Retrieving the three-dimensional matter power spectrum and galaxy biasing parameters from lensing tomography

Abstract

Aims. With the availability of galaxy distance indicators in weak lensing surveys, lensing tomography can be harnessed to constrain the three-dimensional (3D) matter power spectrum over a range of redshift and physical scale. By combining galaxy-galaxy lensing and galaxy clustering, this can be extended to probe the 3D galaxy-matter and galaxy-galaxy power spectrum or, alternatively, galaxy biasing parameters. Methods. To achieve this aim, this paper introduces and discusses minimum variance estimators and a more general Bayesian approach to statistically invert a set of noisy tomography two-point correlation functions, measured within a confined opening angle. Both methods are constructed such that they probe deviations of the power spectrum from a fiducial power spectrum, thereby enabling both a direct comparison of theory and data, and in principle the identification of the physical scale and redshift of deviations. By devising a new Monte Carlo technique, we quantify the measurement noise in the correlators for a fiducial survey, and test the performance of the inversion techniques. Results. For a relatively deep 200 deg 2 survey (z ∼ 0.9) with 30 sources per square arcmin, the matter power spectrum can be probed with 3 − 6σ significance on comoving scales 1 k h −1 Mpc 10 and z 0.3. For 3 lenses per square arcmin, a significant detection (∼10σ) of the galaxy-matter power spectrum and galaxy power spectrum is attainable to relatively high redshifts (z 0.8) and over a wider k-range. Within the Bayesian framework, all three power spectra are easily combined to provide constraints on 3D galaxy biasing parameters. Therein, weak priors on the galaxy bias improve constraints on the matter power spectrum. Conclusions. A shear tomography analysis of weak-lensing surveys in the near future promises fruitful insights into both the effect of baryons on the nonlinear matter power spectrum at z 0.3 and galaxy biasing (z 0.5). However, a proper treatment of the anticipated systematics, which are not included in the mock analysis but discussed here, is likely to reduce the signal-to-noise ratio in the analysis such that a robust assessment of the 3D matter power spectrum probably requires a survey area of at least ∼10 3 deg 2 . To investigate the matter power spectrum at redshift higher than ∼0.3, an increase in survey area is mandatory.

Cosmology with cosmic shear observations: a review

“…GGL becomes of particular cosmological interest when complemented with statistical 3 WEAK COSMOLOGICAL LENSING FORMALISM 21 measurements of other matter tracers, for example spatial galaxy correlations (projected or in redshift space), cosmic shear, or galaxy velocity correlations (Guzik et al 2010, Simon 2012. The combination of those observables allows for detailed and quasi-model-independent analyses of the relation between luminous and dark matter, including the measurement of galaxy bias, in particular its linearity, scaledependence, and stochasticity.…”

Cluster mass calibration at high redshift: HST weak lensing analysis of 13 distant galaxy clusters from the South Pole Telescope Sunyaev–Zel'dovich Survey

“…To estimate it we compute 500 random realizations of the cosmic shear field per cluster for our reference cosmology and the colour-selected source redshift distribution as detailed in appendix B of Simon (2012), with the non-linear matter power spectrum estimated following Takahashi et al (2012). 12 We add these cosmic shear field realizations to the measured shear 12 This approach generates Gaussian random shear fields based on the matter power spectrum.…”

Scale dependence of galaxy biasing investigated by weak gravitational lensing: An assessment using semi-analytic galaxies and simulated lensing data

“…galaxybias for a given wave number k: (i) a bias factor b(k) for the relative strength between galaxy and matter clustering; and (ii) a factor r(k) for the galaxy-matter correlation. The second-order biasing functions can be constrained by combining galaxy clustering with cosmic-shear information in lensing surveys (Foreman et al 2016;Cacciato et al 2012;Simon 2012;Pen et al 2003). In applications of these techniques, galaxy biasing is then known to depend on galaxy type, physical scale, and redshift, thus reflecting interesting galaxy physics (Chang et al 2016;Buddendiek et al 2016;Pujol et al 2016;Prat et al 2016;Comparat et al 2013;Simon et al 2013;Jullo et al 2012;Simon et al 2007;Pen et al 2003;Hoekstra et al 2002).…”