Mitigating Nonlinear Systematics in Weak Lensing Surveys II: Stability and Diagnostics with Intrinsic Alignment

Abstract

The Bernardeau-Nishimichi-Taruya (BNT) transform provides a powerful framework for analysing tomographic cosmic shear data by improving the localization of shear correlations in physical scale. It operates by performing a linear combination of the shear data vector in $\ell$-space, yielding a transformed vector that is better localized in both redshift and $k$-space. BNT is particularly useful for estimating cosmological parameters while minimizing the impact of poorly understood nonlinear physics, without discarding large amounts of information as is typically done with simple scale cuts. In our previous work, we showed that BNT outperforms traditional weak-lensing analyses; however, that study did not include intrinsic alignments (IA). In the present work, we assess the robustness of our BNT-based $k$-cut framework in the presence of realistic IA models. We consider two cases: (i) when the assumed IA model used in sampling is close to, but not identical to, the true one, and (ii) when the assumed IA model is significantly biased compared to the true one. In the first case, the $k$-cut framework yields precise and unbiased $S_8$ constraints even with limited knowledge of large-scale modes. Using Euclid-like mock data and a stringent $k$-cut of $k \le 0.1\;{\rm Mpc^{-1}}$ for all tomographic bins, we found that BNT can constrain $S_8$ with a precision better than 2\% while non-BNT has lost all constraining power. In the second case, the BNT transform serves as a powerful diagnostic tool, revealing internal inconsistencies in $k$-space and redshift-space both exceeding 5$σ$ when the functional form of the sampling and fiducial IA models differ fundamentally.

Figures (9)

• Figure 1: The BNT transform matrix $p^a_i$ calculated with our fiducial cosmology and redshift distribution.
• Figure 2: Panel 1 of 4: BNT Lensing projection weight $\hat{W}_\gamma^2(\chi)/\chi^2$ for the shear-shear term. The original BNT projection kernel. Panel 2 of 4: BNT Lensing projection weight $\hat{W}_{\gamma}(\chi)\hat{W}_{I}(\chi)/\chi^2$ for the shear-shape term with $W_{I}(\chi) = C_1(\chi)W_{N}(\chi)$ under the NLA model with $A_\mathrm{TA} = 1.71$. Panel 3 of 4: BNT Lensing projection weight $\hat{W}_{I}^2(\chi)/\chi^2$ for the shape-shape term with $W_{I}(\chi) = C_1(\chi)W_{N}(\chi)$ under the NLA model with $A_\mathrm{TA} = 1.71$. Panel 4 of 4: The total projection weight $W^2_\mathrm{eff}(\chi) = \hat{W}_\gamma^2(\chi) + 2\hat{W}_{\gamma}(\chi)\hat{W}_{I}(\chi) + \hat{W}_{I}^2(\chi)$ for the shear and shape included total $C_\ell$.
• Figure 3: Ratio of the data vector with $k_{\rm cut}$ to the full data vector (defined in Eq. \ref{['Rfrak_def']}) for the noBNT case $\mathfrak{R}^{(i,j)}(\ell;k_{\rm cuts},\Pi^0)$ (upper-right triangle) and the BNT case $\hat{\mathfrak{R}}^{(i,j)}(\ell;k_{\rm cuts},\Pi^0)$ (lower-left triangle). Each panel shows the ratio for the combination of tomographic bins indicated by $(i,j)$ (for the noBNT case) and $(a,b)$ (for the BNT case). For each tomographic bin, the curves are used to define which cut in $\ell$ corresponds to the constraint that modes $k>k_{\rm high}$ and $k<k_{\rm low}$ should not bias the data vector at a level exceeding $\mathcal{T}_\mathrm{FD}$ for $\ell_{\rm low}^{{(i,j)}}<\ell<\ell_{\rm high}^{{(i,j)}}$ for noBNT (resp. $\hat{\ell}_{\rm low}^{{(a,b)}} < \ell<\hat{\ell}_{\rm high}^{{(a,b)}}$ for BNT). All plots are given for $k_\mathrm{cuts} = (0.1\;{\rm Mpc^{-1}},1.0\;{\rm Mpc^{-1}})$, and the horizontal bright band indicates the fractional threshold $\mathcal{T}_\mathrm{FD} = \pm 0.1$. For each tomographic bin combination, the cut in $\ell$ is shown as the boundary of the cyan and green regions.
• Figure 4: Constraints in the $(\Omega_m,S_8)$ plane for the noBNT (left panel) and BNT (right panel). The thin solid lines indicate the values of the fiducial cosmology. The power spectrum of all models during the sampling process is calculated using the HMcode16-version of HMcode, while the fiducial is calculated using the AxionHMcodeAxionHMcode. The fiducial also included a Samuroff2021HydroIA-fit of TATT model from the IllustrisTNG galaxies. Four posterior contours are represented: the Black solid line corresponds to the case where no $k_{\rm cut}$ and no $\mathcal{T}_\mathrm{FD}$ are applied. The Lime Green, Dark Red and Cyan contours correspond to $k_{\rm cut}=1.0, 0.33, \mathrm{and\ } 0.1\;{\rm Mpc^{-1}}$ respectively, and fixed $\mathcal{T}_\mathrm{FD}=0.02$. Note that the Cyan contours for noBNT and $k_{\rm cut}=0.1\;{\rm Mpc^{-1}}$ exceeds the plot boundary.
• Figure 5: Same to the Figure \ref{['fig:kcut_TATT_OmS8']}, but showing the constraints of $A_\mathrm{TA}$ and $A_\mathrm{TT}$ instead of $\Omega_m$ and $S_8$.