The size and shape dependence of the bispectrum of the SDSS DR17 main galaxy sample

We have measured the spherically averaged bispectrum of the SDSS DR17 main galaxy sample, considering a volume-limited [273 Mpc]^3 data cube with mean galaxy number density 1.76 × 10^-3 Mpc^-3 and median redshift 0.093. Our analysis considers ∼ 1.37 × 10^8 triangles, for which we have measured the binned bispectrum and analyzed its dependence on the size and shape of the triangle. It spans wavenumbers k_1=(0.082-0.472) 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(k_1/1 Mpc^-1)^n, where the best-fit values of A and n vary with the shape. The parameter A is the minimum for equilateral triangles and increases as the shape is deformed to linear triangles where the two largest sides are nearly aligned, reaching its maximum value for squeezed triangles. The values of n are all negative, |n| is minimum (3.31 ± 0.17) for squeezed triangles, and 4.12 ± 0.16 for equilateral. We have also analyzed mock galaxy samples constructed from ΛCDM 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.