The quest for an accurate measurement of cosmic shear

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 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 precisiondeterminationof 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 frommodernCCDcameras 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.


PHYSICS
The quest for an accurate measurement of cosmic shear

Jun Zhang
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 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 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 PERSPECTIVES Armstrong suggest a Bayesian method based on real galaxy morphology distributions [8]; the sFIT method calibrates the shear measurement bias using simulations with a realistic image generation pipeline [9]. It is timely to point out a convenient route in building unbiased shear estimators: through Fourier transformation. It is mainly for the following reasons: (i) linear mappings (e.g. shear) in real space remain linear in Fourier space; (ii) convolutions in real space (e.g. the PSF effect) correspond to multiplications in Fourier space, which is much easier to deal with; (iii) spectral properties of the original source signal and the Poisson noise are distinct, making it straightforward to correct for the bias due to Poisson noise in the Fourier domain; (iv) For images sampled at the Nyquist frequency or higher, multipole moments of the source spectrum defined in Fourier space converge quickly to their right values, without the need for any interpolations of the image in real space. The method of Zhang, Luo, and Foucaud [10] is an example of Fourier-space shear estimator, which indeed enjoys all the above advantages, and performs very well in a recent open test [11]. Several other shear measurement ideas [12,13] are also based in Fourier space. Despite of our partial success in building shear estimators, we caution that there are a number of other related issues need to be solved, including: PSF reconstruction from star images; determination of source boundaries; treatment of bad pixels; etc. Furthermore, it is recently reported that complex photo electronics may introduce a certain level of inhomogeneous or nonlinear pixel response to light, such as the charge-transferinefficiency [14] and the brighter-fatter effect [15], which may affect galaxy shape measurement. It is therefore desirable to further develop current shear estimators, making them available for more general assumptions about astronomical images. This is crucial for fully achieving the scientific potential of the large scale galaxy surveys. The innate immune system can detect the invading microbe components via three major pattern recognition receptors-Toll-like receptors, RIG-I-like receptors and NOD-like receptors as well as a variety of cytoplasmic DNA or RNA sensors. These innate receptors induce a series of intracellular downstream signaling pathways, leading to the efficient innate immune responses to eliminate pathogens (Fig. 1). Meanwhile, a flexible and conditional regulatory network contributes to the fine-tuning of innate immune signaling for the maintenance of immune homeostasis and prevention of immunological disorders. The detailed mechanisms for the initiation and regulation of innate immune signaling are attracting increasing attention in recent years. In this paper, we focus on recent advances in the identification and functional characterization of new activators (in the first two paragraphs) and regu-lators (in the next two paragraphs) of PRR-triggered innate signaling pathways.
First, novel mechanisms of intracellular DNA and RNA sensing in different cell types or in response to different pathogens are recently proposed. It was previously thought that only dsDNA from DNA virus over 40 bp could induce innate antiviral immunity. But a recent study shows that unpaired guanosines flanking short (12-20 bp)