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Register a new userChasing the peak: optimal statistics for weak shear analyses
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Weak gravitational lensing analyses are fundamentally limited by the intrinsic, non-Gaussian distribution of galaxy shapes. We explore alternative statistics for samples of ellipticity measurements that are unbiased, efficient, and robust. We take the non-linear mapping of gravitational shear and the effect of noise into account. We then discuss how the distribution of individual galaxy shapes in the observed field of view can be modeled by fitting Fourier modes to the shear pattern directly. We simulated samples of galaxy ellipticities, using both theoretical distributions and real data for ellipticities and noise. We determined the possible bias $Delta e$, the efficiency $eta$ and the robustness of the least absolute deviations, the biweight, and the convex hull peeling estimators, compared to the canonical weighted mean. Using these statistics for regression, we have shown the applicability of direct Fourier mode fitting. These estimators can be unbiased in the absence of noise, and decrease noise bias by more than $sim 30%$. The convex hull peeling estimator distribution is centered around the underlying shear, and its bias least affected by noise. The least absolute deviations estimator to be the most efficient estimator in almost all cases, except in the Gaussian case, where its still competitive ($0.83<eta <5.1$) and therefore robust. These results hold when fitting Fourier modes, where amplitudes of variation in ellipticity are determined to the order of $10^{-3}$. The peak of the ellipticity distribution is a direct tracer of the underlying shear and unaffected by noise, and we have shown that estimators that are sensitive to a central cusp perform more efficiently, potentially reducing uncertainties by more than $50%$ and significantly decreasing noise bias.
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Upcoming weak-lensing surveys have the potential to become leading cosmological probes provided all systematic effects are under control. Recently, the ejection of gas due to feedback energy from active galactic nuclei (AGN) has been identified as major source of uncertainty, challenging the success of future weak-lensing probes in terms of cosmology. In this paper we investigate the effects of baryons on the number of weak-lensing peaks in the convergence field. Our analysis is based on full-sky convergence maps constructed via light-cones from $N$-body simulations, and we rely on the baryonic correction model of Schneider et al. (2019) to model the baryonic effects on the density field. As a result we find that the baryonic effects strongly depend on the Gaussian smoothing applied to the convergence map. For a DES-like survey setup, a smoothing of $theta_kgtrsim8$ arcmin is sufficient to keep the baryon signal below the expected statistical error. Smaller smoothing scales lead to a significant suppression of high peaks (with signal-to-noise above 2), while lower peaks are not affected. The situation is more severe for a Euclid-like setup, where a smoothing of $theta_kgtrsim16$ arcmin is required to keep the baryonic suppression signal below the statistical error. Smaller smoothing scales require a full modelling of baryonic effects since both low and high peaks are strongly affected by baryonic feedback.
The statistics of shear peaks have been shown to provide valuable cosmological information beyond the power spectrum, and will be an important constraint of models of cosmology with the large survey areas provided by forthcoming astronomical surveys. Surveys include masked areas due to bright stars, bad pixels etc, which must be accounted for in producing constraints on cosmology from shear maps. We advocate a forward-modeling approach, where the impact of masking (and other survey artifacts) are accounted for in the theoretical prediction of cosmological parameters, rather than removed from survey data. We use masks based on the Deep Lens Survey, and explore the impact of up to 37% of the survey area being masked on LSST and DES-scale surveys. By reconstructing maps of aperture mass, the masking effect is smoothed out, resulting in up to 14% smaller statistical uncertainties compared to simply reducing the survey area by the masked area. We show that, even in the presence of large survey masks, the bias in cosmological parameter estimation produced in the forward-modeling process is ~1%, dominated by bias caused by limited simulation volume. We also explore how this potential bias scales with survey area and find that small survey areas are more significantly impacted by the differences in cosmological structure in the data and simulated volumes, due to cosmic variance.
We study the statistics of peaks in a weak lensing reconstructed mass map of the first 450 square degrees of the Kilo Degree Survey. The map is computed with aperture masses directly applied to the shear field with an NFW-like compensated filter. We compare the peak statistics in the observations with that of simulations for various cosmologies to constrain the cosmological parameter $S_8 = sigma_8 sqrt{Omega_{rm m}/0.3}$, which probes the ($Omega_{rm m}, sigma_8$) plane perpendicularly to its main degeneracy. We estimate $S_8=0.750pm0.059$, using peaks in the signal-to-noise range $0 leq {rm S/N} leq 4$, and accounting for various systematics, such as multiplicative shear bias, mean redshift bias, baryon feedback, intrinsic alignment, and shear-position coupling. These constraints are $sim25%$ tighter than the constraints from the high significance peaks alone ($3 leq {rm S/N} leq 4$) which typically trace single-massive halos. This demonstrates the gain of information from low-S/N peaks. However we find that including ${rm S/N} < 0$ peaks does not add further information. Our results are in good agreement with the tomographic shear two-point correlation function measurement in KiDS-450. Combining shear peaks with non-tomographic measurements of the shear two-point correlation functions yields a $sim20%$ improvement in the uncertainty on $S_8$ compared to the shear two-point correlation functions alone, highlighting the great potential of peaks as a cosmological probe.
NonGaussian cosmic shear statistics based on weak-lensing aperture mass ($M_{rm ap}$) maps can outperform the classical shear two-point correlation function ($gamma$-2PCF) in terms of cosmological constraining power. However, reaching the full potential of these new estimators requires accurate modeling of the physics of baryons as the extra nonGaussian information mostly resides at small scales. We present one such modeling based on the Magneticum hydrodynamical simulation for the KiDS-450 and DES-Y1 surveys and a Euclid-like survey. We compute the bias due to baryons on the lensing PDF and the distribution of peaks and voids in $M_{rm ap}$ maps and propagate it to the cosmological forecasts on the structure growth parameter $S_8$, the matter density parameter $Omega_{rm m}$, and the dark energy equation of state $w_0$ using the SLICS and cosmo-SLICS sets of dark-matter-only simulations. We report a negative bias of a few percent on $S_8$ and $Omega_{rm m}$ and also measure a positive bias of the same level on $w_0$ when including a tomographic decomposition. These biases reach $sim 5$% when combining $M_{rm ap}$ statistics with the $gamma$-2PCF as these estimators show similar dependency on the AGN feedback. We verify that these biases constitute a less than $1sigma$ shift on the probed cosmological parameters for current cosmic shear surveys. However, baryons need to be accounted for at the percentage level for future Stage IV surveys and we propose to include the uncertainty on the AGN feedback amplitude by marginalizing over this parameter using multiple simulations such as those presented in this paper. Finally, we explore the possibility of mitigating the impact of baryons by filtering the $M_{rm ap}$ map but find that this process would require to suppress the small-scale information to a point where the constraints would no longer be competitive.
In this paper, we analyze in detail with numerical simulations how the mask effect can influence the weak lensing peak statistics reconstructed from the shear measurement of background galaxies. It is found that high peak fractions are systematically enhanced due to masks, the larger the masked area, the higher the enhancement. In the case with about $13%$ of the total masked area, the fraction of peaks with SNR $ uge 3$ is $sim 11%$ in comparison with $sim 7%$ of the mask-free case in our considered cosmological model. This can induce a large bias on cosmological studies with weak lensing peak statistics. Even for a survey area of $9hbox{ deg}^2$, the bias in $(Omega_m, sigma_8)$ is already close to $3sigma$. It is noted that most of the affected peaks are close to the masked regions. Therefore excluding peaks in those regions can reduce the bias but at the expense of loosing usable survey areas. Further investigations find that the enhancement of high peaks number can be largely attributed to higher noise led by the fewer number of galaxies usable in the reconstruction. Based on Fan et al. (2010), we develop a model in which we exclude only those large masks with radius larger than $3arcmin. For the remained part, we treat the areas close to and away from the masked regions separately with different noise levels. It is shown that this two-noise-level model can account for the mask effect on peak statistics very well and the cosmological bias is significantly reduced.
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