An analytical model for non-local stochastic field-level galaxy bias on the sphere

summary

The gist

The BOLTS model presents a novel analytical galaxy bias model for projected fields on the sphere that incorporates stochasticity and non-locality already at linear order while enforcing physicality

In short

The BOLTS model introduces a novel analytical galaxy bias for projected fields on a sphere that includes non-locality and stochasticity at linear order. It models bias as a random field rather than a deterministic function, allowing fluctuations in bias to enter. This enables efficient forward modeling for simulation inference and improves accuracy over standard linear models.

Key concepts

Galaxy Bias as a Random Field: Instead of using a single deterministic transfer function to map matter density to galaxy density, BOLTS treats the galaxy bias as a statistically isotropic random field. This means the relationship between dark matter and galaxies has inherent fluctuations, which are modeled explicitly through stochastic contributions.
Decomposition into Components: The model decomposes the total bias into two parts: a linear, non-local deterministic component (capturing large-scale structure) and a stochastic component (modeling noise and fluctuations). This separation helps isolate the physical effects of clustering from random sampling errors.
Forward Modeling for Inference: BOLTS allows researchers to efficiently generate galaxy density fields for different redshifts using parameterized functions. This capability is crucial for simulation-based inference, enabling model comparison with large galaxy survey datasets like Euclid and Rubin LSST.
Equilateral Bispectrum: This is a higher-order statistical measure used to probe the non-Gaussian structure of the biased density field. BOLTS predicts this statistic well, even without prior calibration, demonstrating its accuracy in capturing complex correlations beyond simple two-point statistics.

Terminology used across episodes

Reinforcement Learning (RL) — explained in 25 episodes
Federated Learning — explained in 17 episodes
Retrieval-Augmented Generation (RAG) — explained in 16 episodes
Interpretability — explained in 15 episodes
Quantum Fisher Information (QFI) — explained in 15 episodes
Sample Complexity — explained in 15 episodes

This episode discusses

The paper

An analytical model for non-local stochastic field-level galaxy bias on the sphere · Read on arXiv

Maximilian von Wietersheim-Kramsta, Nicolas Tessore, Benjamin Joachimi, Qianjun Hang, Niall Jeffrey, Joop Schaye

Department of Physics, Institute for Computational Cosmology, Durham University · Centre for Extragalactic Astronomy, Durham University · Mullard Space Science Laboratory, University College London Department of Physics and Astronomy, University College London Department of Physics & King’s Institute for Artificial Intelligence, King’s College London · Leiden Observatory Leiden University

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 > 10 11.5, 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 = 10 11.5, 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.

Transcript

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "An analytical model for non-local stochastic field-level galaxy bias on the sphere".

Jocelyn: The BOLTS model presents a novel analytical galaxy bias model for projected fields on the sphere that incorporates stochasticity and non-locality already at linear order while enforcing physicality and statistical…

Vera: First, who's behind it and why it matters.

Paper summary: Vera: So to recap, this paper introduces BOLTS as a novel analytic galaxy bias model specifically designed for projected fields on the sphere. The core thesis is that you can incorporate stochasticity and non-locality into the bias modeling right at linear order while maintaining physical constraints like statistical isotropy ABSTRACT.

Jocelyn: It claims that instead of a simple deterministic transfer function, we should treat galaxy bias as a statistically isotropic random field where fluctuations enter through variations in the bias itself. This means the mapping from matter density to galaxy overdensity isn't fixed; it has its own internal noise ABSTRACT.

Subrahmanyan: The model yields an explicit decomposition into a linear, non-local stochastic and deterministic component in harmonic space. This allows them to cleanly separate what is physically determined from what is just statistical fluctuation ABSTRACT.

Vera: They fit the parameters using projected power spectra from large hydrodynamical simulations called FLAMINGO. This fitting process lets researchers sample galaxy populations based on simulated matter fields while conditioning the model on properties like halo mass or redshift ABSTRACT.

Jocelyn: The real payoff here is that by construction, the model reproduces two-point statistics down to the simulation resolution. Plus, without being calibrated on it, BOLTS recovers the equilateral bispectrum within the sample variance of a simulation down to comoving scales of O(ten Mpc) for halo masses M > ten eleven point five, over redshifts zero < z < three ABSTRACT <ref:2610.12259#pg1>.

Subrahmanyan: This is important because it shows that even without full calibration, this model performs well for measuring the non-Gaussian structure at scales relevant to galaxy clustering studies ABSTRACT.

Vera: They emphasize that relative to local bias prescriptions, this model more accurately captures amplitude-phase correlations and mode coupling in the measured wavelet phase harmonics where the stochasticity of the tracers is stronger than their discreteness ABSTRACT.

Jocelyn: So, what does this mean for how we use these models? It’s a tool that lets us move beyond simple linear assumptions toward a more realistic description of how galaxies trace matter across cosmic time.

Subrahmanyan: It’s about making sure the tools we use for cosmological parameter estimation are robust over the widest possible range of scales, which is what they were aiming for ABSTRACT.

Conclusion: Vera: So looking at this paper "An analytical model for non-local stochastic field-level galaxy bias on the sphere" and its authors von Wietersheim-Kramsta, Tessore, Joachimi, Hang, Jeffrey, Schaye <ref:2610.12259#pg1>, it's clear they’ve built a framework called BOLTS.

Jocelyn: They’ve created this model to tackle the problem of modeling galaxy bias on the sphere by making it stochastic and non-local from the start, which is a significant development for projected analysis ABSTRACT.

Subrahmanyan: The implication is that we can use this framework not just as a fancy fitting tool but as an analytical prescription for galaxy bias in standard likelihood-based analyses ABSTRACT.

Vera: It’s about improving the accuracy of modeling galaxy bias compared to older linear deterministic models by incorporating these non-local, stochastic effects ABSTRACT.

Jocelyn: And it’s designed to be naturally suited for the projected analyses required by major upcoming surveys like Euclid, Rubin LSST, and Roman ABSTRACT.

Subrahmanyan: So the paper gives us a practical simulator for simulation-based inference pipelines and also an analytical prescription for galaxy bias in standard likelihood-based analyses ABSTRACT.

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