Tidal alignment and tidal torquing modeling for the cosmic shear three-point correlation function and mass aperture skewness

TL;DR

This work develops a tidal alignment and tidal torquing (TATT) based model for intrinsic alignment contamination of the cosmic shear three-point correlation function (3PCF) and the mass aperture skewness $\langle M_{ap}^3 \rangle$. It connects EFT-based IA bispectra to TATT parameters ($C_1$, $C_2$, $C_{1\delta}$) and includes a velocity-shear extension ($C_t$), with Limber projections to observable convergence statistics. Using DES Year 3 posteriors, they show that higher-order IA terms substantially modify the 3PCF across triangle configurations and that including higher-order IA terms can dampen the two-point signal while boosting the mass aperture skewness, highlighting the value of joint 2PCF+3PCF analyses to break degeneracies and tighten cosmological and IA constraints. The results underscore the importance of incorporating complex IA models for Stage IV surveys and provide an emulator-ready framework for $\langle M_{ap}^3 \rangle$ analyses.

Abstract

We present a model for the intrinsic alignment contamination of the shear three-point correlation function and skewness of the mass aperture statistic using the tidal alignment and tidal torquing (TATT) formalism. We compute the intrinsic alignment bispectra components in terms of the TATT model parameters. We consider two effective field theory approaches in the literature, relate them to the TATT model parameters and an extension to TATT that includes the velocity-shear (VS) parameter. We compare the impact of changing between NLA, TATT, and TATT+VS on the theoretical computation of the 3PCF using the best fit parameters and tomographic redshift distributions from Dark Energy Survey Year 3. We find that the TATT model significantly impacts the skewed triangle configurations of the 3PCF. Additionally, including the higher-order effects from TATT can introduce opposite effects on the two-point function and on the mass aperture skewness, damping the signal of the former while boosting the signal of the latter. We argue that a joint 2PCF+3PCF analysis with the TATT model can help break the degeneracy between its model parameters and provide more robust constraints on both cosmology and intrinsic alignment amplitude parameters. We show that typical values of order unity for the intrinsic alignment parameters introduce differences of around $10\%$ between NLA and TATT predictions.

Figures (9)

• Figure 1: Ratio between the theoretical shear 3PCF signal with intrinsic alignment contamination and the pure cosmic shear signal. Here we show the real part of $\Gamma^0$. The upper panels use our TATT modeling, while the lower panels use NLA modeling. Here we only show bin combinations that include at least one instance of the lowest redshift bin. The alignment and torquing amplitudes are taken from the best fit of the DES Y3 shear analysis. The x and y axes show two of the triangle sides, where we fix the angle between them at $\phi=60\deg$. The color bars in the upper and lower panels are the same. The TATT contamination varies more strongly across different triangle configurations than the NLA prediction.
• Figure 2: Same plot as Fig. \ref{['fig:3pcfTATT']}, but here we show the 3PCF only for the bin combinations that do not include any instance of the lowest redshift bin, thus having a significantly lower IA contamination. We show the real part of $\Gamma^0$. The upper panels use our TATT modeling, while the lower panels use NLA modeling. The alignment and torquing amplitudes are taken from the best fit of the DES Y3 shear analysis. The x and y axes show two of the triangle sides, where we fix the angle between them at $\phi=60\deg$. The color bars in the upper and lower panels are the same.
• Figure 3: Percent difference between the total $\langle\mathcal{M}_{\rm ap}^3\rangle$ signal computed with a TATT and with an NLA intrinsic alignment contamination. We show how the tidal torquing effect described by the $A_2$ parameter and the inclusion of density weighting shift the theoretical prediction of the mass aperture skewness. The left left panel shows the results for bin combination $(1,1,1)$, while the right panel shows the results for bin combination $(1,3,4)$. We fix our filter aperture radius at $\theta=14'$. For different filters, the parameter dependence is similar, but the overall IA contamination is smaller. We see that the difference between NLA and TATT can approch $10\%$ of the total $\langle\mathcal{M}_{\rm ap}^3\rangle$ signal for $A_1=1$, $A_2=-1$, $b_{\text{TA}}=1.0$ in the case of bin combination $(1,3,4)$.
• Figure 4: Percent difference between the total $\langle\mathcal{M}_{\rm ap}^3\rangle$ signal computed with a TATT+VS and with an NLA intrinsic alignment contamination. We show how the velocity shear strength modulated by the $C_t$ parameter shifts the theoretical prediction of the mass aperture skewness. The left left panel shows the results for bin combination $(1,1,1)$, while the right panel shows the results for bin combination $(1,3,4)$. We fix our filter aperture radius at $\theta=14'$. The impact of the a velocity shear term with magnitude $C_t=4C_1$ is that of a shift of around $5\%-8\%$ on the total $\langle\mathcal{M}_{\rm ap}^3\rangle$.
• Figure 5: Individual contributions of the perturbative expansion terms to the total $\langle\mathcal{M}_{\rm ap}^3\rangle$. The red line is the sum of the first order terms, which are proportional to $C_1$, $C_1^2$ or $C_1^3$, depending on how many shape fields are included. The green line sums the terms proportional to $C_2$, $C_1C_2$, and $C_1^2C_2$. The purple line includes terms that are proportional to $C_{1\delta}$, $C_1C_{1\delta}$, and $C_1^2C_{1\delta}$. Finally, the light blue line includes terms proportional to $C_t$ and its combinations with powers of $C_1$, which are multiplied by -1 for ease of visualization. The black line indicates the total intrinsic alignment $\langle\mathcal{M}_{\rm ap}^3\rangle$ signal. The left panel shows the results for bin combination $(1,1,1)$, while the right panel shows the results for bin combination $(1,3,4)$.