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'''[[:en:CMBMexican coldhat spotwavelet]]'''
<nowiki>{{S|matematica}}</nowiki>
[[Image:ColdSpot.jpg|thumb|right|200px|L'area cerchiata è la macchia fredda]]
[[Image:Wavelet - Mex Hat.png|thumb|150px|Mexican hat wavelet]]
In [[matematica]] e in [[analisi numerica]], la '''wavelet cappello messicano'''
La '''macchia fredda nella radiazione cosmica di fondo''' o '''macchia fredda del [[WMAP]]''', è una porzione della [[Sfera celeste|volta celeste]] che, se vista nelle [[microonde]], appare più larga e fredda rispetto alle proprietà medie della [[radiazione cosmica di fondo]] ('''CMB'''). Mediamente, la fluttuazione tipica delle temperature della CMB è nell'ordine di 10<sup>-5</sup>, mentre la macchia fredda è di 70 [[Kelvin|µK]] più fredda della temperatura media della CMB (approssimativamente di 2,7 [[Kelvin|K]]).
:<math>\psi(t) = {2 \over {\sqrt {3\sigma}\pi^{1 \over 4}}} \left( 1 - {t^2 \over \sigma^2} \right) e^{-t^2 \over 2\sigma^2}</math>
è la seconda [[derivata]] [[Costante normalizzante|normalizzata]] negativa di una [[funzione gaussiana]]. È un caso speciale della famiglia delle [[wavelet continue]] ([[wavelet]] usate nelle [[trasformata wavelet continua|wavelet continue trasformate]]), la famiglia delle [[wavelet hermitiane]].
Questa wavelet viene chiamata ''cappello messicano'' in quanto la sua rappresentazione su grafico ricorda un [[sombrero]], tipico cappello messicano. Tecnicamente, il suo nome è '''wavelet Ricker''', usata frequentemente per modellare dati sismici<ref>[http://www.glossary.oilfield.slb.com/Display.cfm?Term=Ricker%20wavelet Glossario Oilfield]</ref>.
Il raggio della macchia è di 5° circa; il centro si trova alle [[Sistema di coordinate galattiche|coordinate galattiche]]: l<sub>''II''</sub> = 207.8°, b<sub>''II''</sub> = −56.3° ([[Coordinate_celesti#Coordinate_equatoriali|equatoriale]]: ''[[Ascensione retta|α]]'': = 03<sup>h</sup>15<sup>m</sup>05<sup>s</sup>, ''[[Declinazione (astronomia)|δ]]'' = −19<sup>d</sup>35<sup>m</sup>02<sup>s</sup>). Questa si trova nell'[[Emisfero australe|emisfero sud]] della [[Sfera celeste|volta celeste]], nella costellazione dell'[[Eridano (costellazione)|Eridano]].
Secondo i modelli teorici generalmente accettati dalla comunità scientifica, le fluttuazioni più larghe della radiazione di fondo avvengono entro una scala angolare di circa 1°; per questo motivo, macchie fredde grandi come queste appaiono alquanto improbabili. Esistono alcune spiegazioni alterniative per questa macchia, quali il '''[[Vuoto (astronomia)|Supervuoto]] di Eridano''' o il '''Grande Vuoto'''. Questa regione sembra essere grande all'incirca 150 [[megaparsec|Mpc]], ovvero 500 milioni di [[anni luce]], ad uno [[spostamento verso il rosso]] di <math>z\simeq 1</math>, con una densità di materia di molto minore rispetto alla densità media allo [[spostamento verso il rosso]]. Un vuoto così grande influisce sulla radiazione di fondo osservata tramite l'[[effetto Sachs-Wolfe]]. Se esistesse un'altra regione di supervuoto comparabile a questa, sarebbe una delle più [[Struttura a grande scala dell'universo|larghe strutture]] dell'universo osservabile.
In [[mathematics]] and [[numerical analysis]], the '''Mexican hat wavelet'''
==Discovery and significance==
:<math>\psi(t) = {2 \over {\sqrt {3\sigma}\pi^{1 \over 4}}} \left( 1 - {t^2 \over \sigma^2} \right) e^{-t^2 \over 2\sigma^2}</math>
In the first year of data recorded by the [[Wilkinson Microwave Anisotropy Probe]] (WMAP) a region of sky in the constellation [[Eridanus (constellation)|Eridanus]] was found to be cooler than the surrounding area.<ref>Cruz, Martínez-González, Vielva & Cayón (2005), [http://arxiv.org/abs/astro-ph/0405341 "Detection of a non-Gaussian Spot in WMAP"], MNRAS 356 29-40</ref> Subsequently, using the data gathered by WMAP over 3 years, the statistical significance of such a large, cool region was estimated. The probability of finding a deviation at least as high in [[Gaussian random field|Gaussian]] simulations was found to be 1.85%.<ref>Cruz, Cayón, Martínez-González, Vielva & Jin (2007), [http://arxiv.org/abs/astro-ph/0603859 "The non-Gaussian Cold Spot in the 3-year WMAP data"], Astrophys.J. 655 11-20</ref> Thus it appears unlikely, but not impossible, that the cold spot was generated by the standard mechanism of [[quantum fluctuations]] during [[cosmological inflation]], which in most inflationary models gives rise to Gaussian statistics. The cold spot may also, as suggested in the references above, be a signal of non-Gaussian primordial fluctuations.
is the negative [[normalizing constant|normalized]] second [[derivative]] of a [[Gaussian function]], i.e., up to scale and normalization, the second [[Hermite function]]. It is a special case of the family of [[continuous wavelet]]s ([[wavelet]]s used in a [[continuous wavelet transform]]) known as [[Hermitian wavelet]]s. It is usually only referred to as the "Mexican hat" in the Americas, due to cultural association; see "[[sombrero]]". In technical nomenclature this function is known as the '''Ricker wavelet,''' where it is frequently employed to model seismic data.
The hyperdimensional generalization of this wavelet is called the ''[[Laplacian of Gaussian]]'' function. In practice, this wavelet is sometimes approximated by the ''[[Difference of Gaussians]]'' function, because it is separable and can therefore save considerable computation time in two or more dimensions. The scale normalised Laplacian (in <math>L_1</math>-norm) is frequently used as a [[blob detection|blob detector]] and for automatic scale selection in [[computer vision]] applications; see [[Laplacian of Gaussian]] and [[scale-space]]. The Mexican hat wavelet can also be approximated by [[derivative]]s of [[B-spline#Cardinal_B-spline|Cardinal B-Splines]]<ref>Brinks R: ''On the convergence of derivatives of B-splines to derivatives of the Gaussian function'', Comp. Appl. Math., 27, 1, 2008</ref>
==Possible causes other than primordial temperature fluctuation==
===Supervoid=Note==
One possible explanation of the cold spot is a huge [[void (astronomy)|void]] between us and the primordial [[CMB]]. Voids can produce a cooler region than surrounding sightlines from the late-time [[Sachs-Wolfe effect#Late-time Integrated Sachs-Wolfe Effect|integrated Sachs-Wolfe]] effect or [[Rees-Sciama]] effect.<ref>Inoue & Silk, 2006, [http://arxiv.org/abs/astro-ph/0602478 "Local Voids as the Origin of Large-Angle Cosmic Microwave Background Anomalies I"], ApJ 648 23-30 </ref> This effect would be much smaller if [[dark energy]] weren't stretching the void as [[photon]]s went through it.<ref>[http://www.centauri-dreams.org/?p=1427 Centauri Dreams » Blog Archive » Dark Energy Paints the Void<!-- Bot generated title -->]</ref>
In August 2007, Rudnick, Brown & Williams <ref>[http://arxiv.org/abs/0704.0908 "Extragalactic Radio Sources and the WMAP Cold Spot"], ApJ, 671, pp. 40-44</ref> claimed a dip in [[NVSS]] galaxy number counts in the direction of the Cold Spot, suggesting the presence of a [[supervoid]] at redshift ''z'' approximately equal to 1. McEwen et al. <ref>[http://arxiv.org/abs/0704.0626 "Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures"], 2008, MNRAS, 384, pp. 1289-1300</ref> independently found the correlation using a wavelet analysis of the entire area of sky covered by the survey, though they did not explicitly advance the supervoid suggestion.
Although large voids are known in the universe, a void would have to be unusually large to explain the cold spot, perhaps 1000 times larger in volume than expected typical voids. It would be 6-10 billion [[light-year]]s away and nearly one billion [[light-year]]s across, and would be perhaps even more improbable to occur in the [[large scale structure]] than the WMAP cold spot would be in the primordial [[CMB]]. <ref>[http://news.bbc.co.uk/2/hi/science/nature/6962185.stm BBC NEWS | Science/Nature | Great 'cosmic nothingness' found<!-- Bot generated title -->]</ref> <ref>[http://www.nrao.edu/pr/2007/coldspot/ Astronomers Find Enormous Hole in the Universe (August 2007)] </ref> <ref>[http://www.nrao.edu/pr/2007/coldspot/graphics.shtml graphics] </ref>
[[Image:Mean_void_imprint.png|thumb|168px|The mean [[ISW]] imprint 50 supervoids have on the [[Cosmic Microwave Background]]: color scale from -20 to +20 µK (adapted from Granett, Neyrinck & Szapudi).]]
In May 2008, two papers appeared on [[arXiv|astro-ph]] arguing against, and indirectly supporting, the supervoid explanation. Smith & Huterer <ref>[http://arxiv.org/abs/0805.2751 "No evidence for the cold spot in the NVSS survey"], MNRAS, submitted</ref> found that although there is a significant dip in [[NVSS]] galaxy density in the Cold Spot as Rudnick et al. claimed, it is not at the center of it, and there are many other possible circles to draw in the Cold Spot in which there is no dip. This does not prove that the Cold Spot cannot be due to a supervoid as suggested in the [[NVSS]] data; it merely uses a [[Bayesian]] statistical argument to assess the existing evidence that the Cold Spot is entirely due to a supervoid as quite weak.
In the second paper, Granett, Neyrinck & Szapudi
<ref>[http://arxiv.org/abs/0805.3695 "An Imprint of Super-Structures on the Microwave Background due to the Integrated Sachs-Wolfe Effect"], ApJL, submitted</ref><ref>[http://www.ifa.hawaii.edu/cosmowave/supervoids Dark Energy and the Imprint of Super-Structures on the Microwave Background]</ref> found that supervoids and [[superclusters]] in the [[Sloan Digital Sky Survey|SDSS]] Luminous Red Galaxy catalog produce cold and hot spots (respectively) on the CMB, highly significant when the signals from 50 superclusters and 50 supervoids are added together. This is arguably the clearest detection so far of the [[Integrated Sachs-Wolfe]] effect, and provides evidence of [[dark energy]] accelerating the expansion of the universe. This finding supports the supervoid explanation for the Cold Spot because it shows that supervoids can have a measurable effect on the CMB, but the support is indirect because the Cold Spot is not in the [[SDSS]] survey.
===Cosmic Texture===
In late 2007, Cruz et al. <ref>{{cite journal| journal=Science| doi=10.1126/science.1148694| title=A Cosmic Microwave Background Feature Consistent with a Cosmic Texture| first=M.| last= Cruz| coauthors= N. Turok, P. Vielva, E. Martínez-González, M. Hobson| url= http://www.sciencemag.org/cgi/content/abstract/1148694| accessdate=2007-10-25| year=2007| volume=318| pages=1612}}</ref> argued that the Cold Spot could be due to a [[Texture (cosmology)|cosmic texture]], a remnant of a [[phase transition]] in the early Universe. This is an exotic explanation, but worth considering since a supervoid would have to be so big to produce the Cold Spot.
===Parallel universe===
A controversial claim by [[Laura Mersini|Laura Mersini-Houghton]] is that it could be the imprint of [[Multiverse|another universe]] beyond our own, caused by [[quantum entanglement]] between universes before they were separated by [[cosmic inflation]].<ref>[http://space.newscientist.com/article/mg19626311.400-the-void-imprint-of-another-universe.html The void: Imprint of another universe?], [[New Scientist]], 2007-11-24</ref> Laura Mersini-Houghton said, "Standard cosmology cannot explain such a giant cosmic hole" and made the remarkable hypothesis that the WMAP cold spot is "… the unmistakable imprint of another universe beyond the edge of our own." If true this provides the first [[empirical evidence]] for a parallel universe (though theoretical models of parallel universes existed previously). It would also support [[String theory]]. The team claims there are [[Testability|testable]] consequences for its theory. If the parallel universe theory is true there will be a similar void in the northern hemisphere of the [[Celestial sphere]].<ref>[http://www.theblogofscience.com/evidence-for-a-parallel-universe/ Evidence for a parallel universe?], The Blog of Science</ref>
== See also ==
*[[Sloan Great Wall]]
*[[Great Wall (astronomy)|CfA2 Great Wall]]
== Note ==
<references/>
<nowiki>[[Category: VoidsNumerical analysis]] </nowiki>▼== External links ==
*[http://www.dailytech.com/Gaping+Hole+Found+in+Universe/article8598.htm Gaping Hole Found in Universe], Daily Tech
*[http://www.space.com/scienceastronomy/070823_huge_hole.html Huge Hole Found in the Universe], [[Space.com]], [[2007-08-23]]
*[http://news.nationalgeographic.com/news/2007/08/070824-hole-sky.html Gaping "Hole" in the Sky Found, Experts Say], [[National Geographic News]]
*[http://news.bbc.co.uk/1/hi/sci/tech/6962185.stm BBC News: Great 'cosmic nothingness' found]. [[BBC News]], [[2007-08-24]]
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[[Category:Eridanus constellation]]
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