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We investigate various phenomenological schemes for the rapid generation of3D mock galaxy catalogues with a given power spectrum and bispectrum. We applythe fast bispectrum estimator \MODALLSS{} to these mock galaxy catalogues andcompare to $N$-body simulation data analysed with the halo-finder\texttt{ROCKSTAR} (our benchmark data). We propose an assembly bias model forpopulating parent halos with subhalos by using a joint lognormal-Gaussianprobability distribution for the subhalo occupation number and the haloconcentration. This prescription enabled us to recover the benchmark powerspectrum from $N$-body simulations to within 1\% and the bispectrum to within4\% across the entire range of scales of the simulation. A small further boostadding an extra galaxy to all parent halos above the mass threshold$M>2\times10^{14}\,h^{-1} M_\odot$ obtained a better than 1\% fit to both powerspectrum and bispectrum in the range $K/3<1.1\,h\,\text{Mpc}^{-1}$, where$K=k_1+k_2+k_3$. This statistical model should be applicable to fast darkmatter codes, allowing rapid generation of mock catalogues which simultaneouslyreproduce the halo power spectrum and bispectrum obtained from $N$-bodysimulations. We also investigate alternative schemes using the Halo OccupationDistribution (HOD) which depend only on halo mass, but these yield resultsdeficient in both the power spectrum (2\%) and the bispectrum (>4\%) at $k,K/3\approx 0.2\,h\,\text{Mpc}^{-1}$, with poor scaling for the latter. Efforts tomatch the power spectrum by modifying the standard four-parameter HOD modelresult in overboosting the bispectrum (with a 10\% excess). We alsocharacterise the effect of changing the halo profile on the power spectrum andbispectrum.

Advancing the matter bispectrum estimation of large-scale structure: fast prescriptions for galaxy mock catalogues