Cong Liu

Accurate cosmic shear measurement is the key to fully realize the scientific potential of large scale galaxy surveys. The Fourier_Quad (FQ) shear measurement method has been significantly developed to avoid biases caused by various factors, including the point-spread function (PSF), photon noise, pixelation effect, selection effects, etc. Shear statistics have also been optimized using the PDF-SYM method (symmetrization of the Probability Distribution Function of the shear estimators) to achieve the minimal statistical error, without introducing systematic error. Nevertheless, the iterative nature of the PDF-SYM method makes it computationally expensive for massive datasets. To improve computational efficiency, we introduce the self-weighted shear estimation (SWSE) method, which employs a specific self-weighting scheme to naturally suppress the shape noise as well as to balance the contributions from the bright and faint galaxies. Because SWSE is intrinsically biased, the primary focus of this work is to robustly evaluate whether the field-distortion test (FD test, a way to calibrate the shear bias on real data) can accurately recover and correct these inherent multiplicative and additive biases. Using both simulated and real survey data, we demonstrate that the FD test can successfully calibrate SWSE for galaxy–galaxy lensing measurements, while computational benchmarks show a reduction in shear-estimation time by factors of approximately 40–200 relative to PDF-SYM. After calibration, SWSE achieves statistical precision consistent with that of PDF-SYM within the uncertainties examined in this work. Our results demonstrate the potential of combining the FD test with SWSE as a computationally efficient framework for forthcoming large-scale weak-lensing surveys.

The magnitude gap between the central and satellite galaxies encodes information about the mass accretion history of a dark matter halo and serves as a useful observational probe for the mass distribution in a halo. In this work, we perform the first weak lensing test of the connections between the magnitude gap and the halo profile. We measure the halo profiles of isolated central galaxies (ICGs) selected primarily from the Sloan Digital Sky Survey Main Galaxy Sample. Halo mass and concentration are inferred by fitting stacked lensing profiles in bins of central luminosity, L _c , and the central-satellite magnitude gap, L _gap . We detect dependence on the magnitude gap in both halo properties. The dependence is the strongest in the ICG luminosity range of 10 ^10.3 < L _c [ h ⁻² L _⊙ ] ≤ 10 ^10.7 , where halos with smaller gaps have higher masses and lower concentrations. When 10 ^10.7 < L _c [ h ⁻² L _⊙ ] ≤ 10 ^11.1 , however, no significant gap dependence is detected. In the range of 10 ^9.9 < L _c [ h ⁻² L _⊙ ] ≤ 10 ^10.3 , a disordering of the gap dependence is marginally observable. We compare the observational results with predictions by two light-cone catalogs built from the Illustris TNG300 and the Millennium simulations. The gap dependence in the two mock samples show overall consistency with observations, but neither matches them in all L _c bins to a quantitative level, and the flip in the gap dependence in the lowest luminosity bin is not reproduced in the mocks. We also compare the significance of the gap dependence on halo mass and concentration and find that our measurement prefers the halo-mass dependence over the concentration.

The existing large-scale weak lensing surveys typically reserve the best seeing conditions for a certain optical band to minimize shape measurement errors and maximize the number of usable background galaxies. This is because most popular shear measurement methods contain explicit or implicit thresholds on the galaxy-to-point-spread-function size ratio, below which their shape measurement errors increase abruptly. Using the Dark Energy Camera Legacy Survey data, we have previously demonstrated that the Fourier_Quad method performs very well on poorly resolved galaxy images in general. It is therefore a ready tool for shear measurement with multiband images regardless of their seeing conditions. In this paper, we apply the Fourier_Quad pipeline on the multiband images from the third public data release of the Hyper Suprime-Cam Subaru Strategic Program. We estimate the shear measurement bias using the field distortion test. The results show that the multiplicative biases of g ₁ in all five bands ( g / r / i / z / y ) and g ₂ in the g / i / y bands are consistent with zero within ∼2 σ . Only the g ₂ results in r , z bands show somewhat significant biases ( 1 0 2 m 2 r , z = 2.18 ± 0.69, 3.46 ± 0.62 respectively). As for the additive biases, most of them are different from zero by more than 3 σ ( 1 0 4 c 1 g , r , i , z , y = 1.0 ± 1.0, −3.3 ± 0.9, −5.8 ± 0.7, −4.6 ± 0.6, −27.0 ± 0.8; 1 0 4 c 2 g , r , i , z , y =−3.5 ± 0.8, −2.2 ± 0.6, −2.3 ± 0.4, −0.0 ± 0.5, 1.0 ± 0.9). Using the LOWZ and CMASS galaxies as foreground lenses, we show that the error bar in the galaxy–galaxy lensing measurement can be decreased by factors of around 15% by combining shear catalogs from different bands. This indicates that it is worth taking multiband shear measurements for better shear statistics.

Lensing studies are typically carried out around high density regions, such as groups and clusters, where the lensing signals are significant and indicative of rich density structures. However, a more comprehensive test of the cosmological model should also include the lensing effect in low density regions. In this work, we incorporate the stacked weak lensing signals around the low density positions, alongside galaxy-galaxy lensing and galaxy-galaxy two point correlation function to perform a joint cosmological analysis on σ ₈ . The low density positions are constructed from the DR9 data release of the DESI legacy imaging survey, using galaxies with r-band absolute magnitude cut M<-21.5 and in the redshift range of 0.18σ detection for lensing in the low density positions, which significantly improve the σ ₈ constraint compared to galaxy-galaxy lensing and galaxy-galaxy two point correlation function by 14%. For flat ΛCDM model, we constrain σ ₈ = 0.824 ^+0.015 _-0.015 , which shows a good agreement with the PLANCK result. Additionally, the halo mass uncertainty σ _{lg M} and photometric redshift error σ _z are constrained to be 0.565 ^+0.086 _-0.070 and 0.004 ^+0.004 _-0.003 respectively, which are somewhat different from our expectations due to the significant degeneracy of the two parameters.

Xu & Jing reported a monotonic relationship between the host halo mass M _h and the morphology of massive central galaxies, characterized by the Sérsic index n, at fixed stellar mass, suggesting that morphology could serve as a good secondary proxy for the halo mass. Since their results were derived using the indirect abundance matching method, we further investigate the connection between the halo properties and central galaxy morphology using weak gravitational lensing. We apply galaxy–galaxy lensing to measure the excess surface density around CMASS central galaxies with stellar masses in the range of 11.3 < log M * / M ⊙ < 11.7 , using the Hyper Suprime-Cam shear catalog processed through the Fourier_Quad pipeline. By dividing the sample based on n, we confirm a positive correlation between n and M _h , and observe possible evidence of the positive correlation of n and halo concentration. After accounting for color, we find that neither color nor morphology alone can determine the halo mass, suggesting that a combination of both may serve as a better secondary proxy. In comparison to hydrodynamic simulations, we find that TNG300 produces much weaker correlations between M _h and n. Furthermore, using SIMBA simulations with different feedback modes, we find that jet-mode active galactic nuclei feedback might be related to the relationship between the Sérsic index and halo mass.

We report the first detection of the halo ellipticities of galaxy clusters by applying the halo–shear–shear correlations (HSSCs), without the necessity of using major axis determination. We use the Fourier_Quad shear catalog based on the Hyper Suprime-Cam Survey and the group catalog from the Dark Energy Spectroscopic Instrument Legacy Surveys for the measurement of group/cluster lensing and HSSC. Our analysis includes off-centering effects. We obtain the average projected ellipticity of dark matter halos with mass 13.5 < log ( M G h / M ⊙ ) < 14.5 within a 1.3 virial radius to be 0.4 8 − 0.19 + 0.12 . We divide the sample into two groups based on mass and redshift, and we find that halos with higher mass tend to exhibit increased ellipticity. We also reveal that high-richness halos have larger ellipticities, confirming the physical picture from numerical simulation that high-richness halos have a dynamical youth and more active mass accretion phase.

Tele-correlation refers to the correlation of galaxy shapes with large angular separations (e.g., > 100 degrees). Since there are no astrophysical reasons causing such a correlation on cosmological scales, any detected tele-correlation could disclose systematic effects in shear-shear correlation measurement. If the shear estimators are measured on single exposures, we show that the field distortion (FD) signal associated with the galaxy position on the CCD can be retained and used in tele-correlation to help us directly calibrate the multiplicative and additive biases in shear-shear correlations. We use the DECaLS shear catalog produced by the Fourier_Quad pipeline to demonstrate this idea. To our surprise, we find that significant multiplicative biases can arise (up to more than 10%) due to redshift binning of the galaxies. Correction for this bias leads to about 1σ increase of the best-fit value of S ₈ from 0.760^+0.015 _-0.017 to 0.777^+0.016 _-0.019 in our tomography study.

Reconstruction of the point-spread function (PSF) plays an important role in many areas of astronomy, including photometry, astrometry, galaxy morphology, and shear measurement. The atmospheric and instrumental effects are the two main contributors to the PSF, both of which may exhibit complex spatial features. Current PSF reconstruction schemes typically rely on individual exposures, and their ability to reproduce the complicated features of the PSF distribution is therefore limited by the number of stars. Interestingly, in conventional methods, after stacking the model residuals of the PSF ellipticities and (relative) sizes from a large number of exposures, one can often observe some stable and nontrivial spatial patterns on the entire focal plane, which could be quite detrimental to, e.g., weak-lensing measurements. These PSF residual patterns are caused by instrumental effects, as they consistently appear in different exposures. Taking this as an advantage, we propose a multilayer PSF reconstruction method to remove such PSF residuals, the second and third layers of which make use of all available exposures together. We test our method on the i-band data of the second release of the Hyper Suprime-Cam. Our method successfully eliminates most of the PSF residuals. Using the Fourier_Quad shear measurement method, we further test the performance of the resulting PSF fields on shear recovery using the field distortion effect. The PSF residuals have strong correlations with the shear residuals, and our new multilayer PSF reconstruction method can remove most of such systematic errors related to the PSF, leading to much smaller shear biases.

Weak lensing provides a direct way of mapping the density distribution in the Universe. To reconstruct the density field from the shear catalog, an important step is to build the shear field from the shear catalog, which can be quite nontrivial due to the inhomogeneity of the background galaxy distribution and the shape noise. We propose the PDF-folding method as a statistically optimal way of reconstructing the shear field. It is an extention of the PDF-SYM method, which was previously designed for optimizing the stacked shear signal as well as the shear-shear correlation for the Fourier_Quad shear estimators. PDF-folding does not require smoothing kernels as in traditional methods, therefore it suffers less information loss on small scales and avoids possible biases due to the spatial variation in the shear on the scale of the kernel. We show with analytic reasoning as well as numerical examples that the new method can reach the optimal signal-to-noise ratio on the reconstructed shear map under general observing conditions, i.e., with inhomogeneous background densities or masks. We also show the performance of the new method on real data around foreground galaxy clusters.

Weak lensing provides a direct way of mapping the density distribution in the universe. To reconstruct the density field from the shear catalog, an important step is to build the shear field from the shear catalog, which can be quite nontrivial due to the inhomogeneity of the background galaxy distribution and the shape noise. We propose the PDF-Folding method as a statistically optimal way of reconstructing the shear field. It is an extention of the PDF-SYM method, which is previously designed for optimizing the stacked shear signal as well as the shear-shear correlation for the Fourier\_Quad shear estimators. PDF-Folding does not require smoothing kernels as in traditional methods, therefore it suffers less information loss on small scales, and avoids possible biases due to the spatial variation of shear on the scale of the kernel. We show with analytic reasoning as well as numerical examples that the new method can reach the optimal signal-to-noise ratio on the reconstructed shear map under general observing conditions, i.e., with inhomogeneous background densities or masks. We also show the performance of the new method on real data around foreground galaxy clusters.