--- title: Baryonification (BFC) Model url: https://www.emergentmind.com/topics/baryonification-bfc-model type: topic --- # Baryonification (BFC) Model Searching arXiv for recent and foundational baryonification/BFC papers to ground the article. arXiv search query: all:baryonification OR all:"baryon correction model" OR all:BCEmu Baryonification, often denoted **BFC** and closely related to the **baryon correction model** (BCM), is a post-processing framework that transforms a gravity-only \(N\)-body realization into a baryon-corrected matter field by displacing matter around halos according to physically motivated prescriptions for gas, stars, and the baryon-induced response of collisionless matter. Its purpose is to reproduce the redistribution of mass caused by gas cooling, star formation, supernova feedback, AGN feedback, gas ejection, and dark-matter back-reaction without rerunning full hydrodynamical simulations. In contemporary large-scale-structure analyses, baryonification is used to model the nonlinear matter power spectrum, bispectrum, weak lensing, galaxy-galaxy lensing, kinematic and thermal Sunyaev–Zel’dovich signals, and, more recently, fast-radio-burst dispersion-measure statistics [2009.14225; 2406.01672; 2507.07892; 2601.18784]. ## 1. Physical definition and modeling objective The central premise of baryonification is that dark-matter-only simulations capture the collisionless gravitational backbone of structure formation, but omit the redistribution of matter caused by baryonic physics. On sufficiently large scales this omission can be subdominant, whereas on nonlinear scales it directly alters halo density profiles and therefore the observables derived from them. The method is therefore not a replacement for gravity-only evolution; it is a physically motivated correction layer applied after the \(N\)-body calculation [2406.01672; 2409.03822]. A standard formulation begins from a dark-matter-only halo plus its environment and replaces that profile by a baryon-corrected decomposition. In the map-level formulation this is written as \[ \rho_{\rm DMO}=\rho_{\rm NFW}+\rho_{\rm 2h}, \qquad \rho_{\rm DMB}=\rho_{\rm CLM}+\rho_{\rm gas}+\rho_{\rm star}+\rho_{\rm 2h}, \] where \(\rho_{\rm CLM}\) denotes collisionless matter after baryonic response, \(\rho_{\rm gas}\) the redistributed gas, \(\rho_{\rm star}\) the stellar component, and \(\rho_{\rm 2h}\) the two-halo contribution [2409.03822]. Other implementations use a more granular partition into dark matter, central galaxy, satellite galaxies, bound gas, ejected gas, and reaccreted gas [2009.14225], or into hot gas, inner/cold gas, central-galaxy stars, and satellite-galaxy stars [2507.07892; 2507.07991]. This construction is designed to preserve the baryon budget while changing the radial distribution of matter. In BACCO, for example, the baryonified field is built so that \[ \text{(stellar mass + bound gas + ejected gas)}=\frac{\Omega_b}{\Omega_m}, \] which makes the method a field-level prescription rather than a pure fitting formula for a single statistic [2011.15018]. ## 2. Halo decomposition and displacement formalism The defining algorithmic operation is a **radial displacement field** that remaps matter from the gravity-only enclosed-mass profile to the target baryonified enclosed-mass profile. In the standard BCM formulation, the gravity-only halo is modeled as an NFW profile, and particles are moved spherically around halo centers so that cumulative mass ordering is preserved [2009.14225]. The model thereby converts a DMO halo into a sum of parametric halo components, each with its own profile and mass fraction. One widely used generation of BCM includes the following ingredients: dark matter, a central galaxy, satellite galaxies, bound halo gas, ejected gas, and late-time reaccreted gas. The bound-gas component is described by a double-power-law profile, the central galaxy by a compact profile with fiducial inner slope \(\alpha_g=2\), ejected gas is set by mass conservation, and reaccreted gas is assigned a Gaussian-like profile. In that formulation, ejected gas is identified as the dominant driver of power-spectrum suppression, while bound gas and dark-matter back-reaction are responsible for the small-scale bispectrum bump seen especially in Illustris TNG-300 and EAGLE [2009.14225]. A later **component-wise BFC** refines the displacement itself by first splitting each simulation particle into separate dark-matter and baryonic components and then displacing the two species independently. The displacement is written as \[ d_{\rm A}(r_{\rm i}|M_{200},c_{200},\theta_{\rm BFC}) = r_{{\rm A},f}(M_{\rm A})-r_{{\rm A},i}(M_{\rm A}), \qquad {\rm A}=\{{\rm dm,bar}\}, \] with cumulative masses \[ M_{{\rm A},i}(r)=\int_0^r ds\, s^2\rho_{{\rm A},i}(s), \qquad M_{{\rm A},f}(r)=\int_0^r ds\, s^2\rho_{{\rm A},f}(s). \] In this formulation, the initial dark-matter and baryon profiles are both constructed from a truncated NFW halo plus a two-halo term, while the final baryonic sector is decomposed into hot gas, inner gas, and stellar components [2507.07892]. The physical profile choices differ across implementations, but recurring patterns are clear. Hot gas is commonly represented by a cored or double-power-law profile with a mass-dependent slope and an outer truncation; central stars are modeled as compact \(r^{-2}\)-type profiles with an exponential cutoff; and collisionless matter undergoes contraction or expansion in response to the rearranged baryonic potential [2011.15018; 2404.06098; 2507.07892]. Some map-level frameworks replace 3D particle displacements by 2D projected-shell displacements, \[ \Delta d(\theta)=M^{-1}_{{\rm DMB},p}\!\left(M_{{\rm DMO},p}(\theta)\right)-\theta, \] to construct full-sky weak-lensing and tSZ maps efficiently [2409.03822]. ## 3. Parameterization and reduced model families Baryonification is not a single parameterization but a family of related models. A recurrent parameter is \(M_c\), although its operational definition depends on the implementation. In BACCO, \(M_c\) is the parameter that sets the gas fraction retained per halo mass and is identified as the main control on baryonic suppression in the power-spectrum ratio \(S(k)\) [2011.15018]. In BCEmu, \(\log_{10}M_c\) is the characteristic mass scale where the gas-profile slope transitions [2404.06098]. In the FRB-dispersion application, \(M_c\), \(\mu\), and \(\delta\) are the primary drivers of the PDF shape [2601.18784]. The 2020 BCM fit to matter power spectrum and bispectrum uses seven free parameters, \[ M_c,\ \eta,\ \beta,\ M_{1,z0,\rm cen},\ \theta_{\rm inn},\ \theta_{\rm out},\ M_{\rm inn}, \] with \(M_c\) and \(\beta\) controlling retained halo gas fractions, \(\eta\) the extent of ejected gas, and \(\{\theta_{\rm inn},M_{\rm inn},\theta_{\rm out}\}\) the shape of the hot-gas profile [2009.14225]. BACCO embeds this baryonic sector in a 15-dimensional emulator space composed of 8 cosmological parameters and 7 baryonic parameters, while emulating \[ S(k)\equiv \frac{P_{\rm bcm}(k)}{P_{\rm GrO}(k)}, \qquad P_{\rm BCM}(k)=S(k)\,P_{\rm GrO}(k), \] rather than the full power spectrum directly [2011.15018]. For weak-lensing and kSZ inference, BCEmu introduces reduced-complexity variants: **BCEmu1**, where only \(\log_{10}M_c\) varies; **BCEmu3**, where \(\log_{10}M_c\), \(\theta_{\rm ej}\), and \(\eta_\delta\) vary; and **BCEmu7**, where all seven baryonification parameters vary [2404.06098]. The paper states that BCEmu7 and BCEmu3 can reproduce simulated power suppression to better than \(1\%\), whereas BCEmu1 is only accurate at the few-percent level and is generally too restrictive [2404.06098]. The component-wise BFC of 2025 organizes its parameter space into an **8-parameter full BFC** and a reduced model. In the full version the free parameters are \(\log M_c\), \(\mu\), \(\delta\), \(\theta_c\), \(\eta\), \(d\eta\), \(N_{\rm star}\), and \(c_{\rm iga}\); in the reduced version only \(\log M_c\) and \(\delta\) remain free; and a later extension adds one redshift-evolution parameter to form a **2+1 parameter** model [2507.07892]. ## 4. Calibration strategies, emulators, and numerical performance A major attraction of baryonification is that it can be calibrated either to hydrodynamical simulations or, in some applications, to observations. The 2020 BCM study calibrated its seven-parameter model jointly to the matter power spectrum and equilateral reduced bispectrum from six hydrodynamical simulations—BAHAMAS standard AGN, BAHAMAS low-AGN, BAHAMAS high-AGN, EAGLE, Illustris, and Illustris TNG-300—and reported typical accuracies of \(1\text{--}2\%\) for the power spectrum and \(3\%\) for the bispectrum over \(k\le 5\,h\,{\rm Mpc}^{-1}\) and \(0\le z\le 2\) [2009.14225]. The same work showed that calibrating only on the power spectrum can leave the bispectrum wrong by as much as \(20\%\), which established higher-order statistics as a nontrivial constraint on the mass-redistribution model [2009.14225]. BACCO converts this idea into a neural-network emulator trained on roughly \(50{,}000\) baryonified power spectra, with smoothing by a Savitzky–Golay filter, PCA compression to 6 principal components, and a feed-forward network with 2 hidden layers of 400 neurons each, ReLU activations, Adam optimization, and mean-squared-error loss [2011.15018]. The reported emulator precision is unbiased at the \(0.1\%\) level, with \(<0.2\%\) precision for \(k\lesssim 1\,h/{\rm Mpc}\), \(\sim 1\%\) up to \(k=5\,h/{\rm Mpc}\), and an overall quoted accuracy of \(1\text{--}2\%\) over \(0.01