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The theory and measurement of the three-point statistics

Hong Guo (CWRU)

We use N -body simulations, theoretical models and also observational data
to study and analysis the three-point correlation function, bispectrum and their
dependence on scale, shape and luminosity. We \ufb01nd that the second-order
perturbation theory is not accurate enough even on very large scales to
describe the behavior the dark matter bispectrum. The Taylor expansion of the galaxy
density field can be applied to quasi-linear scale of k ~ 0.15 h/Mpc. But accurate determination
of galaxy bias with the bispectrum method requires the precise estimates of the underlying dark
matter bispectrum. The halo model can qualitatively interpret the properties of the
bispectra of both dark matter and galaxies. But it's not good enough to quantitatively
match with the simulations, for which purpose we may need to consider all the possible
inaccuracies in the model configurations. Finally, we calculate the three-point correlation
function (3PCF) and projected function with SDSS data to study their dependence on galaxy
properties. We find that different to the previous findings, the reduced 3PCF of galaxies
shows clear dependence on galaxy luminosity, but such dependence is also coupled with the
scale and shape dependence. The stellar mass dependence is quite similar to that of the
luminosity, but there also exists slight differences. The color dependence of 3PCF seems to
be more significant than the luminosity and stellar mass dependence.