The quest for an accurate measurement of cosmic shear

Jun Zhang
2016 National Science Review  
Gravitational lensing refers to the deflection of light of distant sources by the intervening gravity field. This effect is well described in the theory of general relativity, and can be observed by measuring the systematic shape distortions of background galaxy images. Since the physical explanation of lensing is simple, it is commonly regarded as an effective and direct probe of the cosmic structure, including: the distribution of mass density of all forms; the equations of state of different
more » ... state of different energy components; the expansion history of our Universe; the curvature of space-time; etc. Knowledge collected in these areas are crucial for understanding important questions, such as: whether dark matter is cold or warm; is dark energy simply a cosmological constant; what is the amplitude of neutrino mass; is general relativity correct on cosmic scales [1] . The lensing effect universally exists in all directions of the sky. When averaged on cosmic scales, it typically distorts the image shape (in terms of, e.g. the ellipticity change) on the order of a percent, and is therefore called weak lensing. Current efforts in this field focus on measuring the statistical properties of the weak lensing signal (also called cosmic shear) with a large ensemble of galaxy images (e.g. DES, HSC, KIDs, LSST, WFIRST [2]). The ongoing galaxy surveys typically plan to cover over a thousand square degrees of the sky, with several tens of galaxy images per square arcminute. The size of the galaxy sample for weak lensing measurement will be huge. We shall expect a high precision determination of the cosmological parameters purely from weak lensing statistics. This apparently good news immediately poses an important question: given the typical image quality that we can expect from modern CCD cameras of astronomical purposes, is the systematic error in cosmic shear measurement small enough comparing to the unprecedently small statistical error? Indeed, as we will show, this is a difficult problem [3] . The lensed galaxy images are not directly observable. To the least, they have to be convolved with the point spread function (PSF), and recorded on CCD pixels of finite size. In addition, a certain amount of the sky background noise and the Poisson noise should be added to model the observed galaxy images. This process is shown in Fig. 1 , which is produced by a simulation (also see [4]). As required by stage-IV galaxy surveys, a successful cosmic shear measurement should be able to keep the systematic error less than one percent (indeed closer to 0.1 percent) of the shear signal in the presence of the abovementioned effects. This is challenging because these effects could typically cause image distortions larger than that by the lensing effect, especially for faint and small galaxies [5] . Over the last more than two decades, many different algorithms have been proposed to measure cosmic shear. Original galaxy + Lensing effect + PSF effect + Pixellation + Noise Figure 1 . Illustration of how the original galaxy is typically processed to become an observed image. The mainstream idea is to recover the pre-seeing quadrupole moments of the galaxy. Correction for the PSF effect is achieved typically in three ways: (i) by directly estimating the PSF effect using the multipole moments of the galaxy and PSF images; (ii) by decomposing the galaxy and PSF images into eigenfunctions of an orthogonal basis, and studying the relations between the coefficients and the galaxy ellipticities; (iii) by fitting the galaxy image to a parameterized galaxy model convolved with the PSF function. The accuracy of these methods is often subject to the validity of their assumptions on the galaxy/PSF morphology, or approximations regarding, e.g. image details of high spatial frequencies. The presence of noise and finite pixel size can cause additional systematic errors in shear measurement, which are usually not treated explicitly. It is therefore generally difficult to achieve the subpercent accuracy level in practice. Current methods used on the SDSS data and CFHTlens data have been found to have around a few percent systematic errors in numerical tests [6, 7] . As the quest for an accurate shear estimator is active, new ideas for building shear estimators are frequently proposed. For example, Bernstein and C The Author(s)
doi:10.1093/nsr/nww017 fatcat:6ncqmlssvneu5iwky7pcv6fnp4