The impact of baryons on weak lensing statistics as a function of halo mass and radius

Abstract

Upcoming weak lensing (WL) surveys such as those by {\it Euclid}, LSST, and {\it Roman} require percent-level control over systematic effects. A common approach to mitigating baryonic effects uses semi-analytic baryon correction models (BCMs) that modify halo profiles in dark matter-only (DMO) simulations, calibrated to statistics from hydrodynamic simulations. We investigate the limits of this approach by progressively replacing larger regions around halos of decreasing mass in DMO simulations with their hydrodynamical counterparts. We compare multiple statistics -- the matter ($P(k)$) and weak-lensing ($C_\ell$) power spectra, peak counts, minima, one-point PDFs, and Minkowski functionals -- from "Replace" fields against hydrodynamical and DMO simulations. We find that replacing all halos with $M\geq10^{12}\,h^{-1}\,{\rm M}_\odot$ out to $r\leq5R_{200}$ recovers $\sim 90\%$ of the baryonic suppression in $P(k)$ and $C_\ell$ with the remaining $\sim 10\%$ originating from lower-mass halos or material farther outside of DM halos. Each statistic has distinct sensitivities to baryons: $P(k)$ and $C_\ell$ are sensitive to a broad range of masses and radii, whereas WL peaks are primarily affected by the cores of massive halos. We show that BCMs applied to massive halos and calibrated to match hydrodynamical $P(k)$ make two cancelling "mistakes": they underpredict core masses and compensate by overpredicting baryonic impacts at larger radii, thereby explaining previously reported failures of peak statistics in these models. We provide a framework for diagnosing critical mass/radius regions in baryonic modeling for a range of statistics for next-generation BCMs.

Figures (19)

• Figure 1: Grid showing all Replace models constructed in this work. Each tile represents a specific mass-bin radial-shell configuration, with color indicating the mass fraction of the Replacement region within the TNG300-1 box at $z=0$. The upper-left corner shows discrete (single-bin) models, while the lower-right corner shows fully cumulative models. Note that the $\alpha\in[0, 0.5] \cup \log (M/{\rm M}_\odot)\in[13.5, \infty]$ model is repeated in the figure for clarity, as this model is both discrete (it represents a bin) and cumulative (it represents the smallest possible Replacement). Off-diagonal tiles represent mixed configurations (e.g., cumulative in mass, discrete in radius). The most extensive Replace—halos with $M_{min}>10^{12} h^{-1} {\rm M}_\odot$ out to $r\leq 5R_{200}$—occupy approximately 50% of the total mass and are in the lower-right corner.
• Figure 2: Decomposing the matter power spectrum suppression by mass and radius factor at $z=0.03$. Each column corresponds to a radius factor $\alpha$ (indicated at top), with curves colored by mass thresholds or bins. Top row: Ratio of Replace to DMO power spectra $P_{\rm R}(k)/P_{\rm D}(k)$ for cumulative models. The black curve shows the target Hydro-to-DMO ratio $P_{\rm H}(k)/P_{\rm D}(k)$. Second row: Cumulative response fractions $F_P(M_{\min}, \alpha_{\rm max})$ from Eq. \ref{['eq:cum_resp_func']}. Values of $F=0$ are consistent with DMO power spectra, while $F=1$ corresponds to matching the hydrodynamical TNG exactly. Values outside $[0,1]$ indicate replacement artifacts. Third row: Discrete bin responses $\Delta F_P^{\rm a,i}$ from Eq. \ref{['eq:disc_resp_func']}, showing contributions from individual mass-radius shells. Bottom row: Non-additivity metric $\epsilon(M_{\min}, \alpha; k)$ from Eq. \ref{['eq:non_additivity']}, measuring the degree to which discrete bins sum linearly to cumulative models. Values near $\epsilon = 0$ indicate linear additivity while deviations indicate non-linear coupling between mass-radius bins.
• Figure 3: Weighted mean power spectrum responses at $z=0.03$, summarizing Fig. \ref{['fig:suppression_and_fraction']} into single numbers per model. The structure follows the same as Fig. \ref{['fig:models']}. Rows correspond to $M$ bins, columns to radial shells, with the top left corner showing the discrete models, and the bottom right showing the cumulative models. To achieve $\sim 90\%$ fidelity ($\langle F_P \rangle \gtrsim 0.9$, bottom-right cell), one must correctly model the field level of all halos above $10^{12}\,h^{-1}{\rm M}_\odot$ out to at least $5R_{200}$. The brightest cell for the discrete models (dark red, $\langle \Delta F_P^{\rm a,i} \rangle \sim 0.23$) happens to also be a cumulative model representing the minimal possible replacement at $(M_{\rm min},\alpha_{\rm max} ) = ([10^{13.5}, \infty]\,h^{-1}{\rm M}_\odot, [0, 0.5R_{200}))$, confirming that massive halo cores dominate the baryonic response on $P(k)$. The outermost shell ($\alpha\in[3, 5)$) exhibits $F\sim 0.04$–$0.08$ for all mass-bins, likely due to the two-halo term and extended gas redistribution contributions.
• Figure 4: Redshift evolution of weighted mean power spectrum responses $\langle F_P \rangle(z)$ following Eq. \ref{['eq:weighted_mean_response']} from $z=2.56$ to $z=0.03$ for cumulative (top panels) and discrete (bottom panels) models. Baryonic effects strengthen toward low redshift for all models with $M\geq 12.5\,h^{-1}{\rm M}_\odot$. At low redshift ($z \lesssim 0.5$), massive halos ($M \geq 10^{13.5}\,h^{-1}{\rm M}_\odot$) dominate the response, whereas at high redshift ($z \gtrsim 0.5$), low mass halos ($M \sim 10^{12}$–$10^{12.5}\,h^{-1}{\rm M}_\odot$) become the dominant source of baryonic effects (bottom row left panel). Outer shells ($\alpha > 0.5$) exhibit weaker redshift evolution, with $\langle \Delta F_P^{\rm bin} \rangle$ remaining roughly constant at $\sim 0.03$–$0.08$ across all $z$.
• Figure 5: Baryonic response of the weak lensing angular power spectrum at galaxy source redshift $z_s = 1.03$. The format of the panels follows the identical structure as Fig. \ref{['fig:suppression_and_fraction']}