tokens: the matter power spectrum (left-hand panel) and reduced bispectrum (right-hand panel), defined as S ( k ) ≡ T ( k ) BCM / T ( k ) GrO for T ( k ) = { P ( k ), Q ( k )}, at z = 0. Solid, dashed, dash–dotted and dotted lines are computed with simulations of box side and 768 3 , 512 3 , 384 3 , and 256 3 particles, respectively. Colours are referred to different halo mass bins, expressed in decimal logarithm of , with which the baryon corrections have been computed, according to the legend. APPENDIX B: FOLDING OF THE PARTICLE DISTRIBUTION Measuring the three-point clustering with the classical Fourier estimators can be very expensive in terms of memory and CPU, especially when using covering larger dynamical ranges. In fact, it is easy to see that, being k Ny = π N g / L box the Nyquist frequency of the grid, increasingly large number of grid points N g are required to get a given accuracy at a fixed wavenumber, when using progressively larger simulation boxes L box . Additionally, when using “interlacing” to suppress aliasing, the number of grids used must be doubled (Sefusatti et al. 2016 ). However, since our measurements are limited by discreteness noise (and not cosmic variance), we can obtain accurate estimates of Fourier statistics on small scales by folding the density field (Jenkins et al. 1998 ; Colombi et al. 2009 ). The idea is to fold the particle distribution by re-applying the periodic boundary conditions assuming a new boxsize L ′ = L / f , where we call f the number of foldings. If L ′ is large enough to assure that the modes inside the new box are uncorrelated, we can measure in principle the clustering from a new effective fundamental wavenumber up to a new effective Nyquist frequency, given by . For instance, by folding the box four times, we will get to Nyquist frequency four times higher. In Fig. A3 , we apply this technique to our simulation, folding the particles up to six times, and reaching a with a 64 3 and a 128 3 grid for the power spectrum and the bispectrum, respectively. Even using a TSC scheme on interlaced grids, we note that it is safer to use the measurements up to in the bispectrum. Also, the measurement of the largest modes of the folded box are noisy because they are sparsely sampled; for this reason, it is convenient to discard these modes, taking for instance wavenumbers . Figure A3. Left-hand panels: Matter power spectrum measured in a 64 3 (interlaced) mesh, folding the box up to six times, following the technique explained in the text (coloured dots). For comparison, the matter power spectrum measured with a 696 3 mesh and not folding the box is plotted as a black solid lines. The equivalent Nyquist frequencies for each folded box is plotted as a solid line. In the bottom panel, we display the ratio between the power spectrum measure with a 64 3 and a 696 3 mesh. Right-hand panels: Similarly to the left-hand panels, we display the measured bispectra using a 128 3 mesh and the folding of the box, and
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