The impact of halo shapes on the bispectrum in cosmology

We use the triaxial halo model formalism of Smith & Watts to investigate the impact of dark matter halo shapes on the cosmological bispectrum. Analytical expressions for the dark matter distribution are derived and subsequently evaluated through numerical integration. Two models for the ellipsoidal halo profiles are considered: a toy model designed to isolate the effects of halo shape on the clustering alone; and the more realistic model of Jing & Suto. For equilateral k-space triangles, we show that the predictions of the triaxial model are suppressed, relative to the spherical model, by up to similar to 7 and similar to 4 per cent for the two profiles, respectively. When the reduced bispectrum is considered as a function of triangle configuration, it is found to be highly sensitive to halo shapes on small scales. The generic features of our predictions are that, relative to the spherical halo model, the signal is suppressed for k-vector configurations that are close to equilateral triangles and boosted for configurations that are colinear. This appears to be a unique signature of halo triaxiality and potentially provides a means for measuring halo shapes in forthcoming cosmic shear surveys. The galaxy bispectrum is also explored. Two models for the halo occupation distribution (HOD) are considered: the binomial distribution of Scoccimarro et al. and the Poisson satellite model of Kravtsov et al. Our predictions show that the galaxy bispectrum is also sensitive to halo shapes, although relative to the mass the effects are reduced. The HOD of Kravtsov et al. is found to be more sensitive. This owes to the fact that the first moment of the occupation probability is a steeper function of mass in this model, and hence the high-mass (more triaxial) haloes are more strongly weighted. Interestingly, the functional form of the configuration-dependent bispectrum is, modulo an amplitude shift, not strongly sensitive to the exact form of the HOD, but is mainly determined by the halo shape. However, a combination of measurements made on different scales and for different k-space triangle configurations is sensitive to both halo shape and the HOD.