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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.
Hierarchical structure formation implies that the number of subhalos within a dark matter halo depends not only on halo mass, but also on the formation history of the halo. This dependence on the formation history, which is highly correlated with hal
We derive analytic covariance matrices for the $N$-Point Correlation Functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary $N$ and projected onto the isotropic basis functions of Cahn & Slepian (2020), recently show
We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF) on the basis of the decomposition formalism of the 3PCF using tri-polar spherical harmonics. We perform such an an
The three-point correlation function (3PCF) provides an important view into the clustering of galaxies that is not available to its lower order cousin, the two-point correlation function (2PCF). Higher order statistics, such as the 3PCF, are necessar
We develop an extension of subhalo abundance matching (SHAM) capable of accurately reproducing the real and redshift-space clustering of galaxies in a state-of-the-art hydrodynamical simulation. Our method uses a low-resolution gravity-only simulatio