Triaxial haloes, intrinsic alignments and the dark matter power spectrum

We develop the halo model of large-scale structure to include triaxial dark matter haloes and their intrinsic alignments. As a direct application we derive general expressions for the two-point correlation function and the power spectrum. We then focus on the power spectrum and numerically solve the general expressions for two different models of the triaxial profiles. The first is a toy model that allows us to isolate the dependence of clustering on halo shape alone and the second is the more realistic profile model of Jing & Suto. In both cases, we find that the effect of triaxiality is manifest as a suppression of power at the level of similar to 5 per cent on scales k similar to 1-10 h Mpc(-1), which in real space corresponds to the virial radii of clusters. When considered by mass, we find that for the first model the effects are again apparent as a suppression of power and that they are more significant for the high-mass haloes. For the Jing & Suto model, we find a suppression of power on large scales followed by a sharp amplification on small scales at the level of similar to 10-15 per cent. Interestingly, when averaged over the entire mass function this amplification effect is suppressed. We also find for the one-halo term on scales k < 10 h Mpc(-1) that the power is dominated by ellipsoidal haloes with semi-minor to semi-major axis ratios a/c < 0.7. One of the important features of our formalism is that it allows for the self-consistent inclusion of the intrinsic alignments of haloes. The alignments are specified through the correlation function of halo seeds. We develop a useful toy model for this and then make estimates of the alignment contribution to the power spectrum. Further, through consideration of the (artificial) case where all haloes are perfectly aligned, we calculate the maximum possible contribution to the clustering. We find the hard limit of < 10 per cent. Subject to further scrutiny, the proposed toy model may serve as a means for linking the actual observed intrinsic alignments of galaxies to physical quantities of interest.