Baryonification Mechanism in Cosmology

• Baryonification is a mechanism that applies a physically motivated mapping to gravity-only simulations to emulate the redistribution of matter by baryonic processes.
• It employs a displacement field based on halo mass profiles and cumulative mass matching to account for effects like gas cooling, star formation, and feedback.
• The method has been extended to model both matter clustering and thermodynamic properties, achieving percent-level accuracy compared to full hydrodynamical simulations.

Searching arXiv for recent and foundational papers on baryonification in cosmology. Baryonification is a post-processing mechanism, also called the Baryon Correction Model (BCM), that modifies a gravity-only or dark-matter-only $N$-body realization so that it mimics the redistribution of matter caused by gas cooling, star formation, supernova feedback, AGN feedback, and the quasi-adiabatic response of dark matter. In this framework, baryonic physics is represented as a physically motivated mapping from an original collisionless matter field to a baryon-modified field, usually summarized by a multiplicative correction to the nonlinear matter power spectrum rather than by a first-principles hydrodynamical evolution. Recent work has extended the same logic from matter clustering alone to bispectra, gas pressure, temperature, weak lensing, and thermal Sunyaev–Zeldovich observables (Dolgov et al., 2020, Aricò et al., 2020).

1. Definition and formal observable

The central observable of baryonification is the ratio between a matter power spectrum that includes baryonic effects and its gravity-only counterpart. Two equivalent notations are used in the literature: $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$ and

$S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$

Here $k$ is wavenumber, $z$ is redshift, and $\boldsymbol{\theta}$ denotes cosmological and feedback parameters. The first relation emphasizes cosmology and redshift dependence; the second emphasizes the BCM correction as a multiplicative factor, $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$ (Kammerer et al., 10 Jun 2025, Aricò et al., 2020).

Physically, the mechanism encodes the statement that baryonic processes mainly change the spatial arrangement of mass, not the total cosmic matter budget. Gas cooling can move baryons inward and increase central densities; star formation locks some baryons into compact stellar components; supernova and AGN feedback can eject gas from halos, lowering central densities and suppressing power on small scales. These effects act mainly on small and intermediate scales. By causality, baryonic effects are negligible on the largest scales, so

$$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$

and, because there has been little time for feedback to act at early times,

$$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } z\to \infty.$$

These limits are explicitly enforced in recent analytic fits (Kammerer et al., 10 Jun 2025).

Baryonification is therefore distinct from hydrodynamical simulation. Hydrodynamical models evolve coupled baryon and dark-matter dynamics approximately, with unresolved physics represented by tuned sub-grid parameters. Baryonification does not simulate the baryonic fluid dynamically; it modifies the final matter distribution using a compact analytic or profile-based mapping. This makes it computationally much cheaper and more interpretable, but also more model-dependent in its assumptions (Kammerer et al., 10 Jun 2025).

2. Algorithmic construction from gravity-only simulations

In its standard form, baryonification starts from a gravity-only simulation, identifies halos, replaces the original halo mass distribution by a sum of baryonic and dark-matter components with parametrized density profiles, and then displaces particles so that the simulated field matches the target profiles. The central algorithmic step is the construction of a displacement field from the difference between the initial gravity-only profile and the baryonified profile (Dolgov et al., 2020).

The mapping is spherical and halo-based. For each halo, one computes cumulative mass profiles for the original and target configurations and imposes enclosed-mass matching,

$M_{\rm GrO}(<r_{\rm i}) = M_{\rm BCM}(<r_{\rm f}),$

so that a particle initially at radius $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$0 is moved to $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$1. In this way, baryonic effects are represented as a radial rearrangement of matter around halos rather than as an explicit solution of the Euler, continuity, and energy equations. The method assumes spherical symmetry, halo-based parametrization, mass conservation within the halo decomposition, and an adiabatic or quasi-adiabatic response of dark matter to baryonic redistribution (Dolgov et al., 2020).

An important constraint is that the sum of stellar and gas fractions, including the ejected gas, is fixed to the cosmic baryon fraction $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$2. In that sense, the mechanism does not create or destroy baryons; it redistributes them between halo, galaxy, and diffuse or ejected components. This conservation requirement is one of the reasons the power-spectrum correction can be modeled as a smooth multiplicative factor with physically controlled large-scale limits (Aricò et al., 2020).

The same workflow has also been generalized from displacing a single matter field to constructing separate component fields. In the improved BFC implementation, each original $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$3-body particle is first split into a dark matter particle and a baryonic particle, and then each component is displaced separately. This produces particle-level outputs for gas, dark matter, and stars rather than only a corrected total density field (Schneider et al., 10 Jul 2025).

3. Halo decomposition, mass profiles, and control parameters

The baryonification mechanism is organized around a small number of halo components with direct physical interpretations. In the Aricò et al. (2020) model emulated by recent analytic work, central galaxies are described by an exponentially decaying power-law profile fixed to $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$4, their masses are assigned by halo abundance matching, satellite galaxies carry 20% of the central galaxy mass and follow the dark matter profile, gas bound to halos follows a double power-law profile, a fraction of gas is ejected and modeled with a constant-density profile with an exponential cutoff scale $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$5, and dark matter responds quasi-adiabatically to the modified potential (Kammerer et al., 10 Jun 2025).

Component	Treatment	Function
Dark matter	Quasi-adiabatic contraction or expansion	Back-reaction to baryonic redistribution
Central galaxies	Compact $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$6-type profile; halo abundance matching	Central mass concentration
Satellite galaxies	Trace dark matter; 20% of central galaxy mass	Stellar outskirts
Bound gas	Double power-law profile	Retained halo gas
Ejected gas	Constant-density profile with exponential cutoff $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$7	Small-scale suppression

Later extensions added reaccreted gas and more flexible gas profiles to improve joint fits to power spectra and bispectra. In the A20 implementation discussed in the bispectrum study, the original four components—dark matter, central galaxy, bound gas, expelled gas—were extended to include satellite galaxies and late-time reaccreted gas, and the bound-gas profile was replaced by a more flexible double power-law-like form with $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$8, $$S(k,z,\boldsymbol{\theta}) \equiv \frac{P(k,z,\boldsymbol{\theta})}{P_{\rm nbody}(k,z,\boldsymbol{\theta})},$$9, and inner slope

$S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$0

with $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$1 fixed after checking that it has little impact on the power spectrum and bispectrum (Dolgov et al., 2020).

A standard baryonification parameter set contains seven parameters: $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$2 These govern the characteristic halo mass scale for gas retention, the extent of ejected gas, the halo-mass dependence of the retained gas fraction, the characteristic halo mass scale for central galaxies, and the inner and outer gas-profile shape. Among these, $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$3 is repeatedly identified as the most important parameter because it sets the characteristic halo mass scale for gas retention and therefore controls how much gas remains bound inside halos versus how much is expelled by feedback. In BAHAMAS-like cases, a single parameter, $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$4, is often enough to describe the range of baryonic effects at a given epoch (Aricò et al., 2020).

This parameter hierarchy has direct physical meaning. Lower $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$5 corresponds to more efficient gas depletion in lower-mass halos; $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$6 modulates the mass dependence of the retained gas fraction; $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$7 controls how far ejected gas extends; and the stellar parameters determine the degree of central condensation that can partially counteract feedback suppression on very small scales (Aricò et al., 2020, Kammerer et al., 10 Jun 2025).

4. Impact on clustering statistics and emulator constructions

Baryonification was initially developed as a mechanism for correcting the nonlinear matter power spectrum, but the same displacement picture has been shown to capture higher-order matter statistics. In a joint analysis of six hydrodynamical simulations—BAHAMAS standard AGN, BAHAMAS low-AGN, BAHAMAS high-AGN, EAGLE, Illustris, and Illustris TNG-300—the baryonification model was shown to fit the matter power spectrum, equilateral bispectrum, reduced bispectrum, and squeezed bispectrum over $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$8 and $S(k) \equiv \frac{P_{\rm BCM}(k)}{P_{\rm GrO}(k)}.$9. If the model is fit only to the power spectrum, the bispectrum can be off by as much as $k$0; when the power spectrum and equilateral bispectrum are fit simultaneously, the power spectrum is typically accurate to $k$1–$k$2, the bispectrum to about $k$3, and the squeezed bispectrum to about $k$4 (Dolgov et al., 2020).

The BACCO Simulation Project converted this profile-based mechanism into a neural-network emulator trained on more than 50,000 measurements in a 15-dimensional parameter space. The target quantity is again the baryonic correction ratio $k$5, and the emulator was calibrated over scales $k$6 and redshifts $k$7. To reduce dimensionality, each $k$8 was smoothed with a Savitzky–Golay filter and compressed with PCA; the first six principal components already reconstruct the ratio to better than about $k$9 in most cases. The network itself is a feed-forward model with two hidden layers of 400 neurons each, using ReLU activations. The reported overall precision is $z$0–$z$1, and tests against 74 hydrodynamical simulations and their gravity-only counterparts also gave $z$2–$z$3 accuracy (Aricò et al., 2020).

Analytic compression has been pursued further with symbolic regression. The syren-baryon framework constructed separate symbolic approximations for CAMELS hydrodynamical prescriptions—Astrid, IllustrisTNG, SIMBA, and Swift-EAGLE—as well as for a baryonification algorithm. For baryonification, the symbolic fit is built directly for $z$4, is explicitly parameterized by cosmology and feedback, and is constrained to satisfy $z$5 at both $z$6 and $z$7. The selected fits were obtained with Operon using arithmetic operators only, maximum tree depth 10, model length 60, $z$8-dominance with $z$9, 1000 generations, mutation rate 25%, population size 1000, and tournament selection of size 5. The reported baryonification symbolic fit has better than $\boldsymbol{\theta}$0 RMS error, specifically around $\boldsymbol{\theta}$1, although the error increases on smaller scales (Kammerer et al., 10 Jun 2025).

These developments suggest that baryonification is not merely a convenient correction curve. It is a low-dimensional, physically structured model class whose parameters can be learned from hydrodynamical suites, transferred across cosmologies, and embedded in inference pipelines as an explicit nuisance-physics sector.

5. Thermodynamic extensions and particle-level realizations

A major recent development is the extension of baryonification from density-only corrections to thermodynamically self-consistent gas fields. In the extended BCM for the thermal Sunyaev–Zeldovich effect, the matter field is decomposed into dark matter, galaxies or stars, bound gas in hydrostatic equilibrium, and ejected gas driven out by feedback. The gas density profile inside halos is paired with a polytropic pressure law,

$\boldsymbol{\theta}$2

and the thermal component is obtained from a non-thermal pressure correction,

$\boldsymbol{\theta}$3

The temperature then follows from the ideal gas law,

$\boldsymbol{\theta}$4

This extension introduces only two additional free parameters, $\boldsymbol{\theta}$5 for diffuse gas outside halos and $\boldsymbol{\theta}$6 for the amplitude of non-thermal pressure support. Against BAHAMAS, it reproduces matter suppression at the per-cent level, electron pressure auto- and cross-power spectra to better than $\boldsymbol{\theta}$7, convergence power spectra at $\boldsymbol{\theta}$8, and tSZ power spectra at $\boldsymbol{\theta}$9, down to $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$0 (Aricò et al., 2024).

A related but more explicitly particle-level realization is the improved BFC model. There, each original dark-matter-only particle is duplicated into dark matter and baryonic components, the two components are displaced separately using inverse cumulative mass profiles, and baryonic particles are then assigned probabilistically to gas or stars according to local radial probabilities. Pressure and temperature are assigned to gas particles by combining hydrostatic equilibrium,

$P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$1

with a non-thermal correction and the ideal gas law,

$P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$2

This model was calibrated to gas and stellar mass ratio profiles from FLAMINGO and TNG. After fitting only the profiles and not the power spectrum directly, it achieved $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$3 agreement up to $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$4 across all tested feedback scenarios when each redshift was treated individually, and a reduced $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$5 parameter version matched the hydrodynamical simulations to better than $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$6 over the scales and redshifts relevant for cosmological surveys (Schneider et al., 10 Jul 2025).

These thermodynamic extensions make baryonification suitable for mock catalogues, lightcones, and joint weak-lensing–tSZ analyses rather than only for 3D matter clustering. A plausible implication is that baryonification has become a field-level generative model for multi-wavelength large-scale-structure observables, not merely a post hoc correction to $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$7.

6. Assumptions, limitations, and terminological ambiguity

The mechanism remains phenomenological. Its strengths are fast execution, physically interpretable parameters, and direct application to gravity-only simulations, but its limitations are equally explicit in the literature. The method assumes spherical symmetry of halo displacements and density profiles, a halo-based description in which baryonic effects depend mainly on halo mass, and neglected processes beyond the chosen parametrization, such as highly non-spherical outflows or feedback extending far beyond halo boundaries (Dolgov et al., 2020).

Several papers emphasize that redshift evolution cannot simply be ignored. If $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$8 best-fit baryonification parameters are applied unchanged at $P_{\rm BCM}(k)=S(k)P_{\rm GrO}(k)$9 and $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$0, power-spectrum errors are usually below $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$1 but can reach $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$2–$$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$3 for extreme models, while reduced-bispectrum errors can be $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$4–$$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$5. Extreme AGN prescriptions can also produce features such as step-like suppressions that are not perfectly captured. In the improved BFC framework, the dark-matter back-reaction model is identified as the main weak point at high redshift and high $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$6, and the map-level comparison is still qualitative rather than a fully quantified field-level validation (Dolgov et al., 2020, Schneider et al., 10 Jul 2025).

A recurring misconception is to treat baryonification as a cheap surrogate for hydrodynamics without loss of model dependence. The literature states the opposite more carefully: baryonification is computationally much cheaper and more interpretable, but also more model-dependent in its assumptions. It is best understood as a controlled effective model of halo-scale mass redistribution, calibrated against hydrodynamical simulations and observations, rather than as a replacement for fluid dynamics in all regimes (Kammerer et al., 10 Jun 2025).

There is also a terminological ambiguity. Outside large-scale-structure modeling, the phrase “baryonification mechanism” has been used in particle cosmology for a distinct asymmetric-dark-matter construction in a theory with local baryon number symmetry $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$7. In that context, a primordial $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$8 asymmetry is redistributed by sphalerons among Standard Model and dark-sector fermions while conserving total baryon number, and the final visible asymmetry is written as

$$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } k\to 0,$$9

with $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } z\to \infty.$$0 and $$S(k,z,\boldsymbol{\theta}) \to 1 \quad \text{as } z\to \infty.$$1 in the preferred scenario. This usage is conceptually unrelated to the baryon correction model for matter clustering, even though the terminology overlaps (Perez et al., 2013).

In present cosmological usage, however, baryonification denotes the post-processing mechanism that translates gravity-only structure formation into an effective baryon-modified matter field through halo-based mass redistribution. Its significance lies in providing a controllable interface between expensive hydrodynamical calibration and the scale, speed, and parameter coverage demanded by modern cosmological inference.