Analyze approximations for constructing the collapsed matter field

Determine accurate approximations for the projected collapsed matter density field or dark-matter halo field from the projected matter density field when halo catalogues are unavailable, including their ability to reproduce per-sky realizations and higher-order statistics rather than only ensemble statistics.

Background

BOLTS requires the collapsed matter density field as input when used to model the galaxy field. For applications with only a matter field, the paper tests binary masks, two-dimensional cosmic-web classifications, and conditional excursion-set constructions.

Although conditional excursion-set weighting can reproduce two-point statistics and Poisson-sampled halo counts can also reproduce discreteness and one-point tails, the best approximations have only about 0.5–0.6 cross-correlation with the true collapsed field. Projection-induced non-local scatter remains unresolved, limiting the accuracy of per-sky predictions.

References

A detailed analysis of approximations of the $\delta{\mathrm{c}}$ field or the dark matter halo field from the matter field, $\delta{\mathrm{m}}$, is beyond the scope of this work and will be explored in future work.

— An analytical model for non-local stochastic field-level galaxy bias on the sphere  (2610.12259 - Wietersheim-Kramsta et al., 8 Oct 2026) in Section 5, Section “BOLTS Bias as a forward model”