KiDS+GAMA: Cosmology constraints from a joint analysis of cosmic shear, galaxy-galaxy lensing and angular clustering

TL;DR

This work develops and applies a fast, self-consistent joint analysis of three large-scale structure probes—KiDS-450 cosmic shear, KiDS-based galaxy–matter lensing around GAMA galaxies, and GAMA angular clustering—to constrain flat ΛCDM cosmology. By estimating power spectra through real-space correlation integrals and modeling cosmic shear, galaxy–matter, and galaxy clustering within a single framework, the authors achieve a 26% improvement over cosmic shear alone in constraining S_8 and robustly constrain nuisance parameters such as intrinsic alignments and baryonic feedback. The analysis validates the estimators on simulations, accounts for cross-probe covariance and partial sky overlap, and explores redshift-distribution uncertainties, finding results consistent with Planck and with KiDS-450 cosmic shear analyses while highlighting the value of multi-probe self-calibration. These methods demonstrate the practical feasibility and cosmological payoff of combining large-scale structure probes with coherent treatment of systematics, paving the way for more comprehensive joint analyses in future surveys.

Abstract

We present cosmological parameter constraints from a joint analysis of three cosmological probes: the tomographic cosmic shear signal in $\sim$450 deg$^2$ of data from the Kilo Degree Survey (KiDS), the galaxy-matter cross-correlation signal of galaxies from the Galaxies And Mass Assembly (GAMA) survey determined with KiDS weak lensing, and the angular correlation function of the same GAMA galaxies. We use fast power spectrum estimators that are based on simple integrals over the real-space correlation functions, and show that they are practically unbiased over relevant angular frequency ranges. We test our full pipeline on numerical simulations that are tailored to KiDS and retrieve the input cosmology. By fitting different combinations of power spectra, we demonstrate that the three probes are internally consistent. For all probes combined, we obtain $S_8\equiv σ_8 \sqrt{Ω_{\rm m}/0.3}=0.800_{-0.027}^{+0.029}$, consistent with Planck and the fiducial KiDS-450 cosmic shear correlation function results. Marginalising over wide priors on the mean of the tomographic redshift distributions yields consistent results for $S_8$ with an increase of $28\%$ in the error. The combination of probes results in a $26\%$ reduction in uncertainties of $S_8$ over using the cosmic shear power spectra alone. The main gain from these additional probes comes through their constraining power on nuisance parameters, such as the galaxy intrinsic alignment amplitude or potential shifts in the redshift distributions, which are up to a factor of two better constrained compared to using cosmic shear alone, demonstrating the value of large-scale structure probe combination.

Figures (22)

• Figure 1: Normalised redshift distribution of the four tomographic source bins of KiDS (solid lines), used to measure the weak gravitational lensing signal, and the normalised redshift distribution of the two spectroscopic samples of GAMA galaxies (histograms), that serve as the foreground sample in the galaxy-galaxy lensing analysis and that are used to determine the angular correlation function. For plotting purposes, the redshift distribution of GAMA galaxies has been multiplied by a factor 0.5. The shaded regions indicate the photometric redshift ($z_{\rm B}$) selection of the tomographic source bins.
• Figure 2: Cosmic shear power spectra for KiDS-450, derived with our power spectrum estimator that integrates the shear correlation functions in the range $0.06<\theta<120$ arcmin. The numbers in each panel indicate which shape (S) samples are correlated, with the numbers defined in the legend of Fig. \ref{['plot_zdistr']}. The panels on the left show the E-modes, and the ones on the right the B-modes. Error bars have been computed analytically. The B-modes have been multiplied with $\ell$ instead of $\ell^2$ for improved visibility of the error bars. Solid lines correspond to the best-fitting model, for our combined fit to $P^{\rm E}$, $P^{\rm gm}$ and $P^{\rm gg}$. There is one $\ell$ bin whose B-mode deviates from zero by more than 3$\sigma$, the highest $\ell$ of the S2--S4 cross-correlation; the corresponding E-mode is high as well. We have verified that excluding this bin from the analysis does not change our results.
• Figure 3: Tangential shear and cross shear around GAMA galaxies measured with KiDS sources in tomographic bins, as indicated in the panels. The cross shear measurements have been multiplied with a factor $(\theta/100)^{0.5}$ to ensure that the error bars are visible over the plotted angular range. Open squares show negative points of $\gamma_{\rm t}$ with unaltered error bars. The lensing signal measured around random points has been subtracted, which is consistent with zero on the scales of interest for all but the third tomographic source bin, where it is small but positive on scales $>$20 arcmin. Furthermore, the signal has been corrected for the contamination of source galaxies that are physically associated with the lenses. The errors are derived from jackknifing over 2.5$\times$3 degree non-overlapping patches. They are only used to assess on which scales the signal is consistent with not being affected by systematics; when we fit models to our power spectra we use analytical errors throughout.
• Figure 4: Galaxy-matter power spectrum (top) and galaxy-cross shear power spectrum (bottom) around GAMA galaxies in two lens redshift bins, measured with KiDS sources using four tomographic source bins. The numbers in each panel indicate the foreground (F) sample - shape (S) sample combination, as defined in Fig. \ref{['plot_zdistr']}. The errors are computed analytically and correspond to the 68% confidence interval. $P^{\rm g\times}$ has been multiplied with $\ell$ instead of $\ell^2$ for improved visibility of the error bars. Solid lines correspond to the best-fitting model, for our combined fit to $P^{\rm E}$, $P^{\rm gm}$ and $P^{\rm gg}$. The $P^{\rm g\times}$ in the bottom rows serves as a systematic test, and it is consistent with zero.
• Figure 5: Angular correlation function of the two foreground galaxy samples from GAMA. The inset in each panel shows the signal on large scales with a linear vertical axis. The errors are derived from jackknifing over 2.5$\times$3 degree non-overlapping patches and serve for illustration. When we fit models to our power spectra we used analytical errors throughout.