The size and shape dependence of the SDSS galaxy bispectrum

Abstract

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.

Figures (16)

• Figure 1: Preparation of the volume limited sample from SDSS data. In (a) we show the definition of the volume limited sample in the redshift-absolute magnitude diagram. In (b) we represent the projected distribution of our volume limited sample along with the extracted data cube that we use in the present work. The figure in the bottom panel (c) shows the radial number density of the volume limited sample along with the mean number density.
• Figure 2: Two dimensional slices of galaxy distribution. The different panels show the galaxy distributions in a 2D slice of thickness $50\,\rm Mpc$ through the SDSS data cube, along with the same for red and blue galaxy samples.
• Figure 3: Similar to Figure \ref{['fig:sdss_galaxies']}, but for one realisation of the mock galaxy sample for three different values of the bias as indicated in the figure.
• Figure 4: Power spectrum as a function of $k$. The data points (black circles) show $[P(k)]_{\rm SDSS}$ the power spectrum values for our SDSS galaxy sample. The right panel (a) shows the power spectra for three different mock samples, represented by three lines of different colors. The $1 \sigma$ error bars shown for $[P(k)]_{\rm SDSS}$ have been estimated using $50$ realizations of the mock sample with $b_1 = 1.2$. (b) represents the comparison of the red and blue galaxy power spectrum with that of the entire sample.
• Figure 5: Bispectrum $[B(k_1,\mu,t)]_{\rm SDSS}$ as a function of $k_1$. This figure shows the SDSS bispectrum (black circles) for three different triangle shapes namely equilateral, squeezed and stretched in the three different panels. The results from mock galaxy samples with bias $b_1=1,~1.2$ and $1.4$ are also shown for comparison. The error bars are the $1 \sigma$ errors from $b_1=1.2$ mock sample which provides a good match with the SDSS results.