
three-point correlation functions (3PCFs) for the Sloan Digital Sky Survey
(SDSS) DR7 Main galaxy sample. We compare the 3PCF measurements to the
predictions from three different halo and subhalo models. One is the halo
occupation distribution (HOD) model and the other two are extensions of the
subhalo abundance matching (SHAM) model by allowing the central and satellite
galaxies to have different occupation distributions in the host halos and
subhalos. Parameters in all the models are chosen to best describe the
projected and redshift-space two-point correlation functions (2PCFs) of the
same set of galaxies. All three model predictions agree well with the 3PCF
measurements for the most luminous galaxy sample, while the HOD model better
performs in matching the 3PCFs of fainter samples (with luminosity threshold
below $L^*$), which is similar in trend to the case of fitting the 2PCFs. The
decomposition of the model 3PCFs into contributions from different types of
galaxy triplets shows that on small scales the dependence of the 3PCFs on
triangle shape is driven by nonlinear redshift-space distortion (and not by the
intrinsic halo shape) while on large scales it reflects the filamentary
structure. The decomposition also reveals more detailed differences in the
three models, which are related to the radial distribution, the mean occupation
function, and the velocity distribution of satellite galaxies inside halos. The
results suggest that galaxy 3PCFs can further help constrain the above
galaxy-halo relation and test theoretical models.
