An analytical model for non-local stochastic field-level galaxy bias on the sphere
Abstract
We present the `Bias of Overdensities in Large-scale Tracers on the Sphere' (BOLTS) model, a novel analytic galaxy bias model for projected fields on the sphere that incorporates stochasticity and non-locality already at linear order while enforcing physicality and statistical isotropy. Rather than as a deterministic transfer function, we model galaxy bias as a statistically isotropic random field, allowing stochasticity to enter through fluctuations in the bias itself. The construction yields an explicit decomposition into a linear, non-local stochastic and deterministic components in harmonic space. We fit the model parameters to the projected power spectra measured in large-volume hydrodynamical simulations (FLAMINGO), enabling sampling of galaxy populations from simulated matter fields while conditioning on galaxy properties such as halo mass or redshift. By construction, the model reproduces the two-point statistics down to the simulation resolution, and without being calibrated on it, BOLTS recovers the equilateral bispectrum within the sample variance of the simulation down to comoving scales of 𝒪(10 Mpc) for halo masses $ M_{\rm{h}} > 10^{11.5}\,\rm{M}_{\odot} $ over redshifts 0 < z < 3. Relative to local bias prescriptions, it more accurately captures amplitude-phase correlations and mode coupling in the measured wavelet phase harmonics wherever the stochasticity of the tracers exceeds their discreteness, including low redshifts and lower halo masses Mh = 1011.5 M⊙ where non-linearities become important. This model enables efficient field-level forward modelling for simulation-based inference and model comparison with large datasets from forthcoming galaxy surveys including Euclid, Rubin LSST, and Roman, while improving the accuracy of galaxy bias modelling with respect to standard linear deterministic models.
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BibTeX
@misc{wietersheimkramsta2026analytical,
title = {{An analytical model for non-local stochastic field-level galaxy bias on the sphere}},
author = {Maximilian von Wietersheim-Kramsta and Nicolas Tessore and Benjamin Joachimi and Qianjun Hang and Niall Jeffrey and Joop Schaye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12259},
eprint = {2610.12259},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12259},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An analytical model for non-local stochastic field-level galaxy bias on the sphere
AU - Maximilian von Wietersheim-Kramsta
AU - Nicolas Tessore
AU - Benjamin Joachimi
AU - Qianjun Hang
AU - Niall Jeffrey
AU - Joop Schaye
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12259
UR - https://arxiv.org/abs/2610.12259
AB - We present the `Bias of Overdensities in Large-scale Tracers on the Sphere' (BOLTS) model, a novel analytic galaxy bias model for projected fields on the sphere that incorporates stochasticity and non-locality already at linear order while enforcing physicality and statistical isotropy. Rather than as a deterministic transfer function, we model galaxy bias as a statistically isotropic random field, allowing stochasticity to enter through fluctuations in the bias itself. The construction yields an explicit decomposition into a linear, non-local stochastic and deterministic components in harmonic space. We fit the model parameters to the projected power spectra measured in large-volume hydrodynamical simulations (FLAMINGO), enabling sampling of galaxy populations from simulated matter fields while conditioning on galaxy properties such as halo mass or redshift. By construction, the model reproduces the two-point statistics down to the simulation resolution, and without being calibrated on it, BOLTS recovers the equilateral bispectrum within the sample variance of the simulation down to comoving scales of 𝒪(10 Mpc) for halo masses $ M_{\rm{h}} > 10^{11.5}\,\rm{M}_{\odot} $ over redshifts 0 < z < 3. Relative to local bias prescriptions, it more accurately captures amplitude-phase correlations and mode coupling in the measured wavelet phase harmonics wherever the stochasticity of the tracers exceeds their discreteness, including low redshifts and lower halo masses M_h = 10^11.5 M_⊙ where non-linearities become important. This model enables efficient field-level forward modelling for simulation-based inference and model comparison with large datasets from forthcoming galaxy surveys including Euclid, Rubin LSST, and Roman, while improving the accuracy of galaxy bias modelling with respect to standard linear deterministic models.
ER -