Probabilistic estimators of Lagrangian shape biases: Universal relations and physical insights

¹ Donostia International Physics Center, Manuel Lardizabal Ibilbidea, 4, 20018 Donostia, Gipuzkoa, Spain
² Euskal Herriko Unibertsitatea, Edificio Ignacio Maria Barriola, Plaza Elhuyar, 1, 20018 Donostia-San Sebastián, Spain
³ Department of Astrophysics, University of Vienna, Türkenschanzstraße 17, 1180 Vienna, Austria
⁴ IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain

^★ Corresponding author.

Received: 28 November 2024
Accepted: 16 June 2025

Abstract

The intrinsic alignment of galaxies can provide valuable information for cosmological and astrophysical studies and is crucial for interpreting weak-lensing observations. Modeling intrinsic alignments requires understanding how galaxies acquire their shapes in relation to the large-scale gravitational field, which is typically encoded in the value of large-scale shape-bias parameters. In this article we contribute to this topic in three ways: (i) developing new estimators of Lagrangian shape biases, (ii) applying them to measure the shape biases of dark-matter halos, and (iii) interpreting these measurements to gain insight into the process of halo-shape formation. Our estimators yield measurements consistent with previous literature values and offer advantages over earlier methods; for example, our bias measurements are independent of other bias parameters, and we can define bias parameters for each individual object. We measure universal relations between shape-bias parameters and peak height, ν. For the first-order shape-bias parameter, this relation is close to linear at high ν and approaches zero at low ν, which provides evidence against the proposed scenario that galaxy shapes arise due to post-formation interaction with the large-scale tidal field. We anticipate that our estimators will be very useful for analyzing hydrodynamical simulations, and thereby enhance our understanding of galaxy shape formation, and for establishing priors on the values of intrinsic alignment biases.