Retrieving the 3D matter power spectrum and galaxy biasing parameters from lensing tomography
Patrick Simon · arXiv (Cornell University) · 2012
Aims. With the availability of galaxy distance indicators in weak lensing surveys, lensing tomography can basically be harnessed to constrain the 3D matter power spectrum over a range in redshift and physical scale. Furthermore, by adding 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 2-p oint correlation functions, measured within a confined open ing angle. Both methods are constructed such that they probe deviations of the power spectrum from a fiducial power spectrum. Thereby a di rect comparison of theory and data is achieved, the physical scale and redshift of deviations can in principle be identified. B y devising a new Monte Carlo technique the measurement noise in the correlators is quantified for a fiducial survey, and the performanc e of the inversion techniques is tested. Results. For a relatively deep 200 deg 2 survey (¯ z∼ 0.9) with 30 sources per arcmin −2 , the matter power spectrum can be probed with 3− 6σ significance at comoving scales 1 . k h −1 Mpc. 10 and z. 0.3. For 3 lenses per arcmin −2 , a significant detection (∼ 10σ) of the galaxy-matter power spectrum and galaxy power spectrum is attainable until higher redshifts ( z. 0.8) and over a wider k-range. Within the Bayesian framework, all three power spectra are easily combined to yield constrains for 3D galaxy biasing parameters. Conclusions. A shear tomography analysis of near future weak lensing surveys promises fruitful insights into the effect of baryons on the nonlinear matter power spectrum at z. 0.3 and into galaxy biasing (z. 0.5). However, a proper treatment of anticipated systematics ‐ not included in the mock analysis but discussed here ‐ is likely to reduce the signal-to-noise in the analysis s o that a robust assessment of the 3D matter power spectrum probably asks for a survey area of at least∼ 10 3 deg 2 . For investigating the matter power spectrum at redshift higher than∼ 0.3, an increase in survey area is mandatory.