Position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 10 CMASS sample

We report on the first measurement of the three-point function with the position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 CMASS sample. This new observable measures the correlation between two-point functions of galaxy pairs within different subvolumes, (ř,ř_L), where ř_L is the location of a subvolume, and the corresponding mean overdensities, (ř_L). This correlation, which we call the "integrated three-point function", iζ(r)≡⟨(ř,ř_L)(ř_L)⟩, measures a three-point function of two short- and one long-wavelength modes, and is generated by nonlinear gravitational evolution and possibly also by the physics of inflation. The iζ(r) measured from the BOSS data lies within the scatter of those from the mock galaxy catalogs in redshift space, yielding a ten-percent-level determination of the amplitude of iζ(r). The tree-level perturbation theory in redshift space predicts how this amplitude depends on the linear and quadratic nonlinear galaxy bias parameters (b₁ and b₂), as well as on the amplitude and linear growth rate of matter fluctuations (σ₈ and f). Combining iζ(r) with the constraints on b_1σ8 and fσ₈ from the global two-point correlation function and that on σ₈ from the weak lensing signal of BOSS galaxies, we measure b₂=0.41±0.41 (68% C.L.) assuming standard perturbation theory at the tree level and the local bias model.