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The cold dark matter (CDM) scenario generically predicts the existence of triaxial dark matter haloes which contain notable amounts of substructure. However, analytical halo models with smooth, spherically symmetric density profiles are routinely adopted in the modelling of light propagation effects through such objects. In this paper, we address the biases introduced by this procedure by comparing the surface mass densities of actual  N ‐body haloes against the widely used analytical model suggested by Navarro, Frenk and White (NFW). We conduct our analysis in the redshift range of 0.0–1.5.  In cluster‐sized haloes, we find that triaxiality can cause scatter in the surface mass density of the haloes up to  σ + =+60  per cent and  σ − =−70  per cent, where the 1σ limits are relative to the analytical NFW model given value. Subhaloes can increase this scatter to  σ + =+70  per cent and  σ − =−80  per cent. In galaxy‐sized haloes, the triaxial scatter can be as high as  σ + =+80  per cent and  σ − =−70  per cent, and with subhaloes the values can change to  σ + =+40  per cent and  σ − =−80  per cent.  We present an analytical model for the surface mass density scatter as a function of distance to the halo centre, halo redshift and halo mass. The analytical description enables one to investigate the reliability of results obtained with simplified halo models. Additionally, it provides the means to add simulated surface density scatter to analytical density profiles. As an example, we discuss the impact of our results on the calculation of microlensing optical depths for massive astrophysical compact halo objects in CDM haloes.

An analytical model of surface mass densities of cold dark matter haloes – with an application to MACHO microlensing optical depths