Weak gravitational lensing is a powerful cosmological probe, with non--Gaussian features potentially containing the majority of the information. We examine constraints on the parameter triplet $(Omega_m,w,sigma_8)$ from non-Gaussian features of the w
eak lensing convergence field, including a set of moments (up to $4^{rm th}$ order) and Minkowski functionals, using publicly available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of ray--tracing N-body simulations spanning 91 points in $(Omega_m,w,sigma_8)$ parameter space, replicating the galaxy sky positions, redshifts and shape noise in the CFHTLenS catalogs. We then build an emulator that interpolates the simulated descriptors as a function of $(Omega_m,w,sigma_8)$, and use it to compute the likelihood function and parameter constraints. We employ a principal component analysis to reduce dimensionality and to help stabilize the constraints with respect to the number of bins used to construct each statistic. Using the full set of statistics, we find $Sigma_8equivsigma_8(Omega_m/0.27)^{0.55}=0.75pm0.04$ (68% C.L.), in agreement with previous values. We find that constraints on the $(Omega_m,sigma_8)$ doublet from the Minkowski functionals suffer a strong bias. However, high-order moments break the $(Omega_m,sigma_8)$ degeneracy and provide a tight constraint on these parameters with no apparent bias. The main contribution comes from quartic moments of derivatives.
Lensing peaks have been proposed as a useful statistic, containing cosmological information from non-Gaussianities that is inaccessible from traditional two-point statistics such as the power spectrum or two-point correlation functions. Here we exami
ne constraints on cosmological parameters from weak lensing peak counts, using the publicly available data from the 154 deg$^2$ CFHTLenS survey. We utilize a new suite of ray-tracing N-body simulations on a grid of 91 cosmological models, covering broad ranges of the three parameters $Omega_m$, $sigma_8$, and $w$, and replicating the Galaxy sky positions, redshifts, and shape noise in the CFHTLenS observations. We then build an emulator that interpolates the power spectrum and the peak counts to an accuracy of $leq 5%$, and compute the likelihood in the three-dimensional parameter space ($Omega_m$, $sigma_8$, $w$) from both observables. We find that constraints from peak counts are comparable to those from the power spectrum, and somewhat tighter when different smoothing scales are combined. Neither observable can constrain $w$ without external data. When the power spectrum and peak counts are combined, the area of the error banana in the ($Omega_m$, $sigma_8$) plane reduces by a factor of $approx2$, compared to using the power spectrum alone. For a flat $Lambda$ cold dark matter model, combining both statistics, we obtain the constraint $sigma_8(Omega_m/0.27)^{0.63}=0.85substack{+0.03 -0.03}$.
Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of ray-tracing sim
ulations with random realizations of spurious shear. This allows us to quantify the errors and biases of the triplet $(Omega_m,w,sigma_8)$ derived from the power spectrum (PS), as well as from three different sets of non-Gaussian statistics of the lensing convergence field: Minkowski functionals (MF), low--order moments (LM), and peak counts (PK). Our main results are: (i) We find an order of magnitude smaller biases from the PS than in previous work. (ii) The PS and LM yield biases much smaller than the morphological statistics (MF, PK). (iii) For strictly Gaussian spurious shear with integrated amplitude as low as its current estimate of $sigma^2_{sys}approx 10^{-7}$, biases from the PS and LM would be unimportant even for a survey with the statistical power of LSST. However, we find that for surveys larger than $approx 100$ deg$^2$, non-Gaussianity in the noise (not included in our analysis) will likely be important and must be quantified to assess the biases. (iv) The morphological statistics (MF,PK) introduce important biases even for Gaussian noise, which must be corrected in large surveys. The biases are in different directions in $(Omega_m,w,sigma_8)$ parameter space, allowing self-calibration by combining multiple statistics. Our results warrant follow-up studies with more extensive lensing simulations and more accurate spurious shear estimates.
We compare the efficiency of moments and Minkowski functionals (MFs) in constraining the subset of cosmological parameters (Omega_m,w,sigma_8) using simulated weak lensing convergence maps. We study an analytic perturbative expansion of the MFs in te
rms of the moments of the convergence field and of its spatial derivatives. We show that this perturbation series breaks down on smoothing scales below 5, while it shows a good degree of convergence on larger scales (15). Most of the cosmological distinguishing power is lost when the maps are smoothed on these larger scales. We also show that, on scales comparable to 1, where the perturbation series does not converge, cosmological constraints obtained from the MFs are approximately 1.5-2 times better than the ones obtained from the first few moments of the convergence distribution --- provided that the latter include spatial information, either from moments of gradients, or by combining multiple smoothing scales. Including either a set of these moments or the MFs can significantly tighten constraints on cosmological parameters, compared to the conventional method of using the power spectrum alone.
We study a model in which supermassive black holes (SMBHs) can grow by the combined action of gas accretion on heavy seeds and mergers of both heavy (m_s^h=10^5 Msol) and light (m_s^l = 10^2 Msol) seeds. The former result from the direct collapse of
gas in T_s^h >1.5x10^4K, H_2-free halos; the latter are the endproduct of a standard H_2-based star formation process. The H_2-free condition is attained by exposing halos to a strong (J_21 > 10^3) Lyman-Werner UV background produced by both accreting BHs and stars, thus establishing a self-regulated growth regime. We find that this condition is met already at z close to 18 in the highly biased regions in which quasars are born. The key parameter allowing the formation of SMBHs by z=6-7 is the fraction of halos that can form heavy seeds: the minimum requirement is that f_heavy>0.001; SMBH as large as 2x10^10 Msol can be obtained when f_heavy approaches unity. Independently of f_heavy, the model produces a high-z stellar bulge-black hole mass relation which is steeper than the local one, implying that SMBHs formed before their bulge was in place. The formation of heavy seeds, allowed by the Lyman-Werner radiative feedback in the quasar-forming environment, is crucial to achieve a fast growth of the SMBH by merger events in the early phases of its evolution, i.e. z>7. The UV photon production is largely dominated by stars in galaxies, i.e. black hole accretion radiation is sub-dominant. Interestingly, we find that the final mass of light BHs and of the SMBH in the quasar is roughly equal by z=6; by the same time only 19% of the initial baryon content has been converted into stars. The SMBH growth is dominated at all epochs z > 7.2 by mergers (exceeding accretion by a factor 2-50); at later times accretion becomes by far the most important growth channel. We finally discuss possible shortcomings of the model.
