Dark Energy Survey Year 6 Results: Magnification modeling and its impact on galaxy clustering and galaxy-galaxy lensing cosmology

TL;DR

This work quantifies gravitational lensing magnification in DES Year 6 analyses and demonstrates that accurate modeling of the magnification bias is essential to avoid biased cosmological inferences from galaxy clustering and galaxy–galaxy lensing. The authors estimate the magnification coefficient $C_{\rm sample}$ for the MagLim++ lens sample using Balrog synthetic source injections, flux-perturbation methods, and data-driven flux perturbations, finding consistent results across methods and obtaining Balrog-based priors for the fiducial analysis. They show that neglecting magnification produces significant shifts in $S_8$ and $\Omega_m$, while marginalizing over magnification with informative priors recovers unbiased constraints; cross-bin clustering helps further mitigate biases. The conclusions emphasize that magnification modeling is vital for DES Y6 and will become increasingly important for upcoming surveys, where deeper data will enhance both the need for corrections and the potential to extract magnification information to refine models.

Abstract

Gravitational lensing magnification alters the observed spatial distribution of galaxies and must be accounted for to prevent biases in cosmological probes of the large-scale structure. We investigate its effects on the Dark Energy Survey Year 6 galaxy clustering and galaxy-galaxy lensing analyses using the fiducial lens (position tracer) sample MagLim++. Magnification bias is parameterized by a coefficient that describes the response of the number of selected objects per unlensed area element to a change in the lensing convergence. We quantify this coefficient using the Balrog synthetic source injection catalog to account for the complexity of the selection function, and compare these results with simplified estimates. The resulting values of the magnification coefficients for each redshift bin are [3.16 $\pm$ 0.08, 2.76 $\pm$ 0.21, 4.09 $\pm$ 0.15, 4.42 $\pm$ 0.16, 4.90 $\pm$ 0.29, 4.83 $\pm$ 0.25]. Relative to Year 3, this analysis provides more precise and accurate magnification bias estimates through a larger Balrog area and reweighting to better match the data properties. The cosmological results are robust when tested against various magnification parameter prior choices and also when adding cross-clustering between lens redshift bins. Neglecting magnification, however, introduces significant systematic shifts: relative to the fiducial analysis with Gaussian priors centered on the Balrog-derived estimates, we observe shifts of 1.37$σ$ in $S_8$ and -0.84$σ$ in $Ω_m$ (with cosmic shear included: -0.61$σ$ in $S_8$ and -0.71$σ$ in $Ω_m$), in agreement with findings from simulated data, demonstrating that magnification must be modeled to avoid biases. Freeing the magnification bias in lens bin 2 leads to unphysical negative values, further justifying its exclusion from the fiducial Year 6 analysis.

Figures (20)

• Figure 1: Distributions of measured flux ratio of the same MagLim++ objects in the magnified and regular Balrog runs in the griz bands. The distributions are centered at 1.02 with minimal tails, in agreement with the expected input 2% magnification.
• Figure 2: Magnification coefficient estimates for the six redshift bins of the MagLim++ lens sample, computed using the three methods described in Sec. \ref{['sec:mag_coeff']}. The blue points represent our fiducial estimates from Balrog simulations (Sec. \ref{['sec:mag_coeff_balrog']}), while the green and yellow points correspond to approximate flux-only estimates derived from Balrog and real data, respectively (Sec. \ref{['sec:mag_coeff_flux-only']}). If the Balrog sample were perfectly representative of real data, the flux-only estimates would be identical; therefore, their difference serves as a measure of systematic error in the blue Balrog estimates. We present both statistical errors and the total uncertainty---obtained by adding statistical and systematic errors in quadrature---for the Balrog estimates. The solid line represents zero magnification bias from sample selection alone, while the dashed line accounts for zero magnification bias when also considering changes in the area element. The blue Balrog measurements will be used as the default choice in the DES Y6 3$\times$2pt analysis.
• Figure 3: The impact of magnification on model predictions for galaxy-galaxy lensing ($\gamma_t(\theta)$; top panel) and galaxy clustering ($\omega(\theta)$; bottom panel) across all redshift bin combinations. In each panel, the black line represents the model prediction with lens magnification included, with the surrounding shaded region indicating the corresponding statistical uncertainty. The blue dotted line isolates the lens magnification contribution, derived using fiducial magnification coefficient values estimated from Balrog. The lower sub-panels show the fractional change in the signal relative to its statistical uncertainty, highlighting the contribution of magnification to the overall signal-to-noise ratio. Gray shaded regions indicate the Y6 scale cuts. For galaxy-galaxy lensing, magnification primarily affects combinations involving high-redshift lenses, while most of the signal-to-noise arises from the three lowest-redshift lens bins where magnification biases are minimal. Its impact on clustering auto-correlations is small, and becomes relevant only for cross-correlations between widely separated redshift bins, which are excluded in the fiducial DES Y6 3$\times$2pt analysis.
• Figure 4: Recovered 2D constraints on $S_8$ and $\Omega_m$ derived from a simulated, noiseless data vector, following the DES Y6 modeling strategy. The results explore five different priors on the magnification bias, $C_{\rm{sample}}$, as outlined in Sec. \ref{['sec:exp_mag_cosmology']}: (i) applying Gaussian priors centered on the true values with widths given by the Balrog-derived uncertainties ("Gaussian prior"), the fiducial choice in the Y6 cosmological analyses; (ii) fixing $C_{\rm{sample}}$ to its true values ("Fixed mag"); (iii) fixing $C_{\rm{sample}}$ to 2, thereby removing magnification from the model ("No mag"); (iv) using Gaussian priors shifted by $3\sigma_{C_{\rm{sample}},\rm{tot}}$ ("Gaussian prior shifted"); and (v) wide uniform priors ("Flat prior"). The figure shows the outcomes for both a 2$\times$2pt analysis (Fig. \ref{['fig:contours']}a), and a 2$\times$2pt analysis including the additional cross-clustering signal ("w/ x-corr", Fig. \ref{['fig:contours']}b) that further constrains the magnification effect. The dashed lines mark the true input values. Beyond prior volume effects, the results show that marginalizing over magnification with Gaussian priors recovers unbiased constraints on $S_8$ and $\Omega_m$, while omitting magnification or shifting the Gaussian priors introduces biases; adopting flat priors slightly increases uncertainties without significantly shifting the cosmological parameters, and including cross-clustering slightly improves cosmological constraints.
• Figure 5: Recovered 1D constraints on $S_8$ and $\Omega_m$ from a simulated, noiseless data vector, following the DES Y6 modeling strategy. The results consider the five different priors on the magnification bias, $C_{\rm{sample}}$, outlined in Sec. \ref{['sec:exp_mag_cosmology']}, and are presented for three analysis configurations: the fiducial 2$\times$2pt analysis, the 2$\times$2pt analysis including the additional cross-clustering signal (“w/ x-corr”), which further constrains magnification (Fig. \ref{['fig:contours_panel']}a), and the full 3$\times$2pt analysis (Fig. \ref{['fig:contours_panel']}b). The solid horizontal lines show the 68% marginalized posterior intervals, with the filled circles marking the corresponding posterior means, and the open circles indicating the MAP values. The dashed black vertical lines mark the true input values. The dashed blue vertical lines indicate the posterior means of the fiducial analysis with Gaussian priors, and the shaded regions denote the corresponding $1\sigma$ uncertainty. Note that, because of noise, the MAP estimates may deviate from the true input values (see Appendix \ref{['app:map']}).