Clustering of luminous red galaxies - III. Baryon acoustic peak in the three-point correlation

We present the three-point function xi(3) and Q(3) = xi(3)/xi 2(2) for a spectroscopic sample of luminous red galaxies from the Sloan Digital Sky Survey (SDSS) Data Release 6 and Data Release 7. We find a strong (signal-to-noise ratio > 6) detection of Q(3) on scales of 55-125 Mpc/h, with a well-defined peak around 105 Mpc/h in all xi(2), xi(3) and Q(3), in excellent agreement with the predicted shape and location of the imprint of the baryon acoustic oscillations (BAO). We use very large simulations (from a cubic box of L = 7680 Mpc/h) to assess and test the significance of our measurement. Models without the BAO peak are ruled out by the Q(3) data with 99 per cent confidence. This detection demonstrates the non-linear growth of structure by gravitational instability between z = 1000 and the present. Our measurements show the expected shape for Q(3) as a function of the triangular configuration. This provides a first direct measurement of the non-linear mode-coupling coefficients of density and velocity fluctuations, which, on these large scales, are independent of cosmic time, the amplitude of fluctuations or cosmological parameters. The location of the BAO peak in the data indicates (m) = 0.28 +/- 0.05 and (B) = 0.079 +/- 0.025 (for h = 0.70) after marginalization over spectral index (n(s) = 0.8-1.2) linear b(1) and quadratic c(2) bias, which are found to be in the range: b(1) = 1.7-2.2 and c(2) = 0.75-3.55. The data allow a hierarchical contribution from primordial non-Gaussianities in the range Q(3) = 0.55-3.35. These constraints are independent and complementary to the ones that can be obtained using the two-point function, which are presented in a separate paper. This is the first detection of the shape of Q(3) on BAO scales, but our errors are shot noise dominated and the SDSS volume is still relatively small, so there is ample room for future improvement in this type of measurements.