Two-dimensional turbulence on a sphere

Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.

Developing a unified pipeline for large-scale structure data analysis with angular power spectra – III. Implementing the multi-tracer technique to constrain neutrino masses

In this paper, we apply the multi-tracer technique to harmonic-space (i.e. angular) power spectra with a likelihood-based approach. This goes beyond the usual Fisher matrix formalism hitherto implemented in forecasts with angular statistics, opening up a window for future developments and direct application to available data sets. We also release a fully-operational modified version of the publicly available code CosmoSIS, where we consistently include all the add-ons presented in the previous papers of this series. The result is a modular cosmological parameter estimation suite for angular power spectra of galaxy number counts, allowing for single and multiple tracers, and including density fluctuations, redshift-space distortions, and weak lensing magnification. We demonstrate the improvement on parameter constraints enabled by the use of multiple tracers on a multi-tracing analysis of luminous red galaxies and emission line galaxies. We obtain an enhancement of $44\%$ on the 2σ upper bound on the sum of neutrino masses.

Dark Energy Survey Year 1 Results: Wide-field mass maps via forward fitting in harmonic space

ABSTRACT We present new wide-field weak lensing mass maps for the Year 1 Dark Energy Survey (DES) data, generated via a forward fitting approach. This method of producing maps does not impose any prior constraints on the mass distribution to be reconstructed. The technique is found to improve the map reconstruction on the edges of the field compared to the conventional Kaiser–Squires method, which applies a direct inversion on the data; our approach is in good agreement with the previous direct approach in the central regions of the footprint. The mapping technique is assessed and verified with tests on simulations; together with the Kaiser–Squires method, the technique is then applied to data from the DES Year 1 data and the differences between the two methods are compared. We also produce the first DES measurements of the convergence Minkowski functionals and compare them to those measured in simulations.

Probing the azimuthal environment of galaxies around clusters

Galaxy clusters are connected at their peripheries to the large-scale structures by cosmic filaments that funnel accreting material. These filamentary structures are studied to investigate both environment-driven galaxy evolution and structure formation and evolution. In the present work, we probe in a statistical manner the azimuthal distribution of galaxies around clusters as a function of the cluster-centric distance, cluster richness, and star-forming or passive galaxy activity. We performed a harmonic decomposition in large photometric galaxy catalogue around 6400 SDSS clusters with masses M > 1014 solar masses in the redshift range of 0.1 < z < 0.3. The same analysis was performed on the mock galaxy catalogue from the light cone of a Magneticum hydrodynamical simulation. We used the multipole analysis to quantify asymmetries in the 2D galaxy distribution. In the inner cluster regions at R < 2R500, we confirm that the galaxy distribution traces an ellipsoidal shape, which is more pronounced for richest clusters. In the outskirts of the clusters (R = [2 − 8]R500), filamentary patterns are detected in harmonic space with a mean angular scale mmean = 4.2 ± 0.1. Massive clusters seem to have a larger number of connected filaments than lower-mass clusters. We also find that passive galaxies appear to trace the filamentary structures around clusters better. This is the case even if the contribution of star-forming galaxies tends to increase with the cluster-centric distance, suggesting a gradient of galaxy activity in filaments around clusters.