HEALPix (sometimes written as Healpix), an acronym for Hierarchical Equal Area isoLatitude Pixelisation of a 2-sphere, refers to either an algorithm for pixelisation of the 2-sphere or to the associated class of map projections.The pixelisation algorithm was devised in 1997 by Krzysztof M. Górski at the Theoretical Astrophysics Center in Copenhagen, Denmark, and first published as a preprint in 1998.
The HEALPix projection is a general class of spherical projections, sharing several key properties, which map the 2-sphere to the Euclidean plane.Any of these can be followed by partitioning (pixelising) the resulting region of the 2-plane. In particular, when one of these projections (the H=4, K=3 HEALPix projection) is followed by a pixelisation of the 2-plane, the result is generally known as the HEALPix pixelisation, which is widely used in physical cosmology for maps of the cosmic microwave background. This pixelisation can be thought of as mapping the sphere to twelve square facets (diamonds) on the plane followed by the binary division of these facets into pixels, though it can be derived without using the projection. The associated software package HEALPix implements the algorithm. The HEALPix projection (as a general class of spherical projections) is represented by the keyword HPX in the FITS standard for writing astronomical data files. It was approved as part of the official FITS World Coordinate System (WCS) by the IAU FITS Working Group on April 26, 2006.
The spherical projection combines a cylindrical equal area projection, the Lambert cylindrical equal-area projection, for the equatorial regions of the sphere and a pseudocylindrical equal area projection, an interrupted Collignon projection, for the polar regions.
As the name indicates, at a given level in the hierarchy the pixels are of equal area (which is done by bisecting the square in the case of the H=4, K=3 projection) and their centers lie on a discrete number of circles of latitude, with equal spacing on each circle. The scheme has a number of mathematical properties which make it efficient for certain computations, e.g. spherical harmonic transforms. In the case of the H=4, K=3 projection, the pixels are squares in the plane (which can be inversely projected back to quadrilaterals with non-geodesic sides on the 2-sphere) and every vertex joins four pixels, with the exception of eight vertices which each join only three pixels.
The pixelisation related to the H=4, K=3 projection has become widely used in cosmology for storing and manipulating maps of the cosmic microwave background.
An alternative hierarchical grid is the Hierarchical Triangular Mesh (HTM).The pixels at a given level in the hierarchy are of similar but not identical size. The scheme is good at representing complex shapes because the boundaries are all segments of circles of the sphere. Another alternative hierarchical grid is the Quadrilateralized Spherical Cube.
The 12 "base resolution pixels" of H=4, K=3 HEALPix projection may be thought of as the facets of a rhombic dodecahedron.
The H=6 HEALPix has similarities to another alternative grid based on the icosahedron.
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10−36 seconds after the conjectured Big Bang singularity to some time between 10−33 and 10−32 seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 9 billion years old.
The cosmic microwave background, in Big Bang cosmology, is electromagnetic radiation as a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space. It is an important source of data on the early universe because it is the oldest electromagnetic radiation in the universe, dating to the epoch of recombination. With a traditional optical telescope, the space between stars and galaxies is completely dark. However, a sufficiently sensitive radio telescope shows a faint background noise, or glow, almost isotropic, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1964 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s, and earned the discoverers the 1978 Nobel Prize in Physics.
In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle which ranges from 0° at the Equator to 90° at the poles. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the geodetic latitude as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six auxiliary latitudes which are used in special applications.
In cartography, a map projection is a way to flatten a globe's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. Every distinct map projection distorts in a distinct way, by definition. The study of map projections is the characterization of these distortions. There is no limit to the number of possible map projections. Projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. However, "map projection" refers specifically to a cartographic projection.
The shape of the universe, in physical cosmology, is the local and global geometry of the universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as of a continuous object. The spatial curvature is related to general relativity, which describes how spacetime is curved and bent by mass and energy, while the spatial topology cannot be determined from its curvature; locally indistinguishable spaces with different topologies exist mathematically.
Flexible Image Transport System (FITS) is an open standard defining a digital file format useful for storage, transmission and processing of data: formatted as multi-dimensional arrays, or tables. FITS is the most commonly used digital file format in astronomy. The FITS standard was designed specifically for astronomical data, and includes provisions such as describing photometric and spatial calibration information, together with image origin metadata.
In astronomy, a bulge is a tightly packed group of stars within a larger formation. The term almost exclusively refers to the central group of stars found in most spiral galaxies. Bulges were historically thought to be elliptical galaxies that happened to have a disk of stars around them, but high-resolution images using the Hubble Space Telescope have revealed that many bulges lie at the heart of a spiral galaxy. It is now thought that there are at least two types of bulges: bulges that are like ellipticals and bulges that are like spiral galaxies.
Strongly interacting massive particles (SIMPs) are hypothetical particles that interact strongly between themselves [looks like they scatter off each other - observation of colliding galaxies in the Abell 3827 cluster, where it seemed that dark matter lagged behind the ordinary matter] and weakly with ordinary matter, but could form the inferred dark matter despite this. However, this finding has since been discounted based on further observations and modelling of the cluster.
In astronomy and observational cosmology, The BOOMERanG experiment was an experiment which measured the cosmic microwave background radiation of a part of the sky during three sub-orbital (high-altitude) balloon flights. It was the first experiment to make large, high-fidelity images of the CMB temperature anisotropies, and is best known for the discovery in 2000 that the geometry of the universe is close to flat, with similar results from the competing MAXIMA experiment.
A gnomonic map projection displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints. This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane. No distortion occurs at the tangent point, but distortion increases rapidly away from it. Less than half of the sphere can be projected onto a finite map. Consequently, a rectilinear photographic lens, which is based on the gnomonic principle, cannot image more than 180 degrees.
The Very Small Array (VSA) was a 14-element interferometric radio telescope operating between 26 and 36 GHz that is used to study the cosmic microwave background radiation. It was a collaboration between the University of Cambridge, University of Manchester and the Instituto de Astrofisica de Canarias (Tenerife), and was located at the Observatorio del Teide on Tenerife. The array was built at the Mullard Radio Astronomy Observatory by the Cavendish Astrophysics Group and Jodrell Bank Observatory, and was funded by PPARC. The design was strongly based on the Cosmic Anisotropy Telescope.
In cartography, a Tissot's indicatrix is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.
In astronomy, spinning dust is a mechanism proposed to explain anomalous microwave emission from the Milky Way. The emission could arise from the electric dipole of very rapidly spinning (10–60 GHz) extremely small (nanometer) dust grains, most likely polycyclic aromatic hydrocarbons. The anomalous emission was first discovered as a by-product of Cosmic Microwave Background observations which make very sensitive measurements of the microwave sky which have to identify and remove contamination from the galaxy.
Galaxy mergers can occur when two galaxies collide. They are the most violent type of galaxy interaction. The gravitational interactions between galaxies and the friction between the gas and dust have major effects on the galaxies involved. The exact effects of such mergers depend on a wide variety of parameters such as collision angles, speeds, and relative size/composition, and are currently an extremely active area of research. Galaxy mergers are important because the merger rate is a fundamental measurement of galaxy evolution. The merger rate also provides astronomers with clues about how galaxies bulked up over time.
An inhomogeneous cosmology is a physical cosmological theory which, unlike the currently widely accepted cosmological concordance model, assumes that inhomogeneities in the distribution of matter across the universe affect local gravitational forces enough to skew our view of the Universe. When the universe began, matter was distributed homogeneously, but over billions of years, galaxies, clusters of galaxies, and superclusters have coalesced, and must, according to Einstein's theory of general relativity, warp the space-time around them. While the concordance model acknowledges this fact, it assumes that such inhomogeneities are not sufficient to affect large-scale averages of gravity in our observations. When two separate studies claimed in 1998-1999 that high redshift supernovae were further away than our calculations showed they should be, it was suggested that the expansion of the universe is accelerating, and dark energy, a repulsive energy inherent in space, was proposed to explain the acceleration. While still unexplained in nature and origin, dark energy is often claimed to comprise almost 70% of the Universe's energy density. More up to date studies have called into doubt the statistical significance of these claims, and it has been concluded that the bulk flow of the local Universe has been misrepresented as dark energy in studies of supernovae.
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from supernovae measurements, which showed that the universe does not expand at a constant rate; rather, the expansion of the universe is accelerating. Understanding the evolution of the universe requires knowledge of the starting conditions and what it consists of. Prior to these observations, the only forms of matter-energy known to exist were ordinary matter, dark matter, and radiation. Measurements of the cosmic microwave background suggest the universe began in a hot Big Bang, from which general relativity explains its evolution and the subsequent large scale motion. Without introducing a new form of energy, there was no way to explain how an accelerating universe could be measured. Since the 1990s, dark energy has been the most accepted premise to account for the accelerated expansion. As of 2020, there are active areas of cosmology research aimed at understanding the fundamental nature of dark energy: is it a feature of measurement errors, or do modifications to general relativity need to be made?
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's laws to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics.
Astropy is a collection of software packages written in the Python programming language and designed for use in astronomy. The software is a single, free, core package for astronomical utilities due to the increasingly widespread usage of Python by astronomers, and to foster interoperability between various extant Python astronomy packages. Astropy is included in several large Python distributions; it is part of package managers for Linux and macOS, the Anaconda Python Distribution, Enthought Canopy and Ureka.
In cosmology, intensity mapping is an observational technique for surveying the large-scale structure of the universe by using the integrated radio emission from unresolved gas clouds.