Component-wise Baryonification (BFC)

• Component-wise Baryonification (BFC) is a framework that splits simulation particles into independent dark matter, gas, and stellar components to emulate baryonic effects.
• It models baryonic feedback, gas thermodynamics, and dark matter back-reaction to predict observables like matter power suppression, kSZ, X-ray, and FRB signals.
• Calibrated against FLAMINGO and TNG simulations and jointly constrained with ACT and eROSITA data, BFC offers a self-consistent tool for precision cosmology.

to=arxiv_search 《凤凰大参考json {"query":"Component-wise Baryonification BFC baryonification (Kovač et al., 10 Jul 2025, Schneider et al., 10 Jul 2025, Torkamani et al., 26 Jan 2026)","max_results":10,"sort_by":"submittedDate","sort_order":"descending"}【อ่านข้อความเต็มjson [{"arxiv_id":"(Torkamani et al., 26 Jan 2026)","title":"Baryonification III: An accurate analytical model for the dispersion measure probability density function of fast radio bursts","authors":["Matthieu Schaller","João M. Zorrilla Matilla","Lucas Lombriser"],"abstract":"We develop a fully analytical framework for predicting the one-point probability distribution function (PDF) of dispersion measures (DM) for fast radio bursts (FRBs) using the baryonification (BFC) model. BFC provides a computationally efficient alternative to expensive hydrodynamical simulations for modelling baryonic effects on cosmological scales. By applying the halo mass function and halo bias, we convolve contributions from individual halos across a range of masses and redshifts to derive the large-scale structure contribution to the DM PDF. We validate our analytical predictions against consistency-check simulations and compare them with the IllustrisTNG hydrodynamical simulation across a range of redshifts up to z=5, demonstrating excellent agreement. We demonstrate that our model produces consistent results when fitting gas profiles and predicting the PDF, and vice versa. We show that the BFC parameters controlling the gas profile, particularly the halo mass scale (Mc), mass-dependent slope (μ), and outer truncation (δ), are the primary drivers of the PDF shape. Additionally, we investigate the validity of the log-normal approximation commonly used for DM distributions, finding that it provides a sufficient description for a few hundred FRBs. Our work provides a self-consistent model that links gas density profiles to integrated DM statistics, enabling future constraints on baryonic feedback processes from FRB observations."},{"arxiv_id":"(Kovač et al., 10 Jul 2025)","title":"Baryonification II: Constraining feedback with X-ray and kinematic Sunyaev-Zel'dovich observations","authors":["Alessandro R. Murk","Martijn M. S. L. Brouwer","João M. Zorrilla Matilla","Lukas Schaller","Lucas Lombriser"],"abstract":"Baryonic feedback alters the matter distribution on small and intermediate scales, posing a challenge for precision cosmology. The new, component-wise baryonification (BFC) approach provides a self-consistent framework to model feedback effects for different observables. In this paper we use this framework to fit kinematic Sunyaev-Zel'dovich (kSZ) observations from the Atacama Cosmology Telescope (ACT) alongside halo X-ray gas fractions from eROSITA, investigating baryonic feedback in a cosmological context. We first show that the kSZ data from ACT is consistent with the gas fractions from eROSITA, both suggesting a feedback model that is stronger than what is assumed in most hydrodynamical simulations. This finding is in contrast to older, pre-eROSITA gas fraction measurements that point towards weaker feedback in tension with the kSZ results. We suspect these discrepancies to be due to selection bias in the pre-eROSITA sample, or differences in halo mass estimation between the two data sets. In a further step, we use the BFC model to predict the baryonic suppression of the matter power spectrum. Based on our combined fit to data from ACT and eROSITA, we find a power spectrum suppression that exceeds the percent-level at modes above k=0.3-0.6 h/Mpc, growing to 2-8 percent at k=1 h/Mpc, and to 20-25 percent at k=5 h/Mpc, consistent with strong-feedback hydrodynamical simulations. Finally, we compare our best-fitting model to the observed gas density and pressure profiles of massive galaxy clusters from the X-COP sample, finding excellent agreement. These results show that BFC provides a self-consistent picture of feedback across mass- and length scales as well as different cosmological observables, thus making it promising for applications to multiwavelength studies to jointly constrain cosmology and baryonic effects."},{"arxiv_id":"(Schneider et al., 10 Jul 2025)","title":"Baryonification: An alternative to hydrodynamical simulations for cosmological studies","authors":["João M. Zorrilla Matilla","Lukas Schaller","Anders C. Bygott","Martijn M. S. L. Brouwer","Alessandro R. Murk","Viraj Pandya","Cora Uhlemann","Lucas Lombriser"],"abstract":"We present an improved baryonification (BFC) model that modifies dark-matter-only N-body simulations to generate particle-level outputs for gas, dark matter, and stars. Unlike previous implementations, our approach first splits each simulation particle into separate dark matter and baryonic components, which are then displaced individually using the BFC technique. By applying the hydrostatic and ideal gas equations, we assign pressure and temperature values to individual gas particles. The model is validated against hydrodynamical simulations from the FLAMINGO and TNG suites (which feature varied feedback prescriptions) showing good agreement at the level of density and pressure profiles across a wide range of halo masses. As a further step, we calibrate the BFC model parameters to gas and stellar mass ratio profiles from the hydrodynamical simulations. Based on these calibrations, we baryonify N-body simulations and compare the resulting total matter power spectrum suppressions to the ones from the same hydrodynamical simulation. Carrying out this test of the BFC method at each redshift individually, we obtain a 2 percent agreement up to k=5 h/Mpc across all tested feedback scenarios. We also define a reduced, 2+1 parameter BFC model that simultaneously accounts for feedback variations (2 parameters) and redshift evolution (1 parameter). The 2+1 parameter model agrees with the hydrodynamical simulations to better than 2.5 percent over the scales and redshifts relevant for cosmological surveys. Finally, we present a map-level comparison between a baryonified N-body simulation and a full hydrodynamical run from the TNG simulation suite. Visual inspection of dark matter, gas, and stellar density fields, along with the integrated pressure map, shows promising agreement. Further work is needed to quantify the accuracy at the level of observables."}] Component-wise Baryonification (BFC) is a baryonification framework that modifies gravity-only or dark-matter-only $N$-body outputs to emulate the effects of gas, stars, and baryonic feedback by treating dark matter, gas, and stars as independent fields at the particle level (Schneider et al., 10 Jul 2025). In its modern form, BFC displaces particles so that the final mass distribution is a physically motivated superposition of dark matter, hot and cold gas, and stellar components, while also providing a self-consistent description of hot-gas thermodynamics that can be mapped to kinematic Sunyaev-Zel'dovich (kSZ), X-ray, and related observables (Kovač et al., 10 Jul 2025). The framework has been developed as an alternative to hydrodynamical simulations for cosmological studies, validated against FLAMINGO and TNG, used to jointly constrain feedback with ACT and eROSITA data, and extended to a fully analytical model for the dispersion-measure probability density function of fast radio bursts (FRBs) (Schneider et al., 10 Jul 2025, Kovač et al., 10 Jul 2025, Torkamani et al., 26 Jan 2026).

1. Concept and defining characteristics

BFC is a post-processing tool that modifies gravity-only $N$-body outputs to emulate the effects of gas, stars, and baryonic feedback, but with a crucial change relative to earlier baryonification schemes: it treats dark matter, gas, and stars as independent fields at the particle level (Schneider et al., 10 Jul 2025). Each original DMO simulation particle is duplicated into a dark-matter particle and a baryonic particle; the two start at the same position but undergo different radial displacements around halo centers, with particle masses renormalized to match the cosmic fractions $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$ and $f_{\rm bar}=\Omega_b/\Omega_m$ (Schneider et al., 10 Jul 2025).

The framework differs from earlier baryonification methods in three key ways. First, it performs component-wise modeling across all matter species: gas and stars are decomposed into physically distinct subcomponents, each with its own mass fraction $f_i(M,z)$ and profile $\rho_i(r|M,z)$, enabling simultaneous predictions for gas- and star-sensitive observables alongside total-matter effects such as matter power suppression (Kovač et al., 10 Jul 2025). Second, it implements self-consistent hot-gas thermodynamics by solving for the total pressure via hydrostatic equilibrium and then partitioning it into thermal and non-thermal components with an explicit model for non-thermal pressure support (Kovač et al., 10 Jul 2025). Third, it provides a unified cosmology–feedback forward model in which the same halo component fractions and profiles generate kSZ and X-ray gas-fraction predictions and the dark-matter response that suppresses the matter power spectrum, enabling joint constraints from multiwavelength data without re-calibration to hydrodynamical simulations (Kovač et al., 10 Jul 2025).

A recurring misconception is to treat BFC as merely a fitted correction to the matter power spectrum. The published formulation is broader: it yields particle-level outputs for three components—DM, gas, and stars—and, for gas particles, additionally assigns a thermal pressure and temperature using hydrostatic equilibrium plus an empirical non-thermal pressure prescription and the ideal-gas law (Schneider et al., 10 Jul 2025). This suggests that BFC is intended as a physically organized field-level construction rather than only a summary transfer function for clustering.

2. Mass decomposition, profiles, and transport map

BFC starts from a DMO halo described by a truncated NFW profile and a two-halo term (Kovač et al., 10 Jul 2025). For a halo with $M_{200{\rm c}}$ and concentration $c_{200}$, $r_{200}\equiv r_{200{\rm c}}$ is the radius enclosing 200 times the critical density (Kovač et al., 10 Jul 2025). The matter content is split into five components: dark matter (${\rm dm}$), hot bound gas ($N$0), cold/inner gas ($N$1), central galaxy stars ($N$2), and satellite galaxy stars ($N$3) (Kovač et al., 10 Jul 2025).

The initial and final cumulative radial mass profiles define the radial displacements that map the initial to final density profiles while enforcing mass conservation,

$N$4

Particles are displaced so that the final density equals the prescribed component sum (Kovač et al., 10 Jul 2025). In the formulation used for the transport map, the initial and final “one-halo + two-halo” forms are

$N$5

for dark matter, and

$N$6

for baryons, where $N$7 and $N$8 (Kovač et al., 10 Jul 2025).

The initial halo profile is a truncated NFW,

$N$9

with $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$0, $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$1, $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$2, $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$3, and truncation parameter $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$4 with $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$5 and $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$6 (Kovač et al., 10 Jul 2025). The normalization $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$7 ensures $f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$8 (Kovač et al., 10 Jul 2025).

The hot bound gas profile is modeled with a smooth core, a mass-dependent interior slope, and an outer steepening or truncation,

$f_{\rm dm}=\Omega_{\rm dm}/\Omega_m$9

with $f_{\rm bar}=\Omega_b/\Omega_m$0, $f_{\rm bar}=\Omega_b/\Omega_m$1, $f_{\rm bar}=\Omega_b/\Omega_m$2, $f_{\rm bar}=\Omega_b/\Omega_m$3, and

$f_{\rm bar}=\Omega_b/\Omega_m$4

The mass dependence $f_{\rm bar}=\Omega_b/\Omega_m$5 captures the relative flattening of gas profiles at lower halo masses where feedback is more efficient (Kovač et al., 10 Jul 2025). In the implementation paper, $f_{\rm bar}=\Omega_b/\Omega_m$6 and $f_{\rm bar}=\Omega_b/\Omega_m$7 are fixed in the hot-gas profile (Schneider et al., 10 Jul 2025).

The cold or inner gas fraction is tied to the central galaxy fraction, $f_{\rm bar}=\Omega_b/\Omega_m$8, and is centrally concentrated; in practice, it is a small fraction of the baryons at group and cluster scales and does not affect kSZ significantly (Kovač et al., 10 Jul 2025). The central galaxy stellar profile is

$f_{\rm bar}=\Omega_b/\Omega_m$9

while satellite stars are assumed to trace a rescaled NFW cumulative mass,

$f_i(M,z)$0

where $f_i(M,z)$1 encodes net contraction or expansion effects (Kovač et al., 10 Jul 2025).

At the particle-assignment stage, the displaced baryonic particle is stochastically assigned to become a gas or a star particle with radius-dependent probabilities

$f_i(M,z)$2

stars are assumed to reside within the virial radius, and baryons not belonging to any halo after displacement are assigned to gas (Schneider et al., 10 Jul 2025). A practical rule preserves bound substructure: if a baryonic particle belongs to a neighboring halo, it is displaced using the dark-matter prescription so baryons and DM in that satellite are moved coherently (Schneider et al., 10 Jul 2025).

3. Thermodynamics and dark-matter response

A distinctive element of BFC is that hot-gas thermodynamics is not imposed by a fixed, simulation-calibrated pressure profile. Instead, the total pressure profile $f_i(M,z)$3 is obtained from hydrostatic equilibrium,

$f_i(M,z)$4

and is then split into thermal and non-thermal contributions through a radial and redshift-dependent non-thermal fraction based on the Shaw et al. model (Kovač et al., 10 Jul 2025). In the observational analysis,

$f_i(M,z)$5

with

$f_i(M,z)$6

$f_i(M,z)$7, and $f_i(M,z)$8 fixed in that paper; the cap $f_i(M,z)$9 prevents $\rho_i(r|M,z)$0 (Kovač et al., 10 Jul 2025). The thermal pressure is then $\rho_i(r|M,z)$1 (Kovač et al., 10 Jul 2025). In the implementation paper, the non-thermal correction is given as

$\rho_i(r|M,z)$2

with $\rho_i(r|M,z)$3, $\rho_i(r|M,z)$4, and $\rho_i(r|M,z)$5, and $\rho_i(r|M,z)$6 where the bracket becomes negative in the outer halo (Schneider et al., 10 Jul 2025).

Given the gas mass density, the electron number density used for kSZ and X-ray applications is

$\rho_i(r|M,z)$7

with hydrogen mass fraction $\rho_i(r|M,z)$8 (Kovač et al., 10 Jul 2025). The electron pressure is

$\rho_i(r|M,z)$9

where $M_{200{\rm c}}$0 is the proton mass and $M_{200{\rm c}}$1 are mean molecular weights for total gas and electrons, respectively (Kovač et al., 10 Jul 2025). In the implementation paper, the ideal-gas temperature is

$M_{200{\rm c}}$2

with $M_{200{\rm c}}$3 (Schneider et al., 10 Jul 2025).

BFC also includes an explicit dark-matter back-reaction model. The empirical mapping is written in terms of $M_{200{\rm c}}$4, with terms in the relation producing contraction in the inner halo from stars and cold gas and expansion from ejected hot gas (Schneider et al., 10 Jul 2025). The calibrated values $M_{200{\rm c}}$5 and $M_{200{\rm c}}$6 are fixed across suites, while $M_{200{\rm c}}$7 depends on simulation resolution, taking the values $M_{200{\rm c}}$8 for FLAMINGO m9, $M_{200{\rm c}}$9 for FLAMINGO m8, and $c_{200}$0 for TNG-300 (Schneider et al., 10 Jul 2025). This component is central to the framework’s claim that the same baryonic redistribution governs both gas-sensitive observables and the suppression of the nonlinear matter power spectrum.

4. Parameterization, calibration, and reduced models

The full BFC parameter set comprises gas parameters $c_{200}$1, $c_{200}$2, $c_{200}$3, and $c_{200}$4, and stellar or cold-gas parameters $c_{200}$5, $c_{200}$6, $c_{200}$7, and $c_{200}$8; back-reaction parameters $c_{200}$9, $r_{200}\equiv r_{200{\rm c}}$0, and $r_{200}\equiv r_{200{\rm c}}$1 are fixed as above (Schneider et al., 10 Jul 2025). The stellar fractions follow a double power-law inspired by abundance matching,

$r_{200}\equiv r_{200{\rm c}}$2

$r_{200}\equiv r_{200{\rm c}}$3

with the cold-gas fraction given by $r_{200}\equiv r_{200{\rm c}}$4, and the hot-gas fraction from cosmic closure, $r_{200}\equiv r_{200{\rm c}}$5 (Kovač et al., 10 Jul 2025). In the implementation paper, $r_{200}\equiv r_{200{\rm c}}$6 and $r_{200}\equiv r_{200{\rm c}}$7 are specified in the stellar-fraction model (Schneider et al., 10 Jul 2025).

Calibration targets in the implementation paper are gas and stellar mass-ratio profiles,

$r_{200}\equiv r_{200{\rm c}}$8

measured from the FLAMINGO runs m8, m9, m9 Jet, m9 $r_{200}\equiv r_{200{\rm c}}$9-8${\rm dm}$0, and from TNG-300 (Schneider et al., 10 Jul 2025). Carrying out the test of the BFC method at each redshift individually, the authors obtain a 2 percent agreement up to ${\rm dm}$1 across all tested feedback scenarios; at ${\rm dm}$2, the full 8-parameter and reduced 2-parameter BFC agree with hydro to ${\rm dm}$3 for ${\rm dm}$4 (Schneider et al., 10 Jul 2025). The reduced “2+1 parameter” BFC model takes ${\rm dm}$5 and ${\rm dm}$6 as free feedback parameters and introduces one redshift-evolution parameter ${\rm dm}$7 through

${\rm dm}$8

with ${\rm dm}$9 approximated constant with redshift (Schneider et al., 10 Jul 2025). The 2+1 parameter model agrees with the hydrodynamical simulations to better than 2.5 percent over the scales and redshifts relevant for cosmological surveys (Schneider et al., 10 Jul 2025).

For survey applications, the implementation paper recommends using the reduced 2-parameter BFC at each redshift with $N$00 and $N$01, while fixing stellar parameters via abundance matching or prior fits to survey stellar mass–halo mass relations (Schneider et al., 10 Jul 2025). For a redshift-spanning fit, the same paper recommends the 2+1 parameter model with $N$02 following the redshift law above and $N$03 constant (Schneider et al., 10 Jul 2025).

5. Mapping to observables and empirical constraints

BFC was designed to map component profiles into observables without changing the underlying physical parameterization. For kSZ, the temperature shift is

$N$04

and, in the ACT stacking analysis used in the observational paper, the gas is assumed to move with the halo bulk velocity and the signal is modeled using the RMS line-of-sight velocity of the sample, so that

$N$05

for $N$06 in the relevant redshift range (Kovač et al., 10 Jul 2025). The optical depth profile is

$N$07

and the ACT modeling pipeline computes $N$08 from $N$09, projects to 2D, convolves with Gaussian beams with FWHM $N$10 at 98 GHz and $N$11 at 150 GHz, applies the compensated aperture-photometry filter $N$12, and then computes $N$13 (Kovač et al., 10 Jul 2025).

For X-ray gas fractions, the quantity within overdensity radius $N$14 is

$N$15

with

$N$16

Feedback modifies $N$17 and the dark-matter response, changing $N$18, and the model predicts the full $N$19–mass relation (Kovač et al., 10 Jul 2025).

The same baryonified fields are used to define matter power-spectrum suppression,

$N$20

where $N$21 and $N$22 (Kovač et al., 10 Jul 2025). By construction, $N$23; the suppression grows with $N$24 as gas is pushed to larger radii and stars concentrate at the center (Kovač et al., 10 Jul 2025).

The main observational constraint to date combines ACT DR5 kSZ stacked profiles following Schaan et al. (2021) with halo X-ray gas fractions from eROSITA, specifically eFEDS $N$25 GAMA (Kovač et al., 10 Jul 2025). The ACT observable is the velocity-reconstruction-weighted stacked kSZ temperature profile at 98 and 150 GHz for BOSS CMASS galaxies, over redshift range $N$26–0.6 with mean $N$27, halo mass range $N$28–$N$29, and mean $N$30 (Kovač et al., 10 Jul 2025). The eROSITA observable is stacked X-ray-inferred hot-gas fractions in groups and clusters over $N$31–$N$32, with the analysis excluding $N$33 due to uncertain mass calibration (Kovač et al., 10 Jul 2025).

A joint fit to ACT kSZ and eROSITA $N$34 is described as excellent, with $N$35 and $N$36; the kSZ-only and $N$37-only fits at the joint best-fit point have PTEs of $N$38 and $N$39, respectively (Kovač et al., 10 Jul 2025). The kSZ data strongly constrain $N$40, while eROSITA $N$41 tightens $N$42 and $N$43; the combined data prefer stronger-than-standard feedback, with flattened inner gas profiles and steeper outskirts (Kovač et al., 10 Jul 2025). Even when left free, the best-fit $N$44 matches independent estimates for CMASS halos, specifically the McCarthy et al. (2024) estimate $N$45, implying $N$46 (Kovač et al., 10 Jul 2025).

Quantitatively, the joint fit predicts a matter power suppression that exceeds the percent level for $N$47–$N$48, reaches 2–8 percent at $N$49, and 20–25 percent at $N$50, closely tracking the strong-feedback FLAMINGO $N$51-8$N$52 model and lying well below the fiducial FLAMINGO m8 run (Kovač et al., 10 Jul 2025). Using the kSZ+eROSITA best-fit parameters, the model reproduces the observed X-COP cluster electron density and pressure profiles, with mean $N$53 at $N$54, within $N$55 across radii $N$56–$N$57, despite not fitting X-COP (Kovač et al., 10 Jul 2025).

6. Extensions, limitations, and current scope

BFC has been extended beyond clustering, X-ray, and SZ applications to a fully analytical framework for predicting the one-point probability distribution function of dispersion measures for FRBs (Torkamani et al., 26 Jan 2026). In that application, the dominant ionized component is the hot circumgalactic or collapsed gas, and the hot-gas profile parameters $N$58, $N$59, and $N$60 are identified as the primary drivers of the PDF shape (Torkamani et al., 26 Jan 2026). The analytical FRB model uses the halo mass function and halo bias to convolve contributions from individual halos across a range of masses and redshifts, includes halo clustering via linear bias and Gaussian averaging, and compares favorably with IllustrisTNG across redshifts up to $N$61 (Torkamani et al., 26 Jan 2026). The paper further finds that the log-normal approximation commonly used for DM distributions provides a sufficient description for a few hundred FRBs, while departures can become important as samples grow larger (Torkamani et al., 26 Jan 2026).

The framework’s limitations are stated explicitly. Small-scale gas physics such as metal-dependent cooling, detailed multiphase structure, cold clumps, and feedback mode switching are not explicitly modeled; the inner gas profile $N$62 is phenomenological and mainly improves small-$N$63 upturns at higher redshift (Schneider et al., 10 Jul 2025). Non-thermal pressure and hydrostatic bias are treated with an empirical correction, and deviations from equilibrium and halo-to-halo scatter are not modeled beyond this (Schneider et al., 10 Jul 2025). Dark-matter back-reaction is calibrated to several suites, but $N$64 shows resolution dependence, and at high redshift the smallest-scale upturn in $N$65 is slightly underpredicted (Schneider et al., 10 Jul 2025). Low-mass halos outside the calibration bins contribute more to $N$66 at higher redshift, so extrapolation can degrade small-scale accuracy (Schneider et al., 10 Jul 2025).

The observational program has also exposed a substantive dataset-level tension. Joint fits to ACT kSZ and pre-eROSITA gas fractions from Lovisari et al. (2015), Gonzalez et al. (2013), and Sun et al. (2009) are acceptable but exhibit clear parameter tension: the X-ray-only fit prefers higher gas fractions at group masses, and combining with kSZ forces extreme parameter values and a very steep downturn below the lowest X-ray mass points (Kovač et al., 10 Jul 2025). The likely sources of tension identified in the paper are selection biases in pre-eROSITA samples, which favor X-ray-bright, gas-rich systems, and hydrostatic mass bias and calibration systematics in total mass estimates (Kovač et al., 10 Jul 2025). By contrast, eROSITA uses stacked profiles of optically selected groups with eROSITA X-rays and produces lower and more representative $N$67 at group masses that align with ACT kSZ and with a strong-feedback scenario (Kovač et al., 10 Jul 2025).

Within those stated assumptions, BFC occupies a specific methodological niche. It is presented as an alternative to hydrodynamical simulations for cosmological studies, with multi-probe readiness for weak lensing, galaxy clustering, X-ray, SZ, and FRB statistics, and with physically interpretable parameters linked to halo-scale gas and stellar content and feedback strength (Schneider et al., 10 Jul 2025, Torkamani et al., 26 Jan 2026). A plausible implication is that its main value lies in carrying baryonic structure, thermodynamics, and dark-matter response through a single forward model across observables and across the mass scales relevant for Stage-IV survey analyses.