A 1% accurate method to include baryonic effects in galaxy-galaxy lensing models

TL;DR

This work introduces a practical method to include baryonic effects in galaxy–matter cross-power spectra by correcting the gravity-only cross-spectrum with the square root of the matter suppression, $P_{\rm gm, hydro}(k) = P_{\rm gm, dmo}(k)\sqrt{S_{mm}(k)}$, where $S_{mm}(k) = P_{mm, hydro}(k)/P_{mm, dmo}(k)$. It combines a nonlinear, hybrid Lagrangian galaxy bias model with the Baryon Correction Model (BCM) via the baccoemu emulator to achieve sub-percent accuracy on scales $k\lesssim 5\,h\mathrm{Mpc}^{-1}$ for matter and $k\lesssim 0.7\,h\mathrm{Mpc}^{-1}$ for galaxy spectra, validated against FLAMINGO simulations across multiple baryonic scenarios, redshifts, and tracer selections. The Bayesian analyses show that ignoring baryons in either the galaxy–matter cross-spectrum or the matter spectrum biases galaxy bias and cosmological parameters, whereas incorporating the $\sqrt{S_{mm}}$ correction yields unbiased posteriors consistent with reference (DMO) values, with remaining degeneracies mitigated by physically motivated priors on BCM parameters. The method promises to enhance the analysis of Stage-IV surveys by enabling efficient, accurate, and scalable incorporation of baryonic physics into joint clustering and lensing in 3x2pt-like studies.

Abstract

Galaxy clustering and galaxy-galaxy lensing are two of the main observational probes in Stage-IV large-scale structure surveys. Unfortunately, the complicated relationship between galaxies and matter limits the exploitation of this data. Galaxy bias models -- such as the hybrid Lagrangian bias expansion -- allow describing galaxy clustering down to scales as small as $k = 0.7h$/Mpc. However, the galaxy-matter cross-power spectra are already affected by baryons on these scales, directly impacting the modelling of galaxy-galaxy lensing. We propose to extend models of the galaxy-matter cross-power spectrum $P_{\rm gm}(k)$ (currently only accounting for dark matter) by including a baryonic correction inferred from the matter component ($S_{\rm mm}(k)$), so that $P_{\rm gm, full \, physics} (k) = \sqrt{S_{\rm mm}} P_{\rm gm, gravity \, only}$. We use the FLAMINGO simulations to measure the effect of baryons on the galaxy-matter cross-power spectrum and to assess the performance of our model. We perform a Bayesian analysis of synthetic data, implementing a model based on BACCO's hybrid Lagrangian bias expansion (for the nonlinear galaxy bias) and Baryon Correction Model. Ignoring baryons in the galaxy-matter cross-power spectrum leads to a biased inference of the galaxy bias, while ignoring baryons in both the galaxy-matter and matter-matter power spectra leads to a biased inference of both the galaxy bias and cosmological parameters. In contrast, our method is 1% accurate compared to all physics variations in FLAMINGO and on all scales described by hybrid perturbative models ($k < 0.7h$/Mpc). Moreover, our model leads to inferred bias and cosmological parameters compatible within 1$σ$ with their reference values. We anticipate that our method will be a promising candidate for analysing forthcoming Stage-IV survey data.

Figures (12)

• Figure 1: Open markers: the baryon suppression $S_{\rm mm}(k) = P_{\rm mm, hydro}(k) / P_{\rm mm, dmo}(k)$ as measured for the 9 hydrodynamical simulations considered. Lines: the predictions obtained with the baccoemu emulator for the best fitting BCM parameters for each baryon case (obtained by fitting the measured suppressions from the simulations with baccoemu). On the left we show redshift $z=0$ and on the right $z=1$. Lower panels show the ratio between the $S_{\rm mm}$ predictions obtained with our best fitting parameters and the $S_{\rm mm}$ from the simulations. Different baryonic feedback prescriptions are shown in order of increasing strength of the suppression at $k=1~h ~ \mathrm{Mpc}^{-1}$.
• Figure 2: Example of HODs of galaxies in one of the baryonic models ("Jet, $f_{\rm gas}-4\sigma$") at $z=0$. On the left, galaxies are selected in order of decreasing Stellar Mass; on the right, in order of decreasing Star Formation Rate. Different colors correspond to different number densities, namely $n=\{10^{-2}, 10^{-3}, 10^{-4}\} \, h^3 \, \mathrm{Mpc}^{-3}$.
• Figure 3: Comparison of the suppression $S_{\rm hm}(k) = P_{\rm hm, hydro} / P_{\rm hm, dmo}$ for central haloes in three hydrodynamical simulations (different rows) and the respective DMO at $z=0$. Haloes are split into mass bins (different line colours). First column: the ratio between the halo-matter cross-power spectrum from the hydrodynamic and the DMO simulations; in this case, haloes are matched between the hydrodynamical and DMO simulations. From the second column and to the right: the ratio of the cross-power spectrum of haloes and matter in the hydrodynamical simulation and the cross-power spectrum of the same haloes (from the hydrodynamical simulation) and matter from the DMO simulation; the matter component of the hydrodynamical simulation is either the total matter (second column), only the dark matter (third column), only the gas (fourth column), or only the stellar component (last column). In all cases, the suppression $\sqrt{S_{\rm mm}(k)}$ inferred from the matter fields (from the hydrodynamical versus DMO simulations) is shown for reference as a black dashed line. Haloes of mass $10^{13.5}$ to $10^{14} ~ h^{-1} \mathrm{M}_{\odot}$ (which contribute the most to the total matter power spectrum on the scales of interest here) exhibit suppressions well approximated by $\sqrt{S_{\rm mm}}$, while lower and higher mass haloes exhibit (respectively) stronger and weaker suppressions, due to the different behaviour of their gas and star components and the differences in the consequent DM adiabatic relaxation.
• Figure 4: The ratio $\mathcal{R}(k) = P_{\rm gm, hydro}(k) / [P_{\rm gm, dmo}(k) \sqrt{S_{\rm mm}(k)}]$ obtained with spectra directly measured in the simulations considered. The three columns correspond to samples with number density $n = \{10^{-2}, 10^{-3}, 10^{-4} \} ~ h^3 ~\mathrm{Mpc}^{-3}$. The different rows correspond to SM-selected and SFR-selected galaxies at $z=0$ (upper two rows) and $z=1$ (lower two rows). The vertical black line marks $k=0.7~h ~ \mathrm{Mpc}^{-1}$, i.e. the limiting scale of the hybrid Lagrangian bias expansion model. In all cases, the approximation proposed in this work is 1% accurate on the range of scales allowed by the hybrid galaxy model.
• Figure 5: Coevolutions relations from fits of $P_{\rm gg}$ and $P_{\rm gm}$, where $P_{\rm gm}$ is computed by cross-correlating the galaxy distribution of the hydrodynamical simulations with the matter field of the corresponding DMO simulation. All baryon models at $z=\{0, 1\}$, all galaxy selection criteria (SM and SFR), and number densities $n_{\rm g} = \{10^{-2}, 10^{-3}\} ~ h^3 ~ \mathrm{Mpc}^{-3}$ are reported. The cross-correlation with the matter from the DMO simulations allows us to find the reference values of these bias parameters. Black solid lines and the grey shaded areas represent the coevolution relations and allowed parameter space from ZennaroEtal2022.