The size and shape dependence of the SDSS galaxy bispectrum
We have measured the spherically averaged bispectrum of the SDSS main galaxy sample, considering a volume-limited $[296.75\, \rm Mpc]^3$ data cube with mean galaxy number density $0.63 \times 10^{-3} \, {\rm Mpc}^{-3}$ and median redshift $0.102$. Our analysis considers $\sim 1.37 \times 10^{8}$ triangles, for which we have measured the binned bispectrum and analysed its dependence on the size and shape of the triangle. It spans wavenumbers $k_1=(0.075-0.434)\,{\rm Mpc}^{-1}$ for equilateral triangles, and a smaller range of $k_1$ (the largest side) for triangles of other shapes. For all shapes, we find that the measured bispectrum is well modelled by a power law $A\,\big(k_1/1\mpci\big)^{n}$, where the best-fit values of $A$ and $n$ vary with the shape. We have also analysed mock galaxy samples constructed from $Λ$CDM N-body simulations by applying a simple Eulerian bias prescription where the galaxies reside in regions where the smoothed density field exceeds a threshold. We find that the bispectrum from the mock samples with bias $b_1=1.2$ is in good agreement with the SDSS results. We further divided our galaxy sample into red and blue classes and studied the nature of the bispectrum for each category. The red galaxies exhibit higher bispectrum amplitude $A$ than the blue galaxies for all possible triangle configurations. Red galaxies are old, and their larger bispectra indicate non-linear evolutionary interactions within their environments over time, resulting in their distribution being highly clustered and more biased than younger blue galaxies.