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Cosmic ray backgrounds for dark matter indirect detectionMertsch, Philipp January 2010 (has links)
The identification of the relic particles which presumably constitute cold dark matter is a key challenge for astroparticle physics. Indirect methods for their detection using high energy astro- physical probes such as cosmic rays have been much discussed. In particular, recent ‘excesses’ in cosmic ray electron and positron fluxes, as well as in microwave sky maps, have been claimed to be due to the annihilation or decay of dark matter. In this thesis, we argue however that these signals are plagued by irreducible astrophysical backgrounds and show how plausible con- ventional physics can mimic the alleged dark matter signals. In chapter 1, we review evidence of, and possible particle candidates for, cold dark matter, as well as our current understanding of galactic cosmic rays and the state-of-the-art in indirect detection. All other chapters contain original work, mainly based on the author’s journal publications. In particular, in chapter 2, we consider the possibility that the rise in the positron fraction observed by the PAMELA satellite is due to the production through (hadronic) cosmic ray spallation and subsequent acceleration of positrons, in the same sources as the primary cosmic rays. We present a new (unpublished) analytical estimate of the range of possible fluctuations in the high energy electron flux due to the discreteness of plausible cosmic ray sources such as supernova remnants. Fitting our result for the total electron-positron flux measured by the Fermi satellite allows us to fix the only free parameter of the model and make an independent prediction for the positron fraction. Our explanation relies on a large number of supernova remnants nearby which are accelerating hadronic cosmic rays. Turning the argument around, we find encouraging prospects for the observation of neutrinos from such sources in km^3-scale detectors such as IceCube. Chapter 3 presents a test of this model by considering similar effects expected for nuclear secondary-to-primary ratios such as B/C. A rise predicted above O(100)GeV/n would be an unique confirmation of our explanation for a rising positron fraction and rule out the dark matter explanation. In chapter 4, we review the assumptions made in the extraction of the `WMAP haze' which has also been claimed to be due to electrons and positrons from dark matter annihilation in the Galactic centre region. We argue that the energy-dependence of their diffusion means that the extraction of the haze through fitting to templates of low frequency diffuse galactic radio emission is unreliable. The systematic effects introduced by this can, under specific circumstances, reproduce the residual, suggesting that the ‘haze’ may be just an artefact of the template subtraction. We present a summary and thoughts about further work in the epilogue.
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EVOLUTION OF HIGH-ENERGY PARTICLE DISTRIBUTION IN MATURE SHELL-TYPE SUPERNOVA REMNANTSZeng, Houdun, Xin, Yuliang, Liu, Siming, Jokipii, J. R., Zhang, Li, Zhang, Shuinai 10 January 2017 (has links)
Multi-wavelength observations of mature supernova remnants (SNRs), especially with recent advances in gamma-ray astronomy, make it possible to constrain energy distribution of energetic particles within these remnants. In consideration of the SNR origin of Galactic cosmic rays and physics related to particle acceleration and radiative processes, we use a simple one-zone model to fit the nonthermal emission spectra of three shell-type SNRs located within 2 degrees on the sky: RX J1713.7-3946, CTB 37B, and CTB 37A. Although radio images of these three sources all show a shell (or half-shell) structure, their radio, X-ray, and gamma-ray spectra are quite different, offering an ideal case to explore evolution of energetic particle distribution in SNRs. Our spectral fitting shows that (1) the particle distribution becomes harder with aging of these SNRs, implying a continuous acceleration process, and the particle distributions of CTB 37A and CTB 37B in the GeV range are harder than the hardest distribution that can be produced at a shock via the linear diffusive shock particle acceleration process, so spatial transport may play a role; (2) the energy loss timescale of electrons at the high-energy cutoff due to synchrotron radiation appears to be always a bit (within a factor of a few) shorter than the age of the corresponding remnant, which also requires continuous particle acceleration; (3) double power-law distributions are needed to fit the spectra of CTB 37B and CTB 37A, which may be attributed to shock interaction with molecular clouds.
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The connection between supernova remnants and the Galactic magnetic fieldWest, Jennifer Lorraine 03 1900 (has links)
The study of Supernova Remnants (SNRs) is fundamental to understanding the chemical enrichment and magnetism in galaxies, including our own Milky Way. In an effort to understand the connection between the morphology of SNRs and the Galactic Magnetic Field (GMF), we have examined the radio images of all known SNRs in our Galaxy and compiled a large sample that have an axisymmetric morphology, which we define to mean SNRs with a bilateral or barrel-shaped morphology, in addition to one-sided shells. We selected the cleanest examples and model each of these at their appropriate Galactic position using two GMF models, one of which includes a vertical halo component, and another that is oriented entirely parallel to the plane. Since the magnitude and relative orientation of the magnetic field changes with distance from the Sun, we analyze a range of distances, from 0.5 to 10 kpc in each case. Using a physically motivated model of an SNR expanding into an ambient GMF that includes a vertical halo component, we find it is possible to reproduce observed morphologies of many SNRs in our sample. These results strongly support the presence of an off-plane, vertical component to the GMF, and the importance of the Galactic field on SNR morphology. Our approach also provides a potentially new method for determining distances to SNRs, or conversely, distances to features in the large-scale GMF if SNR distances are known.
The mechanism for acceleration of cosmic rays in SNRs is another outstanding question in the field. To investigate this, the same sample of axisymmetric SNRs was again modelled, but this time using two competing, and physically motivated, Cosmic Ray Electron (CRE) acceleration cases: quasi-perpendicular and quasi-parallel. We find that the quasi-perpendicular CRE acceleration case is much more consistent with the data than the quasi-parallel CRE acceleration case, with G327.6+14.6 (SN1006) being a notable exception. We propose that SN1006 may be an example of a case where both quasi-parallel and quasi-perpendicular acceleration is simultaneously at play in a single SNR. / October 2016
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Large 14C excursion in 5480 BC indicates an abnormal sun in the mid-HoloceneMiyake, Fusa, Jull, A. J. Timothy, Panyushkina, Irina P., Wacker, Lukas, Salzer, Matthew, Baisan, Christopher H., Lange, Todd, Cruz, Richard, Masuda, Kimiaki, Nakamura, Toshio 31 January 2017 (has links)
Radiocarbon content in tree-rings can be an excellent proxy of the past incoming
cosmic ray intensities to the Earth. Although such past cosmic ray variations have
been studied by measurements of 14C contents in tree rings with ≧10 year time
resolution for the Holocene (1), there are few annual 14C data. There is a little
understanding about annual 14C variations in the past with the exception of a few
periods including the AD774-775 annual 14C excursion (2).
Here, we report the result of 14C measurements using the bristlecone pine tree rings
for the period from 5490 BC to 5411 BC with 1-2 year resolution, and a finding of an
extraordinarily large 14C increase (20‰) from 5481 BC to 5471 BC (the 5480 BC
event). The 14C increase rate of this event is much larger than that of the normal
Grand Solar Minima. We propose the possible causes of this event are a special
phase of grand solar minimum, or a combination of successive solar proton events
and a normal grand solar minimum.
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Determining the observer’s velocity using radio continuum surveysRandriamiarinarivo, Nandrianina January 2019 (has links)
>Magister Scientiae - MSc / In the standard (‘concordance’) model of Cosmology, there is a fundamental assumption that the Universe is statistically isotropic and homogeneous on large scales, known as the Cosmological Principle. The Cosmological Principle requires that the dipole anisotropy apparent in the CMB should also be observed in galaxy number counts if this signal occurs due to the aberration and Doppler effects from our peculiar motion. This thesis will investigate the accuracy with which the cosmic kinematic dipole can be determined
by comparing real data from NRAO VLA Sky Survey (NVSS) catalog with the simulated sky maps following its specifications. The mock maps are generated using FLASK code which assumes a lognormal distribution for the radio count density field from z=0 to z =4 and taking as an entry an angular power spectrum from CAMB which assumed a flat ΛCDM cosmology and a redshift distribution. After analising the kinematic dipole, we turn to the analysis of statistical isotropy in the catalog. We used ANalysis Of Variance (ANOVA) test on patches in the sky of different radii as one of the statistical tools for the analysis.
We found that as we go to a higher radius for the patches, we have a better agreement between the theory and the observation as expected. We also saw that the more we are rigorous on the rejection criteria, the smaller is the discrepancy between the observed and simulated number count distribution in the sky. We found an optimum choice of 25◦ as patch size, and if the accepted patches have a maximum of 30% of their pixels masked.
Therefore, we find that the NVSS data agrees with the fundamental assumption of statistical isotropy at angular scales > 20◦.
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"Linhas de Estrutura Fina em Absorção no Espectro de QSOs" / Fine-structure absorption lines in QSO spectra.Silva, Alex Ignácio da 21 May 1999 (has links)
Neste trabalho realizamos cálculos teóricos das razões de povoamento dos níveis de estrutura fina do C0, C+ e Si+ considerando em detalhes os efeitos dos diversos mecanismos de excitação: colisões, fluorescência e a radiação cósmica de fundo. Empregamos dados atômicos recentes coletados na literatura na resolução das equações de equilíbrio estatístico pertinentes. A confrontação das razões de povoamento calculadas com as razões de densidades de coluna observadas disponíveis na literatura nos permite obter informações acerca das condições físicas (densidades volumétricas, intensidade de um campo de radiação UV presente, temperatura da radiação cósmica de fundo) e propriedades (dimensão característica e massa) dos sistemas damped Lyman a e Lyman Limit vistos em absorção no espectro de QSOs. Como um aparte, e por sua relação com o tema do trabalho, também investigamos a lei de temperatura da radiação cósmica de fundo. / In this work we perform theoretical calculations of the population ratios of fine structure levels of C0, C+ and Si+ considering in detail the effect of the various excitation mechanisms: collisions, fluorescence and the cosmic background radiation. We employ recent atomic data, gathered in the literature, to solve the related statistical equilibrium equations. The comparison of the calculated population ratios with the observed column densities ratios available in the literature allows us to obtain informations regarding the physical conditions (volume densities, intensity of a UV radiation field present, temperature of the cosmic background radiation) and properties (characteristic size and mass) of damped Lyman a and Lyman Limit systems seen in absorption in spectra of QSOs. We also investigate the temperature law of the cosmic background radiation, which bears a tight relationship with this work.
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Cenários unificados para a expansão acelerada do Universo / Unified Scenarios for the Accelerated Expansion of the UniverseGraef, Leila Lobato 24 June 2015 (has links)
Nos encontramos atualmente em um momento histórico privilegiado para a cosmologia. Na última década, o grande progresso das observações astronô- micas permitiu que diversos modelos cosmológicos pudessem ser testados com grande precisão. Com uma série de resultados observacionais sendo lançados, obtivemos informações valiosas sobre a expansão acelerada do universo primitivo e a expansão acelerada atual. Em sua essência, tais esforços observacionais buscam esclarecer algumas das questões mais fundamentais da cosmologia moderna, como a compreensão do mecanismo responsável pela aceleração do universo. Muitas perguntas estão associadas à tal questão, entre elas podemos citar: (i) Qual a natureza da substância, ou qual a origem do fenômeno, que está atualmente acelerando a expansão do universo? (ii) Por qual razão esta expansão acelerada iniciou recentemente (nos últimos 5-8 bilhões de anos), e não no passado distante ou no futuro remoto? (iii) Qual a variante inflacionária que operou no universo primitivo e qual sua conexão (se existe alguma) com o atual estágio acelerado do universo? Em nossa compreensão, as indagações acima fazem parte dos maiores problemas da cosmologia atual. A ampla abrangência de tais questões significa que avanços em qualquer uma delas terá implicações teóricas e observacionais em outras áreas envolvendo a interface formada pela Astronomia, Cosmologia e Física de Partículas. As três questões acima estão diretamente conectadas com os objetivos do presente trabalho. Acreditamos também que seu estudo pode lançar alguma luz e melhorar nossa compreensão sobre questões mais fundamentais da física. Neste contexto, analisamos diferentes modelos cosmológicos para a acelera- ção do universo à luz dos mais recentes dados observacionais de supernovas, radiação cósmica de fundo e oscilações acústicas de bárions. Propomos, aqui, alternativas ao Modelo Padrão da Cosmologia, ao mostrar que diversos fenômenos físicos podem estar associados à expansão do universo, gerando a aceleração observada sem a necessidade de se introduzir componentes desconhecidas no universo além da matéria escura. Além de desenvolver uma revisão crítica do Modelo Padrão, discutimos nesta tese especialmente três modelos para a expansão acelerada do universo. O primeiro deles considera a aceleração cósmica como sendo efeito da criação quântica de partículas de matéria escura, ou radiação, às custas do campo gravitacional variando continuamente com a expansão do universo. O segundo modelo considera o processo de viscosidade volumar no fluido cosmológico como sendo responsável pela aceleração. Esta viscosidade volumar se deve à perda de equilíbrio termodinâmico durante a expansão do fluido. O terceiro modelo, o modelo de decaimento do vácuo, considera como responsá- vel pela aceleração uma energia do vácuo que decai nas outras componentes cósmicas continuamente ao longo do tempo. Analisamos as relações existentes entre estes três modelos, além do Modelo Padrão, e as condições sob as quais os mesmos fornecem uma dinâmica equivalente para o universo. Também obtemos interessantes vínculos para os parâmetros destes modelos ao fazermos, além de uma análise observacional, uma análise teórica baseada na dinâmica e na termodinâmica associada a cada cenário. Sugerimos que estes cenários são capazes de aliviar diversos problemas conceituais do Modelo Padrão da Cosmologia. Numa segunda etapa, mostramos que os processos físicos descritos acima podem ser responsáveis tanto pela aceleração cósmica atual, quanto pela aceleração primordial que se supõe ter ocorrido no universo antigo. Tal abordagem fornece uma descrição unificada para a evolução cosmológica. Acreditamos ser de fundamental importância que o processo que dirigiu a aceleração primordial possa ser relacionado com o mesmo responsável pela atual fase de expansão acelerada do universo. Além disto, é possível que as dificuldades que atingem a interface que une a Relatividade Geral, a Cosmologia e a Teoria Quântica de Campos possam ser amenizadas através de uma melhor compreensão do processo de criação gravitacional de partículas, do decaimento do vácuo e suas conexões com o contexto da inflação primordial. Para comparar e vincular os modelos propostos, analisamos também o processo de formação das estruturas cosmológicas nestes modelos. Introduzimos a teoria de perturbações cosmológicas, primeiramente, através de uma análise do Modelo Padrão. A partir daí, apresentamos uma abordagem mais geral para o tratamento das perturbações chamada teoria de campo efetiva para a inflação. Neste contexto, analisamos quais previsões são obtidas ao se quebrar algumas suposições usualmente assumidas nestes modelos. Por fim, através de uma análise do espectro de potências primordial do modelo de criação gravitacional de partículas e do modelo de viscosidade, mostramos, pela primeira vez, que os mesmos podem ser capazes de gerar um cenário inflacionário para o universo primitivo em concordância com as observações atuais. / We are currently in a privileged moment for cosmology. In the last decade, the great progress of astronomical observations made possible that several cosmological models could be tested with great accuracy. With several observational data being released we obtained valuable information concerning the primordial acceleration of the universe and the recent accelerated expansion. Essentially, these observational efforts aim to clarify some of the most fundamental questions of modern cosmology, which concerns the understanding of the mechanism responsible for the acceleration of the universe. Many questions are related to this issue, among them we can mention: (i) What is the nature of the substance, or what is the origin of the phenomenom, responsible for the acceleration of the expansion? (ii) For which reason the accelerated expansion started recently (within the last 5-8 billion years), and not in the distant past or distant future? (iii) What is the inflationary variant that operated in the early universe, and what is its connection (if there is any) with the current accelerated stage of the universe? In our understanding the above questions are part of the biggest problems in modern cosmology. The interconnection between these issues means that advances in any of them will have theoretical and observational implications in other areas involving the interface formed by Astronomy, Cosmology and Particle Physics. The three questions above are directly connected to the objectives of this work. We also belive that their study can shed some light in our understanding of the remaining issues. In this context, we analyze different cosmological models for the acceleration of the universe in the light of the latest data released from supernovae, cosmic microwave background and baryon acoustic oscillations, comparing the results with the ones concerning the Standard Model of Cosmology. We propose alternatives to the Standard Model of Cosmology, by showing that several physical phenomena can be associated to the expansion of the universe, producing the observed acceleration without the need to introduce unknown components in the universe besides the dark matter. In addition to developing a critical revision of the Standard Model, we discuss in this thesis especially three models for the accelerated expansion of the universe. The first one considers the cosmic acceleration as an effect of the creation of dark matter particles, or radiation, at the expense of the gravitational field varying continuously with the expansion of the universe. The second model considers the process of bulk viscosity in the cosmological fluid as being responsible for the acceleration of the universe. This bulk viscosity is due to the loss of local thermodynamic equilibrium during the expansion of the fluid. The third model, the vacuum decaying model, considers as responsible for the acceleration, a vacuum energy which decays continuously into other cosmological components. We analyze the relations between these three models, and also the Standard Model, and the conditions under which they provide an equivalent dynamic to the universe. We also obtain interesting constraints for the parameters of these models by making, besides an observacional analysis, a theoretical analysis based on the dynamics and thermodynamics associated to each scenario. We will show that these alternative scenarios are able to alleviate several theoretical problems of the Standard Cosmological Model. In a second part, we show that the physical phenomena described above may be responsible for the recent cosmic acceleration, as well as for the primordial acceleration that is supposed to have occurred in the early universe. Such approach provides an unified description for the cosmological history. We belive it is of great importance that the process responsible for inflation can be identified with the one responsible for the current phase of accelerated expansion of the universe. Moreover, it is quite possible that the difficulties concerning the interface connecting General Relativity, Cosmology and Quantum Field Theory can be reduced through a better understanding of the gravitational particle creation process, the decay of the vacuum and its connections with the primordial inflationary context. In order to constrain and compare the models proposed here, we also analyse the process of cosmological structure formation in these models. We firstly introduce the perturbation theory through an analysis of the Standard Model. Then we introduce a more general approach to the treatment of cosmological perturbations which is called effective field theory of inflation. In this context, we analyse which predictions are obtained when we break some of the assumptions usually imposed in these models. Finally, through an analysis of the primordial power spectrum of the gravitational particle creation model and the viscosity model, we show, for the first time, that these models are able to describe an inflationary scenario for the early universe totally in agreement with current observations.
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Detecção de chuveiros atmosféricos iniciados por hádrons massivos / Detection of extensive air showers initiated by massive hadronsCarvalho Junior, Washington Rodrigues de 06 August 2008 (has links)
Nesta tese investigamos uma possível componente de partículas previstas por modelos além do modelo padrão da física de partículas, como por exemplo o massive gluino LSP, nos raios cósmicos de altíssimas energias (UHECR). Nosso objetivo é determinar os sinais experimentais em telescópios de fluorescência devidos a hádrons exóticos massivos e neutros, genericamente denominados de UHECRons. Para simular chuveiros iniciados por essa classe de partículas, alteramos o pacote Aires de simulação de chuveiros atmosféricos e o modelo hadrônico Sibyll. Estes chuveiros foram utilizados como entrada em simulações de telescópios de fluorescência por nós desenvolvidas, obtendo-se assim as distribuições dos observáveis desses chuveiros exóticos. A partir da comparação entre as características de chuveiros iniciados uhecrons e prótons, desenvolvemos métodos para a separação de sinais entre esses dois tipos de partículas. Esses métodos podem ser utilizados em uma análise inicial, com o intuito de procurar por sinais de partículas exóticas nos dados reais de observatórios de UHECR. / In this thesis we investigate a possible component of particles predicted by models beyond the standard model of particle physics, like the massive gluino LSP, in the ultra high energy cosmic rays (UHECR). Our objective is to determine the experimental signals on fluorescence telescopes due to exotic massive and neutral hadrons, generically called UHECRons. To simulate showers initiated by this class of particle, we altered the shower simulation package Aires and the hadronic model Sibyll. These showers were used as input in our simulations of fluorescence telescopes, thus obtaining the distribuitons of the observables for these exotic showers. By comparing the characteristics of showers initiated by uhecrons and protons, we developed methods to distinguish the signals between these two particles. These methods can be used in an initial analysis in order to look for signals of exotic particles in the real data of UHECR observatories.
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[en] INTRINSIC FLUCTUATIONS OF EXTENSIVE AIR SHOWERS AND THE CHEMICAL COMPOSITION OF ULTRA HIGH ENERGY COSMIC RAYS / [pt] FLUTUAÇÕES INTRÍNSECAS DE CHUVEIROS ATMOSFÉRICOS EXTENSOS E COMPOSIÇÃO QUÍMICA DE RAIOS CÓSMICOS ULTRA-ENERGÉTICOSMARY LUCIA DIAZ CASTRO 23 July 2012 (has links)
[pt] O Observatório Pierre Auger é um detector de raios cósmicos
ultra-energéticos (E maior ou igual 1018 eV) com características híbridas, que combinam
detectores de superfície e de fluorescência. A determinação da composição
química primária destes raios cósmicos é um dos seus principais objetivos.
Há indícios de que os primários dos raios cósmicos com E maior que 1018.5 eV tem
massa maior, conclusão baseada nos resultados recentes sobre a evolução dos
chuveiros atmosféricos extensos (cascatas de partículas formadas quando da
colisão do raio cósmico primário no topo da atmosfera com moléculas de N2
ou O2). Encontrar parâmetros, que caracterizam o chuveiro, no processo de
sua reconstrução e que forneçam informações associadas a este resultado,
são essenciais para validar esta conclusão. Nesta tese estuda-se a evolução
como função da energia, de parâmetros que caracterizam os chuveiros,
que sejam sensíveis à sua composição primária. Mais especificamente
aqueles determinados pelo detector de superfície, pois há uma estatística
de chuveiros detectados significativamente maior. Damos especial atenção
às flutuações intrínsecas – chuveiro-a-chuveiro – do parâmetro de inclinação
(beta) da Função de Distribuição Lateral, que descreve a variação da densidade
de partículas ao longo da direção perpendicular ao eixo do chuveiro, como
função da distância a esse eixo. Os resultados indicam que a flutuação
intrínseca em beta, para eventos inclinados (45-60 graus) com E maior que 1018.5 eV, possui
uma tendência de diminuição com a energia até valores em torno de 1019.8
eV. Este resultado é consistente com o encontrado anteriormente em análises
de composição química sobre a evolução com a energia da profundidade de
máximo (Xmax) dos chuveiros atmosféricos extensosmedida pelos detectores
do Auger em modo híbrido, em que em energias acima de 1018.5 eV, observase
que os chuveiros tendem a atingir seu máximo numa região mais bem
definida da atmosfera, levando, por conseguinte, a flutuações menores no
sinal no solo. / [en] The Pierre Auger Observatory is an ultra high energy cosmic
ray detector (E more than or equal as 1018 eV) which has hybrid characteristics combining
surface and fluorescence detectors. Determining the cosmic rays chemical
composition is one of its most important challenges. There are evidences
that cosmic ray primaries with energy above 1018.5 eV are heavy and this
conclusion is based on recent results on the evolution of extensive air showers
(cascades of particles formed by the collision of primary cosmic rays in the
top of the atmosphere with nitrogen and oxygen molecules). Therefore, it is
mandatory to find additional parameters supporting that conclusion. In this
thesis, the evolution with energy of parameters characterizing the shower
and with sensitivity to chemical composition are studied. More specifically,
parameters determined by the surface detector are analyzed due to the high
statistics in this operation mode. Special attention is given to the instrinsic
- shower to shower - fluctuations of the slope parameter (beta) of the Lateral
Distribution Function which describes the particles density variation in the
plane perpendicular to the shower axis as a function of distance to that axis.
The results show that the intrinsic fluctuation of Beta, for inclined showers
(45-60 degrees) with energy above 1018.5 eV, where the detector resolution is small
compared to the total fluctuation, has a trend to decrease with energy up
to 1019.6 eV. This result is consistent with recent results on the energy
evolution of the depth of shower maxima (Xmax) of extensive air showers,
where above 1018.5 eV, the distributions of Xmax show less fluctuations,
leading, in turn, to less fluctuations on the ground level.
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Polarização da radiação cósmica de fundo / Cosmic microwave background polarizationReimberg, Paulo Henrique Flose 03 September 2009 (has links)
Utilizando conceitos de macânica quântica e teoria cinética apresentamos uma rederivação da equação de Boltzmann para a polarização. Mostramos a equivalência entre a equação que derivamos e a equação de Boltzmann encontrada na literatura ( [1], [2], [3] ) além de mostrar que essas derivações correspondem a considerar-se o efeito, sobre a polarização dos fótons da radiação cósmica de fundo, de dois espalhamentos Thompson com elétrons durante recombinação. Conduzimo-nos, ainda, a descrever a polarização completamente no espaço real, como iniciado em [4] em um caso especial. Mostramos a possibilidade dessa conversão, recobramos a geometria que está associada ao estudo do problema no espaço real e verificamos satisfeitas as condições de causalidade. / Applying concepts of quantum mechanics and kinetic theory we show a re-derivation of Boltzmann equation for the Cosmic Microwave Background (CMB) polarization. We show the equivalence between our derivation and those already known ( [1], [2], [3] ) and also that these derivations correspond to take into account the effect, on the photon polarization, of two Thompson scattering on electrons while decoupling from matter. We adress ourselves, then, to give a complete formalism for the CMB polarization problem in real space, as started in [4] in a special case. Besides the possibility of complete treatment of the problem in real space, we recover the geometry that describes it and that tha causal relations are satisfied.
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