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Register a new userA new equal-area isolatitudinal grid on a spherical surface
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Authors
Zinovy Malkin
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A new method SREAG (spherical rectangular equal-area grid) is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into latitudinal rings of near-constant width with further splitting each ring into equal-area cells. It is simple in construction and use, and provides more uniform width of the latitudinal rings than other methods of equal-area pixelization of a spherical surface. The new method provides a rectangular grid cells with the latitude- and longitude-oriented boundaries, near-square cells in the equatorial rings, and the closest to uniform width of the latitudinal rings as compared with other equal-area isolatitudinal grids. The binned data is easy to visualize and interpret in terms of the longitude-latitude rectangular coordinate system, natural for astronomy and geodesy. Grids with arbitrary number of rings and, consequently, wide and theoretically unlimited range of cell size can be built by the proposed method. Comparison with other methods used in astronomical research showed the advantages of the new approach in sense of uniformity of the ring width, a wider range of grid resolution, and simplicity of use.
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A new method is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into several latitudinal bands of near-constant span with further division of each band into equal-area cells. It is simple in construction and provides more uniform latitude step be-tween latitudinal bands than other methods of isolatitudinal equal-area tessellation of a spherical surface.
A new method Spherical Rectangular Equal-Area Grid (SREAG) was proposed in Malkin (2019) for splitting spherical surface into equal-area rectangular cells. In this work, some more detailed features of SREAG are presented. The maximum number of rings that can be achieved with SREAG for coding with 32-bit integer is $N_{ring}$=41068, which corresponds to the finest resolution of $sim$16$$. Computational precision of the SREAG is tested. The worst level of precision is $7cdot10^{-12}$ for large $N_{ring}$. Simple expressions were derived to calculate the number of rings for the desired number of cells and for the required resolution.
The main characteristics of a new concept of spherical gaseous detectors, with some details on its operation are first given. The very low energy threshold of such detector has led to investigations of its potential performance for dark matter particle searches, in particular low mass WIMPs : original methods for energy and fiducial volume calibration and background rejection are described and preliminary results obtained with a low radioactivity prototype operated in Laboratoire Souterrain de Modane (Frejus lab) are presented. Typical expected sensitivities in cross section for low mass WIMPs are also shown, and other applications briefly discussed.
The study of particle motion on spherical surfaces is relevant to adsorption on buckyballs and other solid particles. This paper reports results for the binding energy of such dimers, consisting of two light particles (He atoms or hydrogen molecules) constrained to move on a spherical surface. The binding energy reaches a particularly large value when the radius of the sphere is about 3/4 of the particles diameter.
The Spherical gaseous detector (or Spherical Proportional Counter, SPC) is a novel type of par- ticle detector, with a broad range of applications. Its main features include a very low energy threshold independent of the volume (due to its very low capacitance), a good energy resolution, robustness and a single detection readout channel, in its simplest version. Applications range from radon emanation gas monitoring, neutron flux and gamma counting and spectroscopy to dark matter searches, in particular low mass WIMPs and coherent neutrino scattering measure- ment. Laboratories interested in these various applications share expertise within the NEWS (New Experiments With Sphere) network. SEDINE, a low background prototype installed at underground site of Laboratoire Souterrain de Modane is currently being operated and aims at measuring events at very low energy threshold, around 100 eV. We will present the energy cali- bration with 37Ar, the surface background reduction, the measurement of detector background at sub-keV energies, and show anticipated sensitivities for light dark matter search.
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